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Register a new userThe effects of galaxy shape and rotation on the X-ray haloes of early-type galaxies - II. Numerical simulations
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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 $T_x$.
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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.
High resolution 2D hydrodynamical simulations describing the evolution of the hot ISM in axisymmetric two-component models of early-type galaxies well reproduced the observed trends of the X-ray luminosity ($L_mathrm{x}$) and temperature ($T_mathrm{x}$) with galaxy shape and rotation, however they also revealed the formation of an exceedingly massive cooled gas disc in rotating systems. In a follow-up of this study, here we investigate the effects of star formation in the disc, including the consequent injection of mass, momentum and energy in the pre-existing interstellar medium. It is found that subsequent generations of stars originate one after the other in the equatorial region; the mean age of the new stars is $> 5$ Gyr, and the adopted recipe for star formation can reproduce the empirical Kennicutt-Schmidt relation. The results of the previous investigation without star formation, concerning $L_mathrm{x}$ and $T_mathrm{x}$ of the hot gas, and their trends with galactic shape and rotation, are confirmed. At the same time, the consumption of most of the cold gas disc into new stars leads to more realistic final systems, whose cold gas mass and star formation rate agree well with those observed in the local universe. In particular, our models could explain the observation of kinematically aligned gas in massive, fast-rotating early-type galaxies.
X-ray luminosity, temperature, gas mass, total mass, and their scaling relations are derived for 94 early-type galaxies using archival $Chandra$ X-ray Observatory observations. Consistent with earlier studies, the scaling relations, $L_X propto T^{4.5pm0.2}$, $M propto T^{2.4pm0.2}$, and $L_X propto M^{2.8pm0.3}$, are significantly steeper than expected from self similarity. This steepening indicates that their atmospheres are heated above the level expected from gravitational infall alone. Energetic feedback from nuclear black holes and supernova explosions are likely heating agents. The tight $L_X - T$ correlation for low-luminosities systems (i.e., below 10$^{40}$ erg/s) are at variance with hydrodynamical simulations which generally predict higher temperatures for low luminosity galaxies. We also investigate the relationship between total mass and pressure, $Y_X = M_g times T$, finding $M propto Y_{X}^{0.45pm0.04}$. We explore the gas mass to total mass fraction in early-type galaxies and find a range of $0.1-1.0%$. We find no correlation between the gas-to-total mass fraction with temperature or total mass. Higher stellar velocity dispersions and higher metallicities are found in hotter, brighter, and more massive atmospheres. X-ray core radii derived from $beta$-model fitting are used to characterize the degree of core and cuspiness of hot atmospheres.
We address the issue of numerical convergence in cosmological smoothed particle hydrodynamics simulations using a suite of runs drawn from the EAGLE project. Our simulations adopt subgrid models that produce realistic galaxy populations at a fiducial mass and force resolution, but systematically vary the latter in order to study their impact on galaxy properties. We provide several analytic criteria that help guide the selection of gravitational softening for hydrodynamical simulations, and present results from runs that both adhere to and deviate from them. Unlike dark matter-only simulations, hydrodynamical simulations exhibit a strong sensitivity to gravitational softening, and care must be taken when selecting numerical parameters. Our results--which focus mainly on star formation histories, galaxy stellar mass functions and sizes--illuminate three main considerations. First, softening imposes a minimum resolved escape speed, $v_epsilon$, due to the binding energy between gas particles. Runs that adopt such small softening lengths that $v_epsilon gt 10,{rm km s^{-1}}$ (the sound speed in ionised $sim 10^4,{rm K}$ gas) suffer from reduced effects of photo-heating. Second, feedback from stars or active galactic nuclei may suffer from numerical over-cooling if the gravitational softening length is chosen below a critical value, $epsilon_{rm eFB}$. Third, we note that small softening lengths exacerbate the segregation of stars and dark matter particles in halo centres, often leading to the counter-intuitive result that galaxy sizes {em increase} as softening is reduced. The structure of dark matter haloes in hydrodynamical runs respond to softening in a way that reflects the sensitivity of their galaxy populations to numerical parameters.
Nuclear hard X-ray luminosities (Lx,nuc) for a sample of 112 early type galaxies within a distance of 67 Mpc are used to investigate their relationship with the central galactic black hole mass Mbh, the inner galactic structure (using the parameters describing its cuspiness), the age of the stellar population in the central galactic region, the hot gas content and the core radio luminosity. Lx,nuc ranges from 10^{38} to 10^{42} erg/s, and the Eddington ratio Lx,nuc/Ledd from 10^{-9} to 10^{-4}. Lx,nuc increases on average with the galactic luminosity Lb and Mbh, with a wide variation by up to 4 orders of magnitude at any fixed Lb>6x10^9 Lb,sun or Mbh>10^7 Msun. This large range should reflect a large variation of the mass accretion rate dotMbh. On the circumnuclear scale, dotMbh at fixed Lb (or Mbh) could vary due to differences in the fuel production rate from the stellar mass return linked to the inner galactic structure; however, dotMbh should vary with cuspiness by a factor exceeding a few only in hot gas poor galaxies and for large differences in the core radius. Lx,nuc does not depend on age, but less luminous nuclei are found among galaxies with a younger stellar component. Lx,nuc is detected both in gas poor and gas rich galaxies, on average increases with the total galactic hot gas cooling rate L_{X,ISM}, but again with a large variation. The lack of a tight relationship between Lx,nuc and the circumnuclear and total gas content can be explained if the gas is heated by black hole feedback, and/or the mass effectively accreted can be largely reduced with respect to that entering the circumnuclear region. Differently from Lx,nuc, the 5 GHz VLA luminosity shows a trend with the inner galactic structure similar to that of the total soft X-ray emission; therefore they could both be produced by the hot gas.
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