Millimetre and Submillimetre Observations in Cosmology
by
David Leigh Clements
A Thesis Submitted for the Degree of Doctor of Philosophy of the University of London and for the Diploma of Imperial College February 1991
Astrophysics Group Imperial College of Science, Technology and Medicine London SW7 2BZ
1 A bstract
This thesis describes two investigations in observational cosmology at mil limetre and submillimetre wavelengths: observations of recently discovered high redshift radio galaxies in search of dust emission, and observations of the Cosmic Background Radiation (CBR) is search of the Sunyaev-Zeldovich Effect. High redshift radio galaxies such as 0902+34 appear to be essentially nor mal high luminosity radio galaxies but at large redshift. Their optical properties suggest that they are forming stars very rapidly, and that there may be some interaction between the radio jet and the star forming process. If they are form ing stars in a manner similar to nearby starburst galaxies, or if their far infrared properties are similar to the nearby high power radio galaxy (Cygnus A) observed by IRAS, then redshifted far infrared radiation should be detectable at millime- tre/submillimetre wavelengths. Predicted fluxes in the 800 fim window at the JCMT are of order 10 mJy. The observations fail to detect this radiation, and 2 1 designed to observe the S-Z effect are dealt with in the next chapters. This instrument has 2 observational channels and a third to monitor and subtract sky noise. The design is reviewed with special emphasis placed on the data acquisition system. The results of observations at the 1.5 m TIRGO telescope with the instrument are then discussed. These observations were severely contaminated with a source of noise correlated between the channels, and a noise subtraction technique originally developed to remove sky noise is tested on this with some degree of success. 2 Acknowledgements A PhD is never wholly the work of one person, as the help and experience of a host of others are called upon in its completion. I must therefore take this chance to thank all those who have contributed to this work or my time at the IC Astro group. First and foremost must come R.D Joseph, my supervisor, for all his help and encouragement. Without his care and expertise it is doubtful that much of this work would have been completed, or even attempted, and my knowledge of astronomy would be sorely lacking. His departure to Hawaii was a severe blow to both his students and IC, and I wish him luck at the IRTF. Almost as important is Simon Chase, responsible for the 3 Channel Instru ment’s design. His introduction to the mysteries of Helium systems and instru mentation in general will provide a background for all my future work. Good luck to you and your family in Italy! Work on the instrument would not have been possible without the expertise of the Astro Group technical team. Haxry, Mark and Victor and all your apprentices put in sterling service, at some very awkward times, and have taken the sting out of many problems for me. Mick Bartholemew must also be thanked in his absence. On the more concrete side, much of the instrument would not have been built without Bill and the workshop crew. Thank you all! Our collaborators, Peter Ade, Kandiah Shivanandan and J-P Torre have also been invaluable. Operations at telescopes are essential for this sort of work, so it is my pleasures to thank all those who have helped me abroad: Dolores, Gillian and Thor at UKIRT, Rusty and Tom at JCMT, and Areste, Nere, Alfonso and everyone at TIRGO. Apologies for the spelling! Beyond direct assistance, life has been made more worth while by all those I have known in the Astro Group. Geoff and Tim, whose fault it was in the first place, Phil who sorted me out, Andrea, Rene, Martyn, Sepi and Arvind who have had to share offices and lab space with me, Natasha, Tanya, Peter, Phil H., Lee, Peter M. Graeme, Sunil and all the others who have kept the atmosphere fresh and interesting; thank you all. 3 I’d also like to thank those who have helped in the production of this thesis. Bob, Amanda and Natasha for reading bits, Sunil, Graeme and Martyn for keeping the machines running. Science is a creative process, and so the strangest things can contribute. In this sphere I must thank those who’ve kept me sane during my time here: Amanda, Simon B, Tom the Madhatter, The Waveguide, ICSF and ICU, though at times it didn’t seem like it! The best to all of you, wherever you are. This work was supported by SERC. 4 To my parents, without whom it wouldn’t have been possible. And to Amanda, who maae it much better. r C ontents 1 Introduction 15 1.1 Observations in C osm ology...... 16 1.1.1 Fundamental Observations in Modern Cosmology ...... 17 1.1.2 The Hubble F low ...... 17 1.1.3 Primordial Nucleosynthesis of Light Elem ents ...... 17 1.1.4 The Cosmic Background R adiation...... 18 1.2 The Early History of the Universe...... 18 1.2.1 The Geometry of the U n iv e rse ...... 20 1.2.2 The Evolution of the Universe ...... 22 1.3 The Cosmic Background R adiation ...... 24 1.4 Dark Matter ...... 25 1.5 Primordial Fluctuations: The Origin of Large Scale Structure . . . 26 1.5.1 The Nature and Spectrum of Initial Fluctuations ...... 26 1.5.2 Galaxy Formation and Large Scale S tru c tu re ...... 29 1.6 Confrontation of Theories with Cosmological Observations ...... 31 1.6.1 CBR O bservations...... 31 1.6.2 Distant O bjects...... 33 1.6.3 Large Scale S tru c tu re ...... 33 1.7 The Role of this Thesis ...... 34 2 Millimetre and Submillimetre Observations of Distant Galaxies 35 2.1 Introduction...... 35 2.2 High Redshift Galaxies...... 35 2.2.1 D iscovery...... 35 5 2.3 The Properties of High Redshift Radio Galaxies ...... 37 2.3.1 Radio P ro p erties...... 37 2.3.2 Optical and Infrared Properties...... 39 2.3.3 The Nature of High Redshift Radio G a la x ie s ...... 43 2.4 Motivation for Observations...... 45 2.4.1 Target Objects for these O bservations...... 45 2.4.2 Millimetre/Submillimetre synchrotron emission from a HRRG 46 2.4.3 Dust Emission from a neaxby radio galaxy model of a HRRG 48 2.4.4 Dust Emission from a Starburst Model of a HRRG ...... 48 2.4.5 Limitations of these Models ...... 50 2.5 The Observations...... 51 2.5.1 The UK.T-14 Continuum R e c e iv e r...... 52 2.6 C a lib ratio n ...... 55 2.7 Data Reduction ...... 57 2.7.1 Demodulation of D a ta ...... 57 2.7.2 Atmospheric Transmission ...... 58 2.7.3 Removal of S p ik e s ...... 59 2.7.4 Reduction of the Astronomical D a t a ...... 61 2.8 Results...... 70 2.9 Discussion and C onclusions...... 70 2.9.1 Radio Emission in 3C257 ...... 71 2.9.2 Possible Dust Emission in H R R G s...... 71 2.10 Further W o rk ...... 75 2.10.1 Further Millimetre/Submillimetre Observations ...... 75 2.10.2 Primeval Galaxy Searches...... 76 3 The Sunyaev-Zeldovich Effect 78 3.1 Introduction...... 78 3.2 The Derivation of the Sunyaev-Zeldovich Effect ...... 81 3.2.1 The Derivation of the Kompaneets E q u a tio n ...... 82 3.2.2 The Sunyaev-Zeldovich Effect on a Black Body Spectrum . 85 3.2.3 The Sunyaev-Zeldovich Effect and non-Black Body Spectra 87 6 3.2.4 Numerical Calculations of the S-Z Effect...... 88 3.2.5 The S-Z Effect and the Submillimetre B ackground ...... 88 3.3 The Nature of the Hot Gas in Clusters of Galaxies ...... 89 3.3.1 Observational E v id e n ce ...... 89 3.3.2 Cluster Atmosphere M odels ...... 92 3.3.3 Implications for the Sunyaev-Zeldovich E ffect ...... 93 3.4 Previous Observations of the S-Z E ffect ...... 96 3.4.1 Techniques of Radio O bservations...... 97 3.4.2 Millimetre and Submillimetre Observations ...... 104 3.4.3 Results on Specific O b je c ts ...... 106 3.5 Conclusion ...... 110 4 UKT-14 Observations of the Sunyaev-Zeldovich Effect 111 4.1 Introduction...... I l l 4.2 The Advantages of Millimetre O bservations...... I l l 4.3 The Disadvantages of Millimetre Observations...... 113 4.4 Observations of the S-Z Effect at UKIRT Using UKT-14 ...... 115 4.5 C a lib ratio n ...... 116 4.6 Data Reduction...... 119 4.6.1 Extraction of Signal and Baseline ...... 119 4.6.2 Derivation of Atmospheric C ontribution...... 121 4.6.3 Spike R ejection...... 123 4.6.4 Reduction Program m e...... 124 4.7 Data Analysis...... 124 4.8 Extraction of R esults...... 128 4.8.1 Initial Conclusions and D iscussion ...... 129 4.8.2 The Blank Sky D a ta ...... 129 4.9 The Detailed Behaviour of the D a ta...... 131 4.10 Conclusions...... 137 4.11 Reanalysis of 1983 UKIRT d a ta ...... 139 4.11.1 O bservations...... 139 4.11.2 Original Data Reduction and A nalysis...... 140 7 4.11.3 Reanalysis of the 1983 D ata ...... 141 4.11.4 Results of Reanalysis...... 141 4.12 Conclusions...... 141 4.12.1 The S-Z effect in 0016+16...... 141 4.12.2 Long Integration T im e s ...... 142 4.12.3 Sensitivity to the Sunyaev-Zeldovich E ffect ...... 143 4.12.4 The Next S t e p ...... 143 5 The ICSTM 3 Channel Millimetre Wave Photometer 145 5.1 Introduction...... 145 5.2 Design Requirements...... 146 5.3 Design O verview ...... 147 5.3.1 Construction and C ryogenics ...... 147 5.3.2 O p tic s...... 149 5.3.3 F ilte rs...... 149 5.3.4 Baffles and Blocking F ilte rs ...... 155 5.3.5 D e te c to rs...... 155 5.4 Phase Sensitive D etectio n ...... 156 5.4.1 Operating Principles...... 156 5.4.2 Implementation...... 159 5.5 Instrument and Telescope Control Electronics...... 161 5.5.1 Warm P r e a m p ...... 161 5.5.2 Analogue R a c k ...... 163 5.5.3 The Digital R a c k ...... 165 5.5.4 The SBC Softw are...... 169 5.6 The Operator’s C om puter...... 170 5.6.1 BBC Micro Software...... 171 5.6.2 User Commands at BBC Micro ...... 172 5.6.3 Screen Outputs to Operator ...... 174 5.6.4 Structure of SBC Datablock ...... 175 5.6.5 Structure of BBC Data F iles ...... 175 5.7 Tests of PSD System ...... 176 8 5.7.1 Phasing T e s t ...... 176 5.7.2 Linearity and Calibration T e sts...... 178 5.7.3 S u m m ary ...... 178 5.8 Tests on the In stru m en t...... 178 5.8.1 Beam S cans...... 180 5.8.2 Noise T e s ts ...... 180 5.9 S u m m a ry ...... 180 6 Observations with the 3 Channel Photometer 183 6.1 Introduction ...... 183 6.2 The TIRGO Telescope...... 183 6.2.1 Telescope M o u n tin g ...... 184 6.2.2 Optical Arrangement...... 184 6.2.3 Electronic In terfac in g ...... 185 6.3 O bservations...... 185 6.4 Telescope Control S y ste m ...... 186 6.4.1 The Chopper System ...... 186 6.4.2 The Nod S y ste m ...... 187 6.5 Observations of Jupiter ...... 187 6.5.1 Pickup P roblem s...... 187 6.5.2 Optical Responsivity and Sensitivity ...... 188 6.5.3 Beam s c a n s ...... 189 6.6 Blank Sky O bservations...... 192 6.7 Data Analysis...... 192 6.7.1 A Method for Noise S u b tra c tio n ...... 193 6.7.2 Results on Observations with Cryostat Blanked Off ...... 194 6.7.3 Results on Zenith S c a n s ...... 195 6.7.4 Results on Blank Sky Observations...... 195 6.7.5 Results on J u p ite r ...... 197 6.7.6 S u m m ary ...... 198 6.8 Discussion and C onclusions...... 198 9 7 Future Developments: Cosmic Background Observations at Mil limetre and Sub millimetre Wavelengths 200 7.1 Introduction...... 200 7.2 Development of the ICSTM 3 Channel Millimetre Wave Photometer 201 7.3 Future Observations of the S-Z Effect with the 3 Channel Photometer201 7.4 The ICSTM 3 Channel Photometer as an Anisotropy Detector . . 202 7.4.1 Introduction ...... 202 7.4.2 Expected Signals from CBR A nisotropies ...... 203 7.5 The 3 Channel Photometer in Extragalactic Astronomy ...... 206 7.5.1 Possible Observations of Cold Dust in IRAS Galaxies . . . 207 7.6 Future Developments...... 208 7.6.1 S C U B A ...... 208 7.6.2 Space-Based Observations ...... 209 7.7 Other Millimetre and Submillimetre Observations of Cosmological Im p o rtan ce...... 211 7.7.1 Primeval G a la x ie s...... 211 7.7.2 Cosmological Lines: A New S-Z E ffe c t? ...... 214 7.8 Towards a New Astronomy of the Early U niverse ...... 217 A The Frequency Response of the Digital PSD System 219 B Computer Programs 221 B.l Chapter 2 ...... 221 B.2 Chapter 3 ...... 228 B.3 Chapter 4 ...... 234 B.4 Chapter 5 ...... 260 B.5 Chapter 6 ...... 266 C Included Paper 268 10 List of Figures 1.1 The U n iv erse...... 19 1.2 The Expansion of the Universe ...... 21 1.3 The Behaviour of the Scale Factor in different universes ...... 23 1.4 Perturbation T ypes...... 27 1.5 Spectra of Fluctuations from different types of Dark Matter .... 29 1.6 CBR Anisotropies in various M o d e ls...... 32 2.1 SEDs for the Lilly Galaxies...... 40 2.2 The K-z relation for radio g a la x ie s...... 42 2.3 Transmission of Atmosphere at Mauna Kea ...... 53 2.4 Zenith optical depths...... 60 2.5 Several data blocks ...... 62 2.6 Histograms of observational data for each object...... 64 2.7 Metallicity Evolution...... 74 3.1 The Spectral Form of the Sunyaev-Zeldovich Effect...... 80 3.2 The flux changes induced in different models of the Submillimetre Background by the S-Z effect...... 90 3.3 Results of SZ observations of 4 prime candidates ...... 107 4.1 Calibration data for UKT-14 UKIRT measurements ...... 118 4.2 Behaviour of Standard Error as K-S selected data combined. . . . 133 4.3 Behaviour of the mean as K-S selected data combined ...... 134 4.4 Behaviour of the standard error as K-S data combined without 7th or 12th M ay...... 135 11 4.5 Behaviour of the mean as K-S data combined without 7th or 12 th May...... 136 4.6 Log-log plot showing how the noise integrates down...... 138 5.1 3 Channel Millimetre Wave Photometer Cryostat Layout ...... 148 5.2 Optical Layout of 3 Channel Photometer: Side View ...... 150 5.3 Optical Layout of 3 Channel Photometer: Overhead View ...... 151 5.4 1.1 mm Bandpass...... 152 5.5 1.6 mm Bandpass ...... 153 5.6 2.1 mm Bandpass...... 154 5.7 VI Curves of bolom eters...... 157 5.8 Signals used by Digital PSD system...... 160 5.9 Schematic Diagram of 3 Channel Photometer’s Electronics ...... 162 5.10 Frequency response of Post A m plifiers...... 164 5.11 Results of test for V to F converter Linearity...... 166 5.12 Results of Phasing T e s t ...... 177 5.13 Calibration of Digital PSD S y ste m ...... 179 5.14 Measured Instrumental Beam, and Fitted Gaussian ...... 181 6.1 Ithaco Output from Pointed Observations of Jupiter ...... 190 6.2 Beam Scans obtained at T IR G O ...... 191 7.1 Flux Distortion due to Temperature Distortion of ST/T = 10“5 as a function of Frequency for a CBR temperature of 2.7 K ...... 204 7.2 Background Radiations and the Cosmological W indow s ...... 212 7.3 Results of Comptonisation of a Gaussian line spectrum ...... 216 12 List of Tables 2.1 Comparison of the radio properties of High Redshift Radio galaxies and the powerful, low redshift radio galaxy, Cygnus A ...... 38 2.2 Object List for HRRG observations ...... 46 2.3 Observational fluxes predicted from the power law radio component of the target objects...... 47 2.4 Fluxes in observational wavebands predicted for Cygnus A model for the observational targets...... 48 2.5 Fluxes in observational wavebands predicted for a starburst model of the observational targets ...... 50 2.6 Parameters of the UKT-14 Filters ...... 54 2.7 Fluxes used for calibration...... 57 2.8 UKT-14 calibration values used here for 1.1 mm and 800 /xm channels 59 2.9 Results of the Observations on High Redshift Radio Galaxies. . . . 70 2.10 A comparison of the predicted fluxes of HRRGs, and the upper limits to these fluxes set by the observations ...... 71 2.11 Metalicity Fractions...... 73 3.1 Results of S-Z Effect O bservations ...... 100 4.1 Results of Block Selection on 1986 S-Z data ...... 127 4.2 Results of observations on 0016+16...... 128 4.3 Results of blank sky observations...... 130 6.1 Blank Sky R e s u lts ...... 192 6.2 Results from correlation analysis of blanked off observations .... 195 6.3 Results from correlation analysis of blanked off observations .... 196 13 6.4 Nodded Blank Sky Results ...... 197 6.5 Jupiter R e s u lts ...... 197 14 C hapter 1 Introduction From the earliest of times, and for many reasons, man has studied the stars. This study was sometimes practical, for example in navigation, but more often was mystical. The ever present stars were deemed to be the home of the gods, and many inventive astronomers and mythologists even went so far as to determine the constellations which represented their own favoured deities [183]. Nonetheless, quantitative astronomical measurements were made by numerous cultures, and some of these observations are still of use today [157], whilst some of the earliest ‘observatories’, like Avebury or Stonehenge, are among the most impressive relics of prehistory. The advent of relatively modern techniques, and technology such as optical telescopes, fundamentally changed the nature of our study of the sky. Since the burning of Bruno, the study of the stars has passed from the realm of mythology and theology into that of science. Yet the science of astronomy still deals with fundamental questions of the nature of the universe, and the study of the largest scales belongs to cosmology. In this thesis, two problems of fundamental importance to cosmology are ex amined. In Chapter 2, a study of some of the most distant known galaxies is presented. The nature of these high redshift radio galaxies is still very uncertain. If they are young objects we may at last be seeing galaxies in the process of forma tion. If old, then the epoch of galaxy formation is pushed to yet higher redshifts. It is not even certain that the majority of the power output from these galaxies comes from starlight. Another possibility is scattered light emitted by some cen 15 tral engine. Observations at millimetre wavelengths, such as those presented here, may provide a critical test for the age and nature of these galaxies. In the other chapters of this thesis, studies of the Cosmic Background Radi ation (CBR) in search of the Sunyaev-Zeldovich (S-Z) Effect are presented. The theoretical background to this is provided in Chapter 3, and then, in Chapter 4, the results of work to measure the S-Z effect using the UKT-14 photometer at UKIRT are presented. In succeeding chapters, the development of the IC- STM 3 Channel Millimetre Wave Photometer, an instrument purpose-built for CBR studies, is described, and the first observations with this instrument are dis cussed. Finally, the future prospects for the 3 Channel Photometer are examined, together with other aspects of CBR astronomy. In the remainder of Chapter 1 the current state of cosmology is reviewed. Both the fundamental observational and theoretical results are examined, together with some important unanswered questions. 1.1 Observations in Cosmology The importance of observational data in cosmology can hardly be overstated. Theories of the universe abound, and have done so since time immemorial. It is only when their predictions are tested in the light of quantitative observational evidence that we can even attempt to confirm or refute any of the many mod els. Perhaps the earliest example of a fundamental observation in cosmology was Galileo’s refutation of Ptolemaic theory by observations of the Jovian system and the phases of Venus. It is perhaps fortunate for later generations that the authori ties of the time were less worried by observations than by theories, or these results might have been more strongly suppressed. Nevertheless, these observations, and those of other astronomers of the time, ushered in the new era of Copernican theory and observational astronomy and cosmology. One need no longer sit and think about the universe, one could go out and ask it questions! 16 1.1.1 Fundamental Observations in Modern Cosmology The theoretical framework necessary for a proper quantitative discussion of the universe was provided by Einstein’s General Relativity in 1916 [59]. However, the observations that gave the theorists indications of the true context of their models were not made until many years later. Up to that point, there were nu merous conflicting models, and no proper test to discriminate between them. The present dominance of the isotropic hot big bang model has come about because of a number of critical cosmological observations. Principal among these were the discovery of the Hubble Flow, the observational and theoretical work on primor dial abundances, and, in some sense the result that brought it all together, the discovery of the Cosmic Background Radiation (CBR). 1.1.2 The Hubble Flow In 1929, Hubble reported his first findings on the velocities and distances of ex ternal galaxies [75]. He discovered the now-famous Hubble relation which linearly correlates the distance and ‘recession velocity’ of cosmological objects. Although the precise value of Hubble’s constant still remains unclear [141], the existence of the Hubble relation is a central part of modern cosmology. Its discovery ushered in the era of the expanding universe, and demonstrated the applicability of the non-static solutions of Einstein’s General Relativity for models of the universe. 1.1.3 Primordial Nucleosynthesis of Light Elements The origin of the heavy elements, or ‘metals’, has been identified with stellar processes since the 1950’s [28]. But, even before the discovery of the CBR, it was recognised that the cosmic helium abundance was too great to be produced purely in stars [30]. In their 1948 paper, Alpher and collaborators [5] proposed that a large number of free neutrons were present during a brief hot, dense phase, in the earliest stages of the universe. It was proposed that all heavy elements were then built up by successive neutron captures by the protons also present. This early idea failed because of the lack of stable nuclei with mass numbers of 5 and 8 to allow for heavier elements to form, and stellar nucleosynthesis was 17 later accepted as the origin of most of the matter beyond Lithium7. The origin of light nuclei, such as Helium, was still a problem though, and the discovery of the CBR, predicted by the earlier ‘cosmic fireball’ idea, prompted new models of nucleosynthesis to explain the light elements. The theory behind nucleosynthesis in the early universe has since become quite detailed, and has expanded its sphere of interest beyond just helium to heavier, rarer isotopes, and to deal with several areas of interest to cosmologists and particle physicists, such as the number of neutrino families and the universal baryon-to-photon ratio. Krauss [86] provides a useful summary of the current state of Big Bang Nucleosynthesis. 1.1.4 The Cosmic Background Radiation The final observational result that allowed the standard big bang model of the uni verse to become predominant was the 1965 discovery by Penzias and Wilson [127] of the Cosmic Background Radiation (CBR). The discovery of a uniform, isotropic black body radiation yielded many important results for cosmology. Firstly, the homogeneity and isotropy of the CBR validated the assumption of these prop erties in almost every cosmological model. More importantly, it indicated that the universe originated in a hot, dense phase, where matter and radiation were in equilibrium. The cosmic black body radiation would then be the thermal emission of a hot hydrogen plasma, redshifted by a factor > 1000. The discovery of the CBR was, in fact, predicted as part of the original explanations for the primordial helium abundance [5]. 1.2 The Early History of the Universe Armed with these fundamental results in observational cosmology, it becomes possible to construct a history of the early universe. Using the results of theoretical particle physics, as well as cosmology, an attempt can be made to account for the origin of much of the universe. This section outlines the history of the universe in its broadest terms within the framework of the standard hot big bang model, with specific emphasis on the relevance of the work in this thesis. Some representation of the major events and timescales involved is given in figure 1.1. 18 o ...... Figure 1.1: The Universe A diagrammatic history of the universe from Inner Space: Outer Space 1986 1.2.1 The Geometry of the Universe The Hubble flow, expressed as the recessional velocity of an object a distance r from an observer, can be expressed as follows: 7? v = r = H r = —r (1.1) R whereH is the Hubble parameter, and R is a scaling factor representing the overall scale of the universe. The value of the Hubble parameter will change over time, and its present value is termed Hubble’s constant. The observational data shows us that Hubble’s constant is positive, with galaxies isotropically expanding away from us. The universe is thus in a phase of expansion, with R positive. A quantitative description of the expansion of the universe can be made using a Newtonian argument. This models the universe as a homogenous and isotropic sphere with density p, whose expansion is opposed by its own gravitational mass (see figure 1.2). Birkhoff’s theorem in General Relativity [19] shows that New tonian gravity can be applied within this sphere, and that the effects of matter outside the sphere can be neglected. Then, by energy conservation: T ” \* R2PG = const = C1-2 ) To examine the evolution of the universe over time, we must relate the density and pressure of the material in the universe to its expansion rate. This can be done using the 1st Law of Thermodynamics: dU = -P d V (1.3) where U is energy, P is pressure and V is volume. In the early universe, V oc R 3 and U = pc2V. Examining the time dependent behaviour yields: c2p = -3 (c2p + p ) (1.4) This relates the density of the universe to the rate of expansion and the material pressure. The equation of state for the material then relates pressure P to density p and temperature T to yield a description for the time evolution of the universe. Two equations of state are applicable for almost all of the history of the universe, depending on whether the dominant material is relativistic or non-relativistic. 20 Figure 1.2: The Expansion of the Universe • Relativistic material. In the early, hot environment of the universe almost all mass is in a relativistic state, with the cosmic medium in equilibrium with the radiation. In this state P oc p/3, and equation 1.4 leads to: p oc R~4 (1.5) For a radiation field it is also true that p « T4, so that the temperature,T of the radiation in the universe changes as T « 1 (1.6) The early universe, withR small, is thus a very hot and dense place. • Non-relativistic material. This is typified by the universe in its present state, where the matter in galaxies is the dominant form of mass (or perhaps some dark matter species, which has cooled sufficiently to become nonrelativistic). In this situation there is no pressure, so P = 0, and equation 1.4 leads to: p oc iT 3. (1.7) 1.2.2 The Evolution of the Universe The evolution of the universe is described by the way the scale factor R changes with time. There axe three distinct alternatives to the future history of the uni verse which are determined by its density. These alternatives may be considered in the Newtonian approximation discussed above. In figure 1.2, the test particle is acted on by the mass within the sphere shown, and it has a velocity v. In this situation there axe two cleax alternatives for the future motion of the particle. Firstly, it can have a velocity greater than the escape velocity for the mass attract ing it, and the particle will escape to infinity. This is equivalent to an infinitely expanding, or open, universe. Alternatively, the particle may have a velocity less than the escape velocity, and so will travel outward to some maximum distance, and then fall back to the centre of the sphere. This represents a closed universe, where the Hubble expansion will eventually reverse, and all material will fall back in a ‘big crunch’. A third alternative is where the particle has exactly the escape velocity, so that it has an asymptotic velocity of zero at infinite expansion. This 22 n < i R ■> t Figure 1.3: The Behaviour of the Scale Factor in different universes is the so called flat Einstein- de Sitter universe. These alternatives are equivalent to the constant k in equation 1.2 having the values -1, +1 and 0 respectively. The critical density pc, which marks the boarder between open and closed universes, can be found from equation 1.2, taking k = 0, and is: Pc — (1.8 ) The behaviour of each of these models is summarised in figure 1.3. Two further observational parameters are defined which can be used to provide information on the nature of our own universe. These are the Hubble constant, Ho, and the deceleration parameter, qo, where the zero subscript indicates values at the current epoch. They are defined as follows: H0 = (1.9) qo = 24 Using these definitions, and equation 1.2 again, we can produce the useful result that: Hl{2qa - 1) = A (1.10) Thus q0 = 1/2 implies k = 0, with higher values yielding a closed universe, and lower values an open universe. Differentiation of 1.2, and substitution of H0 and q0 yields: _ 8irGp0 po , . 2qo 3Hg ~ pc (1'H ) We further define a symbol ft = po/p c, so that ft > 1 implies a closed universe. The presently measured values of ft and qo sit precariously near to the critical density with 0 < qo < 2 being the best present limits [144]. The value of Ho is currently thought to lie in t-he range 50 < Hq < 100 km s-1 Mpc-1 [76]. 1.3 The Cosmic Background Radiation As has been noted above, the three observational pillars on which current Big Bang cosmology rests are the nucleosynthesis of light elements, the Hubble expansion and the CBR. The Hubble expansion, discussed above, has its nature in the very geometry of the universe, whilst nucleosynthesis occurs during the phase of the universe, a few seconds after the Big Bang, where nucleon ‘chemistry’ could take place. The CBR has its origin at a much later stage, about 105 years after the Big Bang, when the universe had cooled far enough that the primordial matter could combine to form neutral atoms. The photons from the early universe cannot interact with the neutral atoms, and so stream freely away from this surface of last scattering. The CBR we see today is the redshifted black body spectrum of the early universe, the last time it was optically thick. Observations of the CBR have found that its spectrum matches that of a black body very well, over a large range of frequencies [104], and that its temperature is 2.735 ± 0.06 K. They have also shown that the temperature distribution across the sky is very isotropic. Apart from the CBR dipole, due to the motion of the Earth relative to the CBR’s restframe, no deviations have been observed down to a level of AT/T of « 10-5 over scales ranging from a few arcseconds to many degrees. The search for any intrinsic anisotropies in the CBR is very important 24 since such observations are telling us about the structure of the universe at the recombination epoch. 1.4 Dark Matter One final question about the make up of the universe which must be discussed is dark matter. This is based on results over a wide range of astronomical ob jects, stretching from the local galactic neighbourhood, to studies of distant IRAS galaxies and galaxy clusters [173]. All of these studies consist of measurements of the motion of stars within a galaxy, or galaxies within a cluster, and using this information to calculate the gravitational mass of the target object. The rotational velocity of stars within a galactic disk, for example, can be measured. The mass within a given radial dis tance from the galaxy’s core is then calculated from simple Newtonian mechanics. The results from the whole range of dark matter studies are usually quoted as the mass to light ratio for the object in solar units. This ratio is found [173] to increase as larger objects are observed. The visible parts of galaxies thus have M/L « 10, while rich galaxy clusters have M/L « 200, and the largest scales studied have M/L « 700 [112]. This last value is roughly consistent with 0 = 1. This result presents a problem for the standard model. The results of big bang nucleosynthesis models are all consistent with the baryonic content of the universe being about 5 times too small to close the universe, ie. O b ^ 0.2. Whilst baryonic matter can provide some of the dark matter, if Q = 1, as observations on the largest scales suggest, it is necessary to invoke some exotic non-baryonic material which is to make up the rest of the mass of the universe. Theoretical prejudices coming from the theory of Inflation [71] also suggest that fl should be 1, requiring some dark matter species. Possible candidates include assigning a small mass to conventional neutrinos, « 10 eV, or the introduction of new Weakly Interacting Massive Particles, WIMPs. Which of the numerous suggested dark matter particles, if any, proves to be responsible for the missing mass is still unclear and is a very active area of current research. The problem may be tackled in a number of different ways; by direct observation of the particle in a 25 particle physics experiment; by detection of the cosmic flux of these particles; or by analysis of their effect on the large scale structure of the universe, and comparison with astronomical observation. While projects are actively under way to use the first two methods, to date cosmological observations have proved a most fruitful way of examining the nature of the dark matter in the universe. Indeed, further, independent assessments of the mass associated with various classes of objects, such as clusters of galaxies, are also needed. This study is intimately linked with questions of large scale structure and the origin of galaxies. 1.5 Primordial Fluctuations: The Origin of Large Scale Structure The standard big bang model described above has isotropy as an important fea ture. The real universe, however, is clearly anisotropic on many scales, with stars, galaxies, galaxy clusters and superclusters, and many other features which con tinue to be a rich field for observational cosmology. The isotropic requirement must therefore break down at some level, so that galaxies and other structures can form and produce the universe we see. The origins of large scale structure are assumed to be small density fluctuations arising in some process in the early uni verse. These fluctuations then grow over time, and give rise to the stars, galaxies and large scale structure we see today. This section describes current ideas of the initial perturbations and how these theories may be tested. 1.5.1 The Nature and Spectrum of Initial Fluctuations Density fluctuations in the early universe are divided into two types (see figure 1.4: • Adiabatic perturbations, which involve a fluctuation in the energy density, but not in the entropy. This leads to an increase in both the matter density and the photon density. • Isothermal perturbations, which involve a fluctuation in the relative energy density of the various components, but with zero sum. Thus an increase in 26 Matter Density Photon Density Adiabatic Perturbation Matter Density Photon Density Isothermal Perturbation Figure 1.4: Perturbation Types m atter density is accompanied by a decrease in photon energy density. Since the baryon-to-photon ratio is very small, « 10~9, the change in the photon density for any change in baxyon density is also very small. The origin of these fluctuations is as yet unclear, but is assumed to come from some physical process in the early universe, possibly associated with the much vaunted Grand Unified Theories (GUTs) of particle physics. The strength of these initial fluctuations on different scales is then described b y *(r) = ^ - 1 (1-12) where p is the mean density, and p(r) represents the fluctuation amplitude on a scale r. It is more usual to refer to the Fourier transform of this function Sk - f 8(r)e'krdr (1.13) 28' where k is the wavenumber of the fluctuation. This spectrum then evolves over time. At present, there is no generally accepted theory for the origin of the initial perturbations, so the selection of the initial spectrum is a matter of theoretical prejudice. The usual form assumed is a power law, since it seems unnatural that any particular scale should be favoured. Thus: N 2 OC fc" (1.14) In addition, the Fourier components of this spectrum are usually assumed to have random phase. They thus obey Gaussian statistics and axe completely determined by equation 1.14. The only well established model where this is not the case in volves cosmic strings as the seeds of galaxy formation. These are topological defects which may be produced by a phase transition in the early universe [177] which have a considerable energy associated with them. They are thus quite mas sive, and may seed galaxies directly by gravitational attraction. Other processes, involving hydrodynamic effects with galaxies forming in the ‘wake’ of a moving string have also been suggested [174]. Different fluctuation generation processes produce different n. Poisson noise, for example, has n = 0, while the inflationary theories [71] generate n = 1, the Harrison-Zeldovich constant curvature spectrum which has been favoured by theorists for some time [74]. Once a spectrum of density fluctuations has been produced, it is modified by the physical processes taking place in the early universe. As perturbations enter the horizon during the radiation dominated era, the dominant photon-baryon fluid will execute acoustic oscillations at constant amplitude. This will damp fluctuations on sizes equal to the horizon at the time of equal density of matter and radiation. In addition, sound waves are damped further on scales where the photons can diffuse out of their peaks before recombination. This is known as Silk damping [161]. Finally, free streaming of any species which dominates the fluctuations will damp scales which enter the horizon while they are still relativistic. Thus in a neutrino dominated cosmology, with particle mass as low as 10 eV, fluctuations on all except the largest scales are damped. This is termed 28 0 T t— i— i— r T Figure 1.5: Spectra of Fluctuations from different types of Dark Matter Taken from [18 i]. a hot dark matter universe (HDM) since the neutrinos stay hot, i.e. relativistic, until late times. A cold dark matter universe (CDM), dominated by particles with masses of a few GeV (eg. photinos) maintains fluctuations on a large range of scales, since the CDM particles became non-relativistic at a very early times. Theories involving warm dark matter, which is intermediate between the two and could describe a baryon dominated universe, also exist. After recombination, we are thus left with initial fluctuation spectra along the lines of those shown in figure 1.5. 1.5.2 Galaxy Formation and Large Scale Structure After recombination, the formation of large scale structure is controlled by the species of dark matter which dominates the universe. If neutrinos dominate, 30 then fluctuations only remain on the scales of superclusters. For CDM universes, however, fluctuations remain on a much larger range of scales, with the strongest power on small scales. This dichotomy leads to two different scenarios for galaxy and large scale structure formation, and very different predictions for observational results. One additional model, which does not rely on any form of dark matter is also discussed. HDM: Top Down Galaxy Formation In HDM models, such as neutrino dominated schemes, the first bodies to form are on the scales of superclusters. These then fragment into smaller and smaller bodies, until, at quite a late epoch (z = 1 - 2), galaxy scale objects and stars can form. N-body simulations of this process [181] fail to reproduce the large scale structure we presently see, either qualitatively, or quantitatively, as can be tested, for example, by comparing the theoretical and observed galaxy-galaxy correlation function [125]. The formation epoch of galaxies predicted by these models is also much later than observational evidence suggests. An HDM picture of the universe could possibly be saved by the addition of a new method of forming large scale structure. Examples of these include cosmic strings [16] or explosion seeded blast waves [179]. The predictions of such hybrid models have yet to be fully explored. At present, though, we must regard the HDM models as failing to correctly describe our universe. CDM: Hierarchical Clustering In CDM dominated models, density fluctuations remain on all scales after re combination, with the largest perturbations on small scales (see figure 1.5). The first objects that form will then be clusters of stars, which then agglomerate into galaxies and larger mass concentrations. N-body simulations of CDM models have proved quite successful over recent years [58]. A feature of these models is bias ing, whereby galaxies and other luminous mass concentrations are associated with the peaks of the dark matter distribution. Typically a galaxy is associated with a « 2 30 CDM models have so far agreed with most observational data, and it is be coming a ‘standard model’ against which other schemes can be judged. Recent progress in observations of very large scale structure, though, are beginning to come into conflict with some of its predictions. Isothermal Baryon Dominated Models This is a relatively new idea [124] which proposes a low fi universe, dominated purely by baryons. In these models the dark matter is made up of brown dwarfs, dust or black holes in the haloes of galaxies. The initial perturbation spectrum in these models is isothermal, which suppresses CBR anisotropies to a level which may be below the current observational limits. Efstathiou [58] argues that this is not the case. Adiabatic baryon models, in contrast, produce CBR anisotropies considerably above the present upper limits. These models would form galaxies at around z « 10 and can reproduce many of the present results on large scale structure [126]. They are also capable of producing structure on larger scales than CDM, which may prove an advantage if some of the recent results on filaments and walls in the distribution of distant galaxies are confirmed [65]. 1.6 Confrontation of Theories with Cosmologi cal Observations 1.6.1 CBR Observations Perhaps the most fundamental observation that can be made of the early universe is the direct search for the initial density fluctuations as revealed by anisotropies left in the CBR. These anisotropies come as a result of different temperatures at different positions at the surface of last scattering, due, for example, to adiabatic fluctuations. Interactions between photons and the mass distribution before and after last scattering can also produce anisotropies. Given the initial fluctuation spectrum in a theory, and the nature of any dark matter present, it is possible to predict the resulting spectrum of CBR anisotropies. Figure 1.6 shows the predicted anisotropy spectra for several models of the early universe, together with two of 31 Figure 1.6: CBR Anisotropies in various Models Taken from [160] the more stringent observational constraints. For the low Q adiabatic fluctuation, baryon dominated models shown in the left-hand panel, the small scale anisotropy limit already seems to provide a contradiction, whilst the HDM models in the right-hand panel are very close to contradicting the same limit. These results are among those responsible for the probable rejection of the simplest cosmological model, where the universe is open, and dominated merely by those baryons which nucleosynthesis results say are present, i.e. fi = « 0.1 — 0.2. The current favourite models are fi = 1 CDM dominated, and these, as can be seen from the figure, are yet to be constrained by CBR anisotropy measurements. Programmes to improve these limits are progressing rapidly. 33 1.6.2 Distant Objects Objects at large redshift provide us with some indication as to the time when galaxies first formed. At present the most distant objects known are QSOs at redshifts of up to ~ 5. The conclusions which might be drawn from these observa tions, though, are somewhat hampered by our lack of knowledge of the nature of the QSO phenomenon. If they are associated with galaxies, then their existence at such large redshift is a major problem for HDM type models, which predict galaxy formation at quite late times, but they are reasonably easily accommodated by the CDM hierarchical clustering scheme. The discovery of galaxies at large redshift [98] which appear to be normal powerful radio galaxies provides an interesting prospect. If they are indeed similar to nearby objects, and contain an old stellar population, then their existence at redshifts greater than 3 could push back the epoch of galaxy formation to z 5. Whilst CDM does predict the formation of some objects at very large redshift, these are considerably smaller than galaxies and result from density perturbations on very small scales, where the peak CDM fluctuations appear. Alternatively, if the star formation process in these objects is found to be radically different from that seen nearby, or if the source of the optical and infrared emission seen in these objects is not starlight, then we may be dealing with another aspect of the QSO phenomenon, and can say little about the epoch of galaxy formation. The nature of these High Redshift Radio Galaxies (HRRGs) is currently under active study, and is the subject of the next chapter. Primeval galaxies (PGs), those in the very first stages of formation, are perhaps a ‘holy grail’ of observational cosmology, and would answer a great number of questions when discovered. The present results of PG searches place only upper limits on their properties. 1.6.3 Large Scale Structure One of the achievements of CDM theory has been the successful prediction of the galaxy-galaxy correlation function [181]. Extension of correlation measurements to larger surveys offers the possibility of searching for correlations on very large 33 scales. Indeed, the APM survey [103] does seem to indicate greater clustering than is predicted by CDM on scales of « 20h-1 Mpc. Beyond correlation mea surements, the observations of filaments, voids and walls on very large scales in recent redshift surveys [65] also provide evidence for structure on the scales of hundreds of megapaxsecs. The existence of such large scale structure would be damaging to CDM since its hierarchical clustering scheme does not predict this, though some recent work [120] suggests that this assumption may be wrong. Ob servations of coherent streaming motions over large scales can also provide some difficulty for CDM models [142]. 1.7 The Role of this Thesis Two areas of current activity in observational cosmology are tackled in this thesis, both by use of millimetre and submillimetre astronomy. Chapter 2 deals with a study of High Redshift Radio Galaxies in search of the dust emission which would be expected from them if they were identical to similar nearby objects. This study has a bearing on the epoch of galaxy formation, and thus on the origin of all large scale structure in the universe. The proceeding chapters address the Sunyaev-Zeldovich effect and present ob servations of the CBR in search of this spectral distortion. With concrete results for the S-Z effect we may calculate Ho, qo and the mass of clusters of galaxies. It may even be possible to measure the peculiar motions of distant clusters with S-Z effect observations in the millimetre and submillimetre wavebands. The techniques and instrumentation developed here for observations of the S-Z effect are also applicable to searches for CBR anisotropies. These and other possibilities are explored in Chapter 7. 34 C hapter 2 Millimetre and Submillimetre Observations of Distant Galaxies 2.1 Introduction This chapter describes observations at millimetre and submillimetre wavelengths made at the JCMT in search of dust in recently discovered high redshift radio galaxies. The presence or absence of dust in these galaxies, among the most distant galaxies yet discovered, provide important information for determining the nature of these objects. The properties of high redshift galaxies also have a bearing on larger questions of galaxy formation and the search for primeval galaxies. These questions are also discussed. 2.2 High Redshift Galaxies 2.2.1 Discovery Galaxies at high redshift (z > 1) are very difficult to detect because they are exceptionally faint. For example the object 0902+34, a z=3.394 galaxy discovered by Simon Lilly (known as The Lilly Galaxy), has a V magnitude of 22.9 [98]. Several of these objects are also very extended, reducing their surface brightness still further. 3C326.1, a protogalaxy candidate at z=1.82, appears as several blue objects, the brightest of which has V of 23.5 [108]. Discovery of these objects 35 by photographic or CCD surveys is not practical, as it requires many hours of integration on many fields, since those bright enough to detect even after long integrations are rare. Instead, all of the currently known high redshift galaxies have been discovered as part of programmes identifying faint radio sources from such catalogues as 3C, 4C etc. (e.g. [97]). Selection of faint radio sources with steep spectra has proved particularly successful, providing some galaxies with redshifts above 4 [114]. An interesting new method, based upon the optical source identification tech niques outlined above, but avoiding the intermediate step of optical imaging prior to spectroscopy, has been pioneered by Rawlings et al. [133]. This technique uses the result, discussed below, that most high redshift radio galaxies have opti cal emission-line regions extended along the axis of the radio source [108]. Blind spectroscopy is then performed with the spectrograph slit aligned along the axis of the radio source. Any emission line region present will provide both an optical detection, and a redshift for the galaxy. In the first pilot study of this technique, Rawlings et al. [133] achieved detections and redshift measurements for 4 high redshift radio galaxies out of a sample of 5. Another method of searching for high redshift galaxies, though not necessarily radio sources, is to look for companion objects of known, high redshift QSOs. This has been done by Djorgovskii et al [53] using a narrow band Lyman-a imaging technique. In this, a QSO is imaged in a broad-band filter (e.g. R) and in a narrow band filter, centred on the wavelength of Lyman-a at the QSOs redshift. The broad- and narrow-band images are then compared to find objects with excess Lyman-a emission at the QSOs redshift. Follow up spectroscopic observations are then performed. Only 2 such QSO companion galaxies have so far been discovered at high redshift using this technique [165]. The objects appear to be luminous, relatively normal galaxies. The strong Lyman- a emission may be excited by the QSOs radiation field, or may be due to a nuclear starburst similar to NGC 1068 [178]. The lack of radio emission from the QSO companion galaxies is a potential advantage for millimetre/submillimetre observations searching for dust, since there will be no contamination from the high frequency tail of power law radio emission. 36 However, they are very close companions to their QSOs (angular separations < 10 arcseconds), and are therefore not suitable for observations using the large beamsizes (19 arcseconds) necessary at millimetre wavelengths. 2.3 The Properties of High Redshift Radio Galaxies 2.3.1 Radio Properties Lum inosity Since high redshift radio galaxies are detected initially in the radio, they are, not surprisingly, very luminous at radio wavelengths. However, their radio luminosi ties are not in general unusually high when compared to more nearby powerful radio sources. Even the Lilly Galaxy, 0902+34, at a redshift of 3.395, is of compa rable luminosity to such objects as Cygnus A, which, while exceptional, are well known at much lower redshifts. Table 2.1 compares the luminosities, at restframe 178 MHz, of high redshift radio galaxies with the nearby radio galaxy Cygnus A (assuming ft = 1). We may therefore consider as a base hypothesis that the radio source in a high redshift radio galaxy is much the same as the radio sources in nearby powerful radio galaxies. This is borne out by most of the radio properties of high redshift galaxies. Radio Spectrum A comparison of the spectral indices of high redshift and low redshift radio galaxies does not reveal any great discrepancies between the two data sets. Any differences that may be present could in fact be masked by a number of selection effects. George Miley, for example, [114] has conducted searches for optical sources at the locations of unidentified steep spectrum radio sources. This has brought some notable success, and the discovery of several galaxies at extremely high redshift [114], but may bias the presently known high redshift radio galaxies to having a 37 Object Luminosity at 178 MHz Spectral Index Morphology 10 K W H z -'/h (F-R class) 0902+34 3 0.76 Elliptical 3C326.1 9.7 0.71 Type 2 3C257 12 0.84 Type 2 3C294 6.8 1.07 Type 2 Cygnus A 39 0.74 Type 2 Table 2.1: Comparison of the radio properties of High Redshift Radio galaxies and the powerful, low redshift radio galaxy, Cygnus A. steeper spectrum. There is also evidence from the optical and IR data that the steepness of the radio spectrum of a high redshift radio galaxy is correlated with the amount of star-forming activity taking place in the object [96]. If this effect is real, this will place an additional bias on the sample of objects obtained by selecting steep spectra sources (e.g. Miley and collaborators’ work). Radio Morphology In terms of morphology, high redshift radio galaxies are also found to be very similar to lower redshift radio galaxies. Those that are fully resolved appear as conventional Faranof and Riley type 2 (i.e. edge brightened) double-lobed sources, while partially resolved sources appear elliptical. Summary of Radio Properties In terms of their radio properties, it can be seen that high redshift radio galaxies are by no means exceptional. They appear to merely be conventional bright radio galaxies that just happen to be very distant from us. This fact is somewhat intriguing, since it implies that the radio sources in radio galaxies were, perhaps, much the same only « 109 years after the Big Bang. If this is true, the implications for theories predicting galaxy formation at redshifts « 2 - 3 are somewhat dev astating. This conclusion, among others, motivated a number of deep optical and infrared studies of high redshift radio galaxies. 38 2.3.2 Optical and Infrared Properties The optical and infrared properties of high redshift radio galaxies appear to cover a broad range of properties. Figure 2.1 shows the broad band spectral energy distributions (SEDs) for the 9 high redshift radio galaxies discussed in Lilly’s 1989 paper [97]. As can be seen, some of the galaxies (e.g. 0902+34) have a pronounced convex SED, with very blue V-I colours, while others (e.g. 0822+39) have concave SEDs. However, while the visible part of the SEDs of these galaxies appear diverse, the infrared end of the spectrum, at K, conforms very well to the relationship found between K magnitude and redshift for radio galaxies over a very large range of redshift (see figure 2.2). There is also an exceptionally strong Lyman- a line in all these galaxies, suggesting that very rapid star formation is taking place. An estimate of the star formation rate (SFR) in these galaxies can be obtained by using the interpretation [170] that the Lyman-a line is produced by the reprocessing, via case B recombination, of Lyman continuum photons emitted by young, hot O and B stars. The SFRs inferred are all high, ranging from 100 to 500 M©t/r-1. The low dispersion in the K-z relation, the scatter in the blue part of the spec trum, and the strong Lyman-o emission (with the interpretation of massive star formation) can be explained [97] by the presence of two populations of stars. One population, dominating the spectrum and the mass, is an old stellar population, of age at least 2 billion years, while the other, contributing up to about 10% of the blue light, is very young, with age less than 1 billion years. The stellar evolu tion models used to arrive at this result were the Bruzual C-models [27] at ages 1 and 2.5 billion years. A similar scheme was proposed by Lilly and Longair [99] to account for the large range of R - K colours and small dispersion in the K-z relation for the 3C radio galaxy sample. The young population is produced in short erratic bursts of star formation, and the hot, short-lived, O and B stars then boost the blue end of the SED for their short lifetimes. The K band, however, is dominated by the old stellar population, providing a constant source of light over the longer ages of the less massive stars. The K-z relation thus stays quiet while 39 3 >> - t J *W C d) Q X E cO GO O Figure 2.1: SEDs for the Lilly Galaxies. Broad band spectral energy distributions for the high redshift radio galaxies discovered by Lilly [ Si 7 ]. The curve for each galaxy represents the best fit model SED consisting of a young and old stellar population. The young population contributes a factor F to the total light at restframe 500 nm, at a redshift of z. 40 the irregular bursts of young hot stars scatter the R - K colours. Two studies by other groups of both the 3C radio galaxies [57] and the more distant radio galaxies such as 0902+34 [140] confirm this result. However, population synthesis models by a fourth group, [36], using an updated version of the Bruzual models, propose a second interpretation. Using a Scalo initial mass function (IMF) [151], and an empirical correction to the model to account for the poor understanding of the asymptotic giant branch (AGB), [36] Chambers and Chariot find that the observed SEDs can be produced in only « 3 x 108 years, and persist for more than 6 x 108 years. Thus the high redshift galaxies currently being observed could be very young objects, with ages well under 1 Gyr. This model, however, does require that the initial stages of star formation in these galaxies are very short, < 1 x 108 years. Such objects, in their initial stages of formation, would be exceptionally bright and blue objects, due to a large O and B population which has yet to evolve. The scatter on the K-z relation remains small since all the different evolving components -main sequence, massive supergiants, AGB stars and red giants - are found to conspire to maintain a roughly constant visible-to- near -IR ratio for up to 1 Gyr, after which the population evolves passively. This model implies that all the strong radio sources would have undergone such a stage in their evolution. There would thus be a reasonably large population of bright, blue, very distant objects. These are precisely the objects, at just the redshifts (i.e. z = 3-5) that have been the targets of numerous unsuccessful primeval galaxy (PG) searches (e.g. [130]). The model may thus fall foul of these limits. Optical and Infrared Morphologies The optical and infrared morphologies of high redshift radio galaxies (HRRGs) demonstrate a major departure from the properties of closer radio galaxies. While nearby radio galaxies show no effects of the radio source on the distribution of starlight within the galaxy, high redshift radio galaxies have a noticeable elon gation, with the optical axis aligned along the radio axis [37]. Further, narrow band imaging has shown that this light is dominated by Lyman-a emission [164], and spectroscopic work by Chambers and McCarthy [36] has produced evidence 41 d> v s 3 u 0.1 1 Redshift Figure 2.2: The K-z relation for radio galaxies Data taken from [HI ] fS’? ] 43L of stellar absorption lines in the rest frame ultra-violet. This would suggest that much of the emission is from starlight, produced by a population of young, hot stars, formed in some process by the passage of the radio jet thought the inter- galactic medium [135]. Observations by Eales & Rawlings [133], and by Chambers et al. [35] of infrared components aligned with the radio jet in the galaxies 3C256 and 3C368 (at redshifts of 1.079 and 1.132 respectively) can be interpreted as confirmation of this result. However, a more quantitative analysis of the infrared alignments in a sample of 3C galaxies at z w 1 by Lilly [95] suggests that there is no IR alignment effect. Further confusion is added by observations of the optical polarisation of the galaxy 3C368 by Scarrott et al. [153], which produce the surprising result that the aligned emission is up to 13% polarised, and that this polarisation decreases with increasing wavelength. This is very difficult to explain with only starlight as the radiation source, but can be accounted for if the observed optical emission is in fact light from the central engine of the radio galaxy beamed out in the direction of the radio lobes, and scattered toward the observers by an intervening population of dust. They suggest that 3C368 is ‘a giant reflection nebula of galactic proportions’. The decrease of polarisation with increasing wavelength is then accounted for by the reduced effectiveness of dust scattering at longer wavelengths, and by some small underlying emission from stars diluting the red end of the scattered light. This smaller population of stars may be formed by a jet induced star formation process, and would possibly account for the infrared alignments observed by Chambers et al. and Eales Sz Rawlings. 2.3.3 The Nature of High Redshift Radio Galaxies The range of phenomena in high redshift radio galaxies, and the varied interpre tations of their nature, are very much an active field of study. There is no real consensus as to the nature of HRRGs. Indeed, there is even dispute as to the results of some of the observations, such as the presence or absence of an IR align ment effect. At this stage one can produce a menu of possible models for these objects, and attempt to use this list to select observations to distinguish between 43 them. Possible models, then, include the following: • Old galaxies with massive conventional starbursts taking place in them. This is essentially the model for the Lilly Galaxy and the other 1 Jy blank field sources described in [98] and [97]. It requires an unusually eaxly epoch of galaxy formation (z ~ 10), and does not explain the optical alignment with the radio axis. • Old galaxies with massive star formation taking place in them as a result of radio jet induced star formation. This is a modification of the explanation of the 1 Jy field sources, and others, made to account for the alignment seen between the radio jet and the optical structures [97]. • A young object whose first generation of star formation was induced by interaction between the radio jet and the intergalactic medium. This is the model suggested by several authors, including [116], [51] and [36]. It avoids the problem of requiring an early epoch of galaxy formation, and explains the optical/IR-radio alignment, but requires a new method of star formation, and a very large and bright early stage of evolution. In addition, the low dispersion K-z relationship emerges only as a result of a ‘conspiracy’ between the various stellar components of the model. • True primeval galaxies, still forming their first generation of stars. With, perhaps, a jet induced star formation process, this model would ex plain the optical/IR-radio alignment, but fails to explain the low dispersion K-z relationship, and perhaps falls foul of the presence of metal lines in mea sured in these objects (e.g. in [98] Carbon lines are found in the z = 3.4 galaxy 0902+34). • Dust scattering of radiation from a beamed central engine source (cf. the ‘Unified’ models of QSOs, AGNs and radio galaxies [13]). This model is based on the observation of polarisation in only a few more nearby (z ~ 1 — 1.5) objects [153], It still requires some star formation in 44 the jets, but would explain the strong alignment and the powerful Lyman-ct lines. It may also present an explanation for the K-z relation if there is an old underlying star population, but is really only an explanation of the polarisation measurements, which needs some facet of one or more of the other models discussed here to produce a full picture. Given that, though, it is the only successful explanation of polarisation in these objects, and if this is observed in the more distant galaxies, then some element of this model must be introduced into any description of HRRGs. • Conventional radio galaxy, similar to Cygnus A. This is really a baseline model, against which the others may be compared. Whatever other properties the HRRGs have, they are certainly powerful radio galaxies whose properties in the radio are similar to Cygnus As, which can therefore be used at some level as a prototype for them. While none of these models gives an ideal solution for the nature of high redshift radio galaxies, they each address some of the observational results. Their predictions, in relation to cold dust, will now be discussed in turn. 2.4 Motivation for Observations 2.4.1 Target Objects for these Observations The targets for these observations are the objects given in table 2.2. They are all strong radio sources at high redshift. All have been imaged in the optical and have had optical spectra made of them [98] [97] [109]. 3C294 is the only source for which infrared photometry is not available. All of these objects fall very well into the general class of HRRGs described above. They all have very strong Lyman-a emission, large radio luminosity, a FR type 2 radio structure (where resolved), while all those observed in the infrared lie on the low dispersion K-z relation. They thus all conform to the model of a high current star formation rate going on in a galaxy with an existing old stellar population ([97]), or the other models described above. 45 Object RA Dec Redshift 0902+34 09 02 24.7 34 19 57 3.4 3C257 11 20 43.0 05 52 00 2.5 3C326.1 15 53 57.2 20 12 58 1.8 3C294 14 04 34.0 34 25 37 1.8 Table 2.2: Object List for HRRG observations. We can use observations of the millimetre/submillimetre emission from these objects to determine, or place limits on, the far infrared (FIR) properties of these objects. FIR emission in these objects depends on a number of factors, including the presence of dust, and the nature of the star formation processes in these galax ies. Since these are the first millimetre/submillimetre observations of this class of objects, we must base our predictions of the FIR emissions on the properties of more nearby galaxies. The processes which would produce rest frame FIR emis sion in HRRGs include the high frequency end of the power law radio emission, or the presence of a population of cold dust, as seen in the nearby high luminosity radio galaxy, Cygnus A. Star formation may also lead to emission from cool dust as seen in nearby starburst galaxies [170] and may dominate the FIR emission in certain of these objects with high inferred rates of star formation. Quite what dust emission might be expected from the unified scheme models for HRRGs, which explain the polarisation measurements by dust scattering of radiation from a central engine, is unclear. While nearby reflection nebulae are strong sources in the far IR, the amount of dust needed to explain the observa tions is very dependent on models of the dust structure and distribution. It is, apparently, quite possible [3] to produce the observed polarisation measurements with a comparatively small amount of dust. 2.4.2 Millimetre/Submillimetre synchrotron emission from a H R R G The most obvious source of emission at FIR wavelengths in these objects, even in the absence of any dust, will be from the radio lobes themselves. The radio 46 Object Predicted 1.1 mm Predicted 0.8 mm Flux (mJy) Flux (mJy) 0902+34 6.3 4.7 3C257 21 15 3C326.1 5.6 3.3 3C294 4.2 2.7 Table 2.3: Observational fluxes predicted from the power law radio component of the target objects. emission in these sources is generally described as following a power law spectrum, i.e: F oc u~a (2.1) where F is the flux density at the frequency z/, and a is the power law index, measured by radio observations at different frequencies. Given radio flux data at one frequency, including the flux and power law, we can thus extrapolate the power law spectrum to higher frequencies. However, the index a does not necessarily retain the same value over large ranges of frequency. For the target objects of this investigation, radio data is available at 178 MHz in the 3CR [17] catalogue [166] for all except 0902+34. The data on 0902+34 is in the Allington-Smith 1 Jy catalogue [4] at 1.4 GHz. Additional information is available on 3C326.1 [109] from which a high frequency power law index is calculated. This demonstrates the well-known fact that the power law can steepen dramatically at higher frequencies. For 3C326.1, at low frequencies (from 178 MHz to 2695 MHz), the index a has the value 0.71 while between 5 and 15 GHz it has the value 1.3. (The value of 0.12 quoted in [166] is in fact in error. Examination of the primary reference for the 2695 MHz data [2] gives the value 0.71). Assuming that the spectral data available for each of our sources is applicable at the observation frequencies of 264 GHz (1.1 mm) and 394 GHz (800 /xm) the expected radio fluxes for each of our sources are calculated and given in table 2.3. 47 Object Predicted 1.1 mm Predicted 0.8 mm Flux (mJy) Flux (mJy) 0902+34 7.8 16 3C257 6 13 3C326.1 4.8 14 3C294 14 Table 2.4: Fluxes in observational wavebands predicted for Cygnus A model for the observational targets. 2.4.3 Dust Emission from a nearby radio galaxy model of a H RRG The powerful radio galaxy Cygnus A, as discussed above, shares many of the radio properties of the HRRGs. It can therefore be thought of as a baseline model against which other results, such as those presented here, can be com pared. Among its other properties, Cygnus A is a very strong source of thermal emission in the far infrared from a cool (about 30K) dust component. This emis sion was detected by the IRAS satellite in both survey and pointed observations [15]. Fitting this data by a 30K black body, and using the luminosity distance re lation [180] one can calculate the cool dust emission that would be expected from a Cygnus A type object placed at the redshift of each of the HRRGs observed. 2.4.4 Dust Emission from a Starburst Model of a HRRG IRAS observations clearly demonstrated that low redshift galaxies undergoing a burst of star formation are exceptionally strong sources of far infrared emission [170]. This radiation is believed to be produced by dust heated by the copious numbers of high mass, bright, young stars which dominate the luminosity distri bution of the starburst population. The heated dust radiates in the rest frame far-infrared waveband, with the dust spectrum peaking near 100 /fm, implying a temperature of «50 K. In practice, observations of the dust temperature give a range of temperatures, from 45 K for the starbursts that dominate the central few 100 parsecs in M82 and NGC 253 [138], to about 26 K in the extended (3 48 kpc) star forming disk in NGC 1068 [170]. Since the dust is heated by the young stars in the starburst, the strength of the far-infrared emission is proportional to the star formation rate, thus for objects, such as the target HRRGs in this study, with a very high inferred rate of star formation one might expect a similarly high far-infrared luminosity. Numerous authors have modelled the relationship between fax-infrared luminosity and the rate of star formation for various initial mass functions (IMFs) and low mass cut-offs. Telesco [170] reviews the present results. Values for K, defined so that M = KL f ir , range from 1 x 10-10 to 6 x IQ-10 for jow mass cut-offs of 8M© to 0.1©, with up to 50 % of starburst galaxies appearing to have a low mass cut off at the upper end of this range [152]. The rates of star formation in the HRRGs described here are particularly high, ranging from 100 M©/yr for 0902+34 (inferred from fits to the Bruzual models in [98]) to 350 M©/yr for 3C294 (inferred from the Lyman-a emission and Case B recombination). For all the HRRGs observed in this programme, except for 0902+34, the star formation rates were derived by observations of the Lyman-a line. This is achieved by relating the Lyman-a luminosity to the Ha luminosity assuming Case B recombination [26] and employing the relation between L hq and star formation rate given by Kennicutt [83]. This process yields the star formation rates given in the table 2.5. In the case of 0902+34, the star formation rate is not calculated in this way, but comes from the fits of population synthesis models to the spectral energy distributions reported in [98]. Both [98] and [36], in spite of their different inter pretations of the age of this galaxy, give a value of 100 M©/yr as the current rate of star formation. This is the value adopted here. Using these derived star formation rates for the HRRGs, K is used to predict the far infrared luminosities for these objects, assuming that normal starburst behaviour is present. From this luminosity, fluxes into the instrumental wavebands of this investigation axe calculated, and given in table 2.5. 49 Object SFR Predicted 1.1mm Predicted 0.8mm (Me /y r ) Flux (mJy) Flux (mJy) 0902+34 100 2.8 6.1 3C257 200 4.5 10 3C326.1 250 4.8 13 3C294 350 18 Table 2.5: Fluxes in observational wavebands predicted for a starburst model of the observational targets. 2.4.5 Limitations of these Models Both of these models are based on the assumption that the processes underway in the HRRGs are much the same as those observed in lower redshift objects. Clearly, if star formation is occurring by a more exotic means, such as jet induced star formation [51], or if the objects are so young as not to have produced dust [36], then these models will not be valid and fluxes consistent with only the high frequency tail of the power law emission will be found. The starburst predictions axe also somewhat model dependent, with the low mass cut off being the dominant uncertainty. The values given above are for a low mass cut off of 8 M0 . For smaller lower mass cut offs, the fluxes in table 2.5 should be reduced by a factor of 3 for 2 M0, or 6 for 0.1 M0. The Lyman-a flux values may also not be solely due to young hot stars. Lilly suggests [98] that some of the Lyman-a emission in 0902+34 may be due to shock heating. This is supported by the fact that the star formation rate inferred from population synthesis model of 0902+34 is a factor of 3 to 4 lower than would be suggested by the Lyman-a luminosity alone. In addition, if the bulk of the Lyman-a flux is due to scattering of radiation from a central engine, as suggested the observations of polarisation in 3C368 by Scarrott et al. [153], then much of the foregoing discussion would be irrelevant. However, in this reflection model some fax infrared emission may come about by central engine warming of the scattering grains, in a similar manner to the processes in a galactic reflection nebula. The details of such a system, though, are very model dependent, and are thus subject to great uncertainty. 50 Nevertheless, it is clear that studies of the rest frame far infrared emission in HRRGs with millimetre/submillimetre observations can provide a useful insight into the nature of these objects as either conventional radio galaxies, or as normal, old galaxies undergoing a burst of star formation. 2.5 The Observations The observations described here were made in mediocre weather conditions at the James Clerk Maxwell Telescope (JCMT) on Mauna Kea in Hawaii. This is a 15m telescope dedicated to millimetre and submillimetre observations. The observing run consisted of 4 nights, from 4th to 8th of January 1990, in the shift between 1.30 am and 9.30 am. The instrument used was the UKT-14 continuum bolometric receiver system [56]. Chopping and nodding were in azimuth throughout, and a chopping frequency of 7.8125 Hz was used. Azimuth nodding precluded errors resulting from changing airmass between nod positions, which has been found to cause systematic offsets [46]. The observations were made at 800 fim and 1.1 mm. Planets were used as primary calibration sources, with secondary calibrators taken from the JCMT-POINTING list provided by the Joint Astronomy Centre. These objects were observed at wavelengths from 2 mm to 350 fim. Other bright but variable objects, such as QSOs, were used to check and correct the pointing of the telescope throughout the night. The observational procedure was typically as follows. First we conducted a pointing test (‘Fivepoint’) on a calibration or pointing source. If the source were a calibrator, this would be followed by short integrations at 2 mm, 1.3 mm, 1.1 mm, 0.8 /xm, 450 fim and 350 fim. The target nearest to the zenith was then acquired, and integrated on for about an hour in blocks of typically 20 minutes. The cycle was then repeated. When the sun rose in the morning it was also necessary to conduct a focussing run on a calibration source since the telescope parameters are known to change when the atmosphere and telescope superstructure warm up. On the third night of observations it was noted that while the optical depth at 800 /xm was greater than at 1.1 mm, the noise recorded on the strip chart at this wavelength was considerably less than at the lower frequency. Since the 51 instrumental sensitivity at 1.1 mm is superior to that at 800 //m under ideal at mospheric conditions, this effect was presumably caused by the less than optimum sky conditions prevailing during our observations. Because of this, it was decided to change our observing strategy, and to observe at 800 /zm for the remainder of the rum. We thus have observations at both 1.1 mm and 800 /zm for most of our sources. A summary of the observations is included in table 2.9. 2.5.1 The UKT-14 Continuum Receiver The UKT-14 Continuum Receiver [56] is a single channel, general purpose bolo- metric instrument. The detector element is a composite Ge:In:Sb bolometer, mounted in a hemispherical integrating cavity, cooled by liquid Helium 3 to its operating temperature of 0.35 K. UKT-14 has a filter wheel with 9 observational filters, at wavelengths ranging from 2.0 mm to 350 /zm. The principal observation frequencies used in this study were the 1.1 mm and 800 /zm channels, while most of the remaining broadband filters were used in calibration measurements. Table 2.6 summarises the filters available, and the approximate observational sensitivities attainable with the in strument in good conditions. The filters were designed to allow observations in the main atmospheric windows between 350 /zm and 2 mm. Figure 2.3 shows these windows. The transmission, in even the lower frequency windows used for this study, is by no means 100% even on the clearest of nights. With precip- itable atmospheric water vapour of only 0.5 mm, the transmission in the 1.1 mm window is at best 99%, while the 800 /zm channel has only « 85% transparency. Careful consideration is therefore necessary in correcting for the atmospheric ex tinction. Frequent measurements of the extinction are also necessary, since the atmospheric conditions axe variable over a night of observations. This variabil ity, on smaller time scales, poses the additional problem of sky noise making a potentially major contribution to the total system noise. Indeed, observations at shorter wavelengths (e.g. 450 /zm) are almost always sky noise limited. Sky noise can also be the source of numerous systematic errors, and careful consideration of the behaviour of the data over an observing run is especially necessary when 52 WAVELENGTH (»*>) Figure 2.3: Transmission of Atmosphere at Mauna Kea. From [56]. small signals are being sought, as in this investigation. At the wavelengths used for our main observations, UKT-14 is operating at or near the diffraction limit of the JCMT. The beamsize therefore varies with the observational wavelength used, as well as with the aperture used. Throughout our observations, we used the maximum 65 mm aperture, which corresponds to the diffraction limit for 1.1 mm observations, and is slightly larger than the diffraction limit at 800 /xm. The beamsizes for the filters used are also shown in table 2.6. All the sources observed in this programme, apart from Jupiter, were substantially smaller than these sizes, so no discrepancies are expected from the different beam sizes at 1.1 mm and 800 /zm. The signal from the UKT-14 preamp is fed to an analogue phase sensitive de tector (PSD) mounted near the instrument. The output from the PSD is digitised 53 Name Frequency Bandwidth Aperture Beam width Sensitivity (GHz) (GHz) (mm) (Arcsec) (W Hz-1/2) 2.0mm 149 40 65 27.2 1.3mm 233 64 65mm 19.5 1.1mm 266 74 65mm 18.5 0.2 - 0.5 WBMM 290 220 850/im 354 30 800/zm 384 101 65 16.0 47 13.5 600/zm 480 112 65 17.2 450//m 682 84 65 17.5 27 10.0 350/jm 864 113 65 19.0 Table 2.6: Parameters of the UKT-14 Filters via a voltage to frequency converter and fed to the JCMT VAX computer. An individual integration (half of a nod cycle) consists of a number of samples of the output voltage of the PSD. For our observations, the number of samples in an in tegration was typically 27. An on-line despiking routine is applied to these sample values, and those that differ from the mean by 5 standard deviations are rejected. The sample means and errors are then stored to disk for later processing. The telescope then nods, and the process is repeated. During our observations, it was noted that the despiking routine occasionally caused problems in the data logging process. When several spikes occured in one integration, the remaining data in the observation were corrupted, and the data stored to disk after that point were also corrupted. Once we became aware of this problem, we carefully monitored the deglitching process during an observation, and aborted the observation if cor ruption was seen to have occured. When later processed, observations corrupted in this way were hand edited to remove the obviously faulty data. The instrument was originally intended for use on the 3.8 m TJKIRT telescope, also on Mauna Kea, but was transferred full time to the 15 m JCMT in February 1988. The observations of clusters at millimetre/submillimetre wavelengths to 54 detect the Sunyaev- Zeldovich effect, discussed in Chapter 4, were made while this instrument was still at UKIRT. The system was much the same as discussed here. Specific differences in the UKIRT set up will be discussed in the appropriate chapter. 2.6 Calibration UKT-14 has been in operation at Mauna Kea for many years, and at the JCMT since the telescope opened. The stability of the instrument [145] is used in cali brating data in spite of the continuously varying properties of the atmosphere at millimetre wavelengths, since the conversion factor from output mV to received Jy varies very little [145]. The primary calibration sources for this investigation were the planets Mars and Jupiter. These were observed at a number of frequencies, covering most of UKT-14s range of filters, but in the reduction stage discussed below, only the 1.1 mm and 800 fim channels were used. The planets were also used as pointing sources, when visible, and, in the case of Mars, as a focussing check in the early morning when the sun rose. Jupiter was visible during the first third of each of our observation nights, and Mars was visible during the final third. As a secondary calibrator for the middle third, we used the source IRC10216, as it was adequately bright, and relatively near to our main objects. We also used the object G34.3 as a calibrator on one occasion. A failed carousel drive motor during the last night meant that slewing took an inordinate amount of time, so it was necessary to use IRC10216 to calibrate for the early part of the observations as well, and Mars for the final third. The fluxes of our planetary calibrators were calculated using the JCMT-FLUXES program provided at the JCMT. The planetary temperatures used by the program in each waveband are those of Griffin et al. 1986 and Orton et al. 1986 [68] [118]. The Martian fluxes are accurate to only about 5-10 %, but the inaccuracy thus introduced into the calibration is not significant for the work here. The program calculates the total flux of the planet into each of the UKT-14 wavebands, and the flux received into a diffraction limited beam. The diffraction 55 limited data is suitable for the 1.1 mm channel in these observations, but the 800 fim observations were not made using a diffraction limited beam (14.5 arcsec- onds half power beamwidth (HPBM), achieved with an aperture of 47.3 mm), but with the somewhat larger beam achieved by having the aperture at its maximum of 65 mm. This produces a beam of 16.5 arcseconds HPBM. We must therefore make some correction to the planetary flux data to calculate the flux actually received. The flux received, by UKT-14, Fr , from a source of radius D and total flux Fs comes from convolving a Gaussian beam of half power full beam width B with the emission from the planet. Thus: x2Fs Fr = (2.2) 1 - e-*2 with D (2.3) ~ 0.6B The beamwidths are those given in table 2.6. Using these equations and the data from the planetary fluxes program JCMT-FLUXES we then calculate the 800 /xm fluxes of the planets used as calibrators. The object IRC10216 is a star with a dust condensate in its stellar envelope. It was selected as a secondary calibrator based on information supplied in the JCMT POINTING document supplied by the Joint Astronomy Centre (JAC) [145]. However, since the observations were made it was noted that this source is actually variable, and that the flux quoted in the JAC document (1.7 Jy at 1.1 mm) did not match with the flux measured by us (1.92 ± 0.06 Jy). However, the period of variation for IRC10216 is « 600 days, [137] so that the fluxes measured during our 4 day observing run, using a planet as a primary calibrator, will be consistent throughout the observations. The calibration sources for the observations are given in table 2.7. 56 Planet 1.1 mm Flux (Jy) 800 fim Flux (Jy) Mars 141.96 274.94 Jupiter 3296.22 5209 IRC10216 1.92 ±0.06 4.15 ±0.2 Table 2.7: Fluxes used for calibration. 2.7 Data Reduction The data stored from UKT-14 include the mean and standard deviation of the individual integrations on and off source during an observation, and the result of combining these individual integrations. To minimise any systematic errors in the observations, it is necessary to manipulate the individual integration means and errors, rather than using the conglomerated results of any integration. Unfortu nately, the standard UKT-14 reduction package, N0D2, is designed for mapping work, and uses the combined block means rather than the individual integration values. It was therefore necessary to write a number of programs to perform the necessary data manipulation, rather than using a standard STARLINK package. The methods and formulae used are described here. 2.7.1 Demodulation of Data The raw data values are stored as the means and standard errors of the on and off source integrations (ie. separate values for each nod position). The chopping and nodding scheme used in these observations is to alternate integrations with the source in the left (plus) and right (minus) beam in the pattern left-right right-left, or alternatively -| ------h To extract the astronomical signal therefore, the sample means of each cycle of four integrations must be combined as: 51 — (+) - ( - ) (2.4) 5 2 = -(-) + (+) where both Si and S2 are valid measurements of the astronomical signal, with the atmospheric background subtracted. The error in each measurement, derived from the errors in each sample mean aright and °2 ~ ^right + tfeft (2.5) 57 This means that all the data values for the astronomical signals during an inte gration have an individual error associated with them. These can later be used as weightings when the values are combined to give a signal for each observation of an object. 2.7.2 Atmospheric Transmission Given the instrumental signals, we must derive the true astronomical flux. This leads to one of the key problems in the reduction millimetre/submillimetre data, which is to correctly quantify and correct for the attenuation in the radiation introduced by its passage through the atmosphere. If the airmass (cosec of the elevation) of the observations and the atmospheric optical depth at the observa tional frequency are known, then this attenuation is: Fo = Fae~Ar (2.6) where F0 is the flux observed at the telescope, Fa is the flux that would be received if there were no atmospheric absorption, A is the airmass, and t is the atmospheric optical depth at the zenith (i.e. airmass = 1) at the frequency of observation. With the airmass and optical depth known, data can then easily be corrected for atmospheric transmission by simply solving this equation for F0. Thus: ^ = (2‘7) However, the atmospheric optical depth at millimetre/submillimetre wavelengths is an unknown and variable quantity, and may change by a considerable amount over the course of a night. It is therefore necessary to use observations of known calibration sources to measure the optical depth. There are a number of ways of achieving this aim [145]. The simplest of these methods is to measure the power received from a source of known flux, i.e. one of the calibration sources, at a known airmass. The received power and emitted power are then compared, and the zenith optical depth can be readily calculated by inverting equation 2.6 to yield: 58 Filter Aperture Calibration 1.1 mm 65 mm 11.8 800 fim 65 mm 8.5 800 fim 47.3 mm 11.1 Table 2.8: UKT-14 calibration values used here for 1.1 mm and 800 finl channels where A is the airmass of the calibration observation, Fg is the flux received at the telescope, and Fs is the known source flux that would be received by an instrument unhampered by the atmosphere. The value of Fg is calculated from the measured instrumental output in mV using a calibration factor determined by observations made by telescope staff on exceptionally clear and stable nights [146], and is dependent on the filter and aperture combinations used. The stability and reliability of the instrument UKT-14 is such that, for a given filter and aperture combination, this factor is reliably known to «1% unless the configuration of the telescope is changed. This occurs, for example, when the sub-panels of the JCMT dish are adjusted to improve the surface accuracy. However, there had been no major corrections to the dish prior to our observing run, so the calibration factors used here are well known. Thus in equation 2.8 we have: Fg = C (f ilter, aperture) Sq (2-9) where Sq is the voltage output from UKT-14, in mV, and Fg is flux received in Jy. The values of the calibration factor C are given below. Using these methods, the optical depth at the zenith was calculated for each of the calibration measurements, and the variation of the optical depth during each night’s observations were found. This variation is shown in figure 2.4. 2.7.3 Removal of Spikes Spurious high or low data values can occur in the data as a result of a number of factors, ranging from the instrument electronics to the local environment of the telescope. These ‘spikes may be identified in a given set of data by examining the number of standard deviations that separate each data value from the mean. A ‘spike will be identified if it is a sufficiently large number of standard deviations 59 Figure 2.4: Zenith optical depths. . The optical depth at the zenith, (r), measured by observations of calibration sources, as a function of time (UT) of observation for each of our 4 nights. 60 from the mean that the probability of it occurring at random is very low. Quan titatively, given a block of n observations, with mean /i and standard deviation cr, a point with value s may be termed a spike if: N n < 1 (2.10) where N(x) is the value of the Normal distribution with unit mean and variance at x. This spike rejection process is performed iteratively, with a new mean and standard deviation calculated until no new spikes are found. 2.7.4 Reduction of the Astronomical Data Using the methods described above, the individual blocks of data were analysed, with correction for varying atmospheric extinction, and conversion from instru mental mV to Jy using the factors given in table 2.8. Variations in the sky transmission were accounted for by a linear interpolation of the zenith optical depth between the last and next calibration observation, yielding a value for r in equation 2.7 for each data point. The atmospheric correction methods then produce a flux value and a noise in Jy for each integration point. Demodulation then produces a flux value, in Jy, for each nod pair. From this point, if the quality of data is known to be good, in the sense that it obeys Gaussian statistics on both long and short timescales, the data may be combined using each point’s error as a weighting, to produce block and total means and errors. However, it is well known [146] that when observing very low signal levels, the noise levels do not necessarily integrate down in a Gaussian manner, with error decreasing with the square root of integration time. Instead, long integrations are frequently subject to low frequency noise, which can be the source of systematic errors. To cope with this eventuality, the distributions of both the data values within a block, and of all the data values for a given object had to be studied carefully before the method of combining the data could be decided on. If the data were found to be behaving in a reasonable manner then the weighting information could be used, and normal procedures adopted. If not, then the weightings might not be a good indication of the accuracy of a given value, and equal weighting, in some sense, of each data point and each data block would be necessary. 61 i i i i i i i i r r * ] *i i l i j > n i j i i i i j i i i i | i r * r C .1 CJ) 0 -.1 - i _ - J -.2 - I I I I I I I I I I I I I I I ' 1 1 ' I I I I I I ! I I I 10 20 :*»o 'io • no 00 70 HO Inl fural ion Number Figure 2.5: Several data blocks. Plot of 2 data blocks, the upper at 1.1 mm and the lower at 800 //m, showing the raw instrumental output and measured errors for each integration. As can be seen, the error, associated with each point is not necessarily a good indication of its closeness to the block mean. 6 1 Figures 2.5 and 2.6 show the quality of the data. As can be seen from the data within a given block, shown in figure 2.5, the individual point weightings are not a good indicator for the ‘quality’ of a given observation. Over the whole data set it is the case that the scatter in a data block is approximately double the scatter indicated within a given integration, so that the weighting information given by the error on each point is not in fact useful information, and if used would lead to an underestimate of the true noise in the data set. This effect is probably due to the action of sky noise, which is not expected to have a white frequency spectrum, and indicates that the noise on timescales of an integration is less than the noise on timescales of a data block. This result is consistent with those of other workers who have attempted to make observations at very low flux levels [45]. The complete data set for a given object, however, does seem to behave some what better. The histograms in figure 2.6, all except for that of 3C294, are much closer to a Gaussian distribution with reduced \ 2 values typically around 1. The observations of 3C294 axe the result of only 2 data blocks, both taken at the very end of a shift, and are probably those most susceptible to systematic errors introduced by the rapidly changing atmospheric conditions known to occur from about 9 to 10 a.m. local time [44]. The rest of the data, though, axe fit well by Gaussians with mean and standaxd deviations calculated in the noxmal manner, i.e.: = (2-n ) *=i and ,2.12) Where ^ is the observation mean, a the standard deviation, N the number of points in the observation, m,- the value of the ith integration. A spike threshold, as described above, of 5 a was used in this calculation. The standaxd exxox of the means in each of these observations is then calculated thus: a (2.13) V n 63 Figure 2.6: Histograms of observational data for each object. Histograms of the corrected flux values for the complete data set for observations on each object at each wavelength. The curves are Gaussians with the data set mean and variance. 0902+34 at 1.1 mm 64- Frequency C5 t . mm 1.1 at 3C257 66 l,’rc,qn«.,iH:y 3C257 at at 67 0.8 mm 0.8 Fror|ii cney C361 t . mm m 1.1 at 326.1 3C 68 Frequency C361 08 m m 0.8 t a 326.1 3C 69 Frequency 3C249 at 0.8 mm 0.8 at 3C249 70 Object Wavelength Int. Time Signal Error (1 (mm) (secs) (mJy) ( ± m J y ) (J y ) 0902+34 1.1 7660 -16 20 1.7 3C257 1.1 2100 7.1 26 1.2 3C257 0.8 9910 3.5 3.6 0.36 3C326.1 1.1 2600 -70 38 1.9 3C326.1 0.8 6680 5.8 5.1 0.42 3C294 0.8 1070 -5.2 12 0.39 Table 2.9: Results of the Observations on High Redshift Radio Galaxies. 2.8 Results The results obtained by these observations are shown in table 2.9. None of the target sources was detected at any reasonable level of significance. The la l s sensitivities are also included in the table, along with the integration times. These clearly show the poor performance of the 1.1 mm channel, and that the 800 ^m channel was achieving sensitivities about 3 to 4 times better. The telescope strip chart record of the noise in each of these channels showed that the 800 /im noise was about 6 times lower than the 1.1 mm noise. This relative degradation of the lower frequency channel is probably due to strong low frequency components in the 1.1 mm channel noise that are not detected on the time scale of the chopping frequency. While we have failed to detect any of these objects, we can set upper limits for the far infrared emission from these galaxies. 2.9 Discussion and Conclusions We can now compare the upper limits to the rest frame far infrared emission to the fluxes predicted by the models described earlier. Using 2 a (i.e. 95 %) upper limits, table 2.10 shows this comparison. 70 Object Wavelength Radio Cygnus A Starburst Flux Limit (mm) lobes (mJy) dust (mJy) model (mJy) 2 a (mJy) 0902+34 1.1 6.3 7.8 2.8 24 3C257 1.1 21 6 4.5 59 3C257 0.8 15 13 10 10.5 3C326.1 1.1 5.6 4.8 4.8 6 3C326.1 0.8 3.3 14 14 16 3C294 0.8 2.7 14 18 19 Table 2.10: A comparison of the predicted fluxes of HRRGs, and the upper limits to these fluxes set by the observations. 2.9.1 Radio Emission in 3C257 The only object for which there is a conflict between the observational flux limits and the predictions of the synchrotron radio spectrum is 3C257. The predicted 800 fim flux of this object, based on an extrapolation of its radio flux at wave lengths of 178 and 408 MHz [77], is 15 mJy. This is excluded by the observational data at a level of « 3a. This result is not particularly surprising. The spectra of many radio sources steepen at higher frequencies. For example, the radio spectrum of 3C326.1 has a power law constant a — 0.71 at low frequencies, similar to those used to calculate the flux predicted above for 3C257. However, higher frequency VLA data for 3C326.1, at 5 and 15 GHz [108], show that its spectrum at these frequencies has steepened to 1.3. A similar spectral steepening for 3C257 is thus readily accepted. For the 800 /xm emission from 3C257 to be less than the 2a limit set by these observations, the radio spectral index from 408 MHz to 394 GHz must be steeper than 0.94. This is the first conclusion from these observations. 2.9.2 Possible Dust Emission in HRRGs As can be seen from table 2.10 both the models predicting thermal dust emission from 3C326.1 and 3C257 are rejected by the nondetections at 800 ^m. The Cygnus 71 A dust model and the starburst model are excluded at 1.8 a (96 %) in 3C326.1, while in 3C257 the Cygnus A model is excluded at 2.5 a (99 %) and the starburst model at 1.9 a (97 %). Even the poor quality data obtained for 3C294 can be interpreted as excluding the starburst model at 1.9 a (97%). There axe a number of possible interpretations for these results. The starburst models can be modified to avoid the constraint by changing the low mass cutoff. Reducing this to 0.1 M© would reduce the predicted fluxes by a factor of 6. The value of the low mass cut off in these galaxies is dependent on the details of the star formation process. Observations suggest that the IMF is truncated at higher mass in powerful starbursts galaxies than in normal galaxies [152]. If the starburst type phenomena are indeed responsible for the large star formation rate in these HRRGs, then the high cut off mass adopted here would be reasonable. However, if the star formation in these galaxies is dominated by some other process, such as jet induced star formation, the question of the low mass cut off remains open. If the HRRGs are PGs undergoing their first burst of star formation, then the IMF is expected be truncated at quite high mass [48]. The presence of dust in a PG, though, is a difficult question. While the PGs initial metallicity is, almost by definition, very low, it is likely that the rapid evolution of the very first stars to form would quickly spread dust throughout the PG. The interpretation of the results on dust emission from starburst type activity in these galaxies is thus somewhat model dependent. The situation becomes somewhat more interesting when the dust emission from a Cygnus A model of these objects is also found to be rejected at high confidence by these results. Cygnus A represents a quiescent version of these radio galaxies. It has very similar radio properties, but lacks the vigorous star formation inferred from the Lyman-a emission and the spectral energy distributions. In Simon Lilly’s models, the HRRGs are explained as essentially normal radio galaxies which just happen to be undergoing a starburst type episode. This contributes greatly to their optical and UV emission, but little to the infrared, so producing the quiet K-z relation for almost the whole population of radio galaxies. If this is the case, and the majority of stars in these galaxies formed a long time ago, then one would expect there to be a large mass of dust in these objects, comparable to that in 72 Object Redshift Z/Z(now) for Zf — 5 Z/Z(now) for zj = 10 0902+34 3.4 1/3 2/3 3C257 2.5 2/3 0.9 3C326.1 1.8 1.1 1.25 3C294 1.8 1.1 1.25 Table 2.11: Metalicity Fractions. Expected fractions of present metalicities predicted by the Alvensleben models for the HRRGs studied here. similar nearby galaxies (such as Cygnus A), and that it would be emitting at much the same temperature as the dust in those objects. Alvensleben and collaborators [6] have modelled the metal enrichment of galax ies over their entire lifetime for a variety of cosmologies, and for formation redshifts of 5 and 10. Their results are shown in figure 2.7, as is their best fit to the data on Lyman-a absorbers from Sargent and collaborators studies [149] [149]. These models show quite clearly that the metallicity of a galaxy at the redshifts observed here will be a substantial fraction of the local value, even if that object formed as recently as z=5. The expected fractions of local metallicity are given in table 2.11. These models clearly show that large amount of metals will have been produced by the time of our observations, even for a relatively recent formation redshift of zj = 5. It is not unreasonable to assume a direct relationship between the metal enrichment of a galaxy and the presence of dust, since the dust is made up of enriched material. Therefore, we can relate the fractions of present enrichment for these models to the fractions of present dust emission we might expect in these galaxies. Even if the star formation in these objects is a result of jet induced star formation, and not conventional starburst type processes, we would expect to see thermal dust emission in the rest frame FIR, since the dust predicted to be present would be heated by the stellar emissions. Thus in 3C326.1 we would expect comparable dust emission to that from a similar nearby object for either Zf — 5 or 10. The same is true for 3C257 for zj = 10, whilst the dust emission would be reduced by about a third for Zf = 5. The data here excludes all of these expected values by about 2 73 observational data of Sargent et al. compared to the best fit model, namely model, fit best the to compared al. et Sargent of data observational Alvensleben et al.’s models of metalicity evolution as a function of redshift for redshift of function a as evolution metalicity of models al.’s et Alvensleben Metallicity Z Metallicity Z various cosmological models and formation redshifts of 5 and 10. Also the the Also 10. and 5 of redshifts formation and models cosmological various Figure 2.7: Metallicity Evolution Metallicity 2.7: Figure h = 50,2/ = 5, go = 0.5.5, go = = 50,2/ = 75 luminosity as Cygnus A in the FIR. If these observations are confirmed, then we must conclude that the objects are probably quite young. This leads to two possible conclusions. Either the activity which is giving rise to the large Lyman-a emission, or the emission itself, has destroyed the dust, or the dust does not exist. Observation of dust in powerful starburst galaxies suggests that the dust is fairly hardy to the emission from young hot stars, (see discussion above about NGC1068 and M82). It therefore seems likely that we must accept that these objects are deficient in dust, and that this is probably due to these objects being so young that the dust has not yet formed. Taken at face value our observations suggest that these objects are forming stars by an unconventional means, and that they are young objects (< 108 yrs) as proposed in the theories of Chambers, Rees, Daly and others [36] [135] [51]. The observations, though, are very difficult and in need of confirmation before one can definitively say that there is a deficiency of dust in these objects. 2.10 Further Work The conclusions drawn here from one set of observations of four objects in mediocre weather conditions are clearly important. They suggest that the long searches for galaxies in the process of forming the bulk of their stellar population, so called Primeval Galaxies (PGs) may perhaps be nearing success. While HRRGs are so rare that they cannot be the precursors to the bulk of galaxies, finding a set of objects which might be in the process of formation is a definite step forward. Recent results also suggest that a new process of star formation, jet induced star formation, may have been discovered, though this still leaves the origin of the radio source unclear. 2.10.1 Further Millimetre/Submillimetre Observations Of the objects and wavebands listed here, one particularly important observation has not been made. Observations of 0902+34 at 800 fim, by dint of its large redshift, are at a rest frame wavelength of just 181 ^m, very close to the peak of 30 K thermal dust emission. Thus the flux predicted at this wavelength, 16 mJy, 75 is large. The low restframe wavelength of such observations would also probe the possibility that the dust is at somewhat higher temperatures. This observation, clearly, is one which must be attempted. Observations of other objects at both 1.1 mm and 800 fim are also necessary. Given better weather conditions than experienced during this run, much more stringent limits may be placed on the 1.1 mm emission from these objects. At the rated sensitivity of UKT-14 at 1.1 mm (0.2 Jy ltrld) observations over sim ilar timescales will reach a sensitivity of about 3 mJy, enough to make marginal detections of the dust emission and the radio power law emission. Objects to be observed, in addition to those discussed here, would include all those 3C and other radio sources modelled by Chambers and Chariot [36] which are suggested to be young and to have a high rate of star formation. Other distant radio galaxies would also be observed. The ideal source should be distant, so that the 100 /zm peak of the dust spectrum approaches the observational bands, and should have vigorous star formation underway (since higher M implies higher far infrared fluxes). The recently reported [36] distant steep spectrum radio sources, such as 4C41.17, with a redshift of 3.8 and with an inferred star formation rate of 200 M©/?/r, would thus be good targets. 2.10.2 Primeval Galaxy Searches Searches for galaxies undergoing their initial phases of star formation have been conducted since the late 60’s, when Partridge and Peebles published their seminal papers on the origin of galaxies and the possibility of detection of primeval galaxies (PGs). [122]. To date there has been no convincing detection of a PG, in spite of many claims (including one for 3C326.1 [12], one of the target objects of this investigation). The signature of a galaxy in the earliest stages of formation is expected to be very strong Lyman-a emission, from hydrogen ionised by the large population of young, hot, massive stars, that have yet to evolve. The discovery of Lyman-a galaxies such as 3C326.1 and other similar objects led to suggestions that these were indeed forming galaxies. The discovery of infrared emission from 3C326.1, and its excellent fit to the quiet K-z relation has placed doubt on this 76 interpretation. However, the result that there is too little dust in 3C326.1, or the similar object 3C257, for them to be old, indicate that these galaxies may indeed be young, though probably not at the very first stages of formation. The long literature of primeval galaxy searches implies a number of results for these objects. Firstly, since they are very similar to the Lyman-a emitting PG’s unsuccessfully sought by, for example Pritchett and Hartwick [130] [131], it is unlikely that this formation mechanism is the origin of the majority of galaxies in the universe. The Lyman-a PG searches have been sensitive enough to detect a HRRG forming in the manner described by Chambers and Chariot, with a star formation rate of several thousand solar masses a year over 108 yrs. They have also covered sufficient area to detect such PGs if they had formed the majority of galaxies. It is therefore likely that jet induced star formation, if it is the dominant method of star formation in these objects, is important only for relatively rare double lobed radio galaxies such as those observed here. It would thus be an important part in the formation of giant elliptical galaxies but would provide little information on the origin of more normal objects. However, the argument can be turned around, and the techniques developed for searches for bright Lyman-a emitting PGs can be used, over much larger areas, to search for forming HRRGs. This could well prove a promising technique for establishing whether the interpretations of these results, and the models of Chambers and Chariot, are indeed correct. The question of how the majority of galaxies formed, or how the central engines in HRRGs came about, is not addressed by these observations, and will be an active area of future study. 77 C hapter 3 The Sunyaev-Zeldovich Effect 3.1 Introduction The Sunyaev-Zeldovich effect (S-Z effect) is a spectral distortion introduced into a radiation spectrum by inverse Compton scattering of the radiation photons by electrons within a hot plasma. The scattering process preserves photon number, but scatters the photons to higher energies, resulting, approximately, in a bodily shift of the radiation spectrum to a higher energy. For a black body radiation spec trum, this will produce a reduction in effective temperature at long wavelengths, and an increase at short wavelengths. The S-Z effect was first derived by Zeldovich and Sunyaev in 1969 [184] as a possible explanation for deviations in the CBR spectrum from a true black body suggested by rocket borne experiments [159]. In this instance it was postulated that a late injection of radiation ionises the intergalactic medium which then produces the inverse Compton distortion in the CBR. However, the result was not confirmed by further rocket launches [171], [24], or observations from the ground [14]. While the need for inverse Compton scattering to explain a deviation in the CBR disappeared, the S-Z effect as we know it today reappeared in 1972 when Sunyaev and Zeldovich [168] applied the analysis to the hot gas responsible for the then recently discovered X-ray emission in clusters of galaxies. It is the action of this hot intracluster atmosphere on the CBR that is commonly referred to as the S-Z effect today (while the previous incarnation is occasionally referred to as 78 the Zeldovich-Sunyaev effect). The dependence of the S-Z effect flux distortion on wavelength is shown in figure 3.1. It is an interesting historical note that the short wavelength distortions re ported by Shivanandan et al. [159] and others, rejected by later observations, were explained by many of the same processes (dust, Comptonisation) that have been proposed for the submillimetre excess reported by Matsumoto and coworkers [107]. This, also, has now been rejected by the COBE observations. This history illustrates the inherent difficulties of such observations. The possibility of using ground based observations of the S-Z effect to search for CBR distortions, in the millimetre/submillimetre waveband and others, is discussed later in this Chapter and in Chapter 7. The S-Z effect is of importance to observational cosmology for a number of reasons. Firstly, the detection of an S-Z distortion in the CBR is an independent test that the background radiation has its origin at a distance greater than that of the X-ray cluster producing the effect, acting as corroborative evidence that the CBR does genuinely have a cosmological origin. Secondly, the S-Z effect can act as a probe of the mass distribution within a cluster of galaxies, and, in conjunction with X-ray observations, can provide measurements of the mass of the cluster. The difference in dependence of the S-Z effect and the X-ray luminosity on the column density of hot electrons allows the S-Z effect to be used to determine the Hubble constant, and, if more distant clusters are observed, the deceleration parameter qo, can also be found [162]. Also, since the S-Z effect is redshift independent, it can be used to detect the hot gas in very distant clusters. Such detections would appear as anisotropies in the CBR on scales of several arcminutes, and could be identified as due to the S-Z effect only by observations of the spectral dependence of the effect in the millimetre/submillimetre band. Finally, millimetre/submillimetre observations of the frequency at which the flux distortion passes through zero may be used to measure cluster peculiar velocities along the line of sight. Polarization measurements of the S-Z effect [22] are even potentially capable of measuring transverse peculiar velocities. Thus the S-Z effect may allow us to probe the mass distribution at very large scales, in a similar way to the galaxy streaming studies of Collins et al. [49] and Dressier et al., [54]. 79 Figure 3.1: The Spectral Form of the Sunyaev-Zeldovich Effect. Sunyaev-Zeldovich the of Form Spectral The 3.1: Figure 400 h / ' V i_ isrl isrl i_ A£ uj ) iOJSa ±S Q Xflld X 3Q A±iSN JLSia liaO O N From [40]. From 81 The Sunyaev-Zeldovich effect can thus provide information on a large range of questions in observational cosmology. However, observations of the effect axe very difficult, with the small flux changes involved easily swamped by unidentified systematic errors. It has taken many thousands of hours of radio observations by Mark Birkinshaw and coworkers [20] to produce convincing detections of the S-Z effect in a number of clusters. The remaining chapters of this thesis are devoted to the instrumentation, tech niques, and results of observations of the S-Z effect in the nulfimetre/submillimetre waveband. This band offers a number of advantages over the longer radio wave lengths traditionally associated with S-Z observations. These are primarily due to the greater flux distortion at millimetre wavelengths, the use of broadband instru mentation, and better rejection of a number of systematic effects. The presence of greater sky noise in the millimetre/submillimetre band is a disadvantage, and the removal of this is necessary for our observations. Possible techniques for this axe discussed in a later chapter. The rest of this chapter is concerned with the mathematical derivation of the S-Z effect, an examination of the effect in the con text of hot cluster atmospheres, a more detailed examination of the potentials of S-Z observations, and a review of previous work. 3.2 The Derivation of the Sunyaev-Zeldovich Ef fect This section provides the mathematical derivation of the S-Z effect. The deriva tion neatly divides into two sections, which will be dealt with separately. The first examines the action of Compton scattering on a generalised photon distribution, and its result is a differential equation, whose solution for a specific radiation field, gives the Compton distortion. This equation is known as the Kompaneets Equa tion. The second section describes the application of the Kompaneets equation to a black body radiation field, and this produces the well known S-Z flux distor tion. The derivations given here follow those of Kompaneets [85] and Sunyaev & Zeldovich [168]. 81 3.2.1 The Derivation of the Kompaneets Equation The Kompaneets equation describes the effect of Compton scattering on a general radiation field, n^(k,t) by an electron gas with distribution function Ne(p,t). We will assume that the electrons are non-relativistic, and that both the electron and photon distributions are homogenous and isotropic. Bose-Einstein statistics implies that the scattering rate n7(fc, t) —> n^(fc, t) for an ensemble of photons is (dropping subscripts) n(n,+ l) times that for an isolated distribution. Thus the differential transition rate will be: 8T(k,V) = n{ 1 + n')N(p,t) 6W 6T (3.1) where SW is the differential scattering cross section, and 8r is an element of electron phase space. Integrating over all scattering and all of electron phase space then yields the kinetic equation: = - J dr J [n(l + n')N(p) - n'(l + n)iV(/)] dW (3.2) where the C subscript indicates that the only process considered is Compton scattering. From the assumption of isotropy in the photon and electron distributions, the distribution functions n(k.) and N(p) can be simplified to n(w) and N(E ), where 2 u) is the frequency of the radiation and E = ^ is the electron energy. By energy conservation we then have: t2 2 E '= ^ - = ^ - + h(u)-u’) = E + h(u-u>') (3.3) 2ttz 2771 In the non-relativistic regime considered here A = u' — lj a? (3-4) we can thus expand the primed distribution functions in A. It is necessary to expand to second order in A, thus . . dn 1 . 0d?n n « n + A—- + -A^—- (3 .5 ) dco 2 duj 1 82 and N(E') = N(E — HA) a N — hAg + ifc2A2 J p - (3.6) Expressions for 8n = n'—n and 8N = N '—N can then be obtained and substituted into equation 3.2 so that the integrand becomes — N 8n + n ( n 1)8N + (n + l) 8n 8N (3*7) where, to second order, dn A d2n 8n = A (3.8) duo 2 duo2 and diV ^ a 2iv 8N = -ZiA (3.9) 2 dE 2 Now JV, the distribution function of the hot electron gas, will be a Maxwell- Boltzmann distribution, given by N(E) Ae kBTe (3.10) where ks is Boltzmanns constant and Te is the temperature of the electron gas. Using this expression for the electron distribution function, and collecting terms in order A and A2 equation 3.2 becomes: dn d2n , . , + n(n + 1) + 12 — + n(n + l) + 2(n + l ) ^ (3.11) where huo X = (3.12) faTe and the integrals I\ and I 2 are /a(A) = j ( dW AN , (3.13) ( dT J' kBTe f dW A 2 Nh' (3.14) fdTJ 2 klT} This leaves the two integrals I\ and I2 to be evaluated. However, we may avoid the evaluation of one of these integrals by invoking conservation of photon number, which is equivalent to the requirement that the electrons are non-relativistic. The conservation of photon number, under the assumptions of spatial homo geneity and isotropy, is given by: dn \ (3.15) 83 where j ' is the photon current in momentum space. Isotropy then simplifies this to merely the radial component in spherical polar coordinates, and conversion to the variable \ leads to: d n \ 1 d , o . \ (3.16) dtJc = ~x*dx(x Jx) In this, j x is a function of both the frequency x and the photon distribution n. Setting j x = A(x)B(n)> and expanding equation 3.16 yields: f d n \ 2 . . , . . dA . dB -A (X)B(n) + B (n)— + A(X) (3.17) dt J Comparing this with equation 3.11, B(n) must be dn B(n) + C(n) (3.18) ®X where C(n) is some polynomial in n, and A(x) must = —12. When the photons reach equilibrium with the electrons, the photon current in phase space, j x must vanish for all x • In this regime the photons would have a Bose-Einstein distribution function, with n(x) = and ^ = —n(n + 1), and the condition that j x = 0 for all x implies that C(n) = n(n + 1). Thus in equation 3.17 we have: d n \ _ 1 d dn x 2h ( + n(n + !) (3.19) d x ) c X 2 d X 9X Solving between this and equation 3.11 yields an expression for I\ in terms of 12: ( 3 - 2 0 ) The evaluation of I\ is thus avoided. In the low energy limit, the Compton scattering cross section may be replaced by the Thomson cross section, or which is isotropic with respect to scattering angles in the electron rest frame. The photon frequency change on scattering comes directly from the conservation of energy-momentum, and, in the low energy regime, is given approximately by: A uj = (jJ (3.21) c where k and k’ are unit vectors. 84 Substituting these expressions into the equation for I2 yields: I 2(A ) = J dr J dW ^L(w=.(k-k)f a £ j ~ } ( v ) d T J d W (k- k f (3.22) where the electron distribution as a function of velocity, /(v), will be a Maxwellian, and the integral over scattering cross section reduces to « 2(Tt • Integrating the Maxwellian over the electron phase space then yields m \ 2 v4 _™v2_ . 3kBTeNe (3.23) j v*f(v )d T = r n a * (2 ^ ) 2 vs e~ ^ dv m where Ne is the spatial number density of electrons. Thus: h = (3.24) ■fi = gr(4x - X2) Substituting these restdts into equation 3.11 then produces: _ kBTe 1 d dn (?TNe — + n(n + 1) (3.25) dt ) c me 2 X2dx . P x This is an expression for the rate of change of the photon occupation number with time. A more useful physical result is the change of occupation number after the photons have passed through a given line-of-sight electron opacity. Since an element of the photon path length is dl = cdt equation 3.25 may be rewritten in terms of the Comptonisation parameter: dy = aT nJ1 (3-26) to give: l_d_ (3.27) W g + n(n + l) X2 dx This is the Kompaneets equation [85], and describes the change of photon occu pation number after passing an optical depth y of hot electrons. This equation, and the observational evidence that many clusters of galaxies have an intracluster medium consisting of a hot plasma, are the basis for all Sunyaev- Zeldovich effect work. 3.2.2 The Sunyaev-Zeldovich Effect on a Black Body Spec trum Given the Kompaneets equation, there are two approaches that can be taken to calculating the effects of Comptonisation on a given radiation spectrum. Firstly, 85 as is considered in this section, one may derive an analytical expression for the distorted spectrum, given the initial radiation spectrum. Alternatively, numerical techniques may be used to calculate the S-Z effect distortion from a numerical expression for the initial spectrum. In this section the spectral distortion due to the S-Z effect acting on a black body spectrum, such as the CBR, is derived analytically. The photon occupation number for black body radiation is: ~2 1 n(x) = L = (3.28) 2 hv3 ex - 1 where x = —sr-, v is the frequency, Tb is the temperature of the black body *bTb radiation field, and Iu is the intensity of the radiation. In applying the Kompaneets equation to this spectrum, we first change variables in equation 3.27from x = to x as defined above. This allows us to examine the relative importance of the terms in this equation. We find that for radiation temperature Tb A I _ 2 k%Tg 2 ctt J pdl x 4ex ( x /2 \ (3.32) I c2h2 m ec2 (ex — l)2 \tanh(r/2) ) where /pdl is the line of sight integral of the intracluster gas pressure p(r) = nekBTe(r) (3.33) where ne is the electron number density. For a radiation temperature of 2.75 K, appropriate for the CBR, this distor tion is a decrement at long wavelengths, peaks negative in the millimetre region, 86 changes sign at « 1.3 mm, and peaks in increment at about 800 fim. Figure 3.1 shows the spectral form. At the long wavelength, Rayleigh-Jeans, end of the spectrum, a similar analysis gives the temperature decrement: AT = -2 y (3.34) T where y is the Comptonisation parameter defined earlier 3.26. This means that the millimetre/submillimetre S-Z effect spectrum may be redefined in terms of the Rayleigh-Jeans temperature decrement, AT, measured by the radio observations. This yields an easy comparison between millimetre/submillimetre observations and any long wavelength data on the same object. Thus: _ 2kgTjjX4ex I x /2 _ ' (3.35) (ex — l)2 \tanh(x/2) ; This describes the variation of the S-Z effect flux distortion over the whole fre quency range in terms of the Rayleigh-Jeans temperature decrement, and is the function plotted in figure 3.1. 3.2.3 The Sunyaev-Zeldovich Effect and non-Black Body Spectra The S-Z effect will apply to any background radiation passing through a dense ionised medium. The cases described at length above apply only to black body radiation, and the results will be different for different radiation spectra. Small fluctuations (up to « 10% of the total CBR energy density) in the black body spectrum will produce changes in the spectrum of the S-Z effect dependent on the actual spectrum of the distortion from a black body. For example, excess energy introduced at frequencies higher than the 2.75 K black body peak of the CBR (i.e. > 1mm) will tend to flatten the background radiation spectrum and, via the S-Z effect’s dependency on the 1st and 2nd derivative of the spectral energy distribution, will reduce the flux increment expected at short wavelengths. It is therefore possible to search for such spectral distortions in the CBR by examin ing the frequency dependence of the S-Z effect at millimetre and submillimetre wavelengths. 87 3.2.4 Numerical Calculations of the S-Z Effect To examine the changes in the shape of the S-Z effect produced by deviations from a black body spectrum, a program was written to calculate the effect of applying the Kompaneets equation to a general radiation field. The input radiation field appears as a list of flux density (W m"2 sr"1 Hz"1) against frequency (Hz) and may be easily calculated for any desired model. The frequency values need to be a constant step apart so that the numerical method will work properly. The result of the Kompaneets equation is then calculated using a fourth order difference method for the derivatives, and by multiplication by the appropriate constants and variables. The formula used to calculate the derivative at a general point is: d y j _ -t/,+2 -f 8yl+1 - 8t/,-i + y,-_2 (3.36) dx 12(r,—r,_i) where yi and r, are the ith flux and frequency values respectively. This formula produces the derivative accurate to fourth order in 8x = X{ — r,_i. However, since this equation uses values up to 2 steps up and down in y, it is not possible to apply it to the ends of the array of flux values. To allow for this, less accurate methods of obtaining the differential are used at the extremes of the array. The output from the program is a fist of flux density differences, in W m-2 sr-1 Hz-1 against frequency (Hz), and can be directly compared to the analytical results of the Kompaneets equation for a black body background spectrum. 3.2.5 The S-Z Effect and the Submillimetre Background As discussed earlier, rocket experiments by Matsumoto et al [107] suggested that there was excess flux above a black body spectrum in the submillimetre region. This result has not been confirmed by COBE data, but we will use it here as a case study to show how a spectral distortion in the CBR can cause the S-Z effect to change shape. The two main models for this result, discussed in [107] and elsewhere, were: • Dust radiation at 3.55 K with a v ~2 frequency dependence, adding « an extra 10 % of the CBR energy density to a normal 2.75 K CBR. 88 • A Comptonised Black Body spectrum in place of the CBR, with an initial temperature of 2.79K, and a Comptonisation parameter of y = 0.019. These two models produce somewhat different radiation spectra, and will thus produce different results when subject to the S-Z effect. The numerical S-Z effect calculations have been performed on both models and the flux changes induced in the different backgrounds are shown in figure 3.2. Observations of the flux changes due to the S-Z effect at different wavelengths in the millimetre/submillimetre band, could, in principle, have differentiated between these two sources of the proposed CBR distortion. 3.3 The Nature of the Hot Gas in Clusters of Galaxies 3.3.1 Observational Evidence Measurements of X-ray emission from astronomical sources had to await the devel opment of rocket and satellite launching technology, since the atmosphere com pletely absorbs X-rays. The first observations of extragalactic X-ray emission, from the galaxy M87 in the Virgo cluster, were therefore not made until 1966 [31]. Observations of cluster X-ray emission were not successful until 5 years later when both the Coma and Perseus clusters were detected [64] [70] [111]. The Uhuru X- ray astronomy satellites full sky survey [66], soon after these observations, then confirmed the suspicion [33] that galaxy clusters were strong X-ray sources. These observations showed that clusters were bright X-ray sources (1036 to 1037 W) with the emission region spatially extended with a size comparable to the galaxy dis tribution within the cluster [82] [62]. Unlike many other bright X-ray sources, cluster emission was not variable. The source of the cluster X-ray emission was soon identified as being ther mal bremsstrahlung from a hot (« 108 K) low density (« 10 atoms m“3) gas. Estimates of the total mass of this gas are somewhat model dependent, and un certainties exist because the low density regions distant from the cluster core can contribute strongly to the mass, but weakly to the X- ray emission. However, 89 (,.2H ,_■** z_ui a\) aSuaio xny z S Figure 3.2: The flux changes induced in different models of the Submillimetre Background by the S-Z effect. The solid line is the result on a pure black body spectrum, the dashed line the result on the dust model, and the dotted line the result on the Comptonised model. 91 estimates based on a variety of models suggest that the mass of the cluster atmo sphere is comparable to the total mass of the stars in the cluster. Overall cluster masses calculated by Virial theorem methods imply that the gas and galaxies still only contribute about 15 % of the total cluster mass. The discovery of cluster atmospheres did not solve the problem of dark matter in clusters. An interesting property of many of the more luminous X-ray clusters is the presence of cooling gas falling towards the cluster core, and then possibly collecting in a centrally dominant (cD) large elliptical galaxy. This streaming of gas, termed a cooling flow [61], results from the radiative cooling of a fraction of the cluster atmosphere, and may be responsible for excess X-ray emission in the centre of those clusters where they are present [79]. Clusters are often classified by whether they contain a cD galaxy or not, and the presence of a cD is a good indicator for there being a cooling flow in the cluster. The origin of the gas was at first assumed to be due to infall from the volume of space separating the clusters [69]. However, later observations of X-ray line emission, due to ionised species of Iron, in the Perseus [115] Coma and Virgo [155] clusters, demonstrated that the cluster atmosphere had a metallicity similar to that of stars, though it did confirm the thermal emission mechanism. A substantial part of the intracluster gas must therefore have been ejected from the cluster galaxies [9], unless the metal enrichment was due to a pregalactic population of stars [32]. Quite how the galactic, metal enriched, gas comes to form the intracluster atmosphere is still uncertain, but it is clear that normal mass loss rates from the stellar populations observed in the cluster galaxies is not sufficient [148]. Suggested processes include supernovae in an early generation of high mass stars [32], or at a time of more rapid star formation [89], to ram pressure stripping, and collisions between the galaxies [117] [147]. It is clear, though, that relatively normal stellar evolutionary processes within the cluster galaxies cannot produce sufficient enriched gas to give the observed metalicities. There axe a number of possible observations that can be made to begin to select between the numerous models for the formation of cluster atmospheres (see [148] for a review). These include studies of the X-ray emission of distant clusters to examine the evolution of cluster atmospheres over time. Achieving greater 91 angular resolution observations of the cluster emission might find clumping of the gas around galaxies. Finally, measurements of abundance gradients will allow us to assess the importance of infalling primordial material. However, for the discussion of the S-Z effect here, the important factors to consider are not the origin of the cluster atmosphere, but rather its spatial distribution within the cluster at the time when the cluster is observed. Models of the present state of the cluster atmospheres are now discussed. 3.3.2 Cluster Atmosphere Models The first model fitted to the cluster gas [93] was based on the King approximation to an isothermal self gravitating sphere [84], which had earlier been found to be a good fit to the galaxy distribution within clusters. Thus: .2 T 3/2 Pg — 1 + (3.37) where pg is the gas density and rx is the X-ray core radius. While not physically consistent (the function must be artificially terminated at some distance or the mass within the cluster will diverge), this does provide a useful comparison with the galaxy distributions already fit by this equation. Abramopoulos and Ku [7] find that the X-ray core radius is significantly greater than that of the galaxy distribution from examination of 53 Einstein observed X-ray clusters. More physically consistent models of cluster atmospheres have focussed on two separate regimes. The first continues with the assumption behind the King model, that thermal conduction within the cluster is sufficiently rapid that the distribu tion is isothermal. This leads to the extensively used hydrostatic isothermal model e.g. [79]. In this model, both the galaxies and the cluster gas are assumed to be isothermal distributions, bound to the cluster and in equilibrium. However, the gas and galaxies do not have the same velocity dispersion, but are related by /? the square of the ratio between them: pmpa; (3 = (3.38) kBTg where p is the mean molecular weight of the gas, in atomic mass units, m p is the proton mass, ar is the one dimensional galaxy velocity dispersion, and Tg is the 92 gas temperature. The gas and galaxy densities then vary as pg oc Pgal. If the galaxy distribution is taken to be a King analytical isothermal sphere (equation 3.37) then this produces an X-ray surface brightness 7*(6) at a projected radius b thus: -3/9 + 1/2 Ix(b) = i+£ (3.39) This distribution simplifies to that expected for a pure King distribution for the cluster atmosphere if (3 = 1 and rc = rx. Using Einstein data, Forman & Jones [79] have fitted this model to 46 clusters. They find good agreement to this model with (5 at 0.4 to 0.6 for most clusters. An alternative scheme for modelling cluster atmospheres is reached by aban doning the assumption that the gas is isothermal, and by assuming merely that the gas is well mixed. This leads to the adiabatic models, introduced by Lea [92]. In an adiabatic gas, the pressure and density are related by P oc p* (3.40) where 7 is the ratio of the specific heats, and is 5/3 for a monatomic ideal gas. While the value of 5/3 applies for a strictly adiabatic gas, the formalism of equation 3.40 can be used to parameterise a broad range of models, since 7 = 1 implies an isothermal distribution. The parameter 7 is then referred to as the poly tropic index. The range of poly tropic models of cluster gas cover 7 values from 1 to 5/3 since 7 > 5/3 leads to convective instabilities. The general family of polytropic models have gas density and temperature as analytical functions, but the spectra, surface brightness profiles, and S-Z effect profiles are neither analytical nor simply related. 3.3.3 Implications for the Sunyaev-Zeldovich Effect The S-Z effect is given by the line integral of the pressure of the gas in a cluster. Thus the effect at a given angular distance 6 from the cluster centre is given by a projection integral: P(r)rdr Isz{Q) = 2 f (3.41) Jo$ra ( r * - 93 where ra is the angular diameter distance to the cluster [180], and P(r) is the intracluster gas pressure, as defined in equation 3.33. Similarly, the X-ray emis sion at a given angular distance from the cluster core can be found by a similar projection integral: 00 E(r)rdr IX{6) = 2 / Jelora (r2 — 02r2)V2 (3.42) where E(r) is the X-ray emissivity at the position r. The emissivity contains both a temperature dependent term, and the square of the local electron density. Thus the two processes, X-ray emission and the S-Z effect, are dependent on the local electron number density in different ways: Isz oc ne(r) while lx oc nl(r). This different dependency leads to some very useful possibilities for the combination of S-Z effect and X-ray data. The nature of cluster gas Since the S-Z effect has a much weaker dependency on the local electron density than the X-ray emission, the angular extent of the S-Z effect in a given cluster is much more sensitive to the contributions from the lower pressure gas in the outer regions of the cluster. This is the very area of the cluster where the differ ences between the various different models of cluster atmospheres become most apparent. Detailed maps of the S- Z effect profile of a cluster, perhaps produced by an interferometer study, could then determine the exact nature of the cluster atmosphere, and whether it is isothermal or adiabatic. The mass of the cluster When the nature of the cluster atmosphere is well determined, the profile of the cluster gas can provide a means of calculating the gravitational mass of the cluster. How this mass varies in the outer region of the cluster as revealed by S-Z effect profiles could provide useful information on the nature of the dark matter that contributes the majority of the cluster mass. 94 Clumpiness Since the S-Z effect measures the electron number density, while the X-ray ob servations measure the square of the number density, the X-ray results are much more sensitive to dumpiness in the intergalactic medium. Inconsistendes between the S-Z effect predicted assuming an isotropic cluster atmosphere and actual S-Z observations could be a result of the gas being clumpy. Maps of the S-Z effect in a cluster could also provide similar information, as would the higher resolution X-ray imaging that may be possible on future space missions. Information on the dumpiness of cluster gas could determine the importance of gas ejection from individual galaxies to the origin of the cluster atmosphere, or the strength of gas heating by friction between the gas and galaxies passing through it. Determination of H0 and q0 Perhaps the most interesting possibility in cosmological terms for the combina tion of S-Z effect observations and X-ray observations, is the model independent determination of Hubble‘s constant, Ho, and the deceleration parameter qo. This becomes possible, as shown by Silk & White [162], because of the different depen dences of the two effects on the local electron density. In principle, this method uses the redshift independence of the S-Z effect to determine the absolute lumi nosity of the cluster X-ray emission. This is then compared with the observed X-ray emission, and the distance to the cluster can be calculated. This yields the luminosity distance to the cluster, from which a model independent value of Ho can be calculated. If sufficiently distant clusters are observed, the value of qo can also be found. This method probably presents the best possibility for the calcu lation of these fundamental cosmological parameters without the problems that have been associated with similar studies using the cosmological distance ladder. Early applications of this technique [20] produced the result Ho = 20 ± 25 km s-1 Mpc-1. This would seem to exclude Ho = 100 km s-1 Mpc-1 but the errors and uncertainties axe still large. For this technique to proceed, mapping of the S-Z effect must be achieved, either by interferometer, or by small beam radio or mil- limetre/submillimetre observations. This last comment could, in fact, be applied 95 to many of the investigations proposed in this section. Other possibilities The S-Z effect is a potentially very rich source of information, and goes beyond what has been discussed above. Other possibilities include the measurement of cluster peculiar velocities [169], both in the line of sight and, with polarization measurements, even transverse components. The nature of the CBR is confirmed to be non-local by observations of the effect in distant clusters [88]. The technique may also be used to search for distant galaxy clusters not yet observed in X-ray emission, but this area of study blurs into the growing field of searches for CBR anisotropies. Conclusion The potential of the S-Z effect in studies of both galaxy clusters and cosmology is clear. We shall now move on to discuss the numerous previous attempts to detect it. 3.4 Previous Observations of the S-Z Effect Attempts to detect the S-Z effect date back to 1972, the year of its inception, when Parijsky [119] reported a detection of AT = —1.2 ± 0.5 mK at 7.5 GHz in the Coma cluster. Later X-ray observations were found to be strongly inconsistent with this result [148]. Since then there have been numerous attempts to detect the effect in a large range of clusters. Table 3.1 gives a summary of the observers and their results. There is clearly a large degree of ambiguity in these results. Significant Rayleigh-Jeans flux increments , rather than decrements, have even been found in some clusters. The vast majority of this work has been conducted at radio wavelengths (A > ~ 9 mm), with only Meyer et al. [113], Chase et al. [40] and Radford et al. [132] reporting any observations at shorter wavelengths, near to the peak of the CBR. Many of the observations obviously suffered from the presence of systematic errors — from beam spillover observing the local environment, from confusion 96 with radio sources in the main or reference beams, from errors in the gain of the telescope used, and from non-Gaussian statistics from sky noise etc. As a result of this, many of the observations are not in agreement with each other, and most of the results axe in urgent need of independent confirmation. In only a handful of clusters does there seem to be any general agreement that an S-Z effect is present. 3.4.1 Techniques of Radio Observations Single dish Beamswitching Single dish radio observations of the S-Z effect dominate the field to date, and of the numerous techniques available, dual beamswitching (similar to chopping in infrared astronomy) has proven most popular. In this scheme (see eg. [21]), two separate antenna feeds observe the cluster and an adjacent position on the sky. The beamswitched signal, proportional to the difference in the flux from the two positions, is recorded. This process removes much of the sky background, but greater rejection is achieved by going to a second level of differencing by position switching the dual beams (nodding in infrared astronomy). In this process, the telescope alternately observes the cluster through one of the two beams, and then with the other. With this technique sky noise rejection is much more effective. This scheme does have its disadvantages however. Unless the profile of the S-Z effect is well matched to the size of the observing beam (typically several arcminutes) the sensitivity of the observations can be seriously degraded. If the telescope beam is smaller than the expected S-Z profile, then the reference beam, usually separated from the main beam by only 4 — 6 beamwidths, can in fact be seeing the wings of the microwave background decrement, and the sensitivity is reduced. Alternatively, if the observed cluster is much smaller than the beamsize, then there is beam dilution [136] and again the sensitivity of the observations to the S-Z effect is reduced. Thus, in beamswitching observations, the geometry of the receiver system defines which clusters are best observed. A further disadvantage of single dish beamswitching schemes is that a number of effects local to the instrument or its environment can cause the baseline of the observations (the power received by the antenna when all the astronomical sig 97 nal is subtracted) to vary as a complex function of telescope attitude. These so called position-dependent offsets then enter the astronomical data as differences in background flux between beam positions. The offsets are generally regarded as being due to telescope sidelobes and backlobes seeing sources in the local environ ment, and the baseline changes since these sidelobes move as the telescope tracks an object (see e.g. [132]). The contribution of these systematics to the overall measurement can be « 10 mK in antenna temperature [128], more than ten times the expected S-Z effect signal. A large proportion of pointed S-Z effect observations over a range of wave lengths have detected these varying baselines, and made some attempt to subtract their effects. These include Lasenby Sz Davies [90], Lake & Partridge [88], and Perrenod & Lada [128]. The usual technique for removal of these systematics in radio observations is to observe blank sky regions near to the main object to find any flux changes dependent on telescope position. Observations of blank sky po sitions at the same declination, and the same hour angles as the observations, also suffice. Any variations found are then fitted by a polynomial, and the contribu tions of these fitted baseline changes to the S-Z effect measurements are removed. The success of this background subtraction process, though, is somewhat ques tionable. For example, Lake Sz Partridge, and Perrenod &: Lada both used the NRAO 11 m telescope at 9 mm to observe the cluster A2218 for the S-Z effect. They also both used a blank sky technique to detect and remove any position dependent offsets. However, even in such similar experiments, Perrenod & Lada found an S-Z decrement in the cluster (- 1.04 db 0.48 mK) while Lake & Partridge found a flux excess (+0.43 ± 0.21 mK) [128] [88]. Drift and Driven Scanning A different approach to radio observations of the S-Z effect is scanning. Instead of using position switching to remove sky contributions, the telescope is halted ahead of the cluster, and the sky scans the object and nearby regions of blank sky across the instrument. Dual beamswitching is still used to subtract the main atmospheric emission, but the local backgrounds are much better controlled in this technique, since the telescope does not move while observations are underway. The 98 final result can also give some measurement of the S-Z profile of a cluster, should a decrement be detected. However, observing efficiency with drift scans is very low, since most of the time is spent looking at blank sky rather than the cluster of interest. An alternative to drift scanning is to drive the telescope across the object at a higher speed whilst still beamswitching. Rudnick’s 2 cm observations [143] used this technique with some success. However, this has the potential of suffering from both the problems of the previous techniques, since the telescopes position is changing, and the observing time on the object is reduced. The one main advan tage of this technique is that the noise contribution of variations in atmospheric emission on time scales large than & 5 minutes were found to be greatly reduced. Radio Interferometry Observations A third method of observing the S-Z effect at radio wavelengths is to use interfer ometry. In this technique an array of antennae is used to map the entire field of an S-Z cluster over several baselines during one long integration. This technique produces a complete map of the S-Z cluster and the surrounding sky, rather than just a measurement of flux at a single position, allowing much better subtrac tion of any contaminating radio sources (see later). In addition, interferometry provides a large degree of immunity from the position-dependent offsets due to beam spillover that have plagued pointed S-Z effect observations, since the side- lobe signals will not be correlated from one antenna to another. There is also evidence ([43]) that a similar effect allows interferometry to avoid spurious signals from atmospheric noise. This is particularly important at higher frequencies and at sites with poorer, less stable weather. Interferometry, however, is not immune to systematic effects, but suffers from a new class of problems. Errors may be introduced by the correlators, by drifts in the local oscillator frequency, and by antenna-antenna crosstalk, which is especially important for short baselines. The presence of different systematic effects provides a useful cross checking with single dish data. However, interferometry, at least with general purpose instruments such as the VLA, does have a major problem, since only a restricted range of Fourier 99 Authors Wavelength Cluster Temperature (mK) Error (mK) Perenod & Lada 79 9 mm A506 +0.63 0.76 A518 -1.56 0.83 A665 -1.3 0.59 A1472 -1.26 1.02 A2218 -1.04 0.48 A2319 +1.37 0.94 MWC349 +12.11 2.44 Parjiskii 72 19.5 GHz Coma -1 0.5 Birkinshaw 89 20.3 Ghz 0016+16 -0.444 0.065 0302+17 -0.442 0.109 A665 -0.301 0.049 1358+62 -0.183 0.114 A2218 -0.354 0.043 Radford et al. 86 3 mm A478 +0.76 1.2 (drift scans) A1413 -1.01 4.23 A2218 +1.41 0.99 (Pointed) A576 +0.79 0.46 A1413 +0.23 0.6 A2218 +0.4 0.31 Meyer et al. 83 1 to 3 mm A1795 0.2 0.9 Rudnick 78 2 cm A401 -2 1.4 A1656 +0.8 1.8 A2199 -2.2 1.2 A2319 +1 3 Table 3.1: Results of S-Z Effect Observations 100 Authors Wavelength Cluster Temperature (mK) Error (mK) Lake & Partridge ’80 9 mm A376 +1.0 0.42 A426 +1.97 0.6 A545 +0.9 0.24 A576 -0.68 0.15 A665 -0.55 0.37 A777 -0.12 0.24 A910 +0.12 0.29 Coma - 0.1 0.12 A1689 -0.61 0.47 A2079 -0.02 0.13 A2125 +0.39 0.24 A2142 -0.28 0.42 A2218 +0.40 0.21 A2319 -0.16 0.11 A2645 +1.26 0.38 A2666 +0.33 0.17 Uson ’85 19.5 GHz A545 +0.51 0.43 A1763 -0.36 0.25 A2216 -0.29 0.24 Uson ’87 19.5 GHz 0016+16 -0.48 0.12 A401 -0.64 0.18 A665 -0.37 0.14 Lasenby & Davies ’83 5 GHz A576 +1.1 0.44 A2218 +0.23 0.77 Table 3.1 continued 101 Authors Wavelength Cluster Temperature (mK) Error (mK) Birkinshaw & Gull ’84 10.7 GHz 0016+16 -0.72 0.18 A478 +0.44 0.32 A576 -0.14 0.29 A586 -0.09 0.38 A665 +0.03 0.25 A669 +0.38 0.24 1305+29 -0.28 0.22 A1689 +0.24 0.38 A2125 -0.31 0.39 A2218 -0.38 0.19 20.3 GHz 0016+16 -0.37 0.16 A665 -0.55 0.13 A2218 -0.31 0.13 Birkinshaw, Gull Sz 20.3 GHz 0016+16 -0.64 0.08 Hardbeck ’84 A665 -0.34 0.05 A2218 -0.34 0.05 Birkinshaw, Gull & 10.6 GHz A347 +0.34 0.29 Northover ’81 A376 +1.22 0.35 A478 -0.71 0.47 A576 -1.12 0.17 A665 -0.53 0.22 A1904 +0.55 0.4 A2125 -0.39 0.22 A2218 -1.05 0.21 A2319 -0.4 0.29 A2666 +0.34 0.29 Schallwich ’79 10.7 GHz A2218 -1.22 0.25 Andernach ’86 10.7 GHz -0.6 0.15 Table 3.1 continued 102 components of the radio sky are observed. Specifically, baselines less than the size of one antenna diameter cannot be used, so that structure on scales larger than the beam of a single antenna cannot be observed, and structure on scales comparable to the beam of a single dish is only observed by a few baselines. For example, in the only interferometric search for the S-Z effect to date, Partridge et al. [123] used the VLA in the D configuration to observe the possible S-Z effect in the cluster Abell 2218 at 6 cm. In this configuration, the VLA has a synthesised beam with half power full width of only 17 arcseconds, while the S-Z effect in A2218 has a half power full width of « 2 arcminutes. The efficiency of the VLA in detecting signals on such a large scale as the A2218 S-Z effect is therefore considerably reduced from its sensitivity on smaller scales (as 12 //Jy at 19 arcseconds, the scale of the synthesised beam for Partridge et als observations). Indeed, Partridge et al. concluded that they had only reached a sensitivity level of 0.7 mK for temperature changes on the scale of A2218. The prospects for interferometric observations of the S-Z effect, though, are good, since the limitted sampling of large scale information can be surmounted in purpose built instruments. Small antennae may be used, or observations may be made at considerably higher frequencies, so as to increase the beamsize of an individual dish. The Ryle telescope (formerly the 5 km telescope) interferometer array at Cambridge has been adapted to operate up to 15 GHz with its 25 m dishes in a dense packed mode, and will be capable of mapping clusters to a sensitivity of 100—200 fiK in about 8 hours on scales of « 3 arcminutes [150]. This presents an exciting possibility for future efforts in S-Z effect observations. Radio Point Sources A major problem with all radio based observations of the S-Z effect comes from the contamination of any S-Z signal by point sources of radio emission in either the field of the target cluster, or in the reference beams (for single dish beamswitching observations). This is especially difficult for S-Z observations since it is very likely that galaxies within the target cluster contain radio sources. The usual approach to this problem is to obtain an interferometer map of both the target cluster and the reference arcs at a longer wavelength than the S-Z observations to 103 identify any contaminating sources, and to measure their flux density and spectral index. The flux is then extrapolated to the S-Z observation frequency, and the contribution of the source is subtracted from the data. Observations are made at a longer wavelength than the S-Z measurements since point radio sources are predominantly power law in nature with flux increasing with wavelength. The integration time to find faint sources at the frequency of the S-Z measurements is therefore greatly reduced. This technique does, however, suffer from several potential problems. Firstly, any extended emission in the cluster can be very difficult to measure for the same reasons that the S-Z effect is difficult to measure by interferometer techniques. Any diffuse halo sources contaminating the observations are therefore likely to go undetected and uncorrected. It is interesting to note that 2 clusters where there are conflicting reports of an S-Z effect (A2218 and A576) are reported to have extended halo sources in them [90]. Secondly, any flat or shallow spectrum sources present will also go unnoticed if their flux does not rise above the detection level at longer wavelengths, while their contamination of the S-Z observations can remain significant. Interferometer observations of the S-Z effect get around most of these difficul ties since they produce a high resolution map of the cluster field itself, and point sources are easily removed using CLEAN or an equivalent technique. Weak ex tended sources, though, will still cause problems, since they can mask the very flux decrement sought in an S-Z effect observation. The only solution to the problem of extended radio emission is to observe at frequencies high enough that the S-Z effect dominates over the contribution of any contaminating radio sources, point or diffuse. Since radio sources decline with increasing frequency, while the S-Z effect peaks at millimetre wavelengths, it seems sensible to make observations in that wavelength region. 3.4.2 Millimetre and Submillimetre Observations To date there have only been 3 reports of observations in search of the S-Z effect at wavelengths of 3 mm or shorter. In all three cases, special care was neces 104 sary to reduce any systematic effects due to the sky noise which typically limits millimetre/submillimetre observations, particularly in poor weather conditions. Radford et al.’s observations at 3 mm using the NRAO telescope at Kitt Peak [132] used several methods. For their initial observations, they used a drift scan ning technique similar to that discussed above for radio observations. Baseline drifts caused by changing atmospheric conditions were fitted by a polynomial and removed. However, the drift scan data was still found to be contaminated by some source of low frequency noise, which only began to dominate the otherwise white noise spectrum at the longest time scales sampled. This low frequency component was found in both the blank sky data and the cluster fields measured. This excess noise eventually exceeded the white noise by a factor of 5, and was clearly the limiting factor in these observations. Later observations in this programme at the same telescope were not contami nated by these effects, but these used a source tracking technique, and were made after a major upgrading of the primary. These later observations used a conven tional chopping and nodding scheme, similar to the single beam radio observations described above, with integrations on a blank sky position alternating with those on the cluster (i.e. observing efficiency of only 25 %). These pointed observations, while free of the low frequency noise that had limited the drift scan observations, were hampered by the lack of the fast focal plane chopper used very successfully for the drift scan observations, so only a marginal improvement in sensitivity was achieved, and only upper limits were placed on the S-Z effect in the observed clusters. Their final set of observations, on the 7 m Crawford Hill telescope, used a complex chopping scheme involving a 3 x 3 grid of points, centring on the target cluster, and with two blank patches of sky to either side. Points contaminated by spurious noise effects were then identified and rejected by assuming that blank sky points deviating by 2 a from the mean sky value were bad. Again, only limits on the S-Z effect were achieved (see table 3.1). Whilst Radford et al.’s techniques were mainly adaptations of well known radio methods, Meyer et al. [113] used a somewhat more radical approach. They used a four channel He3 cooled bolometer system to observe Abell 1795 between 1 and 3 mm, using normal chopping and nodding techniques. They then used the method 105 of principal components to combine the four observational channels into four new channels with composite passbands, such that the scatter due to atmospheric noise was maximised in some channels, and minimised in others. This had the effect of maximising the sensitivity to the S-Z effect of the composite channel with minimum noise. This low noise channel had nearly twice the sensitivity to the S-Z effect of any other composite channel or any normal instrumental channel. However, no S-Z effect was detected in this cluster by these observations (see table 3.1). The observations by Chase et al. [40] used a technique which can identify any low frequency changes in sky emission, whilst still maximising the observing time spent on the source. This technique, an analysis of new data, and a reanalysis of the old results, will be discussed in a later chapter. 3.4.3 Results on Specific Objects Of the many clusters observed in search of an S-Z effect, only a small number have detections claimed for them, while an even smaller selection have detections confirmed by a number of observers. While these are prime candidates for S-Z effect searches, there are still many problems with the results. We now discuss the observations of these clusters, both for the S-Z effect and in X-rays. For a summary of the results to date see figure 3.3. 0016+16 This is a distant (z = 0.54) cluster of galaxies found to be a very bright X-ray source [182]. Because of its distance, its angular size is fairly small, with an X- ray core diameter of only 1 arcminute. This makes it ideal for small beamsize observations of any S-Z effect, since normal dual beam or chopping action will take the telescope beam well away from the cluster. If the X-ray emission in its direction is truly from 0016+16, and not from the nearby redshift 0.3 cluster, with which it is somewhat confused, then it is an ideal candidate for S-Z effect studies since its X-ray luminosity is very large (2.9 x 1038 W). Observations of this cluster for S-Z effect temperature decrements at the Rayleigh-Jeans end of the spectrum 106 A576 Results A2218 Results 1.5 1.5 q> l c> 0 0.5 J o 0 () o 0 0 -0.5 ^ -0.5 § -1 -1 o § o -1.5 -1.5 -2 4-r —I—i—i—i—i—i—i—i—|—i—i— i—|—i— i— i—i—i—i—i—| —1 ' 1—* I ' '■■■' l '■ ' ' I ' 1 ' I 78 80 82 84 86 88 90 78 80 82 84 86 88 90 YearofPublication Year of Publication A665 Results 0016+16 Results Figure 3.3: Results of SZ observations of 4 prime candidates The results of S-Z observations of the clusters 0016+16, A2218, A665 and A576 plotted against the date of publication of the final report of the investigation, or the most recent report in the case of investigations still underway. Note the evolution of both the error and value of the results as techniques have improved over time. 108 have been conducted by 2 groups, whilst Chase et al. [40] have observed it at millimetre wavelengths while developing their observational strategy. The latter observations had very large errors and so are not useful in this discussion, but all the radio observations, by Birkinshaw and collaborators [20], [22], [21] and Uson [175] have produced significant detections of an S-Z effect in this cluster. These observations used a range of frequencies, from 10.7 GHz to 20.3 GHz, and two different observatories, Owens Valley and NRAO 130-ft. The values are all in good agreement, within the observational errors. While further independent results are needed, this cluster must be a prime candidate for a firm detection of the S-Z effect. A665 A665 is the richest cluster in the Abell catalogue, it is therefore a prime candidate for having the hot, dense intracluster medium required for a large S-Z effect flux decrement. Its redshift is 0.1816, and it has an X-ray luminosity of about 5 x 1037 W [78], It has been a target for S-Z effect observations from the earliest stages, and has consistently produced positive results. However, the magnitude of the Rayleigh-Jeans temperature decrement found has varied considerably. The results of Birkinshaw and coworkers have been fairly consistent, indicating a decrement of about 0.3 mK [20], [22], [21], while Uson [175] provides some confirmation of this. One of the more interesting facets of Birkinshaw‘s most recent work [20] is that the S-Z profile of A665 has its peak decrement offset from the cluster optical centre by about 2 arcminutes. He reports that a similar offset, in both direction and magnitude, has been found independently in the X-ray data. This is good circumstantial evidence in favour of the detection of the S-Z effect in this cluster. Earlier observations of A665, however, clearly demonstrate the early stages of the development of techniques to observe the S- Z effect, with low significance detections, and with very variable values for the flux decrement. A2218 This is a cluster at a redshift of 0.171 [167], and is among the richest of the Abell catalogue (richness class 4). It has been observed in X-rays by both Einstein and 108 Ginga. Observations of this cluster for an S-Z effect, however, have a somewhat chequered history. The initial large decrements reported by Schallwich [154], Birkinshaw [23] and Perrenod [128] were strongly inconsistent with the X-ray data, and with later observations. Operation at higher frequencies, 20.3GHz, were introduced with the 1984 observations of this cluster by Birkinshaw and coworkers [21]. Most work previous to this had been conducted at lower frequencies, 5 or 10 GHz. The higher frequencies are less sensitive to faint power law radio emission, for example from galaxies in the cluster, and these observations yielded both reduced noise and a reduced Rayleigh-Jeans decrement. This suggests that previous observations may have been contaminated by radio emission in either the main or reference beams. The further introduction of VLA maps of both the cluster and reference fields [20] to identify and remove point radio sources does not give a significant change in the results. However, the S-Z effect results from this cluster are still somewhat inconsistent with the latest X-ray data [110], since their combination yields an extremely low value for the Hubble constant, Ho = 24l}okm s_1 Mpc-1. A576 Of the best studied S-Z clusters, Abell 576 is the one most likely not to have an S-Z effect present. It lies at a redshift of 0.04 and has an X-ray luminosity of 7.6 x 1036 W [78]. The initial, low frequency (10.6 GHz) observations by Birkin shaw et al. [23] produced a large significance, large flux decrement detection, -1.12 ± 0.17 mK, but almost all subsequent observations have failed to confirm this. In Birkinshaw et al.’s studies, the introduction of a better beamswitching scheme, and the move to a better site (Owens Valley rather than Chilbolton) produced a result of -0.14 ± 0.29 mK in their 1984 report [22]. The only other group to report a detection of the S-Z effect in this cluster are Lake &: Partridge [88], much of whose data showed significant position dependent offsets which were modelled and subtracted. Meanwhile, the X-ray data on this cluster show rela tively little emission from hot gas [148], suggesting that there should be a much smaller S-Z effect in this cluster than so far reported. Lasenby and Davies [90] suggest that both extended steep spectrum radio emission, and weak flat spectrum 109 sources are present in this cluster. Contamination of the S-Z effect data by emis sion from these sources could explain why large decrements have been detected at low frequencies which appear absent in higher frequency observations. 3.5 Conclusion The S-Z effect is a potentially powerful tool for observational cosmology. How ever, the observational search for the effect has been somewhat confused and inconclusive to date, with very few clear cut detections. Only 0016+16 and A665 seem to definitely possess a detected S-Z effect, whilst other detections are either unconfirmed or of disputed quality. The results on A2218 must be regarded as unconfirmed, since thay are in contradiction with the present X-ray data. Sources of error in observations include radio source contamination, and sidelobe effects which give rise to position dependent offsets. At radio wavelengths, the observa tions take many months, even with the latest equipment, and the reduction and analysis techniques are only now sufficiently developed to yield good detections with little possibility that systematic errors are still present. Millimetre wave observations, however, offer the possibility of making observations in just a few nights of comparable sensitivity to months of radio data . In the next chapter, some of the first such observations are discussed. 110 C hapter 4 UKT-14 Observations of the Sunyaev-Zeldovich Effect 4.1 Introduction The vast majority of observations of the S-Z effect to date have been at radio wavelengths. There are, however, a number of advantages in making such obser vations in the millimetre/submillimetre region. With the developing technology of both telescopes and receivers at these wavelengths, the sensitivities are now sufficiently good that sensitive measurements of the S-Z effect have become pos sible in the short observing runs (i.e. up to a few nights) available on common user millimetre/submillimetre equipment. This chapter describes observations in search of the S-Z effect using the UKT-14 receiver at UKIRT, and reconsiders the results of an earlier observing program using the QMC-Oregon bolometer receiver, also at UKIRT. The observations discussed here were made by S.T. Chase and coworkers, and much of the initial reduction software was also written by him. The reduction itself, the later analysis and many modifications and refinements to the software, though, are part of this work. 4.2 The Advantages of Millimetre Observations There are several clear and obvious advantages in observing the S-Z effect at millimetre/submillimetre wavelengths. The first and most obvious, discernible 111 from figure 3.1, is that the flux distortion due to the effect reaches a maximum in the millimetre/submillimetre region of the spectrum. The availability of broad band bolometric receivers at these wavelengths then allows observations of this flux distortion to be made in reasonably short times. For example, the observations of the S-Z effect at 15 GHz from the Owen’s Valley Radio observatory by Birkinshaw and collaborators [20] reached a 1 a sensitivity of « 100 fiK to the temperature decrement in the Rayleigh-Jeans region of the CBR black body spectrum. These observations took approximately 100 hours on each integration point. At 1.1 mm, in the millimetre waveband, the sensitivity of UKT-14 on the JCMT is 0.2 Jy lcr 1 s [146]. With the S-Z effect strength at 1.1 mm of « 200 mJy mK-1 ^sr-1 (see figure 3.1), for an instrument, with a « 3 arcminute beam this converts to a sensitivity for the S-Z effect of 1 mK lcr 1 s, in terms of the Rayleigh-Jeans temperature decrement. This is typical of the capabilities of broad band bolometer receivers at millimetre/submillimetre wavelengths for S-Z effect observations. Millimetre wave observations, in principle, can thus achieve an accuracy on S-Z effect measurements comparable to the best radio measurements in only a few minutes of integration, as opposed to many tens of hours. Of course the problem is not as simple as that, since most millimetre/submillimetre instruments have been designed to provide high spatial resolution. For example, the UKT-14 instrument has a beamsize of only 18.5 arcseconds at 1.1 mm, considerably smaller than the 4 arcminutes (« 1 fisi) considered above. However, the potential for such observations is clear. Further, the S-Z effect changes sign at « 1.4 mm, from a flux decrement at long wavelengths, to a flux increment at short wavelengths. Since no reasonable source of spurious emission could mimic this behaviour, detection of both the flux increment and decrement at different wavelengths from the same object would provide very good internal confidence that a detection of the S-Z effect had been made. Alternatively, observation of a decrement in an object at radio wavelengths, and an increment at millimetre wavelengths would provide a good independent confirmation that the S-Z effect had indeed been detected. Once high significance detections are made at millimetre/submillimetre wave lengths, a number of other investigations become possible. Sunyaev & Zeldovich [169] have shown that if an S-Z effect cluster is moving relative to an observer, 112 a Doppler-like effect acts to change the wavelength of the zero distortion point. Observations at several frequencies in the millimetre/submillimetre waveband can thus provide information on the line of sight velocities of galaxy clusters, and enable us to probe the distribution of mass on the very largest possible scales. Similar observations of galaxy streaming motions are proving a crucial test of cur rent cosmological theories e.g. [49], [54]. Extending such observations onto the large scales where tantalising results are already arising [25] will no doubt provide some very important new insights. This possibility comes in addition to the other uses for S-Z effect observations discussed in Chapter 3. However, while the potential of millimetre/submillimetre observations of the S-Z effect is clear, there are a number of definite hurdles, both technical and observational, to overcome. 4.3 The Disadvantages of Millimetre Observa tions There are several critical areas where millimetre/submillimetre wave techniques must be developed to have any hope of success in making observations of the S-Z effect. The first of these, which is very much sinea qua non , is sensitivity. While such receivers as UKT-14 undoubtedly possess the required NEP, especially when used on a large millimetre wave telescope such as the JCMT, they do not by any means have a suitable beamwidth. At 1.1 mm, the UKT-14 beamwidth on the JCMT is 18.5 arcseconds (HPBW) [146]. This is equivalent to 6.7 x 10“3 ^sr, so that its sensitivity to extended, low surface brightness sources, like the S-Z effect, is reduced considerably. This is primarily due to the understandable need of most astronomical programmes to achieve the best spatial resolution possible. For this reason, UKT-14 has been designed to operate at the diffraction limit of the JCMT’s 15m dish, rather than to just use the surface area as a large collector and operate at larger scales. To solve this problem, two approaches are possible. Firstly, one can take the same instrument to a smaller telescope, reducing its sensitivity, but increasing the throughput. Alternatively, one can design a different 113 instrument with a much larger beamsize, to use at the JCMT, and in principle elsewhere . In this chapter, the first of these options is taken, and observations are made with UKT-14 on the 3.8 m telescope UKIRT. This gives a beam about 4 times the size of the JCMT beam. The alternative approach, designing a large beam instrument for JCMT, is followed in the later chapters of this thesis. Unfortunately, the problem of getting the right instrument/telescope combina tion is not the only problem with sensitive measurements at millimetre/submillimetre wavelengths. Position-dependent offsets, similar to those polluting many radio ob servations of the S- Z effect, can produce quite severe systematic effects, and have necessitated several different approaches at millimetre/submillimetre wavelengths for their identification and removal such as those used by Radford et al. [132]. These are believed to be caused by the side and back lobe response changing as the telescope moves and different parts of the local environment are ‘seen’ [121]. For any observational set up, a scheme must be devised for the detection and removal of any systematics of this nature that might occur, and the observational experi ence is that these effectswill occur. These correction methods generally result in more time being spent on integrating on blank sky, either during a drift scan, or as part of a complex chopping and nodding scheme [132]. These techniques both lead to a reduced observing efficiency. Finally there is a third, and new, area of difficulty that is introduced by oper ating at millimetre/submillimetre wavelengths. Such observations do avoid many of the problems radio wavelenghts have associated with other sources of astro nomical emission, such as flat spectrum radio sources in the clusters or reference fields observed. However, an additional source of emission emerges to produce new difficulties. The emission from the atmosphere itself varies, on both short and long time scales, and this ‘sky noise’ contribution can pose a severe restric tion to millimetre/submillimetre observations. For example, the 1.1 mm channel observations discussed in Chapter 2 of this work were limited purely by sky noise. There are several possible approaches to combating the atmospheric emission. The most extreme approach, and the most effective, is to use a telescope which is above the atmosphere. Other options require the use of several channels e.g. [113] to identify and subtract sky noise effects. However, the only option with a single 114 channel detector, such as UKT- 14, is to hope that post-processing will identify and reject as much severely contaminated data as possible, and that the sky noise contaminating the remaining data will integrate down in a sensible manner. 4.4 Observations of the S-Z Effect at UKIRT Us ing UKT-14. The observations in this section were made at the UK Infrared Telescope, UKIRT, using the UKT-14 continuum receiver system (see Chapter 2 for general details). Three weeks of morning twilight time were assigned to this project, but condi tions were frequently poor, and 7 mornings were completely weathered out. The primary observing target for this study was the cluster 0016+16 (see Chapter 3), at RA(1950) 00h 15m 58*.7 DEC(1950) +16° 09' 24”, with subsidiary observations made on 2 areas of blank sky at RA(1950) 23h 54m 0*, DEC(1950) 23°39' 0” and RA(1950) 22h l m 12* DEC(1950) +20° 10' 12” to test for residual systematic er rors. Additionally, after the failure of the telescope drive motor, a drift scan at the zenith was performed, providing an extra ‘blank sky observation. A total of 38.5 hours were spent integrating on 0016+16 with 2 and 4 | hours spent on the blank sky areas respectively, and l | hours spent on the zenith drift scan. On UKIRT, the UKT-14 bolometer system has a typical 1 115 changes that are linear functions of time. The data were taken in blocks of typically 60 pairs, taking about 25 minutes of observing time, with calibration measurements at 1 .1 mm and 800 /im at the beginning and end of each block. 4.5 Calibration Jupiter was used as the calibration source for the whole of the observing run. Since observations were conducted over only 5 or 6 hours in morning twilight, the planet was accessible all the time. The flux due to Jupiter was calculated using the planetary data programme HOLD provided by UKIRT. This assumes a thermal spectrum for the planet, with an effective temperature at 1 .1 mm of 166 ±5 K [47] [60]. During the 20 morning observation run, the Jovian flux increased by approximately 8.6%, due to the changing angular diameter of the planet as seen from Earth. This is accounted for in the calibration of the data, where the flux of Jupiter is taken to be: F1.lmm = (6753 + 32 D )Jy 4.1 Fsoonm — (14083 + 66D) Jy where D is the day number. Calibration data was taken at the beginning of each block of data, at approximately half-hourly intervals at 1 .1 mm and 800 //m. The calibration of this data presents difficulties beyond those encountered in Chapter 2 , since the basic response of the instrument, in terms of Jy per V, is not well known for the period that UKT 14 was used at UKIRT. The data for JCMT has only been gathered recently, and cannot be backdated. To calibrate this data, therefore, we must first examine how the flux received from Jupiter varies with airmass, and extrapolate this response back to zero airmass. From equation 2.6 in Chapter 2 we have: F0 = Fee~rA =► ln(F0) = -A t In (Fe) (4.2) where F0 is the observed flux and Fe the flux before atmospheric absorption. Thus we can simply extrapolate back to zero airmass by plotting the natural logarithm of the flux received (in instrumental volts) and use linear extrapolation to find the 116 flux, again in instrumental volts, at the edge of the atmosphere. However, this technique does rely on r, the optical depth of the atmosphere at unit airmass, remaining constant over a sufficiently long time to allow measurements of the flux at a large range of airmass values. Unfortunately, the sky at millimetre wavelengths is very unstable, and usable data for this procedure was only obtained on 7 nights of the run (May 13 and 15 to 20). This data, together with the fits to the atmospheric extinction law, are presented in figure 4.1. The calculated zero airmass response for each night is taken and a weighted mean response is calculated, which yields the calibration factor to be used in the rest of the data reduction process. The calibration is found to be 1.07 dh 0.05 Jy/count at 1 .1 mm. It should be noted that for an investigation such as this, where the ultimate signal to noise ratio is likely to be low, it is more important to derive a reliable rel ative calibration measurement, applicable from block to block, and from morning to morning, than it is to achieve very precise absolute calibration. This is because absolute calibration errors will merely scale the final result by a constant factor, while relative calibration errors will affect the relative weight of each block, allow ing the possibility of additional, systematic errors to contaminate the final result. The process described here, using many mornings worth of calibration data, may not produce a particularly accurate absolute calibration, but the inclusion of as much data as is usable permits the good relative calibration required. Once the basic calibration factor, in terms of instrumental volts per Jansky, is known, the observations of Jupiter taken before and after each data block are used to calculate the atmospheric transmission at the time of the measurement. This also allows the changes in atmospheric transmission over the course of a block to be approximated by linear interpolation between the calibration measurements before and after each block. The complete data set is thus calibrated and corrected for atmospheric absorption, using the techniques described above and in Chapter 2. For observations of the S-Z effect, a further stage of calibration is required to convert the astronomical signal, in Janskys, to a measurement of the Rayleigh- Jeans equivalent temperature decrement due to the S-Z effect. This can be achieved using the following equation, which gives the power received by an in- 117 UKIRT Calibration Data Ln(coimts) Ainnmss Figure 4.1: Calibration data for UKT-14 UKIRT measurements. 119 strument observing over an arbitrary wavelength range due to an S-Z effect which has a Rayleigh-Jeans equivalent temperature decrement of A Trj . 2 k3T 2 r Ssz = -ASIATrj - ^ J G{v,TR)H{v)e~AM^ d v Jy (4.3) where AQ is the throughput of the telescope, in m2 sr, AM is the airmass of the observation, r the atmospheric optical depth, H(y) the instrumental passband, and G(y, Tr ) the form of the S-Z effect given in Chapter 3. The magnitude of any S-Z effect detected by its flux distortion can be derived from the received flux by numerically integrating this equation over the instrumental passband. The data is thus converted from uncalibrated instrumental volts output into the Rayleigh-Jeans equivalent temperature decrement of the S-Z effect, derived from the received flux, with full correction for atmospheric extinction, instrumen tal response and conversion to mK. 4.6 Data Reduction 4.6.1 Extraction of Signal and Baseline In observations such as these, where the flux due to the S-Z effect is expected to be very small, it is of the utmost importance that systematic errors be identified and removed. Previous studies of the S-Z effect, at both radio and millimetre wavelengths, have identified a number of sources of systematic error which often contaminate the observations. Principal among these are the position-dependent offsets measured, for example, by Lake and Partridge [ 88] or by Chase et al. [40] (hereinafter CJRA). Several methods to remove these systematics have been suggested, including drift scans [132] and parallel measurements of blank sky [128], all of which involve a great loss in observing efficiency on the object. The present work uses an improved version of the technique first discussed by CJRA, which uses chopping in right ascension to produce both the astronomical signal, and a measurement of the variation of any position-dependent offset to which the data is subjected. This method avoids the loss of observing efficiency by using the redundant information in the reference beams to measure the variations in the background radiation. This technique is only possible when chopping purely (or 119 almost entirely) in RA, since it is only then that the reference beams track the same portion of sky that the object beam will later traverse. With an ALT-AZ telescope, chopping in either ALT or AZ produces reference beams which move relative to the object, tracing out two reference arcs to either side. Conventional radio telescopes, therefore, cannot trace out the changing backgrounds which will affect the signal with their reference arcs. This precludes the use of this technique in radio observations. With DEC chopping on an equatorial mount telescope, the chop positions stay fixed on the sky, but are always offset from the track made by the object on the sky. Estimates of the background changes can thus be made, but are unlikely to produce optimum subtraction of the position-dependent systematics. In operation, the instrument produces data from two different nod positions; the (+) data set with the object in the positive beam, and the (-) data set with the object in the negative beam. If there is no noise in the system, but merely the as tronomical signal, S and the background R, then the fully calibrated instrumental signal V at either nod position will be: V+ = 5 + B (4.4) for the (+) beam, and: V „ = B - S (4.5) for the (-) beam. These are then combined to give a value for the observed signal, Vs and the background V b for each nod pair: Vs = V+ - V_ = 25 (4.6) providing the signal data set, and V b = ±(V+ + V-) = B (4.7) giving the background data set. We thus have two data sets, giving measurements of the astronomical signal 5 and of the associated background signal B. In the presence of position dependent offsets, B will vary as the telescope tracks the object over a range of hour angles. To extract the position- dependent offset, and to calculate its contribution to the 120 S-Z effect data, a low order polynomial is fitted to the baseline data set to model the variation of the background B with hour angle H. This produces a smooth function B f (H) which gives a good description of the background variation. The contribution that this makes to the S-Z effect data is dependent on the details of the chop and nod scheme used. A detailed analysis of the general case is given in the appendix to CJRA. In the specific instance of pure RA chopping here, the contribution to S-Z measurements is easily obtained from the differential of the polynomial fit with respect to hour angle. Thus: A S sz = H (4.8) where AH is the chop throw in RA (equivalent to hour angle). One form of position-dependent offset that will certainly be present in the data is due to the small difference in airmass between the two chopping positions introduced by chopping in RA. Atmospheric emission will be somewhat different in each of the two chop beams, and this will produce a definite signal. While this effect is reduced by nodding, and by the position-dependent offset scheme described above, it can also be explicitly calculated and the atmospheric contri bution to each data point can be removed as a separate part of the data reduction process, before the background fitting routine. 4.6.2 Derivation of Atmospheric Contribution The atmospheric emission and transmission at millimetre wavelengths is domi nated by water vapour lines, though there is some contribution from O 2 [73] [172]. We may thus use a model of the atmosphere where a single species dominates all the emission effects. For further simplicity, we may also assume that the at mosphere is a stable, stratified structure. Small deviations from this set up will account for sky noise. The emission from our one species is assumed to be ther mal, and the Rayleigh-Jeans approximation to a Planck spectrum is used. The emissivity will thus be a function of frequency only. The formal equation for radiative transfer in an atmosphere in local thermo dynamic equilibrium is [38]: I(s) = ioc,e-rW + f Bv(T)p(s')e(v, s')e-T(*’*'W (4.9) J oo 121 where I00 is the astronomical flux, BV(T) is the black body spectrum, s is the position of the observer, and t(s,s')= f e(i/ix)p(x)dx (4*10) is the integrated line-of-sight opacity between specified end points. Clearly, a rigourous analysis requires a detailed knowledge of the density, p, emissivity, e(y) and temperature T of each species as a function of position and time. In this treatment, though, we assume that only a single species, water vapour, is signif icant, and that the atmosphere is static with some constant, mean temperature T. If we further assume a plane stratified model we obtain s = AM(9)z where s is the integrated line of sight, AM(9) is the airmass, a function of zenith angle 9 only, and z is the altitude. For the plane approximation, AM{9) = sec(9). The expression for r(s,s') thus simplifies to t(s,s') = AMt{z,z’). Furthermore, the atmospheric opacity at the zenith, t , is a known and measured quantity in the astronomical data. Setting s = z = 0 as the point of the observations, ignoring the astronomical flux, and including the foregoing assumptions, equation 4.9 becomes: I(AM) = 2nkB-z [° t 4~ (e~AMr{2)) dz (4.11) C2 Joo dz ' ' where Tiz) = f e(v)p(z')dz’ (4.12) Joo and the zenith opacity r = r(oo). The atmospheric emission thus reduces to: I(AM) = 2* kBJ v * (i _ e-AMr'j (4.1.3) The atmospheric flux density into the telescope beam in thus: It(AM) = SlI(-AM,U^ (4.14) 7T where Q is the solid angle of the telescope beam. At Mauna Kea, typical conditions have a ground temperature of 260 - 275 K, falling to 2 10 K at the tropopause at 16 km altitude, and then rising again into the stratosphere [67]. The scale height of water vapour is 2 km [139], so that the temperatures at lower altitudes are predominant in this evaluation. A value of T « 250 K is thus suitable for our purposes. 122 Signal modulation during chopping will, as discussed above, produce a modu lated signal as a result of the differential airmass entering the beam, if the chop direction is anything other than purely azimuthal. The differential airmass intro duced will be given by: SAM = -N .v (AM) (4.15) whereN is the chop vector, so that the differential flux introduced into a particular observation will, approximately, be: SI(AM, v) = n 2vkBJ v2 Te-AMr6AM (4.16) c2 Given the zenith optical depth, r, the chop throw and direction, this flux con tribution may easily be calculated. The flux contribution to a given half chop cycle from this source may be up several Janskys in these observations, and is thus a potentially significant source of baseline drift. This contribution is cal culated by the reduction programme, which numerically integrates the flux over the instrumental bandpass, and this is then subtracted as a correction to the raw observational data. 4.6.3 Spike Rejection One final source of systematic error which can contaminate the data is the presence of ‘spikes’, rare large-valued (positive or negative) points. These enter the data because of instrumental effects, for example mains spikes, or other causes local to the telescope. Spikes may be identified by examining the deviation of a given point within a data block from the block mean. The best analysis procedure is to calculate the number of block standard deviations that separates each point from the mean. We then remove points which have a very low probability of occurring at random, assuming Gaussian statistics. For consistency, it is then necessary to recalculate the block mean and standard deviation, and repeat the process until no further points are rejected. Throughout the analysis presented here a spike threshold of 3 a was used. Thus the probability of a spike occurring at random in a given block is 0.0027. The blocks used here typically consist of 60 points, and thus the expected number of valid points rejected per block is only « 0.16. 123 4.6.4 Reduction Programme All the data reduction algorithms described above were included in a FORTRAN programme, called Newreduce, written originally by S.T. Chase and modified and improved by myself. The initial data input is the raw instrumental data, in instru mental counts at each chop position, together with data on time of observation, calibration factors, and measured atmospheric opacities before and after each block. The reduction process for each block then proceeded as follows. Firstly the data is fully demodulated and calibrated, to give the Rayleigh-Jeans equivalent temperature decrement derived from each nod pair. The background measured at each point is also calculated for later use. XJncorrected block means and standard deviations are then calculated, and spike rejection is performed for the first time. The atmospheric correction is then applied to each point, and spike rejection re peated. Finally, the position-dependent offsets are calculated. This is achieved by fitting a polynomial to the background variation data, and then using equation 4.8 to calculate the position-dependent offsets contribution at each chop position. This contribution is then subtracted from each chop position. Polynomials up to the seventh order are fitted to the data, and the fit that gives the lowest reduced X 2 value is taken as the best fit. Finally, the fully corrected data has any addi tional spikes removed. The demodulated values for the S-Z effect are output at each stage of the operation, so that the raw data, fully corrected data, and data corrected only for the differential atmospheric emission can be compared. 4.7 Data Analysis The 1986 observing run consisted of 17 mornings of observations. However, much of the work was conducted in very, poor weather. Four mornings of observations were completely weathered out, and several others were hampered by extreme humidity. It is therefore possible that a substantial proportion of the data is con taminated by extreme sky noise, prevalent in poor and humid conditions, and that non-Gaussian noise may present a restriction on the ultimate sensitivity reachable in these observations. Extreme care is therefore necessary in selecting data blocks deemed to be valid for combination to give the final results. 124 To cope with these problems, several techniques were used. The first method was to examine the observing log for any obvious sources of problems with the data. Thus, blocks taken while the windblind entered the beam were rejected, as were those with definite problems with the weather conditions, such as observing through thin cirrus. The main technique was to fit a Gaussian to the data within a given block, using the calculated block mean and standard deviation, and then to use the Kolmogorov- Smirnoff (K-S) test [129] to ascertain how good a fit this was. The K-S test was selected for this job since it preserves all of the data within a block, rather than thex 2 test, where considerable information is lost in the binning process. The K-S test compares the cumulative distribution function of the data with that of the modelled distribution, and finds the largest difference between the two. This ‘K-S statistic can then be used to calculate the probability of this difference between the two distributions arising at random, thus giving the significance of the test. Statistics other than the K-S test were also applied to the data, including the x2 test- All of these produced similar results. One factor that is most important in this procedure is to exclude the spikes previously rejected in the reduction programme, since otherwise the distributions can be radically different. A similar spike rejection routine is thus included in the analysis routines. The block selection procedure is thus to take the fully corrected data values for a given block, to calculate the block mean and standard deviation, rejecting spikes at a similar level to the reduction software. This data is then compared to a Gaussian distribution with the same mean and standard deviation, and a K-S test is performed between the real and predicted cumulative distribution functions. The K-S test then returns the probability that the data block is fitted by the appropriate Gaussian. All those blocks where the fit had a probability of less than 1 % were rejected (i.e. blocks were rejected where there was a 99 % confidence level that they were not Gaussian). The results of this rejection process are show in table 4.1. The block rejection process is applied to all of the data, including those blocks rejected on the basis of having known observational difficulties. Almost all of those blocks rejected for known problems were also rejected by the K-S test. 125 Date Block Reject Date Block Reject 3 May 1 13 May 1 2 2 3 X 3 4 14 May 1 X 5 X 2 X 4 May 1 3 X 2 X 4 X 3 X 5 X 4 6 X 5 X 15 May 1 6 X 2 5 May 1 3 2 X 4 X 3 X 16 May 1 4 X 2 7 May 1 3 2 X 4 3 X 5 X 4 5 17 May 1 6 X 2 7 3 8 X 5 X 9 X 6 X 126 Table 4.1: Results of Block Selection on 1986 S-Z data. Table of blocks accepted and rejected by K-S testing against a Gaussian. An X indicates that the block was rejected. Of 70 data blocks of observations of 0016+16, the K-S test process rejects 31. One further block is rejected because it contains excessive noise (a factor of 5 greater than any other accepted block), leaving 38 blocks of accepted data. Rejected blocks were often those at the very end of the mornings observations, and may fall foul of the rapid change in atmospheric conditions reported by Church et al. from work at the JCMT [44], Indeed, the last blocks are worst since it was only when it was clear that conditions had become poor that a morning’s run was ended. Most of the other rejected blocks are associated with poor conditions, such as large humidities. The observations of nights 7 and 9, for example, were made in humidities generally higher than 70 %, and occasionally as high as 100 %. Nights 5 and 14, containing many rejected blocks, were noted in calibration measurements to have an anomalously low 1 .1 mm transmission, and, on the basis of the K-S tests, this seems to be associated with non-Gaussian noise. We are thus left with 38 blocks of data, representing a total observing time of about 15 hours on 0016+16, over a period of 17 nights. 127 Data correction Mean (mK) Error (±mAT) Raw Data 3.2 2 .1 Airmass Only 2.6 2 .1 Fully Corrected -0.37 2 .1 Table 4.2: Results of observations on 0016+16. Results obtained by combining block values for 1986 data with different corrections for baseline drift. The Raw Data shows the result for the data with no corrections at all, Airmass Only for the data corrected for differential atmospheric emission only, Fully Corrected for the data with polynomial baseline fits and differential atmospheric emission. 4.8 Extraction of Results We have now calculated block means and standard deviations for the whole of the observing run. It is now necessary to combine this data to produce a measurement of the S- Z effect in 0016+16 from the whole of the data. The simplest approach is to combine the blocks together using their means and standard deviations, and assuming that the data within the blocks are Normally distributed samples from some parent Normal distribution. Given the analysis of the data using the K-S test above, this would appear to be a reasonable assumption. The appropriate formulae for this process are: ££* Q ) H = (4.17) £"=i e? £ = (4.18) where //, and e,- are the individual block means and standard errors, // and e are the mean and standard error for the whole observing run. The results from applying this combination technique to the data are shown in table 4.2. 128 4.8.1 Initial Conclusions and Discussion It appears clear from these results that we have not detected an S-Z effect in the cluster 0016+16. Given that the latest reported value for the Rayleigh-Jeans tem perature decrement in 0016+16 is -0.44 mK [ 20] it is not surprising that we have made no detection, since this is about 5 times below our sensitivity. To achieve even a l a detection at this low level of temperature decrement we would require about 375 hours of observations in conditions similar to these. Whilst considerably below the several thousand hours needed for the first radio observations of the S-Z effect, this figure is well beyond any time allocation that could be expected. Since the beam is well matched to the cluster core radius, a larger telescope collecting area would greatly increase the instrumental sensitivity to the S-Z effect, all other factors remaining unchanged. Table 4.2 also demonstrates that the correction techniques have made a sig nificant change to the final result. The total correction amounts to about 1.8 a in this data. This clearly demonstrates the need to carefully consider sources of possible systematic error in observations in search of such low flux levels as we are dealing with in these observations. 4.8.2 The Blank Sky Data The data on blank sky and the zenith drift scan were processed using exactly the same techniques as the observations on 0016+16. This can be used to search for any residual systematic errors in our observations or data analysis techniques. The results from these observations are detailed in table 4.3. It should be noted that the zenith scan is not strictly speaking blank sky data. Various sources, of various natures, will inevitably pass through the beam of the instrument during the course of the observations. However, with the beam size of 73 arcseconds, a typical point source will take only about 5 seconds to pass the instrumental aperture. A small source will therefore contaminate only one individual integration, which will, if the flux from the source is significant, then be rejected as a spike. A relatively large number of spikes are, in fact, seen in the zenith scan data (13 over 279 points as opposed to the 2 or 3 which might be 129 Object Mean (mK) Error (± mK) Position 1 -5.7 9.7 Position 2 -10.2 5.2 Position 2 without 18 May -1.6 7 Zenith Scan -1.3 4.4 Total blank sky -5.1 3.2 Total blank sky without 18 May -1.9 3.5 Table 4.3: Results of blank sky observations. The results of the blank sky integrations produced by combining the blocks of the blank sky positions after full correction for baseline drifts has been made. The total blank sky result comes from combining the results for separate positions as if they were separate blocks. expected on the basis of pointed data), which suggests that real sources are being rejected. The zenith scan data is thus effectively blank sky. As can be seen, most of the blank sky data shows a significant detection of any residual systematic errors. The result on Position 2, which is almost a 2 tt signal, is in fact due solely to the data taken in one block, the sole blank sky observation on 1 8th May. Whilst this block does pass all the tests necessary for its inclusion in the final analysis, it is still substantially different from the three other blocks of observations at this position. Indeed, in its own right, the aberrant block represents an almost 3 a detection. It is therefore possible that some extraneous effect, not accounted for in the foregoing analysis, has contaminated this block. Without the aberrant data block, the results for position 2 become - 1.6 ± 7 mK, which is much more consistent with the rest of the blank sky data. A somewhat more stringent test can be produced by combining the blank sky data together as if they were merely distinct blocks of observations of the same object. This produces a final result of -5.1 ±3.2 mK from the full set of blank sky observations, and -1.9 ± 3.5 mK if the aberrant block of observations on position 2 are rejected. This demonstrates the absence of residual systematic errors at the level of about 3 - 4 mK. However, the problems with the block from 18th May suggest that some rare source of systematic error may still be contaminating some 130 small amount of the data. Some detailed consideration of the behaviour of the data is therefore necessary. 4.9 The Detailed Behaviour of the Data The simple technique applied above relies on the assumption that each block mean is a fair representation of the underlying astronomical signal in the presence of Normally distributed noise. This would not be true if there were residual drifts or offsets contributing to the block means, or, equivalently, if there were an excess low frequency noise component. A second method, using the data from individual points, was therefore devised which is much more sensitive to non-Gaussian noise and systematic drifts from one block, or night, to another. This is somewhat similar to the processes used in Chapter 2 . In this method, all the data from all the nights are combined into one large data block, and the mean and standard deviation are calculated as each point is added to the final calculation. Thus: fi{n) = ^* =1 X‘- (4.19) n yields the mean fi(n) as a function of the number, n, of points, a?«, combined. The standard deviation a is similarly calculated using: o-2(«) = £ - M2(n) (4-20) f e i n The standard error is then simply calculated as: £(n) = ^ (4.21) y/Tl The blocks are collated into the large ‘block’ on a night by night basis, so that observations for each night are combined in one series of operations. If there were remaining systematic differences from night to night, therefore, they would show up as sharp changes in the combined mean, standard deviation and standard error. This process also enables us to make an estimate of the noise level reached after a given integration time. If the assumption that the noise integrates down in the usual Gaussian manner is correct, then the standard error should behave as: e oc -^= a - 7= (4.22) y ft y /n 131 where i is integration time, which is itself proportional to the number of points combined, n. The results of this combination process on the data selected by the K-S test process described above axe shown in figures 4.2 and 4.3. The standard error, clearly, does not steadily integrate down with the square root of the number of data points. While this process would appear to be true over at least some of the observations, there are clearly two regions, one at about 400 points into the run and another about 800 points in, where the standard error increases. This is especially true for the first of these areas. The mean also shows some strange behaviour at these positions. On closer investigation of the data it becomes clear that these large changes in mean and standard error are due to observations performed on two specific nights, 12th May, responsible for the smaller increase 800 points into the data, and 7th May, which produces the large shift nearer the start. The results of combining the data without these two nights of observations are shown in figures 4.4 and 4.5. This data is clearly much better behaved. This suggests that some source of systematic error has crept into the results via the data taken on 7th and 12th May. The night of the7th is distinguished by having a high humidity (around 70% all night), and this may well be associated with the unusual results. About half the blocks from this night were, in fact, rejected by the K-S test as being non-Gaussian, though those included in the final selection passed the required test as well as any other data. The night of the 12th, however, was not particularly exceptional, and the origin of the systematics detected by this analysis is unclear, especially since the problem is so well confined to data taken on the one night. This result serves to emphasise the care with which observations searching for very low power signals, such as the S-Z effect, must be handled. The data without 7th and 12 *** May behaves in a much more reasonable way, with the standard error integrating down, and the mean gradually settling onto a final value. The rate at which the standard error integrates down can be estimated by making a log- log plot of the data shown in figure 4.4. If the data is behaving as would be expected for a large number of separate samplings of some parent Gaussian distribution, the standard error on the mean should go down as f-1/2, 132 NumGor of I’oinls 200 '100 GOO 000 1000 1200 l'100 1GOO 1000 2000 2200 2100 JOJJ3 pjBpUB^S Figure 4.2: Behaviour of Standard Error as K-S selected data combined. 134 ‘Number of Points 200 00 4 GOO 000 1000 1200 1400 1000 1800 2000 2200 2400 (MUI) ibu 3;s UB3JS Figure 4.3 Behaviour of the mean as Iv-S selected data combined. 135 Figure 4.4: Behaviour of the standard error as K-S data combined without 7th or 12th May. 136 200 400 000 000 1000. 1200 1400 GOO I 1000 o o o oooooooe C5 T P5 C\J — —I C\JI I CO I ■'T ! l." (MUl) UB3K Figure 4.5: Behaviour of the mean as K-S data combined without 7th or \2th May. 137 where t is time. In this instance, we are dealing in numbers of data points, rather than seconds, but the dependency should still be the same. Thus a log-log plot of standard error against number of points combined should produce a straight line with a gradient of -0.5. The log-log plot is shown in figure 4.6. Ignoring the initial part of this plot, where only a few points are combined, and taking the gradient from log (points) = 1.6 (i.e. from about 40 points into the data) to the end, we obtain a gradient of -0.5 ± 0.05. This is in excellent agreement with the assumption that the data is sampled from a Gaussian distribution, where the error will integrate down as f 1/2. The values of the final mean and standard error produced by this more sophis ticated analysis are somewhat different from the results of simply combining the blocks, though the differences are not particularly large. For the fully corrected data set, including 7th and 12th May, the result is: -5.7 ± 3.7 mK and for the data without 7th and 12 th May, we find: +0.01 ± 2.5 mK. This compares to -0.37 ± 2.1 mK, the corresponding value calculated by com bining the individual blocks (including those from 7th and VIth May). Thus the simple block combining method underestimates the errors within the data by al most a factor of 2 , when compared to the detailed combination of the individual data points. This is due to the block based calculation merely adding the errors statistically, under the assumption that all of the blocks are drawn from the same parent distribution, while we are now aware, for example, that the data from 7th and 12 th May come from significantly different distributions. 4.10 Conclusions Several results are clear from the foregoing analysis. Firstly, in these observations we failed to detect any S-Z effect in the cluster 0016+16. Indeed, the sensitivity of UKT-14 in the configuration used on UKIRT is probably not sufficiently large to detect the S-Z effect in this cluster over a reasonable period of time. The Rayleigh- Jeans temperature decrement in the 137 L ! r I t—| —i—r—j—t—t_i—p i—i—i “|—i Figure 4.6: Log-log plot showing how the noise integrates down. integrates noise the how showing plot Log-log 4.6: Figure J ' C — C CM -C O C — CM 'T O _ t i — _ r l _ j __ ■ i I i i ■1 ) s i c u p e j p 3 J J O J ( _ i _ : _ !_J—!—i 139 t — r—r _ i_J S _ t o : _ t — i _ r i _ ! _ : _ ! _ !—1—!_:—i—L t r 1 ~i -I 1 J J ~l 1 i - i i =? CM l.o“ (Ntimlicr of I'oinl cluster is « 0.45 mK, [20] whilst in 15 hours of observations, we have only reached a la sensitivity of « 2.5 mK. We would thus need to integrate for « 450 hours to achieve even a 2 a detection of the S-Z effect in this cluster (assuming that the noise continues to integrate down systematically). Secondly, the techniques applied to the data to correct for the systematic errors introduced into the data by varying, position-dependent baselines, do make significant changes to the final results. This emphasises the necessity of very careful consideration of how local sources of radiation can enter the instrumental beam, and how their effects may be measured and removed. The techniques developed here appear to function well, with the blank sky data revealing no residual systematics as far as their sensitivity goes. Finally, we have demonstrated quite clearly that it is possible to use millimetre and submillimetre observations to detect extremely low signal levels by combining data taken over a long period of time. With careful identification of systematic errors, and careful selection of data unaffected by bad atmospheric noise and other effects, it is possible to extend the region over which the noise integrates down with \/i to very low flux levels. A 1 a level of 2.5 mK, with this observational set up, is equivalent to a flux of just 50 mJy which is equivalent to a 1*7 Is sensitivity of about 1 1 Jy, obtained in 15 hours of observation, sustained over 17 days. In comparison, the instrumental sensitivity of UKT-14 on UKIRT in ideal conditions was about 5Jyl 4.11 Reanalysis of 1983 UKIRT data 4.11.1 Observations In September of 1983, R.D. Joseph and S.T. Chase used the QMC-Oregon mil limetre wave photometer (a forerunner of UKT-14) to observe the cluster 0016+16 in search of the S-Z effect. The instrument was modified by the replacement of the usual 65 mm input lens with a 90 mm lens to produce a somewhat larger beam than its usual configuration. The beam was then measured to be a Gaussian with a 1/e full width of 135 arcseconds. The observational arrangement was otherwise 139 broadly similar to the 1986 observations described above. The only other differ ence was that the 3 arcminute chop was oriented to 170 arcseconds in RA and 27 arcseconds in DEC, rather than purely in RA. The cluster 0016+16 was observed for a total of 11.1 hours over the four nights of the observing run. 4.11.2 Original Data Reduction and Analysis The data was calibrated using Jupiter as a primary calibrator and DR -2 1 and Orion as secondary calibrators. The reduction was, again, broadly similar to the methods used on the 86 data. The contribution from differential airmass was subtracted, and the position-dependent offset term was measured and removed. Since the chopping and nodding in this data contained a component in declination rather than being purely in RA, the baseline drift subtraction may not perform quite as well. The processing phase itself differed somewhat in the spike rejection algorithm used. For the 83 data, the spike rejection threshold was set at an absolute flux level, rather than on the basis of an individual blocks standard deviation. This absolute value was chosen to be about 5 times the standard deviation of the first measured block, which was assumed to be typical of the remainder of the data. Unfortunately, this block was one of unusually low noise for the data taken in this observing run, and later blocks have standard deviations up to 3 times that of the first block. This means that when noisier blocks are processed, the high sigma wings will be truncated, and the resultant block will appear to have a lower noise than it actually has. In addition, the distribution of points in the modified block will not be strictly Gaussian. The result of this is that the final error calculated for these observations will be an underestimate of the actual error. The observing conditions during this run were much better than those prevail ing in the 86 observations. Also, the observations were made entirely at night, so that the unstable atmospheric conditions present at Mauna Kea in the morning [44] will not affect the data. The lengthy process of selecting uncontaminated blocks is therefore not necessary. 140 4.11.3 Reanalysis of the 1983 Data The 1983 data was reanalysed using the more sophisticated programs developed for the 1986 data analysis. The data was processed with a 3 g spike threshold based on the measured standard deviation for each individual block. A threshold of 3 a was appropriate here since the blocks typically consist of about 60 to 70 data points. The data was then processed in exactly the same way as the 1986 data. 4.11.4 Results of Reanalysis The result of the original analysis of the 1983 data for 0016+16 [40] was a Rayleigh- Jeans flux decrement of A T r j = —1 .6+ 1.0 mK. When the data is reanalysed using a consistent treatment of the noisier data blocks, as described above, the mean changes somewhat, and the noise, as expected, increases. The new, corrected, result on this cluster is: A T r j = -1.2 ± 1.4mK (4.23) The previous evidence for a 1.6 a detection is thus not confirmed, and we conclude that the earlier claim was mistaken because of an improper treatment of the noise within individual blocks, as discussed above. 4.12 Conclusions 4.12.1 The S-Z effect in 0016+16 The two observing runs discussed above had the cluster 0016+16 as their primary target. After proper analysis, neither observing run detected any sign of the S- Z effect in this cluster. The combined result for both the 1983 and 1986 data, obtained by using the simple combination method described in equations 4.17 and 4.18 is: A T r j = —0.9 ± 1 .2mK (4.24) This represents the final result of all the S-Z observations of 0016+16 made at millimetre wavelengths by the Imperial College group to date. The present radio 141 observations [ 20] indicate that the S-Z effect in this cluster has a Rayleigh-Jeans temperature decrement of -0.444 ± 0.065 mK, and so, while our lack of a detection is not surprising, the limit obtained is consistant with the measured decrement. However, the significant temperature decrements claimed in some of the early S-Z work are comparable to the sensitivity level we have achieved [22]. The fact that we do not detect anything at the levels claimed by these radio studies suggests that the techniques we have developed here axe either not susceptible, or have successfully eliminated the systematic errors responsible for the early claims. In addition, the sensitivities we have achieved are comparable with those achieved in the early stages of the development of techniques to observe the S-Z effect at radio wavelengths e.g. [128]. Our observations also took considerably less time than the radio measurements; the results presented above are from a total of about 20 hours, while those at radio wavelengths typically take much longer, e.g. about 100 hours in [20]. 4.12.2 Long Integration Times A critical part of the analysis of the 1986 data is the elimination of blocks that are contaminated by non-Gaussian noise. Without the elimination of these blocks, the final errors in the result are considerably increased. Point by point combination of the whole run’s observations of 0016+16, with no blocks rejected, yields a standard error of 5.5 mK, rather than the 2.5 mK that results after careful elimination of bad blocks. Thus in this case, adding more observations, and increasing the integration time actually increases the noise! Clearly, long integrations in search of very low flux levels require very careful consideration of the data and all possible sources of systematic error. The techniques described here, both for removing the systematic errors due to baseline drifts etc., and for identifying and eliminating poor data blocks, are clearly necessary to minimise the final noise level achieved by a given set of observations. The overall flux sensitivity of the 1986 data, for the « 12 hours of integration time finally selected, taken over 17 days, is « 10 Jy lals. For the poor sky conditions prevalent at the time, this is close to what would be achieved even for an integration of a few minutes. This is demonstrated 142 by the continuity of the log-log plot shown in figure 4.6, where the noise clearly integrates down with t - 1 /2 from very low numbers of points, all the way to the completion of the data, over a thousand points later. The 1 a Is noise, in this data, is therefore very similar after about 20 points to that after the whole run. Longer integrations, capable of reaching even more sensitive flux levels, may well be feasible, since the gradient of figure 4.6 has not changed even after 15 hours of observations over 17 different mornings. 4.12.3 Sensitivity to the Sunyaev-Zeldovich Effect At the wavelength of these observations, bpth at 1 .1 mm, the integral of the S- Z effect over the passband yields a conversion factor from flux to Rayleigh-Jeans temperature decrement of « 200 mJy ^sr- 1 mK-1. When the beam sizes are included in this conversion, and the flux sensitivities are calculated for the two instruments, we find that the QMC-Oregon Receiver has a flux sensitivity of 20 Jy 1 a 1 s, while the 1986 data gives a 10 Jy 1 a Is figure for UKT-14. However, in almost the same integration time, the QMC-Oregon instrument is almost twice as sensitive to the S-Z effect as UKT-14 (280 mK la Is for QMC-Oregan and 520 mK la Is for UKT- 14). This comes as a result of the larger beamsize used in the 1983 observations with the QMC- Oregan receiver. The solid angle of the beam in 1983 was about 10 times that used by UKT-14. The QMC-Oregon receiver thus received almost 10 times the power from the S-Z effect as UKT-14. This demonstrates that for low surface brightness, extended objects, such as a cluster of galaxies when observed for the S-Z effect, a large throughput device is highly effective. 4.12.4 The Next Step These observations have demonstrated the potential effectiveness of millimetre wave observations for studies of the S-Z effect. In just a few hours of observations we have achieved sensitivities approaching those of the radio observations, where many thousands of hours are required. We have also demonstrated that the noise 143 integrates down systematically, with t - 1 / 2 even over long integration times, taken over a period of 17 days. Sky noise, and other atmospheric fluctuations over longer time scales, though, did present a problem, and necessitated the rejection of a large fraction of the data taken during the 1986 run. We have also shown that a large throughput instrument, such as the QMC- Oregon Receiver, is more sensitive to the type of extended, low surface brightness source that an S-Z effect cluster would appear to be in the millimetre wave region. An ideal instrument for studies of the S-Z effect, therefore, would be designed along the following lines: use a large area telescope, such as the JCMT to maximise collecting area; have a large throughput, roughly matched to the angular size of the cluster on the sky to maximise received power; have some way of monitoring the sky noise, to identify bad blocks, and, preferably, remove the sky noise contributions. The instrument might also benefit from having two observational channels, to observe both the flux increment side of the S-Z effect, peaking at about 800 /im, and another for the flux decrement side, peaking at about 2.1 mm. The instrument described in the next chapter has been designed to meet these criteria, and to become a major advance in observations of both the S-Z effect, and CBR distortions in general. 144 C hapter 5 The ICSTM 3 Channel Millimetre Wave Photometer 5.1 Introduction The results of Chapter 4 indicate that, while broad band bolometric studies of the S-Z effect at millimetre and submillimetre wavelengths show great promise, a common user instrument, such as UKT-14, is not the optimum choice. The ideal instrument for such studies would have a large beamsize, comparable to the extent of the clusters to be observed (i.e. a few arcminutes), multiple channels, to permit the measurement of the characteristic spectral signature of the S-Z effect in the millimetre/submillimetre band, and good sensitivity. The major limitation on sensitivity in the millimetre/submillimetre waveband, especially with a large beam instrument, is the effect of sky noise, so the introduction of some instrumental channel to measure and subtract this sky noise should boost the detection sensitivity. For these reasons, and to take advantage of the soon to be commissioned JCMT, Chase and Joseph, in 1985, undertook the design and construction of a 3 Channel millimetre wave photometer at Imperial College. The first observations with this instrument are described in Chapter 6, and much of the commissioning and interfacing work for this instrument was undertaken as part of this work. This chapter presents an overview of the design, with specific emphasis on the digital PSD system modified from a previous IC design as part 145 of this work. 5.2 Design Requirements The requirements for the design of the instrument were as follows: • Large throughput A large throughput instrument is necessary to maximise the flux received from the low surface brightness extended sources that are the target of this instrument. A typical galaxy cluster for S-Z effect observations has an an gular extent of a few arcminutes. The fastest beam available on the JCMT is at the Cassegrain focus [55] and is f/12. Reasonable dimensions of the input field stop (w 65 mm) thus give a beamsize of « 1.5 arcminutes. • Atmospheric Monitoring To maximise the sensitivity of the observational detectors, some method must be used to remove the sky noise that in practice limits most mil- limetre/submillimetre observations. Since this instrument will have a large beam, and thus need a large chop throw, the sky noise may become even more important. The sky noise may be removed from an observational channel by cross correlating it with the emission from a channel with no astronomical signal. Since the S-Z effect signal is « zero around 1.3 mm, a wavelength coincident with the wings of an atmospheric water vapour line, observations at this frequency may provide the needed sky noise information. • 3 Colinear Channels To conduct observations of both the flux increment and decrement sides of the S-Z effect, and to allow removal of sky noise fluctuations via correlation with a noise channel, three channels must be used. These beams must ideally by colinear so that the instrument is observing the same spot on the sky in all three observational channels. • Sensitive Bolometric Detectors: Cryogenics, Filters and Baffles 146 For the maximum sensitivity to the S-Z effect, ignoring sky noise for the moment, the best detectors are required. For broad band millimetre wave detection, the best available are cryogenically cooled semiconductor bolome ters. These devices have a large temperature coefficient of resistance. When heated by incident radiation, the ensuing change in resistance is detected, and provides the astronomical signal. For these devices to operate effectively very low temperatures are needed to keep background power and noise as low as possible. The bolometers in the instrument described here are cooled to « 0.35 K by a pumped liquid He 3 closed cycle ‘minifridge’ [39]. Back ground radiation must also be avoided, as it will both contribute to noise in the detectors, and extra thermal loading on the system. A comprehensive range of baffles and blocking filters are therefore also needed. These operational requirements provide the general specification for the instru ment. The need for three colinear channels at different wavelengths, for example, requires the use of several bandpass filters. The next section presents an overview of the design of the instrument, showing how these requirements are fulfilled. 5.3 Design Overview 5.3.1 Construction and Cryogenics The detectors, and the major part of the optics, are all housed within an Infrared Laboratories HD3(8) Cryostat. This provides a Liquid He 4 cold surface, at 4 K, and a single helium fill hold time well in excess of 80 hours (provided the Liquid Nitrogen outer reservoir is kept filled). Figure 5.1 shows the overall layout for the instrument within the cryostat. The He3 minifridge must be well thermally sunk to the He 4 cold surface for effective operation. In use, the vapour above the He 4 reservoir is pumped to a pressure of a few millibars, cooling the liquid, the optics and the minifridge to about 1.5 K. At the same time, the activated charcoal pump in the minifridge, which is thermally isolated from the rest of the system, is heated to drive off the adsorbed He3. This vapour then collects in the He 3 reservoir, which is thermally 147 § fS Tf Figure 5.1: 3 Channel Millimetre Wave Photometer Cryostat Layout. 149 isolated from the He 4 reservoir, and condenses to liquid. Once all the He 3 has been driven off, the heater to the pump is turned off. The adsorption pump gradually cools, and begins to adsorb He 3 vapour, reducing the pressure above the liquid, and so cooling it. This cools the minifridge and the detector assembly attached to its cold surface to « 0.35 K in about an hour. The liquid He 3 hold time of this device is about 12 hours at sea level and about 18 hours at altitude (9300 feet, at TIRGO). To reduce the thermal mass on the He3 minifridge, and for reasons of mechan ical stability, the He3 cold stage must be els small as possible. This necessitates mounting the 3 detectors close together, and so places additional constraints on the overall design. 5.3.2 Optics A schematic of the optical layout is shown in figures 5.2 and 5.3. The external Fabry input lens is located at the telescope focal plane and images the telescope primary onto the cold input lens. The beam then falls onto the two metal mesh dichroic beamsplitters, and finally the off-axis ellipsoidal mirrors re-image the input lens at the entrance apertures of the Winston cones which sit in front of the bolometer integration cavities. The optical system for this instrument was designed by S.T. Chase. 5.3.3 Filters There are two different sets of observational filters in the instrument. Firstly, the astronomical channels are defined by metal mesh bandpass filters mounted directly in front of the Winston cone apertures of the 1 .1 mm and 2.1 mm channels. The other filters are metal mesh dichroic beamsplitters (low-pass edge filters) which split the beam into the three channels. The passband for the1.6 mm sky noise monitoring channel is defined by the intersection of the beamsplitter characteristics. The filter bandpasses, measured at QMWC with the help of Dr. P. Ade who also made the filters, are shown in figures 5.4, 5.5 and 5.6. 149 .S c h * h * t i C o u r jjv t o r 3 - ttiw J £ k 'PhotoH£T£A. $to£ v i f O $roio//Jtj verecro^ pot/T/okT (3>icmcj;c3 l wt* j *** *»t * * •* > # ■ ) Figure 5.2: Optical Layout of 3 Channel Photometer: Side View. Diagram due to S.T. Chase. * c H « M T i t T i* * Y W OK 3-CM*****. 'p„n o ntT£K. Cwostat C"»fOutfu. Figure 5.3: Optical Layout of 3 Channel Photometer: Overhead View. Diagram due to S.T. Chase. 152 FREQUENCY FREQUENCY CCM-ID Figure 5.4: 1 .1 mm Bandpass. Data from [ 1 ]. i FREQUENCY FREQUENCY CCM-13 Figure 5.5i 1.6 min Bandpass. Data from [1]. 154 FREQUENCY FREQUENCY CCM-13 Figure 5.6: 2.1 mm Bandpasi Data from [1]. 5.3.4 Baffles and Blocking Filters For proper operation of an optimised bolometer, it is necessary to reduce the back ground radiation loading on the detectors as much as possible. This is important since additional radiation loading introduces extra noise into the observations, and can also lead to warming of the bolometers and a reduction in their responsivity (VW-1). Careful consideration of baffles and blocking filters is therefore neces sary in the design of our millimetre wave photometer. Figure 5.2 shows the overall baffle and blocking filter design as part of the optical system. The baffles are all reflective, and the series of 6 re-entrant baffles before the detector optics will reject almost all stray light entering the instrument. In addition, there are two sets of blocking filters to remove high frequency radiation that will otherwise reach the detectors through high frequency leaks in the beamsplitting and bandpass filters. The blocking filters, constructed by Dr. P. Ade, include black polyethylene, fluro- gold, and a metal mesh blocking filter. The last stage of blocking, and the input field stop, are on the He 4 heat shield, and so are kept at 4.2 K, the temperature of liquid He4. This means that the highest thermal background temperature seen by the detectors from any out-of-beam source is 4.2 K. 5.3.5 Detectors The detectors are three IR Laboratories Si bolometers. These are cooled to « 0.35 K by the He3 minifridge. The bolometers are mounted inside spherical inte grating cavities fed by small Winston cones which, in the case of the astronomical channels, also support the input bandpass filters. The detectors were specifically designed for use in this high throughput instrument, and so their responsivities are not degraded by the large powers incident upon them. Bolometer Operation A bolometer is a radiation detector which has a large temperature coefficent of resistivity. Radiation incident upon a bolometer increases its temperature, and thus its resistance also increases. By placing the bolometer in a circuit in series with a constant load resistance, and with a constant bias voltage across the two, 155 any changes in the resistance of the bolometer are converted into a change in voltage drop across the bolometer. The radiation signal is thus converted into a voltage signal. Bolometers are typically operated at very low temperatures, so that excess photon noise from background power loading is kept to a minimum. They are kept at these temperatures by thermally connecting them to heat baths at low temperatures. In our case, we use pumped liquid He 3 to cool the bolometers to a temperature of about 0.35 mK. The electrical power dissipation in the bolometer from the bias current maintains the bolometer typically about 10 % above the temperature of the heat bath [101]. The responsivity of a bolometer, in Volts per Watt of incident power, is a function of the bias voltage, and is given by [ 10 1], [80]: Z-R 5 = (5.1) 2 E where S is the responsivity, R is the resistance of the bolometer at the operating point, E is the voltage across the bolometer, and Z = dE/dl is the impedance of the bolometer at the operating point. The responsivity can be found by measuring the voltage across the bolometer as a function of the current through the device. In practice this is achieved by measuring the voltages across the bolometer and the constant load resistor for a given bias voltage. Figure 5.7 shows the measured VI curves for the 3 bolometers when used in the instrument seeing ambient room temperature. These measurements thus represent normal observing conditions for the system. Our initial observations, and much of the test work, were carried out with a bias voltage of 1.5 V. From the data in the figure and equation 5.1 this indicates that the responsivity of the bolometers will be « 1.2 x 10 7 V W - 1 for the 2 .1 mm channel, and « 1.5 x 107 V W - 1 for the other two channels. 5.4 Phase Sensitive Detection 5.4.1 Operating Principles At wavelengths longer than those of visible light, the background radiation from the sky and the telescope environment dominate the radiative power falling on 156 1.1 mm (mV) Q -1 .6 mm (mV) a - 2.i mm (mV) V-I Curves for 3 Chan Bolometers 90 80 - | 70 60 - 50 - 40 30 20 0 10 20 30 40 50 I bolo (nA) Figure 5.7: VI Curves of bolometers 158 the detectors. The astronomical signal is only a very small part of the total radiation received by the instrument, since the sky and telescope are generally at temperatures of around 300 K. Thus it is necessary to subtract the contribution of this background component from the total signal received. This is achieved by the processes of ‘chopping’ and ‘nodding’ the telescope. In chopping, the telescope beam is rapidly moved between two positions, one of which includes the object under study, while the other is a nearby piece of empty sky. The output signal from this process consists of a large DC component, which represents the background flux, and a small AC component, varying at the same frequency as the chopping, due to the flux received from the object. A phase sensitive detector (PSD), or lock-in amplifier as it is sometimes called, retrieves and amplifies that part of the signal which is varying at the same frequency as the chopping. The PSD uses the signal which controls the secondary mirror as a reference, and so can provide a stable output, even in the presence of drifts in the chopping frequency. Chopping is generally achieved by moving the telescope’s secondary mirror, or by shifting the beam on the sky by some additional optics, and is typically operated at frequencies from 3 to 20 Hz. Some dead time is introduced into the system as the secondary shifts to its new position. This is dependent on the amplitude and frequency of the chop, but is usually only a few milliseconds. Chopping has the additional benefit of shifting the astronomical signal from DC up to the chop frequency, thus avoiding the worst parts of the 1 /f noise typically found in all systems. ‘Nodding’ is an additional process which aims to remove differences between the two ‘chopped’ telescope beams (caused, for example, by looking at different parts of the primary) and to remove contributions due to changes in the atmo spheric emission. In nodding, the telescope is moved so that the object is alter nately in one of the chopped beams and then the other. The difference between the two is then taken as the astronomical signal, removing any differential effects between the two beams. For more details on this process see the sections dealing with demodulation in Chapters 2 and 4. Nodding takes place at considerably lower frequencies than chopping — at 0.1 Hz or less — and is achieved by moving the whole telescope. It is thus necessary to let the telescope settle in its new position 158 before integrating on the object again, since moving the whole telescope structure is a considerably greater change in telescope position than is necessary when the secondary is nutated in chopping. This settling usually takes a few seconds. 5.4.2 Implementation The chopping and nodding system for the 3 Channel Photometer is provided by a dedicated computer controlled unit, the digital phase sensitive detector (digital PSD). The chopping system generates a square wave output, which provides the telescope with the chop waveform, and to control the timing of other parts of the PSD system. The processing of an astronomical signal is then as follows. Firstly, the telescope chopping converts the DC astronomical signal into an AC signal on top of the DC background. The resulting chopped output then goes through several stages of amplification. A low noise, AC coupled preamp at the cryostat boosts the signal with a gain of 1000 and removes the DC component, and then the remote control postamps provide a further, variable gain (though typically this will again be a factor of 1000). The postamps also include a simple RC low pass filter to provide some immunity to high frequency noise and are AC coupled to remove DC as well. The signal is then fed into a voltage-to-frequency converter. This produces a pulse train whose frequency is directly proportional to the input voltage. This is then fed to a digital counter, which counts the number of pulses, in effect digitising the signal. Phase sensitive detection is then achieved by setting the counters to count up when the object is in the beam, and down when the object is out of the beam (or vice versa if the object is in the negative beam). To cope with the dead time while the telescope is moving from one chop position to another, the counters are disabled while the chop signal is changing sign. Also, a phase difference between the chop waveform and the counter control signals can be introduced to cope with any phase changes produced by the chopper controls, or the filters in the system. Thus, during a long integration, the object+background is measured, then the background subtracted, and then the process is repeated, with the object’s contributions gradually building up. Figure 5.8 summarises the operation. 159 + beam Chopper Signal -beam Instrument Output Up Counter Stop Control Down Figure 5 .8: Signals used by Digital PSD system. 161 Nodding is achieved by sending a command to the host telescope’s control computer after a chop cycle has completed. This initiates a preset shift in the telescope position that switches the positions of the positive and negative chop beams. Demodulation of the nodded data is performed, initially, by the user’s computer, but the raw data is stored for demodulation off line at a later date. Chapters 2 and 4 contain examples of such off line demodulation. 5.5 Instrument and Telescope Control Electron ics The ancillary electronics required for the 3 Channel Photometer consists of four parts. Bolted to the side of the cryostat is a four channel (1 spare) low noise preamp, which also provides the bias current for the bolometers. The signals from the preamps are then fed to the Analogue Electronics Box, which performs post-amplification and digitises the signals. The digitised signals axe then fed to the Digital Electronics Box, which performs the phase sensitive detection of the signals, and controls the instrument and telescope. Finally, the user control of the system, data logging, and some initial data reduction are performed by the User’s Computer. The overall setup of the system is described in figure 5.9. Each hardware part of the system, and then the software, will now be discussed in turn. 5.5.1 Warm Preamp This device was designed and constructed by Mark Hooker and the IC Astro physics Group Electronics workshop. It consists of two subsystems, one to provide the bias currents necessary for the operation of the bolometers, and the second to provide the preamp gain of 1000 before the signal is passed on to the electronics racks. The bias circuits are simple potential dividers driven by a 1.5 V alkaline batteries. The preamp circuit uses a JFET in a follower configuration as an input stage to provide a high input impedance, and then uses a conventional low noise operational amplifier giving a gain of 1000 on the input signal. A high input impedance is needed to match the large impedance of the bolometers (about 10 161 Figure 5.9: Schematic Diagram of 3 Channel Photometer’s Electronics. 163 MU at the operating temperature). This also keeps the current passing through the bolometers as low as possible, keeping any electrical heating to an absolute minimum. 5.5.2 Analogue Rack This is a standard 19.5 inch mains-powered rack which is mounted near to the telescope (typically on the dome floor). Signals are fed to it from the detector preamps via coax cables. The analogue rack performs three distinct tasks, two of which are directly related to the digital PSD process, post amplification and voltage to frequency conversion, while the third, chop amplifier, is concerned with telescope control. Remote Control Postamps There are three remote control postamps on the analogue rack. They are essen tially identical, but may have their gains set separately. The gains can be remotely set to any of 7 values, 0.1, 1, 3, 10, 30, 100, 300, 1000, which is indicated by a number displayed on an LED panel (1 to 6 for gains of 1 to 1000, and 7 for 0.1 ). The postamps are AC coupled, to reject DC signals, and equipped with simple low pass RC filters at the input stage, whose response is set to roll off at about 25 Hz. This is to provide some immunity to pickup from mains noise. A plot of the postamplifier’s frequency response is shown in figure 5.10. Voltage to Frequency Converters There are four voltage to frequency (V to F) converters (one per channel and one spare), using VFC320 chips. They convert an input voltage into a pulse train whose frequency is dependent upon the voltage. This pulse train is then fed to the counters on the digital electronics box. The V to F converter circuits used here are designed to give zero output for an input voltage of -10 V, rising through 50 KHz for 0 V to 100 kHz for a 10 V The linearity of the devices has been tested over the operational range -10 to 10 V and, to a higher precision, in the region around 0 to 1 V. Any non-linearity in the behaviour of these devices is found to 163 Suiter One Systeis Liiited Lir.eer Circuit ir.slwsis Pro^ru ANALYSER II (019S: Circuit Sue: 5 i«t June 19B9 SAIN 6,« PHASE P,+ ANY TWO t Siin itl its) -45 -41 -35 • -31 -I! -2? -15 -18 -5.1 5 Phase (dec) -38* -25? -2?? -15? -1?? -5? « 5? 11? I5i 21? Figure 5.10: Frequency response of Post Amplifiers be < 0.004%. Results of these tests are shown in figure 5.11. The Chopper Amplifier This device takes the TTL chopper signal generated by the chopper control board in the digital electronics box, and amplifies it to provide the output signal and voltage required to drive the telescope secondary mirror control. A BNC connector takes the input signal from the chop controller on the digital rack. This is then amplified to a level set by a variable resistor mounted on the control panel. There are then three separate outputs of this signal, a further output of the TTL level signal, and a switch to change the outputs from positive to negative. The device can also function as a test source for the digital PSD system, where the three outputs can serve as inputs for the three instrumental channels. 5.5.3 The Digital Rack This is a double layer 19.5 inch mains-powered rack which is mounted near to the analogue rack, also, typically, in the telescope dome. It is connected to the analogue rack by 4 coax cables, 3 carrying the V to F signals, and one the chop waveform, and by a multicore cable carrying the amplifier controls. The digital rack is controlled by a single board computer (SBC) based on a 6502 micropro cessor. The SBC controls the other boards in the rack via the ICSTM ’Astrobus’ data bus, a standardised design devised in the IC Astrophysics Group Electronics Workshop. The SBC card also contains the 1 MHz clock used by all the other boards on the rack. There are eight distinct types of board on the digital rack, which will now be looked at in turn. The Single Board Computer (SBC) The SBC is a Rockwell RM 65 single board computer, mounted on a standard Eurocard. It is mounted in a special slot, which converts from the SBC’s pinout to the standard ASTROBUS bus connection used by the rest of the digital rack. The SBC’s processor is a 6502, and it is equipped with a single operating ROM and on board RAM for its operations. A reset switch is mounted on the control 165 V to F Test (high voltages) ▲ Frequency O/P (Hz) 100000 A* .▲ 80000 - 60000 - 40000 - 20000 - 0 i i i i i -10 -6 -2 2 6 10 ■ Voltage V to F Test (low voltages) Frequency (Hz) 56000 55000 - ,|i 54000 - ■ i i » 53000 - „ r i ^ 52000 - n « 1 51000 - I! K " l HH 50000 - i l 1 49000 1 i 1 1 1 1 -1 102 I 102 3 102 5 102 7 102 9 102 1 103 Voltage (mV) Figure 5.11: Results of test for V to F converter Linearity. 167 panel. EPROM Emulator This board merely contains a battery-backed 8K RAM device that acts as an EPROM emulator. The write enable control on the chip is toggled on or off by a switch mounted on the control panel. This enables the chip to act as permanent ROM storage once a fully developed control programme is loaded into it, but during the development phase successive new versions of the software can easily be uploaded. This avoids the time and effort necessary for EPROM burning and erasing, and allows tests and modifications to be made rapidly. Operating software by Mark Hooker is supplied on a ROM on the SBC which allows data to be up- and down-loaded from the EPROM emulator via the RS- 232 connection. Universal Clock This is a real time, battery-backed clock that is used to measure the time at which each integration is made. This data can later be used to calculate the telescope attitude during a given integration and so allow correction for position dependent offsets. The data is relayed to the SBC via the ASTROBUS. Corrections to the time are made by writing to the clock’s memory-mapped location from the SBC. Counter Enable-Disable This board uses a 6522 VIA to generate signals for control of the counters — whether they count up, down or are disabled. With the secondary mirror in the positive position the counters count up, when in the negative position they count down, and when the secondary mirror is moving they must be disabled, since the signals from the instrument are unusable. To achieve this, the 6522 timer on this board runs for half a chop period, minus 2 milliseconds, giving zero output. When this time is up, the 6502 is interrupted, and a new timer value, 2 milliseconds, the counter dead time, is fed to the 6522. The output then goes high, and the counters are disabled for 2 milliseconds while the secondary mirror moves. After this, another interrupt goes to the 6502 which reverses the count direction, and the half chop period is loaded again. 167 This board also provides the overall timing for the PSD process, since the SBC counts the number of interrupts it receives from the Counter Enable-Disable 6522 to find the end of the required integration time. Phase shifts between the chop signal and the output waveform from the postamps can also be corrected with this board. Initially, the chop output and the counter enable-disable waveforms are in phase, but the counter enable- disable period may be lengthened, for a given cycle, to produce a phase difference. On receipt of the appropriate command, the value sent to the 6522 timer is increased or decreased by 1 /2 millisecond in a given cycle, shifting the phase by a small amount. Up-Down Counters There are two counter boards, each containing two 24 bit counters (one for each channel, and one spare). Each counter has an input BNC connector and a lemo connector which provides the enable/disable signal. Connection to the SBC data and address bus is provided by the ASTROBUS edge connector. This allows the SBC to control the counters and read their contents. The counters count the number of pulses fed from the V to F converters on the analogue board, and thus integrate the voltage output from the instrument. They count up or down depending on the chop position, as controlled by the SBC, and can thus perform phase sensitive detection of the modulated astronomical signal. The phase difference between the chop waveform, and the up/down control signal is also under computer control, so that phase differences between the astronomical signal and the chop signal can be accounted for. The enable/disable signal is used so that the counters do not operate while they are being read out, or while the secondary mirror is moving. Postamp Control This board relays the control signals from the SBC to the remote control postamps. A multicore cable carries the control signals to a connector at the rear of the analogue box. 168 RS232 The digital box is supplied with two dual RS232 interface boards to provide the SBC with communication with external computers. At present two of these in terfaces are redundant, but of the others, one is dedicated to serving the User’s computer, whilst the other is used to relay nodding control signals to the host telescope’s computer. Both of these channels axe operated at 9600 baud, allowing for relatively rapid communications. Chop Controller The Chop Controller uses a 6522 VIA in free-running mode to produce a square wave output, which provides the chop waveform. To achieve this, a value is written into the 6522’s latch, which represents half the required chop period in microseconds (since the clock speed is 1 MHz). The 6522 is then set into free- running mode, loading this value into its counter, and sending the output line high. The counter is then decremented on each succeeding clock cycle, until it reaches zero. At this point the output line changes sign, and the latch value is reloaded into the counter. This process generates an output square wave to act as the chop waveform. The output line is fed to a standard BNC coax connector, and to an LED, whose flashing acts as a visual check that the controller is functioning. 5.5.4 The SBC Software The SBC software was originally developed by M. Hooker and M. Bartholomew in the ICSTM Astrophysics group electronics workshop, and was later modified to tailor it for the S-Z instrument. The program is basically divisible into 3 parts, an initialisation routine, an interrupt routine, and the main program. The Initialisation Routine This initialises all the modules to their default states; i.e. 3 channels, up/down mode, a chop rate of 7.63 Hz, a postamp gain of 1 (gain number 0), and an RS-232 speed of 9600 baud. 169 The Main Program This accepts commands from the User computer and acts on them. Most of the time it will be monitoring the RS-232 for incoming data from the User’s computer. The Interrupt Routine This is either called by an interrupt from the counter enable VIA or the RS-232. When called by the counter enable VIA, the counter direction is changed if up/ down counting is in use. If the required number of chop cycles for a complete integration have passed, the counters are latched and their contents are read out and reset. All the necessary data for transmission to the User computer is then assembled in the output buffer, including the time, gains and counter values. The RS-232 then sends a flag (HEX 38) to the User computer telling it that a data block is ready, and RS-232 interrupts are enabled. If the interrupt is from the RS-232, a check is made to see if the User computer has indicated that data is ready to be sent. If it has not, another data ready signal is sent. If it has, then the next byte from the data buffer is sent. After the data buffer has been emptied, the RS-232 interrupts are disabled, and execution continues. 5.6 The Operator’s Computer The final part of the instrument control system is the operator’s computer, a BBC micro, usually housed in the telescope control room. This communicates with the digital rack via an RS232 cable. After the initial setting up of the instrument, all of its functions can be controlled from this computer. It also stores the data from the instrument to floppy disk, performs some initial processing so as to provide some information on the progress of the observations and produces an optional printed summary of the observing. In addition, a D to A converter, attached to the BBC’s User port can produce a strip chart record of the observations in a selected channel of the instrument. 170 5.6.1 BBC Micro Software The software for the BBC micro is written in 6502 machine code and in BBC BASIC. The program can be divided into two sections, an interrupt-driven routine, and a program for normal operations. The Interrupt Routine The interrupt routine is written wholly in 6502 machine code, using the BBC assembler. It is triggered by an interrupt from the RS-423 interface, indicating that data is arriving from the digital electronics rack. Once triggered, the BBC remains in the interrupt routine until all the data from the digital rack is sent, so that there is no chance of data being lost. Once the routine has started, an acknowledge character (HEX 06) is sent to the digital rack to indicate that the BBC is ready to receive data. The data packet is then transferred, and stored to the data buffer. Once the data packet has been transferred, the interrupt routine checks the command buffer for any commands to be sent to the digital rack. Commands axe only sent after receiving data, so that numbers, and not just ASCII characters, can be sent without the possibility of their being mistaken for an acknowledge character. Finally, if enabled, the routine sends the value of the selected channel to the user port, for output, via the A/D converter, to the strip chart. The Main Programme The main programme is written in BBC BASIC, with some 6502 routines to handle keyboard control. It is designed to make operation of the instrument as simple as possible, and to allow the user to monitor the progress of an observation. It displays channel values, gains, and UT as each data packet is sent. It also demodulates the nodding, and calculates a running mean and standard error for each channel as an integration progresses. It also controls the telescope nodding, sending the required command to the digital rack after the required number of chop cycles for a half nod cycle are completed. The telescope is allowed to settle 171 after the nod for a complete integration time. Thus if 2 chop cycles per nod was required for the astronomical data, the BBC program would cause 3 cycles to occur each nod cycle. The first of these takes place at the same time as the nod, and is therefore discarded. The data received from the digital rack are stored in several arrays, and are written to disk after completion of an observation. Commands are entered via the keyboard, and are placed into a command buffer for transmission to the digital rack immediately after the next data packet is received. 5.6.2 User Commands at BBC Micro Commands to the SBC system are available from the keyboard at the user’s com puter. They are all accessed by typing the relevant letter and then any necessary numbers afterwards. A carriage return then terminates the input. The keystrokes are not echoed on the BBC screen since data readout continues while commands are typed. The following commands are available. Where required, numbers to be entered after the command are indicated by n. S Start the PSD system running. X n Set the number of channels. The default number of channels on start up is 3. G n n Set the post amplifier gains. The numbers indicate the channel first (1 to 3) and the gain number (1 to 7) second. Several amplifiers may be set by giving additional pairs of numbers before the carriage return. The gain numbers are described above. C n Set the chop number. This selects the chop period from a range of 20 possible. The chop number is a hexadecimal number ranging from 0 to 1 C, giving frequencies ranging from 61.04 Hz (chop number 0), to the default, 7.63 Hz (chop number 1 C). F n 172 Set the phase difference. This command changes the phase difference between the chop waveform and the counter enable/disable signal, allowing for proper phasing up of the system. The command ‘F ’ is followed by a series of numbers, l ’s or 2 ’s which respectively decrease and increase the phase difference by changing the time difference between the two waveforms by 0.5 milliseconds for one cycle. Readout from the digital PSD system continues while the phase changes are made, so that the output can be maximised in the space of one command. The process consists of typing ‘F ’ and a series of l ’s and 2 ’s and a carriage return when the phase adjustment is complete. P Reset the phase difference. This resets the phase difference to that set previ ously by the ‘F’ command. I n Set the integration time. This sets the integration time in number of 1/2 chop cycles per integration. The number is a hexadecimal ranging from 0 to FF, and should be even. The default value is 20 (1 C in hex). N Nod the telescope. This causes the SBC to send the appropriate command to the telescope control computer to cause the telescope to nod. The appropriate character to send over the telescope RS232 interface must be set up beforehand. At TIRGO, for example, the characters were 1 and 2 for the -f- and - beams. D Set up/down mode. This command sets the counters to operate in up/down mode, the normal mode for astronomical observation. U Set counters to up only mode. This command sets the counters to count up only. Other commands are available which control the BBC’s data capture opera tions, rather than the SBC based digital PSD system. They are as follows. R Start an integration. A 173 Abort an integration. F I to F3 This selects the channel whose output is sent to the chart recorder. Left and R ight cursor keys These increase or decrease the gain on the chart recorder output. The chart recorder D to A works with only 8 bits, and these commands select the 8 bits to be used. Thus if the ’gain’ is set too low, only the lowest order bits from the counter value will be plotted, so no real information on the overall shape of the output wave will be plotted. The gain controls should be used to select the most significant non-zero bits in the value being output. Other functions of the BBC program are controlled by prompting the user for responses. This is mainly done at the start of an observation, and includes setting the number of nods required in the observation (which in effect sets the integration time), whether hardcopy output is needed etc. Also required are the name of the object to used, and header information, which are both saved to the data file for later use. The header block can be used to include observing notes in the output data file, or to store useful data, such as airmass, humidity etc. 5.6.3 Screen Outputs to Operator It is extremely important for a user to be able to assess the performance of an observing run whilst that run is in progress so that any errors, problems or un expected effects can be identified, and the appropriate action can be taken before too much observing time is lost. To this end, the BBC micro program for the 3 Channel system provides some limited data reduction facilities to produce imme diate information about the observations. This is all done on screen, in front of the operator. The operator’s screen consists of two sub displays in the top and bottom halves of the VDU. The lower part of the screen contains a constantly-scrolling display of the counter value for each channel as it is read out. Thus, in normal operation, this contains 3 columns of scrolling hexadecimal numbers. The upper display contains information on the progress of the current observa 174 tion. At the top is a summary of the parameters of the observation: object name, chops per nod, nods per observation, and how many of each have been completed. Below this is a table showing the progress of the observation for each channel. This shows the postamp gain for each channel, which channel is selected for the chart recorder D to A, and the D to A gain, the mean, and the standard error, of the signal in each channel so far. This information is calculated with the nodding demodulated, and so presents a good idea of the real astronomical signal. Finally, the universal time is printed below this. 5.6.4 Structure of SBC Datablock The data sent from the SBC system to the BBC micro via the RS232 has the following format: hh m m ss Time: 3 bytes containing hour, minute, and second values in hex. nn No. of channels: 1 byte containing the number of channels to be sent in hex. g lg 2 etc. Gains: A series of bytes containing the appropriate channel’s gain in highest and lowest nibbles respectively, slh slm sll etc. Signals: 3 bytes per channel sent, containing the counter values’ highest, mid dle and lowest order bytes. 5.6.5 Structure of BBC Data Files The data from the instrument is stored to the BBC micro’s floppy disk. The data format for a file is as follows. Block N am e Character string containing the block identifier. Header information Character string containing additional information on block. Time (hhmmss) Nod position (+1 or -1) 175 Channel gains (ni n 2 n3) Signals (si s 2 s3) Apart from the character based headers, all information is stored in BBC BA SIC numeric format, as denary numbers spaced with tab’s and carriage return/line feeds. The time is stored as a single 6 digit number (hhmmss); nod is either 1 , for positive beam, or - 1 for negative; the gains are the appropriate gain numbers for the remote control postamps; the signals are denary conversions of the hex values sent from the counters. 5.7 Tests of PSD System A range of tests were applied to the digital PSD system. The results of some of these axe summarised here. 5.7.1 Phasing Test A crucial part of the PSD process is the ability to shift the phase of the demod ulation process with respect to the output chop waveform. The permits phase shifts in the observing system to be accounted for when operating at a telescope, and allows retrieval of signals in phase with the reference. In this system this is achieved by shifting the counter up/down control signal with respect to the chop waveform in steps of 0.5 millisecond. This process is tested by taking a signal in phase with the chop waveform, and feeding this into the PSD input amplifiers, and using the F command to find the output counts over a range of phase shifts. This process effectively takes one square wave, the chop waveform, and convolves it with another square wave, the up/down waveform, with the ordinate being the phase shift. The output should thus be a triangular wave. Figure 5.12 shows the result of this test, demonstrating that the phase shifting system works well. As can be seen from this diagram, the maximum (and minimum) points axe quite distinct. The phasing up process is thus relatively easy in spite of the absence of a 90 degree automatic shift such as those provided on analogue PSDs such as the Ithaco Dynatrac. 176 60000 40000 a oq 20000 *-»£ 0> Ot to * e £ •P*tr< ft)(/) cn 0 a oo COe** 9 •♦oQ. a . 9 O tr* g -20000 £ £c n -40000 -60000 Phase Shift 5.7.2 Linearity and Calibration Tests To perform as an adequate PSD system, the calibration factor, in volts per count, should be constant over a large range of input voltages. Any non-linearities over the range can, for example, produce false signals. To test the linearity, an input signal driven by the chop waveform is provided, at variable voltage. The output signal is then compared to the input signal, using an Ithaco Dynatrac to measure the input voltage. Two ranges of input voltage are shown, one at low levels, similar to those we might expect during observations at a telescope. These required the postamp to have a gain of 1000. The other range was at high levels, around 1 V, and used a gain of 1 on the postamp. The output counts from these two tests range from 0 to 40000. The results of these tests are shown in figure 5.13. As can be seen from the figure, the calibration is linear over the ranges covered in both tests. Any non-linearity in the low voltage test is < 2%, whilst in the high voltage range it is < 0.2 %. The calibration factors, counts/V, for the two plots are determined by the postamp gains and by the characteristics of the V to F converter. For zero gain the calibration is expected to be 9500 ± 400, and it is found to be 9700 ± 300 counts/V. The calibration factor for the low voltage range is found to be 1110 0 dr 800 counts/V once the postamp gain of 1000 is accounted for. The digital PSD thus provides a detector which can retrieve the small signals expected in astronomical observations. 5.7.3 Summary In the tests detailed above, and in a number of others, the Digital PSD system performed well, and demonstrated its suitability for use with the 3 Channel Pho tometer. 5.8 Tests on the Instrument Before use at a telescope a number of tests were performed on the instrument as well. Those most relevant to the following chapters are detailed here. 178 O DPSD gain -1 DPSD Linearity Test o d p s d Signal DPSD Linearity Test 350 /f t 300 _ 250 - , r 200 150 A 100 r 50 _ 0 0 10° 5 !0 '3 1 10'2 1 10'2 2 Iff2 2 Iff2 3 Iff2 3 10'24 10'2 Input Y (mV) Figure 5.13: Calibration of Digital PSD System 180 5.8.1 Beam Scans Typical results of laboratory beam scan measurements are shown in figure 5.14. These were performed using a chopped black body source which was focussed onto the input lens of the instrument. The measured black body beam is small (about 20 mm width at the pupil) compared to the size of the entrance pupil (about 80 mm), so the measured beamsize will only be slightly broadened from the actual beamsize. In this configuration the instrumental beam is expected to be about 4.8 degrees, with a roughly Gaussian shape. The figure shows the instrumental beam for the 1.1 mm channels, and similar results axe found for the other channels. A Gaussian is fitted to the measured beam and is also shown. The beamwidths measured for all channels are about 10 % smaller than that expected, with full width 1/e points 4.2 degrees apart. The beamshape measured matches a Gaussian well, but with somewhat stronger wings, whose response is about twice as strong as the fitted Gaussian at the extremes of the beamscan. 5.8.2 Noise Tests These were carried out by Peter Ade using equipment at QMW, with the cryostat aperture open to a room temperature background. The noise on the output voltage from the detectors with the instrument fully functioning was found to be about 35 nV Hz-1/2 [1], Since the conditions under which these measurements were made were broadly similar to those during an observing run, this represents a reasonable estimate of the noise that should be attainable at a telescope. The source of most of this noise is the load resistor, a metal film resistor of 47 Mft. This will produce Johnson noise of about 30 nV Hz-1/2 at 0.35 K. The remaining noise will be from the detector element itself which is expected to produce about 6 nV Hz-1/2 noise with the bias voltage of 1.5 V supplied during this test. 5.9 Summary The ICSTM 3 Channel Millimetre Wave Photometer has been designed specifically for observations of the S-Z effect, and for CBR studies in general. With large 180 Angle (degrees) Figure 5.14: Measured Instrumental Beam, and Fitted Gaussian The measured beam is solid, with the fitted Gaussian dashed. 182 throughput, 2 astronomical channels, and a third channel to allow for the detection and removal of atmospheric sky noise, it represents a major improvement upon existing common user instruments for such studies. After these tests, observing time was awarded, and the instrument saw first light. The results of this observing trip are the subject of the next chapter. 182 C hapter 6 Observations with the 3 Channel P hotom eter 6.1 Introduction In February of 1990, the ICSTM 3 Channel Millimetre Wave Photometer saw first light at the Italian 1.5 m TIRGO telescope. In this chapter I discuss the mechanical, optical and electronic interfacing to the telescope, the performance of the instrument and its ancillary systems, and the results obtained at the telescope. 6.2 The TIRGO Telescope The TIRGO telescope is situated at the Gornagrad Nord station on top of the Kuhlnhotel at Gornagrad in Switzerland. Its altitude is 9600 feet and, during winter, the weather is generally cold and dry. It is primarily used for infrared and optical observations, but provides an adequate site for observations at mil- limetre/submillimetre wavelengths - indeed, a German 3 metre millimetre wave telescope is stationed at the same site. 10 nights of observing time was awarded to us at TIRGO for the commissioning of the 3 Channel Photometer. 183 6.2.1 Telescope Mounting TIRGO has all its instruments mounted at the Cassegrain focus. Up to four instru ments can be mounted around a cube bracket, each with an appropriate dichroic or mirror which can be inserted into the telescope beam when required. In its normal configuration, two pointing cameras are mounted on the telescope, one on the straight-through track of the cube (i.e. at the conventional Cassegrain focus) and another at one of the cube stations. To mount the 3 Channel Photometer onto the telescope, a special mounting bracket had to be made to fit the TIRGO standard mounting. In addition, the cryostat, and thus the instrument, was elec trically and, to an extent, mechanically isolated from the rest of the telescope with polyethylene sheeting. A front-silvered plane mirror was used to reflect the beam into the focal station of the instrument, and placed in the standard dichroic cell. This meant that the object observed by the photometer could not be observed by the telescope pointing camera at the same time. All pointing checks, therefore, had to be made before millimetre wave observations commenced. This included checks on the chop and nod directions and throw. However, since the 3 Channel Photometer’s input beam on the sky is large, no pointing problems were expected to ensue from this arrangement. 6.2.2 Optical Arrangement Only one modification to the usual set up of the 3 Channel photometer was neces sary for its operation on TIRGO. The TIRGO beam is f/20 rather than the f/12 for which the instrument is designed. To cope with this, and to prevent any ex traneous signals from the telescope support structure that might enter the larger beam, an additional cold stop was mounted at the cold input lens at the He4 ra diation shield. This reduced the size of the input beam, so that the instrumental beam did not fall off the secondary mirror, whilst ensuring that little or no extra thermal loading was placed on the detectors or the He3 cold surface. 184 6.2.3 Electronic Interfacing The 3 Channel Photometer electronics must interface with the TIRGO electronics at two points: firstly, to provide a sufficiently large chopper signal so that a chop amplitude of about 10 arcminutes could be produced; secondly, to control the nodding of the telescope. The chopper signals, provided by the chopper amplifier, are fed via coax cable directly to the chopper control system. The standard chopping system at TIRGO uses a signal generator to produce a square waveform of the required frequency. The limiting output voltage from this is 5 V, and produces too small a chop throw for use with the 3 Channel Photometer. Using the chop amplifier, the analogue electronics can produce a square wave output at the appropriate chop frequency with an amplitude as high as 25 V. The nod control for the telescope is provided by the host telescope computer, a PDP- 11. This can be set to shift between two positions, a pre set distance apart in RA and Dec, when it receives appropriate command characters via an RS-232 interface. One of the RS- 232 interfaces on the Digital Electronics box was used to do this, and a routine was written to send the appropriate characters, a ‘1’ for beam 1, and a ‘2’ for beam 2, to the host PDP- 11 when a nod was required. In addition to the digital PSD system, a backup analogue PSD system was also used. This was an Ithaco Dynatrac 3 analogue lock-in amplifier. The only signals this needed from the telescope were the chopper signal and the instrument output. In use, this was integrated with the telescope systems by using two cables from the dome to the control room carrying the appropriate signals from the instrument and the chopper control system. 6.3 Observations The majority of the observations were made to test the instrument and control systems, with actual observations of the S-Z effect, or other astronomical sources of interest, at the lowest priority. The two separate systems of signal detection used different methods of data logging; the Digital PSD stored its data to disk in numerical format, while the Ithaco produced output on a strip chart. 185 10 nights of time on the 1.5 metre were assigned to the first observations by the 3 channel photometer, from the 8th to 18th February 1990. This would have been adequate both for the testing observations and for initial astronomical ob servations. However, in the event severely bad weather curtailed our observations to only 1 and a half nights, on the 18th and 19th February, which were adequate only for testing operations. For the test observations, there were 3 main tasks. Firstly to validate the telescope control system and procedures, secondly to use a bright source, such as a planet, to map out the beam shape, and thirdly to demonstrate the feasibility of the atmospheric sky noise subtraction technique. Test observations on objects fainter than the planetary sources could also be made. 6.4 Telescope Control System The telescope control system, described above, was tested using the built in in struments of the telescope to measure chop throw, mirror performance, and nod throw. The chop and nod systems will be covered in turn. 6.4.1 The Chopper System The output of the chopper amplifier is fed directly into the telescope’s chopper controller, which takes an input waveform, and moves the secondary mirror to a position dependent on the amplitude of the chopper signal. The direction of the chop, RA, DEC or somewhere in between, is separately controlled. To check on the performance of the chopper, a sensor measures the actual position of the secondary mirror, and this is fed back to the telescope control room as a separate signal. The actual chop throw could be measured via the TV monitor connected to the acquisition cameras on the telescope. Using a chop frequency of 7.63 Hz, measurements showed that a driver peak-to-peak voltage of about 12 V gave a chop throw of about 10 arcminutes, which was adequate for our observations, and that a dead time of 2 milliseconds was adequate to cope with the chopper moving time. With higher amplitude chop throws the motion of the chopper, as measured by the sensor, became less and less like a square wave, so that the 186 telescope performance would be greatly degraded if we were to use higher output voltages. 6.4.2 The Nod System The nod control was via the host PDP-11 minicomputer, and was initiated by sending the appropriate ASCII character to this machine via one of the digital rack’s RS-232 ports. The nod amplitude and direction is set via the telescope control panel to be equal to the chop amplitude. The nodding is then monitored on the control room TV. This system was also found to operate well. 6.5 Observations of Jupiter Jupiter was chosen as the main test source for these observations for several rea sons. It is one of the brightest millimetre/submillimetre sources in the sky, has a well determined temperature and size, and was not extended beyond the ex pected size of the instrument’s beam. It was also available for much of the night during our observing run. Later analysis used fluxes calculated by the program JCMTJFLUXES, described earlier. 6.5.1 Pickup Problems It was during these initial observations that it became clear that we had a severe problem with some source of electrical noise. The oscilloscope monitoring the output from the instrument showed a clear oscillation at, or near to, 25 Hz with an amplitude of about 50 mV at the preamp output. Meanwhile the Ithaco output trace showed a distinct sinusoidal variation (see figure 6.1), possibly due to this strong signal beating with the chopper frequency. The DPSD, with poorer high frequency rejection than the Ithaco (gain of about 0.2 at 25 Hz for DPSD compared with gain of 0.02 for Ithaco - also see Appendix A), and less time resolution in the data finally stored to disk, had its sensitivity greatly reduced . The origin of this noise component is unclear, but similar problems, due to electrical pickup or microphonics, have been noted by other observers at TIRGO 187 [158]. The effect was strongest when the telescope was tracking, dropping by a factor of about 5 when the telescope was parked, and so may be due to some part of the drive system. It was also absent when the instrument was removed from the telescope mounting. Unfortunately, since the weather only cleared on the last night of our observing time, we did not have enough time to properly track down and eliminate the source of the problem. Parts of the system which may allow microphonic or electrical pickup include the mounting and electrical connections of the bolometers on the He3 cold surface. The three detectors are mounted on a bracket connected to the cold surface at one point. The bolometer for the 2.1 mm channel is connected nearest to the bracket, while the 1.1 mm channel is furthest from it, and the 1.6 mm detector is intermediate between the two. The bracket is asymmetrical, with a long arm reaching to the 1.1 mm channel bolometer in one direction, and only a short arm for the 2.1 mm channel. This arrangement could lead to microphonics if the bracket arm can vibrate. In addition, the connections for the bolometers are wound round the bracket, and so can, in principle, act as a solenoid aerials. The length of these connections are in the dependent on the bolometers position on the bracket. If the spurious signal at 25 Hz is due to microphonics or electrical pickup at these points, then the strongest effect would be seen in the 1.1 mm channel, with other channels seeing the effect lessen with increasing wavelength. As will be seen in the data presented below, this is indeed the case. This result has motivated a number of subsequent changes on the cold surface which will be described in Chapter 7. 6.5,2 Optical Responsivity and Sensitivity Figure 6.1 shows the output from the analogue PSD for the signal from Jupiter at 1.1 mm. The planet is clearly detected with a very high level of significance. The total output voltage from the Jovian signal is about 6 V peak-to- peak, implying a signal at the bolometers of 2 x 10-5 V. From the program JCMTJFLUXES, the flux density from Jupiter at 1.1 mm, over its entire surface, is « 14000 Jy. Given the instrumental bandwidth of 60 GHz, this implies that the instrument 188 has a total optical responsivity at 1.1 mm of 1.3 x 106 V W-1. The detector responsivity with the bias voltage of 1.5 V used here, is « 1.5 x 107 V W_1 (see Chapter 5), which implies that the optical efficiency of the system is about 9 %. for the 1.1 mm channel. Bearing in mind that the bandpass filter transmission is about 45 % at the peak, of the 1.1 mm passband, this means we have further losses of about a factor of 5 within the rest of optical system, including telescope and instrument. Comparing this figure to the electrical noise of « 35 nV Hz-1/2 measured in the lab at 7.2 Hz, we obtain the optical NEP of the instrument, in the absence of the extraneous pick up noise. The instrumental NEP is thus « 2.5 x 10-14 W Hz”1/2. 6.5.3 Beam scans Beam scans were performed on Jupiter to measure the instrumental beamshape. They were made with the chop aligned purely in declination, with a throw of about 10 arcminutes. The beamscans are shown in figure 6.2. The throughput of the instrument was reduced for the TIRGO observations from the design value of 25 fisr m2 to 9 /zsr m2 to cope with the slower aperture on the telescope. The beamsize should thus be about 8.5 arcminutes full width. From the scan plots, measured FW -l/e beamsizes are 8 ± 0.5 arcminutes in both RA and DEC. This is close to the designed beamwidth, but is also consistent with the « 10% smaller size measured in the laboratory. For a proper assessment of the beamshape, including sidelobe response, better quality data is still required. In an ideal situation, integrations should be performed at positions offset from the source location out to quite large angles to properly map out the beam and to assess the instrumental response to any side lobes. With the strong noise problems we were experiencing, though, this was not possible. 189 Figure 6.1: Ithaco Output from Pointed Observations of Jupiter. 191 I Figure 6.2: Beam Scans obtained at TIRGO BW W 'W WI ll '■» 192 Observation Chan 1 Chan 2 Chan 3 (counts) Zenith Scan, No Nod 12530 ± 63 1419 ± 15 1451 ± 7 Closed Off, No Nod 542 ± 105 -431 ± 29 53 ± 7 Blank Sky with Nod -344 ± 413 -384 ± 68 147 ± 25 Table 6.1: Blank Sky Results 6.6 Blank Sky Observations Blank sky observations at the zenith, and at other positions, were made to test the sky noise subtraction scheme. These observations were made both with an integration times of 1.8 s (or 5 s in the case of the nodded block), with a 10 arcminute chop throw, both with and without nodding. Comparison runs were also made with the instrument’s input closed off, so that the device saw only a reflective surface at ambient temperature. The results in table 6.1 show the mean and standard error of a block of these observations consisting of 100 chop cycles. One thing was clear from these runs without postprocessing; a large offset, of 12530 ± 63 counts in the 1.1 mm channel, was present in the non-nodded data. This is due to some optical signal since it is not present in the closed off runs (see table 6.1). This is possibly due to the large chop amplitude taking some part of the telescope beam off the primary, so that it sees the telescope superstructure at ambient temperature. Nodding, however, removes most of this term. 6.7 Data Analysis While much of the data is contaminated by the spurious pickup described above, we can still attempt to reduce this contribution in the astronomical channels by using cross correlation with the atmospheric channel. This process may be applied to both the blank sky and Jupiter data, whether the observations included nodding or not. 192 6.7.1 A Method for Noise Subtraction The 3 channels of the photometer receive astronomical signals at 1.1 mm and 2.1 mm and sky noise signals at 1.6 mm. The 1.6 mm channel lies in the wings of an atmospheric water vapour line, and we assume that no astronomical flux penetrates the atmosphere in this band. We further assume that the time variation of the atmospheric sky noise is the same in all three bands, since water vapour is the dominant species in atmospheric emission in all the channels. For spurious signals coming from microphonics or electrical pickup, this latter assumption will also be true since all channels are likely to be contaminated, to a greater or lesser extent. The signal S\ in each of the three channels will thus be: 5 2.1 — + F 2.1 S1.6 = a ^ N (i) (6.1 ) 5 1.1 = + F 1.1 where the coefficients a\ represent the strength of the sky noise N (t) in each of the observational channels, F represent^ the astronomical flux in the two observational channels, and S/amMa gives the total output signal. Subscripts indicate the relevant observing wavelength in millimetres. The degree of correlation between the astronomical channels and the sky noise channel is dependent on the atmospheric conditions prevalent during the obser vations which vary over the course of a night, as has been clearly demonstrated in Chapters 2 and 4 . The effect of the spurious pickup signal may also vary over time. It is thus necessary to apply the sky noise correction to the data on a block by block basis, with the correlation factor being determined for each block in turn. The correlation factors a\ may be calculated by simple least squares regres sion techniques. If the signal values in astronomical and atmospheric channels measured at a given time axe treated as the y and x coordinate respectively of a position on a 2-D plane, then a simple linear regression of y on x will give the correlation factor a\ for the appropriate astronomical channel. Thus: n S Si.iSi.6 — S 5 i .i S 5 i .6 ai l~ nS5?.6 - (ES,.^ ( ' ’ where n is the number of points within the block. A similar equation yields the correlation factor for the 2.1 mm channel. The correlation coefficient R [11] will 193 also give an indication of the significance of the correlation. This is given by: n ______nSSi.iSi.6 — S5i.iS5t.fl______, . “ (nSSf.e - (S51.6)2)i/2(nS512! - (E S^)2)1/2 K ' } and similarly for the 2.1 mm channel. This function has a value of +1 for a perfect correlation with positive gradient, through zero for no correlation, to -1 for perfect correlation with a negative gradient. Once the values of a\ are known, the correlated part of the signal in each of the astronomical channels may be subtracted, leaving only the true astronomical signal. Thus: F\ = 5a - axSi.e (6.4) Each point in a given block of observations is corrected by this procedure, using the correlation factors calculated for that particular block. This correction procedure was applied to the observational data recorded by the digital PSD system. The results are detailed below. 6.7.2 Results on Observations with Cryostat Blanked Off These observations were made with the tertiary mirror in the telescope mounting cube closed, so that no signals could reach the instrument from the telescope. This enabled tests to be made on the spurious pickup signal which was found to contaminate much of the observational data. These tests, though, were made with the telescope parked, while the most severe noise contamination occured while tracking an astronomical source. An integration time of 1.8 s was used. The means and standard errors for these blocks of 100 points are shown in table 6.2. A number of conclusions may be drawn from this data. Firstly, there is clearly a significant spurious signal from the instrument when there is zero input optical flux. Secondly, there is a strong correlation between channels 1 and 2, whilst channel 3 is baxely affected by the correlated signal. The geometry of the detec tor mounting may well account for the different effects of the spurious signal in different channels, as discussed above. Finally, the correction procedure reduces the noise in channel 1 by up to a factor of two. These results confirm that the correction procedure does indeed remove noise correlated between one channel and another, with the standard error in the 1.1 194 Channel 1 Channel 2 Channel 3 Obs 1 Unprocessed -5104 ± 327 -404 ± 27 -1 ± 12 Obs 1 a\ 9.9 0.07 Obs 1 R 0.94 0.093 Obs 1 Corrected -1117 dh 193 -404 ± 27 26 ± 11.6 Obs2 Unprocessed -5103 ± 317 -431 ± 23 19 ± 7 Obs2 a\ 13.1 0.08 Obs 2 R 0.98 - 0.1 Obs 2 Corrected 542 ± 105 -431 ± 23 53 ± 7 Table 6.2: Results from correlation analysis of blanked off observations mm channel typically being reduced by a factor of 2/3. They also confirm the presence of an annoyingly strong source of noise local to the observational system, at least a factor of 10 higher than might be expected from the system noise, which contaminates channels 1 and 2 much more than channel 3. 6.7.3 Results on Zenith Scans These observations were made with the telescope pointing at the zenith with a 7.5 Hz chop frequency and a chop amplitude of 16 arcminutes. No nodding was performed, and an integration time of 1.8 seconds was used. Block means and standard errors are again given for blocks of 100 points. These results continue to demonstrate the strong correlation between the 1.1 mm and 1.6 mm signals, with correlation coefficents, R, typically > 0.9. The correction scheme is not as effective with this data, though there is a consistent reduction in the 1.1 mm channel’s noise of around 10 % for most of this data. 6.7.4 Results on Blank Sky Observations These results come from a drift scan at a position away from the zenith. Chop ping and nodding was in DEC, with a throw of about 10 arcminutes and a chop frequency of 7.5 Hz, whilst the sky was allowed to drift in RA. For this run, and the subsequent observations of Jupiter, the integration time was increased to 5 195 Channel 1 Channel 2 Channel 3 Obs 1 Unprocessed 14879 ± 68 1419 ± 15 1520 ± 7.4 Obs 1 a\ 1.7 0.05 Obs 1 R 0.995 0.994 Obs 1 Corrected 12530 ± 63 1419 ± 15 1451 ± 7.4 Obs 2 Unprocessed 12764 ± 85 1158 ± 17 1451±8 Obs 2 a\ 2.6 0.14 Obs 2 R 0.99 0.99 Obs 2 Corrected 9796±72 1158± 17 1286± 7.6 Obs 3 Unprocessed 10573± 135 929 ± 14 1408 ±7.4 Obs 3 a\ 5.3 0.07 Obs 3 R 0.99 0.98 Obs 3 Corrected 5615 ±110 929 ± 14 1344 ± 7.3 Obs 4 Unprocessed 9634 ± 155 865 ± 21 1375 ± 11.6 Obs 4 a\ 2.3 0.11 Obs 4 R 0.97 0.97 Obs 4 Corrected 7629 ± 148 865 ± 21 1281 ± 11.4 Obs 5 Unprocessed 9236 ± 166 828 ± 19 1269 ±14.8 Obs 5 ax 4.4 0.09 Obs 5 R 0.98 0.97 Obs 5 Corrected 5605 ± 143 828 ± 19 1269 ± 14.8 Obs 6 Unprocessed 8570 ± 170 737 ± 23 1353 ± 16.5 Obs 6 a\ 3.0 0.32 Obs 6 R 0.96 0.96 Obs 6 Corrected 6360 ± 155 737 ± 23 1115 ± 14.7 Obs 7 Unprocessed 8010 ± 166 669 ± 20 1351 ±6.9 Obs 7 a\ 3.0 0.1 Obs 7 R 0.96 0.96 Obs 7 Corrected 6019 ± 154 669 ± 20 1285 ± 6.6 Table 6.3: Results from correlation analysis of blanked off observations 196 Channel 1 Channel 2 Channel 3 Obs 1 Unprocessed -3408 dh 679 -384 ± 68 125±25 Obs 1 a\ 8.0 0.06 Obs 1 R 0.87 -0.26 Obs 1 Corrected -344 ± 413 -384 ± 68 147 ± 24 Table 6.4: Nodded Blank Sky Results Channel 1 Channel 2 Channel 3 Obs 1 Unprocessed 71408 ± 17425 50023 dh 19148 15549 ±4077 Obs 1 a\ 0.91 0.20 Obs 1 R 0.97 0.95 Obs 1 Corrected 26091 ± 1646 50023 ± 19148 5642 ± 1497 Table 6.5: Jupiter Results seconds from the previous value of 1.8 s. Mean and standard error is given for a block of 100 points. This test represents a realistic observational scenario for drift scan operation. It clearly demonstrates the combined effectiveness of nodding and correlated noise subtraction.The residual counts are small and reasonably close to zero, whilst the noise in the 1.1 mm waveband has been reduced by a factor of about 1.6. The 2.1 mm channel continues to be relatively poorly correlated with the 1.6 mm channel, and the efficacy of the noise subtraction scheme at this wavelength is debatable. 6.7.5 Results on Jupiter These observations use similar parameters to the blank sky drift scan run, with the exception that a source, Jupiter, was tracked across the sky, and the observation consists of only 40 points. The full telescope drive system was thus used, which is associated with the most severe instances of the pickup or microphonic signal discussed earlier. This effect is borne out in the results in table 6.5. These were the first results taken while the telescope was tracking an object on the sky. It was under these circumstances that the 25 Hz signal most severely contaminated our data, and the resulting increase in ‘noise’ is clearly demonstrated 197 in the above data. The noise per integration time is up by from 16 to 100 times in different channels. However, we nevertheless achieve a reasonable detection of Jupiter in the 1.1 mm channel, and a marginal detection at 2.1 mm. The noise reduction technique is very successful here, reducing the 1.1 mm channel noise by a factor of about 10, and the 2.1 mm noise by a factor of about 3. However, the noise being removed here is not the sky noise the system was designed to detect, but is mainly due to the 25 Hz signal which we found was associated with telescope tracking. 6.7.6 Summary These results demonstrate the efficacy of the sky noise subtraction method in removing a non-astronomical signal from a source that is well correlated from one channel to another. The scheme works best for the 1.1 mm channel, which one would expect to suffer most severely from the sky noise produced by variations in the same water vapour line as is measured by the 1.6 mm channel. However, the source of most of this noise was not atmospheric water vapour fluctuations, but the spurious electrical signal found to contaminate much of our data. Quite how well true sky noise can be suppressed by this technique is still an unknown factor, though the basic scheme for correlated noise removal performs reasonably well. In earlier S-Z effect measurements at millimetre wavelengths, Meyer and coworkers [113] achieved a sensitivity improvement of more than 2 by a similar multichannel technique, and we should be able to approach this level of effectiveness. 6.8 Discussion and Conclusions These observations at TIRGO with the 3 channel instrument clearly do not repre sent an exhaustive and thorough test of the instrument’s observational capabilities. The weather and noise problems placed a strong limit on the observations that it was possible for us to make. While further work is necessary before the instrument is ready for full astronomical use, several conclusions can be drawn. Firstly, the predicted system performance on TIRGO, in the absence of spu rious noise, represents a la Is sensitivity of about 23 Jy. The S-Z effect flux 198 increment at 1.1 mm is about 200 mJy //sr-1 mK-1. For a cluster that fills the TIRGO beam of 8.5 arcminutes, this then converts to a flux of about 1 Jy mK-1. We could thus detect the S-Z effect in 0016+16 at « 3 199 C hapter 7 Future Developments: Cosmic Background Observations at Millimetre and Submillimetre Wavelengt hs 7.1 Introduction The previous chapters haveillustrated the current status of the ICSTM 3 Channel Millimetre Wave Photometer, and S-Z effect astronomy in general. It is clear that the system as it currently stands is in need of a number of improvements and enhancements. In this chapter a number of these future enhancements are detailed, as are possible strategies for achieving some of the observational objectives that we were unable to test during the first run at TIRGO. The future development of the ICSTM instrument, both as a tool of observational cosmology, and in other fields is discussed here. Also discussed are other future programs of importance to the study of the S-Z effect and the CBR in general. 200 7.2 Development of the ICSTM 3 Channel Mil limetre Wave Photometer The first observations at TIRGO with the 3 Channel instrument clearly demon strate that some further development of the system is required. One specific area is the need to eliminate the « 25 Hz noise that interfered with these observations. There axe several possible methods for achieving this. The ideal solution would be to identify the source of the noise and eliminate it from the telescope environ ment, or prevent this signal from being picked up in the bolometer circuits. This latter option may be achieved by rewiring the bias and detector circuits within the cryostat, minimising ‘flying’ wires and reducing the length of the cabling gen erally. This would have the effect of reducing both RF pickup and microphonics. Additionally, cold FETs, mounted on the He4 surface, could be used instead of the warm FETs currently mounted in the external preamp box. This would have the effect of reducing the length of wire acting as a high impedance connection before the FET stage, thereby cutting out much of the wire which can act as an RF antenna. This modification does introduce the additional problem of keeping the cold FET stage at a stable temperature above the minimum operating point of the devices (about 77 K). Instruments such as UKT-14 and its predecessor UKT-12 use such cold FETs successfully. Initial tests on the 3 Channel Photometer using a prototype cold FET stage [41] indicate that this technique may substatially re duce RF pickup and microphonic effects in the instrument, but no noise figures are yet available, and the modified instrument has yet to be succssfully used at a telescope. 7.3 Future Observations of the S-Z Effect with the 3 Channel Photometer While TIRGO forms a useful test bed for the 3 Channel Photometer, the instru ment is primarily designed for use at the JCMT. Stationed at the f/12 Cassegrain focus, the instrument can use its full throughput of 25 ^tsr m2, and benefit from 201 the much greater collecting area of the telescope. On the JCMT the instrumental beam will be reduced to 1.5 arcminutes, which is better matched to the more dis tant and compact S-Z clusters. Assuming the optical NEP arrived at in Chapter 6, i.e. 2.5 x 10-14 W Hz-1/2, when in use on the JCMT, the 3 Channel Instrument will have a 1 a Is sensitivity of 0.25 Jy. For the beam in use, this converts to a sensitivity to the S-Z effect of 9 mK la Is. The S-Z effect in 0016+16 could thus be measured to 10 a in only about 13 hours. This does, of course, assume that the sky noise subtraction technique is successful, so that the instrumental sensitivity is the limiting factor, rather than the atmospheric fluctuations. This compares with the S-Z sensitivity of UKT-14 on the JCMT of about 150 mK la Is. This is mainly due to the small, 19 arcsecond beam the instrument has now that it is used on the JCMT. The benefits of the large throughput design axe thus clearly apparent. The possibility of mapping the S-Z effect in a cluster whose S-Z profile is larger than 1.5 arcminutes is also available with the 3 Channel instrument. In ideal conditions, we could achieve profiles similar to those recently published by Birkinshaw [20] in about a tenth of the time. Perhaps more significant would be measurements of the S-Z effect in a reasonable number of X-ray emitting clusters. With a number of significant detections, it becomes possible to arrive at values of H0 and qQ from a statistical sample, rather than from an individual cluster as has been attempted before [110]. 7.4 The ICSTM 3 Channel Photometer as an Anisotropy Detector 7.4.1 Introduction As emphasised in Chapter 1, the search for CBR anisotropies is now a very im portant area of observational cosmology. To date, in a very similar manner to the early S-Z effect work, almost all CBR anisotropy searches have been con ducted at radio wavelengths. The 3 Channel Photometer opens up the possibility of making these observations at millimetre and submillimetre wavelengths. These 202 wavelengths are potentially advantageous, since different sources of anisotropy will leave different spectral fingerprints at these wavelengths. Comptonisation of the CBR at a distant redshift, caused by relatively recent energetic processes, would produce an S-Z type spectral distortion, while an intrinsic anisotropy would pro duce an equal temperature change at all wavelengths. Indeed, the S-Z distortions introduced into the CBR by as yet undiscovered ‘foreground’ clusters are expected to produce CBR anisotropies with an amplitude similar to, or greater than, the intrinsic anisotropies sought. A multi wavelength anisotropy detector operating at millimetre and submillimetre wavelengths can thus provide some discrimination between intrinsic and extrinsic anisotropies. A milfimetre/submillimetre instru ment is also less susceptible to emission from synchrotron sources, both galactic and extragalactic in origin, which are a possible source of error in radio observa tions of CBR anisotropy [52]. The 3 Channel Photometer thus has several useful advantages for anisotropy searches. 7.4.2 Expected Signals from CBR Anisotropies For a simple intrinsic temperature distortion ST, an analysis of the black body spectrum shows that the intensity distortion SI is: 2h2V4 ehv/kBT SI = - 1 (7.1) kBc2T (ehu/kBT - 1) T at a given frequency v for a basic radiation temperature T, with other symbols indicating the usual constants. The present limits on anisotropies on various scales are ST/T < 10-4 — 10“5 [134] [176] [104]. For anisotropies at the 10-5 level, the expected flux distortion as a function of frequency is plotted in figure 7.1. This shows that the flux distortion spectrum peaks near the peak of the CBR spectrum, very near the astronomical channels of the 3 Channel Photometer. The instrument is thus well suited to operation as a general CBR anisotropy detector. For a proper study of the full spectrum of initial perturbations in the early universe it is necessary to study CBR distortions on several different angular scales. With the 3 Channel Photometer this is relatively easy; one merely uses a telescope appropriate to the angular scale that is of interest. 203 i ( ,.2H ,_JS j. uj M) S.0I = 1 /IV o-j snp uonJOisiQ xnjj Figure 7.1: Flux Distortion due to Temperature Distortion of ST jT = 10-5 as a function of Frequency for a CBR temperature of 2.7 K 205 Small Scale Anisotropies: The JCMT For studies of anisotropies on scales of a few arcminutes, comparable to the work of Uson [176], the JCMT is the best telescope to use. This allows use of the full 25 psr m2 throughput of the instrument, and yields a 1.5 arcminute beam size, and would use a chop throw of around 3 arcminutes. This compares to the 4.5 arcminute scale studied by Uson at Greenbank [176] which produced a 95 % confidence upper limit of ST/T < 2.5 x 10-5. The expected flux density distortion due to a temperature distortion of 10-5, which will produce a 95 % upper limit a little less than Uson’s result, is 2 mJy in the 1.1 mm channel, and 1.6 mJy in the 2.1 mm channel. Using the sensitivity figures derived from the TIRGO run, these flux levels could be achieved in about 5 hours of integration at a single point. Medium Scale Anisotropies Anisotropies on the scale of tens of arcminutes can be studied using a telescope with a primary of about 1 to 1.5 m. Whilst TIRGO fits this bill in principle, its limited field of view does not make optimum use of the instrum ents large throughput. A sensitivity of 8 T / T « 10-5, giving a flux distortion of about 60 mJy at 1.1 mm, can be achieved on TIRGO in about 41 hours, with a beam of 8 arcminutes. If the full throughput is used, however, the beam increases to about 14 arcminutes, and the integration time decreases to 5 hours at 1.1 mm, with a flux distortion of w 180 mJy. The best observations at this scale to date are those made at Owen’s Valley by Lawrence et al. [91], and set limits of £T /T <1.6 x 10“5. Given sufficiently long integration times, the Three Channel Photometer can clearly improve on this limit, which is among the more physically interesting to date. A dedicated 1.5 m telescope, optimised for CBR observations using this instrument at millimetre/submillimetre wavelengths, is currently under construction at ITESRE in Bologna [41]. After commissioning observations in Europe, this instrument would be stationed in Antarctica which provides probably the best observational environment for millimetre/submillimetre observations on the Earth’s surface. 205 Large Scale Anisotropies To probe large scale anisotropies, on scales of several degrees, the Three Channel Photometer can be used without a telescope, using just the input lens to collect radiation, and a plane, movable reflector to chop the beam on the sky. This gives a field of view of about 4 degrees, comparable to Davies et al.’s Tenerife experiment at 10.4 GHz [52], which has produced a tentative detection (about 2 a) of an anisotropy at 8 T / T « 3.7 x 10-5. Using, again, the instrumental sensitivity derived from the TIRGO observations, our instrument would be able to make a 1 a detection of a 5T / T « 10-5 anisotropy, giving a flux distortion of « 260 mJy at 1.1 mm, in 7 hours of integration. Equivalently, we can reach a sensitivity comparable to the Davies result in just 2 hours. Observations to confirm the Tenerife result would probably be the first job for such an instrument. Since the observations would be made in a very different waveband, any such confirmation could be regarded with high confidence. The best place for long term operation of such an instrument would, again, be Antarctica. Conclusions The 3 Channel Photometer can thus provide a useful addition to the radio fre quency instruments that have to date been used for most studies of the CBR. The portability of the instrument, in the sense that the same instrumentation can be used on a large range of angular scales, can also add a useful uniformity to the results, while the two observational channels provide a multiplex advantage and the potential of obtaining some spectral information on any anisotropy detected. 7.5 The 3 Channel Photometer in Extragalactic A stronom y While the 3 Channel instrument has been specifically designed to observe the S-Z effect, and the CBR in general, it also has a role to play in more conventional astronomical observations. Its principal advantages over other instruments are its two astronomical channels, and its very large beamsize. It would thus be an 206 ideal instrument for observations of extended sources with low surface brightness, which would otherwise be so faint that they would be undetectable with common user instruments designed to operate at the diffraction limit, such as UKT-14. Its wavelength of operation constrains it to observing very cold objects, and even they would be observed in the Rayleigh-Jeans end of the spectrum. However, such sources would be very difficult to observe at any other wavelengths, because of the scarcity, and low quality, of atmospheric windows between 1.1 mm and 10 fim. Sources that might be observed with the 3 Channel Photometer would therefore include those detected by IRAS with a spectrum still rising between 60 and 100 fim, indicating that the emitting dust contains is probably at a temperature below about 30 K. Many of the so called IRAS galaxies, for example, would be prime candidates. 7.5.1 Possible Observations of Cold Dust in IRAS Galax ies Very recently 2 irregular galaxies, the Magellanic clouds, have been observed at wavelengths between 1 and 2 mm by a large-beam experiment in Antarctica. This [8] detected strong millimetre wave emission providing evidence for the presence of a significant very cold component in the interstellar medium. Normal galaxies have not received much attention at millimetre wavelengths to date. Because of their extended size, overfilling the beam substantially lowers their detectability. A small sample of spiral galaxies has been studied by Chini and co-workers [42] with a He3 cooled bolometer at 1.3 mm. Seventeen spiral galaxies selected from the IRAS point source catalogue were detected. They found a 1.3 mm flux of order F( 1.3) = , which is indicative of a very cold dust component. Smith et al. [163] have made a selection of spiral galaxies from the IRAS point source catalogue brighter than 4 Jy at 60 /mi with complete redshift information. This selection has produced a list of 22 sources. If these galaxies behave in a similar way to those observed by Chini et al., they should have 1 mm fluxes not less than 40 mJy, extended over angular scales up to several arcminutes. The 3 Channel instrument is thus very well suited to study of these objects, since its 207 large beam can accept the full flux emitted. This allows the extension of Chini’s observation to a larger range of objects to assess the importance of the cold dust in galaxies. We have also selected a sub-sample of Smith’s objects with small size (< 1 arcminute) to maximise the signal into the small UKT-14 beam. These observa tions will provide a pilot programme which will demonstrate the feasibility of a larger study with the 3 Channel Photometer. Four nights of JCMT time have been granted to these initial observations with UKT-14. Low surface brightness millimetre/submillimetre objects, such as the IRAS galaxies discussed above would provide a contaminating foreground population of sources for CBR observations if they existed in sufficient numbers [63]. Obser vations of such sources are therefore important to CBR studies as well as other areas of astronomy. 7.6 Future Developments Beyond the immediate prospects of using the ICSTM 3 Channel Photometer for cosmological observations at millimetre wavelengths, a number of other instru ments and observatories are currently under development which have major po tential for advances in the field. Space-based observations, avoiding the problems associated with the atmosphere and the ground, clearly have a role, but future ground based instruments may also make major advances. 7.6.1 SCUBA SCUBA, the Submillimetre Common-User Bolometer Array [50], is currently un der development at QMW and ROE. It is a submillimetre imaging instrument using an array of bolometers, each working at the diffraction limit. The bolome ter arrays are cooled to about 0.1 K by a dilution refrigerator, which will allow the array bolometers to operate with an NEP of about 1.6 x 10“ 16 W Hz-1/2. The designers hope to be able to remove sky noise contributions to the signal received by looking at fluctuations over the whole array, and by direct observation using subsidiary bolometers observing the sky at wavelengths severely affected by 208 sky noise, in a somewhat similar manner to the 1.6 mm channel in the ICSTM instrument. SCUBA will use two bolometer arrays, each optimised for operation at different frequencies. The long wavelength array will operate at 855 /im, and will contain 37 pixels, each with a beam of about 20 arcseconds. The other array will work at 450 //m, and so will not be useful for S-Z effect work. The sensitivity of an individual SCUBA bolometer is expected to be about 10 times better than UKT-14, implying a 1 a Is figure of « 0.05 Jy for the 855 fim array. SCUBA thus represents a high sensitivity instrument that is capable of mapping large areas of the sky very rapidly. For S-Z effect observations, its utility is somewhat spoilt by the small beam of each pixel. Even still, an individual pixel will have an S-Z effect sensitivity of about 2 mK lcr Is. It could thus produce a full two dimensional map of the S-Z effect in a cluster to good sensitivities in a fairly short time. This result, however, is based on the premiss that the sky noise contribution to the overall noise of the system can be completely eliminated by correlation measurements and ‘flat- fielding’ type techniques. SCUBA is due for delivery to the JCMT in 1992, and should make a major contribution to extragalactic and cosmological observations at submillimetre wave lengths. For S-Z effect measurements, SCUBA is somewhat spoiled by the lack of a long wavelength channel caopable of observing the flux decrement, though it is admirably suited to mapping the flux increment visible in the 850 channel. The ICSTM instrument will remain the only device capable of observing the S-Z effect on both increment and decrement sides near the peak of the CBR spectrum, required for such studies as cluster peculiar velocities. 7.6.2 Space-Based Observations The potential importance of space based observations in the submillimetre wave band can hardly be overstated. In the field of cosmology, for example, the COBE satellite, launched in November 1989, made more, and more accurate, measure ments of the CBR temperature in its first day of operation than the whole com munity had made in the previous 25 years [104]. For pointed observations of relatively small objects, space-based observato 209 ries become very expensive, since the large reflectors needed to produce a small beam size are heavy and thus difficult to launch. The sheer size of a conventional telescope mirror becomes a problem as well. The Hubble Space Telescope, for ex ample, has a primary mirror just over 2 metres in diameter. The main constraint on this dimension, and thus on its eventual spatial resolution (design and con struction errors excluded), was the diameter of the Shuttle payload bay. Similar limitations on satellite dimension exist for most other launch systems, with the possible exception of the Russian Energia launcher. One approach to this problem, which is applicable at millimetre and submil limetre wavelengths, is the deployable antenna. This is a reflector which is only erected after launch, and insertion of the satellite observatory into its eventual orbit. This is the approach taken by both ESA and NASA in their planned sub millimetre missions FIRST and LDR. While their final designs and funding are yet to be decided, FIRST is at the most advanced stage, with a planned 8 metre reflector as its primary. LDR is still in the early stages of development, but it is hoped to have a 20 m deployable reflector. There are many advantages for millimetre and submillimetre observations in space. Firstly the atmosphere, a major source of noise and background power loading, is absent. In addition, the telescope, and those parts of the optical assembly usually at ambient temperature, can be passively cooled to around 100 K. This further reduces the background power loading, and thus the photon noise on the detectors. The full sensitivity of bolometers such as those intended for use in SCUBA can thus be used. For S-Z effect observations, a space based detector similar to SCUBA mounted on FIRST, with individual pixels operating at the diffraction limit of about 30 axcseconds, would have a sensitivity to the S-Z effect of about 1.5 mK 1 210 7.7 Other Millimetre and Submillimetre Obser vations of Cosmological Importance Observations at millimetre and submillimetre wavelengths are important to cos mology not just because of the CBR. The wavelength region from about 1 mm to about 100 /zm, shown in figure 7.2, is a cosmological ‘window’ in which all the foreground emission processes, including starlight, solar system and galactic dust, and, perhaps, IRAS galaxies, reach a minimum. Longward of 1 mm the CBR itself becomes a significant source of emission, whilst shortward of 100 /zm nearby dust and other objects begin to dominate. There is also a cosmological window at about 2 /zm as well, but this is fairly narrow, and not as deep as the submillimetre window. It is also more subject to confusion by faint foreground sources. Nevertheless it too is of use. The 3 Channel Photometer is stationed at the long wavelength end of the main window. It may thus be used, along with other submillimetre instruments, to search for energetic processes in the early universe. Two possible targets for such work, not including CBR observations themselves, and the benefits of different instruments, are considered here. 7.7.1 Primeval Galaxies A long standing problem of observational cosmology has been the search for galax ies in the process of formation. These so called primeval galaxies (PGs) have been sought at a large range of redshifts, from the local neighbourhood to redshifts around 10. Theories of galaxy formation cover an even larger range of redshifts, with some extending as far as z = 100 [29]. PG searches to date have looked for the redshifted optical and UV emission from the young, hot, O and B stars expected to dominate the light from any newly forming stellar population [122]. Some more sophisticated searches have even fo cussed in on the Lyman-a line produced by hydrogen ionised by these stars, which could contribute as much as 10 % of the total luminosity of these primeval galax ies [130]. The redshift of galaxy formation determines the wavelength at which 211 Figure 7.2: Background Radiations and the Cosmological Windows This plot, from [107] shows the ‘local’ backgrounds and the CBR. ZL indicates the zodiacal light contribution, scattered and thermal, ISD indicates the interstellar dust contribution, and SL indicates the contribution of the integrated light of faint stars in the galaxy. Windows on the distant universe occur where foreground contamination is at a minimum, i.e. around 2 /mi, and between 1 mm and 200 - 300 fiin. 213 this emission can be found. Therefore, theories which predict relatively recent galaxy formation can be tested by searches conducted in the blue or UV, while formation redshifts around 10 would require observations in the near infrared. To date, there have been no successful detections of primeval galaxies, despite many years of work, using different techniques over a wide range of wavelengths, from 2.2 fim [48] to 350 nm [131], corresponding to formation redshifts of z « 10 - 2. One possibility, which has received only theoretical attention so far, is that young galaxies will rapidly become shrouded in dust, as the first generation of massive stars reach the end of their evolutionary cycle and eject the metals they have formed. This idea is especially applicable to very rapid star formation, which some of the early models of PGs predict [34]. Primeval galaxies would thus become opaque to the short wavelengths that dominate the emission from O and B stars, which are the very wavelengths that PG searches have concentrated on for the past 20 years. Rather than appearing as optical or near IR objects, PGs would be cool, low surface brightness sources, dominated by thermal dust emission at rest frame wavelengths of perhaps 100 fim. The observational frame peak of this emission would then be determined by the redshift of galaxy formation, but the 1.1 mm or 800 fim wavebands of photometers like UKT-14 would be sensitive to the Rayleigh-Jeans end of the dust spectrum for quite a large range of redshifts. Observations to search for such objects would be best undertaken with sensitive bolometer arrays, such as SCUBA, but may be attempted with the current range of single element instruments. Integration times of the order of 1 hour on the 30 metre IRAM telescope at 1.3 mm would be sufficient to detect a PG at z « 10 with a 100 //m luminosity of « 1026 W m“2 Hz-1, which is similar to that of the nearby starburst galaxy Arp 220. Observations already made at the JCMT searching for anisotropies in the now refuted Berkley-Nagoya (BN) excess [44] do not cover enough area to place useful limits on dusty PGs. In contrast, Kreysa and Chini’s attempts to detect radio quiet quasars at millimetre wavelengths [87] are capable of setting limits on these models. However, the results are possibly contaminated by the radio quiet quasars which were the original targets of the observations, and a detailed reanalysis of the results by Church and Lasenby [43] show some evidence of excess point-to-point variations. This could be explained by flux received from 213 some of the quasars below the detectability level, or by the presence of dusty PGs in some of the instrumental beams. A search conducted on fields known to be free of contamination by other sources is necessary for a proper investigation of dusty PGs. However, the Kreysa and Chini results do demonstrate the feasibility of these observations. 24 hous of IRAM time has recently been awarded this project for observations of blank fields to search for dusty PGs. 7.7.2 Cosmological Lines: A New S-Z Effect? Cosmological emission lines have been suggested by a number of theoretical studies [94] [156]. They are expected to arise in a number of processes in the early universe, ranging from H and He transitions before recombination [102] to radiative cooling of gas clouds during the first stages of star and galaxy formation [94]. The atomic and molecular species dominating this process will contain only H and He since stars have yet to form large quantities of metals. The most important of these is expected to be H 2 [94] with emission lines at restframe wavelengths of 6 to 30 //m. Depending on the redshift of the line emitting process, these fines may distort the CBR from a black body spectrum, or may provide a higher frequency background radiation of their own. Observations have also suggested the presence of a background radiation of a fine-like nature. Matsumoto’s rocket observations at infrared wavelengths [106] in dicate the presence of an isotropic background, approximately Gaussian in shape, centred at about 2.2 //m, with a width of about 20 % and a flux density of « 4.8 ± 1.7 x 10“8 W m-2 sr-1 pm-1. The removal of the foreground component from any experiment searching for an isotropic cosmological background is extremely difficult, especially at higher frequencies where emission from many different foreground sources is expected (see figure 7.2). The approach applied by Matsumoto and collaborators [106] was to map out the foreground contributions, and then to model and remove all the fluxes expected to be spatially varying. This is also the approach that will be adopted by the DIRBE experiment on COBE. Bernardis et al. propose [18] using the expected dipole variation of any cosmological background, due to the Earth’s 214 motion relative to the CBR, to act as a signature of any cosmological radiation. This will require full sky mapping with an instrument with very stable calibration, but may be possible with ISO or COBE. The S-Z effect presents a third method for identifying cosmological lines. This uses the fact that any radiation field passing through the hot plasma in a cluster of galaxies will experience inverse Compton scattering. We can thus detect the cosmological line by comparing the flux received on cluster and off cluster at the frequency of the expected line radiation. Figure 7.3 shows the result of applying the numerical version of the Kompaneets equation, developed in Chapter 3, to a Gaussian input spectrum with a flux of « 2 x 10-12 W cm-2 /zm-1sr_1 for a Comptonisation y parameter of 10~4, appropriate for X-ray clusters. As can be seen, the change in flux produced by the S-Z effect is greatly increased over the black body version. In this case, the change in flux at the centre of the original line amounts to a few percent of the total line strength, even for a Comptonisation parameter of 10"4. However, for line radiation, the assumptions behind the Kompaneets equation fail somewhat, since the spectrum is not particularly smooth. Truncating the series expansion in equation 3.5 to second order is thus not wholly applicable. Loeb et al [100] have produced a full relativistic treatment of inverse Compton scattering which is applicable to line radiation. The correction factor, though, is small. For a line four times narrower than that dealt with in figure 7.3, the relativistic treatment produces a distortion with half the amplitude of the Kom paneets equation treatment. For a line width of 20%, the correction factor should be considerably less. We thus expect Comptonisation of a cosmological line with similar parameters to that suggested by Matsumoto’s observations, to produce a flux change of about -7 x 10-12 W m-2sr-1 over the K-band window for y = 10”4. This yields a flux decrement of about 30 K-magnitudes per arcsecond2. While present ground based telescopes are not capable of detecting this sort of decrement in a reasonable integration time, the next generation of large ground based instruments in the 8 metre class, or proposed space based IR observatories such as SIRTF, may well approach this level of sensitivity. 215 2x10 4x10 0x10 0x10 10 1.2x10 1.4x10 1.0x10 1.0x10 2x10 2.2x10 2.4x10" 2.0x10" 2.0x10 3x|0' © t It s s © © o o o X X X oX X o T wI (,-zH ,.-s t_ui A) sSuwqo xnjj ZS i Figure 7.3: Results of Comptonisation of a Gaussian line spectrum Result of Comptonisation of a Gaussian line, width 20 %, centred on 2.2 /im, with flux « 2 x 10-12 W cm-2 /im“1sr”1. 217 This technique also applies to any other line like background emission at any wavelength, and may present one of the few methods of definitively assigning a cosmological origin to such radiation. 7.8 Towards a New Astronomy of the Early Uni verse Since its discovery, it has been known that the CBR is a potential source of a great deal of information on the earliest epochs of the universe. Precise determination of its spectrum, and the discovery of anisotropies are very important goals for observational cosmology; given the spectrum of CBR anisotropies, we would then be able to work forward to determine a proper theory of galaxy formation, and work backwards to determine the fundamental physical processes producing the initial perturbations. Observations of deviations from a black body spectrum in the CBR may also provide important information on the detailed physics and chemistry of the early universe. However, despite many years of observational and instrumental development, we have only been able to detect one anisotropy, the dipole due to our own motion, and have yet to discover any deviations from a black body spectrum. Whilst this work has by no means been unimportant, indeed several theories have been severely constrained, if not excluded, by this data, a positive detection of a spectral distortion or of some anisotropy would provide more concrete evidence of the dominant physical processes in the early universe. At the present time, CBR astronomy seems to be entering a new and more mature phase. On the one hand, major projects, such as COBE, are providing some of the highest quality data yet seen by CBR astronomers, and very strong constraints are being placed on spectral distortions and large scale anisotropies. At the same time, the ground based observations are becoming increasingly so phisticated, and the community of CBR astronomers is growing. The use of ded icated instruments, such as bolometer arrays and small baseline interferometers, promises to revolutionise the field, and allow us to search for anisotropies an order 217 of magnitude fainter than has so far been achieved. The techniques for analysing CBR observations have also increased in complex ity, with likelihood ratio tests [134] and Bayesian methods [52] becoming almost standard approaches. In this sense CBR studies are very different from much of conventional astronomy. When searching for anisotropies, we are not looking for any discrete object, but instead we are looking at the statistical behaviour of a large number of sources which are all within the observational beam. We are, in effect, working considerably beyond the confusion limit. The statistical consid erations are very much at the heart of the matter, rather than in conventional astronomy where such methods are only called upon only after a large number of objects have been successfully observed. Over the past decade or so the theoretical beastiary of objects which we might expect to discover in the early universe has also increased in complexity. From simple adiabatic and isothermal distortions, we might now find cosmic strings, Population III stars, and pregalactic explosions, to name but a few. All these developments, technological and theoretical, whether within astron omy or particle physics, have contributed to making the search for information about the early universe one of the major topics for astronomy in the late twenti eth century. Once anisotropies of some nature are found, as they must be unless our ideas of the universe are very wrong, then instruments and techniques will be tailored to maximise our knowledge of them. Until we have some idea of the CBR anisotropies to be found in our universe, we must adopt a more omnivorous approach, using a wide variety of techniques on a wide variety of scales. The search will undoubtedly be exciting, and there will be many blind alleys and false leads, but the universe we come to know at the end of it may well be substantially different from the one we think we know. Our studies of the early universe will certainly revolutionise our current ideas of the universe, whether they lead us to accept some of the much vaunted Theories of Everything (TOEs), or if they require us to reject our present models in favour of something completely different. 218 A ppendix A The Frequency Response of the Digital PSD System At the input to the digital PSD system an initial white spectrum will have had very low frequency componants removed by AC coupling in the amplifiers, and will have higher frequencies suppressed by the frequency response of the amplifiers. The input spectrum to the digital PSD is thus: The integration sampling of the V to F / counter system uses the following sampling scheme in the time domain, rather than the Dirac comb used by con ventional A to D converters. -a a Time 220 This sampling yields a sine function in the frequency domain. The frequency responce of the whole scheme is thus: The Nyquist theorem states that for a sampling frequency /, frequencies above f/2 will be aliased back into the frequency range 0 -----//2 . In the scheme used here, then, the final frequency responce of the system will be: As can be seen, the rejection of frequencies in the first few alias bauds is not particularly strong. The system is thus susceptible to noise at, or near, frequencies of a few times the chop frequency. Such noise was encountered on the TIRGO observing run described in Chapter 6. Apart from reducing the strength of this pickup, this noise could also be rejected by improving the rejection of these fre quencies in the amplifiers. This analysis of the performance of the Digital PSD is originally due to P. Hammersley [711. 221 A ppendix B Computer Programs Numerous computer programs have been used in this research, using both in FORTRAN on STARLINK VAX VMS machines and in BASIC and Assembler on smaller microcomputers. The more significant of these programs axe fisted here, with brief descriptions of their purposes. Details of the algorithms used are included within the programs. B.l Chapter 2 Two major programs are used to produce the results in Chapter 2, Meancalc and Normfit. The first of these demodulates the raw UKT-14 data, corrects for atmospheric opacity, making allowances for changing atmospheric optical depth, and converts the resulting values from instrumental output in mV into flux density in Jy. The second program bins the observational data into a histrogram, calculates the mean and standard deviation of the data, and tests the goodness of fit of the data to a Gaussian. It uses a standard NAG routine, S15ABF, to calculate the expected Gaussian distribution. 221 program meancalc CFirst bit of processing of JCMT data. CReads in individual data values from a UKT14 file, demodulates the CNodding (nod pattern is + - - +), accounts for variations in Catmospheric opacity, converts to Jy from mV Cand calculates the mean, SD and SE. implicit none character*20,inputfile,outputfile real*16 x( 500) ,mean, y, z,airmass, ssum, se, e( 500), sig( 250,2) ,noi( 250) integer i,j,nod,n,flag,nn character*80, header real*16 msum,'m,sd real*16 bas(250) real sam, fam, ta u , tau 1, tau2, ca l , p, q, wsum, wssum, w print*,'Name of input file' read(*,'(A20)'), inputfile print*,'Name of output file' read(*,'(A20)’), outputfile print*,'Sigma threshold for rejecting points' read(*,*),m open(unit*i, status®'old',file»inputfile) open(unit«2, status® 'new' , file«*outputfile) read(1,'(A80)'), header print*,header read(l,*), airmass print*,'Airmass i s ',airmass t read{1,*),n print*,'Input starting airmass' read(*,*), sam print*,'Input ending airmass' read(*,*),fam print*,'Input starting optical depth at this wavelength' read(*,*),taul print*,'Input final optical depth' read(*,*),tau2 print*,'Input calibration factor in Jy/mV' read(*,*),cal do i»l,n read(l,*), x(i) end do read(l,*),j do i-l,j read(l,*), e(i) end do j=0 nod=l do i=l,n,2 y=nod*x(i)-nod*x(i+1) z=x(i)+x(i+1) nod=nod*-l j=j+l sig(j,i)-y bas(j)®z noi(j)-((e(i)**2+e(i+l)**2)**0.5) 223 end do CThis bit corrects for atmospheric extinction and converts to Jy do i=l,j p*sam+((fam-sam)/j ) *i tau«taul+((tau2-taul)/j)*i q-sig(i,1)/(exp(-p*tau)) sig(i,1)«cal*q q-noi(i )/(e x p (- p *tau) ) noi(i)-cal*q q-bas(i)/(exp(-p*tau)) bas(i)-cal*q write(2,99),i ,s i g (i ,1),bas(i ),noi(i ) 99format(I4.2,G15.7,G15.7,G15.7) end do lnn=0 flag-0 msum-0 ssum-0 wsum-0 wssum-0 do i-l,j if (sig(i,2).eq.O) then ssum-ssum+(sig(i,1 )**2) msum-msum+sig(i,1) w=l/(noi(i)**2) wsum-wsum+sig(i,1 )*w wssum-wssum+w nn=nn+l end if end do msum-msum/j ( se-(ssum/J)-msum**2 sd-se**0.5 se-(se**0.5)/(j**0.5) print*,m*sd,sd do i=l,j if (sig(i,2).ne.1) then if (((sig(i,1 )-msum)).gt.(m*sd)) then sig(i,2)«l flag=l end if end if end do print*,msum,se,flag,nn if (flag.eq.l) goto 1 Cse-((ssum)**-0.5) print*,'Mean is ',msum print*,'SE is ',se print*,'Weighted mean is ',wsum/wssum print*,'Weighted se is ',wssum**-0.5 print*,'Points is',j close(l) close(2) end 224 program normfit CThis prog takes In signal data, bins it into a histogram arrangement. CThe mean and sd of the data is then calculated and a normal of the same Cmean and sd is fitted to the data. The value of chi sqared canparing Cthe binned data and the appropriate fitted values is then calculated Cto obtain a measure of goodness of fit. implicit none integer n,numbins,i,nn,deadblock,numblocks real szdata(4,10000),binarray(2,100),normarray(2,100),binsize real chisqrd,redchisqrd character*20 fullfilename print*,'Name of file?' read(*,'(A20)'),fullfilename print*,'Number of bins?' read(*,*)numbins open(unit-1,file-fullfilename,status-'old') n=0 do i-l,10000 read(1,*,end-1),szdata(1,i ),szdata(2,i ),szdata(3, i), szdata (4, i) n-n+1 end do lcall bindata(szdata,n,numbins,binarray,binsize,deadblock,nn) call normdata(normarray,n,numbins,binsize,binarray,szdata,nn) call chisqr(normarray,binarray,n,chisqrd,redchisqrd,numbins) call output(chisqrd,redchisqrd,fullfilename,n,deadblock) end * Q************************************************************************ subroutine bindata(szdata,n ,numbins,binarray,binsize) CThis routine collects the sz data into histogram bins in binarray. CThe max and min values of szdata are returned, as is the size of each Cbin. real szdata(4,10000),binarray(2,100),max,min,binsize integer n,numbins,i call maxmin(szdata,n,max,min) call binsetup(binarray,max,min,binsize,numbins) call dobins(binarray,n,szdata,numbins) print*,'This is the real data' do i«l,numbins print*,binarray(1,i ),binarray(2,i ) end do end Q************************************************************************ subroutine normdata(normarray,n,numbins,binsize,binarray,szdata) CThis routine calculates the expected frequencies of the bins on the Cbasis of a normal distribution with same mean and sd as the szdata. CThis is passed via normarray. real normarray(2,100),binarray(2,100),binsize,szdata(4,10000),mean,sd : integer numbins,n,i - -- call setnormarray(normarray,binarray,numbins) 225 call statistics(szdata,n,sd,mean) call calcnormarray(normarray,mean, sd,numbins,n) print*,'This is the fitted data...' do i«l,numbins print*,normarray(1,i ),normarray(2, i) end do end Q************************************************************************ subroutine chisqr(normarray, binarray,n,chisqrd,redchisqr,numbins) CThis routine calculates the chisqured value and the reduced chisqured Cof the real binned data against the normal fitted data. real normarray(2,100),binarray(2,100),chisqrd,redchisqr integer n,numbins call calcchisqred(normarray,binarray,chisqrd,numbins) call reducedchisqr(chisqrd,numbins,redchisqr) end Q******A*A****A****4:***A****A**A****A**i**********************A********** subroutine binsetup(binarray,max,min,binsize,numbins) CSets up the first dimension of binarray to be the low end of the Cappropriate bin. The numbins+1'th value of the first dimension holds the Cend value of the histogram. real binarray(2,100),max,min',binsize integer numbins,i binsize-(max-min)/float(numbins) do i-1,numbins+1 binarray(1,i)-binsize*float((i-1))+min end do end 0************************************************************************ subroutine dobins(binarray,n ,szdata,numbins) CThis calculate the frequency of occurrence of each of the bins in Cbinarray, and places the value into the second dimension of binarray. real binarray(2,100),szdata(4,10000) integer numbins,n,i,j,frequency do i-1,numbins frequency-0 do j-l,n if (szdata(2,j).ge.binarray(l,i)) then if (szdata(2,j).le.binarray(l,i+l)) frequency frequency+1 end if end do binarray(2,i )-frequency end do end q************************************************************************ 0************************************************************************ 226 subroutine setnormarray (normarray ,binarray, numbins) CCopies first dimension of binarray into first dimension of normarray Cto set up the model bins in the same way. real normarray(2,100),binarray(2,100) integer numbins,i do i«l,numbins+l normarray(1,i )-binarray(1,i ) end do end q********* *********** ********************************* ******************* subroutine calcnormarray(normarray,mean, od,numbins, n) CThis places the expected value of frequency for a given bin into the Csecond dimension of the appropriate normarray element.The expectation Cis on the basis of a normaldistribution with the same mean and sd as Cthe real data. real normarray(2,100),mean,sd,ex,p,x,y,u integer n,numbins,i,ifail ifail-0 do i-1,numbins u«((normarray(1,i )-mean)/sd) y-sl5abf(u,ifail) u-((normarray(l,i+l)-mean)/sd) x»sl5abf(u,ifail) ! p-x-y ; ex-p*float(n) normarray(2,i )-ex end do end q************************************************************************ subroutine calcchisqred(normarray,binarray,chisqrd,numbins) CThis calculates the chisquared value of the read data against Cthe normal fit. real normarray(2,100), binarray(2,100), chisqrd integer i,numbins chisqrd-0 do i-1,numbins chisqrd«chisqrd+( (binarray(2, i)-normarray(2, i) )**2/normarray( 2, i)) end do end subroutine reducedchisqr(chisqrd,n,redchisqrd) CThis bit calculates the reduced chi-squared value. real chisqrd,redchisqrd integer n redchisqrd-chisqrd/(n-2) end 0************************************************************************ 0************************************************************************ subroutine output (chisqrd, redchisqrd, full filename, n ) real chisqrd,redchisqrd character*20 fullfilename integer n character*25 outfile print*, 'The result of a normal fit to the data in the file' print*,fullfilename print*,'Chi-squared value is ',chisqrd print*,'Reduced Chi-sqred is ',redchisqrd print*,'Number of points is ',n end 0************************************************************************ 0**** ********************** ********************************************** Q************************************************************************ ( 228 B.2 Chapter 3 In this chapter the program Kompaneets is used to numerically apply the Kom- paneets equation to non-black body spectra. This program uses the subroutine Differentiate to apply the suitable differencing method to the numerical data to calculate the differential. 229 program kompaneets CThis will take in a file consisting of intensity at a given frequency C(ie. 2D (frequency,intensity (Wm-2sr-2)) C and will calculate via the Kompaneets Cequation. dj/j«l/n*integral((dn/dy)dy) Cdn/dy-x**-2(d/dx(x**4(dn/dx+n(n+l)))) Cx=hf/kT and n«I(f)c“2/(2hf“3). Cl*number of points in array. implicit none integer l,m,i parameter (1«1'000) real e(2,1),dj(2,1),te,comp,h,k,n,x,temp(2,1),templ(2,1),ana(2,1) character*20 filename Ch*planks constant, k-boltzman and it might be wrong so check!!!!! call inputfile(e,1,m,comp,te,filename) call szit(e,dj,l,m,te,comp,temp,tempi,ana) call output(e,dj,l,m,comp,te,filename,ana) end 0************************************************************************ 0************************************************************************ subroutine inputfile(e,l,m,comp,te,filename) real e(2,1),comp,te integer m,headers character*20 filename headeers*0 CHeaders is the number of heading lines in the datafile describing it. call getparameters(filename,comp,te) call getdata(e,l,m,filename,headers) end q************************************************************************ subroutine getparameters(filename,comp,te) real comp,te character*20 filename print*,'Name of file with spectrum data?' read(*,'(A20)') filename print*,'Input temparature of electrons?' read(*,*)te print*, 'Input value of Comptonisation parameter?’ read(*,*)comp end 0************************************************************************ subroutine getdata(e,l,m,filename,headers) real e(2,l) integer i ,m ,headers character*20 filename 230 character*80 head open( unit-1, status-'old',file-filename) do i-1,headers read(l,'(A80)')head end do m-0 do i-1,1 read(l,*,end-5)e(l,i),e(2,i) m-m+1 end do 5end C************************************************************************ c************************************************************************ subroutine szit(e,dj,l,m,te,comp,temp,tempi,ana) CApplies the Kompaneets equation to the radiation spectrum in e(2,l) Cto yield dj in the array dj. real e(2,l),dj(2,l),te,comp,temp(2,1),tempi(2,1),ana(2,1) integer m call convert(e,1,te,m,ana) call kompanit(e, 1,m,dj,comp, temp,tempi) Ccall analytical(comp,te,ana,e ,1, m) call deconvert(e,l,te,m,dj,ana) C*******************************end ***************************************** subroutine convert(e,l,te,m,ana) CConverts frequency values into x values, and energy values into Cphoton phase space density. Cx-hf/k*Te in this case. real e(2,l),te,h,k,ana(2,l),c integer i,m parameter(k-1.3806E-23, h-6.626E-34, c-2.9979e8) do i-l,m • e(2,i)-(c**2)*e(2,i)/(2*h*(e(l,i)**2)) e(2,i)«e(2,i)/e(l,i) end do do i-l,m e(l,i)»e(l,i)*h/(k*te) Cana(l,i)-e(l,i) end do end C************************************************************************ subroutine deconvert(e,1,te,m ,dj,ana) CRestores interns in e to their original values...ie. removes the scaling Cto dimensionless units. real e(2,l),te,h,k,dj(2,l),ana(2,l),c parameter (h-6.626E-34,k«1.3806E-23,c-2.9979e8) integer i,m 231 do 1*1, m e(l,i)-k*te*e(l,i)/h d j (1, i)-k*te*dj(1,i )/h ana(1,i )-k*te*ana(1,i )/h e(2,i)-2*h*(e(l,i)**2)*e(2,i)/c**2 e(2,i)«e(2,i)*e(i,l) dj(2,i>- end 0************************************************************************ subroutine kompanlt(e,l,m,dj,comp,temp,tempi) real e(2,l),dj(2,l),temp(2,l),templ(2,l),comp integer 1,1, m CFind dn/dx call differentiate(e,temp,l,m) CNow add n(n+l) to dn/dx and multiply by x**4 do i*l,m temp(2,i)*temp(2,i)+e(2,i)*(e(2,i)+l) temp(2,i)*temp(2,i)*(e(1,i )**4) end do CNow differentiate it all again, call differentiate(temp,tempi,l,m) CMultiply by x**-2 to get dn/dy, and then by (l/n)*comp to get dj/j do i*l,m dj(l,i)-e(l,i) dj(2,i )-tempi(2,i)/(e(l,i)**2) dj(2,i )-d j(2,i )*comp/e(2,i ) end do end 0 * ★ * * ★ ★ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ★ * * * * * * subroutine analytical(comp,te,ana,e ,1, m) CThis gets a blackbody temparature and outputs the analytical SZ solution Cfor that temperature at the frequencies in the data by way of a Ccomparison. real comp,te,ena(2,l),e(2,l),tr integer i,j print*,'What radiation temperature for comparisson output?' read(* , * )tr do i*l,m ana(1,i)«ana(1,i)*te/tr end do do i-l,m ana(2,i)*comp*ana(1,i)*(exp(ana(1,i ))/(exp(ana(l, i))-l)) ana(2,i)«ana(2,i)*(ana(l,i)/(tanh(ana(l,i)/2))-4) end do do i»l,m . . . 232 ana(l,i)«ana(l,i)*tr/te ana(2,i)«ana(2,i) CLast one makes output dj/j end do end subroutine output(e,dj, l,m, comp, te, input file, ana) integer m real e(2,l),dj(2,l),comp,te,ana(2,1) character*20 outputfile,plotfile,inputfile,bbfile character*16- filename print*,'Name of output files (no extension)?' read(*,'(A20)')filename outputfile-filename//'.dat' plotfile-filename//1.pit' cbbfile-filename//’.bbd' open(unit-2, status-'new',name-outputfile) open(unit-3,status-’new',name-plotfile) copen(unit-4,status-'new',name-bbfile) cwrite(2,*)'Result of Kompaneets Operation on file inputfile cwrite(2,*)'Electron Temperature-’,te cwrite(2,*)'Comptonisation prmtr-',comp cwrite(2,*)’Frequency dj/j' do i«l,m cwrite(2,*) dj(l,i),dj(2,i) ? write(3,*) dj(l,i),dj(2,i) cwrite(4,*) ana(1,i ),ana(2,i) CResult on analytical solution only valid here if input spectrum is CPlankian. end do end 233 subroutine differentiate(x,dx,1,n ) CSubroutine to numerically produce the differential of an input C function. The function is specified in array x as a series of C coordinbates, the first ordinate being the Independent variable. CThe differential is then calculated as being C dy/dx-(-l/12y(i+2 )+2/3y(i+1)-2/3y(i-1)+l/2y( i-2)/x(i)-x(i-1) CThis cannot be done for the first and last points so we use the less Caccurate formula C (y(i)-y(i-l))/(x(i)-x(i-l)) CNor will it work for the second or second to last points, so use this Csecond order accurate formula C(y(i+1)-y( i-2)/x(i+l)-x(i-1) C CWARNING WARNING:...... This should not be used with variable step sizes Cin the mesh. C CPassed Variables..... C x .... 2D array of input function Cdx....2D array of output differential C n .....Integer value.... number of points in functions real x(2,1),dx(2,1),delx,dely integer i,n do i*l,n dx(l,i)*x(l,i) end do dx(2,l)«(x(2,2)-x(2,l))/(x(l,2)-x(l,l)) dx(2,2)«(x(2,3)-x(2,l))/(x(l,3)-x(l.l)) do i«3,n-2 ( dx(2,i)»(-(x(2,i+2)/12)+(2*x(2,i+1)/3) *-(2*x(2,i-l)/3)+x(2,i-2)/12)/(x(l,i)-x(l,i-l)) end do dx(2,n-1)«(x(2,n)-x(2,n-2))/(x(l,n)-x(l,n-2)) dx(2,n)*(x(2,n)-x(2,n-l))/(x(l,n)-x(l,n-l)) end C************************************************************************ 234 B.3 Chapter 4 Tins chapter uses several programs. Firstly the program Newreduce performs the necessary processing and correction of the raw XJKT-14 data from XJKIRT. The bulk of this program was written S.T. Chase, with some modifications and corrections by myself. The program Ksnorm2 then applies the Kolmogorov-Smirnoff test to individual data blocks to compare them with a Gaussian. This uses routines from NAG and Numerical Recipes. The program Statistics3 is then used to calculate the cumulative mean and standard deviation as each integration is added into the data. 235 o o o o o o o oonoooo o n^oo noono AND PROCESSES THE DATA. MUST SPECIFY LONGITUDE,LATTITUDE SPECIFY MUST DATA. THE PROCESSES AND NIGHT, FLUX/COUNT & AIRMASS C ORRECTION KAPPA) AT TOP OF TOP AT KAPPA) ORRECTION C AIRMASS & FLUX/COUNT NIGHT, Next bit dumps UT,Bline and UT,Dabar into files basline.dat and basline.dat files into UT,Dabar and UT,Bline dumps bit Next al FILHED(option,Trad,tspike) call INIT(O) call o ae aa o n ih soe i Tn etc., function. a UT(n) in with stored fitted night be to one for ready data have Now DATAIN call IE a 000 Cl iUl iU2 apl ap2 ) kappa2 kappal fidUT2 fidUTl Cal 0.0000 (as FILE ************************************************** open(unit-8,type-'NEW',name-name (4)) open(unit-8,type-'NEW',name-name open(unit-5,type-'NEW',name-name(3)) ' t a ) 'OLD', open type- (unit-4, 'bandllOO.dat') name- open type*'NEW',name-’temp.d (unit-3, 'NEW'type* ,name-name(2)) open(unit-2, ************************************************************ 240.0 • Tatm 1)) ',name*name( D L open(unit-1,type*'O **************A***************A******************* 4) 'SZSIG.' (4 d a -) e 'SZBLIN.' h )- 3 ( d a e h (2) . d a e h 'SZRESULT86.' - ******************************************************** READS BIT NEXT HEADINGS. FILE TRANSFERRED BIT LAST ************************************************************ ****************************************************************** COMMON/lumpf/freq( 36), trans( 36), emis( 36) COMMON/lumpf/freq( edl - 'SZ0086.' - head(l) at, COMMON/date/year,month,day l al,f C kappa(10,2), idUT (10,2) COMMON/lumpc/long, 650), bline( 650), UT( 650), block COMMON/lump3/dabar( at(6,3) ,d COMMON/lumpl/m,n C0MM0N/lump5/omega,npts(10),point (10), HAcos, Tatm HAsin, decos, desin, lcos, lsin, a2 COMM0N/lump6/HA, C0MM0N/lump5/omega,npts(10),point C0MM0N/lump4/sign, night,dRAin,ddecin C0MM0N/lump4/sign, olwn lns huduedrcoysnw frue n T' director STC's in use for sznew: directory use should lines Following Trad,tspike,option,jflag COMMON/lump2/jmax, a(8),sigmaa(B),b(8) DIMENSION long,lat,lcos,lain,night,kappa,omega REAL EIE RMA ALE RGAM 'AIRFIT'. PROGRAMME EARLIER AN FROM DERIVED CHARACTER*14 name(4) CHARACTER*14 HRCE*1 head(4) input CHARACTER*11 CHARACTER*3 PROGRAMME 'NEWAIR' USED ON 1983 S2 DATA, WHICH ITSELF WAS ITSELF WHICH REDUCTION DATA, DATA S2 OF 1983 ON VERSION USED MODIFIED 'NEWAIR' PROGRAMME 1/N0V/1986. S.T.C. NEWREDUCE PROGRAM ************************************************************** NEE ock,option,point,year,month,day l b INTEGER ************************************************************** signal.dat as (x,y) coordinates for use by xyplot. by use for coordinates (x,y) as signal.dat ED*'A)) INPUT READ(*,'(A3)') ED*'F.)) omega READ(*,'(F9.6)') ED*,'(II)’)jflag , READ(* )' (eg.SZ0086. ) from head(l) read to type ead(*,’(All)’ file r print*,'Give RN*'ULDT UPT?1 YS0 NO).' - YES;0 - ?(1 (decimal).' OUTPUT DATA MICROSTERADIANS PRINT*,'FULL IN ANGLE SOLID ’ n n n PRINT*,'BEAM AS NUMBER DAY DD' MM YYYY PRINT*,'ENTER AS year,mont'h,day OBSERVATIONS READ(*,*) OF DATE 'ENTER PRINT*, .00 og a 000 dA dc i arcsec) (in ddec dRA 0.0000 lat long 0.0000 DO i-1,4 DO END DO END aei - head(i)//input - name(i) 236 c '2. ’//input) datadump(ut,bline,dabar,650, call call datadump(ut,bllne,dabar,650, '1. '//input) datadump(ut,bllne,dabar,650, call call datadump(ut,bline,dabar,650, '3. ’//input) datadump(ut,bline,dabar,650, call o no DRIFT NO ONLY, CORRECTED format(//lOX'AIRMASS 100 1 TERM SUBTRACTED.'/) TERM 1 RT( '/1X'UL ORCE AA )’) ” DATA. CORRECTED ,'(//10X''FULLY WRITE(2 , t DRIFT (u bl call ne, i ,nterm, nl , 2 n xbar, j ,i , O b ,b ) l a Trad, C 3 1 - REWIND nterm » nterm CORRECTIONS'')’) NO DATA, 10X''RAW / WRITE(2,'(/ al OUTPUT(1,Cal) call PRINT*,'FULLY CORRECTED DATA.' OUTPUT(option,Cal) CORRECTED call PRINT*,'FULLY CORRECTIONS' NO DATA, PRINT*,'RAW STOP IF END THEN (option.GT.2) IF N - -- - INIT(k) subroutine $$$$$$$$$$$$$’$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ END END IF END F oto.Tl THEN (option.GT.l) IF ts * 1.0 * test ' Oj-1,block j DO WRITE(*,100) WRITE(2,100) al FTESTC(chisav,chisq,nterm,nl,test) call ,(ut REGRES bline, ,call nterm, l n , 2 n ,xbar, i ,j O a ,a isq) h c OUTPUT(option,Cal) call AIRCOR(n,Cal,Tatm) call hsv 100000.0 - chisav tr - 1 - nterm Ok 1,8 - k DO DO WHILE ((test.GT.0.0).AND. (nterra.LT.jmax)) ((test.GT.0.0).AND. WHILE DO END DO END END DO END n - point(j)-nl - tn2 Ji - j 0 aO - b0 l npts(j) - nl O 0.0 - aO () 0.0 - a(k) END DO END k-1,8 DO 237 () a(k) - b(k) hsv chisq « chisav tr - tr 1 + nterm - nterm 2ZZ 5(OOTq' (0S9 ' (099 )3UTiq' (0S9 )^8qBp/edumi/M0WW0D (£'9 )3-ep 'u'ui/idumi/NOWWOO ABp'qquotn'JceaA'q.UTqd'uoTado'MOOiq H303J.NI Bdduic'q.BX'Buox 1Y3H NIYlYa auxanoaqns o $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ o o ON3 NHX1X3H 3 (//. b u iB t s ,'g-gj\ - Pioqsaaqq. 3J(T<5S,xg Z 'E*9J. - PBJi.xg'zi', - NOlidO,'xgx'/ i ,9861 *330 I '33na3drt3N *q passaooad Bq.ua, '*ST V )q.auiaoj 09 eUTds*' j, 'adoi{( 09 '* )31IHM ajfFdsq.' i' adoi{ (os ' Z) 3XIHM 3 Oa 0N3 apaoA'ppaoA'opaoA'qpaoA'BpaoA(, ( (8Y)9), '*)3I,IHM apaoA'ppaoA'opaoA'qpaoA'spaoA( , ( (8Y)9), *Z)3iLIHM apaoA'ppaoA'opaoA'qpaow'epaoA( , ( (8Y)9), ' I)OY3H e ' T - T o a apaoM'ppaoA' opaoA 'qpaoA * BpaoA g»qv3H (aUXdsq.'i'q.doiOaSHTId auxq.noaqns o n o $ss$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$s$s$$$$$$$$$$$$$$$$$$$s O N 3 N d fU S d O a 0 N 3 oa 0N3 0*0-(P'T)aep e ' i - f o a 9 ' I - T o a 0 «ui 3 1 0 N 3 aMTdsq. (, (Z *S3 ), '* )0Y3H .•(asBajd x^niToap) Aap’pqs uj pxoqsaoqq aj{xds aaq.ua/, '»XNIHd uoxqdo ( ,(TI),'*)0Y3H .aaqumu uo-pqdo aaq.ua /,'*l,N IH d o .paqoaaaoo qj-pap x®T“Ou^tod puB sseuiafY - g , '¥XNiHd ,Axuo paqoaaaoo sseuiaxv - Z . ' » i N I H d ,suoxqoaaaoo ou 'asp m b h « I :flN3W NOIidO, '*£NIH d o o a 0 N 3 (T)suuaq.'(T)STura'(T)&aaj (*'*)pBaa 9 0 'T - T o a YJ.YO ONYSSSYd NI 0Y3H O o a 0 N 3 o *o - ( D i n 0*0 - (T)auxxq 0*0 - (T)^eqBp 099'T-T Oa xeuif ( ,(TI), '*)0Y3H , * (papaau Axuo aaBaqu?) lYIWONAlOd 30 H3030 XVW 3AI9 , '*.LNIHd 0A*Z-P»Ji 0-HOOiq 0-u N3HJ (0'03*3f) 31 ( 9 E ) s p n a ' ( g g ) s u u a q * ( g g ) B a a j / j d u m x / N O W W O O j(OOxq' (099)1/1' (099 )9UTXq' (099 )aBqBp/gdumx/N0WWO3 6 » IJ f 'uoxqdo 'ajjxdsq. 'psaj, 'xBmP/zdomx/NOWWOO (£ '9 )*e p '« 'm/ldumx/NOWWOO qu-rod'uoTqdo'spoxq H3031NI asx'Buox 3Y3H C0MM0N/lunip5/omega, npts (10), point (10), Tatm COMMON/lumpc/long, lat. Cal, kappa(10,2), fidUT(10,2) COMMON/date/year,month,day c c chopl - 0.0 chop2 - 0.0 dmark ■ 0.0 DO WHILE (dmark.GT.-20.0) READ(l,*)dat(l,3),dat(2,3),dat(3,3),dat(4,3),dat(5,3),dat(6,3) c TYPE*, dat (1,3), dat (2,3), dat (3,3), dat (4,3), dat (5,3), dat (6,3) dmark - dat(l,3) IF (dmark.GT.0.0) THEN CALL SHIFT(isign) IF (isign.NE.O) THEN CALL CALC(isign,chopRA,chopdc) chopl - chopl + chopRA chop2 - chop2 + chopdc END IF C ELSE IF (ifix(dmark).EQ.O) THEN CALL CONSTS(0) Cal » Cal*omega ELSE block « block + 1 npts(block) - o point(block) « n c WRITE(*, ’ (4X” Block No. ” ,I2,4x ”N o . of pts - ” , 1 13,4 x ’’End Point - ” ,13 )') 2 block, npts (block), point (block) c next ■ block + 1 CALL CONSTS(next) CALL INIT(block) END IF END DO chopl * chopl/n chop2 - chop2/n WRITE(2,'(” Chop is ” ,F8.2,” arcsec RA; ” ,F8.4, 1 '' arcsec dec.'')')chopl,chop2 WRITE (*, ' ( ” Chop is ” ,F8.2,” arcsec RA; ” ,F8.4, 1 '' arcsec dec.’')')chopl,chop2 300 RETURN END c c subroutine SHIFT(isign) c IMPLICIT NONE REAL dat,sign INTEGER m,n,k,isign,jflag COMMON/lumpl/m,n,dat(6,3) c DO k - 1,6 dat(k,1) - dat(k,2) dat(k,2) • dat(k,3) END DO c isign - 0 jflag - IFIX(dat(l,l)) IF (jflag.GT.0) THEN sign ■ dat(4,l) - dat(4,2) isign - IFIX(sign) c IF (isign.NE.O) THEN n - n+1 239 c $$$s$$$$$$$$$$$$$$$$$$$$$$$$$$$sss$$$$$$$$$$$$$$$$$$$ c c ::::::::::::::::::::::::::::::::::::::::::::::: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : c C C u n c 50 n n n ' 3 ACE ’) . C E D ARCSEC .3' 8 'F 1 (6,3) t a (5,3),d t a d 1 $s$s$s$s$$$$s$$$$$$$$$$$$$$$$$$sss$s$$$ss$$s$$$$$$$$$ COMMON/lump3 /dabar (650) /dabar ,bline( 650) ,UT( COMMON/lump3 650), block COMMON/lumpl/m,n,dat(6,3) 1st, long, lat, lcos, REAL lsin, night, kappa, nodRA Oj 1,2 - j DO COMMON/date/year,month,day COMMON/lumpc/long, , at, l l a C kappa (10,2), fidUT (10,2) COMMON/lumpc/long, HAcos, HAsin, decos, desin, lcos, lsin, a2 COMMON/lump6/HA, am(2),da(2),h(2) DIMENSION hpc (a(,) dt32))*sign/57.29577951 ) dat(3,2 - (dat(3,l) - chopdc RETURN dRAin,ddecin WRITE(2,50) N IF ',k, ', END ' - - ’k £idUT(k, 1), , * fidUT E P f TY idUT( k, 2) ELSE ’ 3 . ’F8 : IS ’CHOP X FORMAT(2 READ (1, *) dat (1,3), dat( 2,3), dat (3,3), dat (4,3), long, kappa, lat, Cal, REAL chopRA.chopdc hpA RAt/3.819718634 - chopRA RAin,' ’,d - ’ dRAin , * T PRIN END in FLOAT(isign) - sign CALC( isign,chopRA,chopdc) subroutine COMMON/lumpl/m,n,dat(6,3) dat,dRAin,ddecin,fidUT REAL INTEGER block,year,month,day,ro,n,j INTEGER lat. Cal, kappa (10,2), fidUT( 10,2) COMMON/lumpc/long, RETURN F kE.) THEN (k.EQ.O) IF CONSTS(k) subroutine END IMPLICIT NONE IMPLICIT INTEGER k,m,n INTEGER A - dt2l - dat(2,2))*sign - (dat(2,l) - RAt dec - dat(3,j ) ! dec in degrees !in dec ) dat(3,j - dec RA - dat(2,j) " ! RA in hours !in RA " dat(2,j) - RA t - dat(l,j) ! UT in hours ! in UT dat(l,j) - t ap(,) dat(6,3) - dat(5,3) kappa(l,2) - kappa(l,l) ap(,) dat(6,3) - dat(5,3) kappa(k,2) ■ kappa(k,l) iU(,) dat(4,3) - £idUT(1,2) dat(3,3) - fidUT(l,l) iU(,) dat(4,3) - fidUT(k,2) iU(,) dat(3,3) - fidUT(k,1) dcn dat(6,3) ■ ddecin Ri ■ dat(5,3) ■ dRAin N IF END og dat(2,3) • long Cal - dat(2,3) - Cal a - dat(3,3) - lat N IF END 240 ARCSEC RA,'11X': ARCSEC dcn ',ddecin - ddecin « m+1 « m c c c c c c c c c c c c c c c o o o n o 50 bline(n) - (dat(6,l) + dat(6,2))/2.0 + (dat(6,l) - bline(n) RT( JnodRA,dHA * , WRITE(2 DO END chopcd > chopdc*206264.8062 ! to arcseconds. ! to chopdc*206264.8062 > chopcd WRITE(3,50)sign,nodRA,signal,da(1),da(2),am(1),am(2),ak signal - dabar(n) chopRA - chopRA*206264.8062 ! Convert from radians from ! Convert chopRA*206264.8062 - chopRA C0MM0N/lump6/HA, HAcos, HAsin, decos, desin, lcos, lsin, a2 C0MM0N/lump6/HA, decos,desin,al,a2,radcon,hrdegs,decrad,latrad REAL AIRMAS REAL RETURN decrad hrdegs radcon ,1st,lat,lsin,lcos,HA,HAcos,HAsin c e ,d A R REAL END format(2xf4.1,2xf9.5,2xf10.5,5(2xf10.6)) END RETURN RA Input latrad NONE IMPLICIT AIRMAS(RA,dec,lst,lat) function function CALLST(JYR,JM,JDY,UT,LONG) function desin decos HAsin HAcos signal - (dat(6,l) - dat(6,2))*sign - (dat(6,l) - signal lsin lcos ucint aclt S ie h ae teU and urs). UT o h the (in site date, the the of given LST longitude the calculate to Function UT(n) - (dat(l,1) + dat(l,2) )/2.0 dat(l,2) + (dat(l,1) - UT(n) et - U() fdTkl)(iU(,) fidUT(k,l)) - fidUT(k,l))/(fidUT(k,2) - (UT(n) - delta oR - u RAt - dut - nodRA HA a2 al dHA - (h(l) - h(2))*sign - (h(l) - dat(l,2))*sign - dHA (dat(l,l) - dut da(j) - 1000.0*temp*(terml 1000.0*temp*(terml - da(j) lsin*decos)*chopdc - (desin*lcos*HAcos » term2 k kpakl + kpak2 - ap(, )*delta ) kappa(k,1 - (kappa(k,2) + kappa(k,l) - ak m - IMSR,e,s, ) t a AIRMAS(RA,dec,1st,l am( - ) j em « decos*lcos*HAsin*chopRA « terml h( j HA*3.819718635 -) - lc 1 + block - k ep 10 0035(2* - 1.0/3.0) - 0.00375*(a2**2 - 1.0 - temp IMS (. - 0.00125*(a2**2 - (1.0 - AIRMAS m m m m m m m m m m m t a 1st - CALLST(year,month,day, t,long) CALLST(year,month,day, - 1st cos(latrad) cos(HA) dec/radcon lat and dec hours, in LST and cos(decrad) lat/radcon cshcsdcs lsin*desin + lcos*hacos*decos sin(latrad) sin(decrad) sin(HA) 15.0 57.29577951 1.0/al 1t -RA)*hrdegs/radcon (1st 241 + term2)*(a2**2) ! HA in radians in ! HA C ...... c q c c C c c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * n o o n o non nnnn ********************************************** uruieARO(pit,a,am - nodRA REAL AIRCOR(npoints,Cal,Tatm) subroutine RETURN CALLST END ,long 3 ,c 2 ,c l c REAL bmonth Tu ,lstl,callst,datel,dateO,calcJD, t s ,g t ,u t u b REAL NEE Jyr, Jdy,byear,bmonth,bday y d ,J m ,J r y J INTEGER IMPLICIT NONE IMPLICIT Calculate the full (real) Julian Date Julian (real) full the Calculate oep - MIN(1,MOD(IY,400)) - noleap3 MIN(1,M0D(IY,100)) - noleap2 MIN(1,M0D(IY,4)) - noleapl jd0,JD,leaps,days,year,calcJD,UT REAL JorF * Ml/II ! Returns 1 for Jan or Feb, else 0 else Feb, or Jan for 1 ! Returns Ml/II * JorF AAEE (d - 1721060.0) - (jdO PARAMETER acD J + U - 20 )/24.0 12.0 - UT ( + RETURN JD « CalcJD lasI/-Y10I/0+oepl N. f eper sne JDO. since leapyears of ! No. ) s p a e H ( FLOAT - a is leaps Iyear if 1 ileaps«IY/4-IY/100+IY/400+noleap-l ! Subtracts Idy-noleap+noleap*JorF ■ Idy dateO datel END NEE oepnlalnla2nla3 ' s p a e H noleap,noleapl,noleap2,noleap3, INTEGER Iy, IYEAR,IM,Imonth,ID,Idy,IDay,Ml,II,JorF. INTEGER IMPLICIT NONE IMPLICIT I CALCJD( YEAR, IM0NTH, IDAY,UT) function byear as FLOAT(Idy) - days er FLOAT(IY) - Year year given in number day the Calculate Time. Universal and day month year, the given oep nlalnla2nla3 nla - i Ier s a is Iyear if 0 - ! noleap noleapl-noleap2+noleap3 - noleap a fe OYas Oas 2or ( J 12000 ), 1721060.0 JD (- any 12Hours for OODays Date Julian OOYears the after day calculate to Function d - ID+60+28*(Ml-l)+Il-366*JorF - Idy lstl bday l MDI+,2+ J as ot eknd rmMrh 1 * March from reckoned month J False MOD(IM+9,12)+l - Ml gst but I (3M-)5 2 Zle' cnrec fr re. days irreg. for congruence IZeller's 2 - (13*Ml-l)/5 - II cl D year*365.0+leaps+days+JD0 ■ JD Tu c3 c2 ID-Iday IM-Imonth IY-Iyear M0D(lstl,24.0) ubro ast aeasmn leri a leapyear. a is lyear assuming date to days of Number ut + cl + c2*Tu + c3*(Tu**2) ! GST in hours in ! GST long - c3*(Tu**2) + gst c2*Tu + cl + ) t ut u calcJD(byear,bmonth,bday,b calcJD(Jyr,Jm,Jdy,UT) 0.00002580 ! equation .of time, expressed In hours. In the In expressed .of time, ! equation constants the are numbers ! These 0.00002580 2400.051262 0 6.612732222 90 Bs ae s 2or, t a 1900 Jan 0th 12hours, is date !Base 1900 12.0 1 (datel - dateO)/36525.0 ! No. of Julian centuries Julian of ! No. dateO)/36525.0 - (datel eperuls ot s a o Feb. or Jan is month unless leapyear 242 eper ad 1 f t isn't. it if 1 » and leapyear, c C c c c c c c c c c C c C 5 10 c c c o n x(650),y(650),r(8),array(8,8) 1 COMMON/lump3/dabar( 650), bline( 650), UT( 650), block COMMON/lump3/dabar( Oj l,npoints - j DO 36), trans( 36), emls( 36) COMMON/lumpf/freq( AA o otis aai K corrected mK, in data contains now DABAR 3 REWIND with Omega in microsteradians. in Omega with INTEGER block,point,start,finish INTEGER END RETURN DO END DOUBLE PRECISION array,ymean,sigma,chisq,xmean, sigmax( 8),sigmax( tsig yf it( array,ymean,sigma,chisq,xmean, 650), xmean( 8),DIMENSION sigmaa( 8 PRECISION ), DOUBLE a( 8 ,),(x REGRES ,y nterms, npt, ,subroutine inpnt, O xbar, a nblock, ,a chisq) $$$$$$$$.SS$$$$$S$$$$S$$S$$$SSS$$$$$$$$S$$$$$$$$$S$$$$ ) O O H R * a g e m O * ( A is Cal N.B. emission. atmospheric for INTEGER block,point INTEGER INITIALIZE ALL SUMS & ARRAYS & SUMS ALL INITIALIZE WRITE(6,10)x(pl),x(p2) O - 1,650 - 1 DO O - 1,8 - j DO DO END omt/5’EI T '95 hs EDU - F.' HRS.'/) 'F9.5' - UT END hrs, 'F9.5' - UT format(//5x’BEGIN CUUAEWIHE SUMS WEIGHTED ACCUMULATE O1 l,npt - 1 DO DO END RT(,) ,delf,signal,sz WRITE(*,*)j WRITE(2,*)j,delf,signal,sz ln() bline(j)-13.8*Tatm*(fl+f2)*Cal/1000.0 - -75.0*(signal-delf)/(Cal*sz) bline(j) - dabar(j) ma - 0.0 - ymean hs - 0.0 - chisq sigma sigma ml 0.0 - rmul br ((l + x(p2))/2.0 + (x(pl) - xbar ef 2.*f-2)*sign*Tatm*Cal/1000.0 27.6*(f1-f2 - delf im (aml+am2)/2.0 - airm u ■ 0.0 ■ sum i ipt 1 + inpnt - pi 2 ipt npt + inpnt • p2 z szint(ak,airm,Trad) - sz da2*fint2(ak,am2) « f2 l dal*fint2(ak,aml) » fl READ( READ( 3, *) sign, nodRA, ,signal, al, 2 d , a i d m a am2, ak sigmax(j) imaj - 0.0 - sigmaa(j) ftl - 0.0 - yfit(l) xmean(j) *0.0 ymean « ymean + y(i) + ymean « ymean a(j) r(j) « + inpnt + 1 « i Oj 1,nterms » j DO DO k-1,8 DO END DO END 0.0 0.0 0.0 0.0 243 ra(,) 0.0 « array(j,k) c C C c C C C C C C c c C c c60 c c c c C n o C C c ary4 ,ra(,k)ary6 ,ra(, ,ra(, ) ),array(8,k ),arrav(7,k k ),array(6, k ),array(5, k array(4, 1 ary4k)ary5k)ary6k)ary7k)ary8k) ),array(8,k ),array(7,k ),array(6,k ),array(5,k array(4,k 1 'imx'l «e253'(i' -'el2.5) )«'el2.5,3x'r('il') 'sigmax('il' 1 ACCUMULATE MATRICES R & ARRAY & R MATRICES ACCUMULATE O - l,npt - 1 DO DO END END DO 1.0 -END ) array(j,j l,nterms « j DO al MATINV(array,nterms,det) call N DO END j*l,nterms DO sigmax(j) ■ sigmax(j) + (fctn(x,i,jl,xbar) - xmean(j))**2 - (fctn(x,i,jl,xbar) + sigmax(j) ■ sigmax(j) DO END F dtE..) THEN (det.EQ.0.0) IF MATRIX SYMMETRIC INVERT RT(,'/0,'RA(,) COEFFICIENTS''/)') '(/10X,''ARRAY(J,K) WRITE(2, RT(,'83,l.)))ra(,)ary2k,ra(, , ) '(8(3x,fl0.5)/)')array(l,k),array(2,k),array(3,k), ITE(2, R W '(8(3x,flO.5)/)')array(l,k),array(2,k),array(3,k WRITE(6, l,nterms - k DO COEFFICIENTS''/)') K) * ITE(6, R W (/10X,•'ARRAY(J, WRITE(2,60)nblock,j,xmean(j),j,sigmax(j),j,r(j) ITE( R 6,60)nblock,j,xmean(j),j,sigmax(j),j,r(j) W END DO END omt3’LC ’il,3x'xmean('il')«',el2.5,3x format(3x’BLOCK ma - yinean/fnpt - ymean nt npt « fnpt Oj l,nterras * j DO END DO END () rj + ft(,,lxa) xmean(j))*(y(i)-ymean) - (fctn(x,i,jl,xbar) + r(j) - r(j) sigma » sigma + (y(i) - ymean)**2 - (y(i) + sigma » sigma ra(,) array(j,k)/(freel*sigmax(j)*sigmax(k)) - array(j,k) ra(,) array(j,k) ■ array(k,j) im - dsqrt(sigma/freel) - sigma re « p - 1 - npt « freel ma(l • xmean(jl)/fnpt • xmean(jl) imxj « dsqrt(tsig) « sigmax(j) - + inpnt + 1 - i Ok 1,j-1 - k DO l,j-l - k DO END DO END END DO END » array(j,k) + sidj*sidk k d i s * j d i s + ) k , j ( y a r r a » ) k , j ( y a r r a () r(j)/(freel*sigmax(j)*sigma) j ( r ■ r(j) sg sigmax(j)/freel - tsig END DO END “ l j n imO 0.0 ■ sigmaO - - ) ) l k ( ) ) n l a j ( e n m a x e m - x ) - r a ) b r x a , l b k x , , i l , j x , ( i , n t x ( c f n ( t c f - ( k « d i s j d i s ma(l - ma(l + fctn(x,i,jl,xbar) + xmean(jl) - xmean(jl) chisq chisq ml 0.0 ■ rmul l k - kl i j O 0.0 * aO 244 -0.0 l j ' jl no n ooo n n ooonnonoooo 1 array(4, ), k array(4, array (5, ), k 1 array (6, ), k array (7, ), k array (8, ) k 1 array array (4, ), k 1array (5, ), k array (6, ), k array (7, ), k array ( 8, ) k Oj 1,nterms - j DO RETURN block, nterms, chisq, ftes, chisqr, RPRINT(n call 1,nterms - j DO UNCERTAINTIES CALCULATE N IF END sqrt(sigmaO) « sigmaO DO END chisqr/fnpt « sigmaO DO END chisq/freen - chisqr DO END l,npt - 1 DO DO END 1,nterms * J1 DO SQUARED CHI & COEFFICIENTS,FIT CALCULATE END aO,sigmaO,a,sigmaa,xbar,nfree) ELSE a0 - ymean - a0 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ WRITE(2, '(8(2x,fll.5)/)' )array(l,k),array(2,k),array(3,k) '(8(2x,fll.5)/)' WRITE(2, fe « p - trs 1 - nterms - npt « nfree WRITE(6, ’(8(2X,Fll.5)/)')array(l,k),array(2,k),array(3,k) WRITE(6, 1,nterms « k DO re - ntenns - freej nfree - freen DO END ) ’ ) / COEFFICIENTS” ARRAY(J,K) E S WRITE( 6, R E ' V N I " (/10X, ml sqrt(rmul) - rmul ts (rmul*freen)/((1.0-rmul)*freej) - ftes fti * fti + aO + yfit(i) * yfit(i) imaj « sqrt(sigmaa(j)) « array(j,j)*chisqr/(freel*sigmax(j)**2) sigmaa(j) « sigmaa(j) chisq « chisq + (y(i) - y£it(i))**2 - (y(i) + chisq « chisq () a(j)*sigma/sigmax(j) - a(j) Ok 1,nterms - k DO J),r(j) WRITE(*,*)a( END DO END O a - a(J)*xmean(j) - aO - aO rmul - rmul + a( + j rmul -)*r( j)*sigmax(j)/sigma rmul * + inpnt + 1 * i sigmaO - sigmaO + chisqr*xmean(j)*xmean(k)*alf + sigmaO - sigmaO alf - array(j,k)/(freel*sigraax( j )*sigmax(k)) array(j,k)/(freel*sigraax( - alf Ok • 1,nterms • kl DO O1 l,npt - 1 DO END DO END DO END £ti ■yi() a(j)*fctn(x,i,j,xbar) + yfit(i) ■ y£it(i) RT(,('EEMNN ERO’')’) O R ZE ZERO'’)') WRITE(2,’(''DETERMINANT WRITE(6,'('’DETERMINANT () aj + r(k)*array(j,k) + a(j) - a(j) ts 0.0 - ftes - kl - k “ J1 “ j » + inpnt + 1 » i 245 c subroutine MATINV(array,norder,det) DOUBLE PRECISION array,amax,save DIMENSION array(8,8),ik(8),jk(8) 10 det » 1.0 11 DO 100 k ■ 1,norder c c FIND LARGEST ELEMENT ARRAY(I, J) IN REST OF MATRIX c amax *■ 0.0 21 DO i.« k,norder DO j - k,norder IF (dabs(amax).LE.dabs(array(i,j))) THEN amax ■ array(i,j) ik(k) - i jk(k) - j END IF END DO END DO c c INTERCHANGE ROWS & COLUMNS TO PUT AMAX IN ARRAY(K,K) c IF (amax .EQ.0.0) THEN det * 0.0 go to 140 END IF i ik(k) IF (i - k) 21,51,43 43 DO j ■ 1,norder save ■ array(k,j) array(k,j) ■ arrayd, J) array(i,j) > -save END DO 51 j ' jk(k) IF (j - k) 21,61,53- 53 DO i - 1,norder save ■ array(i,k) array(i,k) < array(i,j) array(i,j) -save END DO c c ACCUMULATE ELEMENTS OF INVERSE MATRIX c 61 DO i - 1,norder IF (i.NE.k) arrayd,k) - -arrayd,k)/amax END DO C DO i « 1,norder DO J - 1,norder IF ((i .N E .k ).A N D .(j .N E .k )) 1 arrayd,j) - arrayd,j) + arrayd,k)*array(k,j) END DO END DO C DO j ■ 1,norder IF (j.NE.k) array(k,j) - array(k,j)/amax END DO array(k,k) ■ 1.0/amax 100 det » det*amax c c RESTORE ORDERING OF MATRIX c DO 1 - 1,norder k - norder -1+1 j - ik(k) ' IF (j.GT.k) THEN DO i - 1,norder 246 save * array(i,k) array(i,k) * -array(i,j) array(i,j ) - save END DO END IF i - jk(k) IF (i.GT.k) THEN DO j - l,norder save - array(k,j) array(k,j) - -array(i,j) array(i,j) - save END DO END IF END DO C 140 RETURN END c c $$s$$$$$$$$$$$$$$$s$$$$$$$$$s$$s$$$$$$$$$$$$s$$$$$$$ c subroutine RPRINT(nblk,nterm,chisq,chisqr,ftes, 1 a0,sigma0,a,sigmaa,xbr,nfree) INTEGER block,point DIMENSION a(8),sigmaa(8) WRITE (2,20)nblk,nfree,ntemi,xbr WRITE(6,20 )nblk,nfree,nterm, xbr 20 format(/15x,'OUTPUT FOR FIT TO BLOCK ',12, 1 5x', No. of degrees of freedom * 'I4/15x, 1 'No. OF TERMS IN FIT - ’l2,5x'Mean UT - 'f8.5) WRITE(2,30 )a0,a(l),a(2),a(3) WRITE(6,30)a0,a(l),a(2),a(3) 30 format(/4x'A0- 'F10.4,5X’A1- 'Fl2.4,5x 1 'A2- 'F12.4,5x'A3- ’fl2.4) WRITE (2,40)sigma0,sigmaa(1),sigmaa(2),sigmaa(3) WRITE( 6,40 JsigmaO,sigmaa(1),sigmaa(2),sigmaa(3) 40 format(3x'Sigma(A0)- 'F10.4,2X'Sigma(Al)- ' 1 F10.4,2x'Sigma(A2)- ’F10.4,2x'Sigma(A3)« 'fl0.4/) WRITE(2,50)a(4),a(5),a(6),a(7) WRITE(6,50)a(4),a(5),a(6),a(7) 50 format(/4x'A4- 'F12.4,5X'A5- 'F12.4,5x 1 'A6- 'F12.4,5x'A7* ’fl2.4) WRITE( 2,60)sigmaa(4),sigmaa(5),sigmaa(6),sigmaa(7) WRITE(6,60)sigmaa(4),sigmaa(5),sigmaa(6),sigmaa(7) 60 format(3x'Sigma(A4)- 'F10.4,2X'Sigma(A5)- ', 1 F10.4,2x'Sigma(A6)- 'F10.4,2x’Sigma(A7)- *fl0.4/) WRITE(2,70)chisq,chisqr,ftes WRITE(6,70)chisq,chisqr, ftes 70 format(1Ox'VARIANCE - ’FI2.4,5x'REDUCED CHI SQUARE - 'F10.4,3x, 1 'FTEST(R) - ’F10.4/) RETURN END c c $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ c subroutine DRIFT(x,y,nterms,npt,inpnt,xbr,nblock, 1 b0,b,Trad,Cal) REAL nodRA DIMENSION x(650),y(650) ,b( 8) COMMON/lump3/dabar(650),bline(650),UT(650),block C0MM0N/lump4/sign, night, dRAin, ddecin COMMON/lumpf/freq(36),trans(36), emis( 36) 10 WRITE(2,20)nblock,nterms,xbr WRITE(6,20)nblock,nterms, xbr 20 format(/15x,'OUTPUT FOR FIT TO BLOCK ',12, 1 /15x'No. OF TERMS IN FIT - ’I2,5x'Mean UT - 'f8.5) WRITE(2,30)b0,b(l),b(2),b(3) WRITE(6,30)b0,b(l),b(2),b(3) 247 30 format(6x'AO- 'F10.4,4X'A1« 'F12.4,4x’A2- 'F12.4,4x’A3- 'fl2.4) WRITE(2,50)b(4),b(5),b(6),b(7) WRITE(6,50)b(4),b(5),b(6),b(7) 50 format(6x'A4- ’F12.4,4X'A5- ,F12.4,4x,A6- 'F12.4,4x*A7- 'fl2.4) c DO j - l,npt i - J + inpnt scor ■ 0.0 bcor - 0.0 DO k « l,nterms bcor - bcor + b(k)*FCTN(x,i,k,xbr) kl - k - 1 scor - scor + k*b(k)*FCTN(x,i,kl,xbr) END DO y(i) - y(i) - bcor - bO READ(3, *)sign,nodRA,signal,dal,da2,ami,am2, ak airm - (ami + am2)/2.0 flcor » -75.0*scor*nodRA/(Cal*szint(ak,airm. Trad)) dabar(i) - dabar(i) - flcor END DO RETURN END c c $$$$$$$$S$$$$$$$$$$$$S$$$$$$$S$$$$$$$$$$$$$$$$$$$$$S$ c subroutine OUTPUT(kopt,Cal) REAL nodRA INTEGER block,point DIMENSION ns(10),bmean(10),sigmab(10),stderr(10) COMMON/lumpl/m,n,dat(6,3) C0MM0N/lump2/jmax,Trad,tspike,option,jflag C0MM0N/lump3/dabar (650), bline( 650), UT( 650), block , C0MM0N/lump5/omega, npts( 10), point (10 ),Tatm IF (kopt.EQ.1) THEN ; 5 REWIND 3 DO j - l,n READ(3,* ) sign,nodRA,signal,dal,da2,ami,am2, ak am - (ami + am2)/2.0 dabar(j) - -75.0*signal/(Cal*szint(ak,am,Trad)) END DO END IF c nptot * 0 nsptot - 0 suroean « 0.0 sigsum - 0.0 sersum - 0.0 c REWIND 3 DO k • 1,block nl ■ point(k) - npts(k) + 1 n2 - point(k) spk - tspike*10000.0 newns - -1 oldns - -2 WRITE(*, ' (5(4X,I5))*)nl,n2,point(k),npts(k),np DO WHILE (oldns.LT.newns) np - npts(k) n s (k ) - 0 bmean(k) - 0.0 sigma2 - 0.0 DO j ■ nl,n2 IF (abs(dabar(j)).LT.spk) THEN bmean(k) ■ bmean(k) + dabar(j) ...ELSE . np - np i ns(k) - ns(k) + 1 248 END IF END DO oldns - newns newns « ns(k) bmean(k) - bmean(k)/np DO j « nl,n2 IF (abs(dabar(j)).LT.spk) 1 sigma2 ■ slgma2 + (dabar(j) - bmean(k))**2 END DO sigsq - sigma2/(np-l) slgmab(k) - sqrt(sigsq) spk - tspike*sigmab(k) stersq - slgsq/np stderr(k) - sqrt(stersq) END DO WRITE( 2,80 )k, bmean( k), slgmab( k), stderr (k ), np, ns (k ), spk WRITE(*,80)k, bmean( k), sigmab(k), stderr(k ),n p , ns (k ), spk 80 format(//,lOX,'BLOCK ',12,/,10X,'MEAN - 'F8.4'mK',5X,'SIGMA - 1 F8.4'mK',5X,'STD. ERR. - ' F8.5' mK',/15X,'No. OF POINTS - ', 2 I4,10X,'No. OF SPIKES - ',13,/,30X,'SPIKE THRESHOLD - ’F10.3) nptot - nptot + np nsptot ■ nsptot + ns(k) sumean * sumean + bmean(k)/stersq sigsum - sigsum + 1.0/sigsq sersum • sersura + 1.0/stersq IF (jflag.EQ.l) THEN WRITE(2,90) 90 format ( / ,3x,'No.’,6x, 'UT',7x,'NEW MEAN',6X,'NEW DATA’, 1 6X,'AIRMASS',6x'SIGN',6x,'K(H20)'/) DO j - nl,n2 READ(3,*)sign,nodRA, signal, dal, da2, aml,am2, ak air - (ami + am2)/2.0 WRITE(2,100) j,UT(J),bline(j),dabar(j),air;sign, ak 100 format( 2x, 14,4(3x, f9.4), 6x, f4.1,6x, £5.3) END DO END IF DO j - nl,n2 WRITE(5,'(2(2x,f10.4))')UT(j),bline(j) WRITE(8,'(2(2x,£10.4))')UT(j),dabar(j) END DO END DO amean - sumean/sersum sigma2 ■ block/sigsum stdev ■ sqrt(sigma2) ster2 » 1.0/sersum ster * sqrt(ster2) WRITE( 2, '(/,•' RESULTS FOR WHOLE NIGHT",/)') PRINT*,'RESULTS FOR WHOLE NIGHT’ WRITE( 2,140 )nptot, nsptot, t spike, amean, stdev, ster WRITE (*,140) nptot, nsptot, tspike, amean, stdev, ster 140 format(/,5x,'No. OF POINTS - ’,I6,5X,'No. OF SPIKES - '13, 1 5X,'SPIKE THRESHOLD - 'F9.2,’ sigma'/,5X,'MEAN - 'F10.5, 2 'mK',5x, 'STD.DEV. - 'F10.5,5X,'STD.ERR. - 'F10.5,'mK') WRITE(2,150)Trad,Cal WRITE(*,150)Trad,Cal 150 format(/,5X,'Trad »'F7.3,5X,'CAL -’F8.5,5X) RETURN END c c $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ c subroutine FTESTC(chisav, chisq,nterm,nl, test) c IF (chisq.EQ.0.0) THEN WRITE(*,'( "CHISQ - 0..." )') WRITE(2,'("CHISQ - 0.")') test -0.0 - . 249 ELSE nfree « nl - nterm - 1 Fchi - (chisav - chisq)*nfree/chisq IF (nfree.LE.20) THEN test ■ 0.0 ELSE IF (nfree.LE.30) THEN test « fchi - 4.2 ELSE IF (nfree.LE.40) THEN test « fchi - 4.1 ELSE IF (nfree.LE.60) THEN test - fchi - 4.0 ELSE IF (nfree.LE.120)THEN test - fchi - 3.9 ELSE test » Fchi - 3.8 END IF WRITE(2,110)Fchi,nfree WRITE(*,110)Fchi,nfree 110 format(/I0x'CHI-SQUARE F-TEST VALUE IS 'F10.5, 1 FOR 'IS* DEGREES OF FREEDOM'/) END IF RETURN END C c $$$$$$$ssss$$$$$$$$$$$$$$$$$s$$$$$$$$$s$$$$$$$$$$$s$$$$$ c function FCTN(x,i,j,xbr) DIMENSION x ( 650) xl * x(i) - xbr IF (j.EQ.O) THEN fx - 1.0 ELSE IF (j.EQ.l) THEN fx « xl ELSE ( fx - xl**j END IF fctn « fx RETURN END c c $$s$$$$$$ss$$$$$s$$$$$$$$$$$s$$$$$$$$$ss$$$s$$$$$$$$$ c function FINT2(ak,airmas) COMMON/lumpf/freq( 36), trans( 36), emis( 36) c sum2 ■ 0.0 DO j - 1,35 j l - J + 1 f - (freq(jl) + freq(j))/2.0 delnu - (freq(jl) - freq(j)) e ■ (emis(jl) + emis(j))*ak/2.0 3 t - (trans(jl) + trans(j))/2.0 term - e*exp(-e*airmas)*(f**2)*t*delnu sum2 - sum2 + term END DO c fint2 > sum2 RETURN END c c $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ c function SZINT(ak,airmas,Trad) COMMON/lumpf/freq( 36 ),trans( 36), emis( 36) Trad -.2.70 hbyk « 1.4388 sum « 0.0 250 DO j 1,35 jl J + 1 f (freq(jl) + £req(j))/2.0 delnu (freq(jl) - freq(j)) t (trans(jl) + trans(j))/2.0 em (emis(jl) + emis(j))/2.0 X hbyk*f/Trad xby2 x/2.0 etox exp(x) thxby2 (etox - 1.0)/(etox + 1.0) Gx (x**4)*etox*((xby2/thxby2)-2.0)/((etox-1.0)**2) atm ak*em*airmas term Gx*exp(-atm)*t*delnu sum sum + term END DO C szlnt - sum*(Trad**2) C RETURN END I 251 program ksnorm2 CThis prog takes in SZ signal data, bins it into a histogram arrangement. CThe mean and sd of the data is then calculated and a normal of the same Cmean and sd is fitted to the data. The value of chi sqared comparing Cthe binned data and the appropriate fitted values is then calculated Cto obtain a measure of goodness of fit. integer n,i,nn real szdata(4,5000),data(5000) real ks,prob,spike character*20 fullfilename call datain(n, szdata, fullfilename,numblocks, spike) call kstest (szdata, da t a , n, ks , prob, spike, numblocks) end subroutine datain(n,szdata,fullfilename,numblocks,spike) CThis routine reads the approprite szdata in, and finds how many points Cthere are in the data set. integer n, numblocks real szdata(4,5000),spike character*20 fullfilename call makename(fullfilename,spike) call readdata(szdata,fullfilename) call findend(szdata,n) j call findblocks(szdata,n,numblocks) end 0************************************************************************ Q************************************************************************ subroutine kstest(szdata,data,n,ks,prob,spike,numblocks) real szdata(4,5000),ks,prob,data(5000),mean,sd integer n,block,nn do block-1,numblocks nn-0 call normdata(n,szdata,mean,sd,spike,block) do i-l,n if (szdata(3,i).eq.block) then if (szdata(4,i).ne.l) then data(i)-szdata(2,i ) nn*nn+l end if end if end do print*,'Block ',block,' Mean ',mean,' SD ’,sd call ksone(data, nn,ks,prob,mean,sd) call output(ks,prob,n,nn,block) end do end q************************************************************************ subroutine normdata(n,szdata,mean,sd,spike,block) 252 CThis routine calculates the expected frequencies of the bins on the Cbasis of a normal distribution with same mean and sd as the szdata. CThis is passed via normarray. real szdata(4,5000),mean,sd,spike integer n,i,block call statistics(szdata,n,sd,mean,spike,block) Cprint*,'Block ',block,'Spike ',spike Cprint*,'Mean-', mean,'SD-',sd end C************************************************************************ subroutine makename(fullfilename,spike) CThis routine produces the filename from which szdata will be read. character*15 name character*20 fullfilename character*3 number character*l dabar real spike print*,'Enter general file name' read(*,'(A15)') name print*,'Enter number of stage for test (1-raw,2»atmos,3-full)' read(*,'(A1)') dabar print*,'Enter day number as 3 digits (eg. 003)' read(*,'(A3)') number fullfilename-name//dabar//'.'//number print*,'Input spike threshold' read*,spike end ( Q**** ***************************************************************** *** subroutine readdata(szdata,name) CThis bit reads from the named file into the 2D array szdata. integer i real szdata(4,5000) character*20 name open(unit-1, file-name,status-'old') do i-1,5000 read(1,*,end-5) szdata(1,i ),szdata( 2, i) end do 5 end 0* ****************************************************** ***************** subroutine findend(szdata,n) CThis bit finds where the actual data in szdata finishes. This is Csignified by the ut and szsig (1st and 2nd dimensions) both - 0. integer n real szdata(4,5000) n*l do while ((szdata(l,n).ne.0.0).and. (szdata(2,n).ne.0.0)) n-n+1 end do * n-n-1 253 end subroutine f indblocks( szdata,n,numblocks) CThis attempts to recover the block structure of the data by looking at Cthe time difference between successive points. If the time difference Cis large then it is taken that there is a block gap at that point. CThe block number for a given data point is put into the third dimension Cof SZDATA. real szdata(4,5000),timediff,blockdiff,block integer n ,i,numblocks parameter (blockdiff*0.02) block*1 szdata(3,1 )*block do i*2,n timediff-abs(szdata(1,i)-szdata(1,i-1)) if (timediff.ge.blockdiff) block*block+l szdata(3,i)-block end do print*,'Number of blocks is block numblocks-block end Q************************************************************************ SUBROUTINE KSONE(DATA,N ,D,PROB,mean,sd) real nrm integer N DIMENSION DATA(5000) CALL SORT(N ,DATA) EN-N D-0. FO-O. DO J * 1 ,N FN*J/EN call norm(data(j ),mean,sd,nrm) FF-nrm DT-AMAX1(ABS(FO-FF),ABS(FN-FF) ) IF(DT.GT.D)D*DT FO-FN end do PROB■PROBKS(SQRT(EN)*D) END q************************************************************************ 0************************************************************************ subroutine norm(x,mean,sd,nrm) COn the basis of the mean and sd of the experimental data, calculates the Ccumulative probability at a given point in the distribution on the basis Cthat the expected distribution is normal. real mean,sd,x,nrm integer ifail ifail-0 u*((x-mean)/sd) nrm=sl5abf(u,ifail) . end 254 0 ************************************************************************ 0************************************************************************ subroutine output(ks,prob,n,nn,block) real ks,prob Ccharacter*20 fullfilename integer n,deadblock,nn,block character*25 outfile print*,' ' print*,'Block'number block print*,'Points in block is ',nn print*,'KS value is ',ks print*,'Probability of fit is ',prob print*,'Number of points is ',n print*,' ' coutfile-’ksout'//fullfilename copen(unit-2,file-outfile,status-'new') cwrite(2,'(A51)')'Normal fit to the data in file ',fullfilename cwrite(2,*)'Points remaining is ',nn cwrite(2,*)'KS test value is ',ks cwrite(2,*)'Probability of a fit is ',prob cwrite(2,*)'Number of points is ',n end 0 ************************************************************************ 0************************************************************************ 255 program statistics3 real x(2,5000), p(5000),sx,ssx,mean,sd.se,ptemp integer i,j,n,pl,p2 character*20 inputfile.outputfile integer*4 seed print*,'Input file name? ' read(*,'(A20)•),inputfile print*,'Output file name? ' read(*,'(A20)'),outputfile print*,’Input seed value (large odd integer)' read*,seed open(unit-1,status-'old',file-inputfile) n-0 do i-1,5000 read(1,*,end-10) x(l,i),x(2,i) n-n+1 end do 10open(unit-2, status-'new',file-outputfile) CThis is S.Spero's algorithm to randomise the order of the data do i-l,n P(i )“i end do cseed*ran(seed) cdo i-1,2000 cpl-int(ran(seed)* n) cp2 * int(r an(s e e d )* n) cptemp=p(p2) cp(p2)=p(pl) cp(pl)-ptemp cend do sx-0 ssx-0 do i-l,n sx-sx+x(2,p(i)) ssx-ssx+x(2,p(i))**2 mean-sx/i sd-((ssx/i)-(mean**2) )**0.5 se-sd/(i**0.5) write(2, *), i.mean,sd,se end do print*,'Final values are' print*,'Mean- '.mean print*,'SE- ',se end 256 B.4 Chapter 5 A number of programs axe used in this chapter to control the digital PSD system. Many of these are hand-assembled 6502 machine code. Included here, though, is the BBC BASIC code for the user’s computer used to drive the whole system. This program is based on an original version by Mark Hooker, heavily modified by myself to tailor it for the 3 Channel Instrument sjrstem. 1 ’TV255.1 2 HDlEH=fc5BFF MON ERROR QCt!Ef0:FRINTFER. ERL: REPORT: STOP 2CW3DE 6 ?WWXscr«n_hea 40PR0Ccold_start 5et>Diccunt%(3.2,50) ,ti»?%(2,50) .on%(8,2.50) ,nod%(2.50) 52DJDfciean(3) ,sd(3) .sun(3) ,ssua(3) ,sssun(3) :aJbort=FRLSE:irit_oJc*^ALSE 55R1M a<.KT% HAS SPACE FOR 3 CHANNELS. 2 CHOPS PEE NX AND 50 NOD CYCLES 60REPEAT ■WPROQww block: PROCscreen update 90REPEAT 1WREPEAT: PROCwait: UMILreadv=miE 110REPEAT: PROOHait: :tMTL (csi=si) ORabort^TRlE i2^IFahcrt=mi£ THmabrxt=f7diE:readN^'ALSE:csi^:GCfIO120 13W10DE 6 14Wru23.1,0;0:®:O: 145 PROCstats l50PR0Cnod:PftXscreeri header: PftOCscreen_urdat e 155 PROCsd 16W.MIL cif=if 162 PROCsd 165 vn.r7:VrU7 l70PROCdataout 175 IF HC*0 PROChardcOTV ie.0OSCLI"A. *.* L" lWOSCLT'CAT" 2O0PPJKT ANCmSt BI/XK?":ASSETS -iiW.MIL 257 2: 290D£FPR0CVcdt 300REPEAT 310PR0CXeyboard .i2CntmL?I%=l 330?D%=0: c±ml-0 345IF ?0%>13 THEH PRIM”TATA OUANITIY ERROR":STOP 35©P0Rn=5TO?Q^SraP3 36®dml««dml+l 370count% (cbnl .csi.cif )=? (S%+n) *410000+? (S%+o+l) *4100+? (S%+n+2) 38CIFccMnt\(cbnl,csi,cif) >&7FFTFTTHDkxmtk(chnl.csi,ciI)»-(tiTrF7F-countk(chnl,csi,cif)) 3 ? w n ii 395ti»?A ;'s i.c if M0OOO*?v*+lOO«? 396REK TIKE STORED AS HffiftSS 397chnl=l 398P0Rn=lTO4 ? 399rm% (dial. csi. c ii) *? (S%+n) DIV16 400an% (cbnl+1. csi. cif) =? ($%+n) WDD16 401chnl*cml+2 ' 402NEXT ' 405 nod%{csi.cif)*=nod 407PROCdat a_to_screen: PROCscreen jupdate 410 IFreadv«='IRUE THmcsi«rsi+l 420Q©PR0C 430: 440JSTPR0Cte\toard 450CALLJ& 46CIF?IViramPR0Ckey_pressed 470D4DPR0C 480: 4:iODETPftCCkev pressed 500?F¥=0 510*1015.1 - - 258 li i:oOTHQfreadv=TOUE EL£Ereadv=FALSE 530n7IAF=ASCrA")THENabort=TRUE ELSEabort=FALSE M0IF?IMASC("O")THQ ^WlF?l>F=A5C("H")raD 560n?L*=l29IHEN?X*=l 570IT?1A=13CTHEX?X%=2 58CIF?L**131THDf?XV=3 590IF?lApl32lHQf?X%=4 6O0IF?1A=133THEX?X\=5 6lOIF?lA=134TaEJf?X*=6 620n?L%=135raEN?XV=7 630]J?I*=136THDr?Xfc8 640IF?lA=14iraEK? «?»+?X%) =? 6MIF?L%*14OTHDJ? (G%+?X%)«? «*+?X%)-l:IF? (G%+?X%) -ScFTIKEN? (GH+?X\) =0 660EHDPROC 670: 680DEFn+jain(A) 69OIFA=0TODM 700IFA=l‘n2J*=3 710IFA“2THDM0 720IFA=3THEW=30 73MFA=4,IHN=100 740IFA=5T«a+*300 750IFft=6raJW=lE3 76ClFA=7raEJ*=. nLSB=0 770: 78flrEFPR0Coc>ld sta rt 790*1X4.2 800*FX225.128 810VrU23.1.e;0;0:0; 820?S%=7 83dn=0: RHi-nT:CALLTt:CALLV*:n=n+l :UrnTL?R%=&96 ORn=10 840IF?R%< >&96THENPRINT'Startup error, press 259 870osrdra=&FFB9 875 INJUTDO YOU VJOT HARDCOPY":AS 876 IF l£FT$(AS.l) p'V ' THEN HC=1 ELSE HOO 880ENDPR0C 890: 9WDEFPR0Chev_block 910REPEAT 920CLS 530DCVP Block ID (7 characters max) ";idS* 94BDOVT' Hew many points in th is block M;i i ' :cLf=0 How marry samples per nod ";si':esi*0:si**si+l 955INPUr' Header information headers 960CLS 970PPJNT'Obiect ID :":idS* 9 SOPRINT'Points cn th is map : '': i f ' 990PPJNrsani>les per integration: ";si' 995PRIHT "Header info: "rbeaderS* lOOOPPJNT’ARE THESE DETAILS CORRECT ":AS-CCTS 1010ttfiTLAS=’T' 102OCLS 1024 YI*.r7:FRINrSET MOD POSITION POSITIVE"'"TO) HIT RETURN" 1025 AS=CETS 1026 nod=l 1027 a s 1030readv-FALSE: ?D«p=0: V=0 1040IFidS < > "’THENf ile-OPDOUT (idS) 1045 K 1050OJDPR0C 1060: 1070DETP80Cdata to screen 1080x tab=l I090iCRn^TO?C)teTiP3 1100PRIHTTAB(x jtab); 260 IIK -D ? (5%m) 1120PPJNT;"?(S%+n); llWlF.M^+ti+l) 1140PRINT; ”? (SMtrtL); 1150IF? ($%-m+2) 1160PRINr;'?(S*m+2); Hite.. tab=x .talH-lO 118«® rr hroehdproc 12W: 1210 PEF FROCstats 1215 FOR dml=l TO 3 1220 FOR 1=1 TO si-1 1225 sffiichnl)=s'JBs(dird)-*iK«i%(I.cli)*count%(ciml.I.cif) 1230 NEXT I 1240 nean(chnlMsunichnl) /( (si-1) • (cif+1))) 1250 NEXT <±nl 1320 ENDPR0C 1400: 1410: 1420 1ST PRCCscreen header 1430 CLS 1440 PRINT‘OBJECT ID ’POINTS PER BLOCK: ‘‘SPC (5) "CCKPIZISD:" 1450 PRINT‘CHOPS PER NODT’SPCfSrOMPICTED:" i460pmrcH. wirre black yell/ v 1470PPJNT‘GUN No.*” “GAIN"' "CHART"'"NEWT * "SET ‘"TIME"‘ STRINGS(40, 1400 VDJ2S,0.24.39.13 1490 ENDPR0C 1499: 1500 PEE PROCscreen update 1510 h v 1^15 1FV=10 THEN PRINT 1520 VDU2S,0.24,39.0 iv 1550 PRINT TAB(14,0)idS 15*60 PRINT TAB(17.1)if:" • 1570 PRINTTAR(17.2)si;" 1560 PRINT TAB(33.1)cif 1590 PRINT TAB(33,2)csi:" 1660 FOR 1670 FOR ciml=lTO3:PRINrTAB{chnl*l0.5);nigain(?m%(cfanl.c5i.cif));:NEXr 1680 FCRdiart=lTO3:PRINTTAB(chart*18,6) :?(G%+cbart);:NBCr 1685 #%=&203©9 1690 FPtoean=lT03: PRINTTAB (raean,'10.7) :aean (mean): :NECT 1710 FCftsd=lTO3:FRINnAB(sd*10.8) ;sd(sd); :NDCT 1720?t=&90a 17„'5 PRINTfAB(5,9)?¥%;" ,,:?{V%+1)";?(V%+2): 1730 VTO28,0.24.39,13 1735 PRINITAB(O.V): 1740 ENDPROC 1800 KT PROCdataout 1810 PRINTtfile, idS 1815 PRINTffil?.headers 1820 FDR M> TO if 1830 FOR 0=1 TO si-1 1840 PRINT §:ile. tine%(J,I).count%{l,J.I) .cc»jnt%(2,J.I) ,count%(3,J,I) .gn%(l,O.I) ,an%(2.J.I) ,an%(3,J,I) ,nod%(J,I) 1850 NHCT J 1660 NEXT I 1870 CLOSEffile 1900 INDPRCC 2000DEF PROCnod 2018 Csi'O 2020di= cif+ l ^.OPROCdoood 2850Q©PROC 2100PEP PROCdotyM . 262 2110 ?1A=ASC("N") 2115 CALL 7>. 2120 nod=ncd*-l 2130 tt-TEE 2140 REPEAT UNTIL TO®=tt+100 2145 ?1A=ASC("Z"> 2147 CALL T% 2i5C4NDffiOC 2200 I5T PROChardccpy 2210 *FX6.0 2220 VDU2 2230 PRINT'FLOCK HANE:".ii> 2240 PRINTUEADER INFO:":headers 2250 PRINT'CHOPS PER NOD:"si.*7COS IN EHOCK:":i: 2260 PRINT'CH. WHITE". /•BLACK". ."YELLOW" 2265 0^420309 2270 PPINTGALN "jsn’rd .csi.rii) .on%{2,csi.cif) .an%(3,csi.cif) 2280PRIM*’MEAW "joeandi .mean (2) ,oean(3) 2260PRINTSP "jsdii)} ,sd(2) ,sdt3) 2295 PRINT'' * 2300 vr*j? 2310 a m o c 5000 1EF PROCsd 3010FDR chnl=l TO3 3040 TOR 1=1 TO si-1 304*1 sssm(chnl)”smsin(chnl)-t 3050 ssiia(ciinl)=ssinidml)+(coijnt%(dinl.I.cil'-l)) ‘2 3060 NEXT I 3070 sd(chnl)=SOR(ABStssvc(chnl) / ((si-l)*cif)-(snsvm(chnl)/( (si-l)* cif)) “2)) /90R( (si-l)*cif) 3080 NEXT chnl 3090 e/i>pfco: 263 B.5 Chapter 6 In this chapter, the program Correct is used to correct for the component of the noise found in channels 1 and 3 found to be correlated with channel 2. program correct CUses routines to find the dependence of 3 channel astronomical Csignals to the atmospheric channel. real z(4,500),sx,sy,ssx,ssy,sxy,a(2),b(2),r real x(4,500) integer j,i,n,l character*20 inputfile,outputfile print*,'Input file name' read(*,'(A20)’)inputfile print*,’Output file name’ read(*,'(A20)’)outputfile open(file-inputfile,unit-1,status*'old') do i*l,500 read(l,*,end*10), z(l,i),z(2,i),z(3,i),z(4,i) n=n+l end do 10print*,n do j-1,2 sx=0 sy*0 sxy*0 ssx*0 ssy=0 do 1=1, n ? sxy*z.( 3, i)*z (2+ (j -1 )*2, i ) +sxy sx*sx+z(3,i) sy-sy+z(2+(j-1)*2,i ) ssx-ssx+z(3,i)**2 ssy-ssy+z(2+(j-l)*2,i)**2 ' end do a (j)*(n*sxy-sx*sy)/(n*ssx-(sx)**2) b(j)-(ssx*sy-sx*sxy)/(n*ssx-(sx)**2) r*sxy/((ssx*ssy)**0.5) print*,'Graph is... y- ’,a(j),'x + ’,b(j) print*,'Correlation coefficent R*',r end do do i*l,n z(2,i)-z(2,i)-(a(l)*z(3,i)) z(4,i)*z(4,i)-(a(2)*z(3,i)) end do open(unit-2,name*outputfile,status*'new') do i-l,n print*,z(l,i),z(2,i),z(3,i),z(4,i) write(2, *),z(l,i),z(2,i),z(3,i),z(4,i) end do end 265 A ppendix C Included Paper The following paper is based on work to which I have contributed: 269 ASTRONOMY & ASTROPHYSICS DECEMBER 1987, PAGE 557 SUPPLEMENT SERIES Astron. Astrophys. Suppl. Ser. 71, 557-560 (1987) COS-B upper limit to the > 70 MeV gamma-ray flux from a gamma-ray burst event of 1979 November 9 T. J. Sumner, D. L. Clements, O. R. Williams (*) and G. K. Rochester Imperial College of Science & Technology, Blackett Laboratory, Prince Consort Road, .London SW7, Great Britain Received March 2, accepted July 6, 1987 Summary. — Using the COS-B data base an upper limit of 2 x 10"7 cm-2 s*1 keV"1 has been set to the high energy (70- 1000 MeV) gamma-ray burst flux from a gamma-ray burst event of 1979 November, 9. This limit is consistent with a power law extension from the lower energy data with a differential index of as - 1.39. An upper limit of 5.4 x 1 0 '11 cm"2 s '1 keV"1 to the persistent emission is also obtained. Key words : gamma-ray bursts. ( 1. Introduction. (i) those with timing information only, (ii) those with timing information and extended loca Several catalogues of gamma-ray burst events now exist tion error boxes which are only partially overlapped by (Hurley, 1980; Mazets etal., 1981a, b, c; Klebesadel the COS-B field of view, etal., 1982 ; Baity etal., 1984 and Atteia etal., 1987). The result of scanning the whole of the recently released (iii) those with timing information and small location COS-B data base (Mayer-Hasselwander etal., 1985) to error boxes completely within the COS-B field of view, look for associated COS-B photon events is reported and here. Detection of high energy gamma-ray emission (iv) those with error boxes completely outside of the significantly beyond 1 MeV would enable distance upper COS-B field of view. limits to be derived beyond which the source would 194 events during active observational periods of COS- become optically thick to y-y pair production (see for B were included within the first two categories. In 2 cases example Verter, 1982 and Schmidt, 1978). This would (1976 Sept. 03) and (1978 Nov. 24) a COS-B photon was allow differentiation between Galactic and extra-Galac- detected within ten seconds of the burst’s Earth crossing tic origins. Existing data now extend to -1 0 MeV on time (Klebesadel etal., 1982 and Atteia etal., 1987). several events (Nolan et al., 1984) with one event having However, in both of these events the COS-B photon been observed up to 100 MeV (Share etal., 1986). A counting rate, evaluated for each event, was such that positive detection in the COS-B energy range (70- the significance of the associations was poor. 1000 MeV) would offer a unique opportunity to examine Only one event falls within the category (iii). This is a a gamma-ray burst source at even higher energies. gamma-ray burst of 1979 November, 9 (Mazets etal., 1981c) which occurred during a short ten hour COS-B 2. COS-B data base search. observation having a very low photon counting rate. The For the purposes of this study the gamma-ray burst position of the COS-B field of view is shown in figure 1. events can be separated into four classes : .Also shown are the KONUS 1 a error box (Mazets et al., 1981c) and the PVO/KONUS 3a error annulus (Atteia etal., 1987). The probability that the source actually lies (*) Current address: University of Leicester, Leicester, in the overlap region is limited by the lcr confidence level Great Britain. of the KONUS error box (see Atteia etal., 1987). For Send offprint requests to : T. J. Sumner. the purposes of this work the whole of the PVO/KONUS Astronomy and Astrophysics n’ 3-S7 December. — 10 270 558 T. J. Sumner et al. N° 3 annulus within the COS-B field of view has been used. Given the preceding discussion an upper limit to the This is equivalent to extending the KONUS error box high energy flux is derived from the fact that no photons linearly by a factor of six. During the whole ten hour were detected by- the COS-B instrument from the observation period only twenty photons were recorded gamma-ray burst. The probability that a given number of by COS-B from within a region consistent with the photons would be detected from such an event is PVO/KONUS annulus, given the COS-B angular resol determined by Poisson statistics. For zero photons the ution. This region is bounded by the dotted lines in probability is~e-m where m is the mean number that figure 1. The photons arrived at apparently random time would be detected from a large number of identical intervals. Those chronologically closest to the burst’s events. To set an upper limit at the 99 % confidence level Earth crossing time (Golenetskii and Guryan, 1981 and we must have m = 4.61. The average differential photon A tteia et al., 1987) arrived ~ 9 min before and ~ 21 s flux, F, is then equal to m /(At A£) cm-2 s-1 keV-1, after. The duration of the burst at lower energies was w here t is the time duration of the burst, AE is the ~ 5 s. As no COS-B photons were detected within ~ 5 s photon energy range to which the instrument is sensitive, of the burst’s Earth crossing time, it is possible to place and A is the effective area which is assumed to be an upper limit on the high energy gamma-ray burst flux. constant over the photon energy range. From Mazets When data from all ten hours of the observation etal. (1981c) the time duration of the burst between half period is used it becomes apparent that there is a non- intensity points was ~ 2.5 s. The effective area of the uniform distribution of COS-B photons over the field of COS-B r-ray telescope, given the inclination of the view making it difficult to subtract the intrinsic instru source to the axis of the instrument and the efficiency ment background from the twenty photons occurring during the observation, was — 10 cm2 and can be taken within the selected region. An upper limit to the as effectively constant over the energy range 70- persistent flux is therefore derived on the basis of these 1000 MeV. Using these data the upper limit to the high twenty photons. energy gamma-ray burst flux is 1.98 x 1 0 '7 cm" 2 s"1 keV “ *. 3. Results. 3.2 U pper lim it to t h e h ig h energy persistent flu x . — The twenty photons which were detected by 3.1 U pper limit to th e h ig h en erg y burst flu x . — COS-B from within a region consistent with the An upper limit to the high energy flux is obtained on the PVO/KONUS annulus during the ten-hour observation basis that no photons were detected by COS-B from the period do not represent a significant detection. If we burst: This assumes that all genuine photon events are assume the gamma-ray bprst source is a point source present in the released COS-B data set. In the case of a then an upper limit to the persistent emission can be rapid burst of photons it needs to be shown under what obtained from the largest grouping of photons, from conditions confused spark tracks from more than one within the twenty photons, which is consistent with the photon recorded in a single frame could have led to the COS-B point spread function. The largest such grouping photons being rejected. For two photons to have been contains eight photons. If all of these eight photons were recorded simultaneously in the COS-B instrument they from the burst source itself then, to a 99 % confidence would have had to have arrived within 500 nsec of each level, the upper limit to persistent flux from the source is other, this time interval being the delay between the 5.4 x 10” 11 cm~ 2 s~1 keV “1. reception of a gamma-ray coincidence signature and the spark chamber high voltage trigger (Bignami etal., 4. Discussion. 1974). The burst count rate would have had to have been ~ 106 s“ 1 for this type of double event to have occurred. Figure 2 shows the derived upper limit for the high After being triggered the spark chamber was « dead » energy gamma-ray burst flux together with the lower while the driving capacitor recharged with a time constant energy data of Mazets et al. (1981c). The upper limit is of 100 msec and most ionising tracks created in this consistent with a power law extension to the data from period would have been lost by diffusion. Nevertheless, a 300 keV with an exponent of as - 1.39. A spectrum with photon arriving within a few milliseconds of the time at an exponent of —1.39 would have resulted in the which the chamber was reactivated might also have detection by COS-B of a mean number of 4.6 photons contributed to a confused picture if a further trigger during the ~ 5 s burst. actually fired the chamber immediately. The event rate Empirical models invoking thermal synchrotron and would have had to have exceeded 103 s"1 over a period of bremsstrahlung mechanisms have been used to explain 100 msec for this second frame to have been rejected. the observed spectra of typical gamma-ray bursts below Even so the first photon would still have been accepted. 1 MeV. Liang et al. (1983) have analysed much of the It is thus difficult to see how a rapid burst of photons data of Mazets et al. (1981a, b c) in terms of thermal could have resulted in a failure to accept at least the first synchrotron models and their results for the particular photon unless the rate were in excess of 106s-1. burst being discussed here would predict a high energy N° 3 COS-B FLUX LIMITS FOR A GAMMA BURST ON 79/11/09 559 gamma-ray flux well below our upper limit. However, as Finally, evaporating black holes are among some of Pavlov and Golenetskii (1986) point out, thermal syn the more exotic models proposed to account for gamma- chrotron models have difficulty in explaining the high ray bursts (Page and Hawking, 1976 and see Verter, energy data of Nolan et .al. (1984), especially when 1982). Depending on the model-parameters such an quantum effects are included ; it has been found neces event could give rise to a peak in high energy gamma- sary to invoke power law contributions with indices rays in the range 100 MeV to 300 MeV. No evidence for between — 1.3 and — 3.7 to fit the data of Nolan et al. such a peak is seen in this work. (1984) up to 9 MeV. Our upper limit falls just within this range. In the single case in which a gamma-ray burst has been observed up to 100 MeV (Share et al., 1986) an Acknowledgements. empirical fit to the data required a significant power law component. Extrapolation of the Mazets et al. 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