Joint Suzaku and Chandra observations of the MKW4 galaxy group out to the virial radius

We present joint Suzaku and Chandra observations of MKW4. With a global temperature of 1.6 keV, MKW4 is one of the smallest galaxy groups that have been mapped in X-rays out to the virial radius. We measure its gas properties from its center to the virial radius in the north, east, and northeast directions. Its entropy profile follows a power-law of ∝r1.1 between R500 and R200 in all directions, as expected from the purely gravitational structure formation model. The well-behaved entropy profiles at the outskirts of MKW4 disfavor the presence of gas clumping or thermal non-equilibrium between ions and electrons in this system. We measure an enclosed baryon fraction of 11% at R200, remarkably smaller than the cosmic baryon fraction of 15%. We note that the enclosed gas fractions at R200 are systematically smaller for groups than for clusters from existing studies in the literature. The low baryon fraction of galaxy groups, such as MKW4, suggests that their shallower gravitational potential well may make them more vulnerable to baryon losses due to AGN feedback or galactic winds. We find that the azimuthal scatter of various gas properties at the outskirts of MKW4 is significantly lower than in other systems, suggesting that MKW4 is a spherically symmetric and highly relaxed system.

Relaxation of the Cahn–Hilliard equation with singular single-well potential and degenerate mobility

The degenerate Cahn–Hilliard equation is a standard model to describe living tissues. It takes into account cell populations undergoing short-range attraction and long-range repulsion effects. In this framework, we consider the usual Cahn–Hilliard equation with a singular single-well potential and degenerate mobility. These degeneracy and singularity induce numerous difficulties, in particular for its numerical simulation. To overcome these issues, we propose a relaxation system formed of two second-order equations which can be solved with standard packages. This system is endowed with an energy and an entropy structure compatible with the limiting equation. Here, we study the theoretical properties of this system: global existence and convergence of the relaxed system to the degenerate Cahn–Hilliard equation. We also study the long-time asymptotics which interest relies on the numerous possible steady states with given mass.

Can fermionic dark matter mimic supermassive black holes?

We analyze the intriguing possibility of explaining both dark mass components in a galaxy: the dark matter (DM) halo and the supermassive dark compact object lying at the center, by a unified approach in terms of a quasi-relaxed system of massive, neutral fermions in general relativity. The solutions to the mass distribution of such a model that fulfill realistic halo boundary conditions inferred from observations, develop a high-density core supported by the fermion degeneracy pressure able to mimic massive black holes at the center of galaxies. Remarkably, these dense core-diluted halo configurations can explain the dynamics of the closest stars around Milky Way’s center (SgrA*) all the way to the halo rotation curve, without spoiling the baryonic bulge-disk components, for a narrow particle mass range [Formula: see text]–[Formula: see text][Formula: see text]keV.

Compressible Navier–Stokes Equations with hyperbolic heat conduction

We investigate the system of compressible Navier–Stokes equations with hyperbolic heat conduction, i.e. replacing the Fourier’s law by Cattaneo’s law. First, by using Kawashima’s condition on general hyperbolic parabolic systems, we show that for small relaxation time [Formula: see text], global smooth solution exists for small initial data. Moreover, as [Formula: see text] goes to zero, we obtain the uniform convergence of solutions of the relaxed system to that of the classical compressible Navier–Stokes equations.

Admissible relaxation in optimal control problems for infinite dimensional uncertain systems

In this paper we present a result on admissible relaxation for a class of systems governed by an uncertain evolution equation on Banach space. We show that the set of original trajectories is dense in the set of relaxed trajectories and that under certain assumptions the relaxed system is equivalent to the original system.