The Effects of Galaxy Shape and Rotation on the X-ray Haloes of Early-Type Galaxies

We present a detailed diagnostic study of the observed temperatures of the hot X-ray coronae of early-type galaxies. By extending the investigation carried out in Pellegrini (2011) with spherical models, we focus on the dependence of the energy budget and temperature of the hot gas on the galaxy structure and internal stellar kinematics. By solving the Jeans equations we construct realistic axisymmetric three-component galaxy models (stars, dark matter halo, central black hole) with different degrees of flattening and rotational support. The kinematical fields are projected along different lines of sight, and the aperture velocity dispersion is computed within a fraction of the circularized effective radius. The model parameters are chosen so that the models resemble real ETGs and lie on the Faber-Jackson and Size-Luminosity relations. For these models we compute T_* (the stellar heating contribution to the gas injection temperature) and T_gm (the temperature equivalent of the energy required for the gas escape). In particular, different degrees of thermalisation of the ordered rotational field of the galaxy are considered. We find that T_* and T_gm can vary only mildly due to a pure change of shape. Galaxy rotation instead, when not thermalised, can lead to a large decrease of T_*; this effect can be larger in flatter galaxies that can be more rotationally supported. Recent temperature measurements T_x, obtained with Chandra, are larger than, but close to, the T_* values of the models, and show a possible trend for a lower T_x in flatter and more rotationally supported galaxies; this trend can be explained by the lack of thermalisation of the whole stellar kinetic energy. Flat and rotating galaxies also show lower L_x values, and then a lower gas content, but this is unlikely to be due to the small variation of T_gm found here for them.Comment: 16 pages, 7 figures, accepted for publication in MNRA

The stellar initial mass function of early type galaxies from low to high stellar velocity dispersion: homogeneous analysis of ATLAS3D^{\rm 3D} and Sloan Lens ACS galaxies

We present an investigation about the shape of the initial mass function (IMF) of early-type galaxies (ETGs), based on a joint lensing and dynamical analysis, and on stellar population synthesis models, for a sample of 55 lens ETGs identified by the Sloan Lens ACS (SLACS) Survey. We construct axisymmetric dynamical models based on the Jeans equations which allow for orbital anisotropy and include a dark matter halo. The models reproduce in detail the observed \textit{HST} photometry and are constrained by the total projected mass within the Einstein radius and the stellar velocity dispersion ($\sigma$) within the SDSS fibers. Comparing the dynamically-derived stellar mass-to-light ratios $(M_*/L)_{\rm dyn}$, obtained for an assumed halo slope $\rho_{\rm h}\propto r^{-1}$, to the stellar population ones $(M_*/L)_{\rm pop}$, derived from full-spectrum fitting and assuming a Salpeter IMF, we infer the mass normalization of the IMF. Our results confirm the previous analysis by the SLACS team that the mass normalization of the IMF of high $\sigma$ galaxies is consistent on average with a Salpeter slope. Our study allows for a fully consistent study of the trend between IMF and $\sigma$ for both the SLACS and \ATLAS samples, which explore quite different $\sigma$ ranges. The two samples are highly complementary, the first being essentially $\sigma$ selected, and the latter volume-limited and nearly mass selected. We find that the two samples merge smoothly into a single trend of the form $\log\alpha =(0.38\pm0.04)\times\log(\sigma_{\rm e}/200\,\mathrm{km~s}^{-1})+(-0.06\pm0.01)$, where $\alpha=(M_*/L)_{\rm dyn}/(M_*/L)_{\rm pop}$ and $\sigma_{\rm e}$ is the luminosity averaged $\sigma$ within one effective radius $R_{\rm e}$. This is consistent with a systematic variation of the IMF normalization from Kroupa to Salpeter in the interval $\sigma_{\rm e}\approx90-270\,\mathrm{km~s}^{-1}$.Comment: 18 pages, 8 figures. Accepted for publication in MNRA

The dynamics of early-type galaxies as a tool to understand their hot coronae and their IMF

Dynamical models of galaxies are a powerful tool to study and understand several astrophysical problems related to galaxy formation and evolution. This thesis is focussed on a particular type of dynamical models, that are widely used in literature, and are based on the solution of the Jeans equations. By means of a numerical Jeans solver code, developed on purpose and able to build state-of-the-art advanced axisymmetric galaxy models, two of the main currently investigated issues in the field of research of early-type galaxies (ETGs) are addressed. The first topic concerns the hot and X-ray emitting gaseous coronae that surround ETGs. The main goal is to explain why flat and rotating galaxies generally exhibit haloes with lower gas temperatures and luminosities with respect to rounder and velocity dispersion supported systems. The second astrophysical problem addressed concerns instead the stellar initial mass function (IMF) of ETGs. Nowadays, this is a very controversial issue due to a growing number of works on ETGs, based on different and independent techniques, that show evidences of a systematic variation of the IMF normalization as a function of galaxy velocity dispersion or mass. These studies are changing the previous opinion that the IMF of ETGs was the same as that of spiral galaxies, and hence universal throughout the whole large family of galaxies

The effects of galaxy shape and rotation on the X-ray haloes of early-type galaxies – II. Numerical simulations

By means of high resolution 2D hydrodynamical simulations, we study the evolution of the hot ISM for a large set of early-type galaxy models, characterized by various degrees of flattening and internal rotation. The galaxies are described by state-of-the-art axisymmetric two-component models, tailored to reproduce real systems; the dark matter haloes follow the Navarro-Frenk-White or the Einasto profile. The gas is produced by the evolving stars, and heated by Type Ia SNe. We find that, in general, the rotation field of the ISM in rotating galaxies is very similar to that of the stars, with a consequent negligible heating contribution from thermalization of the ordered motions. The relative importance of flattening and rotation in determining the final X-ray luminosity $L_x$ and temperature $T_x$ of the hot haloes is a function of the galactic mass. Flattening and rotation in low mass galaxies favour the establishment of global winds, with the consequent reduction of $L_x$. In medium-to-high mass galaxies, flattening and rotation are not sufficient to induce global winds, however, in the rotating models the nature of the gas flows is deeply affected by conservation of angular momentum, resulting in a reduction of both $L_x$ and $T_x$.Comment: 20 pages, 13 figures. Accepted for publication in MNRA