The Ionized Intergalactic Medium and Its Influence on Galaxies And

The Ionized Intergalactic Medium and its Inﬂuence on Galaxies and Galaxy Clusters

A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY

Mohammad Mehdi Lame’e

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

Advisor: Lawrence Rudnick

First of all, I would like to express my special appreciation and thanks to my advisor Prof. Lawrence Rudnick. Without his support, guidance, suggestions, feedbacks and critics this thesis would not have been possible. He thought me to be a critical thinker and question even the most obvious assumptions. Under his supervision, I learned how to properly use the so-called scientific methodology and perform high quality research with only and only one intention in mind: doing science. He has used my mistakes to empower and teach me to learn from failed attempts and use them to improve my research. He, unconsciously, has thought me how to not give up when facing, seemingly, unsolvable obstacles and problems and instead, start thinking about out-of-the-box solutions. It has been such a great honor to work with him. I want to thank my co-advisor Dr. Claudia Scarlata. She gave me the opportu- nity to gain invaluable experience and expertise working with data of some of the most impressive optical telescopes. Her motivation and passion for research was contagious and definitely has played a crucial role in shaping the second chapter of this thesis. I wish to express my sincere gratitude to my committee members Prof. Thomas Jones and Prof. Vuk Mandic for their insightful comments in improving this thesis. I have had many important discussions and conversations with Prof. Jones about the underlying Physics of some of the most interesting findings of this thesis, especially the discovery of a few radio relics and filaments in the intracluster medium of the Abell 2255 merging system. His ideas and suggestions have provided vital

i insights in this thesis. A very special acknowledgment goes out to all my collaborators and colleagues, especially Prof. Frazer Owen, Dr. Peter Capak and Dr. Walter Brisken who helped me overcome technical challenges of reducing radio interferometry as well as optical imaging data obtained by world-class radio interferometer antennas such as the Very Large Array and ground based optical telescopes such as Subaru and Palomar. During several years of my PhD study, I have been so lucky to have the chance to work with some amazing people. I would like to express my thankfulness to all my labmates, in particular, Micaela Bagley who helped me run my ﬁrst onsite observation, Dr. Michael Rutkowski who provided detailed comments on the second chapter of this thesis and Vihang Mehta who helped incorporating the SPLASH project data in the section 2.6 of this thesis. Moreover, I am lucky to have some amazing friends who helped maintain positive attitude and overcome very hard challenges of PhD lifestyle. I am grate- ful to Pedram Baldari, Noushin Hakim, Pejman Roohani, Farnaz Forootaninia, Soroush Sotoudeh, Armin Zare, Samira Bahrami, Maziar Sanjabi, Pardees Azo- danloo, Morteza Mardani, Karen Khatamifard, Sepideh Moghaddam, Meisam Razaviyayn, Nazila Haratipour, Mehrdad Hairani, Zohreh Ebadi, Ellie Ziaie, Roushanak Navab, Mojtaba Kadkhodaie, Mohammadreza Nasiri, Ameer Kian, Sahar Kian, Fateme Sheikholeslami, Karlen Shahinian, Stou Sandalski, Kyle Dolan and Sepehr Salehi who helped me in proofreading parts of this thesis. Last but not the least, I would like to thank my family. My parents, Zahra and Ali, my dear sister, Mahdieh, my lovely brother, Mahan and my beloved wife Behnaz Forootaninia who supported me in all these years with pure unconditional love and absolutely no expectation. I would not be able to complete my journey without them. This research is partially supported by National Science Foundation, NSF, under grant AST-1211595 and National Aeronautics and Space Administration, NASA.

ii Dedication

To my lovely wife Behnaz and my dear parents for their unconditional love and support.

iii Abstract

In this thesis, we studied physical and evolutionary aspects of the intergalactic medium throughout the universe. We used the archived Subaru telescope data and measured the ionization radiation escape fraction of 207 Lyα emitting galaxies at z ' 3.3 in the SXDS field which does not contain any known overdensity region. Our stacking analysis enabled us to put strong limits on the IGM-absorption-corrected UV–to–LyC flux ratio > 13.8 (3σ). The average ionizing radiation relative escape fraction is LyC fesc,rel < 20% (3σ), assuming an intrinsic FUV/FLyC = 3. These limits indicate that the cluster and field populations of Lyα emitters show different properties in their ionizing emissivity. In chapter3, we study the influence of the intervening IGM on depolarizing the synchrotron radiation of radio galaxies. We combined observations of the NVSS at 1.4 GHz and the S-PASS at 2.3 GHz for 533 extragalactic radio sources with total intensity I2.3 > 420 mJy. We found that fractional polarization, π, depends on the source magnetic field disorder, spectral index, size and depolarization. The relationship between the latter three shows that depolarization occurs primarily in the source vicinity. The intrinsic magnetic field disorder is the dominant mechanism responsible for the low π of radio sources at high frequencies. Objects with

π1.4 ≈ π2.3 ≥ 4% typically have simple Faraday structures and therefore, are most useful for studying foreground Faraday screens. At the end, we present deep and high-resolution L-band VLA observations of diffuse radio relics and filaments in the ICM of Abell-2255 merging galaxy cluster. We discovered three thin filaments close to the X-ray center of the cluster and at the tip of the tails of two radio galaxies. The spectral analysis of two filaments suggest that the responsible seed electrons belong to the tail of the same galaxy and have experienced an adiabatic compression due to a passing weak shock with

iv Mach number M ∼ 1.1. We discovered two substructures and a new relic in the southern part and west of the NE relic. In addition, the alignment of three sources, C1, C2 and the Bridge suggests they might be remnants of a giant radio galaxy.

v Contents

Acknowledgementsi

Dedication iii

Abstract iv

List of Tablesx

List of Figures xiii

1 Introduction1 1.1 Diﬀuse intergalactic medium...... 1 1.2 Ionization history of the IGM...... 3 1.2.1 First stars and start of reionization era...... 4 1.2.2 First galaxies and their available ionizing budget...... 4 1.2.3 Completion of the IGM reionization...... 6 1.2.4 Ionization bubbles and HII regions...... 8 1.2.5 Photoionization and recombination equilibrium...... 10 1.2.6 Stromgren radius...... 12 1.3 Inﬂuence of IGM on polarization of background radio galaxies.. 14 1.3.1 Spectrum of synchrotron radiation...... 15 1.3.2 Polarization of synchrotron radiation...... 18 1.3.3 Stokes parameters...... 19

vi 1.3.4 Faraday screens and rotation of the polarization angle.. 21 1.3.5 Depolarization of synchrotron radiation...... 23 1.4 The intracluster medium in merging systems...... 25 1.4.1 The ICM weather and its synchrotron features...... 26 1.4.2 Lifetime of ultra relativistic Cosmic ray electrons..... 29 1.4.3 Merger shocks and Re-acceleration of electrons...... 30 1.4.4 Seed electrons...... 31

2 Ionizing emissivity from galaxies at z ∼ 3: diﬀerences in ﬁeld versus cluster galaxy populations 33 2.1 Introduction...... 33 2.2 Overall strategy...... 36 2.2.1 Observations and data reduction...... 37 2.2.2 Flux measurement...... 41 2.3 Selection of Lyα–emitters...... 42 2.4 Results...... 47 2.4.1 Number density of Lyα emitters in SXDS...... 47 2.4.2 Observed ionizing emissivity...... 49 2.5 Escape fraction of ionizing radiation...... 50 2.6 Stellar mass distribution...... 52 2.7 Discussion and Conclusions...... 53

3 Magnetic ﬁeld disorder and Faraday eﬀects on the polarization of extragalactic radio sources 68 3.1 Introduction...... 69 3.2 Observations...... 72 3.2.1 The 2.3 GHz Data...... 72 3.2.2 The 1.4 GHz Data...... 73 3.3 Creating the new sample...... 74 3.3.1 Cross-matching and selection criteria...... 74 3.3.2 Derived quantities...... 75

vii 3.3.3 Selection Bias...... 82 3.3.4 Statistical tests...... 83 3.4 Results...... 84 3.4.1 Rotation measures...... 87 3.4.2 Distribution of fractional polarization and depolarization. 87 3.4.3 Total intensity and fractional polarization...... 91 3.4.4 Correlation between RRM, ∆RM, π and D ...... 92 3.4.5 Polarization, depolarization and the object angular extent 93 3.4.6 Spatial distribution of depolarization in the sky...... 94 3.4.7 WISE colors and polarization...... 110 3.4.8 Redshift Dependence...... 111 3.4.9 Summary of major results...... 113 3.5 Discussion...... 115 3.5.1 Radio source ﬁeld disorder...... 115 3.5.2 Prospects for high frequency surveys...... 116 3.5.3 Prospects for RM grid experiments...... 117 3.5.4 Origins of depolarization...... 117 3.5.5 Redshift Evolution...... 120 3.6 Conclusions...... 123

4 Abell 2255 Galaxy Cluster 127 4.1 Introduction...... 127 4.2 Deep Very Large Array L band observation...... 129 4.2.1 Data reduction and calibration...... 131 4.2.2 Polarization Calibration...... 132 4.2.3 Self Calibration and Imaging...... 133 4.3 Results...... 135 4.3.1 Total intensity morphology of relics and ﬁlaments..... 135 4.3.2 Spectral analysis...... 149 4.3.3 Faraday Synthesis Analysis...... 157

viii 4.4 Discussion...... 166 4.4.1 The origin of ﬁlaments and relics in A2255...... 166 4.4.2 A2255 ICM Faraday structure...... 167

5 Summary and future work 169

References 174

ix List of Tables

2.1 Properties of the used data in U, B, V, IB527 and IB383 bands.. 39 2.2 Properties of the Sup-Cam and LFC stacked images...... 42 2.3 Average properties of LAEs...... 46 2.4 Photometry in the LyC stacked image...... 50 2.5 Lyα emitter candidates from category A. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux...... 61 2.5 Lyα emitter candidates from category A. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux...... 62 2.5 Lyα emitter candidates from category A. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux...... 63

x 2.5 Lyα emitter candidates from category A. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux...... 64 2.6 Lyα emitter candidates from category B. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux...... 65 2.6 Lyα emitter candidates from category B. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux...... 66 2.6 Lyα emitter candidates from category B. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux...... 67 3.1 Description of the entries in the online catalog...... 85 3.1 Description of the entries in the online catalog...... 87 3.2 Results of non-parametric statistical tests with simulated p-values. 95 3.2 Results of non-parametric statistical tests with simulated p-values. 110 4.1 Summary of the VLA L band observation of A2255...... 130 4.2 A2255 VLA L band total intensity and spectral maps...... 134

xi 4.3 Spectral index of relics and ﬁlaments in A2255...... 155 4.4 Bright polarized features in A2255...... 162

xii List of Figures

1.1 Evolution of the Lyα forest and the IGM absorption features is shown for multiple galaxies in redshift range of 0.16 < z < 6.29..9 1.2 Emission cone of a relativistic electron in two parts of its curved trajectory around the magnetic ﬁeld, borrowed from (1)...... 16 1.3 Theoretical synchrotron proﬁle of a homogenous cylindrical source

in units of frequency ν1 is shown. The optical depth τν1 = 1, borrowed from (2)...... 18 1.4 Theoretical synchrotron total intensity and fractional polarization proﬁles for a cloud of electrons with similar energies and a uniform distribution of pitch angles is shown, borrowed from (3)...... 20 1.5 Left: Our new high-resolution VLA observation of Abell 2255 galaxy cluster at the wavelength of 21 cm (magenta) on top of the Dutch Westerbork image at the wavelength of 85 cm (blue,4). Exam- ples of radio ﬁlaments and relics in the ICM of the merging cluster are shown with solid yellow lines. Right: Optical SDSS image of galaxies at the central region of the cluster...... 28

xiii 2.1 Throughput functions of the LFC IB383 (purple) and Sup-Cam U (cyan), B (blue), IB527 (orange), V (red) and R (brown) bands. The vertical dashed line represents the location of Lyman continuum limit for a spectrum of a 100 Myr old galaxy with constant −1 SFR= 2 M yr and 0.2 solar metallicity at z = 3.3 extracted from (5) library. We manually have added a Lyα emission line to the spectrum for presentation purposes...... 40 2.2 Lyα emission line EW inferred from the IB527−V color is shown as a function of the IB527 total magnitude. LAE candidates in groups A and B are shown with red and cyan bullets. Orange solid lines represent the running median and 0.05 percentile of the EW distribution in each magnitude bin (see text for details). Black solid lines are the best fit to the 0.05 percentile and its mirror image with respect to the median values (the latter is used for the selection of the emission line objects, and is different from 99.95 percentile). The dashed green line shows the equivalent EW= 108A˚ cut.... 47 2.3 Observed EW versus B − V color. LAEs in Groups A and B are shown with red and cyan bullets. The solid vertical green line shows our color cut at B − V = 0.48, and horizontal dashed line is the cut on EW= 108A.˚ ...... 48 2.4 IB527, B and V magnitude distribution of LAE candidates. Blue solid line represents all LAEs while LAEs in group A are shown by red line...... 56 2.5 Distribution of Lyα emission line flux (top), and observed equivalent width (bottom) in our LAE candidate samples. Blue solid line represents all of the LAEs while the red line is only objects in group A...... 57

xiv 2.6 Distribution of R−band magnitudes (which probe the non–ionizing continuum at z ∼ 3), for the field LAEs and for the full proto- cluster sample in (6). We also show the R−band magnitude distribution for proto-cluster LAEs detected in the LyC. For reference, the vertical lines show the 3σ magnitude limits in the two bands that probe the LyC radiation. The depth of the U band is sufficient to detect the field LAEs, if their ionizing to non–ionizing flux density ratio is similar to that of LAEs in the SSA22 proto–cluster. 58 2.7 Stacked LyC image (5800 on a side) of 207 field LAEs. No significant detection is visible in the image. In the central aperture used for the computation of the mean, all 207 stamps were used. In the remaining region of the stamp, the number of stamps in each pixel ranged between 184 and 207...... 58 2.8 Distributions of the modeled stellar masses and dust extinction of the LAEs in this work (green) in comparison to (7) who studied a sample of 21 LAEs at z = 2.85 located in a galaxy protocluster

in the HS1549+1919 ﬁeld with redshift-space overdensity of δgal ∼ 5 (hatched gray). The black and green error bars represent the uncertainties derived based on the Poisson statistics...... 59

2.9 IGM corrected (FUV/FLyC)corr flux ratio versus rest–frame UV magnitude. Arrows show lower limits for the field LAEs. Solid circles show the cluster LAEs with LyC detections in (8) and Mostardi et al. (2015, galaxy MD5). We also show the limits obtained from the stacking analysis of the entire sample of field and cluster LAEs (see legend for details)...... 60 3.1 Distributions of the percentage of contamination in the NVSS total intensity, 100 × Icont , in black solid line and polarization flux Itarget density, 100× Pcont in red dashed line are shown. The catalog only Ptarget contains sources with Pcont < 0.1...... 76 Ptarget

xv 3.2 Distribution of S-PASS fractional polarization for 27 objects with

πNV < NV...... 78

3.3 The ratio of the observed and true fractional polarizations, πobs/πtrue, based on the NVSS and S-PASS bandwidth depolarizations is shown for 364 objects as a function of the cumulative percentile. Only 3% of objects in our sample experience NVSS bandwidth depolariza-

tion which results in πobs/πtrue smaller than 0.9...... 80 3.4 Distribution of spectral indices,α, calculated based on NVSS and S-PASS total intensities. The median spectral index isα ¯ ≈ −0.83. 81 3.5 Distribution of log(D) (top) and 2.3 GHz fractional polarization π (bottom) of objects with Pcont < 0.1 and 0.1 ≤ Pcont < 0.25 SP Ptarget Ptarget are shown with solid and dashed lines respectively. Black, red and blue colors represent objects with detection, upper limits in S-PASS and upper limits in NVSS polarizations. The area under the log(D) histogram of objects with Pcont < 0.1 and detected polarization ﬂux Ptarget densities is colored in gray for clarity...... 86 3.6 Top: The distributions (top) and the scatter diagram (bottom) of

the NVSS, S-PASS rotation measures, RMNS versus TSS09 RMT for the 364 common objects. The three red solid lines in the bottom show one-to-one relations for the three cases of n = [−1, 0, 1].... 96 3.7 Normalized histograms of fractional polarizations, π, for 416 objects with detected polarization in both NVSS and S-PASS and the upper limits. The black and red solid lines represent the NVSS and S- PASS distributions of objects with detected polarizations while the dashed blue and red lines sketches the distribution of upper limits of NVSS and S-PASS polarizations. For comparison we also show the NVSS fractional polarization distribution of the TSS09 catalog 37543 sources with dotted-dashed magenta line...... 97

xvi 3.8 Distributions of log(D) normalized to the total number of objects for steep (top) and ﬂat (bottom) spectrum sources. Black solid histogram represents objects with detected polarization in both NVSS and S-PASS. The red histogram with dashed line is the distribution of the upper limits in depolarization. The lower limits are shown with dotted-dashed blue line. The two red and blue arrows show the direction of movement for the upper and lower limits..... 98 3.9 Distribution of the polarization spectral index β as introduced in (9) assuming a power law depolarization model. The solid blue and dashed red lines represent the steep and ﬂat spectrum sources.. 99 3.10 Spectral index distribution of the re-polarized objects, D < 0.6,

including 24 sources with detection in πNV but only upper limits

on πSP. While it seems there are two separate populations of re- polarized sources with ﬂat and steep spectrums, the majority of them, 61%, have α ≥ −0.5...... 100 3.11 S-PASS fractional polarization versus log(D). The red solid line

represents the running median of πSP calculated in bins of N = 30 objects in log(D) space and the dark-pink shaded region is the estimated uncertainty on the running medians calculated as |M − [p16, p84]|/p(N) where M is the median value and [p16, p84] are the 16 and 84 percentiles. The error bars on the left and right

upper corners are the medians of the intrinsic uncertainties in πSP for the two half of data in log(D)...... 101 3.12 Normalized S-PASS (upper) and NVSS (lower) fractional polarization distribution for objects with | log(D) < 0.23| (solid black), log(D) > 0.23 (dashed red) and log(D) < −0.23 (dotted-dashed blue)...... 102

xvii 3.13 S-PASS fractional polarization of only steep spectrum(α < −0.5) versus their total intensity. The open circles represent the upper limits on the degree of polarization. The black solid line is the

running medians of πSP including the upper limits and the dark- pink shaded region is the estimated uncertainty on the running medians. The red error bars in upper right and left corners show

the median intrinsic uncertainties of πSP for the two half of the data in log(I) space...... 103 3.14 Absolute diﬀerence between rotation measures calculated in this work and in TSS09, |∆RM| versus | log(D)|. Black and green crosses represent depolarized and re-polarized objects respectively. The solid red line is the running median of |∆RM| calculated for bins of 23 objects in | log(D)| space which include both depolarized and re-polarized sources and the dark-pink shaded region is the estimated uncertainty on the running medians. The error bars on the left and right upper corners are the medians of intrinsic uncertainties in |∆RM| for the two halves of the data...... 104

shows an increase with raising |RRMT|. The dark-pink shaded region is the estimated uncertainty on the running medians..... 105 3.16 S-PASS fractional polarization versus the |∆RM| which is a representation of the Faraday structure...... 106 3.17 The | log(D)| distributions of the unresolved (black solid) and extended (dashed red) steep spectrum objects in the NVSS survey. The de-convolved surface area thresholds log(A) ≤ 2.5 arcsec2 and log(A) > 2.5 arcsec2 are used to separate unresolved and extended sources, and the two vertical blue solid and dashed lines represent the medians of | log(D)| for the two samples respectively..... 107

xviii 3.18 The πSP distributions of the unresolved (black solid) and extended (dashed red) steep spectrum objects in the NVSS survey. The deconvolved surface area thresholds log(A) ≤ 2.5 arcsec2 and log(A) > 2.5 arcsec2 are used to separate unresolved and extended sources, and the two vertical blue solid and dashed lines represent the me-

dians of πSP for the two samples respectively...... 108 3.19 Distribution of the 533 objects in the sky, color coded with the depolarization. l and b are the Galactic longitude and latitude coordinates in degrees. Black dots are objects that are not detected in either NVSS or S-PASS polarization. Green, red and blue triangles are objects with depolarization 0.5 < D < 2, D > 2 and D < 0.5 respectively...... 109 3.20 Distribution of objects with steep, α < −0.5 and ﬂat, α ≥ −0.5 spectral indices in the WISE color-color diagram...... 111 3.21 Redshift distribution of the matched radio sources with (10) catalog. Histograms of steep (α < −0.5) and ﬂat (α ≥ −0.5) spectrum sources are shown in dashed blue and dotted-dashed red lines... 112

3.22 Top: Fractional polarizations at 1.4 GHz, πNV, of depolarized steep spectrum sources with D ≥ 1.5 versus redshift. Bottom: depolarization, D, of the same sample of sources versus redshift. The

solid red lines represent the running medians of the πNV (top) and D (bottom) in bins of redshift. The green dotted, dashed blue and purple dashed-dotted lines are representations of the following three cases with B66 depolarization models: 1. A depolarizing screen located at the redshift of the source, 2. Combination of two depolarizing components, one Galactic and one at the redshift of

the source, and 3. An evolving σφ at the depolarizing screen at the source redshift...... 125

xix 3.23 Distribution of the |RRM| for the 206 objects is plotted versus redshift, z. Blue and red crosses represent objects with α < −0.5 and α ≥ −0.5. The solid black line shows the running medians of the |RRM| of all sources. The orange filled circles are the data points extracted from Figure 3 of (11) as discussed in Section 3.5.5. Each circle represents the median value of their |RRM| for each redshift bin...... 126 4.1 The primary beam uncorrected L band image of our central observation point of the A2255 galaxy cluster (synthesized FWHM≈ 4.6 arcsec and rms= 3.6µJy beam−1) with B+C antenna configurations. The galaxies and diffuse structures names are adopted from (4; 12). The center of the image is not the phase center of the observation...... 136 4.2 The primary beam uncorrected L band image of our northern observation point of the A2255 galaxy cluster (synthesized FWHM≈ 5.6 arcsec and rms= 3.2µJy beam−1) with B+C antenna configurations. The galaxies and diffuse structures names are adopted from (4; 12). The location of the new diffuse structure is shown and labeled as NW3 Relic...... 137 4.3 The gray scale zoomed and uv tapered (9.5 arcsec beam) VLA L band image of the new NW3 diffuse structure at ∼ 190 to the west of the NE relic knee. The NW3 diffuse emission seems to have at least two separate components in our maps and the total extent of the structure is ∼ 80 which corresponds to ∼ 740 kpc at the redshift of the cluster...... 138

xx 4.4 The VLA L band total intensity image of the central halo and rectangular relic-like structures of A2255. To show the compact structures and diffuse emissions in one map the high resolution image (3.7 arcsec beam) with only B antenna configuration is overlaid on top of the uv tapered (8 arcsec beam) image with B+C antenna configurations. The new thin filaments located at the southern edge of the halo are also shown and labeled with TRG-F1, TRG-F2 and Sidekick-F...... 140 4.5 The L band total intensity map of the NE relic with its northern, NE-N and southern, NE-S components, and the Bridge, C1 and C2 diffuse emission regions are shown. The high resolution image (3.7 arcsec beam) with only B antenna configuration is overlaid on top of the uv tapered (8 arcsec beam) image with B+C antenna configurations. The dashed box shows the region used to calculate average flux density profile across the minor axis of the relic as shown in Figure 4.6...... 142 4.6 The average flux density as a function of RA and DEC across the minor axis of NE-S relic. The dashed box in Figure 4.5 shows the region used to measure the flux densities used to produce this diagram...... 143 4.7 Zoomed VLA L band image (4.6 arcsec beam) of the Bridge diffuse emission is shown. The morphology and the light profile of the Bridge suggest an structure like a bubble, similar to the lobes of radio galaxies. The two rectangular slices are used to calculate the average light profile along the major axis of each region as shown in Figure 4.8...... 144 4.8 The average flux density profile of the Bridge diffuse emission along rectangular slices in NW-SE (left) and NE-SW (right) directions.The two rectangular regions used to calculate the average light profiles are shown in Figure 4.7...... 145

xxi 4.9 The zoomed and uv tapered (9.5 arcsec beam) VLA L band image of the NW1 and NW2 relics at ∼ 2.45 Mpc and ∼ 2.3 Mpc in projection from the cluster X-ray center. The NW2 relic seems to have at least two separate filamentary structures in our maps... 146 4.10 a: VLA high resolution (3.7 arcsec beam) L band image of the Original TRG and Sidekick radio galaxies is shown in blue. The optical image retrieved from the Digital Sky Survey is also overlaid in red. b: The VLA wide L band spectral map of the Original TRG and Sidekick radio galaxies is shown and color coded...... 148 4.11 Top: VLA L band spectral image (B+C configuration, 4.6 arcsec beam) of the Original TRG and Sidekick radio galaxies as well as their filaments. The three boxes used to calculate the median spectral indices for the TRG-F1 and TRG-F2 filaments are shown

with black-dashed lines. The values of αmed are labeled on top of each box. The three white boxes are used to measure the spectral index profile along the tail of the Original TRG. Bottom: The L band spectral index spatial profile along the tail of the Original TRG and the best fit line are shown in blue and green respectively. The red bullet represents the average spectral index of the TRG-F1. 151 4.12 a: VLA high resolution (3.7 arcsec beam) L band image of the Goldfish radio galaxy is shown in blue. The optical image retrieved from the Digital Sky Survey is also overlaid in red. b: The VLA wide L band spectral map of the Goldfish radio galaxy and its long tail is shown and color coded...... 152 4.13 a: VLA high resolution (3.7 arcsec beam) L band image of the Beaver radio galaxy is shown in blue. The optical image retrieved from the Digital Sky Survey is also overlaid in red. b: The VLA wide L band spectral map of the Beaver radio galaxy is shown and color coded...... 153

xxii 4.14 a: VLA high resolution (3.7 arcsec beam) L band image of the Em- bryo radio galaxy is shown in blue. The optical image retrieved from the Digital Sky Survey is also overlaid in red. b: The VLA wide L band spectral map of the Embryo radio galaxy and its collimated jets and lobes are shown and color coded...... 154 4.15 The VLA L band total intensity maps (15 arcsec beam) of the central and northern regions of A2255 are shown. The dashed magenta boxes represent regions that are used to calculate the spectral indices of relics between L band observation and the WSRT map in 85 cm...... 156 4.16 The L band spectral index of the TRG-F1 ﬁlament, the Bridge, central region of the NE relic, the northern part of the NW1 relic and southeastern part of NW2 relic are plotted against the estimated spectral index between our VLA 20 cm and WSRT 85 cm maps. Black and red solid lines represent the theoretical synchrotron emission spectral energy distribution for a simple power law model and the JP model (low frequency index of -0.5, 13) that takes into account the aging of the electrons population...... 157 4.17 The weighting of each channel used in Faraday synthesis for two sources A (solid ) H (the Original TRG, dashed). (Procedure for determining weights and the reason for the diﬀerences between the two are discussed in the text.)...... 159 4.18 The Faraday transfer function for two sources (A left, Original TRG right)...... 159

xxiii 4.19 Polarization results for sources A, Embryo, Goldfish and Origi- nal TRG from top to bottom. Left: Total intensity contours at 8 arcsec resolution with polarized intensity (the peak amplitude in the Faraday spectrum) in grayscale, at 7.5 arcsec resolution. Mid- dle: Brightness is polarized intensity (as on the left). Color is the Faraday depth (rotation measure) of the peak in the Faraday spectrum, with the color code at the bottom. Right: The cleaned Faraday spectrum at the position of the peak polarized intensity, using a 125 rad m−2 restoring Faraday beam...... 161 4.20 The Faraday amplitude is plotted versus the Faraday depth. Each data point represent a pixel in the our polarization maps. Three A2255 radio galaxies, Embryo, Original TRG, the Goldfish and a background radio source with double lobes are used to generate this plot...... 163 4.21 Faraday spectrum of the Goldfish (left) along the direction shown in the intensity image (right) is plotted...... 165

xxiv Chapter 1

Introduction

1.1 Diﬀuse intergalactic medium

Structure formation in our universe has started a little after the big bang and is still continuing. The current universe contains hundreds of billions of galaxies in which there are billions of stars. The environment between galaxies is also full of mass in both forms (dark matter and baryons) and therefore is subject to evolution through cosmic time and is under the influence of astrophysical feedback processes. The exact definition of the diffuse intergalactic medium (IGM) is not clear due to the smooth transition from the dense interstellar medium (ISM) to the outer regions of the galaxy and toward the low density IGM. One definition adopted by e.g. (14) considers the medium beyond the virial radius of the galaxies and clusters as IGM. This definition of the IGM takes into account the dark matter halo of the gravitationally bound systems instead of only the apparent edge of galaxies. Most of our knowledge about the IGM chemical composition comes from the absorption line features of neutral atoms of H, He and heavier metals imprinted in the spectrum of distant galaxies and quasars. The discrete distribution of these random features implies that the gas density in the IGM is not homogenous but rather clumpy. The IGM contains random over dense clouds of gas with varying

1 2 physical parameters (e.g. metallicity, density and temperature). The discrete absorption features are more common in the spectrum of high redshift quasars, suggesting an evolution in the number density of neutral atoms in the IGM. In fact, we know the early universe was filled with neutral gas and should have gone through a phase transition to ionized state (Reionization epoch). Planck CMB observations and measurements of the IGM Thomson scattering optical depth +1.7 predicts the peak of the reionization process should have happened at z = 8.8−1.4 (15). The IGM at the current time is hot (T > 105K) and almost fully ionized. The average number density of particles is very small due to cosmic expansion 1 but the typical metallicity (∼ 3 solar) is much higher than the IGM at higher redshifts (∼ 10−3 solar). The high temperature and metallicity, especially in the environment of galaxy clusters are mainly the result of structure formation and feedback processes. Shocks related to high energy events such as super nova explosions, galaxy mergers and powerful outflows of AGN jets are examples of some of the astrophysical phenomena that inject energy and metals into the IGM. Observing the IGM at z ≤ 1 through absorption or emission lines is an incred- ibly hard task. Combination of the small number densities and high temperatures leave all the metals in their high ionization state. However, in over dense and hot environment of galaxy clusters, diffuse thermal X-ray and synchrotron radio emission of plasma particles in large scales provide powerful observational tools for studying the IGM. X-ray observations can be used to extract valuable information about the average temperature, density and global dynamics of the cluster. In addition, in presence of magnetic field, plasma electrons emit non-thermal synchrotron radiation which can be observed in radio frequencies. The degree of polarization and brightness of synchrotron radiation at different frequencies are related to the local magnetic field and energy distribution of the plasma electrons. IGM non-thermal diffuse emission provides insight about the strength and direction of the cluster magnetic field and global or local dynamical processes such as mergers shock waves and turbulence. Moreover, the influence of the intervening 3 IGM clouds of magnetic plasma on the synchrotron polarization signal of background radio galaxies through means of Faraday rotation also enables us to study the magnetic field and electron density of the IGM. In this thesis, we look at the IGM history and study sources that might be responsible for ionizing the universe. More specifically, we try to measure the amount of ionizing radiation that could escape from the interstellar medium of the candidate star forming galaxies and penetrate the IGM at the epoch of reionization. Then, we change our perspective and investigate the average influence of the ionized IGM on the observed linear polarization of radio galaxies by studying depolarization mechanisms related to the intervening Faraday screens. At the end, we focus on the weather of the intracluster medium of the merging galaxy cluster Abell 2255 and study large scale diffuse non-thermal radio emissions observed in its IGM. In the next following sections, we cover some of the most important background material related to the physics of the IGM and the research presented in this thesis.

1.2 Ionization history of the IGM

The physical properties of the IGM and its evolution are strongly linked to the structure formation in the universe and mutual interactions of the IGM with galaxies and quasars. The emerge of the IGM can be traced all the way back to when the universe was roughly 400,000 years old (z∼ 1100), the era of the last surface scattering. In that time, the cosmic microwave background (CMB) photons decoupled from the baryons and started to travel freely across the expanding universe, allowing the baryons to cool down due to the adiabatic expansion of the universe. As a result, electrons and protons recombined to form the ﬁrst atoms of Hydrogen. The post-recombination universe was cold, opaque and ﬁlled with neutral atoms of Hydrogen. The era between 1100 < z < 20 is called ”dark ages” since the only observable radiation from that epoch is the Hydrogen faint 21 cm 4 spin emission line, which is impossible to observe with current instruments. Hope- fully, future radio interferometers such as the Square Kilometer Array (SKA) will shed light on the physics of the dark ages by detecting the 21 cm emission from that era.

1.2.1 First stars and start of reionization era

The collapse of cool baryons into primordial density fluctuations gravitational well should have eventually given rise to the birth of the first (popIII) massive stars. These stars are thought to have formed inside the first mini halos with 5 7 total mass of 10 -10 M . Soon enough, the hard ionizing radiation (photons with energies larger than 13.6 eV corresponding to wavelengths shorter than the Lyman continuum limit, λ ≤ 912A)˚ of popIII stars would start to ionize the surrounding medium by breaking the bond between electrons and protons of the neutral atoms of Hydrogen. As a result, small ionized bubbles formed around the first generation stars. The size of these bubbles is a function of the luminosity of central stars and the amount of ionizing budget they emit as well as the recombination rate of free electron and protons and the cooling processes in place. PopIII stars were the first astrophysical sources that started the process of reionizing the IGM. However, they never could produce enough radiation budget to complete it. The lifetime of popIII stars was on the order a few to several million years. The direct outcome of their death, mostly through the super novae events, was enrichment of the IGM with heavier metals. Therefore, the second generation stars were formed from gas with higher metallicity and were less massive with longer lifetime than popIII stars.

1.2.2 First galaxies and their available ionizing budget

5 7 Small halos with masses of 10 -10 M probably could only host a few popIII stars. On the other hand, through the hierarchical structure formation in the evolving 8 universe, larger dark matter halos with masses greater than 10 M were formed 5 later in time at z ∼ 10. The sustainable star formation in these halos is the reason that first galaxies could host thousands and millions of stars. Although, on average stars in first galaxies were less massive and less luminous than popIII stars, especially in hard UV ionizing range of the spectrum, the total ionizing budget produced by these galaxies were by far more than popIII stars. Therefore, they are considered to be the best candidate sources responsible for reionizing the IGM neutral Hydrogen atoms and making the universe transparent as we see it today. Although the big picture of the reionization theory seems to be forming, the details are still a mystery. One of the most uncertain parameters in these theories is the fraction of ionizing radiation that can escape from the ISM of first galaxies and penetrate the IGM, fesc. The ISM of star forming galaxies is filled by dust, molecular and neutral clouds of Hydrogen, Helium and heavier metals. There- fore, the ionization radiation of stars in first galaxies is prone to absorption and scattering processes and might never reach the IGM. From observational point of view, measuring the characteristic value of fesc for first galaxies is extremely hard. Detecting the extremely faint emission of galaxies at reionization era when a large portion of the universe is still filled with neutral gas is an extremely hard task. Despite large campaigns, only handful of galaxies at the reionization era and beyond are detected and confirmed by Hubble space telescope (16). Moreover, the ionizing part of the spectrum of the detected galaxies is almost fully absorbed by the neutral IGM surrounding them. The next best solution for constraining parameters related to the ionizing budget of first galaxies and their escape fraction is to study star forming galaxies at later epochs but still close to the reionization era. For example, star forming galaxies at z ∼ 3 resemble their older ancestors but they live in a universe with ionized and transparent IGM. Ground based telescopes have the potential capabilities to study the stellar properties and ionizing part of the spectrum of these galaxies. In chapter2, we will study galaxies with excess of Lyα emission line at redshift of z = 3.3 and will discuss their relative escape fraction of ionizing radiation. 6 1.2.3 Completion of the IGM reionization

The reionization of the IGM was not an instantaneous process and has lasted roughly 400 million years to be complete by redshift z ∼ 6 when the universe was about 1 Gyr old. The metal absorption features observed in the spectrum of bright distant quasars provide an extremely valuable toolbox for studying the ionization state as well as the composition of the IGM in redshift range 2 ≤ z ≤ 6.

Assuming a simple continuum spectra for a distant quasar at redshift z0, the physics of radiative transfer suggests the emitted radiation should be absorbed and scattered by the neutral atoms of Hydrogen, Helium and heavier metals at z0 ≤ z ≤ 0 along the light of sight, especially at redshifted frequencies corresponding to resonant lines in Lyman series (e.g. Hydrogen Lyα at λ0 = 1215.67A).˚ A detailed explanation of the radiative physical processes happening in the IGM can be found in (17). In summary, the general form of radiative transfer equation for photons with energy hν traveling in direction of ˆn at coordinate r and time t with intensity

Iν(r, t, ˆn) is as following:

1 ∂I (r, t, ˆn) ν + ˆn.∇I (r, t, ˆn) = −α (r, t, ˆn)I (r, t, ˆn) + j (r, t, ˆn) (1.1) c ∂t ν ν ν ν where αν = ρ(r, t)κν(r, t, ˆn) + n(r, t)σν(r, t, ˆn) is the attenuation coeﬃcient and jν is the emission coeﬃcient related to any other radiation source term. For simplicity and for the case of only one background quasar we can assume jν = 0. The attenuation term is a linear superposition of the absorption and scattering terms where ρ is the mass density of particles, κν is the absorption cross section, n is the number density of particles and σν is the scattering cross section. The IGM observed absorption features such as Lyα forest arise from scattering the resonance line photons of the background source. In case of a static scatterer,

σν,L is given by Lorentz profile. However, in reality, the IGM atoms can hardly be described as static. They mostly experience thermal motions due to temperature T as well as ordered flow with fixed velocity or complicated micro-turbulent motions due gravitational infall and shocks. Considering a simple scenario of only 7 thermal motion with Maxwellian distribution results in changing the scattering cross section profile from Lorentz to a convolution of Lorentz profile and Voigt function Φ as following:

Γ Γ Z +∞ exp(−y2) Φ( , x) = ( 2 ) dy 2 2 (1.2) 4πνD 4π νD −∞ (x − y) + (4πνD)

1 σν = σν,L √ Φ, (1.3) πνD where Γ is the damping width related to the electron’s transition between energy q b 2kB T levels, νD = ν c is the Doppler width at frequency ν and b = m is the thermal component of the Doppler parameter, kB is the Boltzman constant and m is the mass of the scatterer particle. Solving for equation 1.1 results in

a(t )3 I (ˆr, t) = I ( ˆr , t ) 0 exp(−τ ) (1.4) ν ν0 0 0 a(t) ν

Z r0 0 0 0 τν = dr n(r , t )σν0 , (1.5) r where a is the cosmological scale factor and τν is the total IGM optical depth at frequency ν between locations r0 and r along direction ˆn. Therefore, the intensity of the emitted radiation at frequency ν0 from the background quasar at r0 and time t0 would be attenuated by a factor of exp(−τν) when observed at time t, location r and frequency ν. This attenuation is due to existence of discrete clouds of gas with number density of scatterers n(r0, t0) at locations r0 and time t0 where 0 0 0 r0 < r < r, t0 < t < t and ν < ν < ν0. This results in forest of absorption features in the observed spectrum of distant galaxies and quasars as shown in Figure 1.11. At large redshifts, almost all of the radiation emitted at rest frame wavelengths λ ≤ 1216A˚ is absorbed by the optically thick IGM, resulting in the Gunn-Peterson trough (18) in the spectrum of distant quasars. Using the latter, it

1http://www.ast.cam.ac.uk/~rfc/ 8 is possible to estimate when the reionization of the IGM is complete and universe is almost fully ionized. To understand the underlying physics of reionization, in the following sections, we will review some of the important physical processes that happen in a simple case of ionization of an HII region in interstellar medium with a central source of radiation. This simple representation, with minor modiﬁcation, can also be applied to the IGM of the early universe when star forming galaxies were the source of heating and ionization.

1.2.4 Ionization bubbles and HII regions

In the interstellar medium, the ionizing radiation field of OB association stars ionizes neutral hydrogen atoms and generates the so-called classical HII region, which is predominantly composed of protons and electrons. The size of an HII region depends on the gas cloud density and the intensity of the radiation field. Energetic photons from stellar clusters are able to penetrate deep into low density gas clouds (with a density of only a few particles per cubic centimeter) and expand the HII regions to radii on the order of hundreds of light years. In higher density clouds (∼ 106cm−3), however, the mean free path of ionizing photons is much smaller and the size of the HII regions decreases to a few light years. The size of an HII region is well defined because the transition from ionized to neutral hydrogen zones is sharp. Photoionization and recombination of atoms are the two main processes that occur in the ionizing bubble around the central source. In the equilibrium condition, the rate of photoionization processes per volume must be equal to the rate of recombination. The balance between photoionization and recombination de- termines the physical properties of the bubbles. The number densities of neutral atoms, photoelectrons and ions, as well as the temperature and physical extent of the region can all be calculated under the ionization equilibrium condition. 9

Figure 1.1 Evolution of the Lyα forest and the IGM absorption features is shown for multiple galaxies in redshift range of 0.16 < z < 6.29. 10 There are multiple mechanisms that cool the gas cloud in HII regions. Re- combinations of electrons and ions, continuum Bremsstrahlung radiation and collisional excitation of metals and ions play roles in the total energy loss from HII clouds. As the universe evolves, the IGM contains more metals and is hotter, and therefore collisional excitation of heavier atoms and ions becomes more efficient. During ionization, the excess energy of the photon is given to the electron in the form of kinetic energy. Collisions between free electrons and ions distribute the kinetic energy among all particles and maintain a Maxwellian velocity distribution. Hydrogen and Helium in neutral and ionized forms are the dominant elements in HII regions. The first excited levels of H and He have energies of ∼ 10 eV , which is more than the average thermal electron’s kinetic energy. As a result, collisional excitation is very inefficient for H and He atoms.

1.2.5 Photoionization and recombination equilibrium

For a simple case of a pure hydrogen cloud in the equilibrium condition, the rate of photoionization from the ground state and the total recombination rate to all energy levels are equal as is represented in the following relation:

Z ∞ 4πJν n aνdν = npneαA(Te). (1.6) ν912 hν

The left hand side of the above equation is the volumetric photoionization rate in a medium with hydrogen atoms with number density n and mean radiation intensity R Iν dω Jν = R dω , where ω is the solid angle and Iν is the brightness of the radiation field at that point. The parameter aν is the cross section of the atom to be ionized by a photon with energy of = hν. The right side of equation 1.6 represents the total volumetric recombination rate in a gas cloud with the proton and electron number densities of np and ne, respectively. The expression αA(Te) is the recombination coefficient for a Maxwellian distribution of electrons with average temperature of Te. The expression αA(Te) contains recombination of all energy levels. All recombinations to the ground level are followed by emission of a Lyman continuum 11 photon, which can be absorbed by another atom in dense environments. Therefore, it is a valid assumption that recombination to the ground state has no effect on the overall ionization balance. For simplicity, we assume that all radiation comes from a central stellar source and ignore the diffused radiation field in the HII region. The flux of photons with energy = hν at distance r from the central source can be written as 4πJ L /hν ν = ν (1.7) hν 4πr2 where Lν is the luminosity density of the source. For a pure hydrogen cloud in ionization equilibrium, the electron and proton number densities are equal and can be written in terms of the neutral hydrogen number density. For simplicity, we introduce the dimensionless parameter X as following:

n X = e (1.8) n

The ionization fraction is deﬁned as

n X ξ = e = . (1.9) ne + n 1 + X

By deﬁnition, fully ionized gas clouds have ξ = 1. Using equations 1.7 and 1.8 we have: Z ∞ Lν 2 2 n 2 aνdν = X n αA(Te) (1.10) ν912 4πr hν The ionization and recombination time scales can be calculated as follows:

1 trec = (1.11) neαA

1 tion = . (1.12) R ∞ Lν 2 aνdν ν912 4πr hν 12 In the case of a pure hydrogen cloud in ionization equilibrium, one can use equations 1.6 and 1.8 and derive the relation between the two time scales:

trec = Xtion (1.13)

1.2.6 Stromgren radius

In 1939, Bent Stromgren studied the ionization of hydrogen around a central source within a perfectly spherical geometry. The Stromgren radius R is deﬁned as the distance from the central source where the transition from fully ionized hydrogen to neutral hydrogen occurs. In other words, R is the radius of a spherical volume in which all of the ionizing photons are absorbed. Inside this volume, the gas is highly ionized and ne = np ≈ ne + n. Outside of this volume, ne = np ≈ 0. In optically thick nebulae, hydrogen atoms in the surrounding medium absorb all of the stellar ionizing photons. The total number of ionizing photons emitted per second from a central stellar source with Planck black body spectrum can be calculated as Z ∞ L Q = ν dν . (1.14) ν912 hν To ﬁnd the volume of the region in which all of the ionizing photons are absorbed, one can integrate the volumetric recombination rate relation over a volume. So, the total number of recombination processes is equal to Q. Z 2 4π nenpαAr dr = Q (1.15) r

Using the relation ne = np = Xn for pure hydrogen cloud and assuming X = 1 or ξ = 0.5, the Stromgren radius is equal to

1 3Q 3 R = 2 . (1.16) 4πn αA 13

For a star with T = 45, 000K and R∗ = 10R , the Stromgren radius is R ≈ 11.4 pc. The transition from the fully ionized regime to the neutral regime is very sharp, and therefore, ξ = 0.5 is a reasonable ionization fraction at the border of an ionizing region. In above calculations, the absorption due to the optical depth of the medium is not taken into account. The ionizing ﬂux of the central source decreases by e−τν along each optical path. The optical depth can be calculated as

Z r τν = naνdr . (1.17) 0

The more accurate way of calculating the rate of photoionization at distance r is to add the extra term e−τν to equation 1.7:

4πJ L e−τν /hν ν = ν (1.18) hν 4πr2

Therefore, the photoionization equilibrium equation changes to

Z ∞ −τν Lνe 2 2 n 2 aνdν = X n .αA (1.19) ν912 4πr hν

Integrating over a spherical volume with radius r (where τν(r) is very large) and

dτν using dr = naν gives

Z ∞ Z ∞ Z r Lν −τν 2 2 2 e dτνdν = X n αAr dr (1.20) ν912 4πhν 0 0 where Z ∞ Z ∞ −τν −τν e dτν = d −e = 1 . (1.21) 0 0 Therefore, Z ∞ L X2n2α r3 ν dν = A . (1.22) ν912 4πhν 3 Setting X = 1 or ξ = 0.5 and solving for radius, we get the same Stromgren radius as calculated in equation 1.16. 14 Unlike the simple case of an HII region in interstellar medium, the Stromgren radius of cosmological HII regions with homogenous density changes over time as a result of continuous reduction of the density of neutral particles due to cosmic expansion. The photoionization-recombination equilibrium can not be achieved at the ionization front unless it encounters an over dense region accidentally. As a result, the cosmological HII bubbles grow until they merge or the central heating source dies. More detailed explanation about the advancement of HII bubbles in the clumpy IGM can be found in (17; 19; 20; 21; 22).

1.3 Inﬂuence of IGM on polarization of background radio galaxies

An interesting aspect of the IGM is its influence on the observed properties of background galaxies and quasars. In section 1.2.3, we discussed the absorption features in the spectrum of distant quasars and galaxies as a signature of clumpy IGM with neutral gas clouds. Here, we discuss the interaction between the ionized plasma in the IGM and the synchrotron radiation of background radio galaxies and AGNs. The non-thermal continuous synchrotron emission is the result of acceleration of relativistic electrons due to the environment magnetic field. By nature, synchrotron radiation has high degree of linear polarization. However, the polarization angle and the overall degree of polarization might change when synchrotron photons travel through the internal (or intervening external) IGM plasma clouds with magnetic field (Faraday screens). In chapter3, we study and discuss the statistical role of Faraday screens in changing the polarization signal of randomly selected sample of extragalactic sources. In the following sections, we summarize the physics of synchrotron radiation to understand the observational properties of the non-thermal emission of background radio galaxies and the influence of IGM on their degree of polarization. 15 1.3.1 Spectrum of synchrotron radiation

For the case of non-relativistic electrons moving with velocity v and pitch angle φ with respect to the magnetic field B, the resulting cyclotron gyration frequency is only proportional to the strength of the magnetic field, νcyc ∝ B. The direct consequence of this proportionality relation is that for a uniform magnetic field with variation in strength, the cyclotron radiation is practically an emission line. However, variation on B can broaden the width of the line to levels that it might look like a continuum emission. Typical magnetic fields of galaxies and IGM are on the order of few to several µG and therefore the resulting cyclotron radiation will have frequencies on the order of few to tens of Hertz. It is impossible to observe such extremely low frequency radiation for multiple reasons. On the other hand, for the case of relativistic electrons, the frequency of synchrotron radiation depends on both the strength of the magnetic field B, and the Lorentz factor γ, which is a function of electrons kinetic energy. For the same

B field, the critical frequency νc of the synchrotron radiation is larger than the corresponding cyclotron emission frequency by a factor of γ2. For synchrotron radiation of a single electron, νc is where the electron emits most strongly and is proportional to the electron’s energy squared and the strength of the perpendic- 2 ular component of the magnetic field, νc ∝ E B⊥. Ultra relativistic cosmic rays and electrons with Lorentz factors γ ≥ 103 in radio galaxies can easily emit at MHz and GHz range in frequency. Figure 1.2 shows the beaming effect and emission cone of a relativistic electron in two parts of its curved trajectory around the magnetic field. In each electron cycle, the relativistic beaming effect causes the observer to only be able to see the synchrotron emission when the line of sight direction is within the emission cone. Therefore, instead of a continuum radiation in time the imaginary observer sees 1 sharp energetic pulses of emission that spans over ∆t ∝ 2 seconds and 2πγ νsycsin(φ) are separated by roughly γ seconds. Since for a relativistic plasma γ 1, 2πνsyc the width of synchrotron pulses are much smaller than the gap between them. In frequency domain the ratio between the gap and width of the spikes is ∝ γ−3 1 16

Figure 1.2 Emission cone of a relativistic electron in two parts of its curved trajectory around the magnetic field, borrowed from (1). and therefore, the synchrotron emission from a single electron is effectively continuum. Moreover, a population of ultra relativistic electrons have different kinetic energies and pitch angles. The magnetic field strength can also vary at different regions. As a result, the overall observed synchrotron radiation of radio galaxies is practically a continuum emission that spans over a wide range of frequencies. The synchrotron emission spectrum of a single relativistic electron in a uniform magnetic field can be modeled with the following relation:

√ e3Bsin(φ) ν Z ∞ pe(ν) = 3 2 K5/3(η)dη, (1.23) mec νc ν/νc where p(ν) is the emitted power per unit frequency and K5/3 is a modiﬁed Bessel function. Equation 1.23 can roughly be approximated by a power law as following:

1/3 pe(ν) ∝ ν , (1.24)

for ν ≤ νc. For the spectrum of a single electron we can claim that approximately half of the energy is emitted at frequencies smaller than νc. The overall synchrotron spectrum of astrophysical sources such as radio galaxies, radio halos and relics in merging galaxy clusters is the superposition of the emitted radiation from all the cosmic ray relativistic electrons at diﬀerent regions with varying magnetic ﬁeld strength and orientation. The spectral energy 17 distribution of astrophysical relativistic electrons present in the interstellar and intergalactic mediums can be approximated with simple power law models as following: n(E)dE ∝ E−δdE, (1.25) or equivalently n(γ)dγ ∝ γ−δdγ, (1.26)

2 where E = γmec is the total energy of the electron. The average synchrotron power radiated per electron can be written as:

2 2 2 ν < pe >∝ B γ ∝ B , (1.27) νcyc where we have assumed all of this radiation is emitted at a single frequency ν ≈ νc. The total energy radiated per unit time, per unit volume and per unit frequency can be calculated simply by multiplying the average power of a single electron by the energy distribution of the electron’s population as:

p(ν) ∝< pe > n(E)dE, (1.28)

−δ 1 ν ν 2 1 2 p(ν) ∝ B2 , (1.29) νcyc νcyc ννcyc

1−δ δ−3 2 2 p(ν) ∝ B ν 2 νcyc , (1.30) where the cyclotron frequency is proportional to the strength of the magnetic ﬁeld. Therefore, we have 1−δ δ+1 p(ν) ∝ ν 2 B 2 . (1.31)

In this work, we deﬁne the radio spectral index, α as following:

1 − δ α ≡ , (1.32) 2 18

Figure 1.3 Theoretical synchrotron proﬁle of a homogenous cylindrical source in units of frequency ν1 is shown. The optical depth τν1 = 1, borrowed from (2).

The parameter α can be measured with radio total intensity observations at minimum of two diﬀerent frequencies, assuming we target the same region of the source in each observation. The above derivation of the synchrotron spectrum is valid for thin plasma with optical depth τν 1. However, in optically thick regions the synchrotron self-absorption dominates the low frequency parts of the spectrum, resulting in spectral index of α ≈ 2.5 for ν < νc. Figure 1.3 shows the theoretical spectrum of a homogenous cylindrical source in terms of frequency ν1 in which the optical depth is τν1 = 1. The physics of synchrotron radiation are discussed with detail in (1; 23; 24).

1.3.2 Polarization of synchrotron radiation

The synchrotron radiation of a single electron with pitch angle φ with respect to the magnetic field B is confined within a beamed emission cone with the opening 1 angle on the order of γ . The emitted power from a single electron is elliptically 19 polarized and can be modeled by two components, p⊥ and pk, perpendicular and parallel to the direction of the projection of the magnetic field on the plane of the sky. On the other hand, a distribution of electrons with varying pitch angles results in destructive superposition of left-handed and right-handed polarizations which makes the overall observed synchrotron radiation partially linearly polarized. For relativistic electrons with power law spectral energy distribution as shown in equation 1.25, the overall fractional polarization can be estimated as following: δ + 1 π = 7 . (1.33) δ + 3 For a typical astrophysical synchrotron source with spectral index of α = −0.7, the above formalism results in a highly polarized signal with fractional polarization integrated over the frequency space of π = 0.72. The theoretical aspect of synchrotron radiation and its polarization has been under investigation for decades. As an example, in 1966 (3) have calculated the total intensity and degree of polarization as a function of frequency for a cloud of electrons, all with the same energy but with a uniform distribution of pitch angles φ. As can be seen in Figure

1.4, the total intensity peaks at νmax and declines afterward, but the degree of polarization increases with frequency.

1.3.3 Stokes parameters

Polarization of a monochromatic electromagnetic wave can be modeled by three parameters: the two perpendicular components of the electric field, Ex and Ey, the phase difference between them, δφ = φ1 − φ2. The electric field vector with frequency of oscillation ω can be written as the following:

−iωt E = (ˆxε1 + ˆyε2)e (1.34)

iφ1 iφ2 where ε1 = E1e and ε2 = E2e are complex components of the electric ﬁeld along ˆx and ˆy, E1 and E2 are the real parts of the electric ﬁelds. As a result, the 20

Figure 1.4 Theoretical synchrotron total intensity and fractional polarization proﬁles for a cloud of electrons with similar energies and a uniform distribution of pitch angles is shown, borrowed from (3). real part of the electric ﬁeld along ˆx and ˆy are as following:

Ex = E1cos(ωt − φ1) (1.35)

Ey = E2cos(ωt − φ2). (1.36)

It can be shown that the geometrical ﬁgure that represents the trace of the electric ﬁeld is a tilted ellipse with angle χ (also called the polarization angle) with respect to x-axis. The general elliptical polarization occurs for an arbitrary value of −π ≤ δφ ≤ π. However, when δφ = 0, ±π the ellipse becomes a line and we have linear polarization. Circular left-handed or right-handed polarizations also π happen when δφ = ± 2 . The polarization state of any mono-chromatic or quasi-chromatic radiation can be modeled with the four Stokes parameters described in the following:

2 2 I =< E1 + E2 > (1.37)

2 2 Q =< E1 − E2 > (1.38) 21

U =< 2E1E2cos(δφ) > (1.39)

V =< 2E1E2sin(δφ) > . (1.40)

It can be shown that the polarization angle in radians and fractional polarizations can be derived as: 1 U χ = tan−1( ) (1.41) 2 Q pU 2 + Q2 + V 2 π = . (1.42) I It must be noted that although circular polarization has been observed in some astrophysical sources, especially with the VLBI imaging of jets of radio galaxies (25), for the sake of simplicity we assume only linear polarization by assigning V = 0.

1.3.4 Faraday screens and rotation of the polarization angle

The linear polarization of the synchrotron radiation in radio regime can be used as a powerful tool to study the properties of the magnetic field structure in galaxies. However, the intrinsic polarized signal of the synchrotron radiation from galaxies can be washed out through different depolarization mechanisms. The presence of electrons and magnetic field in Faraday screens along the line of sight (either Galactic or in the IGM) can change the fractional polarization as well as the polarization angle in radio frequencies. In presence of a homogenous magnetic field B in the plasma in front of any synchrotron source with linearly polarized emission, all the plasma electrons experience two forces due the electric field of the propagating wave, E, and the external B field. The equation of motion of the electrons is as following:

dv e m = −eE − v × B. (1.43) e dt c 22 Any linearly polarized wave can be written as a superposition of the two left- handed (L ) and right-handed (R) circularly polarized wave fronts. If the direction of the magnetic ﬁeld is along the line of sight, the solution to the above equation for a circularly polarized light is:

−ie v(t) = Et, (1.44) me(ω ± ωcyc) where ω is the frequency of the propagating wave. The + and − signs are because of the L or R polarizations which result in diﬀerent answers for the steady state velocity of the electron. From the above relations we see that the propagation of the L and R circularly polarized waves cause diﬀerent conductivities and therefore dielectric constants for the Faraday screen are as following:

2 ωp R,L = 1 − , (1.45) ω(ω ± ωcyc)

q 2 where the plasma frequency is defined as ω = 4πnee . As a result of different p me dielectric constants, the L and R polarizations will become out of phase while traveling distance ds through plasma. This leads into an effective rotation of the linear polarization vector by dχ at frequency ν. This phenomenon is called Faraday rotation. The total rotation in the polarization angle after traveling distance d can be calculated as:

2πe3 Z d ∆χ = 2 2 2 neBkds (1.46) mec ω 0 where Bk is the parallel component of the magnetic field along the line of sight. The integral in equation 1.46 depends on the electron density of the plasma, strength of the magnetic field and the extent of the Faraday screen. However, the rotation angle also depends on the inverse squared of the frequency. It is worth noting that Faraday depth can be described by writing the frequency in equation 1.46 in terms of the wavelength of the light and accounting for the relative redshift 23 of the source as will be shown in chapter3 and equation 3.1. In reality, the synchrotron emission of a distant radio galaxy might travel through multiple Faraday screens at different redshifts and with different plasma properties along the intervening IGM. Even inside each cloud of plasma the distribution of the magnetic field is not necessarily homogenous and the electron density might change as well. Therefore, the above formalism is a very simplistic case of Faraday rotation. For more information about the ICM magnetic field and the physics of Faraday rotation refer to (1; 26).

1.3.5 Depolarization of synchrotron radiation

Although synchrotron radiation is highly polarized by definition, large astronomical surveys such as the NRAO/VLA all sky survey (NVSS, 27) have found majority of extragalactic radio sources show degrees of polarization of only a few percent, which is much smaller than the theoretical predicted values. There are a few different mechanisms that can reduce the overall observed degree of polarization of radio galaxies. In the following paragraphs, we summarize some of the possible depolarizing mechanisms. In practice, a combination of these effects result in the final observed fractional polarization. Line of sight variation in the orientation of the B field: If the orientation of the magnetic field in the synchrotron emitting source is random then radiation from different region along the line of sight will have different polarization angles. The net observed degree of polarization is the vector addition of all the polarized signals. Polarization vectors in random directions cancel out and the overall degree of polarization is reduced. Variation in the orientation of the B field across the source: Most extragalactic radio source are not fully resolved in current surveys. The radiation from different regions across the source is convolved with the synthesized beam of the radio interferometer or antenna on the plane of sky. If the B field orientation is random across the source, the resulting polarization angles are randomly 24 distributed. The effective vector summation of the linearly polarized signal convolved with the synthesized beam wipes out or reduces the polarization signal, leading to a much smaller observed degree of polarization. In this case, improving the spatial resolution of the observation can help to recover the true fractional polarization of the source. Faraday screens: As explained earlier, the intervening Faraday screens along the line of sight can rotate the polarization vector of a linearly polarized synchrotron radiation. The magnitude of this rotation ∆χ(ν) is a function of frequency, ν, of the radiation and the extent of the screen, d, in front of the source. Ignoring all the instrumental effects due to a fixed size bandwidth or a limited spatial resolution, for an extended radio source one can imagine radiation emitted from different regions might experience a thiner or a thicker Faraday screen, resulting in different ∆χ even for the same frequency. For example, if the radiation source is located in the vicinity or inside a cloud of plasma, photons that are emitted from the back of the source have to travel a larger distance within the Faraday screen than photons emitted from the front side. However, this effect will be negligible if the Faraday screen is much further away from the synchrotron source, e.g. somewhere in the intervening IGM at a different redshift or inside our own galaxy. Bandwidth depolarization: Most instruments have a fixed and limited bandwidth for observation, and therefore what they measure is an average intensity of the light within the bandwidth. In presence of Faraday screens and non-negligible rotation of the polarization angle at each frequency, the net degree of polarization measured within the instrument bandwidth is smaller than the actual source fractional polarization. In summary, depolarizing mechanisms have three different origins: Galactic, intervening IGM and local to the source. Our current knowledge about the dominant combination of depolarizing mechanisms is very limited and can be improved by performing multi-frequency polarization surveys of extragalactic sources. Since Faraday rotation is more effective at lower frequencies, comparing the fractional 25 Polarization of sources at minimum of two different frequencies might shed light on the underlying depolarization processes. In chapter3, we will address some of the most important questions regarding the dominant depolarization processes and the role of the IGM Faraday screens. More detailed discussions about the theoretical aspects of depolarization models can be found in (3; 28; 29; 30; 31; 32).

1.4 The intracluster medium in merging systems

Even after ∼ 13.7 billion years from the big bang the hierarchical merging of structures in the universe is still an ongoing process. Galaxy clusters are among the largest and most massive virialized structures in the universe. They contain hundreds or thousands of gravitationally bound galaxies in a volume with a diameter of only a few mega parsecs. The plasma in the surrounding environment of clusters and merging systems is normally denser, hotter and more metal rich than the regular IGM and therefore, we address it by a separate term: the intracluster medium (ICM). The accretion of gas and resulting shocks in the violent environment of merging clusters can heat up the ionized plasma in the ICM to temperatures on the order of ∼ 107−8K, corresponding to typical photon energy of a few keV. The fully ionized and hot ICM emits thermal X-ray emission through mostly the Bremsstrahlung process. As a result, most clusters are surrounded by a gigantic X-ray halo. The morphology and temperature proﬁle of the X-ray halo can shed light on the current dynamical state of the cluster. The observed X-ray halo of most relaxed clusters shows an elliptical morphology that extends up to 1 Mpc from the X-ray core. The X-ray surface brightness can be used to estimate the mass of the hot ICM plasma which is approximately 80%-90% of the baryonic mass of the clusters. 26 1.4.1 The ICM weather and its synchrotron features

Although X-ray observations provide valuable information about the global mass content of the ICM, its temperature and underlying dynamics, most often critical events and more local processes remain unseen. On the other hand, non-thermal synchrotron emission in radio regime is a very powerful observational tool to uncover the hidden structures corresponding to merger shocks and turbulence in the dynamic ICM of galaxy clusters. There are three main types of observed synchrotron emission associated with the ICM of galaxy clusters: Mini halos, Giant halos and filaments and relics. Radio mini halos are mostly observed at the center of relaxed clusters with cool cores such as Perseus (33; 34). They extend up to a few hundred kpc in diameter and their somewhat spherical morphology follows the central hot thermal gas. AGNs and radio galaxies are observed in the center of almost all clusters with mini halos and therefore seem to play important roles in origin of these halos. In addition to outflows from the central active galaxies, other mechanisms such as sloshing of cold gas related to the dynamics of the cluster should contribute to the total budget of high energy cosmic rays in the volume of mini halos. Giant radio halos are observed in clusters that recently have experienced a major-major merging event. The origin of these halos are probably associated with turbulence across the cluster as a result of the merger event. The extent of giant radio halos is on the order of several hundred kpc to a few Mpc. The presence of giant radio halos in association with X-ray emitting regions in many merging clusters such as Coma (35), A520, A665 (36) and A2744 (37) is evidence for the global magnetic field of the cluster with strength of a few µG. The morphology and the observed unpolarized synchrotron radiation from radio halos might be an indication that the volume of the halo is filled with synchrotron emitting plasma in which, combination of Faraday depolarization and varying magnetic field orientation along the line of sight, as described in section 1.3.5, remove any signal of linear polarization in the observed radiation. 27 Large scale radio relics and filaments are also observed mostly in the periphery of merging clusters (e.g. Sausage, Toothbrush and A2256 and A2255 presented in 38; 39; 40; 41; 42) and are probably associated with the dynamics of the merging systems and the resulting large scale shock fronts that travel across the cluster. Unlike halos, the synchrotron radiation of relics is polarized which suggests a well ordered magnetic field confined in a thin but elongated volume of the ICM. Figure 1.5 shows relics and filaments of the merging cluster A2255 as an example. The North-East relic emission of A2255 extends for ∼ 1 Mpc and is associated with a merger shock as confirmed by X-ray observation of the Suzaku satellite (43). We will discuss the dynamic ICM of A2255 and its unique radio filaments and relics in detail in chapter4. The spatial synchrotron spectral index distribution of radio relics flattens with increasing distance from the X-ray center (e.g. radio relics of Coma, A3667, A1240 and Abell 3411-3412 as presented in 44; 45; 46; 47). This is consistent with relics being driven by expanding merger shocks toward the outer radii. The origin and underlying physics of the gigantic radio halos and relics is still under active investigation. To emit large scale (Mpc) synchrotron radiation, cosmic rays and electrons must gain energy and be accelerated to relativistic velocities in presence of magnetic field in the ICM of galaxy clusters. There are several unanswered questions about this process. We do not know how electrons can gain and maintain such energies in such large scales. The source of the seed cosmic rays and the mechanisms that distribute them across the cluster are also not well known. In the following sections, we briefly mention some of the important aspects of the ICM physics in merging clusters with the focus of radio relics and merger shocks. Giant radio halos are most likely due to large scale turbulence across the cluster as a result of the merging event. However, the details of this process and the origin of halo emission are beyond the scope of this thesis. 28

Figure 1.5 Left: Our new high-resolution VLA observation of Abell 2255 galaxy cluster at the wavelength of 21 cm (magenta) on top of the Dutch Westerbork image at the wavelength of 85 cm (blue,4). Examples of radio ﬁlaments and relics in the ICM of the merging cluster are shown with solid yellow lines. Right: Optical SDSS image of galaxies at the central region of the cluster. 29 1.4.2 Lifetime of ultra relativistic Cosmic ray electrons

Relativistic electrons lose their energy quite fast through synchrotron radiation and inverse Compton scattering with CMB photons as:

dE B ∝ −E2 ( )2 + (1 + z)4 , (1.47) dt 3.2 where E is the cosmic ray energy, B is the strength of the ICM magnetic ﬁeld and z is the redshift of the cluster. The characteristic lifetime of a relativistic cosmic ray electron can be derived as below:

3 −1 γ B 2 4 3 300 1 10 γ te(Gyr) ∼ 4 ( ) + (1 + z) + 10 nth 1.2 + ln( ) , 900 3.2 γ 75 300nth (1.48) where the B field is in µG and can be estimated through Faraday rotation analysis of the polarization angle of background sources (48). The number density of −3 −3 thermal plasma electrons, nth ∼ 10 cm can be estimated through the X-ray observation. The above relation implies that high energy electrons with large Lorentz factors have shorter lifetime. As an example, the lifetime of electrons with γ ∼ 104 that are responsible for radio relics observed at GHz frequencies in the nearby universe (e.g. Figure 1.5) is on the order of 0.1 Gyrs, assuming ICM magnetic field of a few µG. Lower energy electrons with synchrotron radiation at MHz and smaller frequencies have a typical lifetime of up to ∼ 1Gyr, which is still orders of magnitudes smaller than the time required to distribute them across the cluster through diffusion and convection processes (so-called diffusion problem). Extremely large diffusion timescales for cosmic rays guarantees that electrons and protons will remain within the ICM of the galaxy clusters and their corresponding energy budget will only increase. However, high energy electrons that are capable of synchrotron radiation in GHz frequencies lose their energy very efficiently and fast. This implies mechanisms that cause radio relics emission in large scales must first re-energize the local cosmic ray electrons. More details about the low energy and high energy cosmic rays energy loss processes and the 30 resulting energy spectrum can be found in (49; 50).

1.4.3 Merger shocks and Re-acceleration of electrons

It can be shown that in a major-major merger event, the two clusters approach each other with slightly supersonic speeds. As a result, weak internal shocks with Mach numbers ∼ 2 − 3 form in the central colliding regions of the merging system. These shocks travel across the ICM and expand to the boundaries and periphery of the cluster and become slightly stronger (higher Mach numbers) since the plasma density and temperature decrease outward of the cluster center. In addition, accretion of cold, never-shocked and un-virialized plasma from outer regions (several Mpc away from the center) can produce external shocks with higher Mach numbers. Merger shocks play a very important role in dissipating the two clusters’ gravitational potential energy into the ICM plasma. Part of this energy is used to re-accelerate and energize the existing cosmic ray particles, especially electrons, to relativistic domain. Although external shocks are stronger than internal shocks, the total dissipated energy through them is much smaller than internal shocks. This is mostly due to the lower ICM densities at the edge of the merging system. The acceleration of charged particles at shock fronts can be done through the first order Fermi acceleration process and is modeled in diffusive shock acceleration (DSA) theory (49; 51; 52; 53; 54). In summary, when shock fronts pass through a medium they typically carry along magnetic field inhomogeneities. Cosmic ray particles in the vicinity of the shock front in upstream or downstream flow are temporarily trapped. Until they escape, each time they hit the moving magnetic field inhomogeneity in the upstream region they will get reflected back and gain energy. This process might happen several times for each particle at the shock front before they scatter away. Therefore, cosmic ray electrons can easily be accelerated to relativistic velocities. Combination of the amount of energy gained in each reflection and the typical lifetime of particles being trapped inside the 31 converging flow at the shock front determine the final energy spectrum of a distribution of cosmic ray particles. If injected particles have a power law energy distribution as described in equation 1.25, the resulting spectrum will be flatter, meaning there will be more high energy particles. The equilibrium power law index for the re-accelerated cosmic rays energy distribution can roughly be related to the shock Mach number as following:

M 2 + 1 δ = 1 + 2 = δ + 1, (1.49) M 2 − 1 inj where δinj is the injection index at the shock front. As discussed earlier, high energy electrons lose their energy through synchrotron radiation and inverse Comp- ton scattering with the CMB photons. So once re-accelerated cosmic rays scatter downstream of the shock front, the maximum electrons energy decreases as:

1 Ee,max ∝ , (1.50) vdt where vd is the electron’s propagation velocity downstream of the shock and t is the time from leaving the shock front. Consequently, the synchrotron spectrum of the shock re-accelerated electrons is expected to show a curvature and steepens downstream of the shock front.

1.4.4 Seed electrons

In high beta plasma of the ICM with weak shocks, only a small fraction (probably < 1%) of the energy dissipated in shocks can be used for accelerating cosmic ray particles. One of the most important parameters in DSA models is the minimum required initial energy for seed electrons so they can be accelerated to a few GeV energies with γ ≥ 104. DSA is only effective if the injected particles have enough energy to cross the shock front several times. Each back and forth reflection at the shock front will add to their energy by a first order Fermi process. Low energy relativistic electrons (γ < 100) in the ICM are subject of rapid Coulomb energy 32 losses due to collisions with thermal electrons. On the other hand, low energy electrons from the thermal pool have a much smaller gyro radii than the thickness of the shock and therefore, they are not capable of crossing it. It is essential to increase the energy of the thermal particles to supra-thermal regime through other mechanisms prior to their injection into the DSA. Such processes are discussed and simulated in the presence of low and high Mach number shocks (e.g. 55; 56). Particularly, with the presence of low Mach number shocks in the environment of galaxy clusters the shock drift acceleration (SDA) described in (55) seems to be playing an important role in energizing electrons to supra-thermal levels. In SDA, the incoming charged particles feel the magnetic field gradient between the upstream and downstream of the shock front and will gain energy from the motional electric field while drifting along the shock. An alternative solution to the problem of initial energy of seed particles might be presence of fossil electrons with supra-thermal energies. The source of these fossil electrons are probably radio galaxies and AGNs in the cluster. Radio galaxies with synchrotron tails that extend hundreds of kpc are observed in many merging systems (e.g. A2255 in Figure 1.5). Active AGNs and radio galaxies constantly inject high energy cosmic rays into ICM. These particles lose their energy through synchrotron emission and inverse Compton scattering and eventually their faint emissions disappear until they become re-accelerated and gain more energy from a passing shock wave. A good evidence for the above argument is Abell 3411- 3412, the first direct connection between a long tail of a radio galaxy and a radio relic is observed (47). The existence of a low Mach number major-major shock at the location of the relic is confirmed by X-ray observation, and therefore a DSA mechanism seems to be responsible for re-accelerating the fossil electrons that were already present in the vicinity of a radio galaxy. Detailed discussion on the energy distribution of the injected particles and different energy loss mechanisms throughout the ICM can be found in (50). Chapter 2

Ionizing emissivity from galaxies at z ∼ 3: diﬀerences in ﬁeld versus cluster galaxy populations

Abstract We present a study of the ionizing emissivity from a sample of 207 Lyα-emitters at z ' 3.3, identified in the Subaru SXDF field. We find that none of the Lyα-emitters is detected individually in the deep U band images. We performed stacking analysis, constraining the UV– to–LyC flux ratio, corrected for IGM absorption, to be larger than 13.8

(3σ). Assuming an intrinsic FUV/FLyC = 3, we constrain the relative LyC escape fraction of ionizing radiation to be fesc,rel < 20% (3σ). Our results indicate that the cluster and ﬁeld populations of Lyα–emitters show diﬀerent properties in their ionizing emissivity.

2.1 Introduction

The reionization of the universe is a global phase transition of the intergalactic medium (IGM) during which most of the diﬀuse hydrogen is ionized by photons

33 34 with energies greater than 1Ryd (i.e., hν > 13.6eV, λ < 912A).˚ The sources of these energetic photons as well as the details of how the reionization process proceeds with time are current subject of debate. We can constrain the redshift at which the reionization was completed, via observations of the Gunn-Peterson trough in high-redshift QSOs and gamma-ray bursts. These measurements indicate that the reionization ended rapidly near z ' 6 (57; 58; 59; 60). Together with observations of the evolving global star-formation history, the new value of the integrated optical depth of electron scattering to the CMB (τ = 0.066 ± 0.012) recently released by the Planck collaboration suggests that the reionization process was rather fast, taking place in the 400 Myrs between 6 < z < 10 (61; 62). Models of reionization depend on a number of assumptions: 1) the intrinsic ionizing spectrum of galaxies, 2) the fraction of ionizing radiation able to escape from them, 3) the hydrogen recombination time-scale (i.e., the clumping factor), and 4) that galaxies are the main contributors to the ionizing flux. The latter assumption follows from the observations of a rapidly declining number density of quasars to z ∼ 6 (63; 64; 65; 66). Recently, 67 (2015, see also 68; 69) suggested that a population of unobscured, faint, high-redshift AGNs may contribute significantly to the reionization. Moreover, recent re-analysis of the photon balance during the reionization era, in view of the newest estimates of the Thomson scattering optical depth released by the Plank collaboration suggest an AGN- dominated scenario might be able to reionize the universe (70). Constraints from the unresolved X−ray background, however, imply that even a population of unobscured AGNs exist they cannot contribute significantly to the ionizing photon budget, and faint galaxies with a mean escape fraction of ionizing photons & 10% are required (71). Because the transmission of the IGM drops substantially, direct measurements of the escape fraction at is extremely hard at z & 4, but can be performed at lower redshifts (72; 73). A huge amount of telescope time has been invested in this endeavor, and hundreds of galaxies, both in the local universe and up to redshift 35 ∼ 3, have been observed (8; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83; 84; 85; 86; 87; 88; 89; 90; 91; 92; 93; 94; 95; 96; 97; 98; 99; 100; 101; 102; 103; 104). However, there are only a few robust detections of Lyman continuum (LyC) radiation (7; 96; 97; 99; 100; 105; 106). For a decade, unsuccessful attempts to find galaxies with high LyC leakage at low redshift universe and only a few detections at higher redshifts resulted in scenarios that suggest physical properties of faint star forming galaxies changes rapidly from z∼ 3 to z∼ 6 and their average ionizing emissivity increases with redshift (85; 103; 104). Only then faint star forming galaxies would be able to complete and maintain the reionization of the universe. At low redshifts, z ∼ 0.3, recent detections of 6% - 13% leakage from 5 low mass and compact green pea galaxies with high surface SFR density, high emission line flux ratio, O[III]/O[II] and high Lyα escape fraction, has introduced new and more efficient techniques to find LyC leakers(96; 97). At intermediate redshifts ,z ∼ 1, we only rely on strong upper limits. In a recent study, (102) targeted a sample of 600 low mass galaxies with strong Hα emission and placed an upper limit of fesc < 9.6% from a sample of galaxies with Hα EW > 200A.˚ At high redshifts, despite thousands of surveyed galaxies there are only a few solid LyC leakage detections reported at z ∼ 3. One of the most recent and exotic high redshift detection cases is the famous Ion2 galaxy with LyC escape fraction between 50% to 100% depending on the IGM attenuation (100). Hubble space telescope observation of Ion2 reveals and unresolved structure for the LyC emitting region with high forbidden Oxygen emission line ratio, O[III]/O[II] > 10. Observed properties of this galaxy is consistent with an optically thin media with cavities blown by probably super nova explosions and stellar winds in a high star forming region. In contrary to observations of galaxies at low and intermediate redshifts, most studies of the escape fraction at z ∼ 3 have targeted galaxies in over dense regions such as SSA22 and HS1549 fields, to increase overall survey efficiency (7;8).

Slightly more frequent detections with larger fesc of high redshift galaxies might be the result of the evolution in the ionization properties of faint star forming 36 galaxies with redshift. However, this result can be interpreted in various ways, as recently discussed in (90). One possible explanation is that environment plays an important role in determining the amount of ionizing radiation from galaxies. It is possible, then, that the interaction between galaxies’ interstellar medium (ISM) and the intracluster gas, together with the increased level of star formation in dense environment at these redshifts are the origin of the high escape fraction observed at z ∼ 3. In order to test this hypothesis we have performed a survey to identify the field LAEs at z ∼ 3.3, and study their Lyman Continuum (LyC) emissivity. In Section 2, we discuss the new and archival observations used in analysis. Section 3 presents the sample selection method and section 4 lists our results and findings. In section 5 and 6 we calculate the upper limits on the escape fraction of the ionizing radiation, and compare the stellar properties of our field LAEs to the ones detected in over dense regions. At the end, we summarize our conclusions in section 7.

In the paper we assume a ﬂat ΛCDM cosmology and ΩΛ = 0.7, ΩM = 0.3 and −1 −1 H0 =70 km s Mpc .

2.2 Overall strategy

Confirmed LyC emitting galaxies at z ∼ 3 are mostly Lyα emitters (LAEs) in the galaxy protoclusters. In this paper we want to test whether leakers are more common in the dense environments compared to the general population of LAEs in the field. We thus designed our survey to target field LAEs, at a redshift comparable to the known LyC leakers. We used a combination of the broad band and intermediate band filters to select LAEs at z = 3.33, and sample their LyC radiation. The filter response curves are shown in Figure 2.1. We used two intermediate band filters. The IB527 filter centered at the 5261A˚ with a width of ∆λ = 246A˚ was used to isolate the Lyα emission from sources at z = 3.33 ± 0.10. We also used the second filter, 37 IB383, to image the rest-frame ionizing radiation. This custom filter is centered at the λ = 3830A˚ and has a width of ∆λ = 200A˚ with a sharp red cut-off (less than 5% transmission above 3955A)˚ to prevent contamination from non–ionizing radiation at z=3.33. The wavelength range covered by the IB383 filter corresponds to the rest-frame 860 − 910Afor˚ galaxies with Lyα emission line at the center of the IB527 filter at z ≥ 3.31. As a result, the IB383 filter samples the non–ionizing radiation of the LAEs at the redshift range of 3.23 ≤ z < 3.31. To avoid any false signal in case of LyC radiation detection through the IB383 filter, a followup spectroscopic observation is necessary. In addition to the IB383 filter, we use deeper U band exposures to probe the ionizing radiation. Although this filter does not have an optimally designed red cutoff, we used it to set the upper limits in the non–detected sources. We also used archival broad band data to sample the non–ionizing continuum of the galaxies. The outline of this paper is as following. The data reduction is described in Section 2.2.1 and the source detection and flux measurement in Section 2.2.2. The selection of the Lyα-emitting galaxies is presented in Section 2.3.

2.2.1 Observations and data reduction

We retrieved archival data in U, B, IB527 and V bands in the SXDS field (RA ∼ 34.54 and DEC ∼ −5.36) using SMOKA data service (107). These data were taken between 2000 and 2010 with the Subaru prime focus camera (Suprime- Cam, 108) mounted on the 8 meter Subaru telescope. The camera includes ten 2048 × 4096 CCDs, arranged in a 5 × 2 pattern. The pixel scale of 0.1500 px−1 provides a total field of view of 340 × 270. For this research observations in the IB383 filter were obtained on the nights of September 26 to 29 2011, using the Large Format Camera (LFC, 109) mounted on the prime focus of the 200 inch Hale telescope at Palomar Observatory. LFC has six 2048×4096 pixel CCDs. With a pixel scale of 0.36500 px−1, it covers an area with an approximate diameter of 240 on the sky. To minimize readout noise, images 38 were binned by a factor of 2 × 2 during the reading process. Table 2.1 presents the total exposure times, and the range of full-width half-maximum (FWHM) of the point spread function (PSF) observed in each filter1. The steps in the data reduction are similar for the LFC and Suprime camera data, and were performed using a collection of IMCAT 2 routines (110). First, we calculate the overscan value from each exposure and subtracted it from each image. During the observing run at Palomar, bias images were obtained each night. We created a super-bias by computing the median of all overscan–subtracted bias exposures and subtracted it from both flat–field and science frames. The pixel-to-pixel response variation was removed during the flat-fielding process. Flat field images were created from the science exposures, with a two-step approach. First, a preliminary flat field was generated by median combining all science exposures. These preliminary flats were used to create bad pixel masks for each of the CCDs. We then normalized the science exposures with the preliminary flat fields. We detected sources in the normalized exposures and created object masks for each frame. Finally, we used these masks to produce the final flat-field by taking the median of the object-masked science exposures. The median was computed in each band using a 2σ clipping algorithm. Science exposures were then normalized using our improved object-masked flat–fielded images. Before the images could be combined into a large scale mosaic, the sky background needed to be subtracted. To do so, we first identified and masked out extended sources and large scale artifacts (such as reflection ghosts around bright stars). We then calculated the local sky background (masking sources) in each position of a grid of 128 × 128 pixels, and fitted a 2rd-order polynomial surface to the grid. The surface was then subtracted from each science exposure. Cosmic ray events were identified and masked by using a sharp edge detection algorithm.

1Nine IB383 exposures were removed from the analysis, and not included in Table 2.1, due their poor seeing (> 2.300). 2An image and catalog manipulation software developed by Nick Kaiser http://www.ifa. hawaii.edu/~kaiser/imcat/ 39

Table 2.1. Properties of the used data in U, B, V, IB527 and IB383 bands.

Filter Instrument Exp time # of exposures Seeing Sec Arc-sec

U Sup-Cam 21600 18 0.57 - 1.37 B Sup-Cam 39780 52 0.41 - 0.70 V Sup-Cam 46229 73 0.36 - 0.77 IB527 Sup-Cam 24720 43 0.38 - 0.72 IB383 LFC 59114 65 1.1 - 2.2

To correct for field distortions and compute the offsets between different exposures, we used the Canada-France-Hawaii-Telescope Legacy Survey deep catalog as a reference astrometric catalog. Because most bright stars are saturated in the deep Subaru and Palomar images, and because very faint objects may not have precise astrometry in the CFHT catalog, we only used objects with CFHT magnitudes between 14 ≤ u0 ≤ 23 (for IB383 and U astrometry) and 19 ≤ r ≤ 22 and 18 ≤ g ≤ 22 (for IB527, B and V astrometry). After the astrometric correc- 00 00 tion is applied, we measured a median ∆RA=RAref −RA= 0.005 ± 0.056 and 00 00 ∆DEC=DECref −DEC = 0.008 ± 0.054 , with no systematic variations across the field of view. Before combining all frames into a mosaic image, and to account for variation in environmental conditions and airmass between exposures, we computed chip-to- chip and exposure-to-exposure scaling factors using high signal-to-noise sources detected in all exposures. We visually inspected each image and masked any remaining artifacts (such as satellite and asteroid trails, and internal reflections). We used the improved flat–field image and the noise in each exposure to create an inverse-variance weight map. Finally, we created the combined mosaic and weight map in each band by computing the weighted average of all exposures, using a 5σ clipping rejection algorithm. Absolute photometric calibration is done on the AB system using the Subaru 40

Figure 2.1 Throughput functions of the LFC IB383 (purple) and Sup-Cam U (cyan), B (blue), IB527 (orange), V (red) and R (brown) bands. The vertical dashed line represents the location of Lyman continuum limit for a spectrum of −1 a 100 Myr old galaxy with constant SFR= 2 M yr and 0.2 solar metallicity at z = 3.3 extracted from (5) library. We manually have added a Lyα emission line to the spectrum for presentation purposes. 41 and Palomar filter transmission curves. We followed (111), who recently performed a re-calibration of the SXDF photometric catalogs using stars identified in the Sloan Digital Sky Survey (112). Briefly, we first computed synthetic magnitudes in the SDSS, Suprime-Cam and LFC filters for the BPGS stellar library templates (113), by convolving the spectra with the appropriate filters and telescope response functions. We then derived color transformation equations between the SDSS and the Subaru and Palomar colors. On average, we found approximately 80 stars in each band that are detected in the SDSS Data Release 8 and that are not saturated in our deep exposures. We used the color transformation equations to convert the SDSS magnitudes to Suprime-Cam and LFC magnitudes, and computed the zero point for each filter as the median offsets between the instrumental magnitude and modeled magnitudes. All magnitudes were corrected for a Galactic extinction of E(B − V ) = 0.0229, based on IRAS 100µm emission maps of (114). Finally, because the V band transmission curve includes the Lyα emission, we added the Subaru R band images from (115) to our dataset. The mosaic has a 3σ magnitude limit of 27.7, and a seeing FWHM of 0.7700.

2.2.2 Flux measurement

We used the Source Extractor (SExtractor) software (116, version 2.8.6), with relative detection threshold parameter set to 1.7 times the background rms, to identify sources in the Subaru mosaic images and measure their flux densities. In order to identify the sample of LAEs, we run SExtractor in dual–image mode using the IB527 band as the detection image, together with the corresponding weight map, and measuring the object flux in the IB527, B, V and R band mosaics. We run SExtractor separately on the images probing the ionizing radiation, i.e., the U and IB383 mosaics. We extracted 84724 objects in the field in IB527 band. Because of the minimal variation in the PSFs of the final Subaru mosaics, we decided not to apply any PSF correction to the Subaru data. For each galaxy we measured the total flux using the SExtractor AUTO magnitude (corresponding 42

Table 2.2. Properties of the Sup-Cam and LFC stacked images.

Band FWHM ZERO POINT 3σ DEPTH (1.5 × FWHM) Arc-Sec Mag

U 1.01 ± 0.14 32.56 27.25 B 0.78 ± 0.06 35.23 29.03 V 0.78 ± 0.06 35.38 28.69 IB527 0.70 ± 0.05 33.82 27.66 IB383 1.60 ± 0.12 31.40 26.15 R 1.04 ± 0.04 34.26 27.70

to the total flux within an elliptical aperture with a semi major axis equal to the Kron’s radius of the galaxy; see 116, for a detailed discussion). We measured the detection limit in each image by evaluating the counts in 10,000 apertures with diameters 1.5 times the seeing FWHM, randomly distributed in mosaics of each band. Because some of the random apertures fell on real sources, the flux distributions were skewed toward high flux values. Thus we computed the standard deviation of the aperture counts by fitting a Gaussian function to the distributions truncated at the mode value. Table 2.2 lists the 3σ detection limit magnitudes for each band.

2.3 Selection of Lyα–emitters

LAEs are routinely selected using a combination of narrow and broad band filters. The central wavelength of the narrow band filter is chosen to probe the Lyα line at a specific redshift. Broad band filters are then used to estimate the continuum flux underneath the emission line. In the past decades, this technique has been used successfully by multiple groups to select large samples of LAEs, with some contamination by low redshift interlopers (e.g.,6; 76; 83; 89; 117). Here we use the IB527 mosaic to isolate Lyα, and the V image to estimate the continuum. 43 In order to identify Lyα emitting candidates, we have computed the equivalent width (EW, as defined in equation 2.6) of an emission line that would be required to reproduce the observed medium–broad band colors. We then identified Lyα- emitting candidates as those objects with inferred emission–line EW significantly above the median of the EW distribution (see below for details). For an object with an emission line, the total line flux can be computed as:

Z Fl = (f(λ) − fc)T (λ)dλ (2.1)

where f(λ) is the flux density of the source, fc is the continuum flux density at the center of the line and T (λ) is the filter throughput. Both f(λ) and fc are in erg units of [ s cm2 A˚ ]. We first define the “line flux density” in the IB527 and V filters as:

Fl fl,527 ≡ , (2.2) ∆λ527

Fl fl,V ≡ ; (2.3) ∆λV

where ∆λ527 = 246A˚ and ∆λV = 984A˚ are the widths of the IB527 and V filters, respectively. With the above definitions, the flux densities measured in the IB527 and V filters can be written as:

f527 = fl,527 + fc, (2.4)

fV = fl,V + fc. (2.5)

The IB527 ﬁlter is fully inside the V band and the respective average wave- lengths3 are less than 200A˚ apart (corresponding to 45A˚ at the redshift of the

3 The average wavelength of a ﬁlter with a transmission curve T (λ) is deﬁned as λavg = R λT (λ)dλ R T (λ)dλ . 44

LAEs). Therefore, we assumed fc to be the same in the two filters. With this assumption, an object with no emission line will have the same AB magnitude in both V and IB527 bands. We used above relations to compute the line EW for all objects in the fields. To first approximation, the observed EW is:

F f ∆λ f ∆λ EW ≡ l ∼= l,V V = l,527 527 . (2.6) fc fc fc Combining 2.4, 2.5 and 2.6 we have:

f f = V , (2.7) c 1 + EW ∆λV

f527 − fc EW = ∆λ527, (2.8) fc

f527 EW EW = (1 + ) − 1 ∆λ527, (2.9) fV ∆λV and, ﬁnally:

f527 − 1 fV EW = ∆λ527. (2.10) 1 − f527 ∆λ527 fV ∆λV Thus, the line EW can be computed from the flux densities measured in the V and medium band filters. It must be noted all of the selected objects were detected with more than 3σ in the V band image. Figure 2.2 shows the measured equivalent width versus the IB527 total magnitude for all objects detected at more than 5 σ in the IB527 filter. As expected, the vast majority of the sources have an EW consistent with zero. Galaxies with an emission line falling in the medium band filter will have an EW> 0. In order to account for photometric scatter in the flux measurements, we computed the median and percentiles of the EW distributions in multiple magnitude bins. We chose the bin size to always include the same number of sources (500), so the bins are larger at the brighter magnitudes. The median (EWmed) and the 0.05 45 percentile (EW0.05) as a function of magnitude are shown in Figure 2.2. We fitted a linear function to the calculated percentiles as a function of magnitude, limiting the fit to those bins with magnitudes IB527 > 23. For bins brighter than IB527 = 23, we assumed a constant value of the percentile. If the EW distribution reflected only the photometric scatter (i.e., if none of the objects had an emission line), the distribution should be symmetric with respect the median value (the median EWmed ' 0 at all magnitudes). We mirrored the the

0.05 percentile with respect to the median EWmed and selected all galaxies with

EW> 2EWmed − EW0.05 as emission line candidates. We found that all galaxies that have successfully passed our selection criteria on the EW have an observed

EWLyα ∼ 108A˚ (or 25A˚ rest–frame). Thus, our selection results in a cut similar to the constant EW cut applied by similar surveys (e.g.8; 118; 119). However, majority of studies have selected rest–frame EW∼ 18A˚ - 20A˚ as their threshold to select LAEs and therefore, our 25A˚ cut is a more conservative criteria. We find 990 objects that satisfy our cut. This sample, however, likely includes also low–redshift contaminants, selected via rest-frame optical emission lines (e.g., through the [OIII] or [OII] lines at z = 0.05 ± 0.02 and z = 0.41 ± 0.03, respectively), as well as low redshift interlopers with extreme B − V colors. Contrarily to low-redshift contaminants, galaxies at z ∼ 3.3, however, are expected to have a red B − V color and to be very faint in the rest frame LyC (i.e., IB383 and U band). The expected red B − V color is due to absorption from the Lyα forest, reducing the flux in the B band filter. We estimate the B − V color expected for +0.69 a star–forming galaxy at z = 3.33 to be B − V = 0.48−0.11 (assuming a median absorption from the IGM, see Section 2.5). The upper and lower uncertainties represent the 16 and 84 percentiles of the distribution of the IGM throughput in random sight-lines. Therefore, we applied a conservative color cut (shown in Fig- ure 2.3), and excluded 757 objects with B −V < 0.48 from our sample, as possible low–redshift contaminants. This color cut eliminates galaxies with extremely blue SEDs and most of the lower redshift contaminants. In addition to the EW and color cuts, we also visually inspected all sources, 46

Table 2.3. Average properties of LAEs.

Sample Number Average < B > < IB527 > < V > < R > < EW > [AB mag] [AB mag] [AB mag] [AB mag] [A]˚

Mean 27.37 25.90 26.44 26.37 387 Group A 121 Median 27.41 26.08 26.57 26.35 272

Mean 27.36 26.03 26.45 26.26 277 All 215 Median 27.40 26.17 26.55 26.28 183

and removed 17 objects with close companions, within the SExtractor aperture.

We also removed the brightest object in the medium-band filter (mIB527 = 21.6, B − V = 0.61). This object, clearly was detected in the U band, and has a photometric redshift from SDSS consistent with the detection of the [OII] doublet in the medium band filter. The final catalog of Lyα-emitting candidates includes 215 objects, which we divided in two groups, according to the significance of the EW measurement. Group A contains 121 objects with EW> 108A˚ + σEW and average < σEW >= 79A˚ which have higher probability of being real LAEs. Group B includes the remaining 94 galaxies with EW> 108A˚ but EW< 108A˚ +

σEW with average < σEW >= 52A.˚ Table 2.3 summarizes the average properties of our two samples of LAEs. For each galaxy we also computed the Lyα emission line ﬂux, combining Equa- tions 2.4 and 2.6, as follows:

f527∆λ527 Fline = . (2.11) ∆λ527 (1 + EW ) Line ﬂuxes are reported in Tables 2.5 and 2.6. Figure 2.4 shows the magnitude distributions of the LAEs in IB527, B and V bands, for both groups. Figure 2.5 shows the histogram of Lyα emission line ﬂuxes in the LAE candidates. As expected LAEs in Group A are on average brighter than those in Group B. 47

Figure 2.2 Lyα emission line EW inferred from the IB527−V color is shown as a function of the IB527 total magnitude. LAE candidates in groups A and B are shown with red and cyan bullets. Orange solid lines represent the running median and 0.05 percentile of the EW distribution in each magnitude bin (see text for details). Black solid lines are the best ﬁt to the 0.05 percentile and its mirror image with respect to the median values (the latter is used for the selection of the emission line objects, and is diﬀerent from 99.95 percentile). The dashed green line shows the equivalent EW= 108A˚ cut.

2.4 Results

2.4.1 Number density of Lyα emitters in SXDS

At redshift z ∼ 3, most of the detections of escaping ionizing radiation were performed in galaxies located in over–dense regions (with over densities up to a factor of 5,6;8; 89). The goal of our work is to test wether the proto-cluster environment is partially responsible for the high detection rate in LyC radiation, observed at z ∼ 3. Thus, before proceeding with the analysis of the ionizing radiation, we show that the inferred surface density of LAEs in SXDS is consistent with the surface density of the general ﬁeld galaxy population. 48

Figure 2.3 Observed EW versus B − V color. LAEs in Groups A and B are shown with red and cyan bullets. The solid vertical green line shows our color cut at B − V = 0.48, and horizontal dashed line is the cut on EW= 108A.˚

(120) and (118) both searched for LAEs with the same narrow band technique. (120) identified 356 z = 3.1 (±0.03) LAEs in 0.95 deg2, down to a rest–frame Lyα EW= 64A.˚ This corresponds to a galaxy surface density of 1.7 ± 0.1 galaxies arcminute−2 per unit redshift. Limiting our sample to the same rest–frame EW cut gives a lower galaxy surface density of 0.7 ± 0.1 galaxies arcminute−2 per unit redshift. (118) identified 162 z = 3.1 (±0.02) LAEs in 0.28 deg2, down to a rest–frame Lyα EW= 20A,˚ corresponding to a galaxy surface density of 4.0 ± 0.3 galaxies arcminute−2 per unit redshift. Including all of our Lyα–emitting galaxies, results in a surface density of 2.6 ± 0.2 galaxies arcminute−2 per unit redshift. Moreover, we have verified that the galaxies are distributed uniformly across the field of view, and are not concentrated in a smaller area, that would indicate the presence of a proto-cluster. 49 2.4.2 Observed ionizing emissivity

Due to the poor seeing during the Palomar observing run, the NB383 mosaic (which cover the LyC radiation at the redshift of the LAEs in SXDS) reaches a 3σ magnitude depth of only 26.15. At this depth, only the brightest galaxies could be detected in the LyC. The Subaru U band filter also probes the LyC radiation at z ∼ 3.3 (see in Figure 2.1), and images in this band reach more than one magnitude deeper than in IB383 (see Figure 2.6, and Table 2.2). Although the U band filter does not have an optimal red-side cutoff, it can still be used to set stronger limits (compared to those those derived with the IB383 mosaic) to the escape fraction of ionizing photons. However, the small (<16%) transmission at λ > 910 × (1 + z) implies that any detection in the U filter cannot be trusted, because it could be due to contamination by non–ionizing radiation. The R−band filter (with its effective wavelength of 6560 A)˚ samples the rest– frame non–ionizing continuum at 1500A,˚ at the redshift of our emitters. The distribution of R magnitudes is shown in Figure 2.6, together with the distributions for the full sample4 of LAEs in the z = 3.1 proto-cluster studied by (6). We also show the distribution of the proto-cluster LAEs with leaking ionizing radiation. Clearly, the field LAEs span the same range of continuum magnitude as the LAEs in the SSA22 protocluster. The observed non–ionizing to ionizing flux-density ratios range between 0.5 and 10.9 in (6). Thus, at the depth of our U band mosaic (hereafter referred to as the LyC–mosaic), we could detect the field LAEs if their escape fractions of ionizing photon was similar to that in cluster’s LAEs. None of our LAEs is individually detected above the 3σ level in the LyC images. Motivated by the non–detection in the LyC band, we stacked both the rest- frame UV and LyC images of our targets with a simple average of all of the images. We first created postage stamps (5800 on a side) for all objects, centered at the coordinates of the LAE. We then used the SExtractor segmentation map to mask

4We removed from the sample the sources that were later spectroscopically identiﬁed as low redshift contaminants (8). 50

Table 2.4. Photometry in the LyC stacked image.

FUV FUV LyC Sample Num LyC hRi LyC − hRi ( )obs ( )corr f FLyC FLyC esc,rel [3σ AB mag] [AB mag] [AB mag] ηint = 1 ηint = 3 ηint = 6

Group A 116 >29.74 26.37 >3.37 >22.2 >9.5 < 0.1 < 0.3 < 0.6

All 207 >30.05 26.27 >3.78 >32.4 >13.8 < 0.07 <0.2 < 0.4

pixels assigned to all sources, except the central LAE, and we subtracted from each stamp any residual sky background (computed from the median values of all non– masked pixels). We excluded from the stacking analysis 8 galaxies, for which the object was located too close to the border of the LyC image. The final sample used in the stacking analysis is thus of 207 field LAEs. The final rest-frame LyC stacked image is shown in Figure 2.7. Clearly, no significant detection is seen in the stack, despite the increased S/N (by a factor of approximately 14). In order to compute the limit on the UV–to–LyC ratio, we sum all of the pixels within an aperture of 00 −32 1.52 (1.5×FWHM) and get a total LyC flux of FLyC = 1.85 ± 1.16 × 10 erg s−1 cm−2 Hz−1, which give an observed (i.e., not corrected for IGM absorption, see below) 3σ limit to the UV–to–LyC ratio of (FUV/FLyC)obs > 32.4. We also performed the stacking using only galaxies in Group A. We do not detect any significant LyC flux in this sample, and the results are summarized in Table 2.4.

2.5 Escape fraction of ionizing radiation

We used the observed UV–to–LyC flux ratio (as 76) to compute the upper limit on the relative escape fraction of ionizing radiation from our field LAEs. This quantity, that can be easily computed from the ratio between the ionizing and 51 non–ionizing flux densities, is defined as:

LyC LyC fesc fesc,rel = UV , (2.12) fesc

LyC where, fesc is deﬁned as:

η f LyC = f UV int × exp(τ ), (2.13) esc esc η IGM,LyC

UV and fesc is the escape fraction of non–ionizing radiation (i.e., the ratio between the intrinsic and observed non–ionizing ﬂux densities), η and ηint are the observed int FUV FUV and intrinsic ratios of UV to LyC ﬂux densities, i.e., η ≡ and ηint ≡ int . FLyC FLyC The τIGM,LyC is the IGM optical depth for LyC photons along the line of sight.

The value of ηint is poorly constrained observationally, and can vary substantially with the properties of the galaxy stellar population. Depending on the assumption on the star-formation history, initial mass function, burst age, and whether or not massive–star rotation and the contribution from X–ray binaries is included, ηint can range between 1 and 6. Following Nestor et al. 2013, we perform the calculations of the escape fraction using a moderate ηint = 3 value, as well reporting in Table 2.4 the values computed assuming ηint = 1 and ηint = 6 (e.g.6;8; 90). In order to estimate the correction term for the IGM absorption, we follow (72), with the updated parameters from (121). We generate synthetic absorption spectra of 4500 z = 3.33 sources, drawing the intervening absorbers according to the following distribution function in redshift, neutral hydrogen column density

(NHI ) and Doppler parameter (b):

∂3N = f(z)g(NHI )h(b); (2.14) ∂z∂NHI ∂b where the functional forms of f(z), g(NHI ) and h(b) are described in Inoue et al. 2008. The optical depth of each absorber with given z, NHI , and b, is computed accounting for both absorption in the continuum (below 912A)˚ and 52 in the Lyman series. The total optical depth of each absorber is then τ(ν) = 5 NHI [σLC (ν) + Σσi(ν)], where σLC is the Lyman continuum cross section and σi is the cross section for absorption in the ith transition of the Lyman series6. The attenuation factor in the LyC is then computed by convolving the averaged spectrum (in the observed frame) of the 4,500 sightlines with the filter transmission curve of the U band filter. The resulting attenuation factor at the assumed redshift z = 3.33 is exp(τIGM ) = 2.34. The resulting 3σ limit on the UV–to–LyC flux density ratio, corrected for IGM absorption, is (FUV/FLyC)corr = 13.8. Finally, using Equations 2.12 and 2.13, we compute the relative escape fraction of ioniz-

LyC ηint LyC ing radiation as f = . Assuming ηint = 3 we ﬁnd f < 0.2 esc,rel (FUV/FLyC)corr esc,rel LyC (3σ). Limits for fesc,rel computed with diﬀerent assumptions on ηint are reported in Table 2.4.

2.6 Stellar mass distribution

To facilitate comparison of our LAEs with other studies we have ﬁt the stellar populations of our galaxies and modeled the stellar masses and dust extinctions. We have used deep images of SPLASH project (Mehta et. al. in preparation), which include 9 broadband ﬁlters: u (CFHT), b, v, r, i, z (Subaru) and J, H, K (UKIRT). We assumed the redshift of z = 3.3 for LAEs in our sample and used (5) GALAXEV library of evolutionary stellar population synthesis models with solar (Z=0.02) and sub-solar (Z=0.008) metallicities, exponentially declining star formation histories with timescales of 0.1, 0.3, 1, 5, 15 Gyr, and (122) IMF to obtain the Physical parameters of the LAEs. We also applied the (123) dust attenuation law allowing for 0 < E(B − V ) < 1.2. Firgure 2.8 shows the distribution of the modeled stellar masses and dust attenuation of our LAEs in comparison to (7) who studied a sample of 21 LAEs at

5 −18 νLyC 3 2 σLC = 6.3 × 10 ν [cm ], where νLyC is the frequency of the Lyman break. √ 2 6 πe fi th σi(ν) = Φi(ν), fi is the oscillator strength of the i transition, Φi(ν) is the line mecνD b profile with central frequency νi and Doppler width νD = νi c . 53 z = 2.85 located in a galaxy protocluster in the HS1549+1919 field with redshift- space overdensity of δgal ∼ 5. Our field LAEs and the ones presented in Mostardi et. al. almost populate the same range in stellar mass as well as dust extinction and have similar distributions, given the uncertainties derived based on the Poisson statistics and the number of objects in each histogram bin.

2.7 Discussion and Conclusions

In this work, we studied the ionizing emissivity (i.e., the emissivity of radiation at shorter wavelength than the Lyman break, 912A)˚ of a sample of 207 Lyα–emitting galaxies at z = 3.33 in the SXDS field. An impressive effort has been devoted in the past decade to constrain the ionizing power of galaxies. The latest observational results point toward an evolution with redshift of the ionizing emissivity (see 85; 124; 125), with higher redshift galaxies having on average a higher escape fraction of ionizing radiation. It is still unclear what drives this evolution (see, e.g. 90), and various explanations are possible. First, most of the LyC–leakers at z ∼ 3 are also LAEs, while targets at lower redshifts have been typically selected based on their UV continuum luminosities. The mechanisms that allow galaxies to have a large escape fraction of Lyα–radiation may also be responsible for the higher observed escape fraction of ionizing radiation (e.g., 98; 126). Recently, (93) and (102) studied the ionizing emissivity of a sample of galaxies at z ∼ 1.5 and z ∼ 1 selected to have extreme Hα EW, finding no individual detections and rel constraining fesc,LyC to be < 20% at z ∼ 1.5 and < 9.6% at z ∼ 1. Although no Lyα observations exist for these objects, (127) recently showed that 100% of galaxies with Hα EW> 300A,˚ have Lyα in emission (see also 82). These results suggest that the mechanisms that allow Lyα to escape, are not responsible for the higher escape fraction of ionizing radiation observed at z = 3. Another possibility, which we tested here, is that the environment in which these LyC–leakers reside is somehow affecting the properties of the interstellar medium, that ultimately regulate the escape of ionizing radiation from galaxies. 54 In fact, most of the detections at z ∼ 3 are in objects belonging to large over– dense regions, such as the HS1549 proto–cluster sat z = 2.85 (89), and the SSA22 proto–cluster at z = 3.09 (6). Using a combination of medium and broad band Subaru data, we have selected a sample of LAEs at z = 3.33. Their surface density of 2.6 ± 0.2 galaxies arcminute−2 per unit redshift implies that these objects are not located in a galaxy over–density, but reside in an average environment. None of the field LAEs is individually detected in our deep U band image (3σ magnitude limit of 27.25 magnitudes). Even after stacking all the objects, we find no clear signal in the LyC image, constraining the observed UV–to–LyC

flux ratio to be (FUV/FLyC)obs > 32.4 (3σ). After correcting for the average IGM absorption in the LyC spectral region covered by our filter, we set the 3σ upper limit to the relative escape fraction of ionizing radiation in field LAEs to LyC be fesc,rel < 20%. In Figure 2.9 we show the IGM corrected UV–to–LyC flux ratio versus the rest–frame UV magnitude. We compare the limits for all the field LAEs with the observed flux ratios for the proto–cluster LAEs in (6), removing the dubious sources identified in (8). Clearly, all but two galaxies in the Nestor et al. sample were within reach of our LyC-band mosaic. In the over dense environment, (6) find that a fraction of 18±4% proto-cluster LAEs are detected in the LyC (the error is based on Poissonian statistics). Based on this, and looking at the distribution of LyC–UV colors in Figure 2.9, we estimate that we should have detected approximately 35±6 sources, at the magnitude limit of our LyC image. Moreover, when stacking all the protocluster LAEs, Nestor et al. (2013) +2.5 report a (FUV/FLyC)corr = 3.7−1.1. This is 4σ away from the lower limit derived for the field LAEs (FUV/FLyC)corr > 13.8, 3σ). As discussed above, it appears that the main physical properties (i.e., stellar mass distributions and dust content) are similar between field and cluster’s LAEs. As a result, our failure in detecting even a single Lyα emitter in the ionizing radiation suggests that physical processes specific to the cluster environment are probably responsible for the higher emissivity of LAEs found in over-dense regions. Ram pressure stripping, often invoked to explain the cessation of star-formation 55 in clusters, is likely responsible for disturbing the distribution of neutral gas, with respect to the star-forming regions. This process may create holes in the neutral interstellar medium, exposing the star–forming regions and allowing the ionizing radiation to escape more easily. Moreover, the hot intracluster medium is effectively transparent to ionizing photons, which may thus have a longer mean free path compared to those emitted by field galaxies. It has recently been suggested that a large number of the z ∼ 3 LyC leakers are in fact due to lower-redshift contaminants along the line of sight of the galaxies. However, low-redshift contamination should not depend on whether the LyC targets are located in cluster or in the field. Our result, therefore, seems to suggest that the contamination may still be related in some way to the cluster environment.

This work is done based on the data collected at Subaru Telescope and obtained from the SMOKA, which is operated by the Astronomy Data Center, National Astronomical Observatory of Japan, and also observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Re- search Council (NRC) of Canada, the Institut National des Science de l’Univers of the Centre National de la Recherche Scientiﬁque (CNRS) of France, and the University of Hawaii. This research is conducted based in part on data products produced at TERAPIX and the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. 56

Figure 2.4 IB527, B and V magnitude distribution of LAE candidates. Blue solid line represents all LAEs while LAEs in group A are shown by red line. 57

Figure 2.5 Distribution of Lyα emission line ﬂux (top), and observed equivalent width (bottom) in our LAE candidate samples. Blue solid line represents all of the LAEs while the red line is only objects in group A. 58

Figure 2.6 Distribution of R−band magnitudes (which probe the non–ionizing continuum at z ∼ 3), for the field LAEs and for the full proto-cluster sample in (6). We also show the R−band magnitude distribution for proto-cluster LAEs detected in the LyC. For reference, the vertical lines show the 3σ magnitude limits in the two bands that probe the LyC radiation. The depth of the U band is sufficient to detect the field LAEs, if their ionizing to non–ionizing flux density ratio is similar to that of LAEs in the SSA22 proto–cluster.

Figure 2.7 Stacked LyC image (5800 on a side) of 207 ﬁeld LAEs. No signiﬁcant detection is visible in the image. In the central aperture used for the computation of the mean, all 207 stamps were used. In the remaining region of the stamp, the number of stamps in each pixel ranged between 184 and 207. 59

Figure 2.8 Distributions of the modeled stellar masses and dust extinction of the LAEs in this work (green) in comparison to (7) who studied a sample of 21 LAEs at z = 2.85 located in a galaxy protocluster in the HS1549+1919 ﬁeld with redshift-space overdensity of δgal ∼ 5 (hatched gray). The black and green error bars represent the uncertainties derived based on the Poisson statistics. 60

Figure 2.9 IGM corrected (FUV/FLyC)corr flux ratio versus rest–frame UV magnitude. Arrows show lower limits for the field LAEs. Solid circles show the cluster LAEs with LyC detections in (8) and Mostardi et al. (2015, galaxy MD5). We also show the limits obtained from the stacking analysis of the entire sample of field and cluster LAEs (see legend for details). 61

Table 2.5. Lyα emitter candidates from category A. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux.

Fline RA DEC EWobs B IB527 V R Detection Fline Fc

J2000 Deg A˚ AB Mag σ IB527 band 10−17 erg cm2.S 34.6256 -5.5573 254± 111 27.64±0.08 26.72±0.13 27.16±0.07 26.95±0.17 5.4 0.5 1.014 34.6164 -5.5220 202± 64 > 28.51 26.29±0.08 26.66±0.05 25.90±0.05 6.7 0.5 1.336 34.4966 -5.5189 220± 72 27.22±0.06 26.32±0.09 26.72±0.05 26.85±0.09 6.6 0.5 1.354 34.6501 -5.5160 199± 73 27.51±0.07 26.51±0.10 26.88±0.05 26.37±0.07 5.0 0.4 1.085 34.6390 -5.5094 434± 144 > 28.51 26.58±0.10 27.21±0.07 27.41±0.18 6.5 0.6 1.446 34.5278 -5.5066 553± 144 27.48±0.07 26.18±0.08 26.90±0.06 26.41±0.06 7.4 0.7 2.253 34.5900 -5.4990 168± 54 27.17±0.06 26.16±0.08 26.48±0.04 25.95±0.05 7.4 0.4 1.352 34.6450 -5.4958 184± 55 26.72±0.05 25.84±0.08 26.19±0.04 25.98±0.06 6.4 0.4 1.915 34.5957 -5.4842 181± 71 27.81±0.10 26.43±0.10 26.77±0.05 26.55±0.07 5.7 0.4 1.103 34.7285 -5.4615 331± 104 27.28±0.07 26.05±0.10 26.59±0.05 26.32±0.06 6.5 0.6 2.105 34.6080 -5.4597 407± 152 28.22±0.13 26.66±0.11 27.27±0.07 26.73±0.09 5.1 0.6 1.304 34.5827 -5.4576 448± 116 28.25±0.14 26.18±0.08 26.83±0.05 26.28±0.08 7.6 0.6 2.107 34.6100 -5.4563 260± 77 27.02±0.06 26.05±0.09 26.50±0.05 26.37±0.07 6.3 0.5 1.897 34.7215 -5.4553 282± 87 27.45±0.08 26.12±0.09 26.60±0.05 26.31±0.14 6.2 0.5 1.841 34.7322 -5.4529 475± 174 27.55±0.08 26.33±0.11 27.00±0.07 26.31±0.08 6.4 0.7 1.874 34.7009 -5.4540 200± 85 27.71±0.07 26.81±0.12 27.18±0.06 26.86±0.09 5.1 0.4 0.823 34.5458 -5.4519 868± 299 27.80±0.11 26.23±0.09 27.11±0.08 27.02±0.15 8.3 0.8 2.429 34.5845 -5.4515 223± 79 27.64±0.07 26.55±0.10 26.95±0.05 26.72±0.09 6.3 0.5 1.107 34.3346 -5.4520 662± 46 26.33±0.04 24.14±0.02 24.92±0.02 25.47±0.03 43.5 0.7 15.645 34.6902 -5.4476 199± 68 27.32±0.05 26.45±0.09 26.82±0.05 26.82±0.09 6.6 0.4 1.142 34.7096 -5.4461 573± 170 > 28.51 26.29±0.09 27.02±0.06 26.97±0.11 6.9 0.7 2.064 34.6938 -5.4455 760± 245 28.20±0.14 26.20±0.09 27.03±0.07 27.50±0.15 7.8 0.8 2.429 34.7307 -5.4449 248± 107 27.79±0.08 26.79±0.13 27.23±0.06 25.96±0.05 6.2 0.5 0.938 34.5236 -5.4432 591± 9 24.17±0.01 22.48±0.00 23.22±0.00 22.17±0.00 215.2 0.7 69.625 34.3391 -5.4383 635± 114 27.58±0.09 25.60±0.05 26.37±0.04 26.45±0.08 13.2 0.7 4.028 34.7448 -5.4375 223± 77 > 28.51 26.18±0.10 26.58±0.04 25.47±0.03 7.2 0.5 1.561 34.5122 -5.4340 860± 372 27.89±0.11 26.50±0.11 27.37±0.10 27.62±0.14 5.4 0.8 1.894 34.3842 -5.4259 253± 61 26.77±0.05 25.78±0.07 26.23±0.04 26.64±0.08 10.2 0.5 2.386 34.4563 -5.4229 1345± 183 26.91±0.07 24.56±0.03 25.58±0.03 26.20±0.07 27.3 0.8 12.250 34.5155 -5.4180 304± 78 28.03±0.13 26.02±0.08 26.52±0.04 26.44±0.08 8.7 0.6 2.103 34.5844 -5.4174 355± 97 > 28.51 26.13±0.08 26.69±0.05 27.01±0.16 7.5 0.6 2.021 34.6221 -5.4166 167± 57 27.45±0.07 26.30±0.09 26.62±0.04 25.98±0.05 8.1 0.4 1.181 34.4098 -5.4157 170± 46 27.51±0.07 26.14±0.07 26.46±0.03 26.55±0.08 8.5 0.4 1.388 34.3304 -5.4121 232± 68 27.86±0.11 26.27±0.08 26.68±0.05 26.44±0.07 8.0 0.5 1.466 34.4003 -5.4111 1228± 475 > 28.51 26.12±0.08 27.11±0.08 > 27.70 7.2 0.8 2.862 34.6767 -5.4106 205± 40 26.78±0.04 25.60±0.05 25.97±0.03 25.97±0.05 13.5 0.5 2.543 62

Table 2.5 (cont’d)

Fline RA DEC EWobs B IB527 V R Detection Fline Fc

J2000 Deg A˚ AB Mag σ IB527 band 10−17 erg cm2.S 34.5930 -5.4056 394± 60 26.97±0.05 25.44±0.05 26.04±0.03 26.20±0.07 14.8 0.6 3.979 34.5912 -5.4045 180± 58 27.26±0.06 26.22±0.09 26.56±0.04 26.70±0.08 7.0 0.4 1.333 34.3886 -5.4005 315± 91 > 28.51 26.26±0.09 26.78±0.05 26.08±0.05 6.1 0.6 1.706 34.4639 -5.4000 183± 46 27.00±0.07 25.59±0.07 25.93±0.03 26.35±0.06 10.9 0.4 2.402 34.5744 -5.3977 194± 81 28.33±0.15 26.60±0.11 26.97±0.05 27.15±0.11 6.4 0.4 0.976 34.4678 -5.3944 239± 71 27.19±0.07 25.94±0.09 26.37±0.04 26.06±0.05 6.2 0.5 2.008 34.5820 -5.3928 174± 48 27.34±0.06 26.12±0.07 26.45±0.03 26.36±0.07 7.9 0.4 1.429 34.4536 -5.3912 271± 115 27.49±0.10 26.38±0.12 26.85±0.07 27.09±0.10 5.7 0.5 1.420 34.5312 -5.3905 449± 120 27.48±0.07 26.18±0.08 26.82±0.05 26.75±0.14 6.7 0.6 2.117 34.4795 -5.3838 270± 94 27.66±0.09 26.38±0.10 26.84±0.05 26.59±0.08 5.3 0.5 1.427 34.4431 -5.3818 191± 63 27.87±0.10 26.45±0.09 26.81±0.04 26.09±0.05 6.3 0.4 1.114 34.5233 -5.3789 180± 52 27.18±0.06 26.00±0.08 26.34±0.04 25.30±0.03 7.9 0.4 1.631 34.7493 -5.3757 285± 101 27.53±0.06 26.48±0.11 26.97±0.05 26.33±0.07 6.3 0.5 1.326 34.5618 -5.3746 430± 127 28.30±0.13 26.53±0.09 27.16±0.05 27.49±0.13 6.2 0.6 1.511 34.4046 -5.3713 239± 79 > 28.51 26.54±0.10 26.97±0.05 25.95±0.05 6.0 0.5 1.153 34.3690 -5.3699 213± 35 26.48±0.04 25.22±0.05 25.61±0.02 25.85±0.04 13.4 0.5 3.671 34.5569 -5.3694 204± 77 27.64±0.08 26.54±0.10 26.92±0.05 26.38±0.08 5.5 0.5 1.062 34.6747 -5.3657 250± 44 26.99±0.05 25.59±0.05 26.03±0.03 25.69±0.05 13.9 0.5 2.839 34.3405 -5.3647 478± 58 26.61±0.05 24.93±0.04 25.60±0.02 25.90±0.04 19.0 0.7 6.829 34.4575 -5.3627 210± 67 28.18±0.12 26.45±0.09 26.83±0.04 26.82±0.11 6.5 0.5 1.178 34.5563 -5.3614 223± 65 27.81±0.09 26.35±0.08 26.75±0.04 26.86±0.11 7.1 0.5 1.334 34.6945 -5.3614 150± 35 27.26±0.08 25.49±0.06 25.78±0.02 24.54±0.02 13.2 0.4 2.335 34.4136 -5.3602 399± 51 26.69±0.05 24.98±0.04 25.58±0.02 25.74±0.04 21.1 0.6 6.131 34.6460 -5.3566 686± 142 27.29±0.07 25.68±0.06 26.47±0.04 26.87±0.10 11.6 0.7 3.826 34.5315 -5.3541 309± 73 27.02±0.07 25.67±0.07 26.19±0.04 25.74±0.05 7.8 0.6 2.896 34.5410 -5.3539 276± 97 27.54±0.09 26.24±0.11 26.72±0.05 26.18±0.06 5.6 0.5 1.633 34.4770 -5.3516 655± 158 27.86±0.11 26.01±0.07 26.79±0.05 27.33±0.12 9.8 0.7 2.769 34.5096 -5.3510 655± 273 28.12±0.13 26.57±0.12 27.35±0.08 > 27.70 5.4 0.7 1.652 34.4118 -5.3508 456± 159 27.74±0.08 26.60±0.11 27.25±0.06 27.06±0.09 5.4 0.7 1.436 34.3606 -5.3473 180± 52 27.36±0.07 26.11±0.08 26.45±0.03 26.51±0.08 7.4 0.4 1.472 34.6317 -5.3467 508± 140 27.81±0.09 26.32±0.08 27.01±0.05 26.68±0.10 6.6 0.7 1.936 34.5227 -5.3460 369± 109 28.01±0.12 26.29±0.09 26.86±0.05 25.86±0.05 5.8 0.6 1.781 34.5014 -5.3462 670± 119 27.33±0.08 25.47±0.05 26.26±0.04 26.99±0.10 12.9 0.7 4.604 34.4052 -5.3417 176± 66 27.29±0.08 26.18±0.10 26.51±0.05 26.45±0.07 6.1 0.4 1.370 34.4600 -5.3398 202± 88 > 28.51 26.68±0.12 27.05±0.06 25.98±0.06 5.2 0.5 0.931 34.5699 -5.3380 188± 51 26.70±0.05 25.76±0.07 26.11±0.04 25.98±0.05 9.5 0.4 2.086 63

Table 2.5 (cont’d)

Fline RA DEC EWobs B IB527 V R Detection Fline Fc

J2000 Deg A˚ AB Mag σ IB527 band 10−17 erg cm2.S 34.4153 -5.3380 423± 62 26.80±0.05 25.29±0.05 25.92±0.03 25.88±0.05 15.2 0.6 4.674 34.5265 -5.3367 173± 63 27.43±0.07 26.34±0.10 26.66±0.04 26.57±0.10 6.1 0.4 1.172 34.4828 -5.3338 583± 209 > 28.51 26.51±0.11 27.25±0.07 26.90±0.11 5.0 0.7 1.691 34.6467 -5.3346 227± 15 25.22±0.02 24.01±0.02 24.42±0.01 24.56±0.02 45.1 0.5 11.600 34.3907 -5.3329 492± 156 > 28.51 26.56±0.10 27.24±0.06 > 27.70 5.9 0.7 1.532 34.5751 -5.3266 752± 202 27.74±0.09 26.13±0.08 26.96±0.05 27.30±0.13 7.6 0.8 2.581 34.6069 -5.3265 579± 154 27.84±0.14 25.82±0.08 26.56±0.05 26.14±0.09 8.8 0.7 3.196 34.5726 -5.3219 189± 71 27.32±0.07 26.30±0.10 26.65±0.05 26.16±0.07 5.5 0.4 1.275 34.4620 -5.3177 195± 36 26.45±0.04 25.29±0.05 25.65±0.02 25.88±0.05 14.7 0.4 3.282 34.4293 -5.3169 974± 187 27.99±0.16 25.44±0.05 26.36±0.04 27.19±0.12 15.2 0.8 5.147 34.5644 -5.3164 360± 63 27.09±0.07 25.41±0.05 25.98±0.03 25.83±0.04 11.8 0.6 3.933 34.4802 -5.3106 403± 125 27.78±0.08 26.61±0.10 27.22±0.06 27.66±0.14 5.5 0.6 1.360 34.5064 -5.3057 162± 42 26.91±0.05 25.90±0.07 26.21±0.03 25.87±0.06 8.5 0.4 1.676 34.6180 -5.3033 548± 108 27.15±0.08 25.52±0.06 26.24±0.04 26.40±0.07 10.7 0.7 4.144 34.7354 -5.3011 310± 111 27.87±0.08 26.67±0.11 27.18±0.05 27.22±0.12 5.9 0.6 1.164 34.7351 -5.2992 511± 65 26.75±0.05 24.94±0.04 25.63±0.02 25.89±0.04 22.1 0.7 6.911 34.6101 -5.2981 1259± 209 27.28±0.08 25.16±0.04 26.15±0.03 26.33±0.06 19.1 0.8 7.005 34.7058 -5.2953 182± 64 27.43±0.06 26.51±0.09 26.85±0.04 26.44±0.08 6.4 0.4 1.027 34.5799 -5.2917 193± 57 26.71±0.06 25.72±0.08 26.08±0.04 25.94±0.05 7.2 0.4 2.204 34.3953 -5.2905 264± 42 26.82±0.05 25.49±0.05 25.95±0.03 26.13±0.06 13.0 0.5 3.197 34.3347 -5.2839 278± 43 26.59±0.05 25.28±0.04 25.75±0.03 26.28±0.06 13.7 0.5 3.980 34.3531 -5.2821 216± 71 27.78±0.07 26.77±0.09 27.17±0.05 27.29±0.12 5.1 0.5 0.885 34.5701 -5.2799 182± 56 27.38±0.07 26.29±0.08 26.63±0.04 26.11±0.07 6.5 0.4 1.258 34.6384 -5.2743 220± 53 27.76±0.09 26.24±0.07 26.64±0.04 27.06±0.10 7.8 0.5 1.461 34.3729 -5.2703 210± 48 27.24±0.08 25.83±0.06 26.21±0.04 25.95±0.05 8.4 0.5 2.082 34.4402 -5.2703 208± 42 26.67±0.04 25.80±0.05 26.18±0.03 25.94±0.06 8.7 0.5 2.135 34.6342 -5.2700 690± 139 27.79±0.11 25.81±0.05 26.61±0.05 27.31±0.16 9.9 0.7 3.378 34.4327 -5.2686 440± 135 28.18±0.18 26.29±0.09 26.93±0.07 26.38±0.09 6.1 0.6 1.898 34.6948 -5.2673 194± 68 27.02±0.07 26.08±0.09 26.44±0.05 25.79±0.06 5.9 0.4 1.579 34.3762 -5.2642 822± 219 28.32±0.20 26.03±0.07 26.89±0.06 26.57±0.10 7.7 0.8 2.889 34.4893 -5.2628 525± 143 28.12±0.12 26.51±0.08 27.21±0.06 27.31±0.12 6.1 0.7 1.640 34.4361 -5.2624 724± 254 28.11±0.15 26.40±0.09 27.21±0.09 26.77±0.14 5.6 0.7 2.000 34.6024 -5.2622 222± 38 26.36±0.04 25.44±0.05 25.84±0.03 26.01±0.05 12.8 0.5 3.082 34.4402 -5.2545 590± 139 27.05±0.08 25.73±0.06 26.47±0.06 26.58±0.08 7.6 0.7 3.490 34.5602 -5.2440 420± 133 27.68±0.11 26.39±0.09 27.01±0.07 27.39±0.11 5.3 0.6 1.705 34.6224 -5.2440 188± 46 26.83±0.05 25.99±0.06 26.34±0.04 26.10±0.05 9.3 0.4 1.693 64

Table 2.5 (cont’d)

Fline RA DEC EWobs B IB527 V R Detection Fline Fc

J2000 Deg A˚ AB Mag σ IB527 band 10−17 erg cm2.S 34.6256 -5.2401 301± 67 27.05±0.07 25.76±0.06 26.27±0.04 26.45±0.09 6.8 0.6 2.638 34.5898 -5.2343 269± 79 27.88±0.09 26.61±0.08 27.07±0.05 26.76±0.09 5.3 0.5 1.154 34.5965 -5.2332 998± 319 28.29±0.19 26.14±0.08 27.06±0.07 > 27.70 7.3 0.8 2.726 34.5893 -5.2167 823± 196 > 28.51 25.97±0.06 26.83±0.05 27.08±0.12 7.6 0.8 3.044 34.5469 -5.2145 121± 12 25.82±0.02 24.63±0.02 24.87±0.01 25.42±0.03 25.8 0.3 4.495 34.6071 -5.2103 233± 23 26.41±0.03 24.98±0.03 25.40±0.01 25.45±0.03 21.2 0.5 4.790 34.4464 -5.2055 173± 43 27.31±0.06 26.19±0.06 26.51±0.03 26.74±0.10 8.1 0.4 1.345 34.5174 -5.2035 240± 28 26.64±0.03 25.25±0.04 25.68±0.02 25.65±0.04 17.8 0.5 3.788 34.5452 -5.1942 324± 66 28.13±0.14 26.05±0.06 26.58±0.04 27.14±0.11 9.0 0.6 2.095 34.5969 -5.1813 229± 74 28.22±0.14 26.47±0.09 26.89±0.05 26.95±0.11 6.0 0.5 1.204 34.4577 -5.1805 150± 19 25.96±0.03 24.92±0.03 25.20±0.01 25.22±0.03 21.8 0.4 3.982 34.6092 -5.1751 916± 285 27.86±0.13 26.11±0.08 27.01±0.07 27.55±0.13 6.2 0.8 2.750 34.5401 -5.1718 706± 51 26.46±0.05 24.30±0.02 25.11±0.02 25.62±0.04 36.6 0.7 13.648 65

Table 2.6. Lyα emitter candidates from category B. The first two columns are RA and DEC coordinates. The third column is the observed equivalent width. Columns 4 to 7 are the B, IB527, V and R band SExtractor MAG-AUTO in AB units. Column 8 represents the detection in IB527 image. Columns 9 and 10 are the ratio of Lyα line to continuum flux densities in IB527 band and the Lyα line total observed flux.

Fline RA DEC EWobs B IB527 V R Detection Fline Fc

J2000 Deg A˚ AB Mag σ IB527 band 10−17 erg cm2.S 34.6485 -5.5395 109± 49 27.87±0.08 26.57±0.09 26.78±0.04 26.29±0.06 6.2 0.3 0.700 34.6385 -5.5182 151± 52 26.92±0.06 25.85±0.08 26.14±0.04 26.02±0.06 6.5 0.4 1.681 34.6215 -5.5038 151± 53 27.19±0.06 26.18±0.08 26.47±0.04 26.14±0.06 7.2 0.4 1.238 34.6203 -5.5035 152± 71 27.43±0.07 26.58±0.11 26.87±0.06 26.63±0.08 5.2 0.4 0.866 34.5046 -5.5016 115± 56 27.57±0.06 26.71±0.10 26.93±0.05 26.73±0.08 5.1 0.3 0.643 34.4877 -5.5015 112± 23 26.43±0.04 25.22±0.04 25.43±0.02 25.20±0.03 16.7 0.3 2.487 34.5458 -5.4979 143± 59 27.52±0.07 26.53±0.10 26.80±0.05 26.92±0.09 5.8 0.4 0.875 34.5875 -5.4944 113± 34 26.50±0.04 25.64±0.06 25.86±0.03 25.69±0.04 10.5 0.3 1.685 34.6466 -5.4918 143± 58 > 28.51 26.16±0.10 26.43±0.05 24.97±0.04 5.4 0.4 1.231 34.5074 -5.4910 130± 46 26.74±0.04 26.01±0.08 26.26±0.04 26.22±0.06 7.8 0.3 1.325 34.5976 -5.4885 154± 62 27.48±0.06 26.62±0.10 26.91±0.05 26.54±0.07 5.9 0.4 0.842 34.4454 -5.4527 136± 38 26.67±0.04 25.80±0.06 26.06±0.03 26.01±0.05 10.8 0.4 1.663 34.4692 -5.4519 109± 50 27.75±0.08 26.51±0.09 26.72±0.04 25.77±0.04 6.7 0.3 0.745 34.5703 -5.4481 143± 63 27.49±0.06 26.67±0.10 26.95±0.05 26.46±0.07 6.2 0.4 0.767 34.7137 -5.4406 159± 53 27.09±0.05 26.19±0.08 26.50±0.04 26.18±0.06 7.9 0.4 1.268 34.7343 -5.4378 125± 63 27.48±0.07 26.48±0.11 26.72±0.05 26.30±0.06 6.1 0.3 0.839 34.5311 -5.4368 184± 82 27.66±0.08 26.71±0.12 27.05±0.06 26.36±0.11 5.0 0.4 0.862 34.5194 -5.4316 113± 48 27.03±0.06 26.07±0.09 26.29±0.04 26.55±0.08 7.1 0.3 1.134 34.6804 -5.4273 163± 75 27.48±0.09 26.42±0.12 26.74±0.06 26.75±0.10 6.3 0.4 1.043 34.3642 -5.4254 138± 34 26.81±0.05 25.64±0.06 25.91±0.03 25.81±0.04 12.3 0.4 1.929 34.4145 -5.4220 113± 25 26.73±0.05 25.37±0.05 25.59±0.02 25.41±0.03 14.0 0.3 2.181 34.4448 -5.4194 146± 47 > 28.51 25.86±0.08 26.14±0.04 25.03±0.03 7.3 0.4 1.638 34.3360 -5.4190 194± 91 27.80±0.09 26.85±0.13 27.21±0.06 26.90±0.15 5.5 0.4 0.780 34.6942 -5.4172 120± 56 27.53±0.08 26.39±0.10 26.62±0.04 26.18±0.07 6.8 0.3 0.882 34.5273 -5.4166 130± 57 27.37±0.07 26.49±0.10 26.74±0.04 26.44±0.07 5.3 0.3 0.849 34.4331 -5.4159 140± 42 27.05±0.06 25.93±0.07 26.20±0.03 26.20±0.06 8.3 0.4 1.498 34.4230 -5.4127 188± 87 27.52±0.08 26.66±0.12 27.01±0.06 26.97±0.11 5.1 0.4 0.914 34.6587 -5.4099 113± 63 27.36±0.06 26.60±0.12 26.82±0.05 26.16±0.07 5.1 0.3 0.699 34.7157 -5.4081 127± 51 26.97±0.05 26.23±0.09 26.48±0.04 26.35±0.07 6.6 0.3 1.064 34.5833 -5.4071 136± 46 > 28.51 25.88±0.08 26.14±0.03 24.77±0.03 7.0 0.4 1.537 34.5280 -5.4069 162± 71 27.19±0.08 26.16±0.11 26.47±0.05 26.73±0.08 5.5 0.4 1.324 34.6280 -5.4032 137± 34 27.01±0.05 25.92±0.06 26.19±0.03 25.92±0.05 9.8 0.4 1.485 34.5315 -5.3990 161± 57 26.99±0.06 26.19±0.09 26.50±0.04 26.07±0.07 6.3 0.4 1.281 34.3450 -5.3962 128± 49 26.90±0.06 25.96±0.09 26.21±0.04 26.09±0.05 6.8 0.3 1.370 34.4447 -5.3943 145± 76 27.74±0.09 26.67±0.13 26.95±0.05 26.94±0.09 5.7 0.4 0.773 34.6536 -5.3927 126± 49 28.22±0.12 26.51±0.09 26.75±0.04 25.45±0.04 6.6 0.3 0.820 66

Table 2.6 (cont’d)

Fline RA DEC EWobs B IB527 V R Detection Fline Fc

J2000 Deg A˚ AB Mag σ IB527 band 10−17 erg cm2.S 34.3495 -5.3918 120± 53 27.28±0.08 26.10±0.10 26.33±0.04 25.68±0.04 6.3 0.3 1.158 34.3583 -5.3896 115± 53 27.08±0.06 26.23±0.10 26.45±0.04 26.16±0.06 5.8 0.3 1.000 34.5735 -5.3883 126± 65 28.15±0.15 26.51±0.12 26.75±0.05 27.16±0.10 5.5 0.3 0.822 34.6467 -5.3845 115± 48 27.46±0.07 26.45±0.09 26.67±0.04 26.19±0.06 6.1 0.3 0.815 34.3952 -5.3807 178± 79 27.83±0.08 26.83±0.12 27.17±0.05 27.49±0.16 5.0 0.4 0.755 34.5702 -5.3770 139± 46 27.17±0.05 26.26±0.08 26.53±0.04 26.51±0.07 7.5 0.4 1.096 34.7083 -5.3676 160± 55 27.47±0.06 26.48±0.09 26.78±0.04 26.54±0.09 6.5 0.4 0.979 34.4833 -5.3648 115± 52 27.39±0.06 26.53±0.10 26.75±0.04 25.84±0.06 6.3 0.3 0.756 34.3703 -5.3643 124± 43 26.50±0.05 25.65±0.08 25.89±0.03 25.58±0.04 9.2 0.3 1.796 34.7495 -5.3637 110± 59 27.62±0.08 26.40±0.12 26.61±0.04 26.10±0.05 6.7 0.3 0.825 34.6371 -5.3608 137± 54 28.17±0.12 26.48±0.09 26.75±0.04 25.51±0.04 6.8 0.4 0.886 34.5201 -5.3599 119± 42 > 28.51 26.15±0.08 26.38±0.03 24.68±0.04 7.3 0.3 1.100 34.4205 -5.3550 111± 33 26.84±0.05 25.78±0.06 25.99±0.03 26.26±0.06 9.5 0.3 1.479 34.5452 -5.3509 171± 74 27.68±0.06 26.82±0.11 27.14±0.05 25.94±0.05 5.1 0.4 0.747 34.6920 -5.3506 161± 64 27.25±0.06 26.36±0.10 26.67±0.04 25.81±0.08 6.0 0.4 1.099 34.5176 -5.3476 164± 63 27.40±0.06 26.52±0.10 26.83±0.04 26.76±0.11 5.5 0.4 0.959 34.4110 -5.3456 146± 65 28.25±0.15 26.52±0.11 26.80±0.05 26.43±0.07 5.2 0.4 0.888 34.6387 -5.3439 119± 37 26.53±0.04 25.75±0.07 25.98±0.03 25.77±0.04 9.2 0.3 1.584 34.6701 -5.3366 131± 48 27.06±0.05 26.25±0.08 26.50±0.04 26.34±0.06 7.3 0.3 1.063 34.5248 -5.3365 131± 89 27.75±0.10 26.82±0.16 27.07±0.06 26.38±0.08 5.1 0.3 0.631 34.5257 -5.3351 143± 42 26.86±0.05 25.86±0.07 26.14±0.03 26.13±0.06 9.6 0.4 1.620 34.5836 -5.3350 115± 39 26.95±0.05 26.03±0.07 26.25±0.03 26.05±0.05 8.4 0.3 1.200 34.6369 -5.3328 123± 55 28.14±0.12 26.50±0.10 26.73±0.04 25.70±0.04 5.5 0.3 0.816 34.3406 -5.3327 111± 52 27.84±0.12 26.27±0.10 26.49±0.04 25.78±0.04 5.7 0.3 0.935 34.5184 -5.3325 112± 29 26.00±0.03 25.26±0.06 25.47±0.02 25.27±0.03 12.5 0.3 2.409 34.5283 -5.3306 133± 50 27.75±0.07 26.54±0.09 26.80±0.04 25.74±0.05 6.3 0.4 0.825 34.7046 -5.3266 129± 54 27.54±0.07 26.42±0.10 26.67±0.04 26.41±0.07 6.1 0.3 0.906 34.3670 -5.3255 120± 61 27.80±0.08 26.77±0.11 27.00±0.05 26.12±0.07 5.0 0.3 0.622 34.3621 -5.3249 141± 38 27.03±0.06 25.74±0.06 26.01±0.03 25.53±0.04 9.3 0.4 1.799 34.5332 -5.3203 136± 62 28.09±0.14 26.33±0.11 26.59±0.04 25.35±0.03 6.0 0.4 1.017 34.7383 -5.3184 160± 79 > 28.51 26.71±0.13 27.01±0.04 25.99±0.05 5.7 0.4 0.794 34.5807 -5.3151 144± 62 28.06±0.10 26.76±0.10 27.04±0.04 26.66±0.12 5.3 0.4 0.706 34.6698 -5.3136 111± 50 27.09±0.05 26.39±0.10 26.61±0.04 26.83±0.08 6.2 0.3 0.837 34.7196 -5.3124 135± 74 27.91±0.14 26.36±0.13 26.62±0.05 26.39±0.06 6.2 0.4 0.981 34.4734 -5.3057 110± 56 27.85±0.10 26.53±0.11 26.74±0.05 26.58±0.08 5.4 0.3 0.735 34.3283 -5.3045 122± 17 25.80±0.03 24.74±0.03 24.98±0.01 25.07±0.02 23.0 0.3 4.078 67

Table 2.6 (cont’d)

Fline RA DEC EWobs B IB527 V R Detection Fline Fc

J2000 Deg A˚ AB Mag σ IB527 band 10−17 erg cm2.S 34.7326 -5.3035 133± 48 27.31±0.06 26.23±0.09 26.49±0.03 26.80±0.08 8.1 0.4 1.099 34.4207 -5.3021 110± 46 27.23±0.05 26.48±0.09 26.69±0.04 26.53±0.07 6.7 0.3 0.767 34.5409 -5.3018 134± 54 27.78±0.09 26.47±0.09 26.73±0.04 26.47±0.08 5.2 0.4 0.882 34.4400 -5.2939 163± 62 28.02±0.09 26.81±0.09 27.12±0.05 26.29±0.07 5.3 0.4 0.734 34.6492 -5.2916 136± 52 27.83±0.10 26.41±0.09 26.67±0.04 25.75±0.04 6.6 0.4 0.942 34.7011 -5.2900 138± 44 27.04±0.07 25.81±0.08 26.08±0.03 26.47±0.08 8.0 0.4 1.650 34.4560 -5.2898 133± 39 26.83±0.05 25.86±0.07 26.12±0.03 26.20±0.06 8.6 0.4 1.545 34.5475 -5.2876 123± 34 27.27±0.07 26.04±0.06 26.28±0.03 26.49±0.07 9.0 0.3 1.236 34.7419 -5.2848 199± 103 27.74±0.08 26.74±0.15 27.11±0.05 26.92±0.11 5.0 0.4 0.871 34.6000 -5.2835 147± 62 27.09±0.07 26.20±0.10 26.48±0.05 26.15±0.06 6.7 0.4 1.198 34.5597 -5.2820 134± 56 28.00±0.09 26.76±0.09 27.02±0.05 26.86±0.10 5.0 0.4 0.678 34.3677 -5.2813 119± 45 27.61±0.06 26.65±0.08 26.88±0.04 26.52±0.08 5.6 0.3 0.691 34.3359 -5.2800 141± 52 26.86±0.06 26.10±0.09 26.37±0.04 26.27±0.06 5.9 0.4 1.287 34.3515 -5.2788 112± 48 27.60±0.09 26.32±0.09 26.54±0.04 25.92±0.05 5.4 0.3 0.898 34.4313 -5.2661 142± 46 27.30±0.08 26.19±0.07 26.47±0.04 26.52±0.07 6.1 0.4 1.187 34.3713 -5.2580 130± 52 27.45±0.09 26.24±0.09 26.49±0.05 26.34±0.08 7.0 0.3 1.074 34.6049 -5.2382 114± 28 26.53±0.04 25.72±0.05 25.94±0.03 25.81±0.04 8.6 0.3 1.594 34.6030 -5.2128 148± 54 27.59±0.10 26.24±0.09 26.52±0.04 25.70±0.05 5.0 0.4 1.166 34.5535 -5.1994 120± 35 27.93±0.14 25.85±0.06 26.08±0.03 25.95±0.05 9.8 0.3 1.464 34.4580 -5.1900 115± 44 27.53±0.08 26.27±0.08 26.49±0.03 25.90±0.05 6.5 0.3 0.960 34.5790 -5.1782 127± 46 27.53±0.07 26.45±0.08 26.70±0.04 26.47±0.07 6.1 0.3 0.868 34.4374 -5.1687 118± 47 27.69±0.10 26.36±0.08 26.59±0.04 > 27.70 6.8 0.3 0.898 Chapter 3

Magnetic ﬁeld disorder and Faraday eﬀects on the polarization of extragalactic radio sources

This chapter is published in the Astrophysical Journal, (128).

Abstract We present a polarization catalog of 533 extragalactic radio sources with 2.3 GHz total intensity above 420 mJy from the S-band Polar- ization All Sky Survey, S-PASS, with corresponding 1.4 GHz polarization information from the NRAO VLA Sky Survey, NVSS. We studied selection eﬀects and found that fractional polarization, π, of radio objects at both wavelengths depends on the spectral index, source magnetic ﬁeld disorder, source size and depolarization. The relationship between depolarization, spectrum and size shows that depolarization

occurs primarily in the source vicinity. The median π2.3 of resolved

68 69 objects in NVSS is approximately two times larger than that of unresolved sources. Sources with little depolarization are ∼ 2 times more polarized than both highly depolarized and re-polarized sources. This indicates that intrinsic magnetic ﬁeld disorder is the dominant mechanism responsible for the observed low fractional polarization of radio sources at high frequencies. We predict that number counts from polarization surveys will be similar at 1.4 GHz and at 2.3 GHz, for ﬁxed sensitivity, although ∼10% of all sources may be currently miss-

ing because of strong depolarization. Objects with π1.4 ≈ π2.3 ≥ 4% typically have simple Faraday structures, so are most useful for background samples. Almost half of ﬂat spectrum (α ≥ −0.5) and ∼25% of steep spectrum objects are re-polarized. Steep spectrum, depolarized sources show a weak negative correlation of depolarization with redshift in the range 0 < z < 2.3. Previous non-detections of redshift evolution are likely due the inclusion of re-polarized sources as well.

3.1 Introduction

There are many open questions regarding the strength and geometry of the magnetic field in radio galaxies and their relation to other properties of the radio source. The observed degree of polarization depends on the intrinsic properties, such as the regularity and orientation of the source magnetic fields as well as the Faraday effects from the intervening regions of ionized gas along the line of sight. The largest current sample of polarized sources is the NRAO/VLA all sky survey, NVSS, at 1.4 GHz (27). It shows that the majority of extragalactic radio sources are only a few percent polarized. Polarization studies of small samples of extragalactic radio sources at other frequencies also show a similar weak average polarization, and suggest the fractional polarization increases at frequencies higher than 1.4 GHz (e.g. 129). It is not clear which mechanism is dominant in reducing the fractional polarization at lower frequencies and depolarizing the 70 sources, although several models have been suggested (28; 29; 30; 31; 32). One key cause for depolarization is Faraday rotation, which can be character- ized to first order by a change in the angle of the linear polarization:

Z n B dl ∆χ = 0.812 e · dz λ2 ≡ φλ2 (3.1) (1 + z)2 dz where ∆χ is the amount of the rotation of the polarization vector in rad, λ is the observation wavelength in m, z is the redshift of the Faraday screen, B is the ionized medium magnetic field vector in µG, ne is the number density of electrons in the medium in cm−3 and dl is the distance element along the line of sight in pc. The term in parentheses is called the Faraday depth, φ. For a single line of sight through a thin ionized screen, this is equivalent to the rotation measure, ∆χ RM, defined by RM ≡ ∆λ2 which can be measured observationally. Different lines of sight to the source all within the observing beam can have different values of φ. Typically, this progressively depolarizes the source at longer wavelengths, but it can also lead to constructive interference and re-polarization, i.e., higher fractional polarizations at longer wavelengths. There are at least three separate possible Faraday screens with different RM distributions along the line of sight: the Galactic component, intervening extragalactic ionized gas, and material local to the source. Multiple studies such as (10; 11; 130; 131; 132; 133; 134; 135; 136; 137; 138) have tried to identify and distinguish these separate components and study the evolution of the magnetic field of galaxies through cosmic time. When many lines of sight each have independent single Faraday depths, this problem is approached statistically. Another long standing puzzle is the anti-correlation between the total intensity of radio sources and their degree of polarization, as observed by many groups such as (139), (140), (141), (142), (143), (144) and (145). The physical nature of this relation has been a mystery for almost a decade, and is confused by the dependency on other source properties. (143) found that most of their highly polarized sources are steep spectrum, show signs of resolved structure on arc-second scales, and are 71 lobe dominated. However, they found no further correlation between the spectral index and fractional polarization. The anti-correlation between total intensity and fractional polarization seems to become weak for very faint objects with 1.4 GHz total intensities between 0.5 mJy < I < 5 mJy as suggested in (146), based on a small sample of polarized radio galaxies in the GOODS-N field (147). Recently, (148) studied a sample of 796 radio-loud AGNs with z < 0.7. They found that low-excitation radio galaxies have a wide range of fractional polarizations up to ∼ 30 %, and are more numerous at faint Stokes I flux densities while high-excitation radio galaxies are limited to polarization degrees less than 15%. They suggest that the ambient gas density and magnetic fields local to the radio source might be responsible for the difference. Using WISE colors, (135) suggested that the observed anti-correlation primarily reflects the difference between infrared AGN and star-dominated populations. Large samples of polarization data at multiple frequencies are required to understand the magnetic field structures and depolarization mechanisms responsible for the low observed polarization fractions. (133) have showed the polarization fraction of compact sources decreases significantly at 189 MHz compared to 1.4 GHz. They studied a sample of 137 sources brighter than 4 mJy and only detected one polarized source with probably a depolarization mechanism intrinsic to the source. Recently, (9) used the (149) (hereafter TSS09) catalog, and assembled polarization spectral energy distributions for 951 highly polarized extragalactic sources over the broad frequency range, 0.4 GHz to 100 GHz. They showed that objects with flat spectra in total intensity have complicated polarization spectral energy distributions (SEDs), and are mostly re-polarized somewhere in the spectrum, while steep spectrum sources show higher average depolarization. As a result, they claimed that the dominant source of depolarization should be the local environment of the source, since the spectral index is an intrinsic property of these highly polarized sources. The current work follows up on their discovery, using a sample selected only on the basis of total intensity at 2.3 GHz. 72 In this work, we use the data from the S-PASS survey, conducted by the Aus- tralian Parkes single dish radio telescope at 2.3 GHz. We cross match the data with the NVSS catalog and generate a new independent depolarization catalog of bright extragalactic radio sources. Unlike other polarization studies such as (9) and (10) our catalog is not selected based on high polarized intensity which enables us to include objects with low fractional polarizations as well. We study the evolution and possible correlation between quantities such as depolarization, spectral indices and RMs. We will tackle the nature of the well-known observed anti-correlation between total intensity and fractional polarization as well as the origin of the dominant component of depolarization. Section 3.2 presents the 1.4 GHz and 2.3 GHz observations. Section 3.3.1 explains the steps in our analysis of the S-PASS total intensity and polarization maps as well as the cross matching with the NVSS catalog. In Section 3.3.2 we derive quantities such as spectral index, residual rotation measure, fractional polarization and depolarization. The main results and their implications are discussed in sections 3.4 and 3.5 respectively. At the end, Section 3.6 summarizes the main findings and conclusions. Throughout this chapter we employ the ΛCDM cosmology with parameters of −1 −1 H0 = 70 km.s Mpc ,Ωm = 0.3 and ΩΛ = 0.7.

3.2 Observations

3.2.1 The 2.3 GHz Data

The S-PASS is a project to map the southern sky at Dec < −1.0 deg in total intensity and linear polarization. The observations were conducted with the 64-m Parkes Radio Telescope, NSW Australia. A description of S-PASS is given in (150) and (151); here we report a summary of the main details. The S-band receiver used is a circular polarization package with system temperature Tsys = 20 K, and beam width FHWM= 8.9 arcmin at 2300 MHz. Data were collected with the digital correlator Digital Filter Banks mark 3 (DFB3) 73 recording the two autocorrelation products (RR* and LL*) and their complex cross-correlation (RL*). The sources PKS B1934-638 and PKS B0407-658 were used for flux density calibration and PKS B0043-424 for polarization calibration. After Radio Frequency Interference (RFI) flagging, frequency channels were binned together covering the ranges 2176-2216 and 2256-2400 MHz, for an effective central frequency of 2307 MHz and bandwidth of 184 MHz. As described in (151), the observing strategy is based on long azimuth scans taken at the elevation of the south celestial pole at Parkes covering the entire Dec range (-89 deg to -1 deg) in each scan. For the current work, the spatial large scale component has been removed from each Stokes parameter, applying a high pass spatial filter to optimize for compact source finding and analysis. A median filter with a window of 45 arc-min was used. The final product was a set of 15×15 deg2 zenithal projection maps covering the entire sky observed by S-PASS. Final maps are convolved to a beam of FWHM = 10.75 arcmin. Stokes I , Q , and U sensitivity is better than 1.0 mJy beam−1. Details of scanning strategy, map-making, and final maps are in (151) and (150) and will be presented in full details in a forth- coming paper (Carretti et al. 2016, in preparation). The confusion limit is 6 mJy in Stokes I (152) and much lower in polarization (average polarization fraction in compact sources is around 2%, see this work). The instrumental polarization leakage is 0.4% on-axis (151) and less than 1.5% off-axis.

3.2.2 The 1.4 GHz Data

The NVSS is a 1.4 GHz radio survey with the Very Large Array (VLA) covering the entire sky north of -40 degrees declination at a resolution of 45 arcsec (FWHM). The rms brightness ﬂuctuations are approximately uniform across the sky at ∼0.45 mJy per beam in Stokes I and ∼0.29 mJy per beam in Stokes Q and U. The astrometry is accurate to within < 1 arcsec for point sources with ﬂux densities > 15 mJy, and to < 7 arcsec for the faintest detectable sources (∼2.3 mJy in Stokes I). The survey has a completeness limit of 2.5 mJy, which resulted in a 74 catalog of over 1.8 million discrete sources in Stokes I. More details about the NVSS can be found in (27).

3.3 Creating the new sample

3.3.1 Cross-matching and selection criteria

We first attempted to construct a joint S-PASS/NVSS catalog using NVSS I,Q, and U images convolved to the processed S-PASS resolution of ∼11’. However, upon convolution, the resulting NVSS images were very heavily mottled because of the lack of short interferometer baselines, and the noise level increased dra- matically above the full resolution images. We therefore followed an alternative approach, viz., measuring the contributions of all individual NVSS sources at the position of each NVSS source, as described further below. There are rare sit- uations where very-low level diffuse NVSS emission could also have contributed significantly to the S-PASS flux (e.g, cluster halos, 153), and would be missed by our procedure, but this very minor possible contribution to our strong total intensity sources has been ignored. We constructed the initial S-PASS catalog by searching the S-PASS maps at the position of all NVSS sources with INV > 10 mJy in the overlap region between the two surveys, and fitting Gaussian functions to the S-PASS total intensity images. For sources with a spectral index of -0.7 (-0.3) this would correspond to a 4(5) σ detection in S-PASS. However, in order to have adequate sensitivity to sources with low fractional polarizations in S-PASS, we adopted a much higher threshold of ISP > 420 mJy for the catalog. Duplicate sources were eliminated. Additional sources were eliminated from the catalog if they had either of these data quality issues: a) Excess noise (>0.75 mJy per beam rms, 1.5 × the mode calculated in bins of 0.01 mJy) in the 7.5’ - 11.25’ annulus around the total intensity NVSS source; b) Excess noise (>3 mJy per beam rms. 2× the average rms value) in the 45’-90’ 75 annulus in either Q or U maps in S-PASS. We verified by visual inspection that the above selection criteria have successfully eliminated the NVSS and S-PASS regions with instrumental artifacts. At the processed S-PASS resolution of ∼11’, many sources identified by the above procedure are actually blends of multiple NVSS sources. In order to derive meaningful information from the sample, we therefore needed to eliminate sources with significant contributions from blending. To do this, we defined a search radius of 16’ (i.e., to the 3.5σ, 2×10−3 level of the S-PASS beam) around each S-PASS source, and calculated the I,Q, and U contributions of each NVSS source (with

INV >10 mJy) at the position of the S-PASS source. Thus, for the NVSS portion of the catalog, we have two values for each Stokes parameter: XNtarget, the flux (I,Q, or U) of the NVSS source with the largest Stokes I contribution at the S-PASS position, and XNcont, the I,Q, or U flux from all other NVSS sources within the 16’ search radius, scaled by their distance from the S-PASS peak position using a Gaussian kernel representing the S-PASS beam. The final values for comparison with S-PASS are then XNtotal ≡ XNtarget + XNcont. Figure 3.1 shows the distribution of the percent contamination of the target source in NVSS total intensity, Icont , and polarization, Pcont . We then adopted a Itarget Ptarget 10% polarization contamination threshold, and only selected sources with Pcont < Ptarget 0.1. The joint S-PASS/NVSS catalog contains 533 sources meeting all of the above criteria. A description of the biases that could result from our contamination threshold is discussed in Section 3.3.3.

3.3.2 Derived quantities

NVSS and S-PASS polarized ﬂux density, fractional polarization and depolarization

We calculated the polarization intensity (averaged over the entire bandwidth) for the NVSS and S-PASS surveys separately. The eﬀect of bandwidth depolarization 76

Figure 3.1 Distributions of the percentage of contamination in the NVSS total intensity, 100× Icont , in black solid line and polarization ﬂux density, 100× Pcont Itarget Ptarget in red dashed line are shown. The catalog only contains sources with Pcont < 0.1. Ptarget is discussed in section 3.3.2. We used Stokes Q and U to calculate the polarized intensity, P , in both NVSS and S-PASS as following:

p P = Q2 + U 2 (3.2) where for NVSS the Q and U include both the target and contamination ﬂux density, Q = Qtarget + Qcont and U = Utarget + Ucont. The bias corrected polarized 77

ﬂux density, Pbc, is approximated as follows:

q 2 2 2 2 Pbc = Q + U − σp − σcont (3.3)

NV where σp is the global rms of U or Q maps (σU,Q ≈ 0.3 mJy per beam and SP σU,Q ≈ 1.7 mJy per 3-arcmin pixel), measured through the entire Q and U maps, and σcont is the total contribution of the contaminant apertures rms noise to the bias in NVSS, scaled for their separation from the target. We also calculated the fractional polarization, π,

SP Pbc πSP = (3.4) ISP

NV Pbc πNV = (3.5) INV where the NVSS total intensity is equal to the target plus the contamination

ﬂux density, INV = Itarget + Icont. The NVSS residual instrumental polarization percentage peaks at NV ≈ 0.12% for a sample of strong and unpolarized sources (27). We used this value as a cutoﬀ for the NVSS fractional polarization; for any

3σp sources below this threshold we report upper limits as the maximum of I , NV . To estimate the S-PASS residual instrumental polarization we selected the 27 objects with πNV < 0.12% in our ﬁnal sample, and plotted the distribution of their

πSP values (Figure 3.2). The median of the distribution,π ¯SP = 0.55%, which we assumed to be a good estimator of the S-PASS residual instrumental polarization percentage, SP. Note that if the residual instrumental polarizations were zero, then the rms noise of 1.7 mJy per beam would result in much smaller fractional polarizations than 0.55% for the 27 mentioned objects. On the other hand, objects with πNV < 0.12% can potentially be more polarized at higher frequencies, so we could be overestimating the instrumental contribution. We ignored this possibility, and chose the more conservative approach of assuming πSP = 0.55% is only due to instrument leakage.

Out of 533 objects, 416 objects are successfully detected (Pbc > 3σp and π > ) 78

Figure 3.2 Distribution of S-PASS fractional polarization for 27 objects with πNV < NV. in both NVSS and S-PASS polarized ﬂux densities. There are 90 sources that are not detected in polarization in S-PASS but are detected in NVSS, whereas 12 objects with no detection in NVSS polarization are detected in S-PASS. There are 15 objects that do not have polarization above our threshold in either survey. The depolarization, D, is deﬁned to be the ratio between S-PASS and NVSS fractional polarizations: π D ≡ SP (3.6) πNV

We calculated the depolarization of all objects with 3σp polarization detection and π > in both S-PASS and NVSS. Upper/lower limits on D are also calculated for sources as appropriate. 79 Polarization angle and rotation measure

Assuming that the contaminating sources have very little impact on the polarization angle of the target source, we used NVSS and S-PASS Q and U ﬂux densities to derive the polarization angles χNV and χSP; where

1 U χ = tan−1 (3.7) 2 Q

These angles are used to estimate the amount of the rotation measure, RMNS, between the NVSS and S-PASS. The median uncertainty on the derived rotation measures is on the order of 1.6 rad m−2. The polarization angle can be wrapped by a positive or negative integer coef- ﬁcient, n, of π radians from the true angle, the so-called nπ ambiguity. In this 2 −2 case, the true rotation measure is RMNS = RM0 ± nπ/λ rad m .

We used the TSS09 rotation measure catalog ( RMT) to ﬁx n by minimizing 2 the absolute values of ∆RM, where ∆RM ≡ RMT − RMNS − nπ/λ for the 364 sources in common. These are not necessarily the correct RMs, since TSS09 has −2 its own nπ ambiguity of 653 rad m , while this ambiguity for RMNS is about 108 rad m−2. However, they provide the most conservative estimate of ∆RM, the inferred non-linearity in the Faraday rotation as a function of λ. The parameter n took values of −1, 0, 1 for all objects except one with n = −2. Note that, including the polarization contamination and recalculating the RMs based on the two NVSS sub-bands could introduce oﬀsets as large as 42 rad m−2.

As a result, using the uncontaminated NVSS RMT is appropriate.

Bandwidth depolarization

When the RM is high, the rotation of the polarization angle across a ﬁxed bandwidth reduces the net degree of polarization, which is called bandwidth depolarization. To evaluate the importance of this eﬀect for our sample, we used the 364 sources overlapping with TSS09. We predicted the NVSS and S-PASS bandwidth depolarizations for our objects based on the measured TSS09 RMT and our 80

RMNS, respectively. As shown in Figure 3.3 the ratio between the observed fractional polarization and the true degree of polarization πobs/πtrue never gets smaller than 0.95 for S-PASS, and only 3% of objects have NVSS πobs/πtrue smaller than

0.9. The median πobs/πtrue for both S-PASS and NVSS are 0.999 and 0.996 respectively, and therefore, bandwidth depolarization will not aﬀect our analysis throughout this work.

Figure 3.3 The ratio of the observed and true fractional polarizations, πobs/πtrue, based on the NVSS and S-PASS bandwidth depolarizations is shown for 364 objects as a function of the cumulative percentile. Only 3% of objects in our sample experience NVSS bandwidth depolarization which results in πobs/πtrue smaller than 0.9.

Spectral index

We used INV and peak S-PASS (11’ beam) intensities, and calculated the power law spectral index, α, where I ∝ να. Figure 3.4 shows the distribution of spectral indices for our 533 objects. The median isα ¯ ∼ −0.83. The contaminating ﬂux 81 contributing to the NVSS intensities can be a small source of uncertainty in the calculated spectral indices; we estimated its median to be σα,Cont ∼ 0.01 while total uncertainties on the derived spectral indices has median value of σα,T ot = 0.05.

Figure 3.4 Distribution of spectral indices,α, calculated based on NVSS and S- PASS total intensities. The median spectral index isα ¯ ≈ −0.83.

Surface area of the object

We used the NVSS catalog de-convolved minor, θm, and major θJ axes of the target object, and calculated the eﬀective area, A as follows.:

1 A ≡ πθ θ (3.8) 4 m J

One must note that almost all sources remain unresolved in S-PASS due to the very large beam size. 82 Uncertainties

We used the measured local rms values as uncertainties of the NVSS Q, U and S-PASS I, Q and U ﬂux densities. The uncertainty of the NVSS total intensities are extracted from the NVSS catalog. Error propagation is used to approximate the uncertainty on all the other derived quantities such as polarized ﬂux density and rotation measure. We note that (154) showed that the rotation measure uncertainties reported in the TSS09 catalog might be underestimated. As a result, we multiplied all the RMT uncertainties by 1.22 as described in (154).

3.3.3 Selection Bias

We do not select objects based on their polarization intensities or fractional polarizations. However, we apply a threshold cut on the contribution of polarized contaminants. There is a higher probability for objects with low polarized intensity, either intrinsic or due to depolarization, to suffer from contaminating neighbors, and to be dropped from our final sample. To investigate a possible missing population, we compared two different sub-samples a) sources in our catalog with Pcont < 0.1 (533 sources, 416 detected in both NVSS and S-PASS) Ptarget and b) objects rejected from our catalog with 0.1 ≤ Pcont < 0.25 (75 sources, 40 Ptarget detected in both NVSS and S-PASS). We compared the fractional polarization and the depolarization properties of these two sub-samples. If we were not creating a selection bias, then they should have similar properties. Figure 3.5 shows the results. Objects with larger polarization contamination have on average lower 2.3 GHz fractional polarization

(medianπ ¯SP = 1.5%) while less contaminated sources haveπ ¯SP = 2.5%. Moreover, the fraction of sources with πSP < 1% is 2.5 times higher (50%) among objects with 0.1 ≤ Pcont < 0.25 than sources with Pcont < 0.1. The Spearman rank test Ptarget Ptarget between D and Pcont with r = 0.22 and p < 0.00001 rejects the null hypothesis of Ptarget no correlation. Thus, we are likely to be missing a population of highly depolarized sources. 83 Figure 3.5 suggests that around 30% of sources with polarized contamination 0.1 ≤ Pcont < 0.25 have depolarizations log(D) > 0.47. Assuming this fraction Ptarget is also valid for sources with contaminations larger than 25% we estimate that we have missed ∼ 50 depolarized objects in our final sample due to the polarized contamination threshold cut. Therefore, our final sample of 533 sources is missing a population (∼ 50 objects) of heavily depolarized sources due to our contamination threshold cut. How- ever, we can not correct for such an effect since the amount of contamination in our 2.3 GHz polarization intensities can not be measured. As a result, one should treat the number of depolarized sources in our sample as a strong lower limit and consider this in interpreting all the other related conclusions. In addition, it is possible that our total intensity and polarization contamination thresholds have resulted in a bias toward less dense regions of the sky. We measured the surface number density of the contaminating neighbors in our sample and the parent NVSS–S-PASS overlap sample with INV > 10 mJy. We used the same aperture with a radius of 16 arcmin and found that the contaminant surface number density in our final sample (4 × 10−3 arcmin−2) is on average 20% less than our parent sample (5 × 10−3 arcmin−2). It is unlikely that the results of this work are affected by such a bias.

3.3.4 Statistical tests

Throughout this work we adopted two nonparametric statistical tests. We calculated the Spearman rank correlation coefficient (rs) to measure the strength of any possible correlation. The two-sample Kolmogorov-Smirnov (KS) test is also used to check the null hypothesis that two sub-samples, divided by a parameter of interest, are drawn from the same parent distribution. The significance of each test is estimated by performing bootstrap sampling simulations and construct- ing 105 random samples from the initial distribution. We have assigned two-tail p-values based on the results of our simulations. 84 Table 3.2 summarizes the result of all the statistical tests performed in this work. In the case of a single hypothesis test we would reject the null hypothesis if the p-value ≤ 0.01. However, we have performed a total 90 tests, counting both KS and Spearman. To avoid the multiple hypothesis testing problem, we adopted the Bonferroni correction as discussed in (155) and chose a conservative significance level threshold of p-value ≤ 10−4. We therefore rejected the null hypothesis of the KS or the Spearman rank tests only if the corresponding p-value is less than or equal to 10−4. In addition, to test the robustness of correlations with p-value less than 10−4 and to identify any possible influence of the total intensity and polarization contaminations on the results we repeated the relevant statistical tests on smaller (by a factor of ∼0.4) but clean samples of objects with less than 1% contamination. Although the strength of some correlations became stronger or did not change, their p-values increased up to 2 × 10−3 due to the much smaller sam- −3 ple size. We therefore, adopted the robustness probability probust of 2 × 10 as a second threshold and treated the correlations with original p-value≤ 10−4 and −3 2×10 0.05 are rejected.

3.4 Results

We have derived a polarization catalog of 533 extragalactic radio sources, which can be downloaded for public use through the VizieR catalog access tool. The description of the entries in the online catalog is listed in table 3.1. 85

Table 3.1. Description of the entries in the online catalog.

Column index Description

1 NVSS name tag 2 NVSS RA in decimal degrees (J2000) 3 NVSS Dec in decimal degrees (J2000) 4 Galactic longitude 5 Galactic latitude 6 NVSS total intensity, INV 7 Uncertainty on the INV 8 NVSS polarized intensity 9 Uncertainty on the NVSS polarized intensity 10 NVSS fractional polarization, πNV 11 Uncertainty on the πNV 12 Upper limit flag on the πNV 13 NVSS polarization angle 14 Uncertainty on the NVSS polarization angle 15 NVSS catalog fitted deconvolved major axis 16 Upper limit flag on the deconvolved major axis 17 NVSS catalog fitted deconvolved minor axis 18 Upper limit flag on the deconvolved minor axis 19 S-PASS peak intensity, ISP 20 Uncertainty on the ISP 21 S-PASS polarized intensity 22 Uncertainty on the S-PASS polarized intensity 23 S-PASS fractional polarization, πSP 24 Uncertainty on the πSP 25 Upper limit flag on the πSP 26 S-PASS polarization angle 27 Uncertainty on the S-PASS polarization angle 28 Spectral index derived from NVSS and S-PASS 29 Uncertainty on the spectral index 30 Depolarization, D 31 Uncertainty on the D 32 Taylor et al. 2009 rotation measure, RMT 33 Uncertainty on the RMT multiplied by 1.22 34 The NVSS & S-PASS rotation measure, RMNS 35 Uncertainty on the RMNS 36 Rotation measure difference, ∆RM 37 Uncertainty on the ∆RM 38 Median RMT 86

Figure 3.5 Distribution of log(D) (top) and 2.3 GHz fractional polarization πSP (bottom) of objects with Pcont < 0.1 and 0.1 ≤ Pcont < 0.25 are shown with Ptarget Ptarget solid and dashed lines respectively. Black, red and blue colors represent objects with detection, upper limits in S-PASS and upper limits in NVSS polarizations. The area under the log(D) histogram of objects with Pcont < 0.1 and detected Ptarget polarization ﬂux densities is colored in gray for clarity. 87 Table 3.1 (cont’d)

Column index Description

39 Number of sources contributed to the median RMT 40 Redshift from Hammond et al. 2012 41 WISE catalog W1 (3.4 micron) magnitude 42 Uncertainty on the W1 43 W1 detection signal to noise ratio 44 WISE catalog W2 (4.6 micron) magnitude 45 Uncertainty on the W2 46 W2 detection signal to noise ratio 47 WISE catalog W3 (12 micron) magnitude 48 Uncertainty on the W3 49 W3 detection signal to noise ratio

3.4.1 Rotation measures

The distribution of RMNS calculated based on NVSS and S-PASS (black) and the Taylor et al. rotation measures, RMT, (red) for the same objects are shown in Figure 3.6. Both distributions are very similar in shape. Their medians are 3.6 ± 2.0 and 0.5 ± 1.9 rad m−2 , respectively, while their standard deviations are 38.4 and 36.4 rad m−2. Some of the scatter in the RM distributions could be due to the uncertainty of the measurements. (154). However, the median error on the RMT for the small bright sample of 364 objects in this work is −2 only σT = 3.5 rad m . The median measurement uncertainty estimated for −2 RMNS is even smaller, σNS = 1.6 rad m . Subtracting the median errors from the observed standard deviation of the RM distributions in quadrature result in −2 −2 residual standard deviations of 36.2 rad m and 38.36 rad m for RMT and

RMNS respectively, and largely represent the spread in Galactic foregrounds.

3.4.2 Distribution of fractional polarization and depolarization

The median NVSS (S-PASS) fractional polarization of all 533 objects isπ ¯ = 0.017 (0.020) including the upper limits. There are 505 (428) objects with detected

NVSS (S-PASS) polarization (P > 3σp and π > ). However, 416 of these objects 88 are detected in both NVSS and S-PASS. The distributions of NVSS and S-PASS fractional polarization of these 416 objects are shown in Figure 3.7. The median (and standard deviation) of NVSS and S-PASS fractional polarization of these common objects are 0.022 (.022) and 0.025 (0.023), respectively. Although the median values of πSP and πNV are very close, the median value of their ratio (the median depolarization) is not necessarily equal to one. The TSS09 catalog was limited to sources with suﬃcient signal:noise in polarization, and is thus biased towards much higher fractional polarizations (median

π¯T ∼ 0.06) than our catalog, which is ∼3.5 times lower, including both measurements and upper limits. Figure 3.8 shows the normalized distribution of log(D) for steep and flat spectrum sources separately. Objects with both S-PASS and NVSS detected polarizations are shown in solid black, and have median depolarizations of D¯ = 1.4 and D¯ = 0.9 for 315 steep and 101 flat sources respectively. The depolarization distribution of steep spectrum sources is skewed toward large values of D. Al- most 28% of steep spectrum (24% of all) objects have D ≥ 2, and only 2% have D ≤ 0.5. On the other hand, flat spectrum sources include both depolarized and re-polarized objects. There are 17% and 13% of flat spectrum sources with D ≥ 2 and D ≤ 0.5 respectively. The results of the statistical tests presented in Table 3.2 confirm that steep and flat spectrum sources do not have the same depolarization distributions. The red dashed histogram in Figure 3.8 shows the normalized distribution of 58 steep spectrum and 31 flat spectrum objects with upper limits on the depolarization. These sources have S-PASS polarizations less than 3σ or πSP < SP but are detected in NVSS polarization. The 12 steep spectrum objects with NVSS

P < 3σp or πNV < NV and detected S-PASS polarization are treated as lower limits on the depolarization. The dotted dashed blue line show the distribution of the lower limits in Figure 3.8. In total, 16 objects are detected in neither NVSS nor in S-PASS polarizations and we do not show them in Figure 3.8. (9) used their multi wavelength polarization spectra and derived an equivalent 89 power law polarization spectral index β, where π ∝ λβ. As long as the power law model is assumed our depolarization parameter D and β are related such λSP that log(D) = log β where the λSP and λNV are the average wavelengths λNV of the S-PASS and NVSS surveys respectively. (9) found weak evidence of a bimodal distribution for β of steep spectrum objects. We do not see any sign of bimodal depolarization within objects with α < −0.5, as shown in Figure 3.9. The β distribution of steep spectrum objects is single-peaked but asymmetric with a longer tail toward depolarized objects. As will be discussed later, the majority of steep spectrum sources in our sample can be classified as IR AGNs according to their infrared colors. A more complete sample which also includes radio galaxies with infrared colors of normal ellipticals can confirm if the weak bimodal depolarization observed by (9) is real. We also looked at the combined sample of steep and flat spectrum sources and classified them into three depolarization categories. The choice of the depolarization boundaries is somewhat arbitrary. However, we designed the three depolarization categories to isolate the peak observed in Figure 3.11, as is discussed below. Sources with 0.6 < D < 1.7 have median spectral index ofα ¯ ∼ −0.82 while sources with D ≥ 1.7 shows a slightly steeper median spectrum withα ¯ ∼ −0.9. The spectral slope is mostly flat for re-polarized objects with D ≤ 0.6, with a medianα ¯ ∼ −0.1. However, there are 14 re-polarized objects with steep spectral indices, α < −0.5. This is consistent with (9) who also found a small population of steep spectrum re-polarized sources. Figure 3.10 shows the distribution of the spectral indices of re-polarized objects. We also included 24 objects with detection in πNV but only upper limits on πSP. Figure 3.10 suggests there are two separate populations of re-polarized sources with flat and steep spectra. Including the mentioned upper limits on D, 61% of re-polarized sources have α ≥ −0.5 (i.e., flat). To understand the relation between fractional polarization and depolarization, we plotted πSP versus log(D), and calculated the running medians in bins of 30 90 objects (Figure 3.11). There is an apparent peak for S-PASS fractional polarization at log(D) ∼ 0, while both depolarized and re-polarized sources show weaker

πSP than sources with fractional polarization above 6%. Both KS and Spearman rank coefficient tests on the | log(D)| and πSP confirm this anti-correlation. We also used two subsamples with log(D) > 0 and log(D) < 0 and performed the two KS and Spearman rank tests on each subsample separately. The results confirmed that fractional polarizations are higher in the vicinity of log(D) ∼ 0 in each subsample. However, the correlation between | log(D)| and πSP of the subsample with log(D) > 0 became uncertain when only including the contamination clean sample of the robustness test. Table 3.2 summarizes the results of these statistical tests. Figure 3.12 shows the S-PASS (top) and NVSS (bottom) fractional polarization distributions for three sub-samples with | log(D)| ≤ 0.23, log(D) > 0.23 and log(D) < −0.23. Objects with log(D) ∼ 0 have almost the same distribution in both S-PASS and NVSS (by construction) with median fractional polarizations ofπ ¯SP = 0.030 andπ ¯NV = 0.028 while depolarized sources have smaller medians,

π¯SP = 0.024 andπ ¯NV = 0.009 with an oﬀset between NVSS and S-PASS as expected. Objects with re-polarization show more complicated behavior. They have a medianπ ¯SP = 0.015 andπ ¯NV = 0.035. By deﬁnition the median degree of polarization of a sample of re-polarized sources is expected to be higher at 1.4

GHz than 2.3 GHz. It is possible that the true medianπ ¯SP andπ ¯NV are lower than the above values because we would have systematically excluded re-polarized objects with πSP less than the detection limit. This results in over estimating the median fractional polarization of re-polarized sources in both NVSS and S-PASS. 91 3.4.3 Total intensity and fractional polarization

Our sample includes total intensities from 0.42 to 10 Jy, which gives us the op- portunity to study possible correlations between the fractional polarization and total intensity. As listed in Table 3.2 both KS and Spearman tests suggest there is a weak anti-correlation between πSP and ISP of the whole sample of sources at 2.3 GHz. More investigation revealed that is true for steep spectrum (α < −0.5) sources alone, while it disappears for ﬂat spectrum (α ≥ −0.5) objects. The anti-correlation among steep spectrum sources became weaker and more uncertain when only including the contamination clean sample of the robustness test, and thus should be treated as a suggestive trend only. Figure 3.13 shows the

S-PASS πSP of only steep spectrum sources versus their logarithm of total intensity. The calculated running medians (including the upper limits on πSP to avoid any selection bias due to our total intensity cut) are shown as well. Objects with

α < −0.5 and log(ISP) < 2.9 have median ofπ ¯SP ∼ 0.03 while sources with larger total intensity are less polarized with medians ofπ ¯SP ∼ 0.02. To shed light on a possible physical origin of the observed anti-correlation we calculated the luminosities, based on the 261 objects in our sample which have redshifts in the (10) catalog. 222 of these sources are detected in both NVSS and S-PASS polarization. Using our spectral indices, we calculated the K-corrected 2.3 GHz luminosities. The 141 steep spectrum objects have median luminosity 27 −1 of Lsteep = 1.7 × 10 WHz . Although there is a nominal diﬀerence between

π¯SP for higher and lower luminosities (2.6% and 2.2%, respectively), these do not appear statistically significant. There is also no statistically significant difference in | log(D)| for the high and low luminosity steep spectrum sources. The 81 flat spectrum sources are at higher redshifts, on average, and have a ¯ 27 −1 median luminosity of Lflat = 3.0 × 10 W Hz . 92 3.4.4 Correlation between RRM, ∆RM, π and D

There are two measures to characterize the Faraday eﬀects that are either local to the source or in the intervening IGM medium, the residual rotation measure RRM, which takes out the Galactic foreground contribution to the observed RM, and ∆RM ≡ RMT − RMNS, which sheds light on the frequency dependency of the RM. The absolute value of |∆RM| is an indicator of the Faraday complexity of the source and its environment. As explained in the following, we found that ∆RM is anti-correlated with π and correlated with | log(D)|. Faraday complex sources, i.e, those with multiple RM components should be both depolarized and have polarization angles which may not vary linearly with λ2. We therefore examined the possible correlation between depolarization and |∆RM|. Figure 3.14 shows |∆RM| versus | log(D)| for all objects with detected polarization in both NVSS and S-PASS. The running medians of the |∆RM| calculated in bins of | log(D)| show an evolution. To quantify this, we calculated the

Spearman rank, which yielded a correlation coefficient of rs = 0.23 and p-value of p = 0.00003 establishing that depolarization and non-λ2 polarization angle behavior are related. A large RM beyond the Galactic foreground RM screen could also indicate the presence of Faraday complexity and depolarization. To estimate this, we removed the Galactic contribution by subtracting the median RM¯ within 3 degrees of each target (excluding the target itself), using the TSS09 catalog. This yields the ¯ ¯ residual rotation measure, RRMT ≡ RM − RM. Subtracting the median RM is not the best method to estimate the extragalactic component of the RM as discussed in (156). However, for objects above the Galactic latitude of |b| > 20 degrees, which is true for most of our sample, the difference between the (156) recipe and our method is small. As shown in Figure 3.15, we find the Spearman −5 rank coefficient of rs = 0.21 and p-value of 7 × 10 which suggests a correlation between |RRMT| and |log(D)|. However, our robustness test on the clean sample failed to confirm such a trend. Thus, only |∆RM| shows a clear sign of a correlation with depolarization. 93 We also found, the 1.4 GHz and 2.3 GHz fractional polarizations show moderate anti-correlations with |∆RM|, as shown in Figure 3.16 and listed in Table 3.2. Thus, depolarization does reduce the fractional polarizations at these frequencies, although the dominant role of field disorder is discussed in Section 3.5.1. More- −5 over, the Spearman rank test with rs = −0.25 and p-value of < 10 suggest an anti-correlation between |RRMT| and πNV. However, our robustness test failed to confirm this significance.

3.4.5 Polarization, depolarization and the object angular extent

To study how the morphology of a system aﬀects the depolarization, we used total intensity deconvolved areas (A) derived from the NVSS catalog (27). Flat spectrum objects in our sample are unresolved in the NVSS synthesized beam while steep spectrum objects include both resolved and unresolved sources. For the steep spectrum sources, Figure 3.17 shows the distributions of the absolute | log(D)| for two sub-samples - unresolved and resolved sources with the dividing line at log(A) = 2.5 arcsec2. On average, resolved sources have smaller | log(D)| with median of 0.12 compared to 0.20 for unresolved sources. The scatter of the two samples is almost the same with standard deviation of 0.21. Beam depolarization should only play a small role, because most resolved sources are only slightly resolved. We also looked at the dependence of fractional polarization on size. Figure 3.18 shows the distributions of the S-PASS fractional polarization for the unresolved and extended samples of steep spectrum objects. On average, resolved and extended steep spectrum objects have 2.3 GHz fractional polarizations,π ¯SP ∼ 4%, two times larger than their unresolved counterparts. Both KS and Spearman tests conﬁrm a strong strong positive correlation between A and πSP of steep spectrum objects. 94 3.4.6 Spatial distribution of depolarization in the sky

We carried out a brief investigation to see if the depolarization properties in our sample were related to their position in Galactic coordinates. Figure 3.19 shows the distribution of 533 objects in the sky, color coded with respect to their depolarization. Visual inspection does not reveal any obvious over-density of depolarized or re-polarized objects. We also calculated the auto correlation between depolarization and angular separation, and the two point angular correlation function for the most depolarized and least depolarized sources. None of these showed any evidence for clustering of depolarization in space. Similarly, the two point angular correlation functions for the highest and lowest fractional polarizations at 2.3 GHz revealed no clustering. Other work has identified some positional dependence to polarizations in the NVSS catalog. (157) discovered regions with angular scales of ∼ 10 degrees in which the density of the polarized sources drops by a factor of 2-4. They named these regions the “polarization shadows,” and found that some of them are associated with the Galactic HII regions while the rest are related to the depolarized areas in the diffuse Galactic radio emission. All polarization shadows in (157) are located within the Galactic plane at |b| < 20 degrees except one which is at Galactic (l = 5, b = +24). Almost all of the objects in our sample have Galactic latitudes of |b| > 20 degrees, and none are located around (l = 5, b = +24), so the Galactic polarization shadows likely do not affect the current work. However, it is interesting to search for high latitude Galactic diffuse emissions in smaller scales and their probable signature on the depolarization of the extragalactic sources in future surveys and larger samples with higher number density. 95

Table 3.2. Results of non-parametric statistical tests with simulated p-values.

Parameters Constraint KS distribution KS samples KS p-value Spearman rank p-value simulated correlation coeﬃcient simulated

*πSP & α - πSP α ≶ −0.5 < 0.00001 −0.24 < 0.00001 ¯ *πSP & Area α < −0.5 πSP A ≶ A < 0.00001 0.36 < 0.00001

*πSP & | log(D)| - | log(D)| πSP ≶ π¯SP < 0.00001 −0.28 < 0.00001

?| log(D)| & πSP α < −0.5 | log(D)| πSP ≶ π¯SP 0.00050 −0.26 < 0.00001

| log(D)| & πSP α ≥ −0.5 | log(D)| πSP ≶ π¯SP 0.022 −0.37 0.00019

?D & πSP D > 1 D πSP ≶ π¯SP 0.00004 −0.25 0.0095

*D & πSP D < 1 D πSP ≶ π¯SP 0.00005 0.50 < 0.00001 ¯ ?ISP & πSP - πSP ISP ≶ ISP < 0.00001 −0.25 < 0.00001 ¯ ?ISP & πSP α < −0.5 πSP ISP ≶ ISP < 0.00001 −0.25 < 0.00001 ¯ INV & πNV - πNV INV ≶ INV 0.050 -0.13 0.0021 ¯ INV & πNV α < −0.5 πNV INV ≶ INV 0.094 -0.16 0.0013 ¯ INV & πNV α ≥ −0.5 πNV INV ≶ INV 0.96 -0.04 0.67 ¯ INV & | log(D)| α < −0.5 | log(D)| INV ≶ INV 0.33 0.08 0.18 ¯ ISP & πSP α ≥ −0.5 πSP ISP ≶ ISP 0.26 -0.06 0.47

LSP & | log(D)| α < −0.5 LSP | log(D)| ≶ 0.13 0.010 0.12 0.16 ¯ LSP & πSP α < −0.5 πSP LSP ≶ LSP 0.21 -0.13 0.11 ¯ LSP & πSP α ≥ −0.5 πSP LSP ≶ LSP 0.32 0.07 0.53 *|∆RM| & | log(D)| - | log(D)| |∆RM| ≶ |∆RM| 0.0010 0.23 0.00003

*|∆RM| & πSP - |∆RM| πSP ≶ π¯SP < 0.00001 −0.40 < 0.00001 *D & |∆RM| D > 1 D |∆RM| ≶ |∆RM| 0.017 0.26 0.00009 D & |∆RM| D < 1 D |∆RM| ≶ |∆RM| 0.12 -0.14 0.12

| log(D)| & |RRMT| - | log(D)| |RRMT| ≶ |RRMT| 0.019 0.21 0.00007

*|∆RM| & πNV - |∆RM| πNV ≶ π¯NV < 0.00001 −0.44 < 0.00001 ¯ ISP & | log(D)| α < −0.5 | log(D)| ISP ≶ ISP 0.40 0.01 0.80 *D & α - D α ≶ −0.5 < 0.00001 −0.26 < 0.00001 D & z α < −0.5 & D ≥ 1.5 D z ≶ z¯ 0.015 −0.36 0.011

ISP & z α < −0.5 ISP z ≶ z¯ 0.014 -0.12 0.14

ISP & z α ≥ −0.5 ISP z ≶ z¯ 0.14 -0.28 0.0062 D & z α < −0.5 D z ≶ z¯ 0.44 -0.03 0.75 D & z α ≥ −0.5 D z ≶ z¯ 0.15 0.10 0.36

|RRMT| & z - |RRMT| z ≶ z¯ 0.074 0.11 0.10

πSP & z α < −0.5 πSP z ≶ z¯ 0.73 -0.05 0.51

πSP & z α < −0.5 & D ≥ 1.5 πSP z ≶ z¯ 0.79 0.12 0.41

πSP & z α ≥ −0.5 πSP z ≶ z¯ 0.59 0.01 0.96

πNV & z α < −0.5 & D ≥ 1.5 πNV z ≶ z¯ 0.15 0.26 0.075 |∆RM| & z - |∆RM| z ≶ z¯ 0.47 0.04 0.55 96

Figure 3.6 Top: The distributions (top) and the scatter diagram (bottom) of the NVSS, S-PASS rotation measures, RMNS versus TSS09 RMT for the 364 common objects. The three red solid lines in the bottom show one-to-one relations for the three cases of n = [−1, 0, 1]. 97

Figure 3.7 Normalized histograms of fractional polarizations, π, for 416 objects with detected polarization in both NVSS and S-PASS and the upper limits. The black and red solid lines represent the NVSS and S-PASS distributions of objects with detected polarizations while the dashed blue and red lines sketches the distribution of upper limits of NVSS and S-PASS polarizations. For comparison we also show the NVSS fractional polarization distribution of the TSS09 catalog 37543 sources with dotted-dashed magenta line. 98

Figure 3.8 Distributions of log(D) normalized to the total number of objects for steep (top) and ﬂat (bottom) spectrum sources. Black solid histogram represents objects with detected polarization in both NVSS and S-PASS. The red histogram with dashed line is the distribution of the upper limits in depolarization. The lower limits are shown with dotted-dashed blue line. The two red and blue arrows show the direction of movement for the upper and lower limits. 99

Figure 3.9 Distribution of the polarization spectral index β as introduced in (9) assuming a power law depolarization model. The solid blue and dashed red lines represent the steep and ﬂat spectrum sources. 100

Figure 3.10 Spectral index distribution of the re-polarized objects, D < 0.6, including 24 sources with detection in πNV but only upper limits on πSP. While it seems there are two separate populations of re-polarized sources with ﬂat and steep spectrums, the majority of them, 61%, have α ≥ −0.5. 101

Figure 3.11 S-PASS fractional polarization versus log(D). The red solid line represents the running median of πSP calculated in bins of N = 30 objects in log(D) space and the dark-pink shaded region is the estimated uncertainty on the running medians calculated as |M − [p16, p84]|/p(N) where M is the median value and [p16, p84] are the 16 and 84 percentiles. The error bars on the left and right upper corners are the medians of the intrinsic uncertainties in πSP for the two half of data in log(D). 102

Figure 3.12 Normalized S-PASS (upper) and NVSS (lower) fractional polarization distribution for objects with | log(D) < 0.23| (solid black), log(D) > 0.23 (dashed red) and log(D) < −0.23 (dotted-dashed blue). 103

Figure 3.13 S-PASS fractional polarization of only steep spectrum(α < −0.5) versus their total intensity. The open circles represent the upper limits on the degree of polarization. The black solid line is the running medians of πSP including the upper limits and the dark-pink shaded region is the estimated uncertainty on the running medians. The red error bars in upper right and left corners show the median intrinsic uncertainties of πSP for the two half of the data in log(I) space. 104

Figure 3.14 Absolute diﬀerence between rotation measures calculated in this work and in TSS09, |∆RM| versus | log(D)|. Black and green crosses represent depolarized and re-polarized objects respectively. The solid red line is the running median of |∆RM| calculated for bins of 23 objects in | log(D)| space which include both depolarized and re-polarized sources and the dark-pink shaded region is the estimated uncertainty on the running medians. The error bars on the left and right upper corners are the medians of intrinsic uncertainties in |∆RM| for the two halves of the data. 105

Figure 3.16 S-PASS fractional polarization versus the |∆RM| which is a representation of the Faraday structure. 107

Figure 3.17 The | log(D)| distributions of the unresolved (black solid) and extended (dashed red) steep spectrum objects in the NVSS survey. The de-convolved surface area thresholds log(A) ≤ 2.5 arcsec2 and log(A) > 2.5 arcsec2 are used to separate unresolved and extended sources, and the two vertical blue solid and dashed lines represent the medians of | log(D)| for the two samples respectively. 108

Figure 3.18 The πSP distributions of the unresolved (black solid) and extended (dashed red) steep spectrum objects in the NVSS survey. The de-convolved surface area thresholds log(A) ≤ 2.5 arcsec2 and log(A) > 2.5 arcsec2 are used to separate unresolved and extended sources, and the two vertical blue solid and dashed lines represent the medians of πSP for the two samples respectively. 109

Figure 3.19 Distribution of the 533 objects in the sky, color coded with the depolarization. l and b are the Galactic longitude and latitude coordinates in degrees. Black dots are objects that are not detected in either NVSS or S-PASS polarization. Green, red and blue triangles are objects with depolarization 0.5 < D < 2, D > 2 and D < 0.5 respectively. 110 Table 3.2 (cont’d)

Parameters Constraint KS distribution KS samples KS p-value Spearman rank p-value simulated correlation coeﬃcient simulated

*W 1 − W 2 & α - W 1 − W 2 α ≶ −0.5 < 0.00001 0.27 < 0.00001 W 1 − W 2 & D - W 1 − W 2 D ≶ 0.6 0.022 −0.12 0.045 W 1 − W 2 & D - W 1 − W 2 0.6 < D < 1.7 & D > 1.7 0.31 -0.06 0.38 W 2 − W 3 & D - W 2 − W 3 0.6 < D < 1.7 & D > 1.7 0.025 0.06 0.38

W 1 − W 2 & D α < −0.5 DW 1 − W 2 ≶ 0.6 0.27 −0.06 0.42

W 1 − W 2 & πSP α < −0.5 πSP W 1 − W 2 ≶ 0.6 0.62 −0.07 0.36

Note: The * symbol in the beginning of some of the rows indicates that at least one of the tests resulted in −4 −3 −4 p-value ≤ 10 and probust ≤ 2 × 10 . The ? symbol represents suggestive correlations with p-value ≤ 10 and −3 2 × 10

3.4.7 WISE colors and polarization

We matched our catalog to the Wide-field Infrared Survey Explorer, WISE, catalog, (158), with a search radius of five arc-seconds. Out of 533 objects, 455 have WISE counterparts. All of them are detected with at least 5σ in the WISE 3.4µm band, W1, while 445 (323) have > 5σ detection in 4.6µm, W2, (12µm, W3) band. W 1 − W 2 and W 2 − W 3 colors can be used to separate different galaxy populations such as AGNs and ellipticals (158; 159). Recently, (160) studied WISE colors of a large sample of resolved radio galaxies from the Radio Galaxy Zoo project, and found that most radio objects can be classified as ellipticals, AGNs and LIRGs. Figure 3.20 shows the WISE color-color diagram of objects in our sample for which we have depolarization measurements and WISE counterparts. All objects used in Figure 3.20 have W1 and W2 detections larger than 5σ and with small errors in the W2 − W3 colors σ(W 2−W 3) < 0.4. We investigated the possible dependence of the polarization and depolarization on WISE colors. The WISE dependence is difficult to isolate, since flat and steep spectrum objects have different WISE and different depolarization distributions.

We therefore looked at steep spectrum objects only, and found that neither πSP 111 or | log(D)| were signiﬁcantly correlated with WISE colors (Table 3.2). We do not sample the “elliptical” region of WISE color space, which makes up a distinct population in the (160) study.

Figure 3.20 Distribution of objects with steep, α < −0.5 and ﬂat, α ≥ −0.5 spectral indices in the WISE color-color diagram.

3.4.8 Redshift Dependence

There are 222 objects in our sample that are detected in both NVSS and S-PASS polarization maps and have redshifts in (10) catalog. Figure 3.21 shows the redshift distribution of the 222 matched sources, as well as the separated distributions of steep and flat spectrum objects. Steep spectrum objects are located within 0 ≤ z ≤ 2.34 with median redshift ofz ¯ = 0.64 while flat spectrum sources, as expected for a flux limited sample, tend to have larger redshifts, 0.22 ≤ z ≤ 2.81, with median ofz ¯ = 1.18. 112

Figure 3.21 Redshift distribution of the matched radio sources with (10) catalog. Histograms of steep (α < −0.5) and ﬂat (α ≥ −0.5) spectrum sources are shown in dashed blue and dotted-dashed red lines.

As discussed earlier, steep and flat spectrum objects have different depolarization distributions and therefore, we studied their redshift evolution separately. We examined the redshift dependence of only depolarized steep spectrum sources (D ≥ 1.5), since we expected to see a change in polarization properties due to the change in rest frame wavelength. We used the threshold D = 1.5 to choose as many highly depolarized sources as possible while excluding the scattered objects that are in the vicinity of the observed peak at D ∼ 1 in Figure 3.11. We found weak evidence for a decrease in depolarization of these sources as redshift increases (Spearman rs = −0.36, p=0.011), which does not cross our conservative detection threshold. The average πNV of 49 steep spectrum sources with D ≥ 1.5 seems to increase fromπ ¯NV = 0.46% at z ≤ 0.5 toπ ¯NV = 1.02% at z ≥ 0.5, while their observed depolarization decreases and πSP stays almost fixed. Figure 3.22 shows the running median of πNV and D calculated in bins of redshift as well as 113 the expected evolutionary behavior of the three depolarizing scenarios. We will discuss this more in Section 3.5.5. On the other hand, we do not find any change with redshift in depolarization of separate samples of steep or flat spectrum sources which include all re-polarized and depolarized sources. The median, log(D) ≈ 0.1, and standard deviation

σlog(D) ≈ 0.26, of steep spectrum objects stay almost constant with increasing redshift. Flat spectrum sources appear to be mostly re-polarized at z < 1 while at higher redshifts the number of re-polarized and depolarized flat spectrum objects are almost the same. However, as listed in Table 3.2, none of the KS and Spearman tests could confirm such a redshift dependence among flat spectrum sources. We also performed both KS and Spearman rank tests on |RRM| and |∆RM|, and did not detect any noticeable redshift dependence (Figure 3.23). The 2.3 GHz fractional polarization of steep and flat spectrum sources also stays fixed at all cosmic times, although have different average values for populations of steep and flat objects.

3.4.9 Summary of major results

1. The majority of extragalactic radio objects with ISP ≥ 420 mJy have degrees of polarization on the order of 2% to 3% at both 1.4 GHz and 2.3 GHz.

2. πSP and | log(D)| are anti-correlated. On average, objects that are not de-

polarized (| log(D)| ≤ 0.23), have median fractional polarizations ofπ ¯SP ≈

π¯NV ≈ 3% − 4%, withπ ¯SP ≈ 2% for more depolarized objects andπ ¯SP ≈ 1%

for re-polarized sources. Objects with high fractional polarizations (πSP ≈

πNV ≈ 10%) are not depolarized (| log(D)| ≈ 0).

3. Flat and steep spectrum objects have diﬀerent polarization properties. 55% of ﬂat spectrum sources are re-polarized, compared to only 24% for steep spectrum sources. Steep spectrum sources have larger degrees of polarization as well as stronger average depolarization. 114 00 4. Extended objects (> 20 ) have higher fractional polarizations (¯πSP = 4%)

and smaller depolarizations (| log(D)| ∼ 0.13) than compact sources (¯πSP ∼ 2%, | log(D)| ∼ 0.20).

5. Almost 24% of the objects with detected polarization have D > 2. An additional 10% of all sources may be too depolarized to be included in our sample.

6. On average, sources with large | log(D)| (depolarized or re-polarized) show larger changes in RM with wavelength (∆RM).

7. We ﬁnd weak evidence for a redshift dependence of the depolarization in a sub-sample of sources, those with steep spectra and D ≥ 1.5.

8. We do not ﬁnd any evidence for changes of the observed 2.3 GHz fractional

polarization, depolarization, |RRMT| and ∆RM from z = 0 to z = 2 when all sources are considered. The median degree of polarization of both steep (141) and ﬂat (81) spectrum sources with known redshift remain almost

constant at πSP ≈ 2.5% and πSP ≈ 2.0% respectively.

9. A large scatter in both depolarization and fractional polarization is seen at all redshifts.

10. We did not ﬁnd any evidence for angular clustering in the distribution of the depolarized sources.

11. Both π and | log(D)| of steep spectrum sources are independent of WISE

W1 − W2 color. 115 3.5 Discussion

3.5.1 Radio source ﬁeld disorder

While radio synchrotron radiation can potentially be highly polarized, the NVSS and S-PASS fractional polarizations of most objects in our sample are around 2% − 3%, and very rarely exceed 10% (Figure 3.7). Depolarization due to the presence of an irregular Faraday screen between the source and the observer, e.g., can potentially reduce the initial degree of the polarization, generally leading to higher fractional polarizations at higher frequencies (28; 29). However, between 1.4 GHz and 2.3 GHz we find that the majority of extragalactic objects experience only small depolarizations, with 60% of the objects have 0.6 < D < 1.7. Moreover, objects with the strongest fractional polarizations (π ≈ 10%) have little depolarization. The reduction from a theoretical maximum of ∼40-70% to either ≈10% with no depolarization, or ≈3%, with modest depolarization, must therefore be due to field disorder. To approximate the necessary number of randomly oriented magnetic field patches within an unresolved source, we performed a simple simulation. We considered a uniform brightness two dimensional source, with equal fractional polarizations π0 = 50% in each patch. By randomizing the polarization angles, we estimated that sources currently unresolved in our beam should contain approximately 70 to 80 independent magnetic patches to reduce the observed fractional polarization to ∼4%. There is a subset of sources where depolarization does play a significant role. Almost, 24% of sources with detected polarizations have D > 2. Moreover, we estimated a missing ≈10% population of heavily depolarized sources. It is not clear how strong an effect field disorder has for that subset. 116 3.5.2 Prospects for high frequency surveys

One important implication of these results is for surveys at higher frequencies, where one might expect to increase number counts by a large factor because of less depolarization. However, changing the frequency of observation from L to S band will not result in a major increase in the number of polarized detections. the number of polarized objects. As an example, the number of sources with polarized flux densities larger than 10 mJy in our sample is almost equal at both 2.3 GHz and 1.4 GHz (368 in S band and 363 in L band). Future polarization surveys and the Square Kilometer Array, SKA (161) precursors such as Polarization Sky Survey of the Universe’s Magnetism, POSSUM (162), Westerbork Observations of the Deep APERTIF Northern sky, WODAN (163), MeerKAT International GigaHertz Tiered Extragalactic Exploration survey, MIGHTEE (164), Very Large Array Sky Survey, VLASS (165) and VLASS Deep will detect hundreds of thousands of polarized sources in different frequencies. The VLASS will operate at S band from 2 to 4 GHz and has angular resolution and sensitivity of ∼ 3.5 arcsec and 0.7 mJy per beam respectively. The number density of flat spectrum sources is expected to be similar in L and S bands since their flux density is almost independent of the frequency, and their median depolarization is D¯ ∼ 1 as shown in Figure 3.8. On the other hand, steep spectrum, α < −0.5, sources in our sample with medianα ¯ = −0.9 are on average fainter at S band by a factor of 1.4. Therefore, their number density at a fixed signal to noise reduces. However, the median polarization of steep spectrum objects in our sample is approximately 1.3 times higher at 2.3 GHz than 1.4 GHz at resolutions as low as S-PASS, ∼ 9 arcmin. This indicates that the median polarization flux density of these objects should have been reduced by ∼17%. (146) showed at 1.6 arcsec resolution there are ∼ 6 polarized sources per squared degree at 0.7 mJy per beam and S:N > 10 in L band, and the integrated number density of objects with polarization flux density −0.6 larger than p goes as Np ∝ p . As a result, one can expect to detect roughly 11% less polarized objects at S band compared to L band at 1.6 arcsec resolution. All in all, considering the larger beam size of the VLASS all sky survey one can 117 expect to detect approximately the same number of polarized sources in S band as the calculation of (146) in L band. This is already a factor of six above the existing surface density of polarized sources from the NVSS catalog in L band.

3.5.3 Prospects for RM grid experiments

There is strong interest in measuring and estimating the intergalactic magnetic field in clusters of galaxies or in cosmic filaments through RM analysis and tomography, e.g. (136). In the presence of a single Faraday screen along the line of sight, the rotation angle of the radio polarization vector of extra-galactic sources depends linearly on λ2. This simple relation makes it possible to estimate the magnetic field of the medium with some assumptions for the electron density, after subtracting out a Galactic component. However, any complication in the structure of the Faraday screen within the observation beam or along the line of sight through the emitting source will result in non-λ2 behavior, and an inability to isolate the foreground screen of interest. We have measured the non-λ2 behavior using ∆RM. As shown in Figure 3.16, large ∆RMs occur preferentially at low fractional polarizations. In order to avoid large values of ∆RM, which would compromise any foreground experiment, it is necessary to use only fractional polarizations (≥ 3 − 4%). This will cause a reduction in the number of available sources; only 33% of sources in our sample 2 have πSP > 3%. However, if reliable χ(λ ) were available for some subset of sources, then it might be possible to increase this number.

3.5.4 Origins of depolarization

As shown in Section 3.4.6 we did not detect any angular clustering of sources by fractional polarization or depolarization, that would have implied a Galactic origin. We can not rule out the possibility of Galactic RM ﬂuctuations on arcsec scales, but these are likely to be extremely small and we do not consider them further here. 118 The dependence of depolarization on spectral index shows that it must primarily occur local to the source. If depolarization is local to the environment of the source, then it may show signs of dependence to some intrinsic characteristics of the source such as spectral index or the luminosity. The results found here on the spectral behavior are consistent with (9) who did a multi-wavelength polarization study on sources selected from the TSS09 catalog. The dependence of polarization properties of objects on their angular extent (Section 3.4.5) also supports the local depolarization scenario. As shown in Fig- ure 3.17, compact sources seem to have larger depolarizations ( | log(D)| ∼ 0.20 vs. ∼ 0.13) and smaller fractional polarizations (¯πSP = 4% vs. 2%) than sources extended in NVSS. This is inconsistent with irregular screens either Galactic or extragalactic, which should yield higher fractional polarizations and less depolarization for compact sources. Thus, the depolarization must arise in a Fara- day component directly related to the source. If Galactic or intervening Faraday screens were the dominant depolarizing components then we expect to see larger depolarization in a sample of extended sources.

The origin of the total intensity and fractional polarization anti-correlation

The anti-correlation between total intensity and fractional polarization at 1.4 GHz has been extensively discussed (such as 139; 140; 142; 143; 144; 145). Recently, (135) used WISE colors to suggest that the anti-correlation was due to the difference in environments between WISE-AGNs (IR colors dominated by AGN) and WISE-Ellipticals (IR colors dominated by starlight). These effects are likely confused by the fact that the anti-correlation is found only among steep-spectrum sources, as discussed in Section 3.4.3. The WISE-AGN class contains a large fraction of flat spectrum objects, for which we find no anti-correlation, while the WISE-Ellipticals are largely steep-spectrum (135). The dependence we found on the spectral index is also consistent with (140) and the stacking analysis of (166).

The limited range of ISP in our sample makes it difficult to study these effects. 119 However, to illuminate the underlying issues, we note that the suggestive anti- correlation between ISP and πSP of steep spectrum sources must arise from some physical difference in properties between the bright and faint sources that are not expected in fair, uniform samples. We have not been able to identify this underlying parameter. We find no statistically significant anti-correlation between

LSP and πSP. We attempted to correct for the size dependence, in case that was a confounding variable, but the anti-correlation remained. Size could still be an important factor, since the resolution of even the NVSS is much larger than the typical source size. Higher resolution observations of this sample could reveal, e.g., that the bright sources are much more compact and dominated by central AGN, as opposed to fainter, lobe-dominated structures with more ordered ﬁelds.

Depolarization might also be playing a role, since πSP is correlated with the

| log(D)|. However, again, the anti-correlation breaks down when we look at LSP and | log(D)|. This leaves us back, again, at some as yet undetermined physical diﬀerence between the faint and bright sources.

Re-polarized objects

We showed that most re-polarized objects have flat spectra (α ≥ −0.5), and are therefore concentrated in the WISE-AGN population (Figure 3.20). This makes it likely that they contain a high proportion of compact nuclei with polarization SEDs influenced by self-absorbed, and perhaps Faraday thick components. This is consistent with (9) who also found flat spectrum objects have complex polarization behaviors. While 61% of re-polarized objects have flat spectra and are optically thick sources, the remaining 39% have steep spectra. The nature of these objects is not clear. However, there are few proposed models in the literature. re-polarization can occur when there is interference between two (or a few) unresolved and separate Faraday patches in the beam of the telescope. This can result in an oscilla- tory behavior of the fractional polarization with changing frequency as discussed in (167) and (168).(169) studied the AGN jet structure of 191 extragalactic radio 120 objects, and found multiple regions along the jets of a few objects show signs of re-polarization. As discussed in (170) they argue that both internal Faraday rotation in the jet medium as well as the configuration of the magnetic fields can explain the observed re-polarization in these optically thin jets. In Faraday thick regions the rotation of the polarization angles might align the polarization vectors from the far and near sides along the line of sight which can potentially result in re-polarization.

3.5.5 Redshift Evolution

The evolution of the magnetic properties of galaxies with time has been subject of multiple studies (such as 10; 11; 130; 171; 172; 173). We distinguish here between two diﬀerent quantities, an observed redshift dependence and an inferred redshift evolution, based on applying the polarization equivalent of a K-correction (redshift dilution). As discussed in Section 3.4.8, we found weak evidence that the average observed depolarization of steep spectrum depolarized sources with D ≥ 1.5 decreases with increasing redshift, while the 1.4 GHz fractional polarization increases (the 2.3 GHz fractional polarization shows no change). The detected redshift variations are weak, compared to the scatter, and their probability (0.011) does not cross our conservative detection threshold. However, given the importance of this issue, we discuss the causes and consequences of redshift dependencies to help clarify the underlying issues. Polarization SEDs are often complex, especially for ﬂat spectrum sources. This is seen in our numerous detections of re-polarization, and the broad wavelength SEDs cataloged by (9). In such cases, it is impossible to predict the trends of depolarization and fractional polarization with redshift expected from the K-correction. In the case where D ∼ 1, no redshift dependence is expected, since there is no wavelength dependence to the fractional polarization. Therefore, the fact that we observe decreasing depolarization and increasing 1.4 GHz fractional polarization 121 at increased redshift only for steep-spectrum sources with D > 1.5 is consistent with K-corrections only, without any physical redshift evolution. We now look at this more quantitatively, assuming the simplest case of an unresolved source with an irregular depolarizing Faraday screen (28)(B66), external to, but at the same redshift as the source. The expected fractional polarization behavior is then 4 π = π0 exp −Cλrest (3.9)

2 where π0 is the initial fractional polarization and C ∝ σφ is a function of the dispersion in the Faraday depth. For a region with electron density n and magnetic

field component parallel to the line of sight Bz, fluctuations in the parameter nBz over the extent of the region is represented by σφ. Assuming no physical change in σφ with time, the redshift dilution effect results in an increase in the observed fractional polarization, π ∝ exp (−Cλ4(1 + z)−4). The observed depolarization 4 4 −4 also decreases with redshift since D ∝ exp (C(λNV − λSP)(1 + z) ). This simplest picture (Model 1), however, is not quantitatively consistent with our observations (Figure 3.22). We therefore considered two additional models based on the B66 screen. Model 2: A combination of two depolarizing components, one Galactic or relatively local to us, and one at the redshift of the source, and Model 3: A physical change in

σφ of the depolarizing screen at the source redshift. As shown in Figure 3.22, the general behavior of the observed πNV, and D as well as πSP (not shown) of the depolarized steep spectrum sources and their evolution with redshift can be explained by models 2 and 3. However, a single depolarizing component, local to the source, with no evolution in σφ does not seem to be consistent with the observation. Larger samples, and resolved polarization maps where the Faraday structure can be directly seen, are needed to clarify these results. As an alternative to the B66 screen, (29) suggested depolarization can be −4/m modeled as power law π ∝ λ at wavelengths larger than λ1/2, at which the degree of polarization is equal to half of its maximum value. The above relation only holds under certain condition in which the Faraday screen RM structure 122 function varies as a power law across the source S(δx) ∝ δxm where S(δx) ≡< [RM(x + δx) − RM(x)]2 > and x is the angular coordinate. If we assume the fractional polarization of unresolved objects follows any power law model with arbitrary exponent −4/m and a constant related to the RM dispersion, π = −4/m Cλ , then the observed depolarization, D = πSP /πNV , and both the redshift and the σφ dependences cancel out. Therefore, one can expect to observe no evolution in the average D even if σφ changes with redshift, contrary to what we observe.

Comparisons to previous work

Earlier work has been based on samples including sources with both flat and steep spectra, and without selections based on depolarization. For our full sample, we find no redshift trends in fractional polarizations or depolarization, or measures of increased Faraday structure such as |RRMT| and |∆RM|. This is consistent with the negative results from (132) and (10). In addition, their samples were taken from the TSS09 catalog, which is biased towards high fractional polarizations, and thus, towards depolarizations D∼1, for which no redshift evolution is expected. Our data are inconsistent with the analysis of (11), who claimed that the rotation measure of galaxies at redshifts larger than z = 1 are on average larger (by ∼ 10 rad m−2) than the low redshift objects, despite the redshift dilution effect. In Figure 3.23 we show |RRMT| versus the redshift of objects in our sample and overlay the (11) median |RRM| values from their Figure 3. Our data are consistent with theirs, and show no evidence for the claimed increase in RRM.

It is possible that a physical increase in σφ and depolarization as a function of redshift could mask the redshift dilution effect, leaving no observed redshift dependence to fractional polarization, RRM, ∆RM or depolarization. This is discussed with more details in (10), (11), (171), (172) and (173). (130) studied the redshift evolution of the depolarization of 26 resolved, powerful radio galaxies and quasars over the cosmic time. They applied corrections to the measured depolarizations based on models of the wavelength and resolution 123 effects at different redshifts. They claim a physical evolution in σφ and depolarization as a function of redshift, but we cannot compare their results to ours, since neither the original data nor the details of the models are shown.

3.6 Conclusions

We constructed a depolarization (D = π2.3/π1.4) catalog of extragalactic radio sources brighter than 420 mJy at 2.3 GHz including total intensities, spectral indices, observed and residual rotation measures, fractional polarization, depolarization as well as the redshift, 2.3 GHz luminosity and WISE magnitudes for almost half of the objects. We looked for possible correlations between these quantities and found that the fractional polarization of extragalactic radio sources depends on the spectral index, morphology, the intrinsic magnetic ﬁeld disorder as well as the depolarization of these sources. We summarize our main conclusions as follows:

Consistent with previous studies over half of flat spectrum sources in our sample are re-polarized while the majority of steep spectrum objects are depolarized. There is also a significant population of steep-spectrum sources that are repolar- ized; their underlying physical structure is currently unknown. Although steep objects are more polarized at 2.3 GHz, they are fainter in total intensity, and therefore future surveys at higher frequencies will result in approximately the same number of sources at fixed sensitivity as the lower frequencies. Depolarization, and thus fractional polarizations, are related to the presence of Faraday structures indicated by the non-λ2 behavior of polarization angles (∆RM). Future studies using polarized sources as background probes need to minimize RM structures intrinsic to the sources. Such clean samples require high fractional polarizations (π ≥ 4%), which will severely limit the number of available sources. Sources with little or no depolarization between 1.4 GHz and 2.3 GHz have fractional polarizations ranging from a few to 10%. This is much lower than the 124 theoretical maximum, and therefore shows the dominant role of field disorder in creating low polarizations. Compact steep spectrum objects in the NVSS catalog have more Faraday structure, and are ∼ 2 times less polarized at 2.3 GHz than the extended sources. We found suggestive evidence for a decrease in the depolarization from z = 0 to z = 2.3, but only when the sample is restricted to the steep spectrum, α < −0.5, depolarized, D ≥ 1.5 objects. More investigation is needed to confirm the depolarization trend. Assuming that it’s real, it is likely the result of the redshift dilution effect (at least partially) but requires more than a simple depolarizing screen local to the source.

The National Radio Astronomy Observatory is a facility of the National Sci- ence Foundation operated under cooperative agreement by Associated Universi- ties, Inc. Partial support for ML and LR comes from National Science Foun- dation grant AST-1211595 to the University of Minnesota. B.M.G. has been supported by the Australian Research Council through the Centre for All-sky As- trophysics (grant CE110001020) and through an Australian Laureate Fellowship (grant FL100100114). The Dunlap Institute is funded through an endowment established by the David Dunlap family and the University of Toronto. We would like to thank G. Bernardi and D. H. F. M. Schnitzeler and the referee for a number of useful conversations and comments on the manuscript. 125

Figure 3.22 Top: Fractional polarizations at 1.4 GHz, πNV, of depolarized steep spectrum sources with D ≥ 1.5 versus redshift. Bottom: depolarization, D, of the same sample of sources versus redshift. The solid red lines represent the running medians of the πNV (top) and D (bottom) in bins of redshift. The green dotted, dashed blue and purple dashed-dotted lines are representations of the following three cases with B66 depolarization models: 1. A depolarizing screen located at the redshift of the source, 2. Combination of two depolarizing components, one Galactic and one at the redshift of the source, and 3. An evolving σφ at the depolarizing screen at the source redshift. 126

Figure 3.23 Distribution of the |RRM| for the 206 objects is plotted versus redshift, z. Blue and red crosses represent objects with α < −0.5 and α ≥ −0.5. The solid black line shows the running medians of the |RRM| of all sources. The orange ﬁlled circles are the data points extracted from Figure 3 of (11) as discussed in Section 3.5.5. Each circle represents the median value of their |RRM| for each redshift bin. Chapter 4

Abell 2255 Galaxy Cluster

4.1 Introduction

Abell 2255 (Hereafter A2255) is a rich galaxy cluster at redshift z = 0.0806 (174) and is currently going through a major cluster-cluster merger event with at least two members. The X-ray emission of the A2255 has been observed and studied many times which has led to the first indications of a non-relaxed cluster (e.g. 175; 176; 177). The elongated X-ray halo as observed by ROSAT and described in (178; 179; 180) is ∼ 20 off from the brightest optical galaxies. Radio observations of (181) have shown an increase in the frequency of radio galaxies in A2255, both AGNs and star forming galaxies, above non-merging clusters. XMM-Newton observations of A2255 also confirm a recent merger event (∼ 0.15 Gyr ago) along the E-W axis based on the detected ICM temperature asymmetries (182). Recently, through the observation of the X-ray Imaging Spectrometer on board of the Suzaku satellite (183) have detected ICM gas bulk motion with relative velocities of ∼ 2100 km s−1 at 2.6σ significance between the A2255 central and NW regions. +181 In the optical regime, (184) have reported a velocity dispersion of 1221−126 km s−1 for the A2255 cluster based on 35 member galaxies. The spectra of several hundreds of A2255 member galaxies obtained by MX and Hydra spectrographs also suggests a velocity dispersion ≥ 1300 km s−1(185). Moreover, (181) found

127 128 current or recent starburst activity in optically faint star forming galaxies of the cluster along the direction perpendicular to the probable merger axis. The optical multi-color photometric observation of (186) has revealed bimodality and large dispersion in the velocity distribution of galaxies with at least two substructures in the NW and SE of the cluster with different radial velocities of −920 km s−1 and +870 km s−1. The dynamic ICM of the A2255 is filled with diffuse synchrotron radio emission in the form of a central halo, relics and filaments. In fact, A2255 has the largest population of radio filamentary structures known today. The (187) VLA observation of A2255 at 1.4 GHz has successfully detected the first polarization signal coincident with a radio halo. They found that the halo of A2255 has extended filamentary structure with strong polarization (20%-40%) and ordered magnetic fields on scale as large as ∼ 400 kpc. However, (188; 189) found that the high fractional polarization of the rectangular features around the halo as well as their small value of rotation measure and its dispersion indicate that they are radio relics separated from the real central halo and on the foreground of the cluster ICM. In fact, the polarimetric properties of these rectangular relics are the same as individual external radio galaxies of A2255. The spectral indices of the NE and NW relics also become flatter moving away from the cluster center, is consistent with electrons re-acceleration models due to expanding shocks toward the cluster periphery. The (187) also have used the ICM Faraday rotation distribution in front of a few polarized radio galaxies in the cluster and estimated a declining average magnetic field strength from ∼ 2.5µG at the center to ∼ 1.2µG calculated over a 1 Mpc3 volume (190). Moreover, in a series of WRST spectral and polarimetric observations at 18, 21, 25, 85, 92 cm and 2 m wavelengths by (4; 42; 188; 189; 191; 192; 193) more radio relics further away from the central halo were discovered. The elongated halo extends to ∼ 500 kpc towards the S and SW directions at 85 cm. Besides the famous NE relic, more diffuse structures (e.g. SW and NW relics) are detected at projected distances ∼ 2 Mpc from the cluster center. The 129 spectral index of the halo between 25, 85 cm and 2 m shows an unusual radial flattening from the center toward the outer rectangular filaments surrounding it. Recently, (43) have found a temperature jump at the location of the NE relic in the Suzaku X-ray observation. Their observation suggest a temperature ratio ∼ 1.44±0.16 corresponds to a shock across the NE relic with X-ray Mach number of MX−ray ∼ 1.4. This is inconsistent with Mach numbers estimated based on the radio observations of (4) at 25 cm, 85 cm and 2 m, M25−85 = 2.77 ± 0.35 and M85−2 > 4.6. This can be an indication that basic model of diffuse shock acceleration (DSA) does not hold for low Mach number cluster shocks, especially that similar inconsistencies are also observed in other clusters and radio relics such as Toothbrush (40), A2256 (41) and A3667 SE (194). In this work, we present the preliminary results of our high resolution VLA L band total intensity and polarization observations of the radio relics and filaments of the A2255 cluster.

Throughout this work we assume the cosmological parameters H0 = 70 km −1 −1 0 s Mpc ,ΩM = 0.27 and ΩΛ = 0.73. For the redshift of A2255, z=0.0806, 1 corresponds to physical distance of ∼ 92 kpc.

4.2 Deep Very Large Array L band observation

We have obtained deep L band Jansky Very Large Array (VLA) observations1 of the central (RA=17h 12m 42.0s and DEC= +64d 09m 44.0s) and northern (RA=17h 11m 41.2s and DEC= +64d 25m 24.0s) regions of the A2255 cluster in two separate points and in two B and C interferometer antenna configurations. We also obtained P band observations in B configuration, which were not analyzed as part of this thesis. The VLA L band covers a wide frequency range between 1.0 GHz to 2.0 GHz in 16 spectral windows with 64 MHz bandwidth and 64 channels per spectral window. The VLA C antenna configuration span the baselines from 35 m to 3.4 km resulting in synthesized beam of ∼ 14 arcsec and a largest

1NRAO VLA project ID of 29637168 130

Table 4.1. Summary of the VLA L band observation of A2255

MS ID Conﬁguration Pointing Exposure time Unﬂagged seconds percent

314 B Central1 24849 36.1 481 B Central 24849 55.8 713 C Central 22315 36.5 759 C Central 22315 52.1 574 C Central 22310 37.4

314 B Northern2 24888 33.7 481 B Northern 24891 53.3 713 C Northern 23150 29.8 759 C Northern 23155 26.8 574 C Northern 23150 34.8

All B+C Central 116638 43.6 All B+C Northern 119234 35.7

1RA=17h 12m 42.0s, DEC= +64d 09m 44.0s 2RA=17h 11m 41.2s, DEC= +64d 25m 24.0s angular scale of ∼ 970 arcsec in L band. The B configuration has minimum and maximum baselines of 210 m and 11.1 km that results in the synthesized beam of ∼ 4.3 arcsec and a largest angular scale of ∼ 120 arcsec. The observations are done in full polarization products mode and with two base-bands of 512 MHz (8-bit). The center of the two base-bands are at 1.256 GHz and 1.776 GHz. The data dump time for C and B antenna configurations are 5.0 seconds and 3.0 seconds respectively. The total exposure time for the central and northern point observations are 13.81 and 13.83 hours in B configuration and 18.60 and 19.29 hours in C configuration respectively. The details of the observation and exposure times are reported in Table 4.1. We also have observed three standard calibrators 3C286, 3C343 and 3C48 for regular calibrations such as flux density, phase, amplitude and polarization. 131 4.2.1 Data reduction and calibration

We have done the main data reduction and calibration steps by running the NRAO Common Astronomy Software Application, CASA2, VLA pipeline on each scheduling block, SB. In the following we list some of the important procedures applied to the data by the pipeline, including the required manual steps.

• Reducing the Gibbs ringing phenomenon in the spectra due to the very bright but narrow spectral features such as sharp Radio Frequency Interfer- ence, RFI, by applying a Hanning smoothing algorithm.

• Applying the first round of flagging due to issues such as an antenna not being on source, shadowing and the first and last 5 channels of each spectral window.

• Making the spectral and spatial models for the VLA ﬂux density standard calibrator.

• Producing calibration tables for atmospheric opacity corrections, antenna oﬀset corrections, etc.

• Determining ﬁrst round values of delays, amplitude gains and phases for the bandpass calibration.

• Flagging some of the the instrumental artifacts as well the bright RFI features.

• In an iterative process the last two steps are repeated a few times until most RFIs are ﬂagged and good delay and bandpass calibration solutions are found.

• Calculating the spectral indices and absolute ﬂux densities for the complex phase and gain calibrator based on the ﬂux density calibrator.

2https://casa.nrao.edu/ 132 • Producing the ﬁnal calibration tables with antenna based solutions for delays, bandpasses amplitude and gain solutions, phase gain and amplitude gain calibrations, etc.

• Applying the final calibration solutions, final round of automatic RFI flagging and re-weighting the visibility data based on the inverse of the data scatter as a function of time.

The pipeline products such as the calibration tables and diagnostic diagrams have been investigated visually and conﬁrmed.

4.2.2 Polarization Calibration

The VLA pipeline up to the date of writing this manuscript does not support the polarization calibration. To measure the correct polarization vector of the target in each spectral window one has to follow these steps: 1. solving for the instrumental frequency dependent leakage, D-terms, 2. solving for the correct polarization angle. The easiest method to estimate the leakage terms is to observe a calibrator that is not polarized within the frequency range of observation. An alternative approach would be to use a calibrator with unknown polarization but extensive parallactic angle coverage during observation and solve for the D-terms as well as the calibrator polarization at the same time. In this work, we have used the phase calibrator 3C343 which has a very good parallactic angle coverage to solve for the source polarization and leakage terms in each spectral window separately. Applying the frequency dependent instrumental leakage calibration guarantees that the total polarization flux is correct. To calibrate for the frequency dependent R-L phase difference and calculate the accurate polarization angles in each frequency interval, the polarized calibrator 3C286 with known polarization angles is used. The polarization calibration tables are applied to all the target and calibrator fields in each MS. 133 4.2.3 Self Calibration and Imaging

Each pointi within the main MS has been split into a separate MS. The remaining RFI and noisy patches of the data are identified and flagged manually as necessary. This manual step represents a major effort, where subjective decisions were required to balance the competing requirements of eliminating data that would negatively affect map quality, while preserving as much data as possible to improve signal-to-noise, u-v coverage, and spectral coverage. Table 4.1 summarizes the percentage of the remaining unflagged data in each MS. New weights for the visibility data points are calculated by taking into account the inverse of the scatter in the data. We carried out a self calibration process for each MS observation point which starts by CASA CLEAN (195) deconvolution and Fast Fourier transform imaging, continues by one or two rounds of gain phase calibration plus CLEAN deconvolution+imaging and ends by one final round of phase+amplitude gain calibrations and a final deconvolution+imaging step. The produced calibration tables during the self calibration process are investigated manually and are confirmed before being applied to the data. Data points with very weak calibration solutions are marked as flagged. To make the final maps in each observation point the CASA CLEAN procedure with Briggs weighting (196), multi-scale multi-frequency deconvolution algorithm (MS-MFS, 197, 198) with two Taylor terms and wide field imaging technique (w-projection, 199) is used. The multi-scale CLEAN algorithm enables us to image sources that have both compact and unresolved features as well as extended and large scale structures. The multi-frequency deconvolution accounts for the wide frequency range of the VLA L band and the frequency dependent variations of the primary and synthesized beams. The MFS CLEAN algorithm with two Taylor terms takes advantage of the wide frequency bandwidth of the observation and makes a spectral index image as well. The w-projection correction is also required due to the combination of the non-coplanar baselines of the interferometer and large extent of the A2255 cluster which results in wide field of view for the 134

Table 4.2. A2255 VLA L band total intensity and spectral maps

Pointing Conﬁguration UV taper Synthesized beam RMS1 Arc-seconds µJy beam−1

Central B No 3.7 4.1 Central B+C No 4.6 3.6 Central B+C 17 kλ 8.0 4.2 Central B+C 8 kλ 14.2 7.3

Northern B No 3.7 4.2 Northern B+C No 5.6 3.2 Northern B+C 17 kλ 9.5 3.5 Northern B+C 8 kλ 15.0 5.0

1The rms is measured from an underpopulated part of the image before applying the wide band primary beam correction. produced total intensity maps (∼ 400) compared to the synthesized beam. The final total intensity maps of the central and northern observation points are made by including all the B+C configurations to image all the emission and only B configuration data for high resolution studies of bright regions. Moreover, to improve the signal to noise ratio for faint and extended emissions from filaments and relics, UV tapers with 17 kλ and 8 kλ thresholds on the baseline are also used. Table 4.2 lists the number of total intensity maps that are produced, with their respective charectristics. To measure the correct intensity and spectral index for sources that are far from the phase center of each field, it is critical to correct for the primary beam of the antenna. The extent of the antenna primary beam response function depends on the frequency of the observation. Therefore, for the wide L band data the appropriate spectral window weights are calculated and the CASA task wide- bandpbcor3 is used to correct both the total intensity and spectral index maps.

3https://casa.nrao.edu/docs/taskref/widebandpbcor-task.html 135 The polarization Stokes I, U and Q maps are also produced from the B+C conﬁguration data with no uv tapering by slicing each spectral window into 8 sub-bands, resulting in maps with 8 MHz width in frequency. The three I, U and Q maps are deconvolved and are imaged independently with the same CLEAN algorithm settings as described above. However, only one Taylor term is calculated for the MS-MFS algorithm.

4.3 Results

4.3.1 Total intensity morphology of relics and ﬁlaments

The total intensity maps of the central and northern observation points without any uv taper are shown in figures 4.1 and 4.2. The positions of famous radio galaxies and relic diffuse emissions are labeled. The radio galaxy names are adopted from (12). The central point include the following radio galaxies: Beaver, Embryo, Goldfish, Double, Sidekick and the original TRG. We also show the NE relic, the Bridge, C1, C2 diffuse emissions (quoted names are from4), as well as the central halo and rectangular relics surrounding it. While the northern observation point also include some of the central structures and galaxies it also include the NW1 and NW2 relics (4) as well as the Bean radio galaxy. 136

Figure 4.1 The primary beam uncorrected L band image of our central observation point of the A2255 galaxy cluster (synthesized FWHM≈ 4.6 arcsec and rms= 3.6µJy beam−1) with B+C antenna conﬁgurations. The galaxies and diffuse structures names are adopted from (4; 12). The center of the image is not the phase center of the observation. 137

Figure 4.2 The primary beam uncorrected L band image of our northern observation point of the A2255 galaxy cluster (synthesized FWHM≈ 5.6 arcsec and rms= 3.2µJy beam−1) with B+C antenna conﬁgurations. The galaxies and diffuse structures names are adopted from (4; 12). The location of the new diﬀuse structure is shown and labeled as NW3 Relic.

A new relic-like diffuse emission, NW3 138 We also have identified a new diffuse and probably relic structure at RA= 17h 09m 30s and DEC=64d 18m 30s, at ∼ 190 west of the NE relic’s knee, as shown by the name ”NW3” in figures 4.2 and 4.3. The NW3 diffuse emission seems to have at least two separate components in our maps and the total extent of the structure is ∼ 80 which corresponds to ∼ 740 kpc at the redshift of the cluster.

Figure 4.3 The gray scale zoomed and uv tapered (9.5 arcsec beam) VLA L band image of the new NW3 diﬀuse structure at ∼ 190 to the west of the NE relic knee. The NW3 diﬀuse emission seems to have at least two separate components in our maps and the total extent of the structure is ∼ 80 which corresponds to ∼ 740 kpc at the redshift of the cluster.

The central halo and the surrounding rectangular relics Figure 4.4 shows the central halo region of A2255 with the three relic like 139 structures (R1, R2 and R3) in a rectangular form surrounding the halo. The Original TRG and sidekick radio galaxies at the SE and S sides of the halo are also visible. The halo emission fills the region between the three relics and extends to the north and west of the Original TRG. The first relics, R1, is located at the north of the original TRG and extends to the NW for ∼ 60 (∼ 550 kpc). The southern part of R1 with flux densities ∼ 3 mJy beam−1 is approximately 2.5 times brighter than the northern regions of R1. The second relic, R2, is towards the NW of the original TRG and almost perpendicular to R1. The western part of R2 is sharply bent toward the NW direction and seems to connect to the end of the third relic structure. R3 is almost parallel to R1 and approximately has the same projected extent. The perpendicular separation between R1 and R3 is roughly ∼ 3.20. 140

Figure 4.4 The VLA L band total intensity image of the central halo and rectangular relic-like structures of A2255. To show the compact structures and diffuse emissions in one map the high resolution image (3.7 arcsec beam) with only B antenna configuration is overlaid on top of the uv tapered (8 arcsec beam) image with B+C antenna configurations. The new thin filaments located at the southern edge of the halo are also shown and labeled with TRG-F1, TRG-F2 and Sidekick-F.

The famous NE relic 141 The NE relic is detected in both the central and northern points and is shown in Figure 4.5 along with the Bridge, C1 and C2 emissions. The northern part of the NE relic (hereafter, NE-N) is thin and ∼ 50 (460 kpc) long. The projected curvature of the NE-N relic changes at the NE-knee as shown in Figure 4.5. The southern part of the NE relic (hereafter NE-S) is larger (∼ 6.70), brighter and becomes thicker in projection. While NE-S is filled with diffuse emission, at least two bright filamentary structures are visible as well. Figure 4.6 shows the average flux density profile across the minor axis of the NE-S relic, measured within the dashed box shown in Figure 4.5. The southern rim of the NE-S relic shows a sharp cutoff in flux density toward SW direction while the diffuse emission flux density decreases in a much slower pace from the northern rim towards the NE direction. 142

Figure 4.5 The L band total intensity map of the NE relic with its northern, NE- N and southern, NE-S components, and the Bridge, C1 and C2 diffuse emission regions are shown. The high resolution image (3.7 arcsec beam) with only B antenna configuration is overlaid on top of the uv tapered (8 arcsec beam) image with B+C antenna configurations. The dashed box shows the region used to calculate average flux density profile across the minor axis of the relic as shown in Figure 4.6. 143

Figure 4.6 The average ﬂux density as a function of RA and DEC across the minor axis of NE-S relic. The dashed box in Figure 4.5 shows the region used to measure the ﬂux densities used to produce this diagram.

The Bridge, C1 and C2 The Bridge diffuse emission is located to the north of the Goldfish radio galaxy and is extended over a ∼ 1.80 by ∼ 1.20 region as shown in Figure 4.7. It has a projected shape of an elongated donut with thickness of ∼ 0.30 and excess of flux in its south-eastern edge. The average flux density profiles along two rectangular slices (Figures 4.7) are calculated and shown in Figure 4.8. In NE-SW direction, the average flux density is at its maximum at the south-eastern rim (∼ 35µJy beam−1), and experiences a sudden decrease to ∼ 15µJy beam−1 then gradually drops down to the background level until it jumps up to ∼ 12µJy beam−1. In the NW-SE direction, the average flux density peaks at ∼ 15µJy beam−1, drops to ∼ 10µJy beam−1 and rises again to ∼ 12 − 13µJy beam−1. The Bridge and C2 are located at approximately similar distances (5.50) but opposite directions from C1. Both C1 and C2 are resolved into two patches connected by diffuse emission. Although C1 is located almost at the edge of the NE relic in projection there seem to be a clear gap between the two regions. 144

Figure 4.7 Zoomed VLA L band image (4.6 arcsec beam) of the Bridge diffuse emission is shown. The morphology and the light profile of the Bridge suggest an structure like a bubble, similar to the lobes of radio galaxies. The two rectangular slices are used to calculate the average light profile along the major axis of each region as shown in Figure 4.8. 145

Figure 4.8 The average flux density profile of the Bridge diffuse emission along rectangular slices in NW-SE (left) and NE-SW (right) directions.The two rectangular regions used to calculate the average light profiles are shown in Figure 4.7.

The two NW relics Figure 4.9 shows the two NW1 and NW2 relics. NW1 is approximately 2.45 Mpc in projection away from the X-ray center of the cluster and has an irregular diffuse structure with flux density variations between 50µJy beam−1 to 80µJy beam−1 in our uv tapered image with a 15 arcsec beam. The NW2 relic is roughly at 90 to the southwest of the NW1 and has a more complicated structure. There are at least two filamentary regions visible in Figure 4.9. 146

Figure 4.9 The zoomed and uv tapered (9.5 arcsec beam) VLA L band image of the NW1 and NW2 relics at ∼ 2.45 Mpc and ∼ 2.3 Mpc in projection from the cluster X-ray center. The NW2 relic seems to have at least two separate ﬁlamentary structures in our maps.

The Original TRG and Sidekick thin filamets The VLA high resolution L band image of the Original TRG and Sidekick radio galaxies are visible in Figure 4.10. The Original TRG is a head tail radio galaxy with lots of structure in its tail. The optical counterpart is located at RA= 17h 12m 23.2s and DEC= 64d 01m 57.0s. The long and bent tail extends toward the NE direction for ∼ 2.10, corresponding to ∼ 193 kpc at the redshift of the cluster. The north-eastern end of the tail connects to a very thin filament 147 (hereafter TRG-F1, RA= 17h 12m 39.8s and DEC= 64d 03m 37.7s) extending in a S-N direction for ∼ 1.20 (110 kpc). We do not detect any associated radio galaxy along the TRG-F1 filament. The thickness of the TRG-F1 is ≤ 5 arcsec which makes it one of the thinnest filamentary structures observed in the ICM of galaxy clusters up to this date. The integrated flux of the TRG-F1 is ∼ 21 mJy while the flux density values along the filament vary from 20µJy beam−1 to 70µJy beam−1. We also have detected another faint filamentary emission (more clear in uv tapered maps), at the immediate eastern side of the TRG-F1 and connected to the northern and southern end of TRG-F1, forming a closed loop-like morphology (4.4). In addition, we have identified a second thin filament (hereafter TRG-F2) at the end of the Original TRG’s tail, elongated in an E-W direction and almost perpendicular to TRG-F1. TRG-F2 has approximately the same angular extent and thickness as TRG-F1. However, its middle part is overlaid on top of the Original TRG’s tail and therefore, we can not measure a reliable integrated flux for the filament alone. The Sidekick is also a head-tail radio galaxy located to the west of the Original TRG. Its tail is extended ∼ 1.10 toward the south direction. Surprisingly, we have detected a third example of filamentary emission (hereafter Sidekick-F) at the southern edge of the Sidekick’s tail. The Sidekick-F extends in SE-SW direction for ∼ 0.90 in projection which corresponds to ∼ 83 kpc at the redshift of the cluster (Figure 4.10). 148

(a) (b)

Figure 4.10 a: VLA high resolution (3.7 arcsec beam) L band image of the Original TRG and Sidekick radio galaxies is shown in blue. The optical image retrieved from the Digital Sky Survey is also overlaid in red. b: The VLA wide L band spectral map of the Original TRG and Sidekick radio galaxies is shown and color coded.

Famous radio galaxies in A2255 A2255 has a good collection of radio galaxies with collimated straight or bent jets as well as head-tail objects. The morphological diversity of radio galaxies in the A2255 is an indication of the dynamic environment and existence of ICM weather. The Goldfish head-tail radio galaxy is located at ∼ 40 to the NE of the cluster center and is shown in Figure 4.12. The long and thin tail of the Goldfish is filled with filamentary structure along its major axis. The long tail of the Goldfish extends almost toward the south direction for ∼ 2.80 (257 kpc) and changes its curvature toward the end. The Beaver is located at 160 (1.5 Mpc in projection) to the south from the cluster center and has the most extended tail emission toward the north. The 85 cm observation of (4) shows that the Beaver tail extends all the way to the central 149 regions. Figure 4.13 shows the high resolution image of the Beaver galaxy. The jets extend ∼ 9 arcsec (∼ 14 kpc) into the ICM before they start bending toward the cluster center. The two jets connect to each other at ∼ 25 arcsec away from the Beaver galaxy. The Embryo is another galaxy at ∼ 160 to the east of A2255 cluster center. As shown in Figure 4.14 the southern jet remains straight for ∼ 1.40 until it forms its lobe. The southern lobe shows sign of a twist. More emission with much fainter flux density is visible beyond the main lobe. On the other hand, the northern jet remains straight for ∼ 33 arcsec and bends toward NW direction after that. The main northern lobe is located at ∼ 1.40 from the galaxy. As a continuos of the northern lobe structure a diffuse emission extends toward the south direction for ∼ 45 arcsec in projection and bends almost 90 degrees toward the cluster center.

4.3.2 Spectral analysis

L band spectral index of TRG-F1 and TRG-F2 ﬁlaments Figure 4.10 shows our high resolution L band spectral map of the Original TRG and the Sidekick radio galaxies. The L band spectral indices of the Original

TRG is αL ≈ −0.6 at the head and steepens to αL ≤ −2 at the tip of the tail. The two TRG-F1 and TRG-F2 filaments seem to have steep spectral indices in the VLA B configuration image with 3.7 arcsec beam size. To improve the signal-to- noise ratio and estimate reliable spectral indices for the two filaments we used the image with B+C configuration data and lower resolution (4.6 arcsec beam). As shown in Figure 4.11 we carefully put boxes on the regions of spectral index map that are away from the edges and have small uncertainties in the corresponding spectral error map. The median value within each box is calculated as the average spectral index, αmed. We have used the spectral indices standard deviation and the median intrinsic uncertainty from the spectral error image to estimate the overall uncertainty on the reported spectral index values, σ2 = std2 + σ2 . As αmed α α a result, for the TRG-F1 filament we have measured αmed = −2.2 ± 0.3. 150 We also have measured the spectral index profile along the tail of the Original TRG. We put three boxes with width of 5 arcsec along the tail and have measured the average spectral index across the box every 1 arcsec. As shown in Figure 4.11, The head of the Original TRG is the flattest region with α = −0.6. The spectral index steepens linearly along the tail with slope of ∼ −0.6 and reaches values around α ≈ −2.1 at the tip of the tail at ∼ 120 arcsec crossed distance. The middle of the TRG-F1 filament is roughly 40 arcsec away from the tip of the tail and our best fit line predicts αpredict = −2.6 which is steeper than the measured median spectral index of the TRG-F1 by a factor of ∼ 1.2. The TRG-F2 lies on top of the Original TRG tail in projection and therefore we can not use the central regions to estimate a reliable spectral index. We carefully have placed two separate boxes on the left and right size of the filament as shown in Figure 4.11. The spectral indices for the TRG-F2 estimated from the left and right box are αmed = −2.4 ± 0.3 and αmed = −2.1 ± 0.3 respectively. The L band spectral index of the tail of the Sidekick radio galaxy steepens from ∼ −0.6 at the head to ∼ −1.4 at the tip of the tail. We could not determine the spectral index of the Sidekick-F filament due to its low surface brightness. 151

Figure 4.11 Top: VLA L band spectral image (B+C configuration, 4.6 arcsec beam) of the Original TRG and Sidekick radio galaxies as well as their filaments. The three boxes used to calculate the median spectral indices for the TRG-F1 and TRG-F2 filaments are shown with black-dashed lines. The values of αmed are labeled on top of each box. The three white boxes are used to measure the spectral index profile along the tail of the Original TRG. Bottom: The L band spectral index spatial profile along the tail of the Original TRG and the best fit line are shown in blue and green respectively. The red bullet represents the average spectral index of the TRG-F1. 152

(a) (b)

Figure 4.12 a: VLA high resolution (3.7 arcsec beam) L band image of the Goldﬁsh radio galaxy is shown in blue. The optical image retrieved from the Digital Sky Survey is also overlaid in red. b: The VLA wide L band spectral map of the Goldﬁsh radio galaxy and its long tail is shown and color coded. 153

(a) (b)

Figure 4.13 a: VLA high resolution (3.7 arcsec beam) L band image of the Beaver radio galaxy is shown in blue. The optical image retrieved from the Digital Sky Survey is also overlaid in red. b: The VLA wide L band spectral map of the Beaver radio galaxy is shown and color coded. 154

(a) (b)

Figure 4.14 a: VLA high resolution (3.7 arcsec beam) L band image of the Embryo radio galaxy is shown in blue. The optical image retrieved from the Digital Sky Survey is also overlaid in red. b: The VLA wide L band spectral map of the Embryo radio galaxy and its collimated jets and lobes are shown and color coded.

L band spectral indices of relics We have used the central and northern uv-tapered images with ∼ 15 arcsec beam size to measure the L band spectral indices of the relics and diﬀuse extended emission throughout the A2255 cluster. For each relic, we have identiﬁed regions with spectral index uncertainties σα < 0.3 that are also under crowded from point sources. We have measured the L band median spectral index, αmed, over the selected regions and calculated its uncertainty as explained before. Table 4.3 summarizes the extracted spectral indices of extended feature in A2255 cluster. Low frequency spectral indices of relics We compared our VLA L band total intensity maps with observation of the WSRT interferometer at 85 cm wavelength (4). The resolution of the 85 cm map is ∼ 10, four times lower than our lowest resolution image. As a result, we have measured the 20 cm and 85 cm total intensities of regions with widths of ≥ 10 throughout the relics. We have calculated the corresponding spectral index, 155

Table 4.3. Spectral index of relics and ﬁlaments in A2255

∗ ∗∗ ∗∗∗ Source αmed α20,85 Region ID L band

TRG-F1 −2.2 ± 0.3 −1.5 ± 0.1 6 TRG-F2 east −2.4 ± 0.3 TRG-F2 west −2.1 ± 0.3 R1 (SE region) −1.3 ± 0.3 −2.0 ± 0.1 5 R2 (NW angle) −1.2 ± 0.1 8 R3 −1.2 ± 0.1 7 The Bridge −1.3 ± 0.2 −1.1 ± 0.1 13 NE relic (central region) −1.7 ± 0.4 −0.8 ± 0.1 4 NE relic (knee) −0.8 ± 0.1 1 NE relic (NW region) −0.9 ± 0.1 2 NE relic (SE region) −1.0 ± 0.1 3 NW1 relic (northern region) −1.3 ± 0.3 −0.7 ± 0.2 10 NW1 relic (southern region) −0.8 ± 0.2 9 NW2 relic (NW region) −0.7 ± 0.2 12 NW2 relic (SE region) -0.8 −0.4 ± 0.6 11

∗The median L band spectral index is measured from our VLA L band spectral images with ∼ 5 arcsec beam. ∗∗Spectral indices between our L band 20 cm and WSRT 85 cm (4) total intensity maps. ∗∗∗The ID of regions used to calculate α between 25 cm and 85 cm. These regions are chosen to be under crowded by point sources and at least ∼ 10 (85 cm map beam) wide and are shown in Figure 4.15.

α20,85, for the selected areas. Figure 4.15 shows the L band cropped images of the central and northern parts of A2255 with overlaying regions used to calculate

α20,85. Table 4.3 lists the values of α20,85 for A2255 features along with the region box ID number used to calculate the corresponding spectral index. 156

(a) A2255 Central region (b) A2255 northern relics

Figure 4.15 The VLA L band total intensity maps (15 arcsec beam) of the central and northern regions of A2255 are shown. The dashed magenta boxes represent regions that are used to calculate the spectral indices of relics between L band observation and the WSRT map in 85 cm.

Comparison of αmed and α20,85 The observed spectrum of the pure synchrotron radiation that have not had experience any loss or gain of energy is a simple power law with fixed spectral index along the whole frequency range of emission. We have measured both αmed and α20,85 for TRG-F1 filament, R1 relic, the Bridge, central region of NE relic, northern region of NW1 and southern part of NW2 relics as listed in Table 4.15 and shown in Figure 4.16. In all relics, except the R1, the spectrum become steeper at higher frequencies, αmed < α20,85 and therefore a simple power law model can not explain the observation. In case of the SE region of R1 the L band spectral index, αmed = 1.3±0.3, is much flatter than the α20,85 = −2.0±0.1. This is most likely due to much lower resolution of the 85 cm map and the confusion 157 from the nearby sources of emission such as TRG-F1 and the radio halo.

Figure 4.16 The L band spectral index of the TRG-F1 ﬁlament, the Bridge, central region of the NE relic, the northern part of the NW1 relic and southeastern part of NW2 relic are plotted against the estimated spectral index between our VLA 20 cm and WSRT 85 cm maps. Black and red solid lines represent the theoretical synchrotron emission spectral energy distribution for a simple power law model and the JP model (low frequency index of -0.5, 13) that takes into account the aging of the electrons population.

4.3.3 Faraday Synthesis Analysis

The polarization maps for each channel were ﬁrst convolved to the lowest resolution, 8.5 arcsec in the Northern ﬁeld and 7.5 arcsec in the Central. They were then corrected for the primary beam at each respective frequency. The maps were assembled into Q and U spectral cubes by the Astronomical Image Processing Sys- tem, AIPS4, and Faraday synthesis performed, as described further below, using a single weight for each spectral channel derived from the noise in that channel. A

4http://www.aips.nrao.edu/ 158 total of 12 sources were detectable in polarization above the noise in the Central field, which varied as a function of position in the field. In the Northern field, 6 sources were found, 3 of which were also detected in the Central field. We also convolved the Q, U cubes to a resolution of 15 arcsec but detected no further polarized sources. We also made a Q, U cube for the phase and polarization calibrator, 3C343, in order to check for any residual instrumental polarization. The average residual polarization was 0.1% . In the following, we focus on the results from the Central field, which were generally of higher quality. In order to more appropriately weight the spectral channels, small cutout cubes were constructed around each detected source, and the off-source rms measured. The noise was a strong function of frequency, especially for sources to the edge of the field where the primary beam correction was strong. Figure 4.17 shows the weighting as a function of λ2, for two different sources, with the corresponding Faraday Transfer Functions shown in Figure 4.18. The width of the main peak is of order 60 rad m−2. Note the significant side lobes, especially for source A, which is further from the field center at RA 17 10 36.3 and DEC +64 29 52. Channels with zero weight were generally due to a complete loss through RFI flagging. 159

Figure 4.17 The weighting of each channel used in Faraday synthesis for two sources A (solid ) H (the Original TRG, dashed). (Procedure for determining weights and the reason for the diﬀerences between the two are discussed in the text.)

Figure 4.18 The Faraday transfer function for two sources (A left, Original TRG right)

We produced Faraday spectra using the AIPS task FARS5, using a resolution of 10 rad m−2 and a range in Faraday depth of ±1000 rad m−2 . The results reported

5http://www.aips.nrao.edu/cgi-bin/ZXHLP2.PL?FARS 160 here are only preliminary because the Q,U cubes have not yet been converted to fractional polarizations at each frequency, i.e., correcting for the spectral index of the total intensity emission. A single Faraday rotating component would produce sine or cosine waves in Q/I, U/I, but here we are performing Faraday synthesis on Q and U directly. This has the result of preserving the dominant Faraday depth, but broadening the distribution, and adding extra spurious power into the side lobes. In addition, a quick examination of the I spectral cube shows that some channels with normal appearing noise do not result in consistent I ﬂuxes. These will be the target of further quality control. For the above reasons, any indications of Faraday complexity, as a opposed to a single foreground rotation, are not yet trustworthy. Fractional polarizations may also be somewhat underestimated because power in the Faraday spectrum will be spread over more than the width of the transfer function. In order to recover some of the power going into the side lobes, we performed a ”CLEAN” operation on the Faraday spectra, using the FARS task and 250 it- erations. We note that this cleaning process itself is not robust, as demonstrated in (200). However, for this preliminary census of polarization, it did improve the side lobe structure. We also took the additional unconventional step of convolving the clean components with a Gaussian of width 125 rad m−2 to smooth out this structure. Figure 4.19 shows cleaned spectra for source ”A” using both the nominal Faraday transfer function width, and the broader 125 rad m−2 value for clean component reconstruction. The nominally restored clean clearly shows spurious side lobe structures, while the broad restoration shows a broadened main peak. This would normally be a sign of Faraday complexity, although that conclusion is not justiﬁed here because of the lack of a spectral correction. 161

Figure 4.19 Polarization results for sources A, Embryo, Goldﬁsh and Original TRG from top to bottom. Left: Total intensity contours at 8 arcsec resolution with polarized intensity (the peak amplitude in the Faraday spectrum) in grayscale, at 7.5 arcsec resolution. Middle: Brightness is polarized intensity (as on the left). Color is the Faraday depth (rotation measure) of the peak in the Faraday spectrum, with the color code at the bottom. Right: The cleaned Faraday spectrum at the position of the peak polarized intensity, using a 125 rad m−2 restoring Faraday beam. 162

Table 4.4. Bright polarized features in A2255

Source Region Fractional polarization Faraday depth At peak P rad m−2

A (background) Northern peak 10% 26.5 Embryo Bright P region N-jet 5%-10% -5.9 Goldﬁsh Head 0.7% -3.2 Original TRG Head 0.6% -0.5

After cleaning, the cubes were searched for the maximum amplitude as a function of Faraday depth for each pixel, using the AIPS task AFARS6. This task also reported the Faraday depth for that peak. Pixels that have no corresponding emission in total intensity can be used to estimate the noise in Faraday amplitude. For the 12 polarized sources in the Central field, the noise ranged from 2.3 to 12.3 µJy beam−1 FTF−1 (nominal restore). For this preliminary exploration of polarization, we report on four sources, three of which have hosts which are members of the A2255 cluster, and one of which (A) is a background source with an r magnitude of 20.7 and a photometric redshift 0f 0.47 ± 0.1. The figures below show a) the polarized intensity (peak Faraday amplitude) with the low level total intensity contours; b) a polarized intensity image color-coded by the Faraday depth at the peak amplitude in the spectrum, and c) the cleaned Faraday spectrum, with ∼ 60 (A), ∼ 125 (Embryo, Goldfish, Original TRG) rad m−2 restoring beam, at the location of the brightest pixel in Faraday amplitude. Polarization values at the location of the brightest polarization feature for each source are summarized in Table 4.4.

6http://www.aips.nrao.edu/cgi-bin/ZXHLP2.PL?AFARS 163

Figure 4.20 The Faraday amplitude is plotted versus the Faraday depth. Each data point represent a pixel in the our polarization maps. Three A2255 radio galaxies, Embryo, Original TRG, the Goldﬁsh and a background radio source with double lobes are used to generate this plot.

Figure 4.20 shows plots of the peak Faraday amplitude Ppeak(x, y) at each RA, Dec pixel vs. the Faraday depth at that pixel. At the lowest levels, the results are consistent with noise, with peaks at all Faraday depths. At higher amplitude 164 levels, specific Faraday depths are seen to be more prevalent. This figure will be discussed in more detail below. Because of the suggestions in the spectra of Faraday complexity (either real or instrumental), we made an estimate of the total polarized flux by adding all the power in the Faraday spectra between -250 rad m−2 and +250 rad m−2, wherever the signal to noise ratio in the peak of the spectrum was greater than 10. This gives a somewhat biased estimate of the total polarized flux Pint(x, y) at each pixel, because we did not correct for the noise. Note that Pint is the total polarized flux that would be observed if there were no Faraday rotation present, e.g., at very high frequencies. As expected, Pint was typically larger than Ppeak. Notes on individual sources: Source A: This double is Source 25 in the compilation of background sources in (188). It is 3.9 Mpc from the cluster center, and therefore is only weakly sensitive to Faraday rotation in the cluster, so it provides an estimate of the foreground Galactic Rotation Measure. (188) measured a fractional polarization of 10% and an RM of 18±7 rad m−2. This is consistent with what we report in Table 4.4. Note that in Figure 4.20 (bottom right) the dominant peak is at a single Faraday depth, with the other points due to either side lobe structures or noise. This justifies our use of the nominal Faraday cleaning, as opposed to the broader reconstruction, and indicates that the Faraday environment of this source is simple, as expected for non-cluster sources. Embryo: This source is located at 1.6 Mpc from the cluster center, and shows variable fractional polarizations and little Faraday complexity, the jets are polarized from approximately 5%-10%, while the faint portions of the lobes are polarized at approximately 20%. Figure 4.20 (upper left) shows that the Faraday depths are dominated by a component near 0 rad m−2; the two peaks on the sides are likely due to side lobe structures. (188) report higher average polarizations, and no significant depolarization, which again argues for little Faraday complexity. The regions where no polarization is detected are therefore likely to have greater field disorder in our 7 arcsec beam. Our somewhat lower fractional polarization 165 values than (188) may be the result of not yet correcting for the spectral behavior in total intensity.

Figure 4.21 Faraday spectrum of the Goldﬁsh (left) along the direction shown in the intensity image (right) is plotted.

Goldfish: The head of this source appears in Figure 7 of (188), but is not discussed in the paper. Here, the polarized flux is well resolved. While the core/head of the source is not clearly detected in polarized flux, (0.5% or less) the fractional polarization to the south of the core is approximately 15%. Figure 4.20 (lower left) indicates some possible Faraday complexity, with Faraday depths ranging from approximately -50 to +100 rad m−2. This complexity can also be seen in Figure 4.21, which shows the Faraday spectrum in gray scale along the line indicated in the total intensity structure to the right. Note the same prominent features in Faraday space as seen in Figure 4.20, except that now we can tell that these values also occur in the same RA, Dec pixel. Original TRG: This source shows considerable structure in the values of the peak Faraday depth, with the strong front of the source, before the bend, having a Faraday dispersion of 150 rad m−2. The polarized fluxes are in the range 166 1%-2%, with some regions < 0.5% polarized. Some of the Faraday patches are spatially resolved, with scale sizes on the order of approximately 12 arcsec, but many features are still unresolved by our 7 arcsec beam. Figure 4.20 (upper right) shows that considerable Faraday structure is present, but because many Faraday patches are unresolved, we cannot distinguish from multiple Faraday peaks along each line of sight, or multiple peaks because of structure across the beam.

4.4 Discussion

4.4.1 The origin of ﬁlaments and relics in A2255

We have detected two thin filamentary structure, almost perpendicular to each other, at the tip of the tail of the Original TRG radio galaxy. The average L band spectral indices of TRG-F1 and TRG-F2 are steep and similar to first order. The spectral index of the TRG-F1 filament changes from αmed = −2.2 and becomes

flatter between 20 cm and 85 cm, , α20,85 = −1.5. This flattening seems to be in agreement with synchrotron emission models that take into account the electrons population loss of energy due to aging. Figure 4.16 shows , αmed vs α20,85.A simple power law model for synchrotron radiation as well as the more complicated Jaffe-Perola (JP, 13) model for spectral aging are overlaid. The TRG-F1 filament spectrum is consistent with the JP model with low frequency spectral index of

αlow ∼ −0.5 to −0.6. As shown in Figure 4.11, the L band spectral index of the tail of the Original TRG follows a linear relation and steepens with increasing the crossing distance from the head and along the tail. However, the L band spectral index of the TRG-F1 does not follow the exact linear trend and is slightly ﬂatter than the predicted value, αpredict = −2.6, for its location. Assuming the JP model with αlow = −0.6 the original JP cutoﬀ frequency seems to be shifted by ∼ 22%.

The morphology of TRG-F1 and the observed ﬂattened αmed could be result of adiabatic compression due to passing a very weak shock with transsonic wave speed at the location of the ﬁlament. For a pure adiabatic compression of a blob 167 0.75 of plasma the density scales with critical frequency as ρ ∝ νc and therefore a

22% shift in νc results in ∼ 16% increase in density. For weak shocks the Mach number and post to pre-shock density ratio can be approximated as M ≈ 1 + and ρ2 ≈ 1 + 4 where 1 and γ is the gas heat capacity. For γ = 5 and ρ1 1+γ 3 ρ2 ∼ 1.16 we estimate ≈ 0.11 and the resulting Mach number for the weak shock ρ1 is M ≈ 1.11. The original source of emission for the C1, C2 and the Bridge is not clear. However, the morphological structure of the Bridge as shown in Figure 4.7 and discussed previously is similar to a slightly elongated bubble seen in lobes of radio galaxies. The three sources of diﬀuse emissions C1, C2 and the Bridge are aligned with NW-SE direction with C1 being at the center and roughly ∼ 505 kpc away from C2 and the Bridge in projection and at the redshift of the cluster. The hot spots of the Bridge bubble is also aligned with the same axis as C1, C2 and the whole Bridge structure. The synchrotron spectral indices of the Bridge only varies from αmed = −1.3 ± 0.2 in L band to α20,85 = −1.1 ± 0.1 which probably can be explained with a typical electrons spectral aging model. As shown in Figure 4.16 the spectral shape of the Bridge lies between a pure power law model and the JP model for spectral aging with low frequency index of -0.5. Putting together all the above evidence, we suggest C1, C2 and the Bridge might have the same origin and probably belong to a giant radio galaxy. Although in our preliminary search we could not locate the host radio galaxy due to lack of the optical counterpart for the radio candidates.

4.4.2 A2255 ICM Faraday structure

The small sample of radio galaxies used in this work has properties consistent with those described by (188), that the amount of Faraday structure is larger towards the center of the cluster than in the outskirts. This is evident both through the lower fractional polarizations seen towards the Goldfish and the Original TRG, as well as the increased level of structure and spatial variation in their Faraday 168 spectra. Assuming this structure to arise in the intracluster medium, then the magnetic field irregularities extend to spatial scales below 20 kpc. There is little evidence for an intracluster medium effect in the Embryo, at a distance of 1.6 Mpc from the cluster center. At the same time, there is still a significant enough medium to lead to the Embryo’s structure, as it interacts with the jets. The more accurate Faraday results will be especially interesting, e.g., at the locations of the filaments associated with the Original TRG. If these do represent compressive features, then both the ICM density and the magnetic field strength should increase at these locations, producing a distinct Faraday discontinuity. At this stage of the analysis, we also do not detect the polarization from the filamentary structures; since they are well-resolved by our 7 arcsec beam, they should appear much weaker than in (188), but may eventually be detectable in our data when convolved to lower resolution. As noted earlier, these polarization results are very preliminary, in that the Faraday spectra were calculated without normalizing for the total intensity spectra. When a more detailed analysis is done, it will be possible to develop estimates for the characteristic magnetic field strength and scale in the ICM, and look for signatures due to local interactions with the radio galaxy structures. More robust techniques than cleaning can also be applied to characterize the Faraday complexity. Chapter 5

Summary and future work

In this thesis, we have studied different physical aspects of the intergalactic medium. Star forming galaxies with excess of Lyα emission at z ∼ 3 are thought to be similar to their ancestors that probably have reionized the IGM at 6 < z < 10. In chapter2, we have measured the ionizing emissivity and relative Lyman continuum escape fraction of a sample of 207 Lyα emitting galaxy candidates at z ∼ 3.33. This sample is made by using 10 years of archived Subaru telescope imaging data in multiple bands and making deep mosaic images of the SXDS field. We specifically have chosen this part of the sky because no galaxy over density is detected in this region while all the other similar studies are performed in over dense neighborhoods and proto-clusters. Our LAE candidates have an estimated observed Lyα equivalent width of EW > 108A˚ (rest frame EW > 25A)˚ and red colors with B − V ≥ 0.48. The color cut is applied to remove lower redshift contaminant interlopers. Unlike other studies that have targeted LAE galaxies in over dense proto-clusters such as SSA22 and HS1549, we did not detect any ionizing LyC emission from any of our LAEs. To improve the signal-to-noise ratio and measure the statistical average LyC flux, we made a deep stacked image of all rest frame LyC stamps of the 207 LAEs. Although no signal is detected in the stacked LyC image, after correcting for the clumpy IGM absorption, we could put a lower limit on the UV-to-LyC flux ratio, (FUV .FLyC)corr > 13.8, and therefore an upper

169 170 LyC limit on the relative escape fraction of the ionized LyC radiation, fesc,rel < 0.2, assuming the intrinsic ratio of UV-to-LyC flux density is ηint = 3. Surprisingly, the UV-to-LyC flux ratio of our LAEs in the SXDS field is ∼ 4 times larger than values observed for LAEs in proto-clusters in similar redshift range. Our analysis suggest physical processes specific to the clusters of galaxies might play a role in providing a suitable condition for the ionizing radiation of star forming galaxies to escape away form the ISM of the host galaxy, resulting in higher relative escape fractions and smaller observed UV-to-LyC flux ratios. In future, obtaining deep spectroscopic observation to confirm the strong Lyα emission line at z = 3.3 for our candidate LAEs will result in a cleaner and more robust sample of galaxies. Further detailed analysis on the properties of these galaxies in comparison to LAEs in proto-clusters might shed light on the cause of very high UV-to-LyC flux ratios observed in this work. In chapter3, we studied the linear polarization of extragalactic radio sources under the influence of the intervening ionized IGM and internal or external Fara- day screens. By cross-matching the VLA NVSS L band catalog of radio galaxies at 1.4 GHz with the Australian S-PASS S band data at 2.3 GHz, we put together a polarization catalog of 533 galaxies with S band total intensity I2.3 > 420 mJy. These galaxies are carefully selected to minimize the selection biases and confusion from the nearby source fluxes, especially in S-PASS survey with the beam size much larger than the NVSS. For each galaxy we have measured important physical parameters such as total intensities at 1.4 GHz and 2.3 GHz and the corresponding spectral index, the extent of each source in the NVSS catalog, fractional polarization at both frequencies, depolarization as defined D = π2.3 , polarization π1.4 angle rotation measures in both frequencies and their difference, ∆RM. We also took advantage of other external datasets to collect more information such as redshift and WISE IR colors of our galaxies. To understand the underlying physics of the depolarization mechanisms, we studied the relationships between different measured physical quantities by performing extensive statistical tests. The results of our analysis indicate that fractional polarization of sources with no observed 171 sign of depolarization varies from a few to 10%, which is on average an order of magnitude smaller than the theoretical predicted values. Therefore, we con- clude that the dominant mechanism for reducing the overall polarization degree of synchrotron radiation of radio galaxies is the intrinsic magnetic field disorder. However, depolarization plays a crucial role in reducing the fractional polarization of galaxies even further. In fact, we have found at least 24% of polarized galaxies have experienced D > 2 depolarization. We also have discussed three possible origins for the depolarizing mechanism associated with Faraday screens: Galactic, environment local to the source and the intervening IGM. We have concluded the dominant origin of depolarization is consistent with Faraday screens local to the source or in its immediate IGM. This is based on the observed dependency between depolarization and the source spectral index as well as the relation between the source fractional polarization and its extent and lack of detection of any angular clustering of galaxies by depolarization or fractional polarization. We also have identified a suggestive evidence for evolution of depolarization of steep spectrum and depolarized (D ≥ 1.5) sources with redshift, between 0 ≤ z ≤ 2.3. It appears that steep spectrum galaxies at higher redshift on average have smaller depolarization. Such an evolution can be explained by models that assume an evolving Faraday dispersion for galaxies. To confirm and study such a trend, large samples of polarized sources with detailed depolarization information as well as resolved Faraday structure maps are needed. While most radio sources are either depolarized or do not show any sign of depolarization, we detected a small number of re-polarized galaxies. The nature of flat spectrum re-polarized galaxies can be explained by physics of self-absorption of synchrotron radiation in a Faraday thick environment. However, 39% of re- polarized sources appeared to have steep spectra. The nature of this population of re-polarized sources is not known. Detailed multi-frequency and high resolution observation of a handful of these source will shed light on their complicated polarization structure. Future radio surveys like SKA and its precursors such as POSSUM, WODAN, 172 MeerKAT, MIGHTEE and VLASS have the capability of detecting millions of polarized radio sources in different frequencies. These large sample of polarized background radio galaxies will enable us to make RM grids and measure the IGM magnetic field properties in the ICM of galaxy clusters and across or along the cosmic filaments through Faraday rotation measurements. However, polarization angle of sources with complicated Faraday structure has a non-λ2 behavior and therefore can not be modeled properly. In this thesis, we showed that galaxies with complicated Faraday structure (large ∆RM) have fractional polarization of on average less than ∼ 4% and therefore, the degree of polarization of extragalactic sources can be used to select reliable samples for such studies. In chapter4, we focused on the dynamically active ICM of the merging galaxy cluster A2255. We presented the VLA deep L band total intensity and polarization observation of the central and northern regions of the cluster in B and C modes of antenna configurations. The ICM of A2255 is filled with diffuse synchrotron emission in forms of radio relics and filaments. Our high resolution maps revealed two new filamentary substructures in the southern part of the NE relic and a new relic type diffuse emission, NW3, at the west of the NE relic. We also discovered the bubble structure of the Bridge diffuse emissions. The alignment of C1, C2 and the Bridge emissions suggest that they might be remnants of a giant radio galaxy. However, we could not find the optical counterpart of the suspected radio galaxy. Moreover, for the first time we have detected three thin filamentary structure at the tip of the tail of Original TRG, close to the X-ray center of the cluster and at the tip of the tail of Sidekick radio galaxies. The elongated and thin morphology (∼110 kpc and < 7 kpc, for TRG-F1) of these filaments are unique in the sense that filaments as thin as TRG-F1 and TRG-F2 with no associated radio galaxy has never been observed in the ICM of galaxy clusters. Our spectral analysis suggest that the seed electron responsible for synchrotron radiation of TRG filaments belong to the long tail of the Original TRG radio galaxy and probably have experienced an adiabatic compression due to a very weak shock wave with 173 Mach number M ∼ 1.1. For the TRG-F1 filament we also see weak evidence of a loop-type morphology and therefore, it might be part of a bigger loop-like structure. Unfortunately, the low S/N of emission from this loop and the Sidekick-F filament did not allow us to estimate their L band spectral index. Future, deep high resolution and multi-frequency observation of these fascinating filaments is necessary to shed light on their origin and physical processes responsible for them. Although we have measured average L band spectral index for some parts of the radio relics of A2255, the low surface brightness of these diffuse emissions did not allow us to estimate the spectral curvature within the L band. In future, combination of our VLA P band observation (not processed in this thesis) and current L band total intensities will help us to distinguish between the underlying mechanism responsible for relic emissions in A2255 (e.g. DSA re-accelration and adiabatic compression of electrons). The Faraday structure and polarization analysis of A2255 presented in this thesis is preliminary and will be improved in future. However, current results suggests more Faraday structure toward the center of the cluster. This is expected to some degree since the ICM in the central regions is under the influence of more activities which might result in magnetic field irregularities. In future, improved polarization and Faraday structure analysis of the radio relics and the thin observed filaments can provide valuable information about the depth and morphology of these features which can be used to understand their origin. References

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