X-ray emission from early-type galaxies

The past decade has seen a large progress in the X-ray investigation of early-type galaxies of the local universe, and first attempts have been made to reach redshifts z>0 for these objects, thanks to the high angular resolution and sensitivity of the satellites Chandra and XMM-Newton. Major advances have been obtained in our knowledge of the three separate contributors to the X-ray emission, that are the stellar sources, the hot gas and the galactic nucleus. Here a brief outline of the main results is presented, pointing out the questions that remain open, and finally discussing the prospects to solve them with a wide area X-ray survey mission such as WFXT.Comment: 6 pages, 4 figures; to appear in the Proceedings of "The Wide Field X-ray Telescope Workshop", held in Bologna, Italy, Nov. 25-26 2009, published by Memorie della Societ\`a Astronomica Italiana 2010 (arXiv:1010.5889

Isothermal Bondi accretion in Jaffe and Hernquist galaxies with a central black hole: fully analytical solutions

One of the most active fields of research of modern-day astrophysics is that of massive black hole formation and co-evolution with the host galaxy. In these investigations, ranging from cosmological simulations, to semi-analytical modeling, to observational studies, the Bondi solution for accretion on a central point mass is widely adopted. In this work we generalize the classical Bondi accretion theory to take into account the effects of the gravitational potential of the host galaxy, and of radiation pressure in the optically thin limit. Then, we present the fully analytical solution, in terms of the Lambert-Euler $W$-function, for isothermal accretion in Jaffe and Hernquist galaxies with a central black hole. The flow structure is found to be sensitive to the shape of the mass profile of the host galaxy. These results and the formulae that are provided, mostly important the one for the critical accretion parameter, allow for a direct evaluation of all flow properties, and are then useful for the above mentioned studies. As an application, we examine the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the black hole, under the hypothesis of classical Bondi accretion. An overestimate is obtained from regions close to the black hole, and an underestimate outside a few Bondi radii; the exact position of the transition between the two kinds of departure depends on the galaxy model.Comment: 18 pages, 6 figures, submitted to ApJ, comments welcom

Stochastic Master Equations in Thermal Environment

We derive the stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. At zero temperature it is well-known that one obtains stochastic differential equations of jump-diffusion type. At strictly positive temperature, we show that only pure diffusion type equations are relevant

The Very-Soft X-Ray Emission of X-Ray Faint Early-Type Galaxies

A recent re-analysis of Einstein data, and new ROSAT observations, have revealed the presence of at least two components in the X-ray spectra of X-ray faint early-type galaxies: a relatively hard component (kT>1.5 keV), and a very soft component (kT\sim 0.2-0.3 keV). We address the problem of the nature of the very soft component, and whether it can be due to a hot interstellar medium (ISM), or is most likely originated by the collective emission of very soft stellar sources. To this purpose, hydrodynamical evolutionary sequences for the secular behavior of gas flows in ellipticals have been performed, and the results are compared with the observational X-ray data: the very soft component could be entirely explained with a hot ISM only in galaxies where the depth of the potential well is quite shallow, otherwise the softest contribution to the X-ray emission comes certainly from stellar sources. As stellar soft X-ray emitters, we consider late-type stellar corone, supersoft sources such as those discovered by ROSAT in the Magellanic Clouds and M31, and RSCVn systems. We finally present a model for the X-ray emission of NGC4365, to reproduce in detail the results of the ROSAT pointed observation (PSPC spectrum and radial surface brightness distribution).Comment: Postscript file, 28 pages. For hardcopy of figures contact [email protected]. BAP 12-1993-040-DD

Complex Obtuse Random Walks and their Continuous-Time Limits

We study a particular class of complex-valued random variables and their associated random walks: the complex obtuse random variables. They are the generalization to the complex case of the real-valued obtuse random variables which were introduced in \cite{A-E} in order to understand the structure of normal martingales in \RR^n.The extension to the complex case is mainly motivated by considerations from Quantum Statistical Mechanics, in particular for the seek of a characterization of those quantum baths acting as classical noises. The extension of obtuse random variables to the complex case is far from obvious and hides very interesting algebraical structures. We show that complex obtuse random variables are characterized by a 3-tensor which admits certain symmetries which we show to be the exact 3-tensor analogue of the normal character for 2-tensors (i.e. matrices), that is, a necessary and sufficient condition for being diagonalizable in some orthonormal basis. We discuss the passage to the continuous-time limit for these random walks and show that they converge in distribution to normal martingales in \CC^N. We show that the 3-tensor associated to these normal martingales encodes their behavior, in particular the diagonalization directions of the 3-tensor indicate the directions of the space where the martingale behaves like a diffusion and those where it behaves like a Poisson process. We finally prove the convergence, in the continuous-time limit, of the corresponding multiplication operators on the canonical Fock space, with an explicit expression in terms of the associated 3-tensor again