Searching for Strong Lensing in Galaxy Clusters a Method for Discovering Lensing Features in Decam Cluster Images

Searching for Strong Lensing in Galaxy Clusters A method for discovering lensing features in DECam cluster images

Leah Zuckerman

A thesis presented for the degree of Bachelor of Science in Physics

Department of Physics Providence, RI May, 2021 Searching for Strong Lensing in Galaxy Clusters

A method for discovering lensing features in DECam cluster image

Leah Zuckerman

Abstract

Einstein’s theory of General Relativity makes remarkable predictions about how the universe should behave on scales invisible to us in our everyday lives. One of the most astonishing and yet fundamental of these is that, despite being massless, photons are affected by gravity. Since Einstein’s initial revelation, the deflection of light by massive objects has been observed abundantly in the universe. Studying these lensing effects has enabled many new lines of astrophysical research. In this project, I investigate some of the most dramatic examples of lensing – rings, arcs, and multiple images – created when massive foreground galaxy clusters bend light from closely-aligned background objects. Using the GALFIT code developed by Dr. Chien Peng of the Carnegie Observatory, I create models for the regions around large galaxies in DECam images of galaxy clusters. I subtract these models out of the original images to observe small background fluctuations, and I show that this subtraction technique is useful for detecting arcs. However, I do not find evidence of previously unobserved lensing effects in any of the clusters I analyze. This lack of new lensing effects could be an indication that observable strong lensing is less common than previously thought.

2 Contents

1 Describing Lensing 4 1.1 Lensing geometry ...... 4 1.2 Rings and Arcs ...... 6 1.3 Multiple Images ...... 8

2 DECam Survey Images 10 2.1 Imaging with DECam ...... 10 2.2 Clusters ...... 11 2.3 Analysis Pipeline ...... 11

3 Methodology 12 3.1 GALFIT ...... 12 3.2 The ﬁtting process ...... 12 3.2.1 Determining the region likely to have lensing ...... 13 3.2.2 Selecting the PSF ...... 14 3.2.3 Other GALFIT input parameters ...... 15 3.2.4 Object models and arc observations ...... 16

4 Results 19 4.1 A3827 ...... 19 4.2 A2029 ...... 20 4.3 A85 ...... 23 4.4 A754 ...... 24 4.5 A1650 ...... 25 4.6 A2597 ...... 26 4.7 A2384 ...... 27 4.8 A3667 ...... 29 4.9 A3266 ...... 33 4.10 A3571 ...... 34 4.11 A2837 ...... 36 4.12 A1606 ...... 37

5 Future Work and Conclusions 39 5.1 Overall statistics and lensing conclusions ...... 39 5.2 Future work ...... 39

3 Chapter 1

Describing Lensing

Gravitational lensing occurs when light is emitted by a source, such as a galaxy, galaxy cluster, or quasar, and passes by a high-mass object whose gravity alters its path. The positions of the source, lens, and observer dictate the degree to which the light is distorted. In this project we focus on strong lensing, which occurs when the source and lens are closely aligned. In order to understand and interpret the observed lensing eﬀects, the geometry of the lensing system must be described mathematically.

1.1 Lensing geometry

A complete treatment of gravitational lensing requires a significant understanding of General Relativity to describe the curvature of spacetime in the presence of high mass objects. However, it is instructive to first consider how similar deflection can occur even in a simple Newtonian model. In this model gravity is considered to be a force acting between two masses, and a small object moving very fast past a massive object will be deflected towards that object by the gravitational force between them. The radius, r, from the small object to the large mass as a function of the angle around the large mass, θ, will take the form of a hyperbola. This is because solutions to the equation of motion of an object under a gravitational force are conic sections, and we are assuming that the small object’s speed is above the escape velocity. The explicit expression for the deflection, α , of the object from its otherwise straight path can be found from the simple assumption that the radius goes to infinity when θ is equal to the angle at which the object comes in and leaves the orbit:

2GM α = 2 (1.1) c rmin This Newtonian view describes the correct qualitative behavior, but it underesti- mates the deflection. Under General Relativity, gravity is not a force but is instead the curvature of spacetime in the presence of a mass (Einstein 1905). The light rays travel on “straight” paths, but spacetime itself is locally curved by massive objects. We can assume that on a large scale the spacetime of the universe is well-described by the (flat) FLRW metric. This means that a point mass represents only a local deflection. For most astrophysical applications this approximation is valid since the gravitational potential of even the types of massive objects that will create visible

4 Searching for strong lensing in galaxy clusters lensing are still much less than c2. In this case the potential can be approximated by the Newtonian potential,

−GM −GM Ψ = = , (1.2) r (z2 + b2)3/2 (Bartelmann and Schneider 2001) and then the deﬂection angle can be found by taking the gradient:

2 Z 2 Z ∞ GM 4GM α = ∇ ⊥ Ψ dx = ds = . (1.3) c2 c2 −∞ (z2 + b2)3/2 c2r

Here b is effectively the minimum distance between the objects, rmin, and z is the distance along Ds (see figure 1.1). This deflection points radially inwards towards the mass.

Figure 1.1: Lensing geometry shown as a cross-section perpendicular to the lensing, image, and source planes and parallel to the path between observer and source. Figure from Revaz 2020.

We can deﬁne an approximate relation between the distances and angles in the lensing geometry by assuming that θ (the angular position of the image), β (the true angular position of the source with respect to a line perpendicular to the observer, lens, and source planes), and α are all small. In a curved spacetime, we must also deﬁne the distances DL,DS, and DLS to be angular diameter distances, so that the approximation (used in many astronomy applications)

object length θ = (1.4) object distance is valid. In this case it is easy to see that

θDs = βDs + αDLS (1.5) D or θ = β + α LS . (1.6) Ds This equation is important because it can be used to explain the many diﬀerent lensing features that are observed. In this work we are interested in only ”strong lensing”, a term used to describe situations in which light is distorted into full rings, arcs, or image duplications. This is in contrast to the case where the light is merely

Chapter 1 Leah Zuckerman 5 Searching for strong lensing in galaxy clusters stretched so that the source appears elongated in a given direction, which is termed ”weak lensing” (see Fort 1993 and ﬁg 1.3). To understand how strong lensing eﬀects occur, it is instructive to consider the case of a point mass lens, for which the (equation 1.6) becomes

DLS4GM DLS4GM θ = β + 2 = β + 2 (1.7) Dsc r Dsc DL and the observer will see images located at

s 1 2 16GMDLS θ = (β ± β + 2 ). (1.8) 2 c DsDL

1.2 Rings and Arcs

In the case (still approximating the lens as a point source) that there is perfect alignment of the source and lens along a radial path from the observer, the angle β will be zero, and so the observer will see the image at angular position given by

s 4GMDLS θE = 2 . (1.9) c DsDL This is called the Einstein radius, because, since the distortion is the same at all angles around the mass, the image will be seen as an “Einstein ring” of this radius around the lens center (Konrad 2003). Although the formulation (1.9) for the radius only applies to the theoretical case of a point-mass lens, similar such rings will occur whenever the source is directly in line with the lens and observer. Of course, this alignment is almost never perfect, so complete Einstein rings are very rare. It is these partial rings and arcs that I am looking for in this work. It might not be immediately obvious that treatment in the preceding paragraphs, in which the source is a point source, can be applied to the real lensing systems we are observing. However, since the deflection angle depends linearly on the mass, the deflection from a lens modeled as a distribution of masses will simply be the sum of the deflections from each individual mass. In most astrophysical applications, the distribution of masses within a lens (for example, the individual galaxies within a cluster) will be very close together along the axis z between the observer, lens, and source. This means that it is reasonable to make a “thin lens approximation” and model the distribution as a set of masses within a plane perpendicular to the line of sight from the observer to the source (see figure 1.2). Thus, a ray passing through a plane containing multiple lenses (each located at a position ~εi in the plane), and intersecting this plane at some location described by the vector ~ε, will come to a minimum radius ~ε - ~εi from each mass and will experience a total deflection of

X X 4GM αtot(~ε) = α(~εi) = 2 . (1.10) i i c (~ε − ~εi) Assuming the lensing mass distribution to be continuous, the sum over the masses can become an integral over the surface density, Σ , and the expression becomes

Z 4G (~ε − ~εi)Σ(~εi) 2 αtot(~ε) = 2 2 d ε. (1.11) c |~ε − ~εi|

6 Chapter 1 Leah Zuckerman Searching for strong lensing in galaxy clusters

This “surface density” is really just the integral of the density distribution across all points ~r in space along the path from the observer to the source, projected onto the lens plane:

Z DS Σ = ρ(~r)dz. (1.12) 0 Plugging in the above expression for the deﬂection angle into the lens equation, gives

Z 4GDLS (~ε − ~εi)Σ(~εi) 2 θ = β + 2 2 d ε. (1.13) c |~ε − ~εi| Clearly, in the limit where the lens is well-approximated by a single point source, the integral over the surface density simply becomes the mass of the lens and the expression obtained for that case is recovered. Even when the lens is not a point mass, if it is spherically symmetric this integral over surface density can be replaced by the total mass inside a certain radius, reducing the equation to one nearly identical to that for the point mass, but diﬀering in the fact that M is now the function M(ε).

Figure 1.2: Schematic of the lensing of a source at angular position β (deﬁned from an arbitrary reference line of sight from the observer through the source and lens planes). Figure form Bartelmann and Schneider 2001.

There are many useful models for these lens mass distributions. Sometimes galaxies and galaxy clusters are described by the projection of an isothermal sphere onto a plane. Other models take into account the ellipticity inherent in many of these objects. The more complex the lensing mass, the more diﬀerent the observed images will be from those created by a simple point-mass lens. However, to understand how

Chapter 1 Leah Zuckerman 7 Searching for strong lensing in galaxy clusters the arcs and rings we are searching for are formed, we can assume that the lensing masses are relatively compact and spherical, so the approximation of the lens as a point mass that we started out with will describe the general behavior. If there is perfect alignment the observer will see the image stretched into a ring, and at lesser degrees of alignment the image will simply be elongated, possibly into partial rings, or arcs. Whats more, since equation 1.8 has two solutions for theta, there can sometimes also be multiple images of the source.

Figure 1.3: This Hubble Space Telescope image shows multiple galaxies that have been weakly lensed (stretched and magniﬁed) by foreground lenses. Image from Duﬀy 2013.

1.3 Multiple Images

As discussed previously, a full ring requires perfect alignment of the source, lens, and observer. Arcs will be seen when the alignment is not quite perfect. Under what circumstances will multiple images been seen? For a given lensing geometry, there will be a critical surface density of the lens deﬁning the mass needed for multiple images to be formed. This is given by

c2D Σ = S (1.14) 4GDLDLS (e.g., Meneghetti 2016). If the density at any point over the lens distribution is greater than this critical density, multiple images can be formed. Clearly, the density needed will be lower when the distance from the lens to the source is larger. This is because the deflection angle does not need to be as large for the observer to see multiple images if the light is traveling a longer distance. The strongest lensing effects will occur when the critical density is lowest, so that the lensing mass does not need to be as large to create strong lensing of the source. This minimum critical density will occur when the lens is halfway between the observer and source. The observation of multiple images is more difficult than the observation of arcs and rings, because it is challenging to determine whether a given object is “real” or

8 Chapter 1 Leah Zuckerman Searching for strong lensing in galaxy clusters simply the twin of another source. Thus, for this project we focus on detecting arcs and rings, which, when apparent, are easy to identify as the marks of strong lensing.

Chapter 1 Leah Zuckerman 9 Chapter 2

DECam Survey Images

2.1 Imaging with DECam

The cluster images that we use in this analysis were taken by the Dark Energy Camera (DECam), a wide-field CCD camera located at the Cerro Tololo Inter- American Observatory in Chile. DECam was built in 2021, and was the primary instrument for the Dark Energy Survey (DES) until its completion in 2019. The power of the DECam camera lies in the width of its imaging field. The camera consists of 62 CCDs (shown in figure 2.1), each with 520 megapixels and the ability to image 3 square degrees at 0.263 arcsecond per pixel resolution (Honscheid 2008). The DECam images used in this work were collected from the NOAO Science Archive, an online database providing access to observations from a wide range of NOAO telescopes and instruments.

Figure 2.1: DECam’s 62 CCDs, each imaging 3 square degrees at 0.263 arcsecond per pixel resolution (image from Grida 2017)

10 Searching for strong lensing in galaxy clusters

2.2 Clusters

An ongoing project in Professor Ian Dell’Antonio’s research group is the processing of the raw DECam images into useable products. I would like to thank all group members who have worked, and are currently working, on this initial image processing, including Professor Ian Dell’Antonio, Shenming Fu, Claire Hawkins, Nick Conroy, and Andrea Minot. The team has processed patches of the DECam data containing a selection of high-mass galaxy clusters. The clusters are all located at < 15N in declination, and they are selected to be very low redshift: 0.003 < z < 0.12. The minimum redshift is set by the field of view of the Dark Energy Camera. At lower redshift the virial region of the clusters will not fit within the field of view. The upper end of the redshift range extends to the point where the catalog is complete in the x-ray band. The high-mass condition is met by selecting clusters only with x-ray luminosities greater than 1.1x1044 erg/s. In order to make sure that there is not too much dust obscuring galaxies within the clusters (large numbers of galaxies are needed to measure the weak lensing signal), clusters are only selected that have r-band extinction less than 0.4 magnitudes. Limiting the amount of dust attenuation in the selected clusters is also important because if there are large variations in the levels of extinction within the cluster there can end up being spatial variations in the colors of the background galaxies, which will make redhisft estimates inaccurate. Finally, all selected clusters have low stellar density. If the density of stars is too high, overcrowding of stars can make the analysis difficult, so clusters are only selected with stellar densities less than 31 per square arcminute.

2.3 Analysis Pipeline

To create the final images, the raw data is passed through a detailed LSST Science Pipeline. First, individual exposures are processed by removing the instrumental signature, and characterizing and calibrating the image. There are multiple components to the instrumental signature, including pixels that are known to be prob- lematic (for example saturated pixels), biases resulting from pixels over- or under- counting photons, and inhomogeneities in the reactions of each pixel to photons. To remove these sources of noise, bad pixels must be masked out, bias frames (images with zero exposure time) must be subtracted, and spatial inhomogeneities in the light detection must be removed using flat frames (images with a known uni- form light distribution). Each image is then characterized by modeling of the Point Spread Function, identifying and subtracting out the bright streaks of cosmic rays, and applying an aperture correction. Finally, the image is compared to external cat- alogs both to calibrate the source positions and to find the photometric zero point (the source brightness that would result in one count per second) for the image. Next, all processed exposures from each photometric band are added together to create final images for each band that have much better signal to noise than any raw image.

Chapter 2 Leah Zuckerman 11 Chapter 3

Methodology

3.1 GALFIT

This project would not have been possible without the extensive use of the GALFIT software developed by Dr. Chien Peng of the Carnegie Observatory (Peng 2012). GALFIT is a two-dimensional fitting algorithm, written in C, that allows single objects within larger astronomical images to be modeled separately from each other. GALFIT is unique in its ability to fit multiple components to a single object while still running efficiently in terms of computational time. Each component is fit with a parametric function to describe its light distribution. Fitting functions include Sersic, Gaussian, de Vaucouleurs, and Nuker profiles, among others. GALFIT’s two-dimensional fitting technique is a distinct improvement over one- dimensional fitting. The benefit of two-dimensional models as opposed to fitting one-dimensional surface brightness profiles is that using the latter eliminates the need to obtain radial profiles from two-dimensional images; that process can intro- duce error when the isophotes that are used to define the radial arcs are complicated. Two-dimensional models are also better able to distinguish between bulge and disk profiles, for which there are often degeneracies in one dimensional fitting. The advantage of two-dimensional fitting has been shown in multiple studies using simulated galaxies (see e.g., Byun and Freeman 1995). Even in comparison to other two-dimensional fitting methods, GALFIT is particularly effective because of its ability to fit a single object with multiple models. Most galaxies are poorly fit by a single light profile, so the ability to assign multiple components to the same object allows for much more detailed fits. There are two ways to run GALFIT: either interactively from the command line (inputting each model individually) or using an input “.feedme” file, in which all models can be listed simultaneously. The input file will also include a “menu” of input items, including the input image, the region to fit, the PSF, and the magnitude photometric zero point for the image. The input file option is much simpler to work with, and thus is our chosen method in this work.

3.2 The ﬁtting process

GALFIT provides an extensive array of ﬁtting options, not all of which are useful for our work in this project. For a full review of all available options in GALFIT, see the GALFIT user manual (available at https://users.obs.carnegiescience.

12 Searching for strong lensing in galaxy clusters edu/peng/work/galfit/galfit.html). Here, I will outline only the techniques pertinent to this project.

3.2.1 Determining the region likely to have lensing The processed cluster images are around 30,000 square pixels. However, the regions that we want to create fits for are much smaller than this. Since lensing will be strongest near high mass concentrations, the most important region of the cluster to model is the first ∼100 arsceonds (a few hundred pixels) around the most massive galaxy, referred to as the Bright Central Galaxy (BCG). It is important to keep in mind that merging clusters will likely have two BCGs, which will need to be fit independently. Additionally, while the BCG(s) of each cluster have the strongest probability of exhibiting visible lensing features, I extend the analysis to other large galaxies nearby. There is a possibility that strong lensing effects could be observed around these less massive objects even when they are not observed around the BCG. It can sometimes be challenging to locate the galaxies of interest within the cluster image. They can often be more easily identified in full-color images than in single bands. While I am fitting images in only one band, full color images from DECam do exist, and a useful viewing tool is available at https://www.legacysurvey.org/ viewer). Once the coordinates of the galaxy are found, the fitting region should be defined as a box of around 500 by 500 pixels centered on the galaxy. Then, if preliminary modeling of the region shows that the central galaxy extends beyond this, the region may need to be expanded out to the radius of the halo to ensure it is modeled correctly. GALFIT accepts input images as .fits files listed in the menu of the input .feedme file. The region to be fit within the input image can also be defined here. Thus, the desired region can be entered to GALFIT in two ways. One method is to create a cutout of the original image, define that as the input image, and identify the fitting region to include the entire input image. The second is to input the full image and define the fitting region as the portion we desire to fit. The second method allows more flexibility in subsequent fits, as it removes the obstacle of re-cutting the original image if it is decided that a larger or smaller region would be a better choice to fit.

Chapter 3 Leah Zuckerman 13 Searching for strong lensing in galaxy clusters

(a) (b) (c)

Figure 3.1: Locating a BCG and finding secondary galaxies to fit in the large DECam image patches can be challenging. It is helpful to first identify the objects in a full color image (a), before locating them within a single-band DECam patch (b and close-up in c). The fitting regions I have used for the first BCG and two secondary galaxies of interest in this cluster are shown in green and blue respectively.

3.2.2 Selecting the PSF The Point Spread Function (PSF) is the uncelebrated hero in creating a good fit. The PSF represents the degree to which an unresolved point source (e.g., a far-away star) has some erroneous distribution in its light profile in the image. The LSST Science Pipelines (described above) include the creation of a modeled PSF for the image, which describes the true PSF well enough for photometry and weak lensing purposes. However, in order to see strong lensing arcs we need GALFIT to create very strong fits of the image components and we originally thought this meant the best practice would to create a more realistic PSF than is generated through the pipeline by manually selected a PSF star.

Figure 3.2: If selecting the PSF directly from the initial image (a), the PSF should be identiﬁed as a bright, round, isolated star (b), with a sharply peaked light distribution (c).

To manually select the PSF, we muct ﬁnd an unresolved object from the region of

14 Chapter 3 Leah Zuckerman Searching for strong lensing in galaxy clusters

(a) (b) (c)

Figure 3.3: Objects that would be poor choices to use as PSFs. While all of these appear to be small, bright, and isolated upon visual inspection in the cluster image, plotting their light profiles shows that (a) is too wide, (b) is not isolated enough (there are smaller peaks corresponding to background objects), and (c) is too high in signal to noise (too dim). the image near the BCG in question (it must be taken from an area near the fitting region because the PSF can vary over the image, introducing error into the final fit). The trick here lies in our ability to be sure that a given source is indeed an unresolved star. On visual inspection, PSF candidates should be small relative to the size of galaxies in the image and should be circular, since objects that are large or elliptical are unlikely to be unresolved point sources. A profile of the light distribution across the object should be Gaussian in form and should not be saturated and/or too wide. A reasonable PSF would have a profile with a distinct peak in the flux (not flat on top) and a relatively small Full Width Half Maximum value (only a few pixels). It is also important that there is a high single-to-noise ratio in the area of the object, which means an isolated object must be chosen to avoid high levels of background light. Figure 3.3 shows profiles of objects that would be poor PSF choices. Once a suitable PSF object has been identified, no processing is required besides creating a cutout .fits image of a region around the object, and defining that to be the PSF in the GALFIT input menu. The cutout region should be square and symmetric around the point source so that GALFIT has an easier time recognizing it, and it and should include as much background sky as possible to increase the signal to noise ratio. The manual PSF selection method can be challenging because it is often hard to find a sufficiently small, bright, isolated, and spherically symmetric object that is close enough to the BCG. However, we recently determined that despite initial concerns about the adequacy of the synthetic PSFs created by the analysis pipeline, in many cases they can actually allow for a better fit than can manually selected PSFs. Shenming Fu has now created a code to extract the PSF images calculated as part of the analysis pipeline. This second method of generating a PSF can remove some of the error and uncertainty in hand-selecting a point source from the original image, and in general will create better fits.

3.2.3 Other GALFIT input parameters Four other important values to be input to GALFIT are the magnitude photometric zero point, the plate scale, the PSF ﬁne sampling factor, and the size of the

Chapter 3 Leah Zuckerman 15 Searching for strong lensing in galaxy clusters convolution box. As noted above, the photometric zero point is calculated during the analysis pipeline. It is an important quantity because it tells GALFIT how to assign magnitude values to the models it fits. For these images, the photometric zero point is 27 mag. The plate scale is simply the viewing angle per pixel for the camera, which is 0.263 arcseconds/pixel for DECam. This value is needed when running GALFIT so that surface brightness (in magnitudes per square arcsecond) can be calculated from flux. The PSF fine sampling factor is the ratio between the plate scales of the image and the PSF. Since we have extracted the PSF directly from the image, the plate scales will be the same and the fine sampling factor will be 1. Finally, the size of the convolution box refers to the size, in pixels, of the PSF image. It is important to remember to change this value if the PSF image is ever replaced during fitting. To complete the discussion of input file parameters, I will note that besides the input image, fitting region, PSF, magnitude photometric zero point, plate scale, PSF fine sampling factor, and convolution box size, there are a few other optional parameters that GALFIT can take as menu input. The first is the sigma image, which is a map of the standard deviations of the data in the image, used to weight the pixels appropriately. Because the sigma image is difficult to compute, and because GALFIT is not particularly sensitive to it, the best course of action is generally to allow GALFIT to create its own. A second optional input parameter is the bad pixel mask, which is simply a text file containing an array of coordinates that GALFIT should ignore during fitting (it can also be input as a fits file image in which the bad pixels have nonzero value). Masking is useful in certain cases, such as when the image region must be extended well beyond where the arcs are likely in order to fit a central giant galaxy. However, generally it is better to attempt to fit all objects instead of masking them out because it is important not to mask out objects whose light overlaps with other, non-masked, objects, and it is difficult to discern whether this is the case visually. Lastly, GALFIT can accept a “constraint file” containing specifications on the range that should be allowed for various fitting parameters. Sometimes it is tempting to use this file as a way to force a fit to work, for example by preventing the radius of an object to becoming too small or the magnitude from becoming too faint. However, in general the constraint file should be avoided for such uses because if the fit is converging on values that are not reasonable, it likely means that other components (even of other objects) in the image are hampering the fit. Forcing one parameter back into a reasonable range will not necessarily make the overall fit stronger. However, the constraint file can be used effectively to couple two or more parameters together, for example demanding that the bulge and disk of a galaxy are centered at the same coordinate.

3.2.4 Object models and arc observations Once the items above have been defined in the input menu, one can start the real work of identifying each object in the fitting region and finding their best-fit models. Most of the objects in the cluster center will be galaxies, which can be fit well using Sersic models. While the whole benefit of GALFIT is that it can converge numerically on the best model parameters, it is still necessary to be able to input rough estimates so that GALFIT does not “wander off in the wrong direction” and

16 Chapter 3 Leah Zuckerman Searching for strong lensing in galaxy clusters

(a) (b) (c)

Figure 3.4: An input image (a) best ﬁt model (b) and residual image (c) for a single galaxy in the A1650 cluster. While it is overall simpler to model a region with a single galaxy, the observed noise in the residual is likely due to the very small size of the image.

ﬁnd itself unable to converge. For a Sersic model, the important parameters are the integrated magnitude and the half-light radius. The integrated magnitude can be estimated from the total ﬂux over the object (the sum of the pixel values), by using the standard relation that

M = −2.5log(f) + M0 (3.1) where f is the total flux and M0 is the zero point magnitude. The half-light radius can be estimated very roughly (but well enough for GALFIT) from the FWHM of a radial light profile taken across the object. Not all the objects in an image will be galaxies; there will likely be a few stars within the fitting region as well. As discussed above, stars can often be identified by the sharp peaks in their light curves and their small FWHM. They will generally also display “spikes” of light pointing radially outward from their centers. Stars can be fit using Moffat or Gaussian models, but generally the best fit is obtained by defining them as unresolved point sources so that GALFIT uses the PSF as the model. The key to the fitting process is to start simply, for example only modeling the central galaxy, and then build up the model until a good fit for the entire region is obtained. Thus, the first iteration of GALFIT will produce a poor fit (a high chi-squared value and a residual image that is far from flat). However, the GALFIT output files and images will still encode a significant amount of information that can be used to improve the fit. The key is then to figure out what parts of the image are being fitted incorrectly and try to adjust the input parameters accordingly. Often, one will need to add more models to a given object to account for an irregular shape. The best way to do this is simply to create another component in the .feedme file for such an object (centered at the same coordinates) with parameters that are almost identical but altered in some small arbitrary way. This tells GALFIT to fit another component to the object and makes it more likely that the new component will not come out identical to the first. Once the model appears to have converged on a good fit for the first object, we want to add more objects without losing the fitting that has already been completed. Best practice is to copy over the converged parameters for the first object from the output file, so that the input parameters for that object in subsequent runs are

Chapter 3 Leah Zuckerman 17 Searching for strong lensing in galaxy clusters already close to the best-fit values. This process should be repeated after a good fit is reached for each newly added object. Additionally, if there are two or more objects that are very close to each other, it can be useful to set the position of the first object fixed before adding a second object nearby. This will make it easier for GALFIT to pick out the individual objects so that it does no try to model them together (which will likely end in the program crashing). Sometimes one will end up with a model that appears very good, but there will still be excess light in the residual. The cause of this is likely that GALFIT is having trouble fitting the background sky because of the presence of a giant elliptical galaxy centered on the cluster center. This will appear as a halo of light in the original image. To fix this, a component can be added for this giant galaxy. The radius will likely be larger than the fitting region being used. It may therefore be necessary to expand the fitting region so that the giant galaxy can be modeled properly. In general, it is likely that many iterations (trial-and-error) will be necessary to converge on a good fit. A low chi-squared is one indicator that the fit is working well, as is a background that contains only very small fluctuations.

18 Chapter 3 Leah Zuckerman Chapter 4

Results

As described in section 1, there is a greater potential to observe lensing around more massive objects. The pre-processed clusters are already selected to be massive, and the subset that I analyze are the ten largest of these. The masses reported in the DECam survey data are the ”M500” values, which describe the mass contained within the region of the cluster that is 500 times the average density of the universe, as calculated from X-ray measurements. Over the course of this project I have achieved fits of twenty-one objects within the ten clusters I have studied. These include twelve BCGs and nine smaller, secondary, galaxies. The results of these fits show that although our technique of light subtraction with GALFIT can be a powerful tool in observing underlying structure, strong lensing may be less common than previously thought. We have not conclusively observed strong lensing in any cluster (excepting A3827, whose lensing is visible even before fitting). What follows is a summary of the fitting and results for each of the processed clusters.

4.1 A3827

Before diving into my search for new strong lensing arcs, I validate our subtraction method by modeling a cluster that is known to have arcs: Abell 3827. This cluster has multiple bright arcs that can be seen even before subtraction of the foreground sources. However, these arcs are very faint in the pre-processed image, which means that we can use A3827 as a test case to show that fitting with GALFIT can indeed bring out arcs when they are present. In figure 4.21, panel (a) shows the arcs in a high-resolution Hubble Space Telescope image of the cluster’s BCG, and panel (b) shows the 500 by 500 pixel region of the DECam patch containing A3827 that I have chosen to fit. Panels (c) and (d) show the final best-fit model and the residual created. The arcs can be seen much more clearly in the residual image than in the initial image, which provides encouragement that our technique may be useful in finding lensing effects that cannot be observed in unaltered images.

19 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.1: BCG of Abell 3827: LSST image in which lensing arcs are highly visible (a), input image (b), best ﬁt model (c), ad residual image scaled to bring out small signals (d).

Because of the known strong lensing eﬀects around the BCG of A3827, there is an increased probability of observable strong lensing around the smaller galaxies nearby to the BCG. However, examination of the area surrounding the BCG shows that no such large, nearby galaxies exist. Thus, the BCG is the only galaxy I ﬁt for the cluster A3827.

4.2 A2029

The most massive of the pre-processed clusters is Abell 2029 (the largest two DECam clusters are too far North or too have too high extinction). In figure 4.2, I show that the input image for the BCG of A2029 (a), the best-fit model (b), and the residual image (c). I also show a scaled residual to bring out small variations in flux (d). The subtraction brings out many background sources that cannot be seen in original image. Some of these sources do appear to exhibit the slight stretching characteristic of weak lensing, and there may also be a slight preferential alignment of the galaxy inclinations perpendicular to the radial direction, which is also indicative of weak lensing. There are additionally some very small “dashes” of light right below the galaxy which could potentially be faint arc segments, but the signal to noise is too low to make a definitive assessment. We do not see any bright extended radial features that would be definitive evidence of strong lensing. In contrast to A3827, in this cluster there are other large galaxies around the BCG, so I extend the analysis to two other galaxies close to the BCG. However,

20 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters while good ﬁts for these galaxies are obtained, neither shows promising evidence of strong lensing (see ﬁgure 4.3 and 4.4). For the second secondary galaxy, we do see some circular arc-like features, but due to the repetitive nature of these features we attribute them to ringing from a merger event as opposed to strong lensing.

(a) (b)

Figure 4.2: BCG of Abell 2029: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

Chapter 4 Leah Zuckerman 21 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.3: One secondary large galaxy in Abell 2029: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

(a) (b)

Figure 4.4: A second secondary large galaxy in Abell 2029: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

22 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters

4.3 A85

The next most massive cluster for which pre-processed DECam images are available is Abel 85. The input image for the BCG of this cluster, as well as the best-fit model and the residual image (scaled in two ways) are shown in figure 4.5. The BCG is relatively isolated, so it is only necessary to fit a few additional objects to achieve a good model. Subtraction brings out the background objects well, but we do not see any extended radial features. From this analysis, it becomes clear that there is no evidence of strong lensing features around the BCG of A85. I next fit a model for a smaller, secondary galaxy near the BCG. This galaxy is also very simple from a fitting perspective. However, as shown in figure 4.6, this smaller galaxy also does not appear to show strong lensing features. Thus, I conclude that we are unlikely to be able to observe strong lensing in A85 even with the aid of the GALFIT subtraction.

(a) (b)

Figure 4.5: BCG of Abell 85: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

Chapter 4 Leah Zuckerman 23 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.6: Secondary large galaxy of Abell 85: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

4.4 A754

A754 is not particularly complex, and the fit is achieved easily. Once again, as shown in figure 4.8, there is no evidence of strong lensing. What’s more, there are no large secondary galaxies near the BCG of A754 which would be likely to have visible lensing. Thus, I conclude an absence of strong lensing effects in this cluster.

24 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.7: BCG of Abell 754: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

4.5 A1650

A1650 is fit easily as well. As shown in figure 4.8, there are a few elongated galaxies near the BCG, but there is no evidence of strong lensing. Again, there are no large secondary galaxies near the BCG which could be interesting to fit.

Chapter 4 Leah Zuckerman 25 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.8: BCG of Abell 1650: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

4.6 A2597

Similarly to A754, no strong lensing eﬀects are observed in A2597, and there are no large nearby galaxies that could be promising to study.

26 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.9: BCG of Abell 2597: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

4.7 A2384

A2384 is a merging cluster, meaning that it is host to two BCGs. Both of these could be locations of strong lensing effects, and so it is necessary to achieve fits of both regions. Neither of these BCGs are particularly complex and so the fits are fairly simple. We do observe a small linear feature in the upper left corner of the first BCG, which could potentially be an indication of a small lensing arc. However, it could also simply be a distant elliptical galaxy or a weakly lensed galaxy. Thus, there is no conclusive evidence for strong lensing in A2384.

Chapter 4 Leah Zuckerman 27 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.10: First BCG of Abell 2384: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

(a) (b)

Figure 4.11: Second BCG of Abell 2384: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

28 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters

4.8 A3667

A3667 is a complex cluster. It is a merging cluster, so it has two BCGs. It also contains a number of large secondary galaxies, increasing the number of regions to fit. The residual for the first cluster is relatively clean, and while there could be some preferential alignment of the background galaxies, the fit reveals no features indicative of strong lensing. For the second BCG, the residual does show long, radial, concentric features. However, the repetitive, regular appearance of these features, as well as the fact that they appear to fade out gradually in the original image, indicates that they are merely ringing from past merger events. True lensing arcs would appear more isolated and irregular. In order to verify this, I fit this second BCG in a second color band to see if the features appear to be of a different color than the BCG, which could indicate they are from a background galaxy that was lensed. Since the ratio of the brightness of the features to that of the BCG doesn’t appear to be remarkably different in the two bands, this technique does seem to confirm that the features are simply ringing from the merger event. The secondary galaxies are challenging to fit due to the presence of many small objects nearby. For example, the first of these galaxies (4.15) is directly to the upper left of an elongated, pointed, object that could be edge-on spiral galaxy. This complicates the fit and creates a messy residual. In the case of the second secondary galaxy (4.16), the galaxy itself is a spiral, which means the fit will necessarily be challenging. However, I did achieve good fits for these objects. The subtractions show that the first secondary galaxy clearly has no arc-like features. It does exhibit rings of light around the center, but instead of being lensing arcs these are simply portions of the spiral that are left over.

Chapter 4 Leah Zuckerman 29 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.12: First BCG of Abell 3667: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

(a) (b)

Figure 4.13: Second BCG of Abell 3667: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

30 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.14: Second BCG of Abell 3667 in the g band: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

(a) (b)

Figure 4.15: First secondary galaxy of A3667: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

Chapter 4 Leah Zuckerman 31 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.16: Another secondary galaxy of A3667: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

32 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters

4.9 A3266

The BCG Abell 3266 is another object that proved quite complex and difficult to model, so the resulting residual is far from flat. Even so, the fit is strong enough to see that no evidence of arcs is uncovered by the subtraction. I have also fit one secondary galaxy in this cluster. This secondary galaxy appeared interesting to me at first because it has a small object off to the upper right, which I initially thought could be a lensing signal. However, completing a fit of the region while leaving this object out shows that it does not appear to be such an arc. The object is too compact and short to be evidence of strong lensing.

(a) (b)

Figure 4.17: BCG of Abell 3266: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

Chapter 4 Leah Zuckerman 33 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.18: Secondary galaxy of Abell 3266: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

4.10 A3571

The BCG of A3571 is less complicated than A3266, but still requires many components to achieve a satisfactory fit due to its elongated nature. The residual is far from flat, but there is no evidence of strong lensing. I also fit one secondary galaxy in this cluster, which at first glance does exhibit arc-like features in the residual image. However, similar to the second secondary galaxy in A3266, this galaxy is a spiral which adds layers of complexity to the fit and can result in arc-like features in the residual that are not lensing arcs. The features appear to be simply portions of the spiral that are difficult to subtract.

34 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.19: BCG of Abell 3571: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

(a) (b)

Figure 4.20: First secondary galaxy of Abell 3571: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

Chapter 4 Leah Zuckerman 35 Searching for strong lensing in galaxy clusters

4.11 A2837

Unlike A3571, A2837 has a relatively simple BCG. After a straightforward fitting process, it becomes clear that no lensing arcs are present in the region. I also fit the largest galaxy close to the BCG. This galaxy initially appeared interesting due to the presence of very faint arc-like features surrounding it. However, subtracting out a very simple, circularly symmetric model brings out these features and confirms that they are much too diffuse and messy to be lensing arcs. As before, they are likely just portions of a complex spiral galaxy.

(a) (b)

Figure 4.21: BCG of Abell 2837: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

36 Chapter 4 Leah Zuckerman Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.22: Secondary galaxy of Abell 2837: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

4.12 A1606

There are many objects that must be fit near the BCG of A1606, making the modeling process complicated. I was able to achieve a reasonable fit, but there is significant over-subtraction as a result of the many components needed. Despite this, the fit is good enough to conclude that no lensing arcs are present in the region. I also fit the largest galaxy close to the BCG. Subtracting out a simple model does bring out dim circular features, but these features are too regular to be evidence of arcs and are most likely ringing from a previous merger event.

Chapter 4 Leah Zuckerman 37 Searching for strong lensing in galaxy clusters

(a) (b)

Figure 4.23: BCG of Abell 1606: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

(a) (b)

Figure 4.24: A secondary galaxy of Abell 1606: input image (a), best ﬁt model (b), residual image (c), and residual image scaled to bring out small signals.

38 Chapter 4 Leah Zuckerman Chapter 5

Future Work and Conclusions

5.1 Overall statistics and lensing conclusions

The goal of my work with GALFIT was twofold. Firstly, I wanted to determine if subtraction of foreground objects could bring out background fluctuations such as lensing arcs. More consequentially, I wanted to identify such arcs in clusters where they had not previously been observed, or at the minimum to identify interesting features that could potentially be arcs. As described in section 4.1, it was easily verified that subtraction with GALFIT can bring out arcs and other features. Additionally, I have shown that multiple clusters have arc-like features that could potentially be small or partial lensing arcs, but that are too faint and blurred in the low resolution DECam images to make a definitive assessment. These include the Abell 2029 and Abell 2384. However, there is no cluster for which subtraction brings out a feature that could be identified with any certainty as a lensing arc. This means that the only statistical conclusions we can draw about the prevalence of lensing in these low redshift clusters are based on the observation that nine of the ten clusters (or eleven of the twelve BCGs) show no strong evidence of lensing. It might be argued that these numbers should be reported as nine out of nine and eleven out of eleven, since the one cluster that did show lensing was pre-selected to have arcs. However, our results do put a very weak bound on the frequency of these lensing arcs, implying that it is unlikely that more than 1/10 of clusters will show evidence of strong lensing.

5.2 Future work

The work I have done in studying these cluster images could be useful in multiple ways in the future. As noted above, some of the ﬁts did reveal arc-like features that may or may not be explained by things other than gravitational lensing. It is possible that higher resolution images of these clusters could reveal that some of these features are lensing arcs. They may simply be too faint and blurry in the DECam images to identify conclusively. Thus, future work may involve seeking observation time on a telescope such as Hubble to image the most promising of these clusters. These images would be useful because they could allow us to study the lensed background clusters and/or the mass distributions of the cluster centers themselves.

39 Searching for strong lensing in galaxy clusters

Another benefit of identifying more arcs with these high resolution images would be that we could achieve a better estimate of the prevalence of these arcs in this low redshift range. As noted above, the only definitive conclusion I can draw from the GALFIT analysis is that at most one in ten clusters, or one in twelve BCGs, is likely to have lensing. If HST images could firmly identify lensing in other clusters by showing that some of the arc-like objects I have observed with GALFIT are indeed lensing features, then our analysis would become much more statistically sound. We would then be able to draw more useful conclusions about the frequency of lenses at low redshift. One way that this could be used would be to compare the prevalence of arcs across redshifts. Previous work has arrived at estimates of lensing frequency at high redshift (where there are in general many more visible arcs). As described in section 1, we should see that lensing effects are most pronounced when the lens is halfway between the source and observer. If this is not what is seen, that indicates that the difference in the number of arcs at different redshifts is not completely explained by the different lensing geometries. If this is the case, it would likely mean that the galaxies in these clusters are more extended than previously thought, such that there is less mass within the Einstein Radius and a lower cross section for lensing. One potential explanation for this would be that previous merger events have caused the galaxies to “puff up” by heating up the orbits of their stars (see Hopkins et al. 2009). Another potential explanation for observing fewer arcs than expected could be that the galaxies are simply less massive than has been estimated. This would likely be difficult to distinguish from the galaxies being extended. A third explanation would be that measurements of the angular diameter distances to the low redshift galaxies are inaccurate. However, this is unlikely because distances to these low redshift galaxies are generally easy to calculate.

40 Chapter 5 Leah Zuckerman Bibliography

Einstein, Albert (1905). “Zur Elektrodynamik bewegter K¨orper. (German) [On the electrodynamics of moving bodies]”. In: Annalen der Physik 322.10, pp. 891–921. doi: http://dx.doi.org/10.1002/andp.19053221004. Bartelmann, Matthias and Peter Schneider (Jan. 2001). “Weak gravitational lensing”. In: Physics Reports 340.4-5, pp. 291–472. issn: 0370-1573. doi: 10.1016/ s0370 - 1573(00 ) 00082 - x. url: http : / / dx . doi . org / 10 . 1016 / S0370 - 1573(00)00082-X. Revaz, Y. (2020). “ Galaxy Clusters as Gravitational Lenses”. In: url: http:// obswww.unige.ch/lastro/misc/TP4/doc/rst/Exercices/Ex04.html. Fort B., Mellier (1993). “Arc(let)s in clusters of galaxies”. In: The Astron Astrophys Rev 5, pp. 239–292. doi: https://doi.org/10.1007/BF008776912. Konrad, K. (2003). “The Basics of Lensing”. In: APS Conference Series. Duﬀy, J. (2013). “GREAT3 challenge seeks new methods for measuring weak gravitational lensing”. In: url: https://phys.org/news/2013-11-great3-methods- weak-gravitational-lensing.html. Meneghetti, Massimo (2016). “Introduction to Gravitational Lensing - Lecture scripts.” In: Universe Today. Honscheid, K. (2008). “The read-out and control system of the DES camera (SISPI)”. In: SPIE 7019, Advanced Software and Control for Astronomy II 7019.7727, pp. 349–350. doi: 10.1117/12.787926. Peng, Chien (2012). “GALFIT User’s Manual”. In: Byun, Y. I. and K. C. Freeman (Aug. 1995). “Two-dimensional Decomposition of Bulge and Disk”. In: 448, p. 563. doi: 10.1086/175986. Hopkins, Philip F. et al. (Mar. 2009). “DISSIPATION AND EXTRA LIGHT IN GALACTIC NUCLEI. III. “CORE” ELLIPTICALS AND “MISSING” LIGHT”. In: The Astrophysical Journal Supplement Series 181.2, pp. 486–532. issn: 1538- 4365. doi: 10.1088/0067-0049/181/2/486. url: http://dx.doi.org/10. 1088/0067-0049/181/2/486.