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 1 GM 4GM α = r ? 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 ~"i in the plane), and intersecting this plane at some location described by the vector ~", will come to a minimum radius ~" - ~"i from each mass and will experience a total deflection of X X 4GM αtot(~") = α(~"i) = 2 : (1.10) i i c (~" − ~"i) 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 (~" − ~"i)Σ(~"i) 2 αtot(~") = 2 2 d ": (1.11) c j~" − ~"ij 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 (~" − ~"i)Σ(~"i) 2 θ = β + 2 2 d ": (1.13) c j~" − ~"ij 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.