arXiv subjects

Liliya L. R. Williams

Publications and source records attributed to Liliya L. R. Williams.

At least 73 records · Page 4Linked to original sources

arXiv2015

Model-free analysis of quadruply imaged gravitationally lensed systems and substructured galaxies

Multiple image gravitational lens systems, and especially quads are invaluable in determining the amount and distribution of mass in galaxies. This is usually done by mass modeling using parametric or free-form methods. An alternative way of extracting information about lens mass distribution is to use lensing degeneracies and invariants. Where applicable, they allow one to make conclusions about whole classes of lenses without model fitting. Here, we use approximate, but observationally useful invariants formed by the three relative polar angles of quad images around the lens center to show that many smooth elliptical+shear lenses can reproduce the same set of quad image angles within observational error. This result allows us to show in a model-free way what the general class of smooth elliptical+shear lenses looks like in the three dimensional (3D) space of image relative angles, and that this distribution does not match that of the observed quads. We conclude that, even though smooth elliptical+shear lenses can reproduce individual quads, they cannot reproduce the quad population. What is likely needed is substructure, with clump masses larger than those responsible for flux ratio anomalies in quads, or luminous or dark nearby perturber galaxies.

astro-ph.GA↗

arXiv2015

Illuminating a Dark Lens : A Type Ia Supernova Magnified by the Frontier Fields Galaxy Cluster Abell 2744

SN HFF14Tom is a Type Ia Supernova (SN) discovered at z = 1.3457 +- 0.0001 behind the galaxy cluster Abell 2744 (z = 0.308). In a cosmology-independent analysis, we find that HFF14Tom is 0.77 +- 0.15 magnitudes brighter than unlensed Type Ia SNe at similar redshift, implying a lensing magnification of mu_obs = 2.03 +- 0.29. This observed magnification provides a rare opportunity for a direct empirical test of galaxy cluster lens models. Here we test 17 lens models, 13 of which were generated before the SN magnification was known, qualifying as pure "blind tests". The models are collectively fairly accurate: 8 of the models deliver median magnifications that are consistent with the measured mu to within 1-sigma. However, there is a subtle systematic bias: the significant disagreements all involve models overpredicting the magnification. We evaluate possible causes for this mild bias, and find no single physical or methodological explanation to account for it. We do find that model accuracy can be improved to some extent with stringent quality cuts on multiply-imaged systems, such as requiring that a large fraction have spectroscopic redshifts. In addition to testing model accuracies as we have done here, Type Ia SN magnifications could also be used as inputs for future lens models of Abell 2744 and other clusters, providing valuable constraints in regions where traditional strong- and weak-lensing information is unavailable.

astro-ph.CO↗

arXiv2015

Non-universality of dark-matter halos: cusps, cores, and the central potential

Dark-matter halos grown in cosmological simulations appear to have central NFW-like density cusps with mean values of $d\logρ/d\log r \approx -1$, and some dispersion, which is generally parametrized by the varying index $α$ in the Einasto density profile fitting function. Non-universality in profile shapes is also seen in observed galaxy clusters and possibly dwarf galaxies. Here we show that non-universality, at any given mass scale, is an intrinsic property of DARKexp, a theoretically derived model for collisionless self-gravitating systems. We demonstrate that DARKexp - which has only one shape parameter, $ϕ_0$ - fits the dispersion in profile shapes of massive simulated halos as well as observed clusters very well. DARKexp also allows for cored dark-matter profiles, such as those found for dwarf spheroidal galaxies. We provide approximate analytical relations between DARKexp $ϕ_0$, Einasto $α$, or the central logarithmic slope in the Dehnen-Tremaine analytical $γ$-models. The range in halo parameters reflects a substantial variation in the binding energies per unit mass of dark-matter halos.

astro-ph.CO↗

arXiv2014

Mass-Galaxy offsets in Abell 3827, 2218 and 1689: intrinsic properties or line-of-sight substructures?

We have made mass maps of three strong-lensing clusters, Abell 3827, Abell 2218 and Abell 1689, in order to test for mass-light offsets. The technique used is GRALE, which enables lens reconstruction with minimal assumptions, and specifically with no information about the cluster light being given. In the first two of these clusters, we find local mass peaks in the central regions that are displaced from the nearby galaxies by a few to several kpc. These offsets {\em could\/} be due to line of sight structure unrelated to the clusters, but that is very unlikely, given the typical levels of chance line-of-sight coincidences in $ΛCDM$ simulations --- for Abell 3827 and Abell 2218 the offsets appear to be intrinsic. In the case of Abell 1689, we see no significant offsets in the central region, but we do detect a possible line of sight structure: it appears only when sources at $z\ga 3$ are used for reconstructing the mass. We discuss possible origins of the mass-galaxy offsets in Abell 3827 and Abell 2218: these include pure gravitational effects like dynamical friction, but also non-standard mechanisms like self-interacting dark-matter.

astro-ph.CO↗

arXiv2014

Statistical mechanics of collisionless orbits. IV. Distribution of angular momentum

It has been shown in previous work that DARKexp, which is a theoretically derived, maximum entropy, one shape parameter model for isotropic collisionless systems, provides very good fits to simulated and observed dark-matter halos. Specifically, it fits the energy distribution, N(E), and the density profiles, including the central cusp. Here, we extend DARKexp N(E) to include the distribution in angular momentum, L^2, for spherically symmetric systems. First, we argue, based on theoretical, semi-analytical, and simulation results, that while dark-matter halos are relaxed in energy, they are not nearly as relaxed in angular momentum, which precludes using maximum entropy to uniquely derive N(E,L^2). Instead, we require that when integrating N(E,L^2) over squared angular momenta one retrieves the DARKexp N(E). Starting with a general expression for N(E,L^2) we show how the distribution of particles in L^2 is related to the shape of the velocity distribution function, VDF, and velocity anisotropy profile, β(r). We then demonstrate that astrophysically realistic halos, as judged by the VDF shape and β(r), must have linear or convex distributions in L^2, for each separate energy bin. The distribution in energy of the most bound particles must be nearly flat, and become more tilted in favor of radial orbits for less bound particles. These results are consistent with numerical simulations and represent an important step towards deriving the full distribution function for spherically symmetric dark-matter halos.

astro-ph.CO↗

arXiv2012

Collisionless dynamics in Globular Clusters

Since globular clusters (GCs) are old, low-N systems their dynamics is widely believed to be fully dominated by collisional two-body processes, and their surface brightness profiles are fit by King models. However, for many GCs, especially those with HST-resolved central regions, and `extra-tidal' features, King models provide poor fits. We suggest that this is partly because collisionless dynamics is also important and contribute to shaping the cluster properties. We show using time-scale and length-scale arguments that except for the very centers of clusters, collisionless dynamics should be more important than collisional. We then fit 38 GCs analyzed by Noyola and Gebhardt (2006) with (collisional) King and (collisionless) DARKexp models over the full available radial range, and find that the latter provide a better fit to 29 GCs; for six of these the fit is at least ~5x better in term of rms. DARKexp models are theoretically derived maximum entropy equilibrium states of self-gravitating collisionless systems and have already been shown to fit the results of dark matter N-body simulations. (We do not attempt fits with ad hoc fitting functions.)

astro-ph.CO↗

arXiv2012

Entropy Production in Collisionless Systems. II. Arbitrary Phase-Space Occupation Numbers

We present an analysis of two thermodynamic techniques for determining equilibria of self-gravitating systems. One is the Lynden-Bell entropy maximization analysis that introduced violent relaxation. Since we do not use the Stirling approximation which is invalid at small occupation numbers, our systems have finite mass, unlike Lynden-Bell's isothermal spheres. (Instead of Stirling, we utilize a very accurate smooth approximation for $\ln{x!}$.) The second analysis extends entropy production extremization to self-gravitating systems, also without the use of the Stirling approximation. In addition to the Lynden-Bell (LB) statistical family characterized by the exclusion principle in phase-space, and designed to treat collisionless systems, we also apply the two approaches to the Maxwell-Boltzmann (MB) families, which have no exclusion principle and hence represent collisional systems. We implicitly assume that all of the phase-space is equally accessible. We derive entropy production expressions for both families, and give the extremum conditions for entropy production. Surprisingly, our analysis indicates that extremizing entropy production rate results in systems that have maximum entropy, in both LB and MB statistics. In other words, both thermodynamic approaches lead to the same equilibrium structures.

astro-ph.CO↗

arXiv2011

Surface mass density of the Einasto family of dark matter haloes: Are they Sersic-like?

Recent advances in N-body simulations of dark matter halos have shown that three-parameter models, in particular the Einasto profile characterized by d ln ρ(r)/d ln r / r with a shape parameter α < 0.3, are able to produce better fits to the 3D spatial density profiles than two-parameter models like the Navarro, Frenk and White (NFW), and Moore et al. profiles. In this paper, we present for the first time an analytically motivated form for the 2D surface mass density of the Einasto family of dark matter haloes, in terms of the 3D spatial density parameters for a wide range of the shape parameter 0.1 < α < 1. Our model describes a projected (2D) Einasto profile remarkably well between 0 and (3 - 5) r_{200}, with errors less than 0.3 per cent for α < 0.3 and less than 2 per cent for α as large as 1. This model (in 2D) can thus be used to fit strong and weak lensing observations of galaxies and clusters whose total spatial (3D) density distributions are believed to be Einasto-like. Further, given the dependence of our model on the 3D parameters, one can reliably estimate structural parameters of the spatial (3D) density from 2D observations. We also consider a Sersic-like parametrization for the above family of projected Einasto profiles and observe that fits with a Sersic profile are sensitive to whether one fits the projected density in linear scale or logarithmic scale and yield widely varying results. Structural parameters of Einasto-like systems, inferred from fits with a Sersic profile, should be used with caution.

astro-ph.CO↗

arXiv2011

Surface Brightness and Intrinsic Luminosity of Ellipticals

{Abridged} We show that the surface brightness (SB) profiles of elliptical galaxies can be parametrized using a linear superposition of 2-3 components, described by functions developed in Dhar & Williams as the 2D projections of a 3D Einasto profile. For a sample of 23 ellipticals with -24 < Mv < -15, our multi-component models span a range of up to 10^6 in SB and 10^5 in radius, have a median rms of 0.032 mag arcsec^-2, and are statistically justified at >3σ. Our models indicate that i) the central component is more concentrated than the outer component; and ii) the central component of 'core' galaxies is much more luminous, extended and concentrated than that of 'cuspy' galaxies, with their near exponential central profiles indicating disk-like systems whose existence must be verified spectroscopically. While such central excess components are not necessarily contrary to the notion of a mass deficit in 'core' galaxies, we show that the existence, amount, radial extent and sign of mass deficits disagree substantially in the literature, both for a given galaxy and on an average over a sample. We discuss possible implications and suggest that SMBH binaries are unlikely to be the sole mechanism for producing the large 'cores'. We also deduce conditions under which the 3D light density can be described with a multi-component Einasto model for both cuspy and core galaxies; indicating an universality in the functional form of the 3D density of light in galaxies and dark matter in LCDM N-body haloes. Finally, we show that our result - the outer component of the SB profiles of massive galaxies has 5 < n < 8 - could imply i) a common feature of collisionless systems; and ii) that galaxies with such n for their outer component are dark matter dominated.

astro-ph.CO↗

arXiv2011

The Fundamental Surface of Quad Lenses

In a quadruply imaged lens system the angular distribution of images around the lens center is completely described by three relative angles. We show empirically that in the 3D space of these angles, spanning 180 x 180 x 90 degrees, quads from simple two-fold symmetric lenses of arbitrary radial density profile and arbitrary radially dependent ellipticity or external shear define a nearly invariant 2D surface. We give a fitting formula for the surface using SIS+elliptical lensing potential. Various circularly symmetric mass distributions with shear up to 0.4 deviate from it by typically, rms~0.1 deg, while elliptical mass distributions with ellipticity of up 0.4 deviate from it by rms~1.5 deg. The existence of a near invariant surface gives a new insight into the lensing theory and provides a framework for studying quads. It also allows one to gain information about the lens mass distribution from the image positions alone, without any recourse to mass modeling. As an illustration, we show that about 3/4 of observed galaxy-lens quads do not belong to this surface within observational error, and so require additional external shear or substructure to be modeled adequately.

astro-ph.CO↗

arXiv2011

Light/Mass Offsets in the Lensing Cluster Abell 3827: Evidence for Collisional Dark Matter?

If dark matter has a non-zero self-interaction cross-section, then dark matter halos of individual galaxies in cluster cores should experience a drag force from the ambient dark matter of the cluster, which will not affect the stellar components of galaxies, and thus will lead to a separation between the stellar and dark matter. If the cross-section is only a few decades below its current astrophysically determined upper limit, then kpc-scale separations should result. However, such separations will be observable only under very favorable conditions. Abell 3827 is a nearby late stage cluster merger with four massive central ellipticals within 20 kpc of each other. The ten strong lensing images tightly surrounding the ellipticals provide an excellent set of constraints for a free-form lens reconstruction. Our free-form mass maps show a massive dark extended clump, about 6 kpc from one of the ellipticals. The robustness of this result has been tested with many reconstructions, and confirmed with experiments using synthetic lens mass distributions. Interpreted in terms of dark matter collisionality, our result yields sigma/m ~ 4.5 10^{-7} (t/10^{10} yr)^{-2} cm^2/g, where t is the merger's age.

astro-ph.CO↗

arXiv2011

Entropy Production in Collisionless Systems. I. Large Phase-Space Occupation Numbers

Certain thermal non-equilibrium situations, outside of the astrophysical realm, suggest that entropy production extrema, instead of entropy extrema, are related to stationary states. In an effort to better understand the evolution of collisionless self-gravitating systems, we investigate the role of entropy production and develop expressions for the entropy production rate in two particular statistical families that describe self-gravitating systems. From these entropy production descriptions, we derive the requirements for extremizing the entropy production rate in terms of specific forms for the relaxation function in the Boltzmann equation. We discuss some implications of these relaxation functions and point to future work that will further test this novel thermodynamic viewpoint of collisionless relaxation.

astro-ph.GA↗

arXiv2010

Statistical mechanics of collisionless orbits. I. Origin of central cusps in dark-matter halos

We present an equilibrium statistical mechanical theory of collisionless self-gravitational systems with isotropic velocity distributions. Compared to existing standard theories, we introduce two changes: (1) the number of possible microstates is computed in energy (orbit) space rather than phase space and (2) low occupation numbers are treated more appropriately than using Stirling's approximation. Combined, the two modifications predict that the relaxed parts of collisionless self-gravitating systems, such as dark-matter halos, have a differential energy distribution N(E) ~ [exp(phi_0 - E) - 1], dubbed "DARKexp". Such systems have central power-law density cusps rho(r) ~ r^-1, which suggests a statistical mechanical origin of cusps in simulated dark-matter halos.

astro-ph.CO↗

arXiv2010

Statistical mechanics of collisionless orbits. II. Structure of halos

In this paper, we present the density, ρ, velocity dispersion, σ, and ρ/σ^3 profiles of isotropic systems which have the energy distribution, N(E)\propto[\exp(ϕ_0-E)-1], derived in Paper I. This distribution, dubbed DARKexp, is the most probable final state of a collisionless self-gravitating system, which is relaxed in terms of particle energies, but not necessarily in terms of angular momentum. We compare the DARKexp predictions with the results obtained using the extended secondary infall model (ESIM). The ESIM numerical scheme is optimally suited for the purpose because (1) it relaxes only through energy redistribution, leaving shell/particle angular momenta unaltered, and (2) being a shell code with radially increasing shell thickness it has very good mass resolution in the inner halo, where the various theoretical treatments give different predictions. The ESIM halo properties, and especially their energy distributions, are very well fit by DARKexp, implying that the techniques of statistical mechanics can be used to explain the structure of relaxed self-gravitating systems.

astro-ph.CO↗

arXiv2010

Statistical mechanics of collisionless orbits. III. Comparison with N-body simulations

We compare the DARKexp differential energy distribution, N(E) \propto \exp(ϕ_0-E)-1, obtained from statistical mechanical considerations, to the results of N-body simulations of dark matter halos. We first demonstrate that if DARKexp halos had anisotropic velocity distributions similar to those of N-body simulated halos, their density and energy distributions could not be distinguished from those of isotropic DARKexp halos. We next carry out the comparison in two ways, using (1) the actual energy distribution extracted from simulations, and (2) N-body fitting formula for the density distribution as well as N(E) computed from the density using the isotropic Eddington formula. Both the methods independently agree that DARKexp N(E) with ϕ_0\approx 4-5 is an excellent match to N-body N(E). Our results suggest (but do not prove) that statistical mechanical principles of maximum entropy can be used to explain the equilibrated final product of N-body simulations.

astro-ph.CO↗

arXiv2010

Understanding micro-image configurations in quasar microlensing

The micro-arcsecond scale structure of the seemingly point-like images in lensed quasars, though unobservable, is nevertheless much studied theoretically, because it affects the observable (or macro) brightness, and through that provides clues to substructure in both source and lens. A curious feature is that, while an observable macro-image is made up of a very large number of micro-images, the macro flux is dominated by a few micro-images. Micro minima play a key role, and the well-known broad distribution of macro magnification can be decomposed into narrower distributions with 0,1,2,3,... micro minima. This paper shows how the dominant micro-images exist alongside the others, using the ideas of Fermat's principle and arrival-time surfaces, alongside simulations.

astro-ph.CO↗

arXiv2009

The Radial Orbit Instability in Collisionless N-Body Simulations

Using a suite of self-gravitating, collisionless N-body models, we systematically explore a parameter space relevant to the onset and behavior of the radial orbit instability (ROI), whose strength is measured by the systemic axis ratios of the models. We show that a combination of two initial conditions, namely the velocity anisotropy and the virial ratio, determines whether a system will undergo ROI and exactly how triaxial the system will become. A third initial condition, the radial shape of the density profile, plays a smaller, but noticeable role. Regarding the dynamical development of the ROI, the instability a) begins after systems collapse to their most compact configuration and b) evolves fastest when a majority of the particles have radially anisotropic orbits while there is a lack of centrally-concentrated isotropic orbits. We argue that this is further evidence that self-reinforcing torques are the key to the onset of the ROI. Our findings support the idea that a separate orbit instability plays a role in halting the ROI.

astro-ph.CO↗

arXiv2009

Dark Matter Angular Momentum Profile from the Jeans Equation

Cosmological simulations of dark matter structures have shown that the equilibrated dark matter structures have a fairly small angular momentum. It appears from these N-body simulations that the radial profile of the angular momentum has an almost universal behavior, even if the different dark matter structures have experienced very different formation and merger histories. We suggest a perturbed Jeans equation, which includes a rotational term. This is done under a reasonable assumed form of the change in the distribution function. By conjecturing that the (new) subdominant rotation term must be proportional to the (old) dominant mass term, we find a clear connection, which is in rather good agreement with the results of recent high resolution simulations. We also present a new connection between the radial profiles of the angular momentum and the velocity anisotropy, which is also in fair agreement with numerical findings. Finally we show how the spin parameter $λ$ increases as a function of radius.

astro-ph.CO↗