Estimating multidimensional probability fields using the Field Estimator for Arbitrary Spaces (FiEstAS) with applications to astrophysics

The Field Estimator for Arbitrary Spaces (FiEstAS) computes the continuous probability density field underlying a given discrete data sample in multiple, non-commensurate dimensions. The algorithm works by constructing a metric-independent tessellation of the data space based on a recursive binary splitting. Individual, data-driven bandwidths are assigned to each point, scaled so that a constant "mass" M0 is enclosed. Kernel density estimation may then be performed for different kernel shapes, and a combination of balloon and sample point estimators is proposed as a compromise between resolution and variance. A bias correction is evaluated for the particular (yet common) case where the density is computed exactly at the locations of the data points rather than at an uncorrelated set of locations. By default, the algorithm combines a top-hat kernel with M0=2.0 with the balloon estimator and applies the corresponding bias correction. These settings are shown to yield reasonable results for a simple test case, a two-dimensional ring, that illustrates the performance for oblique distributions, as well as for a six-dimensional Hernquist sphere, a fairly realistic model of the dynamical structure of stellar bulges in galaxies and dark matter haloes in cosmological N-body simulations. Results for different parameter settings are discussed in order to provide a guideline to select an optimal configuration in other cases. Source code is available upon request.Comment: 15 pages, 4 figures, accepted in Comp. Phys. Com

A phenomenological model of galaxy clusters

We present a simple model to describe the dark matter density, the gas density, and the gas temperature profiles of galaxy clusters. Analytical expressions for these quantities are given in terms of only five free parameters with a clear physical meaning: the mass M of the dark matter halo (or the characteristic temperature T_0), the characteristic scale radius a, the cooling radius in units of a (0<alpha<1), the central temperature in units of T_0 (0<t<1), and the asymptotic baryon fraction in units of the cosmic value (f~1). It is shown that our model is able to reproduce the three-dimensional density and temperature profiles inferred from X-ray observations of real clusters within a 20 per cent accuracy over most of the radial range. Some possible applications are briefly discussed.Comment: 7 pages, 4 figures, submitted to MNRA

FiEstAS sampling -- a Monte Carlo algorithm for multidimensional numerical integration

This paper describes a new algorithm for Monte Carlo integration, based on the Field Estimator for Arbitrary Spaces (FiEstAS). The algorithm is discussed in detail, and its performance is evaluated in the context of Bayesian analysis, with emphasis on multimodal distributions with strong parameter degeneracies. Source code is available upon request.Comment: 18 pages, 3 figures, submitted to Comp. Phys. Com

Pressure from dark matter annihilation and the rotation curve of spiral galaxies

The rotation curves of spiral galaxies are one of the basic predictions of the cold dark matter paradigm, and their shape in the innermost regions has been hotly debated over the last decades. The present work shows that dark matter annihilation into electron-positron pairs may affect the observed rotation curve by a significant amount. We adopt a model-independent approach, where all the electrons and positrons are injected with the same initial energy E_0 ~ m_dm*c^2 in the range from 1 MeV to 1 TeV and the injection rate is constrained by INTEGRAL, Fermi, and HESS data. The pressure of the relativistic electron-positron gas is determined by solving the diffusion-loss equation, considering inverse Compton scattering, synchrotron radiation, Coulomb collisions, bremsstrahlung, and ionization. For values of the gas density and magnetic field that are representative of the Milky Way, it is estimated that pressure gradients are strong enough to balance gravity in the central parts if E_0 < 1 GeV. The exact value depends somewhat on the astrophysical parameters, and it changes dramatically with the slope of the dark matter density profile. For very steep slopes, as those expected from adiabatic contraction, the rotation curves of spiral galaxies would be affected on ~kpc scales for most values of E_0. By comparing the predicted rotation curves with observations of dwarf and low surface brightness galaxies, we show that the pressure from dark matter annihilation may improve the agreement between theory and observations in some cases, but it also imposes severe constraints on the model parameters (most notably, the inner slope of halo density profile, as well as the mass and the annihilation cross-section of dark matter particles into electron-positron pairs).Comment: 14 pages, 10 figure

Effect of dark matter annihilation on gas cooling and star formation

In the current paradigm of cosmic structure formation, dark matter plays a key role on the formation and evolution of galaxies through its gravitational influence. On microscopic scales, dark matter particles are expected to annihilate amongst themselves into different products, with some fraction of the energy being transferred to the baryonic component. It is the aim of the present work to show that, in the innermost regions of dark matter halos, heating by dark matter annihilation may be comparable to the cooling rate of the gas. We use analytical models of the dark matter and gas distributions in order to estimate the heating and cooling rates, as well as the energy available from supernova explosions. Depending on the model parameters and the precise nature of dark matter particles, the injected energy may be enough to balance radiative cooling in the cores of galaxy clusters. On galactic scales, it would inhibit star formation more efficiently than supernova feedback. Our results suggest that dark matter annihilation prevents gas cooling and star formation within at least $0.01-1$ per cent of the virial radius