We study mass models that correspond to MOND (triaxial) potentials for which the Hamilton-Jacobi equation separates in ellipsoidal coordinates. The problem is first discussed in the simpler case of deep-MOND systems, and then generalized to the full
MOND regime. We prove that the Kuzmin property for Newtonian gravity still holds, i.e., that the density distribution of separable potentials is fully determined once the density profile along the minor axis is assigned. At variance with the Newtonian case, the fact that a positive density along the minor axis leads to a positive density everywhere remains unproven. We also prove that (i) all regular separable models in MOND have a vanishing density at the origin, so that they would correspond to centrally dark-matter dominated systems in Newtonian gravity; (ii) triaxial separable potentials regular at large radii and associated with finite total mass leads to density distributions that at large radii are not spherical and decline as ln(r)/r^5; (iii) when the triaxial potentials admit a genuine Frobenius expansion with exponent 0<epsilon<1, the density distributions become spherical at large radii, with the profile ln(r)/r^(3+2epsilon). After presenting a suite of positive density distributions associated with MOND separable potentials, we also consider the important family of (non-separable) triaxial potentials V_1 introduced by de Zeeuw and Pfenniger, and we show that, as already known for Newtonian gravity, they obey the Kuzmin property also in MOND. The ordinary differential equation relating their potential and density along the z-axis is an Abel equation of the second kind that, in the oblate case, can be explicitly reduced to canonical form.
The ISM evolution of elliptical galaxies experiencing feedback from accretion onto a central black hole was studied recently with high-resolution 1D hydrodynamical simulations including radiative heating and pressure effects, a RIAF-like radiative ef
ficiency, mechanical input from AGN winds, and accretion-driven starbursts. Here we focus on the observational properties of the models in the X-ray band (nuclear luminosity; hot ISM luminosity and temperature; temperature and brightness profiles during quiescence and during outbursts). The nuclear bursts last for ~10^7 yr, with a duty-cycle of a few X (10^-3-10^-2); the present epoch bolometric nuclear emission is very sub-Eddington. The ISM thermal luminosity lx oscillates in phase with the nuclear one; this helps reproduce statistically the observed large lx variation. In quiescence the temperature profile has a negative gradient; thanks to past outbursts, the brightness profile lacks the steep shape typical of inflowing models. Outbursts produce disturbances in these profiles. Most significantly, a hot bubble from shocked hot gas is inflated at the galaxy center; the bubble would be conical in shape, and show radio emission. The ISM resumes a smooth appearance on a time-scale of ~200 Myr; the duty-cycle of perturbances in the ISM is of the order of 5-10%. From the present analysis, additional input physics is important in the ISM-black hole coevolution, to fully account for the properties of real galaxies, as a confining external medium and a jet. The jet will reduce further the mass available for accretion (and then the Eddington ratio $l$), and may help, together with an external pressure, to produce flat or positive temperature gradient profiles (observed in high density environments). Alternatively, $l$ can be reduced if the switch from high to low radiative efficiency takes place at a larger $l$ than routinely assumed.
73 -
P. Di Cintio (1 Max Planck Institute for then Physics of Complex Systems
, Dresden - 2 Astronomy Dept.
2011
The process of relaxation of a system of particles interacting with long-range forces is relevant to many areas of Physics. For obvious reasons, in Stellar Dynamics much attention has been paid to the case of 1/r^2 force law. However, recently the in
terest in alternative gravities emerged, and significant differences with respect to Newtonian gravity have been found in relaxation phenomena. Here we begin to explore this matter further, by using a numerical model of spherical shells interacting with an 1/r^alpha force law obeying the superposition principle. We find that the virialization and phase-mixing times depend on the exponent alpha, with small values of alpha corresponding to longer relaxation times, similarly to what happens when comparing for N-body simulations in classical gravity and in Modified Newtonian Dynamics.
We find, from high-resolution hydro simulations, that winds from AGN effectively heat the inner parts (~100 pc) of elliptical galaxies, reducing infall to the central SMBH; and radiative (photoionization and X-ray) heating reduces cooling flows at th
e kpc scale. Including both types of feedback with (peak) efficiencies of 3 10^{-4} < epsilon_mech < 10^{-3} and of epsilon_rad ~10^{-1.3} respectively, produces systems having duty-cycles, central SMBH masses, X-ray luminosities, optical light profiles, and E+A spectra in accord with the broad suite of modern observations of massive elliptical systems. Our main conclusion is that mechanical feedback (including all three of energy, momentum and mass) is necessary but the efficiency, based on several independent arguments must be a factor of 10 lower than is commonly assumed. Bursts are frequent at z>1 and decline in frequency towards the present epoch as energy and metal rich gas are expelled from the galaxies into the surrounding medium. For a representative galaxy of final stellar mass ~3 10^{11} Msun, roughly 3 10^{10} Msun of recycled gas has been added to the ISM since z~2 and, of that, roughly 63% has been expelled from the galaxy, 19% has been converted into new metal rich stars in the central few hundred parsecs, and 2% has been added to the central SMBH, with the remaining 16% in the form hot X-ray emitting ISM. The bursts occupy a total time of ~170 Myr, which is roughly 1.4% of the available time. Of this time, the central SMBH would be seen as an UV or optical source for ~45% and ~71$% of the time, respectively. Restricting to the last 8.5 Gyr, the burst occupy ~44 Myr, corresponding to a fiducial duty-cycle of ~5 10^{-3}.
Both radiative and mechanical feedback from Active Galactic Nuclei have been found to be important for the evolution of elliptical galaxies. We compute how a shock may be driven from a central black hole into the gaseous envelope of an elliptical gal
axy by mechanical as well as radiative feedback (in the form of nuclear winds) using high resolution 1-D hydrodynamical simulations. We calculate the synchrotron emission from the electron cosmic rays accelerated by the shocks (not the jets) in the central part of elliptical galaxies, and we also study the synchrotron spectrums evolution using the standard diffusive shock acceleration mechanism, which is routinely applied to the scaled volume case of supernova remnants. We find good agreement quantitatively between the synchrotron radio emission produced via this mechanism with extant observations of elliptical galaxies which are undergoing outbursts. Additionally, we also find that synchrotron optical and X-ray emission can co-exist inside elliptical galaxies during a certain phase of evolution subsequent to central outbursts. In fact, our calculations predict a synchrotron luminosity of $sim 1.3times 10^6 L_{odot}$ at the frequency 5 GHz (radio band), of $sim 1.1times 10^6 L_{odot}$ at $4.3times10^{14}$ Hz (R band, corresponding to the absolute magnitude -10.4), and of $sim 1.5times 10^{7} L_{odot}$ at $2.4times10^{17}$ Hz (soft X-ray, 0.5 -- 2.0 keV band).
The importance of the radiative feedback from SMBHs at the centers of elliptical galaxies is not in doubt, given the well established relations among electromagnetic output, black hole mass and galaxy optical luminosity. In addition, feedback due to
mechanical and thermal deposition of energy from jets and winds emitted by the accretion disk around the central SMBH is also expected to occur. In this paper we improve and extend the accretion and feedback physics explored in our previous papers to include also a physically motivated mechanical feedback. We study the evolution of an isolated elliptical galaxy with the aid of a high-resolution 1-D hydrodynamical code, where the cooling and heating functions include photoionization and Compton effects, and restricting to models which include only radiative or only mechanical feedback. We confirm that for Eddington ratios above 0.01 both the accretion and radiative output are forced by feedback effects to be in burst mode, so that strong intermittencies are expected at early times, while at low redshift the explored models are characterized by smooth, very sub-Eddington mass accretion rates punctuated by rare outbursts. However, the explored models always fail some observational tests. If we assume the high mechanical efficiency of 10^{-2.3}, we find that most of the gas is ejected from the galaxy, the resulting X-ray luminosity is far less than is typically observed and little SMBH growth occurs. But models with low enough mechanical efficiency to accomodate satisfactory SMBH growth tend to allow too strong cooling flows and leave galaxies at z=0 with E+A spectra more frequently than is observed. We conclude that both types of feedback are required. Models with combined feedback are explored in a forthcoming paper [abridged]
Estimating the temperature and metal abundance of the intracluster and the intragroup media is crucial to determine their global metal content and to determine fundamental cosmological parameters. When a spatially resolved temperature or abundance pr
ofile cannot be recovered from observations (e.g., for distant objects), or deprojection is difficult (e.g., due to a significant non-spherical shape), only global average temperature and abundance are derived. After introducing a general technique to build hydrostatic gaseous distributions of prescribed density profile in potential wells of any shape, we compute the global mass weighted and emission weighted temperature and abundance for a large set of barotropic equilibria and an observationally motivated abundance gradient. We also compute the spectroscopic-like temperature that is recovered from a single temperature fit of observed spectra. The derived emission weighted abundance and temperatures are higher by 50% to 100% than the corresponding mass weighted quantities, with overestimates that increase with the gas mean temperature. Spectroscopic temperatures are intermediate between mass and luminosity weighted temperatures. Dark matter flattening does not lead to significant differences in the values of the average temperatures or abundances with respect to the corresponding spherical case (except for extreme cases).
We have tested a previous analytical estimate of the dynamical friction timescale in Modified Newtonian Dynamics (MOND) with fully non-linear N-body simulations. The simulations confirm that the dynamical friction timescale is significantly shorter i
n MOND than in equivalent Newtonian systems, i.e. systems with the same phase-space distribution of baryons and additional dark matter. An apparent conflict between this result and the long timescales determined for bars to slow and mergers to be completed in previous N-body simulations of MOND systems is explained. The confirmation of the short dynamical-friction timescale in MOND underlines the challenge that the Fornax dwarf spheroidal poses to the viability of MOND.
