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Register a new userAnalytical shear and flexion of Einasto dark matter haloes
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Added by
E. Retana-Montenegro
Publication date
2012
fields
Physics
and research's language is
English
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N-body simulations predict that dark matter haloes are described by specific density profiles on both galactic- and cluster-sized scales. Weak gravitational lensing through the measurements of their first and second order properties, shear and flexion, is a powerful observational tool for investigating the true shape of these profiles. One of the three-parameter density profiles recently favoured in the description of dark matter haloes is the Einasto profile. We present exact expressions for the shear and the first and second flexions of Einasto dark matter haloes derived using a Mellin-transform formalism in terms of the Fox H and Meijer G functions, that are valid for general values of the Einasto index. The resulting expressions can be written as series expansions that permit us to investigate the asymptotic behaviour of these quantities. Moreover, we compare the shear and flexion of the Einasto profile with those of different mass profiles including the singular isothermal sphere, the Navarro-Frenk-White profile, and the Sersic profile. We investigate the concentration and index dependences of the Einasto profile, finding that the shear and second flexion could be used to determine the halo concentration, whilst for the Einasto index the shear and first and second flexions may be employed. We also provide simplified expressions for the weak lensing properties and other lensing quantities in terms of the generalized hypergeometric function.
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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 matter 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.
Current theories of structure formation predict specific density profiles of galaxy dark matter haloes, and with weak gravitational lensing we can probe these profiles on several scales. On small scales, higher-order shape distortions known as flexion add significant detail to the weak lensing measurements. We present here the first detection of a galaxy-galaxy flexion signal in space-based data, obtained using a new Shapelets pipeline introduced here. We combine this higher-order lensing signal with shear to constrain the average density profile of the galaxy lenses in the Hubble Space Telescope COSMOS survey. We also show that light from nearby bright objects can significantly affect flexion measurements. After correcting for the influence of lens light, we show that the inclusion of flexion provides tighter constraints on density profiles than does shear alone. Finally we find an average density profile consistent with an isothermal sphere.
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 {rho}(r)/d ln r / r with a shape parameter {alpha} < 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 < {alpha} < 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 {alpha} < 0.3 and less than 2 per cent for {alpha} 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.
Using estimates of dark halo masses from satellite kinematics, weak gravitational lensing, and halo abundance matching, combined with the Tully-Fisher and Faber-Jackson relations, we derive the mean relation between the optical, V_opt, and virial, V_200, circular velocities of early- and late-type galaxies at redshift z~0. For late-type galaxies V_opt ~ V_200 over the velocity range V_opt=90-260 km/s, and is consistent with V_opt = V_maxh (the maximum circular velocity of NFW dark matter haloes in the concordance LCDM cosmology). However, for early-type galaxies V_opt e V_200, with the exception of early-type galaxies with V_opt simeq 350 km/s. This is inconsistent with early-type galaxies being, in general, globally isothermal. For low mass (V_opt < 250 km/s) early-types V_opt > V_maxh, indicating that baryons have modified the potential well, while high mass (V_opt > 400 km/s) early-types have V_opt < V_maxh. Folding in measurements of the black hole mass - velocity dispersion relation, our results imply that the supermassive black hole - halo mass relation has a logarithmic slope which varies from ~1.4 at halo masses of ~10^{12} Msun/h to ~0.65 at halo masses of 10^{13.5} Msun/h. The values of V_opt/V_200 we infer for the Milky Way and M31 are lower than the values currently favored by direct observations and dynamical models. This offset is due to the fact that the Milky Way and M31 have higher V_opt and lower V_200 compared to typical late-type galaxies of the same stellar masses. We show that current high resolution cosmological hydrodynamical simulations are unable to form galaxies which simultaneously reproduce both the V_opt/V_200 ratio and the V_opt-M_star (Tully-Fisher/Faber-Jackson) relation.
We have performed a series of numerical experiments to investigate how the primordial thermal velocities of fermionic dark matter particles affect the physical and phase space density profiles of the dark matter haloes into which they collect. The initial particle velocities induce central cores in both profiles, which can be understood in the framework of phase space density theory. We find that the maximum coarse-grained phase space density of the simulated haloes (computed in 6 dimensional phase space using the EnBid code) is very close to the theoretical fine-grained upper bound, while the pseudo phase space density, Q ~ {rho}/{sigma}^3, overestimates the maximum phase space density by up to an order of magnitude. The density in the inner regions of the simulated haloes is well described by a pseudo-isothermal profile with a core. We have developed a simple model based on this profile which, given the observed surface brightness profile of a galaxy and its central velocity dispersion, accurately predicts its central phase space density. Applying this model to the dwarf spheroidal satellites of the Milky Way yields values close to 0.5 keV for the mass of a hypothetical thermal warm dark matter particle, assuming the satellite haloes have cores produced by warm dark matter free streaming. Such a small value is in conflict with the lower limit of 1.2 keV set by observations of the Lyman-{alpha} forest. Thus, if the Milky Way dwarf spheroidal satellites have cores, these are likely due to baryonic processes associated with the forming galaxy, perhaps of the kind proposed by Navarro, Eke and Frenk and seen in recent simulations of galaxy formation in the cold dark matter model.
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