Lucky Imaging Optical Polarimetry of HL Tau and XZ

Home , 88 Tauri, CI Tauri, HL Tauri, Sigma Tauri, T Tauri, XZ Tauri

Optical lucky imaging polarimetry of HL and XZ Tau

Master of Science Thesis in Astrophysics

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-2 200 AU -3 -6 -5 -4 -3 -2 -1 0 1 2 Magnusarcseconds Persson Department of Astronomy Stockholm University 2010 Abstract

Optical lucky imaging polarimetry of HL Tau and XZ Tau in the Taurus-Auriga molecular cloud was carried out with the instrument PolCor at the Nordic Opti- cal Telescope (NOT). The results show that in both the V- and R-band HL Tau show centrosymmetric structures of the polarization angle in its northeastern outflow lobe (degree of polarization∼30%). A C-shaped structure is detected which is also present at near-IR wavelengths (Murakawa et al., 2008), and higher resolution optical images (Stapelfeldt et al., 1995). The position angle of the outflow is 47.5±7.5◦, which coincides with previous measurements and the core polarization is observed to decrease with wavelength and a few scenarios are reviewed. Measuring the outflow witdh versus distance and wavelength shows that the longer wavelengths scatter deeper within the cavity wall of the outflow. In XZ Tau the binary is partially resolved, it is indicated by an elongated intensity distribution. The polarization of the parental cloud is detected in XZ Tau through the dichroic extinction of starlight. Lucky imaging at the NOT is a great way of increasing the resolution, shifting increases the sharpness by 000. 1 and selection the sharpest frames can increase the seeing with 000. 4, perhaps more during better conditions.

About this thesis

This thesis is the written part towards a Master of Science Degree in Astro- physics at Stockholm University Astronomy Department. The corresponding work was done under the supervision of Professor Göran Olofsson at Stockholm University. The work involves observations with the PolCor instrument, built by Pro- fessor Göran Olofsson and Hans-Gustav Florén, mounted on the NOT and the following reduction, calibration and analysis of the data. The observations were carried out between 26th and 30th October 2008 and are of two young stellar objects: XZ Tau and HL Tau in the Taurus-Auriga molecular cloud complex. The reduction routines are written in the Python programming language. The result of the reduction is analysed and reviewed. This work has made use of the SIMBAD database and NASA’s Astrophysics Data System. This document was typeset by the author in LATEX 2ε.

Acknowledgements

First I would like to thank Göran Olofsson for making all of this possible, if I never would have sent that e-mail to the wrong Olofsson this would probably never have happened. You gave me the opportunity to do everything from start to ﬁnish, and I have learned so much, thank you. Hans-Gustav Florén for answering questions about the reduction software and the company on the observation run. Matthias Maercker and Soﬁa Ramstedt for their help and support during the years. Ramez and Daniel, it would have been really lonely here without you around. My girlfriend Anca Mihaela Covaci for putting up with me and my childishness, I hope you can bear with me the rest of your life. Contents

1 Introduction 1 1.1 Star formation ...... 1 1.1.1 Background - The Nebular Hypothesis...... 2 1.1.2 ISM - Structures & clouds...... 3 1.1.3 Early evolution of Low-mass stars ...... 4 1.1.4 Feedback processes...... 9 1.1.5 The Main-Sequence ...... 9 1.1.6 HL Tau and XZ Tau as part of Lynds 1551 in Taurus . . 10 1.2 Polarimetry...... 11 1.2.1 Background...... 11 1.2.2 Polarization in Astronomy...... 13 1.2.3 Detecting linearly polarized light...... 15 1.3 Diﬀraction limited imaging from the ground...... 17 1.3.1 Introduction ...... 17 1.3.2 Correction methods ...... 19

2 Observations and Data reduction 21 2.1 Observations ...... 21 2.1.1 The PolCor instrument ...... 21 2.1.2 Observations ...... 24 2.2 Data reduction ...... 27 2.2.1 Overview ...... 27 2.2.2 Dark frame and ﬂat ﬁelding...... 28 2.2.3 Determining the centre of reference object...... 28 2.2.4 Sharpness...... 29 2.2.5 Shifting and adding ...... 30 2.3 Data analysis...... 31 2.3.1 Stokes and additional parameters...... 31 2.3.2 Polarization standards...... 31

3 Results 33 3.1 Results...... 33 3.1.1 XZ Tau ...... 34 3.1.2 HL Tau...... 38 3.1.3 Lucky astronomy...... 45 3.2 Summary of results...... 49 3.2.1 HL Tau...... 49 3.2.2 XZ Tau ...... 49 3.2.3 Parameters vs sharpness/psf improvement...... 49

4 Discussion 51 4.1 Discussion...... 51 4.1.1 HL Tau...... 51 4.1.2 XZ Tau ...... 54 4.1.3 Other ...... 54 4.2 Summary ...... 55 List of Figures 57 List of Tables 59 Bibliography 61 Appendix 69 A. Data with three valid angles observed...... 69 B. Python code description ...... 70 B.1 Introduction ...... 70 B.2 Help Functions...... 70 B.3 Classes, Attributes and Methods...... 71 B.4 Example Usage...... 72 “Space is the place.” Sun Ra 1 Introduction

This thesis consists of work in the areas low-mass star formation, lucky imaging and polarimetry. This chapter gives an introduction to these areas. The first part is dedicated to the star formation process, the main topic of this thesis. Second part is an introduction to polarimetry, and lastly an introduction to lucky astronomy; a technique to obtain diffraction limited images from ground based telescopes. Section 1.1 consists of a brief history of the star formation process, a description of interstellar clouds, the early evolution of low-mass1 stars followed by feedback processes, the main sequence (MS), and lastly a description of the star forming cloud were the sources in this thesis are located - the Lynds 1551 (L1551) nebula in the Taurus Molecular cloud. In order to understand how the observations where made an introduction to polarimetry is given in section 1.2. The section give a background to polarimetry and a review of polarization in astronomy, were the technique to detect circumstellar dust is described and lastly the theory behind the detection technique is explained. The last section (1.3) gives and introduction to various techniques to obtain (near) diffraction limited images.

1.1 Star formation

Stars form out of the gravitational instability in a turbulent density enhance- ment, called molecular cloud (MC) in the interstellar medium (ISM), the collapse form a protostar. The protostar starts to accrete matter thus forming an accretion disk and a bipolar outflow. When it has accreted enough a pre-Main Sequence (pre-MS) star emerges, the circumstellar envelope starts to dissipate and by the time the core has ignited its nuclear burning of Hydrogen it has settled on the Main Sequence (MS) and there is just a small debris disk left. Somewhere on the journey planets are formed through collisions and coagulation. The protostellar and pre-MS phases are sometimes grouped together and the object is then be referred to as a Young Stellar Object (YSO), also the phases of star formation are classified from the Spectral Energy Distribution (SED) of the unresolved object, i.e. the classification systems origin depended on whether the object was resolved or not.

1 Low-mass stars M≤ 2 M , intermediate-mass 2 8 M .

1 CHAPTER 1. INTRODUCTION

A lot of important and energetic chemistry takes place in forming a star, the neutral Hydrogen in the MC goes from neutral H2 in the cold MCs to ionized H+ in the core of stars, complex chemistry on dust grains in the cloud takes place and creates complex molecules. The enormous density contrast between typical cloud densities and the hydrogen-burning centres of the final stars is typically about 24 orders of magnitude. The following is a description of the current star formation paradigm, which applies to low- and possibly intermediate-mass stars that form in isolation. Al- though most stars seem to be formed in clusters (Lada and Lada, 2003); groups of several stars of different masses, from brown dwarfs to O and B stars. By having other, possibly more massive, stars forming in the vicinity could effect the protostar in serious ways. The outflow could trigger other gravitationally unstable clouds to collapse into stars, but also if the other star has a strong radiation field it could photoevaporate the circumstellar cloud of the protostar and limit the growth of the star during its accretion phase. For a recent review in star formation see McKee and Ostriker(2007) and for a recent review of the advances in numerical studies of star formation see Klessen et al.(2009).

1.1.1 Background - The Nebular Hypothesis The idea that stars are formed out of interstellar clouds have been present for several centuries. The initial idea, that the Sun and Planets formed out of a rotating cloud or disk of material was called the Nebular Hypothesis, which was formulated by Emanuel Swedenborg in 1734. It sprung from the realisation that the orbital planes of the Planets around the Sun are all, to a good approximation in the same plane and direction, due to the formation process. Although the theory was successful in explaining the motion of the Planets, it could not explain why the Sun has the low, much lower than expected from the theory, angular momentum. Thus other theories were worked out during the years. In 1945 Alfred Joy analysed 11 irregular variable stars that shared photomet- ric and spectral properties (Joy, 1945). The characteristics included variability in the optical lightcurve and emission lines including that from Hydrogen (Hα) and Calcium (Ca II). The stars, ranging from spectral type F5 to G5 were associated with nebulae. Some of them were located in the constellations of Taurus and Auriga, after the strongest one he called them T Tauri stars. Being spa- tially associated with massive O and B stars, i.e. inheritably young they where suggested to also be young stars but of less mass (Ambartsumian, 1947). Herbig (1952) saw that the T Tauri stars were found to be systematically brighter than MS spectral counterparts, suggesting that they were still contracting towards the MS, confirming Ambartsumians suggestion. Continuing his work Herbig (1957a) found that their emission line profiles suggested an outflow of material, and wide absorption lines Herbig(1957b) which indicates a higher rate of stellar rotation than a MS counterpart, both indicating their youth. In the two decades after this Mendoza V.(1966, 1968); Cohen(1973) both detected IR excess emission and suggested the excess to be due to thermal emission of circumstellar dust. With the fact that this dust was in the form of a circumstellar disk, the probable site of planet formation, confirms the Nebular Hypothesis as the main theory of the formation of our solar system.

2 1.1. STAR FORMATION

1.1.2 ISM - Structures & clouds

The average particle density of the ISM in the solar vicinity is 1 cm−3. Consist- ing of gas and dust, the main gas components are hydrogen (90 percent) and helium (10 percent) with traces of of heavy elements while the dust comprise only 1 percent of the total ISM mass with graphite and silicate as main grain components. In the ISM, MCs are formed due to gravitational instabilities, supersonic turbulence and magnetic ﬁelds. The MCs vary in size from small globules with a 4 few hundred M in mass and giant molecular clouds (GMCs) with over 10 M . GMCs which are found in the spiral arms (Cohen et al., 1980; Dame et al., 1987) is where most of the stars in the milky way and other galaxies with star forming activity form. With typical mass, size and temperature ranging between 104 to 6 10 M , 10 to 100 pc and ∼15K (Stark and Blitz, 1978; Sanders et al., 1985; Ostlie and Carroll, 2007; McKee and Ostriker, 2007).

Figure 1.1: A 2×2 degree field centred at l = 60◦, b ∼ 0◦ in the constellation of the Southern Cross. The images are taken with both the PACS and SPIRE instruments aboard the Herschel spacecraft. Blue denotes 70 µm, green 160 µm and red is the combination of all SPIRE bands; 250/350/500 µm. The wavelengths traces the dust in the molecular cloud and by following the red filaments in the image, which denotes colder regions, we see where stars are most likely to form. The structure is clearly filamentary with intricate structures at different scales. Image credits ESA & the SPIRE and PACS consortia.

3 CHAPTER 1. INTRODUCTION

The low temperatures in MCs makes H2 difficult to detect, direct detection of cold interstellar H2 is usually only possible through UV absorption observations from space. Luckily the shielding of UV radiation provided by the higher densities relative to the ISM allows molecules to form, carbon monoxide (CO), water (H2O), ammonia (NH3), hydroxide (OH) and hydrogen cyanide (HCN) to name some common examples. −4 Due to the relatively high abundance of CO to H2, ∼10 × H2, the by H2 collisionally excited J=1–0 line of CO is usually used when mapping MCs (Ostlie and Carroll, 2007; McKee and Ostriker, 2007). Since MCs do not emit any radiation in the optical they can usually be seen as dark streaks across the sky, provided they lie in front of bright diffuse emission or stars. Another possibility to trace the MCs is to observe the cold dust at mid- and far-IR, in figure 1.1 the space observatory Herschel have observed a star forming region in our galaxy. Thermally radiating dust grains traces the cold cores. The smaller MCs form only low- to intermediate-mass stars while the large GMCs also form high-mass stars. The primary sites of star formation are GMCs, thats is were star formation in the Milky-Way and other galaxies primarily occurs. Density fluctuations create an internal structure of GMCs which exhibit extremely complex, often filamentary and sheet-like structure (Blitz et al., 2007) sometimes also described as fractal e.g. Stutzki et al.(1998). Historically clear substructures have been classified as follows; larger sub-clouds with masses of a few hundred solar masses and sizes of parsecs are referred to as clumps and smaller structures with masses of up to tens of solar masses and sizes up to half a parsec are referred to as cores. The density fluctuations is attributed to supersonic turbulence and thermal instabilities, and some of the resulting density fluctuations exceed the critical mass and density of gravitational stability. This brings us to the next phase — the collapse of the cloud core.

1.1.3 Early evolution of Low-mass stars Collapse The collapse and subsequent star formation of a cloud core is governed by the complex interplay between gravitational compression and agents such as turbulence, magnetic ﬁelds, radiation, rotation, viscosity and thermal pressure that resists or helps compression. The always quoted attempt at describing this the- oretically was the one by Sir James Jeans in 1902, who deduced the minimum mass required for a gravitationally bound system to collapse, the Jeans mass. With a sphere of uniform density ρ, and temperature T the Jeans mass is

3 /2 3 5kBT MJ = ' 4πρ GµmH 3/ 1/ T 2 10−19 g cm−3 2 ' 1.1 M gas . 10 K ρ The last equation is normalised for typical initial conditions and µ is the mean molecular weight (Zinnecker and Yorke, 2007). Thus a gravitationally

4 1.1. STAR FORMATION bound sphere with mass higher than this mass should collapse because gravity overcomes the internal thermal pressure. This simplified equation does not account for magnetic field support, turbulence and radiation fields. Although, it is apparent that it is easier to form stars from a cold and dense core than a warm and sparse one since it lowers the amount of gas required to undergo collapse. Two density cases have been identified, from which end products is quite different. In the high density core a strong external compression forms a turbulent core that, during the collapse fragments into several star forming cores creating a cluster of stars. In contrary to this the low density case end products is just one or a few star forming cores, caused by the lower external pressure. This is further supported by a connection between the core mass function and the stellar initial mass function (IMF) (Nutter and Ward-Thompson, 2007). The collapsing core is cold T ∼ 10 K and optically thin at sub-mm and mm wavelengths allowing radiation to escape and causing the contraction to be approximately isothermal and on a free-fall timescale. The free-fall timescale is defined as the time that a pressureless sphere of gas with initial density ρ requires p to collapse to infinite density under its own gravity tff = 3π/(32Gρ), with typical values of ∼105 years (Galván-Madrid et al., 2007) although simulations suggest the actual collapse phase lasts about ∼106 years due to turbulence and magnetic fileds (Ward-Thompson et al., 2007) With rising density, the Jeans mass decreases and the collapse continues. At a density of ρ ∼10−12 g cm−3, the central regions become optically thick, thus starting the adiabatic part of the collapse with a rise in temeprature as effect (Masunaga and Inutsuka, 2000; Stamatellos et al., 2007). When the centre of the collapsing core reaches densities of ∼10−9-10−8 g cm−3 it becomes thermally supported – a hydrostatic core has formed. The core subsequently contracts, while material falls on the newly formed central hydrostatic core from the surrounding medium. This continues until the central temperature reaches T ∼2000 K and at that point H2 dissociates, thus absorbing thermal energy causing a break in the hydrostatic balance. The breaking causes a second collapse which continues until all the H2 is exhausted and a subsequent hydrostatic core is formed — a protostar.

Protostar The heavily embedded object, a protostar, represents the earliest stages of star formation, the dense central object accrete matter from its surrounding envelope and continues to contract on a Kelvin-Helmholtz timescale, radiating away the thermal energy from the collapse. The early protostars have masses of about −2 10 M (Larson, 2003), thus somewhere between this stage and the final MS star a large increase in mass takes place. This occurs during the protostellar phase, derived from the observational properties of YSOs. When the central object is less massive than the protostellar envelope and the observable SED is that of a greybody (modified blackbody), i.e. thermal dust emission from the cold outer region of the molecular core, the object is referred to as having a Class 0 SED (Andre et al., 1993, 2000). Due to the conservation of angular momentum the initial rotation of the prestellar core is greatly increased during the collapse and a flattened circumstellar disk is formed around the protostar (Terebey et al., 1984). This disk acts

5 CHAPTER 1. INTRODUCTION as a bridge for matter accreting onto the star; gas accretes onto the disk, which then channels material inwards to the central star. Viscous forces transport the material inward and allow angular momentum to be transported outwards. The viscosity in disks around young stars is not completely understood, it has been suggested that it may be due to magneto-rotational instabilities (Tout and Pringle, 1992). When matter reaches the innermost parts of the disk, parts of it accretes onto the protostar and the rest is centrifugally ejected along open magnetic ﬁeld lines, carrying away angular momentum. Exactly how it accretes onto the surface of the protostar is currently unknown, one idea is that the circumstellar material at the innermost parts couples with the protostars magnetic ﬁeld, diverts out from the disk plane and falls on to the protostar through accretion columns creating hot continuum when crashing on the surface (Hartmann, 1998).

Infrared Visible

Disk Herbig-Haro objects

Jet

Protostar Bow shock

Figure 1.2: A protostellar outflow with the protostar and its disk, HH111 in the Orion molecular cloud. The outflow reach far out in the parental cloud. Names of different structures are marked with lines and text. Perpendicular to the outflow is the flared disk. Image credits NASA/B. Reipurth.

As mentioned, the in-fall of matter is accompanied by outflow of matter through bipolar jets perpendicular to the plane of the disk, usually along the rotation axis of the system. The jet removes excess angular momentum from the system, to understand the importance of this one should bare in mind the share difference in spatial scales between the parental cloud core and the finished MS star. The cloud core contract by a factor ∼106 in radius when a star is formed, thus the angular momentum has to be transported away during the collapse for the cloud to continue to contract. With a launching speed of a few hundred kilometres per second the jet transfer energy to the surrounding molecular gas, entrain material and accelerates it to tens of kilometres per second. Protostellar outflows can have sizes extending −2 to several parsecs and masses between 10 to 200 M . The interaction between the outflows and the ISM leads to the formation of supersonic shock fronts, the cooling regions are called Herbig-Haro objects (Herbig, 1951; Haro, 1952). The infalling material and the outflow are in close relationship, the infall drives the outflow and while most of the mass is expelled in the outflow some of it is accreted onto the protostar. The outflow–accretion connection was observed by Hartigan et al.(1995) by looking at the correlation between forbidden line luminosities with accretion luminosities derived from the optical or UV emission

6 1.1. STAR FORMATION in excess of photospheric radiation. When the star have accreted enough matter so that the protostar and the disk start to contribute signiﬁcantly to mid-IR wavelengths the object is referred to as having a Class I SED (Lada, 1987; Wilking et al., 1989). The timescale of the protostellar phase is relatively short, around 105-106 years.

CoKu Tau/1 DG Tau B Haro 6-5B

IRAS 04016+2610 IRAS 04248+2612 IRAS 04302+2247

Figure 1.3: Six protostars, they all show the outﬂow as a glowing cone with sharp edges, perpendicular to the outﬂow lies the disk and there, heavily enshrouded in gas an dust lies the infant star. Image credits D. Padgett (IPAC/Caltech), W. Brandner (IPAC), K.Stapelfeldt (JPL) and NASA.

Pre-Main Sequence

With time the outflow disperses the surrounding envelope that have not fallen onto the accretion disk. The central source can usually be observed in the optical at this time, the accretion and outflow continues although at a greatly diminished rate, most of the final mass has already been accreted. The protostar is left with a circumstellar disk, a protoplanetary disk. Low-mass stars in this stage are called T Tauri stars (T Tauri phase), the general type Classical T Tauri Stars (CTTS), and also the observable spectra is identified as a Class II SED; essentially a stellar spectrum with thermal dust emission from mid-IR to sub-mm wavelengths. Except the forementioned variablity, characteristic emission lines and association with nebulosity the CTTS usually exhibit strong Hα emission and IR-excess stemming from the hot and thermally radiating circumstellar disk. The pre-stellar core continues to contract, releasing gravitational energy. The relatively “calm” protoplanetary disk is likely to be in vertical hydrostatic equilibrium at all radii, Shakura and Sunyaev(1973) expressed the

7 CHAPTER 1. INTRODUCTION scaleheight, h of such a disk as

1/ H r 2 = cs . 1.1 r GM? § ¤ ¦ ¥ Showing that the scaleheight of the disk increases as a power law H ∝ rβ, i.e. a flared disk. This was observationally confirmed by Kenyon and Hartmann (1987), by modelling the SED of a flared disk and comparing it to observations. Dust grains in the disk grows through collisions and coagulation, which causes them to decouple from the gas and settle at the mid-plane of the disk (Beckwith and Sargent, 1991; Miyake and Nakagawa, 1993; D’Alessio et al., 1999, 2001). The higher density in the mid-plane increases collisions and causes the grains to grow into pebbles, and later into planetesimals which in turn are the beginning building blocks for either gaseous planets (the core of), if the gas is still present or rocky planets. The pre-MS star is still accreting material from the disk, the strong magne- tosphere carve out a hole in the disk, typically a few stellar radi out (Shu et al., 1994; Kenyon et al., 1996). The magnetic field lines, locked both in the star and the inner edge of the disk, are twisted due to the differential rotation between the two mount points. When the field lines reconnect causes X-ray flares e.g. Preibisch(2007). Matter is channelled away from the disk along the field lines and crashes on to the surface of the star (Shu et al., 1994). Crashing in to the hot surface of the pre-MS star causes hot spots with temperatures of 104 K. The UV excess and blue veiling observed in CTTS attributed to Balmer continuum and line emission along with Paschen continuum emanate from these hot spots (Kuhi, 1974; Kuan, 1975; Rydgren et al., 1976). Pre-MS stars that exhibit a variable mass loss rate between 100-1000 times greater than CTTS are called FU Orionis stars, explanations to the violent eruptions are still unknown but some suggests that the additional energy is produced when large planets are destroyed at the stellar surface or a sudden and temporary increase in the accretion rate triggered by thermal instabilities (Hartmann and Kenyon, 1985). When the dust has settled in the mid-plane of the disk, the gas in the disk can be removed through photo-ionization over timescales of 105 years. Haisch et al.(2001) concluded that most protoplanetary disks are likely to be cleared after 6 million years, and once cleared the star still shows stronger activity than MS stars. The accretion–outflow connection mentioned in the previous section also predicts that when no accretion occurs, the outflow should also be absent, this is furthered by the sub-group of weak-lined-TTS (WTTS) which lack both detectable forbidden line emission and excess emission. This does not necessary imply that the WTTS are in a later stage of evolution than the CTTS, the accretion may be absent owing to the natal environment of the star. Another sub-group is characterised by an almost dissipated disk and thus much weaker Hα emission lines, Naked T Tauri Star (NTTS) with a observable spectrum referred to as Class III SED. The T Tauri phase lasts a few million years and finally the density and temperature have increased enough in the central parts for nuclear burning to start and the star settles on the Main Sequence.

8 1.1. STAR FORMATION

1.1.4 Feedback processes The formation of stars starts with the fragmentation of an MC into smaller clumps and cores, but what keeps the star formation going in a cloud? Since molecular cloud cores are observed to not only house newly ignited main- sequence stars, but also stars in the making there must be something that triggers star formation over and over again. Several theories have been presented over the years, example triggers include outside forces such as super- novae, and mechanisms inside the cloud; outflows from young stars, the strong radiation field from high-mass stars. What is believed today is that the injection of turbulence in a cloud is important for the initiation and continuation of star formation since the turbulent compression can fragment clumps in the MC with high enough density for the collapse to start. In the beginning there is an initial supersonic turbulence in the cloud that decays quickly (Mac Low et al., 1998; Stone et al., 1998; Padoan and Nordlund, 1999). After this it is unclear what mechanism continues the injection of turbulence, but without turbulence the MC would be in complete free-fall collapse. As mentioned protostellar outflows is a probable mechanism and numerical MHD simulations by Li et al.(2006) showed that the initial turbulence helps to form the first stars and then protostellar, outflow-driven turbulence is the dominating turbulence for most of the cluster members. Contrary to this Banerjee et al. (2007) showed that the impact of collimated supersonic jets on MC is rather small and that protostellar outflows can not be the cause for continued star formation. Brunt et al.(2009) investigated on what physical scales the turbulent energy is injected in. Comparing simulated molecular spectral line observations of numerical MHD models and corresponding observations of real MCs showed that only models driven at large scales, with a minimum size corresponding to size of the cloud, are consistent with observations. Candidates on large scales are supernova-driven turbulence, magneto-rotational instability and spiral shock forcing. Small-scale driving mechanisms, such as outflows are also important, but on limited scales and they can not replicate the observed large-scale velocity fluctuations in the MCs. One aspect of the results is that the turbulence in the model was driven by random forcing which will not represent energy injection by point-like sources very well. Although the importance of protostellar outflows in injecting turbulence to the cloud is controversial they do inject large amounts of energy into the parental cloud and limit the amount of mass a star can accrete from a cloud.

1.1.5 The Main-Sequence When igniting the nuclear burning core and settling on the MS the accretion has stopped and the disk has been replaced by a debris disk, dust produced by collision between comets, asteroids etc and the gas is more or less gone. This debris disk produces small but detectable IR excess as well, and the ﬁrst MS star observed to have this was the standard star Vega (Aumann et al., 1984). Later on, Vega was shown to have a dust disk, and the most observed debris disk is the one of β Pictoris, a intermediate mass star. Olofsson et al.(2001); Brandeker et al.(2004) showed that β Pictoris also have a gas disk in addition to the debris disk. Even our own star, the Sun show evidence of this subtle

9 CHAPTER 1. INTRODUCTION disk-remnant in the form of the zodiacal light.

The structured walk-through of the early evolution of a low-mass star entailed above, including its circumstellar components, is our earnest endeavour at struc- turing the continuous nature of the star formation process.

1.1.6 HL Tau and XZ Tau as part of Lynds 1551 in Taurus In the northeastern region of the Taurus-Auriga Molecular Cloud lies XZ Tau and HL Tau, two YSOs at a rough distance of 140 pc e.g. Elias(1978); Kenyon et al.(1994); Torres et al.(2009). XZ Tau, a binary system composed of a T Tauri star and a cool companion (total mass 0.95 M , Hioki et al.(2009)). HL Tau, just a bit west of XZ Tau (∼2500) is a heavily embedded protostar with a rather massive envelope and powerful jet (∼120 km s−1 both jet and counterjet Anglada et al.(2007)), the inclination of the jet is ∼60◦ with respect to the plane of the sky (Anglada et al., 2007). In the ﬁgure below a S [II] image taken with the NOT of the region is shown; dust enshrouded HL/XZ Tau and the edge on HH 30 YSO with its long northern jet that almost spans the entire ﬁeld.

XZ Tau HL Tau

1' (8400 AU)

HH 30

Figure 1.4: The norhtern region of the L1551 cloud, containing HL Tau and XZ Tau along with the HH 30 YSO. The jet from HL Tau reaches speeds of 120 km s−1 and has an inclination of aout 60◦ with respect to the plane of the sky. From Anglada et al.(2007)

HL Tau Cohen(1983) proposed that HL Tau is associated with a nearly edge-on circumstellar disk, after this several attempts at imaging this disk were carried

10 1.2. POLARIMETRY out (Sargent and Beckwith, 1991; Wilner et al., 1996; Looney et al., 2000). It has been the proposed source for a molecular outflow e.g. Torrelles et al.(1987); Monin et al.(1996). As being the brightest nearby T Tauri star in the mm and sub-mm continuum it is estimated to have one of the most massive circumstellar envelopes (Beckwith et al., 1990). A infalling or rotating circumstellar envelope has been suggested by mm synthesis observations (Sargent and Beck- with, 1991; Hayashi et al., 1993), although Cabrit et al.(1996) showed that the kinematics are complicated by the orientation of the outflow in respect to the observer. The envelope has a estimated mass of ∼0.1 M which gives it enough material to form a planetary system (Sargent, 1989; Beckwith et al., 1990). It has a well studied collimated optical bipolar jet (Mundt et al., 1990; Rodriguez et al., 1994; Anglada et al., 2007). It has been observed to harbour a 14 MJ protoplanet orbiting at a radius of ∼65 AU (Greaves et al., 2008). HL Tau has been classified as beeing in the boundary inbetween Class I and Class II YSOs, having a relatively flat spectrum inbetween 2 and 60 µm (Men’shchikov et al., 1999). Thus it still has its large circumstellar envelope, but the extinction has dropped enough for the central regions to be observed in the NIR with high resolution.

XZ Tau Located ∼2500 to the east of HL Tau is XZ Tau, a binary system; a T Tauri star accompanied by a cool companion with separation of 000. 3 (Haas et al., 1990). Just as HL Tau, XZ Tau is the source of a optical outﬂow e.g. Mundt et al. (1990). Krist et al.(1999) used the Hubble Space Telescope (HST) to take an image sequence of XZ Tau that revealed the expansion of nebular emission, moving away with a velocity of ∼70 km s−1. Being very diﬀerent from the collimated jets usually seen around young stars, further studies by Krist et al.(2008) showed a succession of bubbles and a fainter counterbubble, and also revealing that in addition both components of the binary are driving collimated jets. High angular resolution radio observations of XZ Tau by Carrasco-González et al.(2009) show signs of a third component, that XZ Tau in fact could be a triple system. At the wavelength of 7 mm the southern component is resolved into a binary with 000. 09 (13 AU) separation.

1.2 Polarimetry

This section describes polarized light in the astronomical context; the history of polarimetry, the theory that lies behind the technique used in the observations, and how the linearly polarized light is produced in young stars.

1.2.1 Background

Introduction 2In the last decade or two polarimetry have matured to become a important tool in an astronomers arsenal. Other than the most evolved techniques in the

2Most of the section taken from T. Gehrels(1974) and Tinbergen(1996)

11 CHAPTER 1. INTRODUCTION optical, near-infrared and radio regimes, other wavelength regimes are catch- ing up rapidly. The history of polarimetry starts with the discovery of double refraction in calcite (Iceland spar) by Erasmus Bartholinus in 1669, and an attempt to describe it by Huygens a year later in terms of a spherical and elliptical wave front. Two years later, 1672 Newton drew parallels of light and the crystal to poles of a magnet, which leads to the term “polarization”. In 1845 Michael Faraday discovered the rotation of the plane of linearly polarized light passing through certain media parallel to the magnetic field, today known as Faraday rotation. Then, 1852 Stokes studies of polarized light led him to describe the four Stokes parameters (G.C. Stokes, 1852). The first astronomical use of polarimetry, done by Lyot of the sunlight scattered by Venus in 1923 marks the start of polarization in astronomy. In 1946 Chandrasekhar predicts linear polarization of Thomson-scattered starlight (Chandrasekhar, 1946), later discovered in eclipsing binaries. A lot of new discoveries and applications of polarimetry is presented in the later half of the 2000-century, a few of the important ones are the observation of interstellar optical polarization, first detection of polarized astronomical radio emission, polarized X-ray and radio emission (from the Crab nebula) and the list goes on.

Describing light

y' y

z A sinβ x'

φ β 0

Figure 1.5: A polarization ellipse, from this ﬁgure the Stokes parameters are deﬁned.

One way of representing (partly) polarized light is by means of the Stokes parameters, as mentioned above introduced by Sir George Gabriel Stokes in 1852. The four parameters, often denoted I, Q, U, V and components in a four-vector S, describe an incoherent superposition of polarized light waves, i.e. no information about absolute phase of the waves. The Stokes I is non-negative and denotes the total intensity of the wave. Q and U relates to the orientation of the polarized light relative to the x-axis, Q = U = 0,V 6= 0 is completely circular polarized light. Lastly V describes the circularity, it measures the axial ratio of the ellipse, it can be positive or negative, and when V = 0 the light is linearly polarized. All of the parameters denote radiant energy per unit time, unit fre-

12 1.2. POLARIMETRY quency interval and unit area. With help of ﬁgure 1.5 the Stokes parameters are deﬁned in terms of properties of the polarization ellipse. Where A is the amplitude of the wave, β the angle relating the two principal axes of the ellipse, ϕ0 the polarization angle and z is the direction of propagation. π When β = 0, ± 2 the wave is linearly polarized (V = 0). The mathematical realtionship between the parameters are

 I   A2  2  Q   A cos 2β cos 2ϕ0  S =   =  2  1.2  U   A cos 2β sin 2ϕ0  § ¤ 2 V A sin 2β ¦ ¥

Here the set of parameters are set up in a vector, the Stokes vector. To 2 understand the relation between Q, U and A , 2ϕ0 we can think of Q and U as 2 Cartesian components of the vector (A , 2ϕ0). The polarization angle PLthen becomes a simple function of Q, U and I as we shall later discover.

1.2.2 Polarization in Astronomy

Polarimetry can reveal information about objects in astronomy inaccessible to ordinary observational techniques. Some sources emit polarized radiation, such as synchrotron radiation from relativistic electrons under influence of a strong magnetic field. Two other relevant sources of polarization are scattering and extinction; scattering of light and dichroic extinction by dust. Here the effect is due to the interaction of unpolarized radiation with dust. The general theory for scattering of particles is called “Mie scattering”, it account for the size, shape, refractive index and absorptivity of the scattering particles; a well known special case of Mie scattering is Rayleigh scattering. When light is scattered off a dust particle, the scattered light is polarized in all directions except the forward direction (Bohren and Huffman, 1998). Mie theory, as it also is referred to uses Mueller 4 × 4 matrices to change the incident Stokes vector, the completeness of the calculations makes it a prime method for modelling polarized radiation from protostars. To visualise and explain the scattering process, figure 1.6 emphasis the schematics. The unpolarized light is incident from the left, its perpendicular E¯ component sets the electronic oscillators in a dust particle in similar forced vibrations, thus re-emitting radiation, in all directions. Any light scattered into a certain direction can only include those identical E¯-vibrations by the oscillators along the y- and z-directions. An observer at A in the figure will only see polarized light corresponding to vibrations along the z-direction, an oscillator vibrating in the y-direction can not radiate in the direction of vibration (Ry- bicki, 2004). At B the light would be partially polarized. Putting it all in one sentence; the direction of vibration of the electric vector of the scattered radiation is at right angles to the scattering plane, the plane containing the incident and scattered rays (Tinbergen, 1996). As mentioned, the forward scattered light shows the same polarization as the incident light.

13 CHAPTER 1. INTRODUCTION

A B

Figure 1.6: Scattering of light by dust particle, geometry. The scattered radiation attain maximum polarization at right angles to the incident radiation (inspired from Pedrotti and Pedrotti, 1992,, p. 305).

Analysing linear polarization gives possibilities to

• identify the scattering mechanism

• locate an obscured source

• attain information on the properties of the source, i.e. orientation and/or the scattering medium i.e. size, shape, alignment e.t.c.

Circular polarization is known to occur due to single scattering of linearly polarized light by a non-spherical grain.

Dichroic extinction An exception to the statement that light in the forward direction is not polarized is when we account for dichroic extinction; the diﬀerential extinction of orthogonally polarized radiation components. This is simply due to the fact that the dust particles are non-spherical and/or have crystalline structure which results in a diﬀerent scattering cross-section for light linearly polarized parallel to the geometric or crystalline axis than for light polarized perpendicular to it. Adding a mechanism that aligns the dust grains an overall systematic polarization is attained. This is common in protostars when viewing the central source through the very optically thick disk, although multiple scattering can interfere with the pattern.

Grain alignment The mechanism that align grains has long been debated since its discovery in 1949 (Hall, 1949; Hiltner, 1949). Today several ideas exists as to how the grains are aligned, the most prominent are paramagnetic alignment, mechanical

14 1.2. POLARIMETRY alignment and radiative torque alignment. They are all thought to be important within different limits (Lazarian, 2007). As the names suggests, in paramagnetic alignment the change of grain magnetization due to free electrons in relation to the external magnetic field causes it to loose rotation energy, this is called the Davis-Greenstein mechanism after Davis and Greenstein(1951). The grain align with the longer axes perpendicular to the magnetic field. The second mechanism referred to as the Gold mechanism after Gold(1952), mechanical alignment, is caused by bombardment of the non-spherical grains by atoms, thus transfering momentum and forcing an alignment of the grains. The last mechanism, radiative torque works by aligning the grains with the radiative pressure of starlight. On AU scales (100-104 AU), and grain sizes 0.02 to 0.5 µm radiative torque align the grain with the longer axes perpendicular to the photon flux (Lazarian, 2007).

Young Stellar Objects in polarization With their dense circumstellar envelope together with outflows and a emerging radiation field YSOs exhibit strong polarization due to scattering and extinction, both linear and circular polarization. This polarization has been shown to be wavelength dependent, in the core region it seems as the polarization get higher with shorter wavelength, possibly attributed to the importance of dichroic extinction or the fact that the core region is unresolved (Beckford et al., 2008; Lucas and Roche, 1998). The maximum polarization in HL Tau have a dependence on wavelength that is opposite that of the core polarization, reflecting the increasing importance of multiple scattering to rising albedo (Lucas and Roche, 1997; Beckford et al., 2008). Non-spherical dust grains align in the protostellar environment so that they precesses around the axis of the local magnetic field with their axis of greatest rotational inertia. These magnetically aligned grains produce a much broader region of aligned polarization vectors than the classic polarization pattern of centrosymmetric vectors. As discussed the alignment mechanism may not be a magnetic field, so finding out the alignment mechanism is important for unlocking the structure of YSOs.

1.2.3 Detecting linearly polarized light Introduction To describe the intensity measured by a detector behind a linear polarizer of some sort (i.e. analyser), one usually deﬁnes an angle, ϕ between a line towards the north celestial pole and the analyser, measured counter-clockwise and also the degree of linear polarization PLalong with the angle of polarization ϕ0. Let us also deﬁne the transmittance of two identical analysers oriented parallel, Tk and the transmittance of two perpendicularly oriented analysers, T⊥. The intensity then reads (Serkowski, 1974, p.364)

1 1 /2 /2 0 Tl + Tr Tl − Tr I (ϕ) = I + IPL cos 2(ϕ − ϕ0). 1.3 2 2 § ¤ To understand the equation we consider light with intensity I falling on to a¦ in-¥ p strument consisting of an analyser and a detector. The ﬁrst term, I 0.5(Tl + Tr) tells us how much of the intensity that is transmitted in average over one turn

15 CHAPTER 1. INTRODUCTION

p of the analyser. The next term, 0.5(Tl − Tr)IPL cos 2(ϕ − ϕ0) accounts for the intensity of linearly polarized light at a speciﬁc orientation of the analyser. 1 For an ideal analyser Tk = /2 and T⊥ = 0, i.e. half of incident unpolarized light comes through, and the light after the analyser is 100% polarized. Replacing 1 I /2 with I0 as a measure of the average intensity that is let through along one turn of the analyser we have the equation

0 I (ϕ) = I0 (1 + PL cos 2(ϕ − ϕ0)) . 1.4 § ¤ Here we see that if the degree of linear polarization is 100%, i.e. PL = 1,¦ the¥ minimum intensity will be zero, since all the light is polarized and when the analyser is perpendicular to the polarization angle, no light will be transmitted. On the other hand if some light is not linearly polarized, which is usually the case the minimum intensity will be I0(1 − PL) If the analyser is oriented parallel to the polarization angle (ϕ = ϕ0) a maximum occurs, and in addition to the unpolarized part that is let through, I0PL is added to the detected intensity. Moreover the intensity with the analyser ◦ oriented perpendicular to the polarization angle (ϕ − ϕ0 = 90 ) harbours a minimum in the detected intensity, since then the polarized component would not pass. This fact is represented with a factor of two in the argument of the cosine statement, when the analyser has turned 360◦ it has recorded two maxima, with a 180◦ interval. Now, how do we determine these parameters; mean intensity I0, degree of linear polarization PLand and polarization angle ϕ0 from observations?

Determining the unkown Observing the intensity at angles 0◦, 45◦, 90◦ and 135◦ the system of equations becomes over-determined, three unknown and four equations. The intensity at the formentioned angles put into equation 1.4 then becomes with some simple trigonometric relations

0 ◦ I (0 ) = I0 (1 + PL cos 2ϕ0) 1.5 § ¤ 0 ◦ π I (45 ) = I0 1 + PL cos − 2ϕ0 = I0 (1 + PL sin 2ϕ0) ¦1.6 ¥ 2 § ¤ 0 ◦ I (90 ) = I0 (1 + PL cos (π − 2ϕ0)) = I0 (1 − PL cos 2ϕ0) ¦1.7 ¥ § ¤ 0 ◦ 3π I (135 ) = I0 1 + PL cos − 2ϕ0 = I0 (1 − PL sin 2ϕ0) ¦1.8 ¥ 2 § ¤ Here we have four equations and three unknown. We then form the diﬀerences¦ of¥ pairs in which the analyser is perpendicularly oriented in respect to one another, thus surpressing the unpolarized intensity that passes through the analyser with the same intensity.

S1 = I0(0◦) − I0(90◦) 1.9 § ¤ S2 = I0(45◦) − I0(135◦) 1.10 §¦ ¤¥ and also the mean intensity over all angles. ¦ ¥ (I0(0◦) + I0(90◦) + I0(45◦) + I0(135◦)) S0 = 1.11 4 § ¤ ¦ ¥ 16 1.3. DIFFRACTION LIMITED IMAGING FROM THE GROUND

These gives

0 0 S1 = I (0) − I (90) = 2I0PL cos 2ϕ0 0 0 S2 = I (45) − I (135) = 2I0PL sin 2ϕ0 (I0(0) + I0(90) + I0(45) + I0(135)) S0 = = I 4 0

2 2 S2 To solve the system further, we calculate S1 + S2 and /S1 .

2 2 2 2 S1 + S2 = 4I0 PL r 1 S12 + S22 → PL = 1.12 2 S02 § ¤ S2 sin 2ϕ0 ¦ ¥ = = tan 2ϕ0 S1 cos 2ϕ0 1 S2 → ϕ0 = arctan 1.13 2 S1 § ¤ ¦ ¥ These relations are what is used in the routines when analysing the reduced data, since what is observed is the intensity in each position of the analyser. The Stokes parameters are related to S0, S1 and S2 as

I = 2S0 Q = S1 U = S2 thus concluding the ﬁnal following relations already mentioned in the deﬁnitions of the Stokes parameters (Serkowski, 1974, p.363).

pQ2 + U 2 PL = 1.14 I § ¤ 1 U ¦ ¥ ϕ0 = arctan 1.15 2 Q § ¤ ¦ ¥ In the previous discussion the important equations are 1.9, 1.10, 1.11, 1.12 and 1.13 which are all used in the data reduction and analysis. The degree of polarization consists of the polarized flux divided by the total flux, so we can also define

p 2 2 IL = S1 + S2 1.16 § ¤ as the polarized ﬂux. ¦ ¥

1.3 Diﬀraction limited imaging from the ground

1.3.1 Introduction Shortly after Galileo turned his telescope towards the night sky he described how the objects in the telescope seemed to flicker (Galilei, 1610). He was first to describe the effects of turbulence on astronomical observations. The turbulent

17 CHAPTER 1. INTRODUCTION energy is injected at large scales by wind shear. Taking many short exposure images of a point source shows how the they change in both shape and position during the observation, see figure below. Thus the usual long integration times in imaging that seeks to increase the signal-to-noise causes images to be a sum of all these fluctuations; blurred. The image fluctuations have their origin in continuous changes of the turbulence structure above the telescope. Essentially the shape of the point source (point spread function, PSF) is very variable, it moves around and distorts on small timescales. Short exposure images take the form of speckle patterns, multiple distorted and overlayed copies of the PSF that the telescope would have if there were no atmosphere disturbing the image, i.e. short exposure images retain information about the diffraction limited PSF.

Figure 1.7: An example set of V-band 45◦ analyser angle PolCor raw images from the observation run at the NOT. The frames are sequential 100 ms exposures (framerate 10 Hz), time increases from left-to-right and up-to-down. The resolution is 000. 12/pixel. The image motion and speckle patterns are clearly seen.

Long exposure images are highly blurred, and the diffraction limited PSF for a 2.5m telescope is normally 5-15 times sharper than the summed long exposure atmospherically effected PSF. The size of a diffraction limited aperture which has the same resolution as an infinite seeing-limited aperture, r0 is the general characteristic quantity that describes the total atmospheric turbulence strength. Deduced by Tatarski(1961) from studies by Kolmogorov the atmospheric turbulence is commonly modelled using a Kolmogorov power spectrum. Although supported by experimental mea- surments (e.g. Colavita et al., 1987; Buscher et al., 1995) some studies have found deviations from Kolmogorov statistics (e.g. di Folco et al., 2003). The effect of the quantity r0 on imaging is that a telescope with an aperture much smaller than it will be diffraction limited in its imaging. Telescopes much

18 1.3. DIFFRACTION LIMITED IMAGING FROM THE GROUND

larger than r0 will be turbulence limited, Fried(1966) expressed the seeing disk size at a wavelength λ as λ = 0.98 . r0 00 At the best sites, r0<50 cm and the seeing FWHM∼0. 5 while the theoretical diffraction limit of a 2.5 m telescope is ∼000. 05 (not accounting for any obstructing secondary mirror). How short does the exposures have to be for lucky imaging to work? Well there are two timesscales of atmospheric turbulence, first the seeing it self changes on a wide range of timescales. Secondly the short exposure timescale, τ0 gives the scale over which high resolution imaging systems must be able to correct incoming turbulence errors. τ0 has been measured by several researchers, e.g. Dainty et al.(1981); Roddier et al.(1990); Vernin and Munoz-Tunon(1994) and result in values on the order of a few milliseconds or tenth of milliseconds. The fluctuations are very local, observing one patch and correcting for turbulence does not mean that another patch separated with an angle will have the same distortions. This largest angular distance at which the corrections are still valid is called isoplanic angle.

1.3.2 Correction methods There are several correction methods, the most successful ones being lucky imaging, adaptive optics (wavefront correction), tip/tilt correction, speckle interferometry and interferometry. Lucky imaging relies on the fact that among the rapid turbulent fluctuations of the atmosphere, moments (tens of milliseconds) of stable air appear. Thus imaging at a high frame rate that is comparable to τ0 allows the observer follow these variations and select those images when the seeing is much better than the average. The flaw is that the observational efficiency is decreasing because one is only integrating during periods of better seeing. Adaptive optics (AO) systems senses the distortion of the wavefront imposed by the turbulent layers above the telescope and actively corrects it in realtime before it reach the detector. Either the shape of a nearby guide star is tracked, or an artificial laser guide star (LSG) that relies on downwards Rayleigh scattering or on the excitation of the high altitude sodium layer of the atmosphere. The corrections are made by a deformable mirror in the light path and these systems are common in the near-IR. Tip/tilt correction corrects for the motion of the centroid over the course of observation, it uses an simple tip/tilt mirror in the light path to account for the motion. Usually tip/tilt sensors are integrated in AO systems. Speckle interferometry was first suggested by Labeyrie(1970) and relies on that the final image I(x, y) is the convolution of the object function O(x, y) (objects brightness distribution) with the speckle image of a point object P (x, y) (the atmospheric PSF).

I(x, y) = O(x, y) ∗ P (x, y)

As mentioned, since the speckle pattern contains information at the diﬀraction limit of the telescope. When the speckle patterns are relative simple, as in imaging binary stars, it can be a very useful technique (e.g. Horch et al., 2002).

19 CHAPTER 1. INTRODUCTION

In interferometry the incoming wavefront is combined from diﬀerent telescopes producing a set of fringes from which the target objects brightness distribution can be calculated. In the radio regime, interferometric observations are carried out routinely. In the near-IR both the Keck Interferometer and VLTI interferometers are available to observers.

The work in this thesis uses data from the PolCor instrument (described below) that uses the lucky imaging technique to obtain images, but with the correct settings the data can be analysed as speckle interferometry.

20 “In God we trust, all others must have data.” C.R Reynolds, 1981 2 Observations and Data reduction

2.1 Observations

2.1.1 The PolCor instrument

Overview The PolCor instrument is a combined lucky imager, polarimeter and corona- graph built for the Nordic Optical Telescope (NOT) by Göran Olofsson and Hans-Gustav Florén at Stockholm University. The PolCor system is compact and light (∼ 50 kg), during the observations for this thesis it was mounted in the cassegrain focus of the NOT. The main idea of the instrument is rotating a polarizer rapidly into five positions, 0◦, 45◦, 90◦, 135◦, and “dark”. At each position the fast Andor IXon EMCCD camera takes many short exposures, typically 30 or more during one second and position. Doing this repeatedly during one observation averages atmospheric variations. The data is stored on disk and reduced afterwards. By simply shifting and adding images one can gain factor of two in sharpness, more so if also applying a frame selection criteria (lucky imaging). The polarizing element, the analyser, is a high-quality polarizer which is designed for the 410 − 750 nm region. To detect circumstellar structures PolCor has a set of coronagraphic masks. Except for the filter and the cryostat window the optics in the instrument is all-mirror design, and with good margin diffraction limited. The reflectivity of the four mirrors in the light path is 99.5% each, resulting in only 2% losses over the sensitivity range of the detector. With a 1:1 imaging of the relay optics the pixel scale at the NOT is 000. 12 per pixel. For speckle interferometry there are two barlow lenses with two and three times magnification available. To mask the secondary mirror support blades and minimise the extent of diffraction stripes, PolCor is equiped with a computer controlled Lyot stop. Also the mask is slightly undersized to block the diffraction rings caused by the coronagraphic disks, this blocking suppresses the point spread function wings by 1-2 order of magnitude. The standard filters for PolCor are Bessel U, B, V, R and I filters, in addition narrow-band filters in the 0.3 − 0.5 nm region exists. Two filters are fitted in the filter holder and the active filter is choosen in the observation software during operation. For coronagraphy there is a choice of three sizes of coronagraphic disks with diameters of 100. 5, 300 and 600. Each size with three different optical densities; 5,

21 CHAPTER 2. OBSERVATIONS AND DATA REDUCTION

8.75 and 12.5 magnitudes. Not using totally opaque disks allow for centring of the star. Usually the observer is limited by the atmospheric conditions at the site of observation. By applying the lucky exposure technique, PolCor can overcome many of the troubles with having an turbulent atmosphere between the observer and object, even attain near diffraction limited imaging. During a long exposure the atmosphere effects the light on its way down to the detector; moving around and getting blurred. Since taking a longer exposure becomes the sum of all the shifted images the source is not point-like any longer, but a Gaussian. Correcting for this image motion by taking short exposures and shifting and adding images typically improves seeing from 000. 7 to 000. 4, if using frame selection the resolution will improve to 000. 2-000. 3. The specifics of lucky imaging is covered in section 1.3.

The detector The Electron Multiplying CCD camera (EMCCD), Andor iXon+ 897 uses a thinned back-illuminated 512 × 512 CCD array with 15 µm pixels and the chip is cooled to -90◦ C by a thermo-electric cooler. The camera have two modes of operation, classic and electron multiplying (EM). Classic mode has a read-out noise of 6 e− rms and the EM mode has a on-chip gain up to 1000 which is particularly useful for low light levels. The camera has also a very fast readout time, fastest full-frame readout rate is 33 Hz, and even higher when deﬁning a sub-image area on the chip. With a suﬃciently high time resolution, speckle interferometry is possible.

Figure 2.1: The Andor iXon+ 897 QE versus wavelength graph. As seen the QE in the V and R band region is high. From http://www.andor.com/scientiﬁc_cameras/ixon/models/.

The detector utilises a frame transfer CCD structure, in this structure there are two areas on the chip, one sensor area where the photons are captured and one storage area. After being captured the image is transfered to the storage area - usually identical in size to the capture area but covered with an totally opaque mask. While the sensor area continues the imaging, the image in the

22 2.1. OBSERVATIONS storage area is transfered to the readout register and onwards to the multiplica- tion register where the data is amplified. To understand how the amplification occurs one must understand clock-induced charge (CIC) - normally considered a source of noise in imaging. In the process of moving the charges through the register there is a very tiny probability that the charges being clocked creates additional charges by impact ionization. When a charge has enough energy to induce an electron-hole pair and add a electron to the conduction band one speaks of impact ionization. This is how the amplification occurs, and as sus- pected this probability gets higher the more energy the electron has. So by clocking with a higher charge the amplification gets higher, also the probability increases with lower temperatures hence cooling the chip increases the amplification. The probability of amplification within any one cell is very low but taken over the whole register the amplification is very high and gains of up to thousands can be achieved. This amplification allows for single detections, photons to be amplified over the "noise-floor" and thus photon counting is possible with the right intrument design. In the table below the main characteristics of the detector is shown.

Manufacturer Andor Technologies Model EM+ DU-897 CCD Type Back-illuminated EM-CCD Pixel size 16 µm Active pixels 512 × 512 Image area 8.2 × 8.2 mm Pixel well 160 000 e− (max: 220 000 ) Max readout rate 10 MHz Plate scale @ NOT 000. 12 per pxl Read noise <1 to 49 e− @ 10 MHz (typical)

206265µ Table 2.1: CCD detector characteristics. The ﬁeld of view is calculated as Ω = /1000f where µ is the pixel size of the CCD and f the focal length of the primary mirror in mm (28160 mm for NOT).

The software stores the raw-data from the detector in the FITS-format on an external hard-drive connected to the instrument computer. Also an accumulated image for each of the analyser positions is stored in a C-binary format.

A walk through PolCor The instrument layout can be seen in figure 2.2. In the figure the numbers 1 to 9 marks the important parts of the relaying optics, masks, polarizer e.t.c. From the right (1) the telescope f/11 rays enters the instrument, (2) marks the placement of the analyser. The analyser, a high quality polarizer optimized for the operational wavelength, is during polarimetry mode turned rapidly to the 5 positions (0◦, 45◦, 90◦, 135◦ and dark). A classical imaging mode is possible, just by pulling away the analyser from the light path in the handle above it. In (3) the focusing mechanics resides and after this, in the image plane the coronagraphic masks sits on a wheel (4). After being collimated (5), the rays are parallel and passes the filter wheel (6), where two different filters are loaded. Directly after the filter wheel sits the computer controlled Lyot stop (7) to mask

23 CHAPTER 2. OBSERVATIONS AND DATA REDUCTION diﬀraction stripes from the secondary mirror support blades, it turns with the same angular speed as the NOT ﬁeld rotator but in opposite direction. The the light is focused to an image through (8) and (9) down to the EMCCD camera.

Figure 2.2: The PolCor instrument, it has a very light and compact design. The red lines follow the light through the instrument. The light enters from the telescope (1) and passes through the analyser (2), letting through light of the selected polarization angle. The light passes the focusing mechanics (3) to the mask selection wheel (4), hits the first mirror and the collimator (5) so the rays are parallel when going through the filter (6) and the spider mask Lyot stop. After this it is deflected (8 and 9) to the camera below in the image. Image by Hans-Gustav Florén.

2.1.2 Observations The complete observation run was from the 25th to the 31th October 2008, due to sever weather only one successful night of observations were carried out,

24 2.1. OBSERVATIONS between the 27th and 28th. On the dusk and dawn of the observation run clouds, gusts of wind and rain put and end to the hopes of ﬂat-ﬁelds. So the data is reduced and analysed without accounting for uneven sensitivity of the CCD.

Atmospheric conditions Lucky imaging is something that is supposed to improve image quality towards the diﬀraction limitation of the telescope. The appalling weather conditions during the observation run limited the number of observable nights. The seeing was on average around 100. -100. 5 when observations could be made.

40 6.0

35 5.5

5.0 30

4.5 25 Storm 4.0 20 3.5

15 Temperature (C) Wind Speed (m/s) 3.0

10 2.5

5 2.0

0 1.5

18:0019:0020:0021:0022:0023:0000:0001:0002:0003:0004:0005:0006:0007:0008:00 18:0019:0020:0021:0022:0023:0000:0001:0002:0003:0004:0005:0006:0007:0008:00

100 774.0

773.5 80

773.0

60 772.5

Humidity (\%) 40 Pressure (mbar) 772.0

Approx. typical pressure 771.5 20

771.0

18:0019:0020:0021:0022:0023:0000:0001:0002:0003:0004:0005:0006:0007:0008:00 18:0019:0020:0021:0022:0023:0000:0001:0002:0003:0004:0005:0006:0007:0008:00

Figure 2.3: Atmospheric conditions during the observation run 27th to 28th October. In comparison to the other nights of the week, this was the only one with weather good enough to make any observations at all. The “approximate typical pressure” is for the season, it varies rather greatly over the year. During the acquisition of the HL/XZ Tau data, at 04:00-05:00 clouds started to build up around the mountain.

25 CHAPTER 2. OBSERVATIONS AND DATA REDUCTION (135) I with “Cal” inobjects, the “Corrupt” comments are meansway calibration that but objects, the for calibration raw “Sci”and data data science “G” the was followed accumulated by image corruptstandard. a was in number still is some useful the gain settings if other than the observation was corrupt even in the accumulated image, therefore modiﬁed formulas to retrieve (135) I 108 15:36:21.1642 +63:54:00.362 20:35 V 0.1 30-10 Cal ◦ HD 236633 BD 64 01:09:12.3410HL+XZ Tau +60:37:40.937HL+XZ Tau 04:31:39.250 20:2804:31:39.250 +18:13:57.450 V +18:13:57.450 04:23 05:01 V R 0.1 0.1 30-10 0.1 Cal, G:3200 30-100 Sci 30-77 Sci HD 198478 HD 198478 20:48:56.2909HD 204827 20:48:56.2909 +46:06:50.88421:28:57.7610 +46:06:50.884 20:14 +58:44:23.238 R V 3 V Cal, Corrupt Cal, Corrupt Cal, Corrupt, even acc. Object RA DEC UT Filter Integration Mode Comments Observation log In the following tableobject, the right observation log ascension,(seconds), is exposure show, declination, mode the ﬁlter and columns additional band, are comments. integration In the time objects Table 2.2:catalogue, Observational BD log, - thethe Bonner “Mode” polarization Durchmusterung. angle column The e.t.c V-band reads had HD as to 204827 be exposure used time for – the algebra cycles see so Appendix 30-100 1 (A1 is on 30 page second). 69 exposures and 100 cycles. Catalogues: HD - Henry Draper

26 2.2. DATA REDUCTION

2.2 Data reduction

The raw data from PolCor comes in 6 different types, the darks, flat-fields and then the 4 different polarization positions (0◦, 45◦, 90◦ and 135◦). The existing routines to reduce and analyse PolCor data was written by Göran Olofsson in IDL12 . The expensive licsenses, avaliability i.e. running scripts on local server e.t.c. led to the suggestion to write the routines in Python3, and also add some routines to the reduction steps to ascertain what different information can be extracted from this kind of data.

2.2.1 Overview In the following list the basic reduction steps will be outlined and later explained in detail. 1. Calculate the average darkframe of every cycle and and average dark of all exposures. 2. Calculate the median flat field for each cycle. 3. Determine where the guide star and background field is, by means of point-and-click. 4. Cut out a square around the guide star and background field from every frame. 5. Calculate the moments of every guide star frame. 6. Determine where the strongest speckle is in every guide star frame. 7. Calculate the median position of the star, set this as the reference position of the guide star and calculate the pixel-level deviation of every frame from this median, calculate for both the moments and strongest speckle centres. 8. Calculate the sharpness in each frame centred around the coordinates of the moments. 9. Let the user choose an (or several) acceptance sharpness with the aid of a histogram of the sharpness in all frames. 10. Shift and add the frames with the given pixel-offset. 11. Repeat from9 with the strongest speckle as method of determining the star position instead. 12. All steps from step3 is repeated for all polarization angles. After this the final reduction steps of the four polarization angles are 1. The guide star’s position is read in and a two dimensional gaussian is fitted to each frame at the star’s position.

1Interactive Data Language by ITT http://www.ittvis.com/ProductServices/IDL.aspx 2Actually H-G. Florén and R. Nilsson of the Stockholm University Astronomy department have their own reduction routines as well 3http://www.python.org/

27 CHAPTER 2. OBSERVATIONS AND DATA REDUCTION

2. The 0◦ polarization image is used as reference and all the other angles are shifted with sub-pixel precision to match it.

3. Then S0, S1, S2, polarized ﬂux, polarization degree and polarization angle are all calculated.

2.2.2 Dark frame and ﬂat ﬁelding

The number of dark frames are the same as the number of frames in a polarization position i.e the number of cycles times the number of exposures. A typical dark frame is seen in ﬁgure 2.4 together with a histogram of the pixel distribution. The master dark for each cycle is calculated as the mean of all the exposures in the cycle. Also an average master dark is calculated from all frames in all cycles. The pixel distribution in ﬁgure 2.4 peaks around 92, the overall shape of the distribution is that of a skew gaussian, with a longer tail towards higher values.

500 6000 108

400 104 5000

100 4000 300

96 3000

200 92

2000 88

100 84 1000

80 0 0 0 100 200 300 400 500 85 90 95 100 105

Figure 2.4: Left: V-band typical dark frame, averaged over one cycle (i.e. 30 frames averaged). A small gradient exists in the left of the image, this could be due to that when read out the pixel rows last in line can be exposed to dark current longer. It could also be uneven response of the CCD which could be corrected for by taking ﬂat ﬁelds. Right: Pixel ditribution (histogram) over dark values. Typical gaussian distribution with tail towards high values of the random noise in the dark current.

Because of the weather conditions during dusk and dawn, flat fields were never taken. Although the flat is calculated from the median of several exposures taken at an evenly illuminated surface. Each filter has its own flat field, and since the flat field measures uneven response of the CCD it is normalised and applied by dividing the science frame (and dark) with the normalised flat field so that pixels with lower response will be compensated.

2.2.3 Determining the centre of reference object

Different methods can be used to determine the centre of a point-source. The two methods used in this thesis are loosely referred to as moment of flux and maximum speckle. Determining the centre by calculating the moment of flux is the most widely used, it is also referred to as the centroid of an image. If the

28 2.2. DATA REDUCTION total ﬂux in the frame is

N Ny Xx X Ftot = f(xi, yj) 2.1 i=0 j=0 § ¤ ¦ ¥ where f(xi, yi) is the value of the xi, yi pixel, the moment of ﬂux is (Berry, 2005, p.218)

PNx PNy PNx PNy xif(xi, yj) yifi(xi, yj) x¯ = i=0 j=0 andy ¯ = i=0 j=0 2.2 Ftot Ftot § ¤ ¦ ¥ for x and y respectively. To save some time and not looping throuht all pixels one can realise that

PNx PNy Nx xif(xi, yj) P x F (x ) x¯ = i=0 j=0 = i=0 i y i 2.3 Ftot Ftot § ¤

Ny X ¦ ¥ where Fy(xi) = f(xi, yj) 2.4 j=0 § ¤ ¦ ¥ The fact that makes this possible is that the equation weights each pixel along each axis separetly by the amount of starlight that have hit the pixel. Still, doing this on 3000 frames takes time, but in Python this can be done rather elegantly and fast with methods on multi-dimensional array objects, without having to do loops on the highest level. The result is the centroid of each frame, (¯xi, y¯i). The other method uses the strongest pixel in the frame as the star position, and it is exactly as simple as it sounds. The maximum speckle in an area close to the guide star is used as the star position in that frame.

2.2.4 Sharpness

The sharpness of each image is a measure of the quality of the data. With a high sample rate, the sharpness varies with time and gives a measure of the atmospheric disturbances. If two boxes are deﬁned in the image around the object of which the sharpness is to be measured for. One large, referred to as f1 and one small, referred to as f2. The sharpness is then simply the fraction of the two.

f s = 2 2.5 f1 § ¤ ¦ ¥ The sharpness is used to discriminate between data with high and low quality, since the source is a point source, the fraction is ideally equal to 1. The histogram of the sharpness helps to determine the acceptance sharpness that is applied later to the data when determining which images to be used in the ﬁnal image.

29 CHAPTER 2. OBSERVATIONS AND DATA REDUCTION

120 60 2250 100 50 2000

1750 80 40 1500

60 30 1250 pixels 1000 20 40 750

500 10 20 250 0 0 0 10 20 30 40 50 60 0 20 40 60 80 100 pixels Sharpness (%)

Figure 2.5: Left:An example of a 64x64 pixel box around the guidestar (XZ Tau) used in the 45◦ polarimetry dataset in the R-band. A 20x20 pixel (f1) and 6x6 (f2) box are drawn around the centroid (star sign). The sharpness in this image is 24% which is rather poor, in frames with higher sharpness the ﬂux in the f2 box (small) is higher and more concentrated. Right: Histogram over sharpness in all frames in the R-band data (2310 frames), it peaks around 50%.

100 60 2250

50 2000 80

1750 40 1500 60

30 1250 pixels 1000 40 20 750

500 20 10 250 0 0 0 10 20 30 40 50 60 0 20 40 60 80 100 pixels Sharpness (%)

Figure 2.6: Left: Same as ﬁgure 2.5 but with the centre and boxes around the strongest speckle Right: Histogram over all R-band images in 45◦ position with the centre at the strongest speckle.

2.2.5 Shifting and adding

After the acceptance sharpness has been determined, the images are ready to be shifted and added. Each image is now associated with a shift and sharpness, so when adding the frames the routines check if the shift is not too far, e.g. say a shift of more than 4 pixels and also if the sharpness meets the requirements. Before adding the specific image the average dark of the corresponding cycle is subtracted, and the image devided by the normalised flat-field. Below is an example of the 0◦ position final image with a sharpness criteria of 40% and a maximum shift-distance of 4 pixels, but not flat-fielded.

30 2.3. DATA ANALYSIS

Figure 2.7: The 0◦ position ﬁnal image with a sharpness criteria of 40% and a maximum shift- distance of 4 pixels. The size of the image is 512×512 pixels and to the left XZ Tau is seen.

2.3 Data analysis

2.3.1 Stokes and additional parameters With a shifted, dark subtracted, flat fielded and average added final image in every position of the analyser, what is left to do is to calculate the parameters S0, S1, S2, ϕ0,ILand the PLof the field. The specifics are covered in section 1.2.3 on page 16, the important equations are repeated here.

S1 = I0(0) − I0(90) = Q S2 = I0(45) − I0(135) = U (I0(0) + I0(90) + I0(45) + I0(135)) 1 S0 = = I 4 2 1 U ϕ = arctan 0 2 Q p 2 2 IL = Q + U r 1 Q2 + U 2 I P = = L L 2 S02 2S0

2.3.2 Polarization standards The analyser is not aligned with a line towards the north celestial pole, so the analyser has a certain shift for all observations. To find out how to compensate for this one performs polarization calibration, and by measuring the polarization of a polarization standard object one finds out how much the difference is and the shift applied as

ϕ0,true = ϕ0,obs − ϕ0,calib. 2.6 § ¤ 31¦ ¥ CHAPTER 2. OBSERVATIONS AND DATA REDUCTION

This assumes that the relation between the literature and the observed value is linear, i.e. that the angle with which the analyser turns between each position is exactly 45◦. If this is not the case, it will raise some concerns with the polarization measurements made. The calibration objects and their coordinates are listed in the observations log, below is a list of the measured values of ϕ0 and PL. Although some technical diﬃculties arose during the acquisition of calibration data, which resulted in only accumulated images to be used for calibration.

PL(% ) PL,litt(% ) ϕ0 ϕ0,litt HD-198478 (R) 2.47 2.8 103.007◦ 3◦ HD-198478 (V) 2.63 2.8 103.295◦ 3◦ HD-204827 (V) 5.32 160.883◦ 58.73◦ BD 64◦1080 (V) 5.52 5.69 21.07◦(+180◦) 96.63◦ HD-236633 (V) 3.15 5.49 16.61◦(+180◦) 93.76◦

Table 2.3: Calibration measurements, the literature values are taken from the NOT homepage on Polarization standards.

120

100 y=-96.324+0.963*x 80 t

t 60 i l , 0 ϕ 40

20 80 100 120 140 160 180 200 220 ϕ0,obs

Figure 2.8: Polarization calibration, the linear ﬁt has the equation y = −96.324 + 0.963x. The inclination coeﬃcient is not equal to one, which is not good.

As seen in table 2.2 the I0(135) measurment was corrupt, even in the accumulated image. So the formulas derivated in subsection “Analysing linearly polarized light” had to be modiﬁed. The derivation of those formulas is located in Appendix 1 on page 69.

32 “I don’t believe in astrology; I’m a Sagittarius and we’re skeptical.” Arthur C. Clarke 3 Results

3.1 Results

In the following chapter the results are given, and were possible, conclusions will be drawn and presented. The only visible objects in the images are XZ Tau and HL Tau, therefore those objects have been “cut-out” and displayed in their respective sections. The resulting datasets, i.e. S0, S1, S2, IL,PL and ϕ are shown below; for both filters, V- and R-band and for both objects, HL Tau and XZ Tau. To visualise structures and the scattering in the sources a combination of different results are drawn in a vector plot, where the arrows point along the polarization angle and a contour of the polarized flux is drawn, in HL Tau the length of the arrows correspond to the degree of polarization (PL) The data was reduced and analysed for five different scenarios referrd to as normal, zero, low, medium and high, depending on the chosen acceptance sharpness.

1. Normal, i.e. no shifting, no frame selection, just adding all frames together. This is what the image probably would look like after a normal continuous integration of ∼100 seconds.

2. Zero, only shifting, using all images and calculating a shift through the centroid positions.

3. Low, using shifting and frame selection and setting the acceptance sharpness to the median sharpness subtracted by 15, using about 80 % of all the frames.

4. Medium, using shifting and frame selection and setting the acceptance sharpness to the median sharpness subtracted by 5, resulting in about 60 % of the frames were used.

5. High, using shifting and frame selection and setting the acceptance sharpness to the maximum sharpness subtracted by 7. This resulted in the use of between 1 and 6 % of the frames.

In “low”, “medium” and “high” the limit for the excursion of the centroid from the median position is 4 pixels, otherwise there was no limit set. The motivation for the values chosen is just to get a good spread of the sharpness values and the frame selection to be able to investigate the eﬀect of frame selection on image

33 CHAPTER 3. RESULTS sharpness. The resulting acceptance sharpness and the percentage of the total number of frames used are shown in the table below.

Filter Angle Low Medium High 0◦ 36 (77) 46 (62) 68 (1) 45◦ 34 (79) 44 (63) 63 (4) V 90◦ 36 (75) 46 (61) 63 (6) 135◦ 35 (75) 45 (60) 67 (1) 0◦ 31 (80) 41 (62) 59 (3) 45◦ 30 (82) 40 (63) 61 (1) R 90◦ 30 (79) 40 (59) 59 (3) 135◦ 30 (79) 40 (62) 64 (1)

Table 3.1: Acceptance sharpness, i.e. percentage of flux that resides in the small box in comparison to the big box around the centroid, for the different angles and filters. The number in parenthesis is the percentage of all frames that where used.

Although the two objects are of similar mass and age, they show very different structures. In HL Tau the wide-spread reflection nebulosity is clear, in S0 the object is faint in comparison to the bright and confined intensity that XZ Tau show. The polarization is high in both R- and V-band data for HL Tayu. XZ Tau does not have the kind of gas and dust envelope as HL Tau, thus the wide-spread reflection nebulosity is not present. Although the observational conditions where not optimal, the elongation of XZ Tau at least hints the binary nature of the object. Several interesting investigations of HL Tau is made possible due to the data being polarimetric. The lack of error estimates here resides in the fact that it is rather cumbersome to calculate and with the rather high intensities that is shown in the images below it is not needed. The structures are significant, although in the “high” scenario, only the S0 image is shown to have enough information to show structures.

3.1.1 XZ Tau R-band

In the figure below the resulting S0, S1, S2, IL,PL and ϕ0 R-band images of XZ Tau are shown, the acceptance sharpness is set to medium, east is left and north is up. The mean intensity over all angles of the analyser (S0) shows that the object is slightly elongated in a south-east to north-west direction. Hinting the binary (multiple) system that it is. If the weather conditions had been more normal for the site, with around 000. 7 FWHM mean seeing, the binary system would probably have been resolved. The upper right image and the middle left shows the S1 and S2 data. In S1 the negative intensity is confined to a south-west to north-east stroke while in S2 it is shifted 90◦. What is expected from an object that creates polarized radiation by scattering, in a approximate spherical cloud around the central object, is that the intensities in S1 and S2 are at an 90◦ angle from one another, a butterfly shape. Both S1 and S2 shows a tendency towards this. In the final figures, the IL,PLand ϕ0 it becomes obvious that the degree of polarization in the system is low, less than 2% . The polarized intensity, the few percent that is polarized and have high intensity show even stronger the elongated structure.

34 3.1. RESULTS

S0 S1

3.6 100 40 3.2 40 75 2.8

30 ) 30 50 2.4 U D A

( 25 0 ADU 1

20 2.0 g 20 o l 0 1.6 10 10 25 1.2 50 0 0.8 0 0 10 20 30 40 0 10 20 30 40

S2 IL 2.0 80 1.8 40 40 40 1.6 0 30 30 1.4 ) U

40 D A

1.2 ( 0 ADU 1

20 80 20 g o 1.0 l 120 10 10 0.8 160 0.6 0 200 0 0 10 20 30 40 0 10 20 30 40 0.4

PL ϕ0 5.0 160 4.5 40 4.0 40 140 3.5 120 30 30 3.0 100

2.5 % 80 20 2.0 20 degree 60 1.5 10 10 40 1.0 0.5 20 0 0 0 10 20 30 40 0.0 0 10 20 30 40

Figure 3.1: R-band XZ Tau S0, S1, S2, IL,PLand ϕ0 images at medium acceptance sharpness. ◦ ◦ Polarization angle ϕ0 is set between 0 and 180 . The degree of polarization of the central source seen in IL is low, PL∼2% and the patterns in S1 and S2 reveal a structure sometimes described as a “butterﬂy”. The negative values in S1 are conﬁned in a south-west to nort-east direction while the “wings” are half-moons in the perpendicular direction. S2 has the same tendency but with a 90◦ shift. The intensity map, S0 and the polarized intensity ILshows signs of the binary system with an elongated structure. The polarization angle is constant where the polarized intensity is high, roughly at 45◦, which is perpendicular to the orientation of the ellipse created by the unresolved binary system.

35 CHAPTER 3. RESULTS

In the next figure (3.2) a combination of the polarization angle ϕ0 and the polarized flux IL is shown. The direction of the arrows show the polarization angle, up is 0◦ with positive direction counter clock wise and the contours are the polarized flux. The angles were filtered away where values of IL are below the median added with one standard deviation. In the region where the intensity is highest, i.e. above 53 in the contours, the angles is constant at an angle roughly perpendicular to the ellipse of the unresolved binary system. Due to the low degree of polarization this is probably just the polarization of the parental cloud/ISM, caused by dichroic extinction of the source starlight.

220

210

200

190

180

100 AU

170 120 130 140 150 160 170

◦ Figure 3.2: XZ Tau R-band vector plot, where the direction is the polarization angle ϕ0 and 0 is up (North). The contours are the polarized flux ILwith levels (from red to yellow) at 22.75, 44.5, 66.25 and 88. The centre source, where the flux is above 44.5, shows a approximately constant angle of polarization which is perpendicular to the ellipse created by the unresolved binary system. The data was filtered with the polarized flux so that sufficiently high levels of flux is shown. The length of the arrows are constant.

V-band

The V-band images of low acceptance sharpness are shown below. Beginning with the mean intensity, S0 shows the same elongated ellipse as in the R-band data. Hinting the binary nature of XZ Tau. The intensity in these images is less than half that of the R-band. In the V-band images S1 and S2 shows similar butterﬂy structures with a 90◦ shift to one another. The red in the S1 image is inclined, roughly speaking in a east-south-east to west-north-west direction, while S2 is inclined ∼90◦ to this. Just as with the R-band data the structure is not as prominent in S2, in IL it looks like the main scattering occurs along the S1 shape of positive values. Comparing IL with S0 and looking at PL, it has roughly the same degree of polarization in the brightest parts as in the R-band.

36 3.1. RESULTS

S0 S1

40 3.0 32 40 40 2.7 24 2.4

30 ) 30 16 2.1 U D A

( 8 0 ADU 1.8 1

20 g 20 o

l 0 1.5 8 10 1.2 10 0.9 16

0 0.6 0 24 0 10 20 30 40 0 10 20 30 40

S2 IL

30 1.50

40 15 40 1.35

0 1.20

30 30 ) 1.05 U 15 D A ( 0 ADU 0.90 1 20 30 20 g o l 0.75 45 10 10 0.60 60 0.45 0 75 0 0 10 20 30 40 0 10 20 30 40

PL ϕ0 5.0 160 4.5 40 4.0 40 140 3.5 120 30 30 3.0 100

2.5 % 80 20 2.0 20 degree 60 1.5 10 10 40 1.0 0.5 20 0 0 0 10 20 30 40 0.0 0 10 20 30 40

Figure 3.3: V-band XZ Tau S0, S1, S2, IL,PLand ϕ0 images. S0 shows the same elongated structure due to the unresolved binary system, and S1 and S2 shows the butterﬂy shape, this time with a east- south-east to west-north-west direction in S1 and a less prominent but 90◦ shifted similar structure in S2. The degree of polarization is low, around 2% where the intensity in IL is the greatest. The polarization angle at that same point in IL is constant, perpendicular to the ellipse direction of the unresolved binary. The acceptance sharpness is set to low.

37 CHAPTER 3. RESULTS

In the next ﬁgure the vector plot of the V-band data around XZ Tau is shown. As in the longer wavelength, the centre of the object, where the polarization is the greatest the polarization angle is perpendicular to the elongated structure that is the unresolved binary.

220

210

200

190

180

100 AU

170 120 130 140 150 160 170

Figure 3.4: XZ Tau V-band vector plot. The direction of the arrows is the polarization angle ϕ0 ◦ (0 is up) and the contours are the polarized flux IL at the levels (from red to yellow) 9.25, 18.5, 27.75 and 38. The polarization vectors in the centre, where the flux is above 18.5 (second level), are constant. Just as in the R-band data they are perpendicular to the orientation of the major axis of the ellipse that is the unresolved binary system. The data was filtered with the polarized flux so that only the significant data is represented and the acceptance sharpness is low.

3.1.2 HL Tau

R-band

In the figure below the resulting S0, S1, S2, IL,PLand ϕ0 R-band images of HL Tau are shown. The mean intensity S0 is very nebulous with lots of gas and dust around the YSO, the low intensity wide-spread reflection nebulosity shows a C-shaped structure. The central source is completely obscured at these wavelengths, but at longer wavelengths the source can be seen (Close et al., 1997). Which is what characterise HL Tau, its circumstellar envelope surrounds the young star, but in the outflow direction the optical depth is higher and thus letting the photons that scatter against the wall of the outflow to escape. S1 and S2 does not show much structure. The polarized flux and the degree of polarization is interesting, the degree of polarization is high, ∼30% the polarized flux is strong and wide-spread, showing no direct signs of the C-shape that is obvious in the S0; the shape in IL is usually described as cometary. The polarization angle shows clear a structure, fading from 180◦ red (0◦, blue) in the lower left to roughly 100◦in the upper right. This shows that the scattered radiation escapes the envelope after just one or a few scattering events

38 3.1. RESULTS so that it reaches this high degree of polarization. The plus sign and circle shows the possible location of the protostar (see the next paragraph for the explanation of how the possible location was deduced).

S0(high) S1

6.0 6.0 15 2.50 0 4.5 2.25 4.5 15 3.0 2.00 3.0 )

U 30

1.75 D A

1.5 ( 1.5 0 45 ADU 1

1.50 g o arcseconds arcseconds 0.0 l 0.0 60 1.25 75 -1.5 -1.5 1.00 90

-3.0 0.75 -3.0 105 -6.0 -4.5 -3.0 -1.5 0.0 1.5 -6.0 -4.5 -3.0 -1.5 0.0 1.5 arcseconds arcseconds

S2 IL

6.0 140 6.0 1.8

120 4.5 4.5 1.6 100 3.0 3.0 1.4 )

80 U 1.2 D A

1.5 1.5 ( 0 ADU 60 1 g

1.0 o arcseconds arcseconds l 0.0 40 0.0 0.8 -1.5 20 -1.5 0.6 0 -3.0 -3.0 0.4 -6.0 -4.5 -3.0 -1.5 0.0 1.5 -6.0 -4.5 -3.0 -1.5 0.0 1.5 arcseconds arcseconds

PL ϕ0 40 6.0 6.0 160 36 4.5 32 4.5 140

28 3.0 120 3.0 24 100 1.5

1.5 20 % 80 0.0 degree

arcseconds 16 arcseconds 0.0 60 12 -1.5 40 -1.5 8 -3.0 4 20 -3.0 -6.0 -4.5 -3.0 -1.5 0.0 1.5 0 -6.0 -4.5 -3.0 -1.5 0.0 1.5 arcseconds arcseconds

Figure 3.5: HL Tau R-band S0, S1, S2, IL,PLand ϕ0 images. S0 shows an approximate C-shape. The outflow has carved a hole in the envelope and photons scatter against the walls of this outflow and this scattering causes the observed polarization pattern. The degree of polarization is high ∼30%, and the polarization pattern shows structure around the star that tells us that the outflow is optically thin for the scattered photons. The images uses the frame selection scenario low, except S0 which uses high.

39 CHAPTER 3. RESULTS

HL Tau has a thick disk that obscures the central object at these wavelengths, but the polarization angle is perpendicular to the scattering plane (plane of incident and scattered rays) and by drawing lines perpendicular to the polarization angle should give the rough position of the central source. In figure 3.6 this is shown, the possible location of the source is shown by a circle with radius of 000. 6 (84 AU, 0.2400/pixel). Also the approximate PA angle of the outflow is drawn with white lines. The angles of the lines are at 40◦ and 55◦, giving an estimate of the PA of the outflow equal to 47.5±7.5◦. The data have been binned (2 × 2) so that the pixel scale is 0.2400/pixel, this increases the significance of the measurements and makes structures more prominent.

1 arcseconds

-1

-2 200 AU -3 -6 -5 -4 -3 -2 -1 0 1 2 arcseconds Figure 3.6: HL Tau R-band pinpointing the central object, where the arrows are drawn perpendicular to the polarization angle, and extra long. The “waist” of the hourglass-shaped object hints the position of the central source. The circle with radius of 000. 6 (84 AU, 0.2400/pixel (binned)) shows the likely position of it. The angles of the lines are at 40◦ and 55◦, giving an estimate of the PA of the outﬂow equal to 47.5±7.5◦.

The next image shows a vector plot with polarization angle represented by the direction of the arrows, the degree of polarization by length of the arrows and the contours represents the polarized intensity with levels at 18.75, 37.5, 56.25 and 75 (red to yellow). The circle shows the previous pinpoint of the central source with a radius of 000. 6 (84 AU). The fact that the counter-jet (and receding outﬂow lobe) is not visible as in near-IR observations by e.g. Lucas et al.(2004) shows that the envelope/disk blocks radiation at shorter wavelengths. The source is obscured by the envelope/disk, but the polarization vectors at the presumed location of the object are constant. They all point in a south-east direction, the structure is usually attributed to multiple scattering in the disk and the structure referred to as a polarization disk (Bastien and Menard, 1988; Whitney and Hartmann, 1993). The absence of scattered intensity around the outﬂow shows the thick envelope

40 3.1. RESULTS that surrounds the object. By averaging the degree of polarization in the circle that marks the location of the central source, an estimate of the core polarization can be made. The average core polarization of HL Tau R-band is 12.1%.

1 arcseconds 0

-1

-2 200 AU -3 -6 -5 -4 -3 -2 -1 0 1 2 arcseconds

Figure 3.7: HL Tau R-band vector plot. The direction of the arrows represents ϕ0, length of arrows -PL, contour IL and the corresponding levels are 18.75, 37.5, 56.25 and 75 (red to yellow). The data have been binned (2 × 2) and the circle shows the previous pinpoint of the central source with a radius of 000. 6 (84 AU, 0.2400/pixel). The observed structure shows how the photons scatter against the wall of the outﬂow and is polarized in the process. The polarization is perpendicular to the scattering plane. The classical centro-symmetric polarization pattern is clear and stretches for several hundred AUs. At the pinpointing of the central source there is a line of vectors that are aligned, this structure is usually appointed to multiple scattering in the disk and is referred to as a polarization disk.

V-band

The V-band images for HL Tau shows the same structures, but with a lower intensity. S0 shows the wide-spread nebulosity that characterises Class I/II YSOs with large envelopes. It also has the C-shape in S0 as the R-band. S1 and S2 also shows the same structure as the longer wavelength images while IL has the cometary shape but with about one third of the intensity which causes a higher noise level. The prominent structure of the polarization angles in the image is also present and also the high degree of polarization. At shorter wavelengths it is obvious that the object is less luminous and the intensity in S0 is roughly a bit less than half that of R-band (from ∼360 to ∼160 ADU).

41 CHAPTER 3. RESULTS

S0(high) S1

6.0 6.0 2.2 8

4.5 2.0 4.5 0

1.8 8 3.0 3.0 )

1.6 U 16 D A

1.5 ( 1.5 1.4 0 24 ADU 1 g o arcseconds arcseconds 1.2 l 0.0 0.0 32 1.0 40 -1.5 -1.5 0.8 48

-3.0 0.6 -3.0 56 -6.0 -4.5 -3.0 -1.5 0.0 1.5 -6.0 -4.5 -3.0 -1.5 0.0 1.5 arcseconds arcseconds

S2 IL

6.0 6.0 1.50 60 4.5 4.5 1.35 50 1.20 3.0 3.0

40 )

1.05 U D

30 A 1.5 1.5 ( 0 ADU 0.90 1 g o arcseconds arcseconds

20 l 0.0 0.0 0.75 10 -1.5 -1.5 0.60 0 0.45 -3.0 10 -3.0 -6.0 -4.5 -3.0 -1.5 0.0 1.5 -6.0 -4.5 -3.0 -1.5 0.0 1.5 arcseconds arcseconds

PL ϕ0 40 6.0 6.0 160 36 4.5 32 4.5 140

28 3.0 120 3.0 24 100 1.5

1.5 20 % 80 0.0 degree

arcseconds 16 arcseconds 0.0 60 12 -1.5 40 -1.5 8 -3.0 4 20 -3.0 -6.0 -4.5 -3.0 -1.5 0.0 1.5 0 -6.0 -4.5 -3.0 -1.5 0.0 1.5 arcseconds arcseconds

Figure 3.8: HL Tau V-band S0, S1, S2, IL,PLand ϕ0 images. S0 shows a non-circular structure that can be approximated with a thick C-shape. S1 and S2 shows no special structures, perhaps S1 hints that there is a polarization structure due to its distribution of positive and negative values. The acceptance sharpness used is low and the degree of linear polarization is high (∼30%) but being less luminous causes the noise to be higher, which is seen in PL and the ϕ0. Just as in R-band the scattering occurs at the walls of the outﬂow, and creates a centro-symmetric pattern.

42 3.1. RESULTS

In the next figure the pinpointing of the source in the V-band is shown. Just as with the R-band data it shows a hourglass shape that pinpoints the central source to the same approximate location. The possible location of the source is shown by a circle with radius of 000. 6 (84 AU, 0.2400/pixel). Also the approximate PA angle of the outflow is drawn with white lines. The angles of the lines are at 40◦ and 55◦, giving an estimate of the PA of the outflow equal to 47.5±7.5◦. Noteworthy is that both the R- and V-band images are aligned within 0.1 pixels before pinpointing the source, this so that the pinpointing would be done in the same image coordinates. The average core polarization of HL Tau in the V-band is 14.8%.

1 arcseconds

-1

-2 200 AU -3 -6 -5 -4 -3 -2 -1 0 1 2 arcseconds

Figure 3.9: HL Tau V-band pinpointing of central source and PA of outflow. The arrows are drawn perpendicular to the polarization angle, and extra long. Due to the geometry of the scattering and the outflow an hourglass-shaped structure like this is attained. The “waist” of this figure is where the central source most likely resides. This is a way of pinpointing the source when viewing at angles and wavelengths where it is heavily obscured. The circle marking the central source location has a radius of 000. 6 (84 AU, 0.2400/pixel, binned). The angles of the lines are at 40◦ and 55◦, giving an estimate of the PA of the outflow equal to 47.5±7.5◦. The acceptance sharpness was set to low.

The V-band vector plot below shows the same structure as in the R-band, albeit with a lower confidence level due to the lower intensity. The arrows are perpendicular to the scattering plane and shows the extent of the outflow region where the light scatters. Roughly perpendicular to the outflow axis lies the disk. In this region around the central source the vectors are more or less aligned. As previously presented, this is commonly referred to as a polarization disk. The V-band it is significantly weaker, but it still stands out from the random noise.

43 CHAPTER 3. RESULTS

1 arcseconds 0

-1

-2 200 AU -3 -6 -5 -4 -3 -2 -1 0 1 2 arcseconds

Figure 3.10: HL Tau V-band vector plot. The direction of the arrows represents ϕ0, length of arrows - PL, contour IL and the corresponding levels are 8, 16, 24 and 32 (red to yellow). In this image it is also easy to see that there is more noise present due to the lower luminosity at the ﬁlter wavelength. The data have been binned (2 × 2) and the circle shows the previous pinpoint of the central source with a radius of 000. 6 (84 AU, 0.2400/pixel). Although the lower signiﬁcance level, the classic and clear centrosymmetric polarization pattern can be seen and also the polarization disk at the position of the source.

Combining R- and V-band

One question that is raised is whether the distance and angle from the source where the scattering takes place is wavelength dependent. Usually the scattering occurs deeper within the outflow wall for longer wavelengths, at least comparing near-IR wavelengths (Close et al., 1997). In the next figure a comparison between R- and V-band relative intensity versus distance is shown. What is seen is the mean normalised flux in a 5 and 17 pixel column centred around the outflow axis, starting at the pinpoint circle going outwards along the outflow axis. For the 5 pixel column, it seems as if the V-band scatters closer to the source. Looking at the other figure, taking the mean of a wider column, 17 pixels, it looks as the flux is the same over all distances. This shows that light in the R-band scatters deeper in the outflow walls, the intensity is spread out wider in the R-band than in the V-band. Turning the argument around; the light in the V-band scatters closer to the outflow axis.

44 3.1. RESULTS

1.0 R-band 1.0 R-band V-band V-band

0.8 0.8

0.6 0.6

0.4 0.4 relative flux (5 pixels) relative flux (17 pixels) 0.2 0.2

0.0 0.0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 pixels pixels

Figure 3.11: The mean normalised polarized flux, IL/max(IL) in a 4 and 16 pixel column respectively as a function of distance from the position of the central source, outward along the 48◦ outflow for both R- and V-band. Each data point is the mean of 5 and 17 pixels along a 2 pixels wide line perpendicular to the outflow axis. In the V-band 5 pixel column mean the peak polarized flux comes after 15 pixels while the peak in the R-band resides at 19. On the other hand this is not present in the 17 pixel column mean. This difference between the two graphs can be interpreted as a wavelength dependent scattering depth. Longer wavelengths scatter deeper in the outflow walls, thereby creating an apparently wider outflow.

The average core polarization in the two ﬁlters where 12.1% for the R-band and 14.8% for V-band, i.e. the core polarization is inversely proportional to the wavelength. That is if the estimate of the location of the central source is good within the diameter of 10 pixels (100. 2, 178 AU). The rough inclination of the polarization disk is ∼135◦, i.e. ∼90◦to the outﬂow axis.

3.1.3 Lucky astronomy In this section the results of the part that involves lucky astronomy is presented. The aim is to do a small evaluation of the usefulness of the technique to improve image sharpness at the NOT. Since the XZ Tau binary is unresolved, it can be used to analyse seeing and image quality. Most of the values presented are derived by fitting a rotatable 2D Gaussian function to XZ Tau in each frame. This way, a time evolution of the different parameters fitted can be analysed. As previously briefly mentioned, speckle imaging was attempted, and the routines were implemented in the code (see Appendix B), but the time and spatial resolution were to low for it to work. The method of choosing the strongest speckle as the most significant position of the star is a good method when the time and spatial resolution is high enough, otherwise choosing the centroid is more robust.

Image motion Below is a figure of the image motion during the V-band observation. The positions of the values represents the x and y positions of the fitted 2D Gaussian in each frame. The circle shows the excursion limit of 4 pixels for the low, medium and high scenarios, where images that have moved further away than this limit is not used in the final shift and add routine, regardless of their sharpness. As seen the image movement is highly random but is mostly confined to within the circles border.

45 CHAPTER 3. RESULTS

15 15 10 5 0 5 10

Figure 3.12: Image movement in the V band data, positions (x,y) of the fitted Gaussians. The dashed circle shows the excursion limit, i.e. points outside of the circle are not included in the final shifted and added images. The positions are mostly confined within the circle but moves very far out, at times as far as ∼16 pixels (∼200, pixelscale 000. 12/pixel). A mechanical tip-tilt system will manage to counteract this image movement.

Elongation

In the next ﬁgure, the elongation (σx/σy) is shown, it has a empty stripe at σx/σy∼1. This could be due to the fact that the object used as reference is not completely circular, but elliptical. Since XZ Tau is a binary and evidently a bit elongated as shown in the previous sections this shows it is not optimum for determining the image sharpness. Never the less, the mean of these values seem to be roughly unity.

46 3.1. RESULTS

2.5

0 ◦

45 ◦

90 ◦

135 ◦ 2.0

1.5 FWHP, arcsec

1.0

0.5

0 2000 4000 6000 8000 10000 12000 14000 Frames used (%)

Figure 3.13: The figure shows the elongation (σx/σy ) of the reference object, XZ Tau in all the V-band frames as a function of time. Between the positions, no difference seems to be evident. The curious aspect of the figure is that the values seems to avoid unity, that is the object never seems to be a circle but allways an ellipse. This could be due to the unresolved (partially) binary causing an elliptical shape, as shown in the S0 images of section 3.1.1 on page 34.

Sharpness improvement

To see how the image sharpness is improved with the diﬀerent reduction scenarios described in the beginning of the chapter, a ﬁgure of the Full Width at Half Power (FWHP) versus the percentage√ of frames used is shown below. The FWHP is calculated as FWHP = = 2 2 ln 2σ ¯ where σ¯ = (σx + σy)/2.

The first conclusion is that by just accounting for image motion, the sharpness improves around 000. 1. By setting a frame selection criteria based on sharpness and centroid excursion the gain is ∼000. 4 (the “high” scenario). These conclusions apply to the conditions during the night of observation and the site, i.e. an acceptable seeing and the Observatorio del Roque de los Muchachos. A normal seeing for the site is around 000. 7, in which case the improvement of lucky imaging could have been enough to resolve the XZ Tau binary (000. 3). Depend- ing on what information that is to be extracted from the final data, different acceptance sharpness should be set. If broad structures and overall geometry is to be studied a low acceptance sharpness should be used so that the low surface brightness regions reach above the noise. Contrary to this, if attempting to resolve, say a binary or small but bright structures, a high acceptance sharpness should be chosen. Comparing the different filters, the sharpness in the V-band is approximately 000. 1 systematically sharper for almost all scenarios.

47 CHAPTER 3. RESULTS

1.10 0 1.05 ◦ 45 ◦ 1.00 90 ◦

0.95 135 ◦

0.90

0.85

0.80

0.75 FWHP, arcsec 0.70

0.65

0.60

0.55

0 10 20 30 40 50 60 70 80 90 100 Frames used (%)

Figure 3.14: FWHP in arcseconds versus the percentage of frames used. The circles are the V-band and the stars the R-band, while the marker colour is the same as in the legend for all ﬁlters. See table 3.1 for details about the acceptance sharpness for the diﬀerent scenarios. Only shifting and adding increases the sharpness with 000. 1 while applying a frame selection criteria it can improve as much as 000. 4. From right to left; uppermost values are the Normal, below them lies Zero, to the left Low, then Medium and lastly High scenario.

The next image shows histograms of the sharpness in both of the filters. The scale on the x- and y-axis is the same for both figures. Around 10% have values higher then 100. 5 in both filters. The sharpness for the V-band is significantly better, as also shown in previous figure.

R-band V-band

5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 0 1 2 3 4 5 0 1 2 3 4 5 FWHP, arcsec FWHP, arcsec

Figure 3.15: Histograms showing the sharpness/seeing, full width at half power (in arcseconds) for all exposures in R- and V-band. The V-band histogram shows more sharper images, which dominates the seeing as seen in previous ﬁgure, but it also has a few more with worse sharpness. The tail towards low sharpness shows that alot of the images in the data have low sharpness.

48 3.2. SUMMARY OF RESULTS

3.2 Summary of results

3.2.1 HL Tau HL Tau is a embedded source where the radiation detected at these wavelengths is scattered light from the envelope mainly in the outflow where the optical depth is lower. The mean intensity (S0) shows this nebulosity, and also a C-shaped structure. The degree of polarization in the outflow is high, around 30%. The polarization angle vector plot shows clear structures with vectors forming an arc around the central source where the outflow is, the pattern is said to be centrosymmetric. Since the central source is completely obscured at these wavelengths, there was an attempt at pinpointing the central source. This is realised through the fact that the polarization angle is perpendicular to the scattering plane, and by drawing lines long the scattering plane the central source was pinpointed within a 000. 6 radius. This endeavour also produced an estimate of the PA of the outflow to about 47.5±7.5◦. The absent counter-jet and receding lobe, observed by others at Near-IR filter bands, indicates that the envelope/disk blocks radiation at these wavelengths. What also is seen is a polarization disk, that extends roughly perpendicular to the outflow axis (∼135◦) and through the pinpointed source. The core polarization increases from 12.1% in the R-band to 14.8% in the V-band. The intensity is approximately half in the V-band in comparison to the R-band. An investigation of the flux versus width of the outflow concluded that the radiation in the R-band scatters deeper within the outflow walls, and the intensity is spread out wider in the images than in the V-band.

3.2.2 XZ Tau The mean intensity, S0 shows a (partially) unresolved binary system with its elliptic shape. The polarized intensity (IL) also shows this elliptical shape. It also shows scattering in a spherical manner a bit away from the central source, although it is hard to interpret due to the low degree of polarization. The polarization pattern in the most central regions show aligned vectors with low (<2%) degree of polarization. The intensity in the V-band is less than half of that in the R-band, this is the most significant difference between the filters.

3.2.3 Parameters vs sharpness/psf improvement Most frames does not shift above the excursion limit. The elongation of the image is attributed to that the measurements were done on a binary system, although not resolved it has an elongated structure that would tend to increase the uncertainty in measuring the sharpness (FWHP) of the image. With this in mind the sharpness improvement is significant, by just shifting images 000. 1 in sharpness can be gained. Going further and selecting images with high sharpness one can gain as much as 000. 4; by selecting the ∼1% of all the frames that are the sharpest. The low number of frames used for images with high sharpness affects the sensitivity of the image. Hence, depending on what information that is to be extracted different selection criteria should be applied. Broad nebulous structures and overall shapes suggests a low sharpness criteria, causing

49 CHAPTER 3. RESULTS much of the images to be used, causing the low surface brightness regions to reach above the noise limit. On the contrary, resolving a binary only a high sharpness criteria can give the resolution necessary. Around 10% of the images have a sharpness (FWHP) greater than 100. 5, which is very bad. With better site/weather conditions, a higher overall sharpness would have been achieved. Comparing the ﬁlters, we see that the V-band sharpness is about 000. 1 higher.

50 “All truths are easy to understand once they are discovered; the point is to discover them.” Galileo Galilei 4 Discussion

4.1 Discussion

4.1.1 HL Tau The mean intensity image, S0 shows the nebulous region around HL Tau, the intensity extends far out (∼300. 6, 500 AU) and is wide (∼200. 4, 340 AU) from the central source. Stellar light escapes the dense and dusty flared disk/envelope along the upper cavity cleared by the jet, light is then scattered in the cavity walls, toward the observer. In figure 4.2 below an illustration of the scenario is shown. This reflection nebula is what is seen in the S0 image and it is responsible for the observed large degree of polarization (∼30%). Interestingly, both R- and V-band shows a C-shaped structure with an ∼100. 1 (∼154 AU) extension. Close et al.(1997) and Murakawa et al.(2008) both show that this structure is prominent at J and H band, but at longer wavelengths the central object is more visible and the feature is harder to distinct. In the optical HST images of HL Tau by Stapelfeldt et al.(1995) show the C-shaped structure with high resolution. A figure from that article is shown below together with this thesis S0 contours. As seen the pinpointing is OK, the VLA source marked with a plus sign in the data from Stapelfeldt et al.(1995) is at the norteastern edge of the pinpointed circle.

2 arcseconds

-2 -4 -2 0 arcseconds

Figure 4.1: HST FW555 ﬁgure from Stapelfeldt et al.(1995) and S0 contours from the results of this thesis. The C-shape is seen in both ﬁgures and the location of the central source is not at the same position. Although the positioning in this thesis is OK.

51 CHAPTER 4. DISCUSSION

The origin of this C-shape in the outflow is unknown, the polarized intensity seems to be higher in the part of the C that is further away from the source (in the northeast). Stapelfeldt et al.(1995) argue that the shape could be produced by either the distribution of absorbing material, causing lower intensity in the centre of the C-shape, or the distribution of reflecting material causing light hitting the ridge of the C-shape to be reflected stronger. The absorbing material could be a foreground clump in the circumstellar envelope that would superpose a dark blot on the otherwise classical cometary nebula. The high-resolution data from Murakawa et al.(2008) show this C-shape in their intensity maps with higher intensity approximately along the C-shaped ridge. The cause of the C-shape is probably complex, owing to the orientation of the system and the scattering geometry in combination with higher density cloud components in the envelope. Further multi-wavelength high-resolution investigations could shed some light on the dark spot creating the C-shape in this outflow. A bipolar nebula seen approximately edge-on show a centrosymmetric polarization vector pattern in the lobes and a polarization disk in the equatorial plane where the disk resides, as shown by both observations (e.g. Lucas and Roche, 1997; Perrin et al., 2004; Beckford et al., 2008) and computational modelling (e.g. Bastien and Menard, 1988; Whitney B. A. and Wolff M. J., 2002). The resulting model consists of a flared disk and an infalling envelope accompanied with a jet/outflow (e.g. Fischer et al., 1994). With this in mind we turn our focus on to the results in this thesis. The centrosymmetric polarization pattern shows that at least one of the lobes of the outflow is visible. The pattern is roughly perpendicular to the observed optical jet reported by several authors (Mundt et al., 1990; Rodriguez et al., 1994; Anglada et al., 2007). The absence of a bipolar structure in the images suggests that the opacity in the south-western lobe is high enough for the light to be completely extinct, the extinction in the cloud is AV ≈ 24−30 mag (Monin et al., 1989; Beckwith and Birk, 1995; Close et al., 1997). This can be explained by a system where the north-eastern outflow axis is tilted towards the observer (Hayashi et al., 1993; Mundy et al., 1996). At the possible location of the central source extending roughly perpendicular to the outflow axis a polarization disk is seen in both R- and V-band polarization vector fields. The alignment of polarization vectors along the disk location can be produced by multiple scattering and the illusory disk arising from limited spatial resolution (Lucas and Roche, 1998). The figure showing the normalised polarized intensity versus distance from source and filter, figure 3.11 on page 45 show that the R-band scatters deeper in to the disk wall than the V-band. R-band is steadily rising about 0.1 points above V-band in both figures and since the outflow is inclined towards us, it is natural that the intensity will be higher closer to the source in the image plane in the R-band. Also the sum of the small stripe (5 pixels) causes the V-band to reach its maximum value earlier than the R-band for the same width, but in the wide stripe, they reach the maximum at the same, this also points to the fact that the R-band polarized intensity is wider along the outflow axis than the V-band which is confirmed in the J, H and K band by Close et al.(1997). The high extinction together with the youth of the star causes the R-band flux to be roughly twice that of the V-band. Knowing where the star is in relation to all the detected structures, that have their origin in the central source, is obviously important. Since the central

52 4.1. DISCUSSION

Figure 4.2: An illustration of the structure of the protostar HL Tau. The inclination of the outﬂow is 60◦towards the observer. The envelope is thick, with a centrally peaked density distribution and evacuated bipolar cavities. Light emanating from the protostar scatter of the cavity walls and escape the envelope through the optically thin regions as shown by the solid lines. The stellar light is extinct in the envelope, and only longer wavelength photons (near-IR) can penetrate through the envelope and reach the observer. The ﬁgure was inspired by a similar in Whitney et al.(1997).

star starts to become visible in the H, perhaps K band it is not seen in any of the data. Since the data lacks accurate coordinates and enough objects to register the images there is no way of knowing. A simple approach was made to position the central source. By drawing extra long polarization vectors with a 90◦ shift a position was deduced, other more sophisticated methods exists, e.g. Murakawa et al.(2005), but the lack of bipolar structure in the data causes the pinpointing carried out here to be the best way. The lack of error analysis causes the results to be a bit doubtful, just by adopting an polarization angle error of about 5∼10◦ causes a rather large error. Assuming the pinpointing here is roughly correct, we see that the extinction is indeed very high, there is no sign of the source in the data. The dense disk/envelope covers the young star so that the only signpost for it is the scattering of its light in the outflow. In positioning a rough location of the source, the PA of the outflow was derived (∼47.5±7.5◦). In comparison to other measurements of this; e.g. the jet - Mundt et al.(1990) 48.5 ◦ and Anglada et al.(2007) ∼45◦ it stands rather good. Thus the jet coincides with the outflow as expected. The core polarization decreases with wavelength, from ∼14.8% in the V-band to ∼12.1% in the R-band. The dependence on wavelength can give information about the scattering and absorption mechanisms. Beckford et al.(2008) investigated the wavelength dependence in the near-IR of 10 class I, 7 class II and 1 class II sources and came to the same conclusion of wavelength dependence. If dichroism is the mechanism responsible for the polarization this is expected.

53 CHAPTER 4. DISCUSSION

Although there are a couple of possible scenarios where scattering can produce the same dependence, one is if the unresolved underlying scattering polarization averages to the observed polarization (Whitney et al., 1997). The polarization could be attributed to multiple scattering, and this would produce the observed pattern (Lucas and Roche, 1998). At shorter wavelengths the Rayleigh limit (wavelengthgrain size) is reached and scattering becomes more eﬃcient.

4.1.2 XZ Tau

The binary in XZ Tau was not resolved, but the parts of highest intensity in the S0 image show an elongated structure in a southeast to nortwest direction. Which is the direction that the two stars line up at (Haas et al., 1990; Hioki et al., 2009). The polarized intensity shows the same structure and it shows that even though the binary is not resolved, with further observations using one of the barlow lenses and perhaps a higher temporal resolution the binary can be resolved. In S1 and S2 the faint butterﬂy structure could indicate a spherical region where scattering of starlight occurs. This is probably just scattering in the foreground cloud that is detected, just as with the polarization in the core region, where IL is strongest. As shown by Krist et al.(1999) there are bubbles of gas/dust to the northeast and southwest of the system, which then could scatter light into the observer’s direction. The degree of polarization in the core region is low, <2% which is close to the cloud polarization of 1.6% reported by Vrba et al.(1976). Thus, what is seen is aligned grains in the surrounding cloud that causes dichroic extinction, which explains the low degree of polarization.

4.1.3 Other

The lack of error analysis is a flaw when looking at structures that only are a few standard deviations above the noise. For examples of how the error analysis could have been done see Sparks and Axon(1999); Murakawa et al.(2004, 2005). The axial ratio of the guide star/reference star is not unity, instead it is fluctuating without really equalling one. This can be interpreted as that the object is elliptical to the shape, or perhaps it is observed as that because of aberrations in the light path. Being a unresolved binary it is natural that the object should be elongated, but since this is the case here it is not optimal to measure sharpness variations on a object like that. The gain in lucky astronomy is clearly evident, tip/tilt corrections in this data increases sharpness with 000. 1 and using frame selection up to 000. 4. The systematically 000. 1 sharper V-band images in the different scenarios is opposite to normal seeing conditions. Usually the longer wavelength filters have higher sharpness. The fact that the R-band dataset is smaller than the V- band (77 cycles R, 100 in V) and the fluctuating weather conditions could cause the discrepancy between the measured values and the expected. The weather conditions indeed seems to worsen during the R-band run when looking at the weather graphs on page 25.

54 4.2. SUMMARY

4.2 Summary

Optical polarimetry of HL Tau show a centrosymmetric pattern, indicating scattering of light by dust around a protostar. The dust grains resides in the outflow, the evacuated out less denser part of the circumstellar cloud. Because the opacity is lower in the cleared cavity of the outflow the scattered photons escape the envelope and reach the observer with relatively high degree of polarization, ∼30% for both R- and V-band. The outflow of HL Tau show a structure in the intensity that can be described by a “C”, the origin of this shape is unknown but several theories exists. The outflow has a approximate PA of 48.5±7.5◦ coinciding with the previously detected jet. A polarization disk is observed which is probably produced by multiple scattering and the illusory disk arising from limited spatial resolution. The core polarization has a wavelength dependence, decreasing with wavelength, but the exact mechanism producing this is unknown. The apparent width of the outflow in HL Tau changes with wavelength, longer wavelengths scatters deeper into the cavity walls thus creating a wider intensity map.

Although the XZ Tau binary is not resolved, an elliptical shape extending in the same direction as the known binary is seen. The polarization that is detected is the polarization of the surrounding cloud (<2%).

The gain in sharpness is 000. 1 for tip/tilt corrections and up to 000. 4 when also using frame selection. The gain is applicable to the same observation site and conditions. Lucky astronomy is a powerful tool, combining it with polarimetry shows promising results.

List of Figures

1.1 PACS and SPIRE image of a star forming region...... 3 1.2 Protostellar outﬂow - HH111 - the structure of a protostar.... 6 1.3 Six protostars showing the structure of a protostellar disk.... 7 1.4 L1551 of the Taurus-Auriga star forming cloud in S II ...... 10 1.5 Polarization ellipse showing the Stokes parameters ...... 12 1.6 Scattering of light by dust particle, geometry ...... 14 1.7 Sequential raw images from observation run illustrating speckle patterns...... 18

2.1 Andor iXon+ 897, quantum efficiency (QE) versus wavelength . 22 2.2 The PolCor instrument layout and light path...... 24 2.3 Atmospheric conditions 27th-28th October 2008...... 25 2.4 Typical V-band dark frame and pixel distribution...... 28 2.5 Sharpness boxes for moment of flux and histogram of sharpness . 30 2.6 Sharpness boxes for strongest speckle centre and histogram of sharpness ...... 30 2.7 0◦ final image...... 31 2.8 Polarization calibration ...... 32

3.1 XZ Tau R-band S0, S1, S2, IL,PLand ϕ0 ...... 35 3.2 XZ Tau - R-band vector plot ...... 36

3.3 XZ Tau V-band S0, S1, S2, IL,PLand ϕ0 ...... 37 3.4 XZ Tau - V-band vector plot ...... 38

3.5 HL Tau R-band S0, S1, S2, IL,PLand ϕ0 images...... 39 3.6 HL Tau - R-band pinpointing the central object...... 40 3.7 HL Tau - R-band vector plot ...... 41

3.8 HL Tau V-band S0, S1, S2, IL,PLand ϕ0 images...... 42 3.9 HL Tau - V-band pinpointing the central object...... 43 3.10 HL Tau - V-band vector plot ...... 44 3.11 Polarized ﬂux versus distance from source...... 45 3.12 Image movement in the V band data...... 46 3.13 Elongation of the reference object (XZ Tau) in all V-band frames versus time ...... 47 3.14 FWHP versus percentage of frames used...... 48 3.15 Histogram of the FWHP, i.e. the sharpness/seeing R- and V-band 48

57 LIST OF FIGURES

4.1 Comparison of shapes and intensity of HL Tau between this thesis and Stapelfeldt et al.(1995)...... 51 4.2 Illustration of HL Tau structure...... 53

58 List of Tables

2.1 CCD detector characteristics ...... 23 2.2 Observational log...... 26 2.3 Polarimetry calibration...... 32

3.1 The acceptance sharpness values ...... 34

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68 Appendix

A. Data with three valid angles observed

Removing one of the detected intensities for an angle of the analyser (equations 1.5 to 1.8) we end up with

0 ◦ I (0 ) = I0 (1 + PL cos 2ϕ0) A1.1 § ¤ 0 ◦ I (45 ) = I0 (1 + PL sin 2ϕ0) A1.2 §¦ ¤¥ 0 ◦ I (90 ) = I0 (1 − PL cos 2ϕ0) . A1.3 ¦§ ¤¥ Now we have a system of three unknown and three equations. To solve this¦ we¥ ﬁrst take equation A1.1 and add A1.3

I0(0◦) + I0(90◦) I0 = . A1.4 2 § ¤ ¦ ¥ This is the mean intensity, then we take equation A1.1 and solve for PL

0 I (0)/I0 − 1 PL = A1.5 cos 2ϕ0 § ¤ ¦ ¥ For the polarization angle we take equation A1.1 and add A1.2

I0(0) + I0(45) = 2 + PL cos 2ϕ0 + PL sin 2ϕ0 I0 Now inserting equation A1.5 we get

I0(0) + I0(45) I0(0) I0(0) = 2 + − 1 + − 1 tan 2ϕ0 I0 I0 I0 I0(45) /I0 − 1 tan 2ϕ = 0 I0(0) /I0 − 1 0 1 I (45) − I0 ϕ0 = arctan 0 A1.6 2 I (0) − I0 § ¤ ¦ ¥ Which is the last equation we need.

69 B. PYTHON CODE DESCRIPTION

B. Python code description

B.1 Introduction

Here is a description of the Python code that was written for the reduction of PolCor data. Python was also used to analyse the final data and produce all the graphs in the thesis. First there is a description of the help functions, functions that were used in conjunction to the main class with its methods. A short description of both the help functions and the main class with its methods is covered in the coming to sections. Lastly a short example of how the PolCor python module can be used. The code produced is not finished, for example it does not have a method for handling flat field data since there was not such data, which would be very simple to implement if needed in the future.

B.2 Help Functions lsFiles(arg0, arg1) Takes as input a file extension to search for and returns all the files in the specified path containing this file extension. arg0 is the path and arg1 is the file extension. display(f, fsize, image, **kwargs) Function that displays image into figure number f, with figure size fsize as a tuple. Additional keyword arguments are; csor=0/1 - if the cursor should be marked with a cross, title=’string’ - title of plot, xlabel=’string’ - x label and ylabel=’string’ - y label. getCursor(*args) Gets the cursor position at click for an arbitrary number of characteristic strings as input, e.g. getCursor(’star’,’sky’) will first ask user to click on star then on sky and subsequently return two positions. saveatbl(filename, dataList, names) Saves a list of data arrays (dataList) in to a table with the column names (names) as an ASCII file with name filename (can include path as well). loadatbl(filename) Loads a list of data arrays in filename, returns a array of the data (loads arrays saved with the savetable command). An example, a = loadtable(filename) and then a[:,0] for first column, a[:,1] for second and so on. infoatbl(filename) Returns the lines with comments (i.e. the column names) from an *.atbl file. phot(frame, boxside,R=0,R1=0,R2=0) Asks for cursor input from user and calculates aperture photometry on a centroid at the cursor position, with the radius R, R1 and R2 representing the inner annulus (star) outer radius, outer annulus (sky) inner radius and outer annulus outer radius. It calculates the flux as

Cannulus F = Caperture − naperture nannulus where C denotes the sum of pixel values within the corresponding annulus

70 APPENDIX

and n the number of pixels within it, from Berry(2005, p.277) 1. imstat(cube, skycube) Returns simple image statistics on a two cubes of images, on with a star in it and the other a sky-area. The statistics that are determined are median, average, standard deviation, simple photometry (only on star frame; removes median sky and sums all pixels in frame). gaussphot(cube, skycube) Subtracts the median of the corresponding skyframe from the skycube and ﬁts a rotatable, elliptical gaussian to each of the frames in the cube. Returns height, amplitude, x, y, widthx, widthy and rotation angle of every frame as lists. sig2fwhp(sig1=0, sig2=0, scale=0.12) Calculates the FWHP, supply the sigma(s) (gaussian width(s) in pixels) and the plate scale (arcsec/pixel), it returns the FWHP (arcsec)for√ the given plate scale in arcsec/pxls. Calculated as FWHP = = 2 2 ln 2σ ¯ where the σ¯ is the mean sigma when two is supplied. load_CBinary(file, shape=0) Loads a binary ﬁle saved in C, in some cases the shape has to be supplied for it to load correctly.

B.3 Classes, Attributes and Methods The main class is named Data it has several attributes and methods that does a particular thing with the data, and in the end the final shift and added images are saved and returned. class Data A class that defines data from the PolCor instrument, when initiated the main path to the data have to be supplied; the directory where all data from the different polarization angles are stored, i.e. one path per object. In addition to this the names of the folders where the different polarization angles are stored and if the shift is to be on a sub-pixel level have to be supplied. An example would be

PATH=’/path/to/data’ FOLDERS = (’Dark’,’pos0’, ’pos45’,’pos90’,’pos135’) obsNov08 = Data(PATH, FOLDERS, sbpxl=False)

The methods that are avaliable are (except the initiator and _str_ method): calcDark, readIn, getBoxes, getCenterOfFlux, getStrongestSpeckle, getSharp- ness and shiftAndAdd. Before any of the methods can be used the data has to be initiated as the example above. calcDark(darkframename, avgdarkname) Reads in all the dark frames and calculates the average dark for each cycle and over all cycles, then saves the ﬁles as darkframename and avgdarkname. Example: obsNov08.calcDark(’mdark.fits’, ’avgdark.fits’). readIn(polangle, n) Read in images from n cycles and return the average image of them, polangle refer to from what data the images should be read in from, 0=0◦, 1=45◦, 2=90◦, 3=135◦. Example: data_to_display = obsNov08.readIn(0, 3).

1 The equation given in Berry(2005) has a typo, instead of Cannulus it says Caperture.

71 B. PYTHON CODE DESCRIPTION

getBoxes(starpos, skypos, boxside, skyboxside, polangle) Cuts out boxes from the data at the guidestar position and a sky patch position given. Retrieves boxes of size boxsize x boxsize, and the same for skyboxside around the given positions starpos=[x,y] and skypos=[x,y] for the given polangle (defined as above). This way the memory imprint is low, ∼240 MiB each (3000*50*50*32/1e6) for a boxside of around 50 pixels and 32-bit floating point precision. Example: starcube, skycube = obsNov08.getBoxes([194,177], [200,300], 50, 90, 0). getMaxSpeckle(starcube) Returns the position of the speckle with the maximum intensity in all the frames of the cube. Example: centers = obsNov08.getMaxSpeckle(starcube). getMoments(starcube) Calculates moments of flux (centroid) for each frame in input starcube. Example: centers = obsNov08.getMoments(starcube). getSharpness(starcube, big, small, centers) Returns the fraction of flux in a box with side small divided by the flux in a box of side big, both centred around the given center. This is done for each frame in the cube that is supplied. Example: sharpness = obsNov08.getSharpness(starcube, 20, 6, centers). shiftAdd(darkfile, flatfile, sharpness, accept_sharp, excursion, deltacent, polangle, starpos, method) Applies the dark frame, the flat field frame, shifts and adds images with acceptance sharpness higher than accept_sharp and within sqrt(excursion) pixels. sharpness is the array with the calculated sharpness of all frames, darkfile is a path to the dark frame (.fits), flatfile the flat field frame. deltacent is the excursion from the median position that each frame have, method describes the method of determining the center (‘speckle’ or ‘moments’) and the rest is defined as before. Returns the final frame for that polarization angle, number of files used, total number of frames available and exactly which frames that were used. Example: final_data,nfiles,ntot,frameindices = obsNov08.shiftAdd(darkfile, sharpness, 30, 16, deltacent, 0, [194,177], ’moments’).

B.4 Example Usage

1 # importing module 2 from polcordata import * 3 # initiating data 4 FOLDERS = (’Dark’,’pos0’, ’pos45’,’pos90’,’pos135’) 5 obsNov08 = Data(PATH, FOLDERS, subpixelshift) 6 # calculating dark frame 7 DARKFILE = ’mdark.fits’; AVGDARKFILE = ’avgmdark.fits’ 8 mdark, avgmdark = obsNov08.calcDark(DARKFILE, AVGDARKFILE) 9 # getting guide star and sky positions 10 preview = obsNov08.readIn(polangle,3) 11 display(0,(6,6),preview,csor=1) 12 xystar, xysky = getCursor(’GUIDESTAR’,’SKY’) 13 # rounding off to integers 14 xstar = []; ystar = [] 15 xstar, ystar = (array(xystar[0])-0.49).round().astype(’int’) 16 xsky, ysky = (array(xysky[0])-0.49).round().astype(’int’) 17 # reading in the data, cutting out boxes 18 starcube_noskysub, skycube = obsNov08.getBoxes([xstar, ystar], [xsky, ysky], cubesize, skyboxsize 19 , polangle) 20 # subtracting sky 21 for i in xrange(starcube_noskysub.shape[0]): 22 starcube[i] = starcube_noskysub[i] - median(skycube[i])

72 APPENDIX

23 # calculating and saving statistics 24 stats, stats30 = imstat(starcube_noskysub, skycube) 25 filename = str(FOLDERS[polangle+1]) +’_stats.atbl’ 26 saveatbl(PATH+filename, stats, [’sum’, ’std’, ’mean’, ’med’, ’max’, ’skymed’]) 27 filename = str(FOLDERS[polangle+1]) +’_stats30.atbl’ 28 saveatbl(PATH+filename, stats30, [’sum’, ’std’, ’mean’, ’med’, ’skymed’]) 29 # fitting a gaussian to all frames and saving the statistics 30 statsgauss = gaussphot(starcube_noskysub, skycube) 31 filename = str(FOLDERS[polangle+1]) +’_statsgauss.atbl’ 32 saveatbl(PATH+filename, statsgauss, [’height’, ’amplitude’, ’X’, ’Y’, ’dX’, ’dY’, ’ROT’]) 33 # calculating the centroid (moment of flux) for each frame 34 moments_centers = []; moments_deltacent = []; moments_median_center = [] 35 moments_centers, moments_deltacent, moments_median_center = obsNov08.getMoments(starcube) 36 # correcting the star coordinates to the new ‘best’ position 37 xstar, ystar = [xstar, ystar] + median_center - cubesize/2 38 # calculating the sharpness of every frame, and saving the values 39 bigbox = 20; smallbox= 6; sharpness = [] 40 sharpness = obsNov08.getSharpness(starcube, bigbox, smallbox, centers) 41 sharpness = (sharpness*100).round() 42 filename = str(FOLDERS[polangle+1]) +’_’+method+’_sharpness.atbl’ 43 saveatbl(PATH+filename, [sharpness], [’sharpness’]) 44 # shifting and adding. accept_sharp, excursion and method not defined here 45 final, used, ntot, f_index = obsNov08.shiftAdd(DARKFILE, sharpness, accept_sharp_values[i], ex- 46 cursion[i], deltacent, polangle, starpos, method)