Confinement and diffusion time-scales of CR hadrons in AGN-inflated bubbles

While rich clusters are powerful sources of X-rays, gamma-ray emission from these large cosmic structures has not been detected yet. X-ray radiative energy losses in the central regions of relaxed galaxy clusters are so strong that one needs to consider special sources of energy, likely AGN feedback, to suppress catastrophic cooling of the gas. We consider a model of AGN feedback that postulates that the AGN supplies the energy to the gas by inflating bubbles of relativistic plasma, whose energy content is dominated by cosmic-ray (CR) hadrons. If most of these hadrons can quickly escape the bubbles, then collisions of CRs with thermal protons in the intracluster medium (ICM) should lead to strong gamma-ray emission, unless fast diffusion of CRs removes them from the cluster. Therefore, the lack of detections with modern gamma-ray telescopes sets limits on the confinement time of CR hadrons in bubbles and CR diffusive propagation in the ICM.Comment: 8 pages, 2 figures, accepted for publication in MNRA

The first measurement of temperature standard deviation along the line-of-sight in galaxy clusters

Clusters of galaxies are mainly formed by merging of smaller structures, according to the standard cosmological scenario. If the mass of a substructure is >10% of that of a galaxy cluster, the temperature distribution of the intracluster medium (ICM) in a merging cluster becomes inhomogeneous. Various methods have been used to derive the two-dimensional projected temperature distribution of the ICM. However, methods for studying temperature distribution along the line-of-sight through the cluster were absent. In this paper, we present the first measurement of the temperature standard deviation along the line-of-sight, using as a reference case the multifrequency SZ measurements of the Bullet Cluster. We find that the value of the temperature standard deviation is high and equals to (10.6+/-3.8) keV in the Bullet Cluster. This result shows that the temperature distribution in the Bullet Cluster is strongly inhomogeneous along the line-of-sight and provides a new method for studying galaxy clusters in depth.Comment: 5 pages, 1 figure, published in MNRAS Letter

Can electron distribution functions be derived through the Sunyaev-Zel'dovich effect?

Measurements of the Sunyaev-Zel'dovich (hereafter SZ) effect distortion of the cosmic microwave background provide methods to derive the gas pressure and temperature of galaxy clusters. Here we study the ability of SZ effect observations to derive the electron distribution function (DF) in massive galaxy clusters. Our calculations of the SZ effect include relativistic corrections considered within the framework of the Wright formalism and use a decomposition technique of electron DFs into Fourier series. Using multi-frequency measurements of the SZ effect, we find the solution of a linear system of equations that is used to derive the Fourier coefficients; we further analyze different frequency samples to decrease uncertainties in Fourier coefficient estimations. We propose a method to derive DFs of electrons using SZ multi-frequency observations of massive galaxy clusters. We found that the best frequency sample to derive an electron DF includes high frequencies $\nu$=375, 600, 700, 857 GHz. We show that it is possible to distinguish a Juttner DF from a Maxwell-Bolzman DF as well as from a Juttner DF with the second electron population by means of SZ observations for the best frequency sample if the precision of SZ intensity measurements is less than 0.1%. We demonstrate by means of 3D hydrodynamic numerical simulations of a hot merging galaxy cluster that the morphologies of SZ intensity maps are different for frequencies $\nu$=375, 600, 700, 857 GHz. We stress that measurements of SZ intensities at these frequencies are a promising tool for studying electron distribution functions in galaxy clusters.Comment: 11 pages, 12 figures, published in Astronomy and Astrophysic

An Equivalence Between Adaptive Dynamic Programming With a Critic and Backpropagation Through Time

We consider the adaptive dynamic programming technique called Dual Heuristic Programming (DHP), which is designed to learn a critic function, when using learned model functions of the environment. DHP is designed for optimizing control problems in large and continuous state spaces. We extend DHP into a new algorithm that we call Value-Gradient Learning, VGL(λ), and prove equivalence of an instance of the new algorithm to Backpropagation Through Time for Control with a greedy policy. Not only does this equivalence provide a link between these two different approaches, but it also enables our variant of DHP to have guaranteed convergence, under certain smoothness conditions and a greedy policy, when using a general smooth nonlinear function approximator for the critic. We consider several experimental scenarios including some that prove divergence of DHP under a greedy policy, which contrasts against our proven-convergent algorithm