We use the Beyond Ultra-deep Frontier Fields and Legacy Observations (BUFFALO) strong lensing image catalog of the merging galaxy cluster Abell 370 to obtain a mass model using the free-form lens inversion algorithm GRALE. The improvement of the stro
ng lensing data quality results in a lens plane rms of only 0.45 arcsec, about a factor of two lower than that of our existing HFF v4 reconstruction. We attribute the improvement to spectroscopic data and use of the full reprocessed HST mosaics. In our reconstructed mass model, we found indications of three distinct mass features in Abell 370: (i) a $sim 35$ kpc offset between the northern BCG and the nearest mass peak, (ii) a $sim 100$ kpc mass concentration of roughly critical density $sim 250$ kpc east of the main cluster, and (iii) a probable filament-like structure passing N-S through the cluster. While (i) is present in some form in most publicly available reconstructions spanning the range of modeling techniques: parametric, hybrid, and free-form, (ii) and (iii) are recovered by only about half of the reconstructions. We tested our hypothesis on the presence of the filament-like structure by creating a synthetic cluster - Irtysh IIIc - mocking the situation of a cluster with external mass. We also computed the source plane magnification distributions. Using them we estimated the probabilities of magnifications in the source plane, and scrutinized their redshift dependence. Finally, we explored the lensing effects of Abell 370 on the luminosity functions of sources at $z_s=9.0$, finding it consistent with published results.
Galaxy lenses are frequently modeled as an elliptical mass distribution with external shear and isothermal spheres to account for secondary and line-of-sight galaxies. There is statistical evidence that some fraction of observed quads are inconsisten
t with these assumptions, and require a dipole-like contribution to the mass with respect to the light. Simplifying assumptions about the shape of mass distributions can lead to the incorrect recovery of parameters such as $H_0$. We create several tests of synthetic quad populations with different deviations from an elliptical shape, then fit them with an ellipse+shear model, and measure the recovered values of $H_0$. Kinematic constraints are not included. We perform two types of fittings -- one with a single point source and one with an array of sources emulating an extended source. We carry out two model-free comparisons between our mock quads and the observed population. One result of these comparisons is a statistical inconsistency not yet mentioned in the literature: the image distance ratios with respect to the lens center of observed quads appear to span a much wider range than those of synthetic or simulated quads. Bearing this discrepancy in mind, our mock populations can result in biases on $H_0$ $sim10%$.
In the near future, ultra deep observations of galaxy clusters with HST or JWST will uncover $300-1000$ lensed multiple images, increasing the current count per cluster by up to an order of magnitude. This will further refine our view of clusters, le
ading to a more accurate and precise mapping of the total and dark matter distribution in clusters, and enabling a better understanding of background galaxy population and their luminosity functions. However, to effectively use that many images as input to lens inversion will require a re-evaluation of, and possibly upgrades to the existing methods. In this paper we scrutinize the performance of the free-form lens inversion method Grale in the regime of $150-1000$ input images, using synthetic massive galaxy clusters. Our results show that with an increasing number of input images, Grale produces improved reconstructed mass distributions, with the fraction of the lens plane recovered at better than $10%$ accuracy increasing from $40-50%$ for $sim!!150$ images to $65%$ for $sim!1000$ images. The reconstructed time delays imply a more precise measurement of $H_0$, with $lesssim 1%$ bias. While the fidelity of the reconstruction improves with the increasing number of multiple images used as model constraints, $sim 150$ to $sim 1000$, the lens plane rms deteriorates from $sim 0.11$ to $sim 0.28$. Since lens plane rms is not necessarily the best indicator of the quality of the mass reconstructions, looking for an alternative indicator is warranted.
We report near simultaneous imaging using LMIRCam on the LBTI of the quadruply imaged lensed quasar HS 0810+2554 at wavelengths of 2.16, 3.7 and $4.78~mu$m with a Full Width Half Max (FWHM) spatial resolution of $0^{primeprime}!!.13$, $0^{primeprime}
!!.12$ and $0^{primeprime}!!.15$ respectively, comparable to HST optical imaging. In the $rm{z} = 1.5$ rest frame of the quasar, the observed wavelengths correspond to 0.86, 1.48, and $1.91~mu$m respectively. The two brightest images in the quad, A and B, are clearly resolved from each other with a separation of $0.187^{primeprime}$. The flux ratio of these two images (A/B) trends from 1.79 to 1.23 from 2.16 to $4.78~mu$m. The trend in flux ratio is consistent with the $2.16~mu$m flux originating from a small sized accretion disk in the quasar that experiences only microlensing. The excess flux above the contribution from the accretion disk at the two longer wavelengths originates from a larger sized region that experiences no microlensing. A simple model employing multiplicative factors for image B due to stellar microlensing $(m)$ and sub-structure millilensing $(M)$ is presented. The result is tightly constrained to the product $mtimes M=1.79$. Given the observational errors, the 60% probability contour for this product stretches from $m= 2.6$, $M = 0.69$ to $m= 1.79$, $M = 1.0$, where the later is consistent with microlensing only.
The galaxy-scale gravitational lens B0128+437 generates a quadrupole-image configuration of a background quasar that shows milli-arcsecond-scale subcomponents in the multiple images observed with VLBI. As this multiple-image configuration including t
he subcomponents has eluded a parametric lens-model characterisation so far, we determine local lens properties at the positions of the multiple images with our model-independent approach. Using PixeLens, we also succeed in setting up a global free-form mass density reconstruction including all subcomponents as constraints. We compare the model-independent local lens properties with those obtained by PixeLens and those obtained by the parametric modelling algorithm Lensmodel. A comparison of all three approaches and a model-free analysis based on the relative polar angles of the multiple images corroborate the hypothesis that elliptically symmetric models are too simplistic to characterise the asymmetric mass density distribution of this lenticular or late-type galaxy. In addition, the model-independent approach efficiently determines local lens properties on the scale of the quasar subcomponents, which are computationally intensive to obtain by free-form model-based approaches. As only 40% of the small-scale subcomponent local lens properties overlap within the 1-$sigma$ confidence bounds, mass density gradients on milli-arcsecond scales cannot be excluded. Hence, aiming at a global reconstruction of the deflecting mass density distribution, increasingly detailed observations require flexible free-form models that allow for density fluctuations on milli-arcsecond scale to replace parametric ones, especially for asymmetric lenses or lenses with localised inhomogeneities like B0128.
Abell 2744, a massive Hubble Frontier Fields merging galaxy cluster with many multiple images in the core has been the subject of many lens
Dark-matter halos grown in cosmological simulations appear to have central NFW-like density cusps with mean values of $dlogrho/dlog r approx -1$, and some dispersion, which is generally parametrized by the varying index $alpha$ 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, $phi_0$ - 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 $phi_0$, Einasto $alpha$, or the central logarithmic slope in the Dehnen-Tremaine analytical $gamma$-models. The range in halo parameters reflects a substantial variation in the binding energies per unit mass of 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 com
puted in energy (orbit) space rather than phase space and (2) low occupation numbers are treated more appropriately than using Stirlings 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.
There is no accepted mechanism that explains the equilibrium structures that form in collisionless cosmological N-body simulations. Recent work has identified nonextensive thermodynamics as an innovative approach to the problem. The distribution func
tion that results from adopting this framework has the same form as for polytropes, but the polytropic index is now related to the degree of nonextensiveness. In particular, the nonextensive approach can mimic the equilibrium structure of dark matter density profiles found in simulations. We extend the investigation of this approach to the velocity structures expected from nonextensive thermodynamics. We find that the nonextensive and simulated N-body rms-velocity distributions do not match one another. The nonextensive rms-velocity profile is either monotonically decreasing or displays little radial variation, each of which disagrees with the rms-velocity distributions seen in simulations. We conclude that the currently discussed nonextensive models require further modifications in order to corroborate dark matter halo simulations. (adapted from TeX)
We investigate the connection between collisionless equilibria and the phase-space relation between density $rho$ and velocity dispersion $sigma$ found in simulations of dark matter halo formation, $F=psd propto r^{-alpha}$. Understanding this relati
on will shed light on the physics relevant to collisionless collapse and on the subsequent structures formed. We show that empirical density profiles that provide good fits to N-body halos also happen to have nearly scale-free psd distributions when in equilibrium. We have also done a preliminary investigation of variables other than $r$ that may match or supercede the correlation with $F$. In the same vein, we show that $rho/sigma^m$, where $m=3$ is the most appropriate combination to use in discussions of the power-law relationship. Since the mechanical equilibrium condition that characterizes the final systems does not by itself lead to power-law $F$ distributions, our findings prompt us to posit that dynamical collapse processes (such as violent relaxation) are responsible for the radial power-law nature of the psd distributions of virialized systems.
