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Register a new userTwo-component galaxy models with a central BH -- II. The ellipsoidal case
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L. Ciotti
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Recently, two-component spherical galaxy models have been presented, where the stellar profile is described by a Jaffe law, and the total density by another Jaffe law, or by an $r^{-3}$ law at large radii. We extend these two families to their ellipsoidal axisymmetric counterparts: the JJe and J3e models. The total and stellar density distributions can have different flattenings and scale lengths, and the dark matter halo is defined by difference. First, the analytical conditions required to have a nowhere negative dark matter halo density are derived. The Jeans equations for the stellar component are then solved analytically, in the limit of small flattenings, also in presence of a central BH. The azimuthal velocity dispersion anisotropy is described by the Satoh $k$-decomposition. Finally, we present the analytical formulae for velocity fields near the center and at large radii, together with the various terms entering the Virial Theorem. The JJe and J3e models can be useful in a number of theoretical applications, e.g. to explore the role of the various parameters (flattening, relative scale lengths, mass ratios, rotational support) in determining the behavior of the stellar kinematical fields before performing more time-expensive integrations with specific galaxy models, to test codes of stellar dynamics, and in numerical simulations of gas flows in galaxies.
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The dynamical properties of spherically symmetric galaxy models, where a Jaffe (1983) stellar density profile is embedded in a total mass density decreasing as $r^{-3}$ at large radii, are presented. The orbital structure of the stellar component is described by the Osipkov--Merritt anisotropy; the dark matter halo is isotropic, and a black hole is added at the center of the galaxy. First, the conditions for a nowhere negative and monotonically decreasing dark matter halo density profile are derived; this profile can be made asymptotically coincident with a NFW profile at the center and at large radii. Then the minimum value of the anisotropy radius for phase-space consistency is derived as a function of the galaxy parameters. The Jeans equations for the stellar component are solved analytically; the projected velocity dispersion at the center and at large radii is also obtained, for generic values of the anisotropy radius. Finally, analytical expressions for the terms entering the Virial Theorem are derived, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, built following an approach already adopted in our previous works, can be a useful starting point for a more advanced modeling of the dynamics of elliptical galaxies, and can be easily implemented in numerical simulations requiring a realistic dynamical model of a galaxy.
Dynamical properties of spherically symmetric galaxy models where both the stellar and total mass density distributions are described by the Jaffe (1983) profile (with different scale-lenghts and masses), are presented. The orbital structure of the stellar component is described by Osipkov--Merritt anisotropy, and a black hole (BH) is added at the center of the galaxy; the dark matter halo is isotropic. First, the conditions required to have a nowhere negative and monothonically decreasing dark matter halo density profile, are derived. We then show that the phase-space distribution function can be recovered by using the Lambert-Euler $W$ function, while in absence of the central BH only elementary functions appears in the integrand of the inversion formula. The minimum value of the anisotropy radius for consistency is derived in terms of the galaxy parameters. The Jeans equations for the stellar component are solved analytically, and the projected velocity dispersion at the center and at large radii are also obtained analytically for generic values of the anisotropy radius. Finally, the relevant global quantities entering the Virial Theorem are computed analytically, and the fiducial anisotropy limit required to prevent the onset of Radial Orbit Instability is determined as a function of the galaxy parameters. The presented models, even though highly idealized, represent a substantial generalization of the models presentd in Ciotti et al. (2009), and can be useful as starting point for more advanced modeling the dynamics and the mass distribution of elliptical galaxies.
The first resolved, multiply imaged supernova Type Ia, iPTF16geu, was observed 4 years ago, five decades after such systems were first envisioned. Because of the unique properties of the source, these systems hold a lot of promise for the study of galaxy structure and cosmological parameters. However, this very first example presented modelers with a few puzzles. It was expected that to explain image fluxes a contribution from microlensing by stars would be required, but to accommodate the magnitude of microlensing, the density slope of the elliptical power law lens model had to be quite shallow, $rho_{2D} propto r^{-0.7}$. Furthermore, the center of mass had to be displaced from that of observed light by ~0.1 kpc, and the position angle of light distribution was misaligned with that of mass by ~40 degrees. In this paper we present mass models that resolve the first two problems, and suggest a resolution of the third. Motivated by observations of local ellipticals, and some recent analysis of galaxy-scale lenses, our mass models consist of two offset (baryonic) mass components. The resulting mass distributions have a single centroid, but are lopsided, and have isodensity contours that are not purely elliptical and not self-similar with radius. For many of our models the microlensing requirements are modest, and the ring formed by the extended supernova host galaxy resembles the observed one.
Strong scaling relations between host galaxy properties (such as stellar mass, bulge mass, luminosity, effective radius etc) and their nuclear supermassive black holes mass point towards a close co-evolution. In this work, we first review previous efforts supporting the fundamental importance of the relation between supermassive black hole mass and stellar velocity dispersion ($M_{rm BH}$-$sigma_{rm e}$). We then present further original work supporting this claim via analysis of residuals and principal component analysis applied to some among the latest compilations of local galaxy samples with dynamically measured supermassive black hole masses. We conclude with a review of the main physical scenarios in favour of the existence of a $M_{rm BH}$-$sigma_{rm e}$ relation, with a focus on momentum-driven outflows.
In the last decade, using single epoch virial based techniques in the optical band, it has been possible to measure the central black hole mass on large AGN1 samples. However these measurements use the width of the broad line region as a proxy of the virial velocities and are therefore difficult to be carried out on those obscured (type 2) or low luminosity AGN where the nuclear component does not dominate in the optical. Here we present the optical and near infrared spectrum of the starburst/Seyfert galaxy NGC 6221, observed with X-shooter/VLT. Previous observations of NGC 6221 in the X-ray band show an absorbed (N_H=8.5 +/- 0.4 x 10^21 cm^-2) spectrum typical of a type 2 AGN with luminosity log(L_14-195 keV) = 42.05 erg/s, while in the optical band its spectrum is typical of a reddened (A_V=3) starburst. Our deep X-shooter/VLT observations have allowed us to detect faint broad emission in the H_alpha, HeI and Pa_beta lines (FWHM ~1400-2300 km/s) confirming previous studies indicating that NGC 6221 is a reddened starburst galaxy which hosts an AGN. We use the measure of the broad components to provide a first estimate of its central black hole mass (M_BH = 10^(6.6 +/- 0.3) Msol, lambda_Edd=0.01-0.03), obtained using recently calibrated virial relations suitable for moderately obscured (N_H<10^24 cm^-2) AGN.
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