An Investigation of Radio-Quiet Quasars Using Gravitational Lensing

AN INVESTIGATION OF RADIO-QUIET QUASARS USING GRAVITATIONAL LENSING

A thesis submitted to the University of Manchester for the degree of Master of Science in the Faculty of Engineering and Physical Sciences

2015

By Hannah Ruth Stacey Jodrell Bank Centre for Astrophysics School of Physics and Astronomy Contents

1 Introduction 1 1.1 Gravitational lensing ...... 3 1.1.1 History of gravitational lensing ...... 3 1.1.2 Gravitational lens theory ...... 7 1.1.3 Galactic substructure ...... 11 1.1.4 Microlensing ...... 14 1.2 Radiative Processes ...... 16 1.2.1 Thermal emission ...... 16 1.2.2 Synchrotron emission ...... 16 1.2.3 Free-free emission ...... 18 1.3 Radio-quiet quasars ...... 20 1.3.1 Quasar morphology ...... 20 1.3.2 Radio properties ...... 21 1.3.3 Source of radio emission from radio-quiet quasars . . . . . 26

2 Fundamentals of radio interferometry 29 2.1 Aperture synthesis ...... 29 2.2 The two-element interferometer ...... 31 2.3 u-v coverage ...... 33 2.4 Limitations ...... 36 2.5 Sensitivity ...... 37 2.6 Calibration ...... 37 CONTENTS

2.7 Imaging and Deconvolution ...... 39

3 Observations 41 3.1 Sample selection ...... 41 3.2 e-MERLIN observations ...... 42 3.3 Data reduction ...... 44 3.3.1 Loading the data ...... 44 3.3.2 Calibration ...... 48 3.3.3 Imaging the target ...... 57

4 Results 60 4.1 HS 0810+2554 ...... 60 4.2 RX J0911+0551 ...... 69 4.3 SDSS J1251+2935 ...... 77 4.4 SDSS J1330+1810 ...... 80

5 Summary and Conclusions 81

Appendix A i

Appendix B iii

Appendix C vii List of Tables

3.1 Details of e-MERLIN observations at L-band...... 42 3.2 Details of JVLA observations...... 44 3.3 List of L-band antenna weights (Argo, 2015)...... 58

4.1 Details of HS 0810+2554 from CASTLES (Kochanek et al., 2013). The position of each image, relative to image A, is given in arcseconds. The optical flux at I-band is given in apparent magnitude. . 62 4.2 e-MERLIN L-band image fluxes of HS 0810+2554, from JMFIT. The error given is the RMS noise in the data...... 66 4.3 JVLA X band image fluxes of HS 0810+2554. Results from Jack- son et al. (2015)...... 67 4.4 Model fitting results for HS 0810+2554 and RX J0911+0551 from JVLA observations. The source position is given relative to the galaxy position. For RX J0911+0551, the galaxy critical radius corresponds to the Einstein radius measured along the major axis. Results from Jackson et al. (2015)...... 69 4.5 Details of RX J0911+0551 from CASTLES (Kochanek et al., 2013). The position of each image, relative to image A, is given in arcseconds. The optical flux at I-band is given in apparent magnitude. . 70 4.6 JVLA C-band image fluxes of RX J0911+0551...... 74 List of Figures

1.1 The first lens discovered, quasar Q0957+561, at 4885 MHz with the JVLA from Reid et al. (1995). The two images of the quasar are shown (centre top and bottom) with large separation of 6”. The core of the quasar falls within the caustic of the lens galaxy, producing a lensed image of the core (bottom). The jets of the quasar fall outside the tangential caustic and are not lensed. . . . 4 1.2 Hubble image of so-called ‘Cosmic Horseshoe’, SDSS J1148+1930, an elliptical galaxy lensing a background galaxy. The extended source produces large arcs, close to an Einstein ring. Image credit: ESA/Hubble...... 5 1.3 Hubble image of Q2237+030, a quasar lens with image angular separation of 1.6”. The compact source is close to the line of sight through the centre of the galaxy, creating four images known as an ‘Einstein cross’. Image credit: ESA/Hubble...... 6 1.4 A simplified gravitational lens diagram. A light ray is emitted from source at diameter η and angular size β. It is deflected by the gravitational field of an object on the image plane at impact parameter ξ and angular size θ. The angle of deflection isα ˆ. . . . 8 1.5 The resulting images produced when the source is on a cusp of the astroid caustic. The caustics mapped onto the source plane are in red; the lens critical curve and time-delay contours are in green. . 12 LIST OF FIGURES

1.6 The resulting images produced when the source is on a fold of the astroid caustic...... 12 1.7 SED for NGC 253 from Peel et al. (2011). The blue dotted line traces the thermal emission, which peaks in the infrared and drops out at microwave frequencies. Free-free emission is traced by the red dotted line, which dominates below ∼100 GHz. The synchrotron emission is traced by the pink dotted line, which begins to dominate at frequencies of a few GHz...... 17 1.8 Synchrotron spectra of three astronomical sources at radio frequencies between 10 MHz and 30 GHz. The synchrotron emission from Cygnus A becomes self-absorbed at ∼20 MHz. Figure from Baars et al. (1977)...... 18 1.9 The unified model of active galactic nuclei: along the jet axis, the AGN is seen as a blazar; perpendicular to the jet axis, the AGN is seen as a Type 2 Seyfert galaxy; at intermediate angles, the source is observed as a Type 1 Seyfert or quasar. The different AGN morphological properties are labelled in the figure: the nucleus/black hole (BH) (and surrounding source of x-ray emission), broad line region (BLR), accretion disk (AD) and narrow line regions (NLR). Figure from Jovanovic and Popovic (2009)...... 21 1.10 Radio-loud quasar 3C175 at 4.9 GHz observed with the JVLA. The quasar can be seen in the centre, with characteristic double lobes from relativistic jets spanning 212 kpc. Figure from Bridle et al. (1994)...... 22 1.11 Optical against radio flux for samples of quasars at redshift 0.3 < z < 1.5 (Goldschmidt et al., 1999)...... 24 1.12 Optical against radio flux for samples of quasars at redshift 1.5 < z < 2.5 (Goldschmidt et al., 1999)...... 24 LIST OF FIGURES

1.13 The median radio ﬂux is correlated with the optical ﬂux. Each bin represents the median of thousands of radio-quiet quasars in the SDSS DR3 catalogue...... 25

2.1 Illustration of the antenna power pattern for a single antenna and projection onto the celestial sphere. Figure from Kraus (1966). . . 30 2.2 Simpliﬁed diagram of a two-element interferometer. There is a time

delay, τg, in the wavefront between the antennae, which must be corrected for before the signals are correlated. The incoming signal is shifted to a lower frequency by a local oscillator for analysis. The resulting signals are multiplied and integrated by the correlator. . 32 2.3 Vectors describing the relations between an interferometer baseline and the target source. B is the baseline vector between two telescopes; b is the projected baseline;s ˆ describes the unit vector in the direction of the source; σ is the vector from a point on the source to the source centre...... 34 2.4 Plot of u-v tracks for the e-MERLIN observation of RX J0911+0551 over a period of 10 hours. The e-MERLIN array has 7 antennae (21 baselines) with a maximum baseline of 220 km. The colours represent the frequencies across the band. The source has a low declination, so there is less extension in the v-direction (y-axis) and as a result the u-v tracks are more elliptical...... 35

3.1 The locations of the seven e-MERLIN telescopes around the UK (O’Brien, 2009)...... 43 3.2 Phase and amplitude data for point source calibrator OQ 208, without any ﬂagging and before any calibration had been applied. Note the reduced sensitivity at the edge of each IF. The data is displayed in POSSM by baseline for stokes LL polarisation only. . 46 LIST OF FIGURES

3.3 Phase and amplitude data for point source calibrator OQ 208, after flagging, before calibration. The channels at the edges of each IF have been flagged, as well as significant outliers. The data is displayed by baseline for stokes LL polarisation only...... 47 3.4 Delay solution table for point source calibrator OQ 208, shown baseline by baseline for LL polarisation only. The delays are within a few nanoseconds. The plots were generated using the AIPS task SNPLT...... 49 3.5 POSSM plot of OQ 208 amplitude and phases after the delay calibration is applied. Note that the phase slopes have been removed and they are now flat across each IF...... 50 3.6 POSSM plot of OQ 208 amplitude and phases after phase calibration applied, showing the LL polarisation only. The resultant phases are around zero. The amplitudes are unchanged...... 52 3.7 1407+284 amplitude and phases after flux and bandpass calibration. The amplitudes are smooth across the band, except for the Lovell-Cambridge baseline which is not as well calibrated...... 54 3.8 u-v-distance-amplitude plot for phase calibrator, J0901+0448, after calibration but before final flagging. Every 153rd visibility is plotted. The colours show the frequencies across the band. . . . . 56

4.1 CASTLES I-band image of HS 0810+2554 (Kochanek et al., 2013). North is up, and East is left. The lens system has a fold-configuration, with a merging south-western pair. The merging pair show a 0.7- magnitude difference in brightness, contrary to expectations. . . . 61 4.2 e-MERLIN L-band observation of HS 0810+2554 with robust weighting. Each of the four components of the source are detected at >5σ confidence. Image produced with CASA...... 63 4.3 Map of the confusing source, quasar SDSS J0813+2542, located 6’ from HS 0810+2554...... 64 LIST OF FIGURES

4.4 JVLA X-band image of HS 0810+2554, with RMS noise level of 3 µJy. The images are labelled clockwise from the most Westerly component. Image produced with CASA (McMullin et al., 2007). 68 4.5 Attempt to model HS 0810+2554 with a point source and PSF. The left image is the true data, the central image is the PSF model, the right image is the residuals when the model is subtracted from the data. The residuals show significant features, particularly around images A and B, showing the lensed images are not well fit by the PSF model. The white bar represents 1”. Figures from (Jackson et al., 2015)...... 69 4.6 The MCMC probability distribution for the intrinsic source size and source axis ratio of HS 0810+2554. Figure from Jackson et al. (2015)...... 70 4.7 HST observation of RX J0911+2554 in I-band from CASTLES (Kochanek et al., 2013). In this map the lens galaxy (G1) and it associated galaxy (G2) are can be seen...... 71 4.8 RX J0911+0551 observed at C-band with the JVLA. The lensing galaxy is also detected (centre). Image produced with CASA. . . 73 4.9 Attempt to fit point source with PSF to RX J0911+0551. The lens galaxy has been blocked out. The data is not well fit by a PSF, with significant residuals around A-B-C. The white bar represents 1”. Figure from Jackson et al. (2015)...... 74 4.10 Modelling of the lens system RX J0911+0551. Left to right: the model source, the lensed model source, the data, and the residual. The white bar represents 1”. Figure from Jackson et al. (2015). . 75 4.11 Histogram of the noise in the cleaned map of RX J0911+0551, fitted with a Gaussian function. The plot was created by the AIPS task IMEAN...... 78 LIST OF FIGURES

4.12 Histogram of the noise in the cleaned map of RX J0911+0551, on a log scale, ﬁtted with a Gaussian function...... 79

5.1 Intrinsic L-band radio ﬂuxes of optically-selected lensed quasars, including HS 0810+2554, RX J0911+0551, SDSS J1251+2935 and SDSS J1330+1810 (shown in red). The tail-end of the best ﬁt to the White et al. (2007) plot is shown by the curve on the right. Data and lens models from Ratnatunga et al. (1999); Wisotzki et al. (2002); Reimers et al. (2002); Burud et al. (1998); Inada et al. (2003a,b); Ghosh and Narasimha (2009); Anguita et al. (2009); Jackson (2011); Wucknitz and Volino (2008); Kayo et al. (2007); Oguri et al. (2008); Assef et al. (2011); Blackburne et al. (2011), taken from Jackson et al. (2015)...... 83 Abstract

Despite being some of the most luminous objects in the universe, quasars are not well understood. Only a fraction of quasars are radio-loud, and it is not clear whether this dichotomy represents two populations of quasars with different underlying radio emission mechanisms. The effects of gravitational lensing allow the radio-quiet quasar population to be studied where they would otherwise be too faint to detect. In this thesis, four gravitationally-lensed radio-quiet quasars are observed with e-MERLIN: HS 0810+2554, RX J0911+0551, SDSS J1330+1810 and SDSS J1251+3925. HS 0810+2554 is detected at a high level of significance, the other sources are not detected. A spectral index of α = -0.55 ± 0.1 is derived for HS 0810+2554, consistent with the existence of a milliarcsecond-scale jet from an AGN. A spectral index of α > −0.5 can be inferred from the observation of RX J0911+0551. It is not clear to what extent the source is consistent with jet emission, as it may be due to obscured AGN jets or starburst activity. Intrinsic fluxes of the lensed sources are inferred, which allow extension of the quasar optical-radio relation down to the µJy level. The observations are part of a joint effort to address the nature of the radio emission from radio-quiet quasars, the analysis of which is discussed concurrently with results of JVLA observations of HS 0810+2554 and RX J0911+0551. The University of Manchester Hannah Stacey Master of Science 2015 Jodrell Bank Centre for Astrophysics Alan Turing Building Oxford Road Manchester M13 9PL Supervisor: Dr Neal Jackson Declaration

No portion of the work referred to in the thesis has been submitted in support of an application for another degree or qualiﬁcation of this or any other university or other institute of learning. The work of the author of this thesis is part of a larger eﬀort to investigate the radio components of radio-quiet quasar lenses. The author is responsible for analysis and interpretation of e-MERLIN observations, which is discussed concurrently with results of JVLA observations conducted simultaneously by other members of the research group.

Hannah Stacey Jodrell Bank Centre for Astrophysics Alan Turing Building The University of Manchester Oxford Road Manchester M13 9PL 2015 Copyright

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To my supervisor, Neal Jackson, for his much valued support and guidance, and for many bowls of chips. To my fellow students in 3.205 for their friendship and helpful advice. To my parents, for their unfailing support and encouragement in whatever path I choose to take. Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suﬀer much, because they live in a grey twilight that knows not victory nor defeat.

- Theodore Roosevelt Chapter 1

Introduction

Quasars, or quasi-stellar objects (QSOs), are compact, variable objects within a host galaxy. They are among the most luminous objects in the universe, but despite this, they are not well understood. Only a small fraction of the quasar population has significant radio emission that has been studied at high resolution with interferometry. Such quasars have been designated radio-‘loud’ (Strittmatter et al., 1980). It is not clear whether the dichotomy between radio-‘loud’ and radio-‘quiet’1 represents a continuous population of quasars whose radio emission is driven by AGN-powered jets, or a superposition of two quasar populations with different underlying emission mechanisms. Strong gravitational lensing, where a background source is lensed and magnified by a foreground object along the line of sight, provides a useful tool for investigating radio-quiet quasars. Whereas the source surface brightness is con- served, the increased size and flux density of the lensed source allow it to be observed with typically 5-10 times better signal-to-noise ratio. This presents an opportunity to probe compact, fainter sources at higher resolution and sensitivity. With telescopes such as the Multi-Element Radio Linked Interferometer Network (e-MERLIN) and the Jansky Very Large Array (JVLA), the magnification effect potentially allows detections of sources with intrinsic flux at the nJy level, which

1Radio-‘quiet’ quasars are not radio silent, like the name suggests, they do in fact have radio components. From this point on, the quotation marks will be dropped.

1 CHAPTER 1. INTRODUCTION 2 will not otherwise be possible until the era of the Square Kilometre Array. One of the faintest objects yet discovered is the lensed quasar SDSS J1004+4112 whose ﬂux (without lensing) would be ∼1 µJy at radio frequencies (Jackson, 2011). In this thesis, e-MERLIN observations of four known gravitationally-lensed radio-quiet quasars are described and analysed: HS 0810+2554, RX J0911+0551, SDSS J1251+2935, and SDSS J1330+1810, the aim of which is gain insight into their radio emission mechanisms. The work has been conducted concurrently with analysis of JVLA observations of HS 0810+2554 and RX J0911+0551, the combined results of which have been accepted for publication in the Monthly Notices of the Royal Astronomical Society (Jackson et al., 2015). This chapter will begin with an overview of gravitational lensing theory, fol- lowed by a brief explanation of radio emission mechanisms, then ﬁnally some background on quasars and the radio dichotomy. CHAPTER 1. INTRODUCTION 3

1.1 Gravitational lensing

1.1.1 History of gravitational lensing

The deflection of light through a gravitational field was postulated long before Einstein: by von Soldner and John Mitchell, among others. However it wasn’t until Einstein’s General Theory of Relativity that the effect was correctly quan- tified. General relativity describes gravity as a geometric property of spacetime: in other words, the curvature of spacetime is dependent on the matter within it. In 1919, the theory was confirmed by Eddington, who observed the gravitational deflection of starlight by the sun during a solar eclipse (Eddington et al., 1920). As a consequence, it was postulated that if a source and a foreground massive object were perfectly aligned along the line-of-sight, the light from the source would be lensed around the massive object to be imaged as a ring around the object. Such an effect has been called an ‘Einstein ring’. If the alignment is not perfect, the source could instead be seen as multiple images (Zwicky, 1937). It was thought for some time that such effects could not be observed as the angular separation of the images would be far too small to be resolved. However, in 1979 the first gravitational lens system, Q0957+561, was discovered by Walsh et al. at Jodrell Bank Observatory. They discovered what appeared to be a pair of quasars with identical colours, redshifts and spectra: they are in fact two images of the same quasar. A galaxy cluster close to the lens galaxy contributes to the lensing potential, resulting in a large image separation of 6” (figure 1.1). Technological advances have since allowed many different lensing systems to be discovered, including four-image systems (Schneider et al., 1988), large arcs (Kubo et al., 2009), and near-perfect Einstein rings (Belokurov et al., 2007). CHAPTER 1. INTRODUCTION 4

Figure 1.1: The ﬁrst lens discovered, quasar Q0957+561, at 4885 MHz with the JVLA from Reid et al. (1995). The two images of the quasar are shown (centre top and bottom) with large separation of 6”. The core of the quasar falls within the caustic of the lens galaxy, producing a lensed image of the core (bottom). The jets of the quasar fall outside the tangential caustic and are not lensed. CHAPTER 1. INTRODUCTION 5

Figure 1.2: Hubble image of so-called ‘Cosmic Horseshoe’, SDSS J1148+1930, an elliptical galaxy lensing a background galaxy. The extended source produces large arcs, close to an Einstein ring. Image credit: ESA/Hubble. CHAPTER 1. INTRODUCTION 6

Figure 1.3: Hubble image of Q2237+030, a quasar lens with image angular separation of 1.6”. The compact source is close to the line of sight through the centre of the galaxy, creating four images known as an ‘Einstein cross’. Image credit: ESA/Hubble. CHAPTER 1. INTRODUCTION 7

1.1.2 Gravitational lens theory

In this section follows a brief summary of gravitational lens theory. For in- depth accounts see Kochanek, Schneider, and Wambsganss (2004), Schneider et al. (1992), Petters et al. (2001). Throughout, distances used are the comoving angular diameter distances and the source is assumed to be point-like.

The lens equation

The general relativity field equations describe how light propagates along the null geodesics of the space-time metric, i.e. it describes straight-as-possible lines in curved space-time. In gravitational lens theory, these field equations can be approximated as linear by assuming the gravitational field is relatively weak at the point of deflection. This is true when the impact parameter, ξ, the perpendicular distance between the centre of the lens and the projected path of the light ray

(as shown in ﬁgure 1.4), is much greater than the Schwarzchild radius, RS, of the lensing mass (if it were a point mass).

A spherically symmetric mass at a distance Dd from an observer deflects light from a source at distance Ds, defined in figure 1.4. As angleα ˆ 1, the small angle approximation can be used sinαˆ ≈ tanαˆ ≈ αˆ. The radial deflection of light rays by angleα ˆ, at a distance θ from the centre of a lens with a mass contained within ξ is described by the equation

4GM(< ξ) Dds α = 2 . (1.1) c ξ Ds

The lens equation can then be written as

Ds η = ξ − Ddsα.ˆ (1.2) Dd

By introducing angular coordinates so that ξ = Ddθ and η = Dsθ, the lens CHAPTER 1. INTRODUCTION 8

source plane η

Dds α image plane ξ

β Dd

observer

Figure 1.4: A simplified gravitational lens diagram. A light ray is emitted from source at diameter η and angular size β. It is deflected by the gravitational field of an object on the image plane at impact parameter ξ and angular size θ. The angle of deflection isα ˆ. CHAPTER 1. INTRODUCTION 9 equation can be reduced to β = θ − α(θ), (1.3) meaning a source at true position β will be seen by the observer to be located at positions θ. More than one solution to the lens equation means multiple images will be produced, as discussed in the following section. The deflection angle of a collection of mass points is the vectorial sum of the deflections due to each component. For a three-dimensional mass distribution the surface mass density is Σ(Ddθ). The critical mass density, Σcr and the convergence, κ, are defined as

2 c Ds Σcr = (1.4) 4πG DdDds and

Σ κ(θ) = . (1.5) Σcr The critical mass density is the characteristic scale for which multiple images or rings are produced. Where θ is equal to the Einstein radius, θE, κ = 1. This denotes the radius of the tangential critical curve (ﬁgure 1.5 and 1.6).

Magniﬁcation and shear

The lens equation 1.3 yields solutions which denote the positions of the images of the source. Each image is deflected differently and thus will result in different distortions and magnifications. Assuming the lens can be described by the thin sheet approximation (i.e. assuming a single point of deflection for a light ray) this is described by the following matrix:

  1 − κ − γ1 −γ2 A(θ) =   , (1.6) −γ2 1 − κ + γ2 CHAPTER 1. INTRODUCTION 10

where κ is the convergence, as in equation 1.5. γ1 and γ2 are the complex com- p 2 2 ponents of ‘shear’, γ = γ1 + γ2 , which quantiﬁes the shape distortion of the image. From this the magniﬁcation can be expressed,

1 1 µ = = . (1.7) detA (1 − κ)2 − |γ|2

The sign of µ denotes the parity of the image: a negative parity denotes a mirror- symmetric image of the source. The three types of stationary point solutions are characterised as minima, where γ < 1 − κ ≤ 1, which have µ ≥ 1 and positive parity; saddlepoints, where (1 − κ)2 < γ2, which have negative parity; and maxima, where (1 − κ)2 > γ2, have positive parity and typically have the largest time delays.

Multiple imaging

The geometry of the lens system determines the number of images produced. An odd number of images is always produced, including an image close to the centre of the lens at the Fermat maximum. In lens systems where the foreground object is a galaxy, κ is much larger than 1 at the centre of the lens, resulting in a demagnification of the central image. This, and the addition of propagation effects due to the concentration of dust and ionised gas in the centre of the lensing galaxy, is likely the reason why the central image is usually not observed in these lenses. The geometry of the lens system is modelled with curves, known as ‘critical curves’. Caustics are mapped onto the source plane, which denote the boundaries where detA(θ) → 0 and µ → ∞ 2. Images will appear at maximum flux and magnification close to a ‘cusp’ or ‘fold’ of the astroid caustic. Within the caustic(s) multiple images of the source will be produced. Four images are produced inside the astroid caustic and two images inside the tangential caustic. Outside

2In reality, sources cannot have infinite magnification. Sources have a finite size and thus will have a finite observed magnification. CHAPTER 1. INTRODUCTION 11 the tangential caustic no multiple imaging occurs. Figures 1.5 and 1.6 show the images formed when the source is in different positions relative to the astroid caustic of a galaxy lens. In cluster lenses, the caustics are more complex. Lens systems in which the source is close to a cusp or fold have a defined flux ratio, where R → 0 as the distance from the cusp → 0, and their magnifications (when parity is taken into account) sum to zero. For a source close to the cusp, three images are produced close together (as shown in figure 1.5) and have flux ratios of µA + µB + µC Rcusp = . (1.8) |µA| + |µB| + |µC | For a source close to a fold, as shown in figure 1.6,

µmin + µsaddle Rfold = (1.9) |µmin| + |µsaddle| where the two close images have the same magniﬁcation and opposite parity. See Kochanek et al. (2004) for a more detailed illustration. In this section it has been assumed that the source object is a point source. If the source is extended, the resulting images are also extended into arcs and Einstein ring-like features as shown in ﬁgure 1.2.

1.1.3 Galactic substructure

The properties of cusp and fold lenses have been utilised as a tool to probe sub- galactic scale structure. Fluxes are often less well fitted by smooth mass models than the image positions due to the fact that they are more sensitive to small asymmetries in the mass distribution caused by substructure. Divergence from expected flux ratios can be evidence for the existence of substructure within the lensing galaxy, which add perturbations to the lensing potential. The effect of substructure was proposed by Mao and Schneider (1998) for the case of cusp lens B 1422+231, which found violations in the flux ratio expected CHAPTER 1. INTRODUCTION 12

Figure 1.5: The resulting images produced when the source is on a cusp of the astroid caustic. The caustics mapped onto the source plane are in red; the lens critical curve and time-delay contours are in green.

Figure 1.6: The resulting images produced when the source is on a fold of the astroid caustic. CHAPTER 1. INTRODUCTION 13 from a smooth mass model in the three merging images. Only small perturbations in the lens galaxy mass are required to create observed flux violations (∼1%), which could be explained by small luminous substructure such as globu- lar clusters, or by larger smooth perturbations such as in spiral arms. There have been several examples of similar flux anomalies (Koopmans et al., 2007; More et al., 2009; Kratzer et al., 2011; MacLeod et al., 2013). As gravitational lensing is sensitive to both dark and baryonic matter, the effect has been employed to investigate dark matter substructure. The cosmological model of cold dark matter (ΛCDM), which is at present the most promising theory to describe the large-scale structure of the universe, describes hierarchical structure formation. Dark matter forms in clumps throughout the universe. As baryons lose energy through non-gravitational means, they fall into the potential wells of dark matter, creating galaxies and galaxy clusters (White and Rees, 1978). Whereas the model appears to correctly explain the structure of the universe on a large scale, it is not clear how well it holds up on sub-galactic scales. Dark matter is expected to form halos that dominate the baryonic matter within galaxies. The effect of these halos is demonstrated in the rotation curves of spiral galaxies, which appear to flatten out to radii beyond the regions where there is high density luminous matter (Sofue and Rubin (2001), for example). ΛCDM also predicts the existence of a significant number of satellite galaxies within dark matter halos. Surveys of the local group suggest the number and mass function of luminous satellites are much lower than expected, the so-called ‘missing satellites problem’ (Moore et al., 1999). It is possible that there are non-luminous dark matter satellites that cannot be detected, or that the Milky Way is atypical. Either way, gravitational lensing provides a way to test the ΛCDM paradigm by measuring the small-scale mass anomalies in lens galaxies. Quadruple lens systems have been discovered with flux violations that have been explained by the existence of CDM substructure (for example, Metcalf and Madau (2001); Metcalf and Zhao (2002); Biggs et al. (2004); Saha et al. (2007); CHAPTER 1. INTRODUCTION 14

Vegetti et al. (2012)). Statistical analysis of these systems potentially provides a test for the amount of dark and baryonic sub-galactic-scale structure predicted by the CDM paradigm. Dalal and Kochanek (2002) ﬁnd a mass fraction of 2% in

6 9 substructures 10 − 10 M , in agreement with CDM predictions, from a sample seven lenses. Consistent constraints on the mass fraction were derived by Vegetti et al. (2014) from a sample of 11 galaxy-galaxy lenses. Xu et al. (2009) employed the Aquarius high resolution N-body dark matter simulation to test how well CDM subhalos could account for observed flux anomalies. They find that lenses with small image separation, hence larger magnification, are more likely to exhibit flux anomalies as a result of CDM substructure. However, the overall probabilities of CDM substructure to cause flux anomalies at the level of observed values are too low to explain their abundance. They conclude that CDM alone cannot explain the flux ratios, but that propagation effects and inadequate lens modelling may also be responsible (Xu et al., 2015).

1.1.4 Microlensing

For a compact source, such as a quasar, the effect of microlensing can also cause flux anomalies. Stars within the lensing galaxy produce their own caustics, which differentially magnify the source as they move through the host galaxy. As the image fluxes are dependent on the second derivative of the lensing potential, they are very sensitive to small changes in the position of the source relative to the complex network of caustics produced by individual stars. This causes violations in cusp-fold ratios, as with the presence of substructure. However, unlike substructure violations, they are variable on timescales of years. The phenomenon was first detected by Irwin et al. (1989), who noted the photometric variation in one of the components of lensed quasar Q2237+0305. The different angular sizes of quasars at different frequency bands provides a way to distinguish the influence of microlensing from that of substructure (Wisotzki et al., 2003). The compact size of quasars at optical frequencies means CHAPTER 1. INTRODUCTION 15 that they are particularly sensitive to microlensing. Quasars have a larger angular size at radio wavelengths and therefore provide a baseline for comparison. Radio microlensing is possible in principle, provided the radio component is compact enough. The size of a compact radio source is determined by the point at which it becomes optically-thick due to synchrotron self-absorption (section 1.2.2). This is ∼1 mas for a source of 1 Jy at ∼GHz frequencies and is smaller for increasing frequency, decreasing as the square root of its brightness. The scale of the microlensing caustic pattern is ∼1 µas, so the radio component will be larger than this for sources brighter than ∼1 µJy (Jackson, 2013). The effect can therefore be ignored for all but the faintest of sources. There are claims for the existence of radio microlensing, for example Koop- mans and de Bruyn (2000), however they can be explained by propagation effects. Koopmans et al. (2003) found extrinsic variability in quasar lenses close to the galactic plane, suggesting galactic scintillation is the cause of the apparent flux anomalies. The way that sources of different sizes respond to microlensing could make the effect a useful tool for probing quasar morphology (discussed in section 1.3). It is expected that the observed quasar size will be different at different frequencies, as the temperature of the accretion disk decreases with radius. Differencing the image light curves, taking into account time delays due to the different path lengths, removes the intrinsic source variability to leave only the extrinsic variability caused by microlensing. The resulting light curves can be compared at different frequency bands to derive the relative sizes of the emitting regions, and thus the size of the nucleus and accretion disk (see for example Morgan et al. (2008); Muñozet al. (2011); Poindexter et al. (2008); Blackburne et al. (2011)). Results from these studies are varied. Poindexter et al. (2008) find results consistent with the standard model of accretion disks. However, the Blackburne et al. (2011) estimates from a multiwavelength sample are greater by up to an order of magnitude. CHAPTER 1. INTRODUCTION 16

1.2 Radiative Processes

1.2.1 Thermal emission

All objects above absolute zero have some internal motion from particles vibrat- ing, causing emission of radiation. The spectrum and intensity depends on the temperature of the emitting object. For an object such as a galaxy, the thermal emission is a compound of the emission from all the matter within it. The thermal emission spectrum from galaxy NGC 253 is denoted by the blue line in ﬁgure 1.7. This typically peaks in the infrared, with only very cool objects having any emission in the radio. The radio observations discussed in this thesis (8, 5 and 1.5 GHz) are at frequencies where there will be no appreciable contribution to the emission from thermal processes.

1.2.2 Synchrotron emission

Synchrotron radiation is responsible for the majority of radio emission in the universe. This type of radiation is known as ‘non-thermal’ because the emission is from charged particles in a magnetic field, rather than from thermal motion. As an electron interacts with a magnetic field, it travels in a helical path around field lines: the angular acceleration of the electrons causes them to emit radiation at radio frequencies. As electrons with a range of energies are accelerated within the magnetic field, the resulting spectrum is the superposition of the spectra from individual electrons, which results in continuum emission. At higher radio frequencies, the spectrum is approximated as a steep negative

α power slope, Sν ∝ ν , where α ≈ −0.7 is typical for a radio galaxy (Peterson, 1997). The optically thin end of the synchrotron spectrum is traced by the pink dotted line in the spectral energy distribution (SED) of NGC 253 in ﬁgure 1.7. The emitting region becomes ‘optically-thick’3 at lower frequencies, where

3Optically-thick does not refer to optical wavelengths speciﬁcally, but to the attenuation of any radiation. CHAPTER 1. INTRODUCTION 17

Figure 1.7: SED for NGC 253 from Peel et al. (2011). The blue dotted line traces the thermal emission, which peaks in the infrared and drops out at microwave frequencies. Free-free emission is traced by the red dotted line, which dominates below ∼100 GHz. The synchrotron emission is traced by the pink dotted line, which begins to dominate at frequencies of a few GHz. synchrotron self-absorption dominates. At this point the radiation is absorbed at the same rate it is emitted, and the radiation observed is emitted from only the outer shell of the emitting region. The turn-over frequency is higher for greater electron density, and the spectrum below it follows a power law where α = 5/2 (Peterson, 1997). The turn-over frequency is typically in the range of a 101 − 102 MHz, depending on the nature of the source (Kraus, 1966). As synchrotron self- absorption is proportional to the size of the emitting region, only very compact sources are self-absorbed at GHz frequencies. The synchrotron spectrum of bright quasar Cygnus A becomes self-absorbed at 20 MHz, as shown in ﬁgure 1.8. Also note the steepening of the spectrum above 103 MHz: spectra are not always well ﬁt by the power law approximation. CHAPTER 1. INTRODUCTION 18

Figure 1.8: Synchrotron spectra of three astronomical sources at radio frequencies between 10 MHz and 30 GHz. The synchrotron emission from Cygnus A becomes self-absorbed at ∼20 MHz. Figure from Baars et al. (1977).

1.2.3 Free-free emission

Free-free (or Bremsstrahlung) radiation is continuum emission from scattered electrons passing through an ionised medium. The mechanism is known as free- free because the electron is unbound both before and after interaction with an ion (Burke and Graham-Smith, 1997). The electrons in a medium have a distribution of velocities and impact parameters, so the resulting spectrum is a superposition of many transitions from CHAPTER 1. INTRODUCTION 19 a continuum of energy states. At higher frequencies, the spectrum is nearly ﬂat with α ≈ −0.1 as can be seen in the SED of Cygnus A in ﬁgure 1.7. At low frequencies, the medium becomes optically-thick and acts as a black body. The

2 spectrum depends only on electron temperature, so it drops oﬀ with Sν ∝ ν (Burke and Graham-Smith, 1997). The turnover frequency is typically 1 GHz (Kraus, 1966). Free-free radiation accounts for only a small proportion of the radio sky, which is synchrotron-dominated, and is typically emitted by intracluster gas or local HII regions (Burke and Graham-Smith, 1997). CHAPTER 1. INTRODUCTION 20

1.3 Radio-quiet quasars

1.3.1 Quasar morphology

Quasars, or quasi-stellar objects, are compact variable objects at high redshift and luminosity within a host galaxy. They are the most luminous objects in the universe. Schmidt and Green (1983) deﬁne an arbitrary cut-oﬀ for quasars of

MB ≤ −23 to distinguish them from bright Seyfert galaxies. Although they were discovered in the 1960s, quasars are relatively rare and still poorly understood. They are a class of active galactic nuclei (AGN) thought to be powered by a matter accreting onto a supermassive black hole. In the optical, the emission region is very compact with the quasar outshining the host galaxy by several magnitudes. They are characterised by time-variable continuum emission, large UV flux with broad emission lines, and large redshifts (Peterson, 1997). The large variability on short timescales in all wavebands implies an extremely dense, compact source with a size of a few light days. There are a number of AGN classifications - quasars, Seyfert galaxies, radio galaxies, and blazars, among others - which have diverse properties. A single, unified model has been proposed to explain the diversity, whereby the properties of the AGN are dependent on the geometric angle at which it is observed (shown in figure 1.9). The model consists of a nucleus of a central supermassive black hole,

6 9 10 − 10 M , of size ≤0.01 pc (Burke and Graham-Smith, 1997). The angular momentum of infalling matter forms a thin accretion disk, which is heated by friction and turbulence. The energy of the AGN derives from the gravitational potential energy, as well as part of the rest-mass-energy, of the material falling into the black hole. Energetic material is transported away from the nucleus by collimated jets along the polar axis (Peterson, 1997). Surrounding the accretion disk is a broad line region (BLR), which has the size of a few light days. Outside of this is a lower-density narrow-line region CHAPTER 1. INTRODUCTION 21

(NLR), where gas and dust motions are dominated by gravity, which is the source of continuum emission as well as narrow-line emission. The NLR is the smallest scale that is observed in the UV to IR spectrum, which may be due to obscuration of the accretion disk and BLR by an optically-thick, dusty torus (Peterson, 1997).

Figure 1.9: The unified model of active galactic nuclei: along the jet axis, the AGN is seen as a blazar; perpendicular to the jet axis, the AGN is seen as a Type 2 Seyfert galaxy; at intermediate angles, the source is observed as a Type 1 Seyfert or quasar. The different AGN morphological properties are labelled in the figure: the nucleus/black hole (BH) (and surrounding source of x-ray emission), broad line region (BLR), accretion disk (AD) and narrow line regions (NLR). Figure from Jovanovic and Popovic (2009).

1.3.2 Radio properties

Radio emission from quasars at GHz frequencies is characterised by ﬂat spectrum emission from the optically-thick compact core region, and steep spectrum emission from optically-thin relativistic jets. The 5 GHz radio emission from bright CHAPTER 1. INTRODUCTION 22 quasar 3C 175 is shown in ﬁgure 1.10, which has the characteristic double-lobe structure formed from jets.

Figure 1.10: Radio-loud quasar 3C175 at 4.9 GHz observed with the JVLA. The quasar can be seen in the centre, with characteristic double lobes from relativistic jets spanning 212 kpc. Figure from Bridle et al. (1994).

The population was ﬁrst noted to be bimodal by Strittmatter et al. (1980), who found radio observations strongly weighted towards higher values. Miller et al. (1990) also conﬁrmed this anomaly with a larger sample of quasars between

26 −1 1.8 < z < 2.5, and found nine radio-loud sources with flux L5GHz 10 W Hz −1 25 −1 −1 sr , 96 radio-quiet source with flux L5GHz < 10 W Hz sr , and none in between. Radio-quiet quasars dominate the population of quasars, contributing around 90-95% to the population (Peterson, 1997). Although bright at optical wavelengths, their radio components are several magnitudes fainter than radio-loud quasars. Figures 1.11 and 1.12 from Goldschmidt et al. (1999) demonstrate the bimodality of the quasar population: there is a continuous distribution in the optical range, but a clear separation in the radio with most quasars having a CHAPTER 1. INTRODUCTION 23 radio luminosity < 1024 W Hz−1 sr−1 with a few brighter outliers. Although FIRST (Faint Images of the Radio Sky at Twenty-one centimetres) (Becker et al., 1995) revealed many intermediate sources and appeared to fill in the gaps in the distribution (White et al., 2000), Ivezićet al. (2002) showed this to be a selection effect and confirmed that the FIRST and SDSS data is consistent with an empirical dichotomy. The radio components associated with radio-quiet quasars were discovered by White et al. (2007) by stacking the optical positions of the SDSS DR3 (Sloan Digital Sky Survey, Digital Release 3) quasar catalogue in the FIRST survey. The process allowed radio properties of the quasar sample to be measured that are well below the FIRST detection limit of 1 mJy. The study found a radio-optical relationship whereby radio flux decreases rapidly with optical magnitude. The median flux of the sources binned with optical magnitude are shown in figure 1.13. The analysis suggests quasars not detected above the FIRST limit of 1 mJy are likely to have a flux of 10 − 100 µJy. The populations are distinguished in several respects. Peacock et al. (1986) associate the differences in the radio-optical ratio to host galaxy properties. They conclude that there is a change in radio properties at MB ∼ −24. They conclude that quasars of MB < −24 are hosted within massive elliptical galaxies, and are associated with strong radio emission; those with MB > −24 are within spiral galaxies, have weak radio emission, and are thus a brighter population of Seyfert galaxies. Whereas Peacock et al. distinguish the populations an absolute sense, Keller- man et al. (1994) distinguish them on the basis of radio-optical flux ratio and radio flux: radio-loud quasars as those with a radio/optical emission ratio, R > 10

25 −1 or having a flux, L5GHz > 10 W Hz ; Radio-quiet quasars, having a flux of 23 25 −1 10 < L5GHz < 10 W Hz or R < 10. Miller et al. (1993) further differen- tiate the population by defining radio-‘intermediate’ quasars with optical-radio luminosity ratio of 25 < R < 250, between the radio-loud and radio-quiet subsets. CHAPTER 1. INTRODUCTION 24

Figure 1.11: Optical against radio ﬂux for samples of quasars at redshift 0.3 < z < 1.5 (Goldschmidt et al., 1999).

Figure 1.12: Optical against radio ﬂux for samples of quasars at redshift 1.5 < z < 2.5 (Goldschmidt et al., 1999). CHAPTER 1. INTRODUCTION 25

Figure 1.13: The median radio ﬂux is correlated with the optical ﬂux. Each bin represents the median of thousands of radio-quiet quasars in the SDSS DR3 catalogue. CHAPTER 1. INTRODUCTION 26

Regardless of the boundaries that are imposed on the radio-loudness distribution, the issue of the dichotomy remains. Many studies have speculated whether the dichotomy represents a true bimodality, in which there are two types of quasars, which may be governed by similar or different physical processes. Black hole properties have been implicated as responsible for the radio luminosity of radio-loud quasars (for example Wilson and Colbert (1995); Laor (2000); Shankar et al. (2010)), which have been shown to drive outflowing jets (Blandford and Payne, 1982). Sikora et al. (2007) find there is a strong relationship between quasar radio-loudness and Eddington luminosity ratio. The Eddington ratio is description of the accretion rate of the AGN, which is related to the black hole’s spin and determines the power of the outflowing jets. Large black hole spins are only found in early-type galaxies, as the result of major mergers, rather than in spiral galaxies. As radio-loud quasars are found primarily in early-type galaxies, it is possible that the small radio-loud population represent a subset of galaxies whose AGN have been influenced by second-generation mergers.

1.3.3 Source of radio emission from radio-quiet quasars

Radio-quiet quasars are strongly accreting, as observed at higher frequencies. However, there is a lack of evidence for jets that transport energy and angular momentum from the nuclei, and so is not clear how far the emission mechanisms that power radio-loud quasars can be applied to the radio-quiet end of the population. There are several hypotheses that have been proposed to explain the compact radio emission. Radio-quiet and radio-‘intermediate’ quasars with ﬂux density of a few mJy are observed with VLBI to have small-scale jets of 100-1000 pc and core luminosities with the size of a few pc (Blundell and Beasley, 1998; Blundell et al., 1996; Leipski et al., 2006; Ulvestad et al., 2005). There is also evidence of large fractional ﬂux variation on timescales of weeks to months (Barvainis et al., 2005), CHAPTER 1. INTRODUCTION 27 characteristic of emission from AGN, and spectra indicative of non-thermal emission (Ulvestad et al., 2005). If radio-quiet quasars represent a less powerful component of this population, they have smaller central engines with milliarcsecond jets that are below the resolving power of current radio VLBI arrays. Cold gas accretion fuels both the AGN and starburst activity in the most luminous quasars at high redshifts, which provides a source of radio emission. For quasars fainter than a few mJy, starburst activity could contribute the major source of radio emission. Condon et al. (2013) infer this from analysis of the population density of quasars. The spatial density of quasars per magni-

24 −1 tude radio luminosity turns up sharply below L1.4GHz < 10 W Hz , suggesting the emergence of a second population of sources where star formation activity in the quasar host galaxy dominates. For these quasars, star formation rates of 20 − 500M /year could account for the observed radio luminosities in their sample. The emission would exhibit a steep spectral index typical of optically- thin synchrotron emission. The characteristic size of star forming regions are reasonably compact, with a linear size of 5-10 kpc at 1.4 GHz (Wrigley, 2015). A combination of the two is very possible. White et al. (2015) perform a stacking analysis of quasars from the VIDEO survey to probe radio luminosities of a few 10s µJy. They find that the radio source counts cannot be described by a power law, as there is an excess of sources at low luminosities. They suggest this is due to a contribution from star formation. However, a comparison with star forming rates suggests that AGN are the primary source of emission. Blundell and Kuncic (2007) propose a thermal origin for the emission. VLBI observations of the AGN of NGC 1068 appear to suggest free-free emission, rather than synchrotron, is responsible for the radio emission. The core shows pc-scale structure extending perpendicular to the jet axis and reasonably flat spectra, with α = 0.3 (Gallimore et al., 2004). These features are more consistent with free-free emission. In addition to this, NGC 1068 has a brightness temperature too low for synchrotron self-absorption. This mechanism provides a less-directional way, CHAPTER 1. INTRODUCTION 28 compared to jets, to disperse mass and energy away from the AGN. If there is significant mass loss as a result of super-Eddington accretion rates, the resulting optically-thin free-free emission from the disk wind could be large enough to explain the radio luminosities of radio-quiet quasars. However, Steenbrugge et al. (2011) provide evidence against this. They conclude from X-ray studies of 22 quasars, that a high column density associated with a disk wind was not sufficient to explain both the radio and X-ray luminosities. It is likely this mechanism is not the sole source of the emission. Laor and Behar (2008) suggest a mechanism of emission whereby the AGN coronae is magnetically-heated. The correlation between the variability in X-ray and radio luminosities of radio-quiet quasars is similar to the Güdeland Benz (1993) relation for coronally-active stars. The relation suggests that such stars are magnetically-heated. As this process is thought to be the origin of X-ray emission from AGN, it may also be the physical process responsible for the radio emission from radio-quiet quasars. If this is the case, radio-quiet quasars should exhibit a very compact core 1 mas in size, with a flat spectrum at a few GHz due to synchrotron self-absorption. The corona should be visible at a few hundred GHz. Large amplitude, rapid variability would be expected, with correlation between X-ray and radio fluctuations. The predicted size of the emitting region means that the source will be difficult to resolve in the radio, as resolutions of 1 mas with the required sensitivities are beyond near-future capabilities. However, millimetre-VLBI with ALMA, or space VLBI with the SKA, could in principle reach scales of tens of µas at µJy sensitivity (Godfrey et al., 2012). Chapter 2

Fundamentals of radio interferometry

Interferometry is an astronomical technique that is the basis for the new generation of radio telescopes, such as e-MERLIN and the Square Kilometre Array. The technique enables high resolution imaging otherwise impossible with single dishes. This chapter will give a brief overview of the techniques of radio interferometry drawn from the treatments in Thompson (1999); Crane and Napier (1989); Fomalont and Perley (1999); Wrobel and Walker (1999); Briggs et al. (1999); Bridle and Perley (1999) and Walker (1999).

2.1 Aperture synthesis

The angular resolution of a single dish telescope is given by

λ resolution ∝ , (2.1) D where λ is the wavelength and D is the diameter of the telescope aperture. The telescope ‘beam’ (the main lobe of the antenna power pattern, ﬁgure 2.1) creates

29 CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 30

Figure 2.1: Illustration of the antenna power pattern for a single antenna and projection onto the celestial sphere. Figure from Kraus (1966). CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 31 a point spread function which can be described by A(θ), where θ is the angle oﬀset from the source centre. This convolves with the true sky brightness distribution, I(θ), so what is actually observed is the modiﬁed sky brightness distribution:

I˜(θ) = I(θ)A(θ). (2.2)

The antenna power pattern also had ‘side lobes’ where radiation from the antenna environment leaks into the aperture. Interferometry employs the technique of ‘aperture synthesis’, which combines the signals of many telescopes, to produce measurements at high angular resolution. Each telescope in the array acts as an element of a large aperture. As the telescopes move with the rotation of the earth, they begin to ﬁll the virtual aperture equivalent to a telescope the size of the distance between the antennae. For an interferometric array, the shortest spacings between telescopes determine the largest angular structures which can be detected. The resolution limit is determined by the longest distance (or baseline) between two telescopes in the array, i.e. ∝ |B|, where |B| is the length of the baseline. This enables very high resolution radio images to be produced that would not be possible with a single telescope. Interferometry works on the principle that two waves that are in phase add constructively, whereas waves that have diﬀerent phases add destructively, creating a fringe pattern. The signals from the telescopes are cross-correlated (multiplied and added) to produce a map of an astronomical source.

2.2 The two-element interferometer

A simple diagram of a two-element interferometer is shown in ﬁgure 2.2. For an interferometer observing away from the zenith, there will be a time delay between the telescopes receiving an incident wavefront. This corresponds to a phase diﬀerence between the two signals, so must be corrected before the signals CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 32

Figure 2.2: Simpliﬁed diagram of a two-element interferometer. There is a time delay, τg, in the wavefront between the antennae, which must be corrected for before the signals are correlated. The incoming signal is shifted to a lower frequency by a local oscillator for analysis. The resulting signals are multiplied and integrated by the correlator. CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 33 are correlated. For a basic two-element interferometer, the correlator multiplies the signals from each telescope and integrates them over a period of time. A set of complex Fourier components, or ‘visibilities’, is produced for each baseline in the array, containing the fringe amplitudes and phases. A single visibility is given by:

V (u, v) = Aeiφ, (2.3) where φ is the fringe phase. The Fourier components measured by an interferometer are determined by the projected baseline, which is the distance between the antennae normal to the direction of the source. This is measured in wavelengths corresponding to 2-D coordinates, given by u and v. Assuming the source is suﬃciently compact, a visibility is the Fourier transform of the sky brightness distribution with angle of source (van Cittert, 1934; Zernike, 1938). The observed sky brightness distribution is related to the true sky brightness distribution by the equation

Z I˜ = eikB.¯ sˆ I(¯σ)eik¯b.σ¯. (2.4)

The first exponential term describes the fringe pattern created by the baseline relative to the direction of the source, and the second describes the fringes created by the projected baseline relative to the offset of a displacement of a point from the source centre. These vectors are described in figure 2.3.

2.3 u-v coverage

A visibility is obtained for a single u-v position, corresponding to a sky brightness at a speciﬁc angular scale and orientation. As the Earth rotates with respect to the source, the projected baselines rotate and the associated u-v positions change, and so a set of visibilities are obtained. The greater the coverage of the u-v plane, CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 34

b α B

Figure 2.3: Vectors describing the relations between an interferometer baseline and the target source. B is the baseline vector between two telescopes; b is the projected baseline;s ˆ describes the unit vector in the direction of the source; σ is the vector from a point on the source to the source centre. the more complete the mapping of the sky brightness distribution. For a fixed array, it is not possible to achieve complete u-v coverage as all possible values of |B| cannot be made. This reduces the sensitivity of the map, equivalent to convolving the modified sky brightness distribution with a sampling function. Figure 2.4 shows the u-v coordinates traced out through an observation with e-MERLIN. The amount of u-v coverage depends on the number of baselines, the length of observation and the declination of the target source. Sources at low declinations will have poorer u-v coverage as the resolution in the v-direction approaches zero, even with several North-South baselines. Arrays with fewer elements must observe for longer to obtain sufficient u-v coverage: the JVLA has 27 telescopes, hence 351 baselines, so has good instantaneous sampling; e- MERLIN has only 7 antennae, making 21 baselines, so must observe for longer periods to cover an equivalent area of the u-v plane. CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 35

Figure 2.4: Plot of u-v tracks for the e-MERLIN observation of RX J0911+0551 over a period of 10 hours. The e-MERLIN array has 7 antennae (21 baselines) with a maximum baseline of 220 km. The colours represent the frequencies across the band. The source has a low declination, so there is less extension in the v-direction (y-axis) and as a result the u-v tracks are more elliptical. CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 36

2.4 Limitations

The field of view of an interferometer is limited in several ways. It is limited fundamentally by the primary beam, but additional limits are created by the electronics of the receiver system. A radio telescope receiver acts over a finite bandwidth, so the detected signal is not monochromatic. Thus, the fringe patterns created by an interferometer system are combined over a range of frequencies and become incoherent at a short distance from the phase centre. For e-MERLIN, at 5 GHz with a bandwidth of 2 GHz, this would result in a field of only 125 mas. The effect of a finite bandwidth is mitigated by dividing the band into many small spectral channels, typically ∼1 MHz, so for each sub-band the fringes become incoherent at a large distance, resulting in a wider field of view. There is also a limitation due to a finite integration time. The interferometer must integrate over a sampling time sufficient to allow a good signal-to-noise ratio in each measurement, however, as the source moves through the sky it creates a phase difference which washes out the fringe pattern. A happy medium between the two is typically achieved with an integration time of a few seconds, for which the field of view limits are less than the limits due to bandwidth smearing (Bridle and Perley, 1999). Additional smearing is created due to the curvature of the celestial sphere, i.e. σ¯ is not truly perpendicular tos ˆ. The sky curvature becomes significant where

Bλ > 1 (2.5) D2

(Cornwell et al., 2005). The limit is not exceeded for the sources studied in this thesis. In the case of confusing sources at the edges of the field of view, the effects can be handled in the data reduction process. Objects far from the centre of the field of view may be affected by time and bandwidth smearing, but this did not affect these observations. CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 37

2.5 Sensitivity

In the observation of a weak source, the image sensitivity is the combined sensitivity of the interferometer baselines integrated over the total observing time on target. The noise limit determines the faintest objects that can be detected in the map. The RMS noise level for an interferometric array is given by the radiometer equation (for full derivation see Crane and Napier (1989)) √ 2kTsys ∆S(Jy) = √ √ , (2.6) t∆νAηa nb per polarisation, where ∆ν is the bandwidth, Tsys is the system temperature,

A is the collecting area of each telescope, ηa is the telescope efficiency, t is the integration time and k is Boltzmann’s constant. nb is the number of baselines, i.e. N(N − 1)/2 where N is the number of telescopes in the array. For antennae of different sizes, such as e-MERLIN, it is sometimes more useful to express the noise in terms of the system equivalent flux density (SEFD) to compare antenna performance analogously. The SEFD is related to the RMS noise for a single baseline between antennae i and j by

r 1 SEFDiSEFDj ∆Sij(Jy) = , (2.7) ηa t∆ν where the SEFD is in units of Jy, per polarisation.

2.6 Calibration

While the geometric delay can be precisely accounted for, additional phase delays and errors are accumulated due to the eﬀects of telescope instrumentation and the atmosphere. Errors in the frequency domain are mainly due to instrumentation

(the correlator, filters and amplifiers), which causes delay errors (τi) and creates phase gradients across the band and has a frequency-dependence in sensitivity, CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 38 which causes slopes or ripples in amplitude across the band. These errors are generally stable on timescales of a few hours, although there can be jumps in τi. Atmospheric errors are the main cause of phase and amplitude errors in the time domain. Most of these are due the ionosphere, which causes phase rotation, but there is a small contribution from the troposphere which absorbs radio emission. These effects are especially problematic for interferometers with large baselines, such as e-MERLIN, where the telescopes observe through different parts of the atmosphere, and are worse at lower elevations due to the increased optical depth. The errors are significant on the order of minutes at frequencies of a few GHz (Walker, 1999). The relationship between the observed visibilities and the true visibilities can be described by the equation

˜ Vij(t, ν) = Vij(t, ν)Gij(t)Bij(t, ν), (2.8)

˜ where Vij is the ‘true’ visibility and Vij is the measured visibility for two antennae, i and j. Gij is the complex ‘continuum’ gain and Bij is the frequency-dependent gain (Fomalont and Perley, 1999). The baseline-based complex gain can be con- sidered the product of the antenna-based gain,

∗ i(φi(t)−φj (t)) Gij = gi(t)gj (t) = ai(t)aj(t)e , (2.9) as most of the data corruption occurs before the signals are correlated and the residual baseline-based gain is typically small. Time-dependent phase and amplitude errors are corrected for with phase- referencing: switching between the target and a nearby bright calibrator source, whose structure and ﬂux are known, on timescales within which the errors occur. The phase reference source can also be used to correct for time-variable, CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 39

frequency-dependent phase errors and remove τi: this must be corrected for before phase calibration as delay errors of about 160/∆ν nanoseconds1 (where ∆ν is in MHz) result in significant phase and amplitude decorrelation (Fomalont and Perley, 1999). The flux scale is set with observations of a flux calibrator source, whose visibility across the band is known. For e-MERLIN this source is typically 3C 286. The amplitude and phase corrections for each baseline can be determined by comparing the calibrator observations to their known visibilities. Algorithms then solve for the antenna-based gain correction, which are interpolated onto the target observations (Fomalont and Perley, 1999).

The frequency-dependence function of the gain, Bij(νk), for frequency channel k, is found by observing a bright source with a flat or well-known spectrum for long enough so that there is a high signal-to-noise ratio in each channel, and dividing the observed visibilities by the correct visibilities. The source is ideally unresolved, so its flux is the same on all baselines. Due to the slow time- dependence, observing once or twice in a 12 hour run is sufficient. Calibration is an iterative process, with the phase and amplitude corrected incrementally in the frequency and time domain to achieve stability across the band and the observation period, before the data is averaged to produce a map.

2.7 Imaging and Deconvolution

The image reconstructed from inverse Fourier transform of the calibrated data is known as the ‘dirty’ map. The fundamental sensitivity limit of an image is determined by the properties of the observing system, such as the telescope receivers (2.5). There are also external contributions, such as spillover from terrestrial sources in the receiver sidelobes, and the tail end of the cosmic microwave background spectrum. However, even after good calibration, image artefacts occur

1Ideally, the delay errors should be an order of magnitude more accurate than this for successful calibration. CHAPTER 2. FUNDAMENTALS OF RADIO INTERFEROMETRY 40 due to interopolation across the unsampled parts of the u-v plane. The aim of deconvolution is to recover the true sky brightness distribution from the dirty map. The CLEAN algorithm, introduced by Högbom (1974), is a method of deconvolution that assumes the sky can be represented by a sum of point sources. The algorithm finds the brightest point of the map and calculates the convolution of a delta function with a fraction (typically 10%) of the flux density of this point, with the telescope response function. It then removes the result from the map and saves the flux and position of those points (‘CLEAN components’). The process is repeated iteratively until the residual map contains only noise. The CLEAN components are then restored and convolved with a Gaussian which forms the ‘clean’ map. Data reduction software, such as AIPS, uses a more efficient variant of this, the Clark algorithm (Clark, 1980). The algorithm has major and minor cycles. In the minor cycles, the Högbom algorithm is performed in a way that reduces the influence of the beam sidelobes. In the major cycles, the CLEAN components from the minor cycle are removed from the visibilties in the Fourier plane. Chapter 3

Observations

This chapter will discuss the sample selection process, the speciﬁcs of the observations, and ﬁnally an overview of the methods of data reduction and analysis.

3.1 Sample selection

Much of previous research on radio-quiet quasars has focused on optically-bright quasars selected from the Palomar survey (for example Miller et al. (1993); Blun- dell and Beasley (1998); Leipski et al. (2006)). These have intrinsic fluxes of a few hundred µJy, in accordance with the optical-radio flux correlation (figure 1.13). However, as discovered by White et al. (2007), all quasars are expected to have a radio component at some level. The majority of strongly-lensed quasars are radio-quiet sources. Those with detected radio components consist mostly of 22 sources discovered in the Cosmic Lens All-Sky Survey (CLASS) (Myers et al., 2003; Browne et al., 2003), with a small number from other surveys (such as Winn et al. (2002)), representing a fraction of the true population of lensed quasars. The sources chosen for observation are optically-selected four-image quasar lenses with no detected radio emission in the NVSS and FIRST 1.4 GHz surveys, down to a noise level of ∼1 mJy (Condon et al., 1998; Becker et al., 1995). These

41 CHAPTER 3. OBSERVATIONS 42 lenses are part of sample investigated concurrently with the JVLA as part of the Jackson et al. (2015) collaboration. A further two lenses from the Sloan Digital Sky Survey Quasar Lens Search (SQLS) were observed with e-MERLIN, which have had no other observations at radio wavelengths.

3.2 e-MERLIN observations

The results of this thesis were obtained using the Multi-Element Radio Linked Interferometer Network (e-MERLIN). e-MERLIN comprises an array of seven radio telescopes, making 21 baselines with a maximum baseline length of 217 km. The telescopes are located around the United Kingdom, linked by optical fibres to a central correlator based at Jodrell Bank Observatory in Cheshire. The Lovell Telescope and Mark II are at Jodrell Bank, with the other telescopes at Pickmere, Darnhall, Defford, Cambridge and Knockin (figure 3.1). HS 0810+0554, RX J0911+0551, SDSS J1251+2935, and SDSS J1330+1810 were observed with e-MERLIN at L-band. The details of these observations are listed in table 3.1. The L-band (1287-1799 MHz) receiver is divided into 8192 spectral channels of 62.5 kHz, enabling a resolution of 150 mas and a field of view of 20”. For a full imaging run, a sensitivity of ∼10 µJy can be obtained depending on source declination and data quality (estimated from Beswick (2013)).

Source Phase cal Date Exposure HS 0810+2554 JVAS 0813+2435 31/03/2013 8 hrs RX J0911+0551 SDSS J0901+0448 26/04/2013 7 hrs SDSS J1251+2935 J1257+3229 02/04/2014 8 hrs SDSS J1330+1810 J1333+1649 02/04/2014 8 hrs Table 3.1: Details of e-MERLIN observations at L-band.

Observations of nearby phase calibrators were carried out, as listed in table 3.1, with cycles of 7 mins on the target and 3 mins on a phase calibrator. In all CHAPTER 3. OBSERVATIONS 43

Figure 3.1: The locations of the seven e-MERLIN telescopes around the UK (O’Brien, 2009). CHAPTER 3. OBSERVATIONS 44 cases, 3C 286 was observed as a ﬂux calibrator and OQ 208 was the bandpass calibrator. The calibrators were observed within two weeks of the targets and are unlikely to have varied signiﬁcantly between epochs. Data reduction was carried out with AIPS as detailed in section 3.3. The data was reduced in frequency to 8 IFs (intermediate frequency sub-bands) each with 64 1 MHz channels. With HS 0810+2554, the data was averaged in time every 5 seconds. No time averaging was performed for the other sources. Table 3.2 details the JVLA observations of these sources, the results of which will be discussed alongside the results of the e-MERLIN observations.

Source Date Frequency Exposure HS 0810+2554 26/10/2012-24/11/2012 8.4 GHz 7.5 hrs RX J0911+0551 31/10/2012-24/11/2012 5 GHz 7.5 hrs Table 3.2: Details of JVLA observations.

3.3 Data reduction

The data used in this thesis was edited, calibrated and analysed using the AIPS (Astronomical Image Processing Software) package by NRAO (Bridle et al., 1994). The software does not alter the original visibilities, but produces tables attached to the file so the original data remains intact. This is beneficial as any bad calibration solutions can be easily deleted and the calibration process repeated, with different calibration parameters or after flagging of the bad data. An outline of the data reduction process will be given in this section, with discussion of some specific examples of the processes used for the target sources.

3.3.1 Loading the data

The data was loaded, concatenated and averaged using the e-MERLIN pipeline (Argo, 2015), and standard procedures then used to calibrate the data as detailed CHAPTER 3. OBSERVATIONS 45 in the AIPS cookbook (Belles et al., 2015). The pipeline loads the FITS files containing the raw data into AIPS using the task FITLD. The task DBCON concatenates the target and calibrator data files into a single file. DQUAL reorders the source table and re-labels the data within it, so sources of the same name have the same source index. The SERPent software (Peck and Fenech, 2013) automatically flags RFI in the data and creates an FG (flag) table attached to the file. The data is then averaged in frequency from 512 to 64 channels per IF to make it manageable for calibration. Further flagging is then carried out ‘manually’ as necessary using the task SPFLG, which displays the data by channel for each baseline. The amplitude and phase of each data point can be displayed and the bad data flagged interactively by the user. The task INDXR is run to create the initial calibration table (CL 1), which contains null entries (amplitude 1, phase 0) for all sources. The initial CL table is created with entry intervals of 5 minutes as a default. For long baseline arrays such as e-MERLIN and VLBI, the telescopes observe through different parts of the atmosphere and phase changes happen quickly, so a shorter time interval is necessary. The entry interval used for the data calibration in this thesis was 8 seconds, standard practice for e-MERLIN data, previously established by trial and error. The flux and bandpass calibrators used for the data reduction in this thesis are 3C 286 and OQ 208. 3C 286 (or 1331+305) is a standard flux calibrator used for radio interferometric observations. Models exist for the source structure at a variety of wavebands, including L-band, and the fluxes are catalogued within AIPS. OQ 208 (or 1407+284) is bright compact radio source that is unresolved with e-MERLIN, which makes it an ideal bandpass calibrator as it has the same flux at all baselines. CHAPTER 3. OBSERVATIONS 46

Figure 3.2: Phase and amplitude data for point source calibrator OQ 208, without any ﬂagging and before any calibration had been applied. Note the reduced sensitivity at the edge of each IF. The data is displayed in POSSM by baseline for stokes LL polarisation only. CHAPTER 3. OBSERVATIONS 47

Figure 3.3: Phase and amplitude data for point source calibrator OQ 208, after flagging, before calibration. The channels at the edges of each IF have been flagged, as well as significant outliers. The data is displayed by baseline for stokes LL polarisation only. CHAPTER 3. OBSERVATIONS 48

3.3.2 Calibration

Calibration of the data was performed as described in the e-MERLIN cookbook (Belles et al., 2015). An overview of the process will be given in this section. Before beginning calibration, the flux densities of the flux calibrator and point source calibrator need to be scaled against known values. This is checked using the task PRTAB with inext ‘SU’, which lists the fluxes for each IF. The flux density and spectral index of 3C 286 are well established and can be set by AIPS using the task SETJY and optyp ‘CALC’. In this work, the values used were those defined by Perley and Butler (2013), which are scaled to account for the fraction of the flux resolved out by e-MERLIN.

Fringe ﬁtting

Fringe fitting is performed with the AIPS task FRING. This process corrects for time-variable instrumental delays between telescopes in a baseline. All calibrator sources are used to create the delay solutions which form the first solution table, SN 1. The solutions are then applied applied to all the sources by using the task CLCAL, which extrapolates the solution table to all the sources, creating a new calibration table CL 2. Some of the delay solutions for point source calibrator OQ 208 for the calibration of HS 0810+2554 are shown in figure 3.4, generated using the task SNPLT. The solutions are within a few nanoseconds of zero. Figure 3.5 are plots generated with POSSM, showing the amplitude and phase data for the source with the delay calibration applied. The phase slopes have been removed from the data and they appear flat across each IF.

Phase calibration

The task CALIB is employed to compute the phase solutions of the antenna gains. This is done twice, because the ﬂux calibrator is resolved so it ﬁrst needs to be CHAPTER 3. OBSERVATIONS 49

Figure 3.4: Delay solution table for point source calibrator OQ 208, shown baseline by baseline for LL polarisation only. The delays are within a few nanoseconds. The plots were generated using the AIPS task SNPLT. CHAPTER 3. OBSERVATIONS 50

Figure 3.5: POSSM plot of OQ 208 amplitude and phases after the delay calibration is applied. Note that the phase slopes have been removed and they are now flat across each IF. CHAPTER 3. OBSERVATIONS 51 calibrated against a model containing its structural information. To counter the poor sensitivity at the edges of IFs only the middle 75% of the band is used for calibration. The initial calibration of 3C 286 produces a solution table, SN 2. CALIB is then run again on the other calibrator sources. A short solution interval of 0.5 minutes is typically possible as the calibrators are strong sources. Within CALIB, the parameter weightit is set to 1 to force the data weights to be the square root of the error. The parameter soltype is set to ‘L1’ to calculate the least-difference solution. These parameters are usually set for e-MERLIN data to reduce the sensitivity to outliers. The resulting solutions are then written into SN 2, so all the phase solutions are in one table. SNPLT with optype ’PHAS’ is used to check the solutions. CLCAL then extrapolates the solutions to CL 3. The phase calibrator with these applied calibrations, if it is unresolved, should have zero resultant phases. POSSM plots for OQ 208 with phase calibration applied are shown in figure 3.6.

Flux and Bandpass calibration

The goal of bandpass calibration is to correct for the frequency-dependent part of the gains. This causes errors in the measured fluxes, so it is important to correct for this before flux calibration. An initial bandpass calibration is performed on the point source calibrator OQ 208, as the spectral index has not yet been taken into account. In fact, OQ 208 is known to have a steep spectral index. This is performed with the task BPASS, which creates a bandpass table, BP 1. The initial complex gain solutions are now computed for the calibrator sources with the task CALIB. As before, the flux calibrator is first solved for using the existing model of the source. The amplitude solutions for the phase and bandpass calibrators are then solved for and written into the same table, SN 3. A larger solution interval of 2 minutes is required for amplitude calibration. The resulting CHAPTER 3. OBSERVATIONS 52

Figure 3.6: POSSM plot of OQ 208 amplitude and phases after phase calibration applied, showing the LL polarisation only. The resultant phases are around zero. The amplitudes are unchanged. CHAPTER 3. OBSERVATIONS 53 gain solutions are roughly constant for each IF, unless the calibrator has a steep spectrum. The fluxes and spectral indices of the calibrators are now derived to refine the flux and bandpass solutions. The task GETJY is now run for the bandpass and phase calibrators, using 3C 286 as the calibrator to set the flux scale and SN 3 created previously. For the e-MERLIN data in this paper, the Lovell telescope was excluded from this calibration as its high sensitivity affects the scaling. The task SOUSP then plots the fluxes for the bandpass and phase calibrators and fits a spectral index. These can then be checked against catalogue values, such as in the VLA Calibrator Manual (NRAO, 2012). The task run with parameter doconfrm=1 will then create an SU table with spectral index solutions. In some cases an IF will exhibit an erroneous flux and cause a bad fit of the spectral index, and this can be fixed ‘manually’ using the task SETJY. This was the case for some of the observarions in this work. Now the true spectral indices have been derived, better flux calibration can be performed. The initial flux and bandpass calibration tables, BP 1 and SN 3, are deleted and the processes run again with the BPASS parameter specindx set to the correct value of the spectral index. The flux calibration is run as before, but with the CALIB parameter doband=4 to apply the bandpass solutions. The new SN 3 table is then applied to the data with CLCAL, to create CL 4. Figure 3.7 shows the data for OQ 208 after the flux and bandpass calibration had been applied. Note that the amplitudes are now the more consistent and smoother across the band. After the initial flagging and calibration, there may be bad data that could not be calibrated. It is necessary to remove this data before proceeding to image the phase calibrator, as large gains from the bad data will create artefacts in the map when inverse Fourier transformed. To view any obvious outliers in the data, the task UVPLT is used to plot the amplitude as a function of uv-distance. The CHAPTER 3. OBSERVATIONS 54

Figure 3.7: 1407+284 amplitude and phases after flux and bandpass calibration. The amplitudes are smooth across the band, except for the Lovell-Cambridge baseline which is not as well calibrated. CHAPTER 3. OBSERVATIONS 55 plot is be used to determine a threshold above which the data can be flagged with the task CLIP. The u-v distance-amplitude plot for phase calibrator, J0813+2435, after calibration, is shown in 3.8. There was some bad data, particularly on the short baselines, that needed to be flagged.

Self-calibration of the phase calibrator

The amplitude and phase calibration is limited by random and systematic errors which lead to noise and artefacts in the final image. Self-calibration (Cornwell and Wilkinson, 1981) is a way of refining the calibration solutions to minimise these errors. The self-calibration process uses the CLEAN components of a map as a model to enforce constraints on the source structure, which are then used to improve the phase solutions. These solutions are then applied to all the data, and the process is then repeated until it converges (Cornwell and Fomalont, 1999). Convergence is reached when the following have been achieved: the peak flux of the phase calibrator in the map stops increasing; the image does not improve; the phase solutions are within 1 degree and dominated only by noise. The AIPS map-making task is IMAGR, which performs the inverse Fourier transform of the u-v data to produce the dirty map. The task produces map files with the suffix ‘.ICL001’1 and a map of the beam with suffix ‘.IBM001’. The parameters imsize and cellsize set the desired image size in pixels and pixel size in arcseconds. The pixel size should be at least the Nyquist sampling rate (i.e. < λ/2d) to include all the data. As the data in this thesis was made at L-band, cellsize was set as 0.04 arcsec/pixel. The CLEAN component (CC) table is attached to its associated map file, and the appropriate number of CCs for self-calibration can be specified in CALIB. Initially, at least, a small number of iterations (e.g. 300) are set to ensure

1The class name depends on the imaging parameters. An image made with no cleaning will have the extension ‘.IIM001’; an image made with stokes ‘FULL’ will be ‘.FCL001’. A map file is created for each other fields, i.e. ‘.ICL00n’ where ‘n’ is the number of the field. CHAPTER 3. OBSERVATIONS 56

Figure 3.8: u-v-distance-amplitude plot for phase calibrator, J0901+0448, after calibration but before final flagging. Every 153rd visibility is plotted. The colours show the frequencies across the band. CHAPTER 3. OBSERVATIONS 57 only true flux components are removed from the map and not noise or artefacts. Several iterations should be performed with phase calibration only before proceeding to phase and amplitude calibration. For the calibration of the sources in this thesis, the phase calibrators were unresolved so did not require many self- calibration loops for the process to converge. Once a good set of time-dependent phase and amplitude solution had been derived from the phase-reference source, they were interpolated, along with the delay and bandpass corrections, onto the target observations.

3.3.3 Imaging the target

After the self-calibration of the phase calibrator, the calibration process is complete and the target data can be separated out into another data file. This can be achieved with the task SPLAT, which separates out the target data with all the previous flags and calibration applied. As the target source is usually very faint, as it was for the sources in this thesis, and the data continues to look like noise even after calibration. The target data can now be viewed in UVPLT, without any averaging, and a threshold determined for flagging with CLIP. There may be bad data at identified some specific uv-distances, as with the phase calibrator, which can be removed by baseline with SPFLG. The data is re-weighted by antenna using the task WTMOD to improve the noise level in the map. The antennae are weighted by their sensitivity, resulting in an overall lowering of the noise level. This is particularly important for e- MERLIN data as the antennas are different sizes, so have different sensitivities. The Lovell telescope is weighted highly, as it has a much larger collecting area and therefore much better sensitivity. The weights used for this analysis were the standard L-band weights given in the cookbook (table 3.3). As well as making a map of the target, a wide field map can be made to check for other sources in the field. In the case of HS 0810+2554, this revealed CHAPTER 3. OBSERVATIONS 58

Antenna Weight Lovell 30.3 Mk2 1.00 Knockin 0.73 Deﬀord 0.61 Pickmere 0.77 Darnhall 1.00 Cambridge 1.74

Table 3.3: List of L-band antenna weights (Argo, 2015).

a bright 200 mJy source 6’ from the target. The placement of this source within the field of view caused errors in the phases and a higher noise level in the map. The effects of the confusing source were mitigated by multi-field imaging and CLEAN, and self-calibrating on the CCs of the confusing source, which resulted in a lower noise level. Self-calibration of the target can be performed provided the signal-to-noise ratio is high (>5σ) and the source is simple (Cornwell and Fomalont, 1999). This did not succeed in the case of HS 0810+2554 as the signal-to-noise was not sufficient. CLEAN boxes are used to improve the map, which can be identified by IMAGR input parameters or interactively. Areas are specified for cleaning so that only flux likely to be genuine is added to the model and used a as a basis for subtracting sidelobes. This is particularly necessary for fainter sources whose flux may be barely above the noise level, as was the case for HS 0810+2554, where boxes were used to distinguish true flux (determined from previous observations) from noise. Visibility weighting schemes can be employed to emphasise different properties of the data. The natural weighting scheme weights the visibilities of each baseline by the signal-to-noise quality, so the effect of weak visibilities is reduced. As there are more visibilities on short baselines, the weighting is better for imaging large-scale structure but less effective for compact sources (Briggs et al., 1999). CHAPTER 3. OBSERVATIONS 59

Natural weighing offers the lowest noise level, however the effects of sidelobes create noise ripples. A more even sampling of the u-v plane is achieved with uniform weighting, which makes the weights the inverse of the density of visibilities at each u-v position. The effect of the beam sidelobes is reduced with uniform weighting, however, at the expense of the sensitivity of the resulting map. The robust weighting scheme (Briggs, 1995) provides a medium between uniform and natural, which allows a ‘robustness’ parameter to be specified that tempers the effect of uniform weighting. In the case of HS 0810+2554, robust weighting (with robustness parameter of 0) reduced the effects of the confusing source and resulted in the best noise level after CLEAN. Chapter 4

Results

This chapter will summarise prior work on the four sources observed in this thesis, before discussing the results of the e-MERLIN observations (performed by this author) alongside the JVLA results by other members of the Jackson et al. (2015) collaboration.

4.1 HS 0810+2554

HS 0810+2554 was discovered in the optical with the HST by Reimers et al. (2002). It has a fold configuration, consisting of four images with a merging pair. The source is a narrow absorption line quasar at redshift z=1.51. X-ray absorption lines have been detected from relativistic outflow from the AGN, which may be magnetically-driven (Chartas et al., 2014). The lensing galaxy is at an unknown redshift, but was estimated by Mosquera and Kochanek (2011) to be z=0.89, based on image separations and typical lens population redshifts. High precision position and flux information on the lens were obtained by the CfA-Arizona Space Telescope Lens Survey (CASTLES) (Kochanek et al., 2013), which are detailed in table 4.1. The observation is shown in figure 4.1. There is a 0.7 magnitude difference in brightness of the merging pair (A and B), contrary to expectations based on smooth mass models which would predict the two images

60 CHAPTER 4. RESULTS 61

Figure 4.1: CASTLES I-band image of HS 0810+2554 (Kochanek et al., 2013). North is up, and East is left. The lens system has a fold-conﬁguration, with a merging south-western pair. The merging pair show a 0.7-magnitude diﬀerence in brightness, contrary to expectations. CHAPTER 4. RESULTS 62

ABCD ∆RA 0.000±0.000 0.087±0.003 0.774±0.003 0.610±0.003 Position ∆dec 0.000±0.000 -0.163±0.003 -0.257±0.003 0.579±0.003 Flux I-band 15.63±0.09 16.48±0.33 17.29±0.29 18.61±0.41

Table 4.1: Details of HS 0810+2554 from CASTLES (Kochanek et al., 2013). The position of each image, relative to image A, is given in arcseconds. The optical flux at I-band is given in apparent magnitude. to have the same magnification (equation 1.9). The source was observed with e-MERLIN at L-band. The four components of the lensed source are detected, but the lens galaxy is not detected. The map is shown in figure 4.2. Each of the component images is detected at >5σ confidence, and the lens system itself is at 11σ. There are additional points of flux that appear at the ∼5σ level, such as the point North of image A, however these are likely to be noise artefacts as they do not appear in the JVLA map. Mapping of HS 0801+2554 was complicated by SDSS J0813+2542, a bright 200 mJy source 6’ to the South-West of the phase centre (figure 4.3), which con- taminated the phases and increased the noise level. The effects were reduced by simultaneously mapping the target and the confusing source, with CLEAN performed on both fields. Subsequent self-calibration with the CLEAN components of the confusing source yielded an RMS noise level of 29 µJy with robust weighting. Further analysis was made of the confusing source to improve the result. An map of the confusing source was made for each IF, to determine if it was necessary to account for the spectral index of the source when using CLEAN. For example, if the source had had a steep spectral index, more flux would be removed from the lower frequencies. This would be achieved by setting the spectral index with SETJY. However, the cleaned flux density was approximately the same in all the maps, implying the source has a flat spectrum and no spectral index correction was required. This is confirmed from catalogued photometric data on NED (NASA/JPL). The flux is lower that the catalogued value of 290 mJy the CHAPTER 4. RESULTS 63

Figure 4.2: e-MERLIN L-band observation of HS 0810+2554 with robust weighting. Each of the four components of the source are detected at >5σ conﬁdence. Image produced with CASA. CHAPTER 4. RESULTS 64

Figure 4.3: Map of the confusing source, quasar SDSS J0813+2542, located 6’ from HS 0810+2554. CHAPTER 4. RESULTS 65

Green Bank Survey (White and Becker, 1992). This is likely due to its position in the primary beam, on the edge of the beam of the Lovell telescope, meaning the sensitivity of the field is reduced (section 2.4). The reduced flux may also be due to the source being partially resolved out. A further improvement was attempted by reweighting the data by the sensitivity in each IF. A Python script was written to calculate the weighted mean flux density of the confusing source based on the cleaned flux density and RMS error in each IF map. The weighted mean was calculated to be the same as the cleaned flux and RMS in the full-band map, so no correction by IF was necessary in subsequent self-calibration cycles. The minimum possible noise level for the u-v data was determined using the dosefd function of the e-MERLIN pipeline. The pipeline uses the AIPS task UVHGM, which creates a histogram by flux of the data and fits a Gaussian distribution. The pipeline then calculates the SEFD for each IF and each antenna. A Python script (Appendix A) was written to calculate the RMS noise (equation 2.7, section 2.5) over all baselines and IFs. The ideal RMS noise level was found to be 12 µJy, based on the good data that remained after flagging and calibration, demonstrating that the effects of the confusing source could not be entirely eliminated. The image fluxes were determined by fitting a PSF using JMFIT. The positions were initially set with the positions from CASTLES and allowed to vary along with the flux. The best fit image fluxes are shown in table 4.2. The image positions and relative positions, found by JMFIT, are close to those of CASTLES, confirming the detection. Markov Chain Monte Carlo (MCMC) analysis was attempted using the emcee Python implementation (Foreman-Mackey et al., 2013) to find errors on the PSF fit. MCMC analysis is a method of Bayesian inference that employs a number of ‘walkers’ that randomly sample parameter space to define a probability distribution for each parameter. A Python script (Appendix B) was written to CHAPTER 4. RESULTS 66

Flux (µJy) A 161 ± 29 B 173 ± 29 C 129 ± 29 D 216 ± 29 Table 4.2: e-MERLIN L-band image ﬂuxes of HS 0810+2554, from JMFIT. The error given is the RMS noise in the data.

fit a PSF to the lensed components in the e-MERLIN map. The algorithm was given initial positions from CASTLES and fluxes derived with JMFIT, which the MCMC algorithm would then sample. The relative positions of the images, determined from CASTLES, were fixed. Six initial parameters (fluxes of the four images and coordinates for image A) were then given to the emcee sampler. However, due to the poor SNR, the algorithm was unable to obtain a reasonable probability distribution as a similar χ2 fit could be obtained for many different parameter values. The lens was observed with the JVLA as part of the Jackson et al. (2015) collaboration. The observations were taken at X-band (7988-10036 MHz) in A- configuration, at a resolution similar to the e-MERLIN observation, and analysed by Hector Vives-Arias. All lensed components of the source are detected. The flux of each component was found using the AIPS task JMFIT, a Gaussian-fitting algorithm, the results of which are detailed in table 4.1. There is no evidence of a flux ratio anomaly as detected in the observations at optical wavelengths: the measured flux of the merging A and B images are equal, within errors, as expected with a smooth mass model. It is therefore likely that the optical ratio is due to microlensing, rather than substructure. The lensing galaxy is not detected, placing a 3σ limit of µJy on its flux density. The JVLA observation is shown in figure 4.4. The components in the image appear to show extended structure, particularly around A and B where there is a faint arc. The components were fit with the interferometer point spread function (PSF), as shown in figure 4.5. As expected, they are not well fit by this model, CHAPTER 4. RESULTS 67 demonstrating that the images are not point sources. There are residuals around components A and B, and between B and C. This is clear evidence of resolved extended structure.

Flux (µJy) A 85.1 ± 3.7 B 83.7 ± 3.7 C 60.0 ± 3.7 D 49.1 ± 3.7 Table 4.3: JVLA X band image ﬂuxes of HS 0810+2554. Results from Jackson et al. (2015).

Modelling of the lens system was conducted by other members of the research group, Neal Jackson and Amit Tagore. The lens was modelled by an isothermal ellipsoid mass distribution with external shear from nearby galaxies, and the source was assumed to be a simple ellipse. The best fit parameters are detailed in table 4.4. The errors on the source parameters were found using Markov Chain Monte Carlo (MCMC) analysis, with the emcee Python implementation (Foreman-Mackey et al., 2013).The probability distribution of source size against axis ratio are shown in figure 4.6. The best fit parameters were an intrinsic size of 10 mas, corresponding to a true linear size of 70 pc, with an intrinsic source flux of 3.6 µJy, and a magnification in the brightest components of 25. This result is different from that found by Assef et al. (2011), who derive a magnification of around 50 with a similar method using the CASTLES observation. It is likely this is because the source is close to the fold of a small astroid caustic, where small relative positional changes have a big effect on magnification (section 1.1.2). Accurate flux ratios cannot be reliably obtained from the e-MERLIN data due the high noise level, however a spectral index can be inferred by comparing the sum of the flux of each component in the JVLA and e-MERLIN data. The spectral index is found to be α = −0.55 ± 0.1, which puts the intrinsic flux of the

+1.8 source at L-band at 9.0−2.2 µJy. CHAPTER 4. RESULTS 68

Figure 4.4: JVLA X-band image of HS 0810+2554, with RMS noise level of 3 µJy. The images are labelled clockwise from the most Westerly component. Image produced with CASA (McMullin et al., 2007). CHAPTER 4. RESULTS 69

Figure 4.5: Attempt to model HS 0810+2554 with a point source and PSF. The left image is the true data, the central image is the PSF model, the right image is the residuals when the model is subtracted from the data. The residuals show signiﬁcant features, particularly around images A and B, showing the lensed images are not well ﬁt by the PSF model. The white bar represents 1”. Figures from (Jackson et al., 2015).

Variable HS 0810+2554 RX J0911+051 Source position/mas 0.1 E, 13.0 S 468 E, 28 S +15 Source major axis/mas 12±1 131−11 +0.3 Source ﬂux/µJy 3.6±0.2 3.7−0.2 +0.06 Source b/a 0.66−0.09 ≡1.0 Source position angle (47±5)◦ – +11 Galaxy critical radius/mas 473±10 1047−38 +0.03 Galaxy ellipticity 0.0003±0.0003 0.15−0.09 ◦ +0.033 ◦ External shear 0.023±0.006, (29±4) 0.373−0.011, (9±2) Table 4.4: Model ﬁtting results for HS 0810+2554 and RX J0911+0551 from JVLA observations. The source position is given relative to the galaxy position. For RX J0911+0551, the galaxy critical radius corresponds to the Einstein radius measured along the major axis. Results from Jackson et al. (2015).

4.2 RX J0911+0551

RX J0911+0551 was discovered in X-ray frequencies in the ROSAT All-Sky Sur- vey by Bade et al. (1997), and was conﬁrmed to be a lens by Burud et al. (1998). It is a cusp lens system, with a three-image complex to the East and a faint fourth component to the West of the lens. The quasar is at redshift z=2.80 (Bade et al., CHAPTER 4. RESULTS 70

Figure 4.6: The MCMC probability distribution for the intrinsic source size and source axis ratio of HS 0810+2554. Figure from Jackson et al. (2015).

1997) and the lens at z=0.77 (Kneib et al., 2000). The lens is red elliptical galaxy which is part of a massive cluster centered 38’ to the South-West (Burud et al., 1998). The lens also has a small satellite to the North-West (Kneib et al., 2000) within the Einstein radius of the galaxy (ﬁgure 4.7).

ABCD ∆RA 0.000±0.000 0.260±0.003 -0.018±0.003 -2.972±0.003 Position ∆dec 0.000±0.000 0.406±0.003 0.960±0.003 0.792±0.003 Flux I-band 18.38±0.02 18.64±0.02 19.36±0.01 19.66±0.03

Table 4.5: Details of RX J0911+0551 from CASTLES (Kochanek et al., 2013). The position of each image, relative to image A, is given in arcseconds. The optical ﬂux at I-band is given in apparent magnitude.

The ﬂux and position details of the lens components from CASTLES are CHAPTER 4. RESULTS 71

Figure 4.7: HST observation of RX J0911+2554 in I-band from CASTLES (Kochanek et al., 2013). In this map the lens galaxy (G1) and it associated galaxy (G2) are can be seen. CHAPTER 4. RESULTS 72 detailed in table 4.5. As with HS 0810+2554, there is a flux ratio violation. The Eastern A-B-C complex has a flux ratio of approximately 2:2:1 (Burud et al., 1998; Sluse et al., 2012), inconsistent with the cusp ratio for a smooth mass model which predicts the magnification of image B to be the sum of those of A and C (equation 1.8). Sluse et al. (2012) model the lens system to derive expected flux ratios based on a smooth mass model. The lens was modelled as an isothermal ellipsoid, with the associated galaxy as an isothermal spheroid assumed to be at the same redshift. Taking into account the large shear from nearby galaxies, the resulting flux ratios are 1:1.87:0.88:0.34, contrary to the optical astrometry. Due to the low declination of RX J0911+0551, there was less u-v coverage of the source with e-MERLIN resulting in a higher noise level. The noise could be reduced to 16 µJy with CLEAN and robust weighting (with robustness parameter of 1), close to the ideal value of 14µJy estimated based on observing time and data quality (as before). Despite this noise level, the source was not detected: the flux recovered with JMFIT was consistent with noise. The lensing galaxy was also not detected. A source is detected 5” South and another source 3’ South- West, confirming that this is a true non-detection and not a result of errors in the data reduction process. The source was observed with the JVLA at C-band (4488-6512 MHz) as part of the Jackson et al. (2015) collaboration. The data was analysed by Carl Roberts and all four components of the lens were detected (4.8). A source was detected 5” South of the lens system, as appears in the e-MERLIN observation. The fluxes of the lensed images and lens galaxy obtained with JMFIT are detailed in table 4.6. The ratio of the image fluxes are 1:2.05:0.73:0.35, within errors of the Sluse et al. (2012) estimations for a smooth mass model, confirming that the optical flux violation is due to the effect of microlensing, rather than substructure. The lens galaxy was detected at flux density 18 µJy, which corresponds to an intrinsic 5 GHz luminosity of 5 x 1022 W Hz−1. This is close to the limit of what can be ascribed to star formation activity, and at the boundary between CHAPTER 4. RESULTS 73

Figure 4.8: RX J0911+0551 observed at C-band with the JVLA. The lensing galaxy is also detected (centre). Image produced with CASA. CHAPTER 4. RESULTS 74 the 1.4 GHz radio luminosity functions of nearby star forming galaxies and AGN found by Condon et al. (2002) and Kimball et al. (2011). Burud et al. (1998) found no evidence of ongoing star formation in optical and infra-red observations, suggesting the radio emission may be AGN-powered.

Flux (µJy) A 26.9 ± 2.2 B 53.2 ± 2.2 C 19.7 ± 2.2 D 9.4 ± 3.0 G 18.3 ± 2.2 Table 4.6: JVLA C-band image ﬂuxes of RX J0911+0551.

Figure 4.9: Attempt to fit point source with PSF to RX J0911+0551. The lens galaxy has been blocked out. The data is not well fit by a PSF, with significant residuals around A-B-C. The white bar represents 1”. Figure from Jackson et al. (2015).

As with HS 0810+2554, the JVLA observation has some evidence of extended emission. The lensed images fit with a PSF are shown in figure 4.9. There are features in the residuals around the A-B-C complex suggesting the source has been at least partially resolved. Modelling of the lens system was performed by Amit Tagore, with an isothermal ellipsoid and external shear from the nearby galaxies. The modelling is shown in figure 4.10 and the derived parameters of the lens and source are detailed in CHAPTER 4. RESULTS 75

Figure 4.10: Modelling of the lens system RX J0911+0551. Left to right: the model source, the lensed model source, the data, and the residual. The white bar represents 1”. Figure from Jackson et al. (2015). table 4.4. The intrinsic flux is found to be 3.7 µJy. The source is more extended than that of HS 0810+2554, with an intrinsic size of 100-150 mas, corresponding to a true linear size of 1 kpc. The flux of the brightest component (image B) in the JVLA data is 53 µJy, so it is expected that the component should be detected with at least 3.3σ significance in the e-MERLIN data, assuming the spectral index α ≤ 0 at GHz frequencies. Further analysis of the e-MERLIN data was performed to attempt to extract a detection from the noise. The components of the lens were stacked using the AIPS tasks OGEOM and COMB. OGEOM was used to create new maps with the positions of each component shifted to the image centre. The data in the maps were then summed with COMB. The stacked lens components should appear as one object at 3.4σ significance, but they were again not detected. It is possible that the reason the components were not detected is that they have been resolved out by the long baselines of e-MERLIN. To put some constraints on the flux of the of the components, in the event that it was resolved out, a map of the source was made with the same resolution as the JVLA data. This was achieved by using the parameter UVTAPER within the AIPS task IMAGR, which weights down the long baselines and results in a lower resolution image. The rejection of a significant amount of visibilities increased the noise level. The resulting RMS noise in the position of the A-B-C complex is 100 µJy, CHAPTER 4. RESULTS 76 after accounting for the number of beams in the area, corresponding to a 3σ error of 300 µJy. This put a loose limit on the spectral index of α > −1. A more definitive solution to the problem was found by simulating the data to predict whether the source could be resolved out, or indeed detected at all, with e-MERLIN. The simulation was written (Appendix B) using the AIPS- Python interface, ParselTongue (Kettenis and Sipior, 2012). The map was simulated with four gaussian functions, with the flux derived from the JVLA map and positions from CASTLES. The components were of the size of the JVLA resolution. As the components are not fully resolved by the JVLA, this represents an upper limit on the true size of the images. The spectral index is expected to be zero at most (section 1.2), so the JVLA flux represents a lower limit on the flux. The Gaussian functions were added to the CC table (which contains the flux and position of CLEAN components, section 2.7) of a template image file in AIPS. The simulated images were then convolved with the e-MERLIN u-v sampling function using the AIPS task UVCON. The u-v sampling function was calculated from the baselines in the array, the source declination, and observing period. Gaussian noise was added to the simulated data with UVCON parameters so that the convolved map had an RMS noise level equal to that of the e-MERLIN observation (i.e. 16 µJy). The map was then fit with Gaussian functions by JMFIT, where the position and sizes were fixed to the known values, and the maximum allowed to optimise. As with the true observation, the results were consistent with noise and the source was not detected. The same simulation was run again with different parameters. When a source is smaller than the e-MERLIN resolution is simulated (i.e. the source will appear unresolved) it was also not detected, implying that the noise is the primary factor for the non-detection rather than the resolution. The simulation was run again with the initial JVLA parameters, but flux of the components were increased until they could be extracted with JMFIT. Component B could be detected with flux at the 4σ level. However, a signal-to-noise ratio of ∼10 was required for the CHAPTER 4. RESULTS 77 true flux to be recovered within 1σ error. It is likely higher signal-to-noise ratio is required for detection due to gaps in the u-v sampling function, which contributes to the non-Gaussianity of the noise. The deviation from a Gaussian distribution can be seen by plotting the noise distribution. A histogram of the noise in the cleaned e-MERLIN map, fitted with a Gaussian function, is shown in figure 4.11. The noise deviates from Gaussian noise at both positive and negative ends, which is more obvious in the log-scale plot (4.12). The prevalence of outliers may be due to effects of confusion on the edges of the primary beam and CLEAN artefacts, which are exacerbated by the range of beam sizes of the telescopes in the array (Muxlow et al., 2005). A comparison of the e-MERLIN result with the JVLA data implies that the source has a flat or shallow spectral index. If a detection limit of 4σ is assumed, the flux upper limit of image B is 63 µJy, and the spectral index of the source is α ≥ −0.1 with 1σ confidence and α ≥ −0.5 with 3σ confidence. The upper limit on the flux of the lensing galaxy is 65 µJy at 4σ, thus the spectral index is α > −1.

4.3 SDSS J1251+2935

SDSS J1251+2935 is a cusp lens discovered at optical wavelengths by Kayo et al. (2007) in SQLS. The lens was confirmed by spectroscopic analysis, which found that the lens is a red elliptical galaxy at redshift z=0.41, and the source is a quasar at redshift z=0.80. As with the other previous discussed, this lens also presents with a flux ratio anomaly. While image positions are well fit by mass models, the flux ratios differ significantly from expectations for a typical cusp lens. The ratios of the A-B-C complex at I-band are 2.6:2:1, violating the cusp ratio principle. Simple lens modelling, assuming the lens is a single isothermal ellipsoid with external shear, found in a magnification of 24 for the highly magnified saddle CHAPTER 4. RESULTS 78

Figure 4.11: Histogram of the noise in the cleaned map of RX J0911+0551, ﬁtted with a Gaussian function. The plot was created by the AIPS task IMEAN. CHAPTER 4. RESULTS 79

Figure 4.12: Histogram of the noise in the cleaned map of RX J0911+0551, on a log scale, fitted with a Gaussian function. CHAPTER 4. RESULTS 80 point (image B)1. The source was observed for the first time at radio wavelengths with e- MERLIN. The source was not detected at an RMS noise level of 40 µJy, placing an upper limit of 160 µJy on the maximum flux of any of the images assuming flux at 4σ is be required for detection (as implied from analysis of the e-MERLIN observation of RX J0911+0551). A high noise level resulted from the fact that much of IF 5-8 were removed by the correlator so the data obtained for analysis was reduced. Based on the magnification values found from lens modelling, an upper limit of ≤6.7 µJy could be derived.

4.4 SDSS J1330+1810

SDSS J1330+1810 is fold-configuration lens, also discovered in SQLS by spectroscopic analysis Oguri et al. (2008). The lens is at redshift z=0.37, and the source is a quasar at redshift z=1.40. The lensed images do not exhibit a flux ratio violation: the lens system is well fit by a smooth mass model, with external shear caused by a foreground galaxy cluster at redshift z=0.31 centered 120” South-West of the lens galaxy. The source was observed in X-ray by Blackburne et al. (2011), who derive image positions and fluxes consistent with Oguri et al.. Blackburne et al. (2011) model the lens system with an isothermal ellipsoid, and derive a magnification of 27 for the highly magnified minimum and saddle point. As with SDSS J1251+2935, the e-MERLIN observations of this source suffered from much of the data being removed by the correlator. In this case, all of IF 5-8 had been lost. A noise level of 50 µJy could be achieved in the clean map with natural weighting, placing an the upper limit on any of the lensed radio components is 200 µJy (again, assuming 4σ detection limit). Based on the Blackburne et al. (2011) modelling, this corresponds to a limit on the intrinsic source flux of ≤7.5 µJy.

1N. Jackson, private communication Chapter 5

Summary and Conclusions

This thesis has been a part of a larger effort to detect radio emission from radio- quiet quasars to understand the nature of their radio emission mechanisms. Grav- itational lensing provides a tool for investigating these sources in greater detail: the magnifying effect of lensing enables observations of faint sources that are otherwise out of reach of current radio telescopes. Whereas previous studies have focused on quasars of a few hundred µJy, this work enables observation of quasars with intrinsic fluxes of a few µJy. In this thesis, two gravitationally-lensed radio- quiet quasars were observed with e-MERLIN. The analysis of the e-MERLIN data was concurrent with analysis of JVLA data of the same sources, and the results have been discussed together. Both lens systems of HS 0810+2554 and RX J0911+0551 were detected with the JVLA at a high level of significance. One of the lens systems was detected with e-MERLIN, HS 0810+2445, at 11σ significance with each quasar component detected at >5σ level. The lensed flux ratios from the JVLA observations are consistent with a smooth mass model, with no evidence of flux ratio violations as seen in optical observations, implying the optical violations are due to microlensing rather than substructure in the lensing galaxy. The lensing galaxy of RX J0911+0551 was detected in the JVLA observations at flux corresponding to an intrinsic 5 GHz luminosity of 5 x 1022 W Hz−1. This

81 CHAPTER 5. SUMMARY AND CONCLUSIONS 82 is close to the limit of what can be ascribed to star formation activity, and at the boundary between the 1.4 GHz radio luminosity functions of nearby star forming galaxies and AGN found by Condon et al. (2002) and Kimball et al. (2011). Burud et al. (1998) found no evidence of ongoing star formation in optical and infra-red observations, thus the radio emission is likely to be AGN-powered. The lensed components in the JVLA observations showed some extended resolved structure not fit by a point source model. The intrinsic properties of the quasars were inferred using lens models and MCMC analysis. The fluxes were found to be ∼4 µJy with a size of ∼100 mas. The spectral index of the HS 0810+2554 was found to be α = −0.55± 0.1, consistent with optically-thin synchrotron emission. The spectral index of RX J0911+0551 is unclear, but it appears shallower than that of HS 0810+2554. Simulations reveal that noise is likely the primary reason for the non-detection, and place a lower limit on the spectral index of α > −0.5. The derived intrinsic fluxes of these sources allows for an extension of the White et al. (2007) quasar optical-radio relation (section 1.3.2). The intrinsic source fluxes of HS 0810+2554, RX J0911+0551, SDSS J1251+2935 and SDSS J1330+1810, are plotted in figure 5.1 alongside existing data as well as two further sources derived from modelling JVLA observations (SDSS J0924+0219 and HE 0435-1223). In some cases only an upper limit has been inferred from their absence in the FIRST survey. The median flux inferred by the White et al. stacking analysis is an order of magnitude higher than the results of this work, suggesting there is either a large scatter or a dichotomous luminosity distribution. A larger sample is required to make a more definitive conclusion. The results of these observations enables insight into potential emission mechanisms and their compliance with existing models. The intrinsic sizes of the quasars are 70 and 1000 pc in physical scale. An emitting region of this size rules out the Blundell and Kuncic model of free-free emission from a disk wind, and the Laor and Behar model of coronal heating. Both predict compact emitting CHAPTER 5. SUMMARY AND CONCLUSIONS 83

Figure 5.1: Intrinsic L-band radio fluxes of optically-selected lensed quasars, including HS 0810+2554, RX J0911+0551, SDSS J1251+2935 and SDSS J1330+1810 (shown in red). The tail-end of the best fit to the White et al. (2007) plot is shown by the curve on the right. Data and lens models from Ratnatunga et al. (1999); Wisotzki et al. (2002); Reimers et al. (2002); Burud et al. (1998); Inada et al. (2003a,b); Ghosh and Narasimha (2009); Anguita et al. (2009); Jackson (2011); Wucknitz and Volino (2008); Kayo et al. (2007); Oguri et al. (2008); Assef et al. (2011); Blackburne et al. (2011), taken from Jackson et al. (2015). CHAPTER 5. SUMMARY AND CONCLUSIONS 84 regions < 1 pc, so cannot be a dominant form of emission in these cases. They also predict flat radio spectra, which is inconsistent with HS 0810+2554. The physical scale of these sources also disfavour the model proposed by Con- don et al. (2013), that the radio emission is driven by starburst activity, as the size is a magnitude smaller than the size of star formation regions in circum- nuclear disks (Wrigley, 2015). This mechanism cannot be ruled out completely without further observations and a larger sample size, however Muxlow et al. (2005) deduced from a study of the Hubble Deep and Flanking Fields that the radio sizes of star forming galaxies do not have a large variance. The size and steep spectral index of HS 0810+2554 are most consistent with optically-thin synchrotron emission from a milliarcsecond-scale jet, powered by the quasar’s AGN. This may mean that the radio emission from quasars is dominated by this mechanism, with the radio-quiet subpopulation containing a less powerful central engine than those seen in radio-loud quasars. This is in contrast to the Wucknitz and Volino (2008) result, which found no evidence for a compact core in VLBI observations of the lensed quasar of J1131-1231, implying the radio emission is dominated by star formation. A proposal has been made for a further 72 hours of e-MERLIN L-band observations of HS 0810+2554. The longer observing period can potentially achieve a noise level of 5 µJy (Beswick, 2013), which would result in a cleaner map and allow for more accurate flux determinations. It is not clear to what extent RX J0911+0551 is consistent with the AGN model in light of its apparently shallow spectral index. The extended size of the emitting region implies that the emission cannot be dominated by a synchrotron self-absorbed core. It is unusual, although not unprecedented, for an AGN jet to have flat (or even inverted) radio spectra at GHz frequencies: absorption by thermal electrons HII regions has been implicated for GHz spectral turnovers in AGN (Vermeulen et al., 2003; Guainazzi et al., 2004; Alonso-Herrero et al., 2013). The same is true for starburst galaxies (Condon et al., 1991; Sopp and Alexander, 1991). Deeper observations are required to better constrain the spectral index CHAPTER 5. SUMMARY AND CONCLUSIONS 85 and resolve the extended structure implied by the JVLA observation. Further research on these lenses would benefit from higher resolution observations. The lensed flux of the sources are within the limits of Very Long Baseline Interferometry (VLBI), which would provide a definitive test by confirming the presence of a compact core characteristic of an AGN. Depending on which baselines are used, the European VLBI Network can achieve a resolution of 3-15 mas at L-band and a sensitivity of <2 µJy for a full imaging run (EVLBI, 2015). Future work will involve further observations with e-MERLIN and the JVLA of optically-selected four-image lenses, from surveys such as CASTLES, to in- crease the radio lens sample and further challenge the models of radio-quiet quasar emission mechanisms. The use of four-image lenses has uncovered some of the faintest sources yet detected, and it is likely that further research will enable detection of sources at the nJy level. Appendix A

Listed below is the Python code used to determine the ideal noise level in the data based on the SEFDs calculated by the AIPS pipeline. The pipeline produces a text ﬁle named here ‘SEFDs.txt’.

import numpy as np f=open(’SEFDs.txt’) lines=f.readlines() f.close() array=np.zeros(56) k=0 for line in lines: words=line.split(’ ’) for word in words: try: #print float(word) array[k]=float(word) except:

i APPENDIX A. ii

continue k+=1 new array=np.reshape(array,(8,7)) #print ’printing array’,new array def SEFD(x,y): noise=np.sqrt(x∗y)/(0.95∗np.sqrt(2∗25000∗6.25e7)) return noise total noise=0 for IF in range(0,8): IF noise=0 for i in range(0,7): #print ’i=’,i,’IF=’,IF for j in range(i+1,7): #print ’i=’,i,’j=’,j,’IF=’,IF noise=SEFD(new array[IF,i],new array[IF,j]) IF noise=IF noise+(1/noise∗∗2) # print np.sqrt(1/IF noise) total noise=total noise+(IF noise) print np.sqrt(1/total noise) Appendix B

Listed below is the Python code used to simulate the data for RX J0911+0551. The code uses the ParselTongue package Wizardry. A text file named ‘MERLIN.UVCON’ contains the antennae information (relative positions, sizes, etc.) to be read into UVCON, along with observation information (hour angles, integration time, etc.). A template image file is read into AIPS, named ‘0911ICL1.ICL001’, whose CC table is written into with the simulated flux.

from math import ∗ from AIPS import AIPS, AIPSDisk from AIPSTask import AIPSTask, AIPSList from AIPSData import AIPSUVData, AIPSImage from Wizardry.AIPSData import AIPSUVData as WizAIPSUVData from Wizardry.AIPSData import AIPSImage as WizAIPSImage import re, sys, numpy as np, scipy as sp, os, pyfits, matplotlib from matplotlib import pyplot as plt; from pyfits import getdata AIPS.userno=4713 t inna, t incl, t indi, t inseq = ’0911ICL1’,’ICL001’,1,1 # noisemult approx gives noise in uJy

iii APPENDIX B. iv hamin,hamax,inttime,freq1,nif,incr,noisemult = −6.0,6.0,20.,20.25,16,112.0,4.0 cellsize,imsize,niter,bmaj,bmin,bpa = 0.006,512,250,0.035,0.035,0.0 mask = [70./(1000∗cellsize),170/(1000.∗cellsize)] # mas cc = np.array([[0.0,0.0,0.283],[934.987,−1258.092,15.6e −3],\ [869.0,−1147.0,25.e−6]]) merlinfile = ’/raid/scratch/hstacey/RXJ0911+0551/MERLIN. UVCON’ ##################################################### # aips tasks def runuvcon (infile, in2name, in2class, in2seq, in2disk, outname,\ outclass, outdisk,dec): uvcon = AIPSTask(’uvcon’) uvcon.infile=infile uvcon.in2name,uvcon.in2class = in2name, in2class uvcon.in2seq,uvcon.in2disk = in2seq, in2disk uvcon.outname,uvcon.outcl,uvcon.outdisk = outname, outclass, outdisk uvcon.aparm[1:] = [freq1,0,dec,hamin,hamax,0,inttime, incr,nif,0] uvcon.bparm[1:] = [noisemult,0,0,0,0,0,0,0,0,0] uvcon.go() def runimagr(inname,inclass,indisk,outname,outdisk): imagr = AIPSTask(’imagr’) APPENDIX B. v

imagr.inname, imagr.inclass, imagr.indisk = ’SIM0911 ’,’UVDATA’,t indi imagr.outname, imagr.outdisk = ’SIM0911’,t indi imagr.cellsize[1:] = [cellsize,cellsize] imagr.imsize[1:] = [imsize,imsize] imagr.niter = niter imagr.nchav = nif imagr.bmaj, imagr.bmin, imagr.bpa = bmaj, bmin, bpa imagr.go() def runfittp(inna,incl,indi,dataout): fittp = AIPSTask(’fittp’) fittp.inname, fittp.inclass, fittp.indisk = inna,incl ,indi fittp.dataout=dataout fittp.go()

##################################################### INDE = 3140.892822265625 # value corresponding to aips INDE im=AIPSImage(t inna,t incl,t indi,t inseq) im.table(’CC’, 2).zap() im=WizAIPSImage(t inna, t incl, t indi, t inseq) oldcc=im.table(’CC’,1) newcc=im.attach table(’CC’,2) for i in range(len(cc)): k=oldcc[0] k[’deltax’] = cc[i,0]/3.6E6 APPENDIX B. vi

k[’deltay’] = cc[i,1]/3.6E6 k[’flux’] = cc[i,2] newcc.append(k) newcc.close() # −−−−−−−−− AIPS part −−−−−−−−−−−−−−− runuvcon (merlinfile, t inna, t incl, t inseq, t indi, ’ SIM0911’,’UVDATA’, \ t indi,im.header[’crval’][1]) im.clrstat() runimagr(’SIM0911’,’UVDATA’,t indi,’SIM1030’,t indi) AIPSImage(’SIM0911’,’IBM001’,1,1).zap(); os.system(’rm sim0911.fits’) runfittp (’SIM0911’,’ICL001’,t indi,’./sim0911.fits’) Appendix C

Listed below is the code written for the MCMC analysis of the PSF ﬁt to the e-MERLIN observations of HS 0810+2554. The code reads in an FITS image ﬁle, which contains the clean map, and outputs histograms corresponding to probability densities for each of the parameters.

import emcee import numpy as np,njj,os,random,sys,pyfits,matplotlib, scipy as sp,warnings from matplotlib import pyplot as plt from scipy.optimize import fmin from pyfits import getdata plt.rcParams[’figure.subplot.wspace’]=plt.rcParams[’ figure.subplot.hspace’]=0.01 plt.rcParams[’image.origin’]=’lower’ plt.rcParams[’image.interpolation’]=’nearest’ o = np.array ([[0.00,0.00],[−5.69,−10.79],[−51.61,−17.11],[−40.67,38.63]]) x0=np.array([0.0257,0.0387,0.0239,0.0596]) xc=277.37

vii APPENDIX C. viii yc=248.54 a=getdata(’HS0810 63 1.fits’)[0][0] noise,isz,pix1arc = 2.8e−5,512,66.7 psf = [14.9,1.71,45.47] niter=1000 nwalkers=18 nburn=100 def goodness(params, ∗x): f0,f1,f2,f3 = params a1 = njj.mkgauss([isz,isz],[xc+o[0,0],yc+o[0,1]],f0, psf[0],psf[1],psf[2]) a2 = njj.mkgauss([isz,isz],[xc+o[1,0],yc+o[1,1]],f1, psf[0],psf[1],psf[2]) a3 = njj.mkgauss([isz,isz],[xc+o[2,0],yc+o[2,1]],f2, psf[0],psf[1],psf[2]) a4 = njj.mkgauss([isz,isz],[xc+o[3,0],yc+o[3,1]],f3, psf[0],psf[1],psf[2]) model = a1+a2+a3+a4 goodness = (((model−a)/noise)∗∗2) np.putmask(goodness,((model<3.∗noise)&(a<3.∗noise)), np.nan) #for i in range(len(params)): #k=params[i]−x0[i] #if abs(k)>1.0∗params[i]: # goodness=goodness+(500∗abs(k)) return −0.5∗np.nanmean(goodness) APPENDIX C. ix def mcmcinit(params): print params array=np.tile(params,(nwalkers,1)) for r in range(nwalkers): for c in range(len(params)): k=((random.random()−0.5)/10)+1 array[r,c]=array[r,c]∗k return array print ’beginning ensemble sampler’ smc = emcee.EnsembleSampler (nwalkers,len(x0),goodness, args=[x0]) print ’calling mcmcinit’ p0 = mcmcinit(x0) print ’running mcmc’ pos,prob,state = smc.run mcmc(p0,nburn) print pos,prob,state smc.reset() print ’running mcmc again’ smc.run mcmc(pos,niter,rstate0=state)

# Print out the mean acceptance fraction. In general, acceptance fraction has an entry for each walker. print("Mean acceptance fraction:", np.mean(smc. acceptance fraction))

# Estimate the integrated autocorrelation time for the time series in each parameter. print("Autocorrelation time:", smc.get autocorr time()) APPENDIX C. x

# Plot the projected histograms of the samples #plt.hist(smc.flatchain[:,0], 100, label=’X pixels’) #plt.show() #plt.savefig(’psf fit mcmc x.png’,bbox inches=’tight’) #print np.mean(smc.flatchain[:,0]), np.std(smc.flatchain [:,0]) #plt.hist(smc.flatchain[:,1], 100, label=’Y pixels’) #plt.show() #plt.savefig(’psf fit mcmc y.png’,bbox inches=’tight’) #print np.mean(smc.flatchain[:,0]), np.std(smc.flatchain [:,0]) plt.hist(smc.flatchain[:,0], 100, label=’Flux of A’) plt.show() print np.mean(smc.flatchain[:,0]), np.std(smc.flatchain [:,0]) plt.hist(smc.flatchain[:,1], 100, label=’Flux of B’) plt.show() print np.mean(smc.flatchain[:,1]), np.std(smc.flatchain [:,1]) plt.hist(smc.flatchain[:,2], 100, label=’Flux of C’) plt.show() print np.mean(smc.flatchain[:,2]), np.std(smc.flatchain [:,2]) plt.hist(smc.flatchain[:,3], 100, label=’Flux of D’) APPENDIX C. xi plt.show() print np.mean(smc.flatchain[:,3]), np.std(smc.flatchain [:,3]) np.savetxt(’mcmc psf flatchain fix 100.txt’,smc.flatchain ) Bibliography

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