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تسجيل مستخدم جديدThe lensing properties of the Einasto profile
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In recent high resolution N-body CDM simulations, it has been had found that nonsingular three-parameter models, e.g. the Einasto profile has a better performance better than the singular two-parameter models, e.g. the Navarro, Frenk and White in the fitting of a wide range of dark matter halos. A problem with this profile is that the surface mass density is non-analytical for general values of the Einasto index. Therefore, its other lensing properties have the same problem. We obtain an exact analytical expression for the surface mass density of the Einasto profile in terms of the Fox H-function for all values of the Einasto index. With the idea of facilitate the use of the Einasto profile in lensing studies, we calculate the surface mass density, deflection angle, lens equation, deflection potential, magnification, shear and critical curves of the Einasto profile in terms of the Meijer G-function for all rational values of the Einasto index. The Meijer G-function have been implemented in several commercial and open-source computer algebra systems, thus the use of the lensing properties of the Einasto profile in strong and weak lensing studies is straighforward. We also compare the Sersic and Einasto surface mass densities profiles and found differences between them. This implies that the lensing properties are not equal for both profiles.
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Recent high-resolution N-body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matte
r haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the Sersic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.
The lensing signal around galaxy clusters can, in principle, be used to test detailed predictions for their average mass profile from numerical simulations. However, the intrinsic shape of the profiles can be smeared out when a sample that spans a wi
de range of cluster masses is averaged in physical length units. This effect especially conceals rapid changes in gradient such as the steep drop associated with the splashback radius, a sharp edge corresponding to the outermost caustic in accreting halos. We optimize the extraction of such local features by scaling individual halo profiles to a number of spherical overdensity radii, and apply this method to 16 X-ray-selected high-mass clusters targeted in the Cluster Lensing And Supernova survey with Hubble. By forward-modeling the weak- and strong-lensing data presented by Umetsu et al., we show that, regardless of the scaling overdensity, the projected ensemble density profile is remarkably well described by an NFW or Einasto profile out to $R sim 2.5h^{-1}$Mpc, beyond which the profiles flatten. We constrain the NFW concentration to $c_{200c} = 3.66 pm 0.11$ at $M_{200c} simeq 1.0 times 10^{15}h^{-1}M_odot$, consistent with and improved from previous work that used conventionally stacked lensing profiles, and in excellent agreement with theoretical expectations. Assuming the profile form of Diemer & Kravtsov and generic priors calibrated from numerical simulations, we place a lower limit on the splashback radius of the cluster halos, if it exists, of $R_{sp}/r_{200m} > 0.89$ ($R_{sp} > 1.83h^{-1}$Mpc) at 68% confidence. The corresponding density feature is most pronounced when the cluster profiles are scaled by $r_{200m}$, and smeared out when scaled to higher overdensities.
We outline our methods for obtaining high precision mass profiles, combining independent weak-lensing distortion, magnification, and strong-lensing measurements. For massive clusters the strong and weak lensing regimes contribute equal logarithmic co
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(Abridged) The analysis of the rotation curves (RCs) of spiral galaxies provides an efficient diagnostic for studying the properties of dark matter halos and their relations with the baryonic material. We have modeled the RCs of galaxies from The HI
Nearby Galaxy Survey (THINGS) with the Einasto halo model, which has emerged as the best-fitting model of the halos arising in dissipationless cosmological N-body simulations. We find that the RCs are significantly better fit with the Einasto halo than with either a pseudo-isothermal sphere (Iso) or Navarro-Frenk-White (NFW) halo models. In our best-fit models, the radius of density slope -2 and the density at this radius are highly correlated. The Einasto index, which controls the overall shape of the density profile, is near unity on average for intermediate and low mass halos. This is not in agreement with the predictions from LCDM simulations. The indices of the most massive halos are in rough agreement with those of cosmological simulations and appear correlated with the halo virial mass. We find that a typical Einasto density profile declines more strongly in its outermost parts than any of the Iso or NFW models whereas it is relatively shallow in its innermost regions. The core nature of those regions of halos thus extends the cusp-core controversy found for the NFW model with low surface density galaxies to the Einasto halo with more massive galaxies like those of THINGS. We thus find that the Einasto halo model provides, so far, the best match to the observed RCs, and can therefore be considered as a new standard model for dark matter halos.
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