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The Sersic law reproduces very well the surface brightness profile of early-type galaxies, and therefore is routinely used in observational and theoretical works. Unfortunately, its deprojection can not be expressed in terms of elementary functions for generic values of the shape parameter $n$. Over the years, different families of approximate deprojection formulae have been proposed, generally based on fits of the numerical deprojection over some radial range. We searched for a very simple, accurate, and theoretically motivated deprojection formula of the Sersic law, without free parameters, not based on fits of the numerical deprojection, and holding for generic $n > 1$. The formula has been found by requiring it to reproduce the analytical expressions for the inner and outer asymptotic expansions of the deprojected Sersic law of given $n$, and by matching the two expansions at intermediate radii with the request that the total luminosity coincides with that of the original Sersic profile of same $n$. The resulting formula is algebraically very simple, by construction its inner and outer parts are the exact (asymptotic) deprojection of the Sersic law, and it depends on two coefficients that are analytical functions of $n$ of immediate evaluation. The accuracy of the formula over the whole radial range is very good and increases for increasing $n$, with maximum relative deviations from the true numerical deprojection of $\simeq 8\,10^{-3}$ for the de Vaucouleurs profile. In the Appendix, the extension of the proposed formula to profiles with $n <1$ is also presented and discussed. The formula obtained is a useful tool of simple use in the modeling of early-type galaxies. Its ellipsoidal generalization is immediate., Comment: 8 pages, 3 figures, accepted for publication in A&A

Using Large Binocular Telescope deep imaging data from the Smallest Scale of Hierarchy Survey (SSH) and archival Hubble Space Telescope data, we reveal the presence of two elongated stellar features contiguous to a bar-like stellar structure in the inner regions of the dwarf irregular galaxy NGC 3741. These structures are dominated by stars younger than a few hundred Myr and collectively are about twice as extended as the old stellar component. These properties are very unusual for dwarf galaxies in the nearby Universe and difficult to explain by hydro-dynamical simulations. From the analysis of archival 21-cm observations, we find that the young stellar "bar" coincides with an HI high-density region proposed by previous studies to be a purely gaseous bar; we furthermore confirm radial motions of a few km/s, compatible with an inflow/outflow, and derive a steeply-rising rotation curve and high HI surface density at the center, indicating a very concentrated mass distribution. We propose that the peculiar properties of the stellar and gaseous components of NGC 3741 may be explained by a recent merger or ongoing gas accretion from the intergalactic medium, which caused gas inflows towards the galaxy center and triggered star formation a few hundred Myr ago. This event may explain the young and extended stellar features, the bar-like structure, the very extended HI disc and the central HI spiral arms. The high central HI density and the steeply rising rotation curve suggest that NGC 3741 may be the progenitor or the descendant of a starburst dwarf., Comment: Accepted for publication in MNRAS. Corrected typo in the list of authors

The gravitational potentials of realistic galaxy models are in general non-integrable, in the sense that they admit orbits that do not have three independent isolating integrals of motion and are therefore chaotic. However, if chaotic orbits are a small minority in a stellar system, it is expected that they have negligible impact on the main dynamical properties of the system. In this paper we address the question of quantifying the importance of chaotic orbits in a stellar system, focusing, for simplicity, on axisymmetric systems. Chaotic orbits have been found in essentially all (non-St\"ackel) axisymmetric gravitational potentials in which they have been looked for. Based on the analysis of the surfaces of section, we add new examples to those in the literature, finding chaotic orbits, as well as resonantly trapped orbits among regular orbits, in Miyamoto-Nagai, flattened logarithmic and shifted Plummer axisymmetric potentials. We define the fractional contributions in mass of chaotic ($\xi_{\rm c}$) and resonantly trapped ($\xi_{\rm t}$) orbits to a stellar system of given distribution function, which are very useful quantities, for instance in the study of the dispersal of stellar streams of galaxy satellites. As a case study, we measure $\xi_{\rm c}$ and $\xi_{\rm t}$ in two axisymmetric stellar systems obtained by populating flattened logarithmic potentials with the Evans ergodic distribution function, finding $\xi_{\rm c}\sim 10^{-4}-10^{-3}$ and $\xi_{\rm t}\sim 10^{-2}-10^{-1}$., Comment: Accepted for publication in MNRAS. 15 pages, 11 figures

We present the theoretical framework to efficiently solve the Jeans equations for multi-component axisymmetric stellar systems, focusing on the scaling of all quantities entering them. The models may include an arbitrary number of stellar distributions, a dark matter halo, and a central supermassive black hole; each stellar distribution is implicitly described by a two- or three-integral distribution function, and the stellar components can have different structural (density profile, flattening, mass, scale-length), dynamical (rotation, velocity dispersion anisotropy), and population (age, metallicity, initial mass function, mass-to-light ratio) properties. In order to determine the ordered rotational velocity and the azimuthal velocity dispersion fields of each component, we introduce a decomposition that can be used when the commonly adopted Satoh decomposition cannot be applied. The scheme developed is particularly suitable for a numerical implementation; we describe its realisation within our code JASMINE2, optimised to maximally exploit the scalings allowed by the Poisson and the Jeans equations, also in the post-processing procedures. As applications, we illustrate the building of three multi-component galaxy models with two distinct stellar populations, a central black hole, and a dark matter halo; we also study the solution of the Jeans equations for an exponential thick disc, and for its multi-component representation as the superposition of three Miyamoto-Nagai discs. A useful general formula for the numerical evaluation of the gravitational potential of factorised thick discs is finally given., Comment: 18 pages, 7 figures, MNRAS accepted. Significant changes in response to the referee's comments; a new section is devoted to the application of the code to exponential thick discs

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., Comment: 21 pages, 10 figures. MNRAS accepted

A hot plasma is the dominant phase of the interstellar medium of early-type galaxies. Its origin can reside in stellar mass losses, residual gas from the formation epoch, and accretion from outside of the galaxies. Its evolution is linked to the dynamical structure of the host galaxy, to the supernova and AGN feedback, and to (late-epoch) star formation, in a way that has yet to be fully understood. Important clues about the origin and evolution of the hot gas come from the abundances of heavy metals, that have been studied with increasing detail with XMM-Newton and Chandra. We present recent high resolution hydrodynamical simulations of the hot gas evolution that include the above processes, and where several chemical species, originating in AGB stars and supernovae of type Ia and II, have also been considered. The high resolution, of few parsecs in the central galactic region, allows us to track the metal enrichment, transportation and dilution throughout the galaxy. The comparison of model results with observed abundances reveals a good agreement for the region enriched by the AGN wind, but also discrepancies for the diffuse hot gas; the latter indicate the need for a revision of standard assumptions, and/or the importance of neglected effects as those due to the dust, and/or residual uncertainties in deriving abundances from the X-ray spectra., Comment: 6 pages, 5 figures, Proceedings of the XMM-Newton 2019 science workshop "Astrophysics of hot plasma in extended X-ray sources", to be published in Astron. Nachr

The Smallest Scale of Hierarchy (SSH) survey is an ongoing strategic large program at the Large Binocular Telescope, aimed at the detection of faint stellar streams and satellites around 45 late-type dwarf galaxies located in the Local Universe within $\simeq$10 Mpc. SSH exploits the wide-field, deep photometry provided by the Large Binocular Cameras in the two wide filters $g$ and $r$. This paper describes the survey, its goals, and the observational and data reduction strategies. We present preliminary scientific results for five representative cases (UGC 12613, NGC 2366, UGC 685, NGC 5477 and UGC 4426) covering the whole distance range spanned by the SSH targets. We reach a surface brightness limit as faint as $\mu(r)\sim$ 31 mag arcsec$^{-2}$ both for targets closer than 4$-$5 Mpc, which are resolved into individual stars, and for more distant targets through the diffuse light. Our analysis reveals the presence of extended low surface brightness stellar envelopes around the dwarfs, reaching farther out than what traced by the integrated light, and as far out as, or even beyond, the observed HI disk. Stellar streams, arcs, and peculiar features are detected in some cases, indicating possible perturbation, accretion, or merging events. We also report on the discovery of an extreme case of Ultra Diffuse Galaxy ($\mu_g(0)=27.9$~mag/arcsec$^2$) in the background of one of our targets, to illustrate the power of the survey in revealing extremely low surface brightness systems., Comment: Accepted for publication in MNRAS

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., Comment: 12 pages, 6 figures, accepted for publication in MNRAS. arXiv admin note: substantial text overlap with arXiv:1707.08822

We present new Hubble Space Telescope (HST) imaging of a stream-like system associated with the dwarf galaxy DDO 68, located in the Lynx-Cancer Void at a distance of D$\sim$12.65 Mpc from us. The stream, previously identified in deep Large Binocular Telescope images as a diffuse low surface brightness structure, is resolved into individual stars in the F606W (broad V) and F814W ($\sim$I) images acquired with the Wide Field Camera 3. The resulting V, I color-magnitude diagram (CMD) of the resolved stars is dominated by old (age$\gtrsim$1-2 Gyr) red giant branch (RGB) stars. From the observed RGB tip, we conclude that the stream is at the same distance as DDO 68, confirming the physical association with it. A synthetic CMD analysis indicates that the large majority of the star formation activity in the stream occurred at epochs earlier than $\sim$1 Gyr ago, and that the star formation at epochs more recent than $\sim$500 Myr ago is compatible with zero. The total stellar mass of the stream is $\sim10^{6} M_{\odot}$, about 1/100 of that of DDO~68. This is a striking example of hierarchical merging in action at the dwarf galaxy scales., Comment: ApJ in press

We present chemical abundances and radial velocities of six HII regions in the extremely metal-poor star-forming dwarf galaxy DDO 68. They are derived from deep spectra in the wavelength range 3500 - 10,000 {\AA}, acquired with the Multi Object Double Spectrograph (MODS) at the Large Binocular Telescope (LBT). In the three regions where the [O III]$\lambda$4363 {\AA} line was detected, we inferred the abundance of He, N, O, Ne, Ar, and S through the "direct" method. We also derived the oxygen abundances of all the six regions adopting indirect method calibrations. We confirm that DDO 68 is an extremely metal-poor galaxy, and a strong outlier in the luminosity - metallicity relation defined by star-forming galaxies. With the direct-method we find indeed an oxygen abundance of 12+log(O/H)=7.14$\pm$0.07 in the northernmost region of the galaxy and, although with large uncertainties, an even lower 12+log(O/H)=6.96$\pm$0.09 in the "tail". This is, at face value, the most metal-poor direct abundance detection of any galaxy known. We derive a radial oxygen gradient of -0.06$\pm$0.03 dex/kpc (or -0.30 dex $R_{25}^{-1}$) with the direct method, and a steeper gradient of -0.12$\pm$0.03 dex/kpc (or -0.59 dex $R_{25}^{-1}$) from the indirect method. For the $\alpha$-element to oxygen ratios we obtain values in agreement with those found in other metal-poor star-forming dwarfs. For nitrogen, instead, we infer much higher values, leading to log(N/O)$\sim-1.4$, at variance with the suggested existence of a tight plateau at $-1.6$ in extremely metal poor dwarfs. The derived helium mass fraction ranges from Y=0.240$\pm$0.005 to Y=0.25$\pm$0.02, compatible with standard big bang nucleosynthesis. Finally, we measured HII region radial velocities in the range 479$-$522 km/s from the tail to the head of the "comet", consistent with the rotation derived in the HI., Comment: Accepted for publication in MNRAS

The fully analytical solution for isothermal Bondi accretion on a black hole (MBH) at the center of JJ two-component Jaffe (1983) galaxy models is presented. In JJ models the stellar and total mass density distributions are described by the Jaffe profile, with different scale-lengths and masses, and to which a central MBH is added; all the relevant stellar dynamical properties can also be derived analytically. In these new accretion solutions the hydrodynamical and stellar dynamical properties are linked by imposing that the gas temperature is proportional to the virial temperature of the stellar component. The formulae that are provided allow to evaluate all flow properties, and are then useful for estimates of the accretion radius and the mass flow rate when modeling accretion on MBHs at the center of galaxies., Comment: 4 pages, 4 figures; proceedings of the IAUS342 "Perseus in Sicily: from black hole to cluster outskirts"

The fully analytical solution for isothermal Bondi accretion on a black hole (MBH) at the center of two-component Jaffe (1983) galaxy models is presented. In a previous work we provided the analytical expressions for the critical accretion parameter and the radial profile of the Mach number in the case of accretion on a MBH at the center of a spherically symmetric one-component Jaffe galaxy model. Here we apply this solution to galaxy models where both the stellar and total mass density distributions are described by the Jaffe profile, with different scale-lengths and masses, and to which a central MBH is added. For such galaxy models all the relevant stellar dynamical properties can also be derived analytically (Ciotti & Ziaee Lorzad 2018). In these new models the hydrodynamical and stellar dynamical properties are linked by imposing that the gas temperature is proportional to the virial temperature of the galaxy stellar component. The formulae that are provided allow to evaluate all flow properties, and are then useful for estimates of the scale-radius and the mass flow rate when modeling accretion on massive black holes at the center of galaxies. As an application, we quantify the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the MBH, under the hypothesis of classical Bondi accretion., Comment: 14 pages, 7 figures, submitted to ApJ, comments welcome

A recent determination of the relationships between the X-ray luminosity of the ISM (Lx) and the stellar and total mass, for a sample of nearby early-type galaxies (ETGs), is used to investigate the origin of the hot gas, via a comparison with the results of hydrodynamical simulations of the ISM evolution for a large set of isolated ETGs. After the epoch of major galaxy formation (after z~2), the ISM is replenished by stellar mass losses and SN ejecta, at the rate predicted by stellar evolution, and is depleted by star formation; it is heated by the thermalization of stellar motions, SNe explosions and the mechanical (from winds) and radiative AGN feedback. The models agree well with the observed relations, even for the largely different Lx values at the same mass, thanks to the sensitivity of the gas flow to many galaxy properties; this holds for models including AGN feedback, and those without. Therefore, the mass input from the stellar population is able to account for a major part of the observed Lx; and AGN feedback, while very important to maintain massive ETGs in a time-averaged quasi-steady state, keeping low star formation and the black hole mass, does not dramatically alter the gas content originating in stellar recycled material. These conclusions are based on theoretical predictions for the stellar population contributions in mass and energy, and on a self-consistent modeling of AGN feedback., Comment: 7 pages, 1 figure, accepted for publication in The Astrophysical Journal

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., Comment: 16 pages, 5 figures. MNRAS, accepted

One of the most active fields of research of modern-day astrophysics is that of massive black hole formation and co-evolution with the host galaxy. In these investigations, ranging from cosmological simulations, to semi-analytical modeling, to observational studies, the Bondi solution for accretion on a central point mass is widely adopted. In this work we generalize the classical Bondi accretion theory to take into account the effects of the gravitational potential of the host galaxy, and of radiation pressure in the optically thin limit. Then, we present the fully analytical solution, in terms of the Lambert-Euler $W$-function, for isothermal accretion in Jaffe and Hernquist galaxies with a central black hole. The flow structure is found to be sensitive to the shape of the mass profile of the host galaxy. These results and the formulae that are provided, mostly important the one for the critical accretion parameter, allow for a direct evaluation of all flow properties, and are then useful for the above mentioned studies. As an application, we examine the departure from the true mass accretion rate of estimates obtained using the gas properties at various distances from the black hole, under the hypothesis of classical Bondi accretion. An overestimate is obtained from regions close to the black hole, and an underestimate outside a few Bondi radii; the exact position of the transition between the two kinds of departure depends on the galaxy model., Comment: 18 pages, 6 figures, submitted to ApJ, comments welcome

We report on five compact, extremely young (<10Myr) and blue (\beta_UV<-2.5, F_\lambda =\lambda^\beta) objects observed with VLT/MUSE at redshift 3.1169, 3.235, in addition to three objects at z=6.145. These sources are magnified by the Hubble Frontier Field galaxy clusters MACS~J0416 and AS1063. Their de-lensed half light radii (Re) are between 16 to 140pc, the stellar masses are ~1-20 X 10^6 Msun, the magnitudes are m_uv=28.8 - 31.4 (-173, elusive even in the deepest blank fields. We discuss how proto-GCs might contribute to the ionization budget of the universe and augment Lya visibility during reionization. This work underlines the crucial role of JWST in characterizing the rest-frame optical and near-infrared properties of such low-luminosity high-z objects., Comment: 19 pages, 9 figures, 2 tables. MNRAS, version accepted by the referee

We present 2D hydrodynamical simulations for the evolution of early-type galaxies containing central massive black holes (MBHs), starting at age 2 Gyr. The code contains accurate and physically consistent radiative and mechanical AGN wind feedback, with parsec-scale central resolution. Mass input comes from stellar evolution; energy input includes Type Ia and II supernova and stellar heating; star-formation is included. Realistic, axisymmetric dynamical models for the galaxies are built solving the Jeans' equations. The lowest mass models (Mstar = 8 10^{10}Msun) develop global outflows sustained by SNIa's heating, ending with a significantly lower amount of hot gas and new stars. In more massive models, nuclear outbursts last to the present epoch, with large and frequent fluctuations in nuclear emission and from the gas (Lx). Each burst last ~ 10^{7.5} yr, during which (for r < 2-3 kpc) cold, inflowing, and hot, outflowing gas phases coexist. The Lx-T relation for the gas matches that of local galaxies. AGN activity causes positive feedback for star formation. Roughly half of the total mass loss is recycled into new stars (DeltaMstar), just ~ 3% of it is accreted on the MBH, the remainder being ejected from the galaxy. The ratio between the mass of gas expelled to that in to new stars, the load factor, is ~0.6. Rounder galaxies shapes lead to larger final MBH masses, DeltaMstar, and Lx. Almost all the time is spent at very low nuclear luminosities, yet one quarter of the total energy is emitted at an Eddington ratio > 0.1. The duty-cycle of AGN activity approximates 4% (Abridged)., Comment: 26 pages, 15 figure, submitted to ApJ. Comments welcome

We present new photometry of the dwarf irregular galaxy DDO 68, one of the most metal-poor and least massive dwarfs, located in the Lynx-Cancer Void. The images were acquired with the Large Binocular Telescope in the g and r passbands, and show unequivocally that DDO 68 has previously unknown stellar streams related to the accretion of at least two smaller companions: a flea with smaller fleas biting it, to put it in Jonathan Swift's words. Our data provide direct observational evidence of multiple merging occurring at very low galactic mass scales. We present the results of an N-body simulation of the interaction of three dwarf galaxies which reproduces well the main morphological features of DDO 68., Comment: Accepted for publication on ApJL

Accretion onto central massive black holes in galaxies is often modelled with the Bondi solution. In this paper we study a generalization of the classical Bondi accretion theory, considering the additional effects of the gravitational potential of the host galaxy, and of electron scattering in the optically thin limit. We provide a general analysis of the bias in the estimates of the Bondi radius and mass accretion rate, when adopting as fiducial values for the density and temperature at infinity the values of these quantities measured at finite distance from the central black hole. We also give general formulae to compute the correction terms of the critical accretion parameter in relevant asymptotic regimes. A full analytical discussion is presented in the case of an Hernquist galaxy, when the problem reduces to the discussion of a cubic equation, therefore allowing for more than one critical point in the accretion structure. The results are useful for observational works (especially in the case of low-luminosity systems), as well as for numerical simulations, where accretion rates are usually defined in terms of the gas properties near the, Comment: 13 pages, 5 figures, submitted to MNRAS. Comments welcome

Early-type galaxies (ETGs) host a hot ISM produced mainly by stellar winds, and heated by Type Ia supernovae and the thermalization of stellar motions. High resolution 2D hydrodynamical simulations showed that ordered rotation in the stellar component results in the formation of a centrifugally supported cold equatorial disc. In a recent numerical investigation we found that subsequent generations of stars are formed in this cold disc; this process consumes most of the cold gas, leaving at the present epoch cold masses comparable to those observed. Most of the new stellar mass formed a few Gyrs ago, and resides in a disc., Comment: 2 pages, 1 figure, to appear in proceedings of IAU Symposium 315, "From Interstellar Clouds to Star-Forming Galaxies: Universal Processes?", P. Jablonka, F. Van der Tak & P. Andre', eds

AGN feedback from supermassive black holes (SMBHs) at the center of early type galaxies is commonly invoked as the explanation for the quenching of star formation in these systems. The situation is complicated by the significant amount of mass injected in the galaxy by the evolving stellar population over cosmological times. In absence of feedback, this mass would lead to unobserved galactic cooling flows, and to SMBHs two orders of magnitude more massive than observed. By using high-resolution 2D hydrodynamical simulations with radiative transport and star formation in state-of-the-art galaxy models, we show how the intermittent AGN feedback is highly structured on spatial and temporal scales, and how its effects are not only negative (shutting down the recurrent cooling episodes of the ISM), but also positive, inducing star formation in the inner regions of the host galaxy., Comment: 4 pages, 1 figure, to appear in Proceedings of IAU Symposium 315 "From interstellar clouds to star-forming galaxies: universal processes?", P. Jablonka, F. van der Tak and P. Andre', eds. - Correction of affiliations

In the last years, stellar migration in galactic discs has been the subject of several investigations. However, its impact on the chemical evolution of the Milky Way still needs to be fully quantified. In this paper, we aim at imposing some constraints on the significance of this phenomenon by considering its influence on the chemical evolution of the Milky Way thin disc. We do not investigate the physical mechanisms underlying the migration of stars. Rather, we introduce a simple, heuristic treatment of stellar migration in a detailed chemical evolution model for the thin disc of the Milky Way, which already includes radial gas flows and reproduces several observational constraints for the solar vicinity and the whole Galactic disc. When stellar migration is implemented according to the results of chemo-dynamical simulations by Minchev et. al. (2013) and finite stellar velocities of 1 km s$^{-1}$ are taken into account, the high-metallicity tail of the metallicity distribution function of long-lived thin-disc stars is well reproduced. By exploring the velocity space, we find that the migrating stars must travel with velocities in the range 0.5 -2 km s$^{-1}$ to properly reproduce the high-metallicity tail of the metallicity distribution. We confirm previous findings by other authors that the observed spread in the age-metallicity relation of solar neighbourhood stars can be explained by the presence of stars which originated at different Galactocentric distances, and we conclude that the chemical properties of stars currently observed in the solar vicinity do suggest that stellar migration is present to some extent., Comment: Accepted for publication by ApJ

The mass returned to the ambient medium by aging stellar populations over cosmological times sums up to a significant fraction (20% - 30% or more) of their initial mass. This continuous mass injection plays a fundamental role in phenomena such as galaxy formation and evolution, fueling of supermassive black holes in galaxies and the consequent (negative and positive) feedback phenomena, and the origin of multiple stellar populations in globular clusters. In numerical simulations the calculation of the mass return can be time consuming, since it requires at each time step the evaluation of a convolution integral over the whole star formation history, so the computational time increases quadratically with the number of time-steps. The situation can be especially critical in hydrodynamical simulations, where different grid points are characterized by different star formation histories, and the gas cooling and heating times are shorter by orders of magnitude than the characteristic stellar lifetimes. In this paper we present a fast and accurate method to compute the mass return from stellar populations undergoing arbitrarily complicated star formation histories. At each time-step the mass return is calculated from its value at the previous time, and the star formation rate over the last time-step only. Therefore in the new scheme there is no need to store the whole star formation history, and the computational time increases linearly with the number of time-steps., Comment: 8 pages, 4 figures, submitted, comments welcome

To facilitate the study of black hole fueling, star formation, and feedback in galaxies, we outline a method for treating the radial forces on interstellar gas due to absorption of photons by dust grains. The method gives the correct behavior in all of the relevant limits (dominated by the central point source; dominated by the distributed isotropic source; optically thin; optically thick to UV/optical; optically thick to IR) and reasonably interpolates between the limits when necessary. The method is explicitly energy conserving so that UV/optical photons that are absorbed are not lost, but are rather redistributed to the IR where they may scatter out of the galaxy. We implement the radiative transfer algorithm in a two-dimensional hydrodynamical code designed to study feedback processes in the context of early-type galaxies. We find that the dynamics and final state of simulations are measurably but only moderately affected by radiative forces on dust, even when assumptions about the dust-to-gas ratio are varied from zero to a value appropriate for the Milky Way. In simulations with high gas densities designed to mimic ULIRGs with a star formation rate of several hundred solar masses per year, dust makes a more substantial contribution to the dynamics and outcome of the simulation. We find that, despite the large opacity of dust to UV radiation, the momentum input to the flow from radiation very rarely exceeds L/c due to two factors: the low opacity of dust to the re-radiated IR and the tendency for dust to be destroyed by sputtering in hot gas environments. We also develop a simplification of our radiative transfer algorithm that respects the essential physics but is much easier to implement and requires a fraction of the computational cost., Comment: 25 pages, 17 figures, submitted to MNRAS

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

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 efficiency, 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., Comment: 40 pages, submitted to ApJ

The importance of feedback (radiative and mechanical) from massive black holes at the centers of elliptical galaxies is not in doubt, given the well established relation among black hole mass and galaxy optical luminosity. Here, with the aid of high-resolution hydrodynamical simulations, we discuss how this feedback affects the hot ISM of isolated elliptical galaxies of different mass. The cooling and heating functions include photoionization plus Compton heating, the radiative transport equations are solved, and the mechanical feedback due to the nuclear wind is also described on a physical basis; star formation is considered. In the medium-high mass galaxies the resulting evolution is highly unsteady. At early times major accretion episodes caused by cooling flows in the recycled gas produced by stellar evolution trigger AGN flaring: relaxation instabilities occur so that duty cycles are small enough to account for the very small fraction of massive ellipticals observed to be in the QSO-phase, when the accretion luminosity approaches the Eddington luminosity. At low redshift all models are characterized by smooth, very sub-Eddington mass accretion rates. The mass accumulated by the central black hole is limited to range observed today, even though the mass lost by the evolving stellar population is roughly two order of magnitude larger than the black hole masses observed in elliptical galaxies., Comment: 20 pages, 4 (low-resolution) figures. Abbreviated version of the article to appear in book "Hot Interstellar Matter in Elliptical Galaxies", D.-W. Kim and S. Pellegrini eds., Astrophysics and Space Science Library (ASSL), Springer

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 interest 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., Comment: 6 pages, 3 figures, accepted in the International Journal of Bifurcation and Chaos

In galaxies like the Milky Way, cold (~ 10^4 K) gas ejected from the disc by stellar activity (the so-called galactic-fountain gas) is expected to interact with the virial-temperature (~ 10^6 K) gas of the corona. The associated transfer of momentum between cold and hot gas has important consequences for the dynamics of both gas phases. We quantify the effects of such an interaction using hydrodynamical simulations of cold clouds travelling through a hot medium at different relative velocities. Our main finding is that there is a velocity threshold between clouds and corona, of about 75 km/s, below which the hot gas ceases to absorb momentum from the cold clouds. It follows that in a disc galaxy like the Milky Way a static corona would be rapidly accelerated: the corona is expected to rotate and to lag, in the inner regions, by ~ 80-120 km/s with respect to the cold disc. We also show how the existence of this velocity threshold can explain the observed kinematics of the cold extra-planar gas., Comment: 10 pages, 6 figures, 1 table. Accepted for publication in MNRAS. Several typos corrected

By means of a one-zone evolutionary model, we study the co-evolution of supermassive black holes and their host galaxies, as a function of the accretion radiative efficiency, dark matter content, and cosmological infall of gas. In particular, the radiation feedback is computed by using the self-regulated Bondi accretion. The models are characterized by strong oscillations when the galaxy is in the AGN state with a high accretion luminosity. We found that these one-zone models are able to reproduce two important phases of galaxy evolution, namely an obscured-cold phase when the bulk of star formation and black hole accretion occur, and the following quiescent hot phase in which accretion remains highly sub-Eddington. A Compton-thick phase is also found in almost all models, associated with the cold phase. An exploration of the parameter space reveals that the closest agreement with the present-day Magorrian relation is obtained, independently of the dark matter halo mass, for galaxies with a low-mass seed black hole, and the accretion radiative efficiency ~0.1., Comment: Accepted for publication in A&A, 12 pages, 5 figures

We extend the black hole (BH) feedback models of Ciotti, Ostriker, and Proga to two dimensions. In this paper, we focus on identifying the differences between the one-dimensional and two-dimensional hydrodynamical simulations. We examine a normal, isolated $L_*$ galaxy subject to the cooling flow instability of gas in the inner regions. Allowance is made for subsequent star formation, Type Ia and Type II supernovae, radiation pressure, and inflow to the central BH from mildly rotating galactic gas which is being replenished as a normal consequence of stellar evolution. The central BH accretes some of the infalling gas and expels a conical wind with mass, momentum, and energy flux derived from both observational and theoretical studies. The galaxy is assumed to have low specific angular momentum in analogy with the existing one-dimensional case in order to isolate the effect of dimensionality. The code then tracks the interaction of the outflowing radiation and winds with the galactic gas and their effects on regulating the accretion. After matching physical modeling to the extent possible between the one-dimensional and two-dimensional treatments, we find essentially similar results in terms of BH growth and duty cycle (fraction of the time above a given fraction of the Eddington luminosity). In the two-dimensional calculations, the cool shells forming at 0.1--1 kpc from the center are Rayleigh--Taylor unstable to fragmentation, leading to a somewhat higher accretion rate, less effective feedback, and a more irregular pattern of bursting compared to the one-dimensional case., Comment: 15 pages, 10 figures, ApJ 237:26. Updated to match published version

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 the 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}., Comment: 41 pages, 11 figures (bitmapped, low-quality), ApJ accepted

It is argued that galaxies like ours sustain their star formation by transferring gas from an extensive corona to the star-forming disc. The transfer is effected by the galactic fountain -- cool clouds that are shot up from the plane to kiloparsec heights above the plane. The Kelvin-Helmholtz instability strips gas from these clouds. If the pressure and the the metallicity of the corona are high enough, the stripped gas causes a similar mass of coronal gas to condense in the cloud's wake. Hydrodynamical simulations of cloud-corona interaction are presented. These confirm the existence of a critical ablation rate above which the corona is condensed, and imply that for the likely parameters of the Galactic corona this rate lies near the actual ablation rate of clouds. In external galaxies trails of HI behind individual clouds will not be detectable, although the integrated emission from all such trails should be significant. Parts of the trails of the clouds that make up the Galaxy's fountain should be observable and may account for features in targeted 21-cm observations of individual high-velocity clouds and surveys of Galactic HI emission. Taken in conjunction with the known decline in the availability of cold infall with increasing cosmic time and halo mass, the proposed mechanism offers a promising explanation of the division of galaxies between the blue cloud to the red sequence in the colour-luminosity plane., Comment: 12 pages, 8 figures, 1 table. Accepted for publication in MNRAS

Star-forming disc galaxies such as the Milky Way need to accrete $\gsim$ 1 $M_{\odot}$ of gas each year to sustain their star formation. This gas accretion is likely to come from the cooling of the hot corona, however it is still not clear how this process can take place. We present simulations supporting the idea that this cooling and the subsequent accretion are caused by the passage of cold galactic-fountain clouds through the hot corona. The Kelvin-Helmholtz instability strips gas from these clouds and the stripped gas causes coronal gas to condense in the cloud's wake. For likely parameters of the Galactic corona and of typical fountain clouds we obtain a global accretion rate of the order of that required to feed the star formation., Comment: 2 pages, 1 figure, to appear in "Hunting for the Dark: The Hidden Side of Galaxy Formation", Malta, 19-23 Oct. 2009, eds. V.P. Debattista & C.C. Popescu, AIP Conf. Ser

The kinematics of the extra-planar neutral and ionised gas in disc galaxies shows a systematic decline of the rotational velocity with height from the plane (vertical gradient). This feature is not expected for a barotropic gas, whilst it is well reproduced by baroclinic fluid homogeneous models. The problem with the latter is that they require gas temperatures (above $10^5$ K) much higher than the temperatures of the cold and warm components of the extra-planar gas layer. In this paper, we attempt to overcome this problem by describing the extra-planar gas as a system of gas clouds obeying the Jeans equations. In particular, we consider models having the observed extra-planar gas distribution and gravitational potential of the disc galaxy NGC 891: for each model we construct pseudo-data cubes and we compare them with the HI data cube of NGC 891. In all cases the rotational velocity gradients are in qualitative agreement with the observations, but the synthetic and the observed data cubes of NGC 891 show systematic differences that cannot be accommodated by any of the explored models. We conclude that the extra-planar gas in disc galaxies cannot be satisfactorily described by a stationary Jeans-like system of gas clouds., Comment: 14 pages, 7 figures, accepted for pubblication in MNRAS

The passively evolving stellar population in elliptical galaxies (Es) provides a continuous source of fuel for accretion on the central supermassive black hole (SMBH), which is 1) extended over the entire galaxy life (but declining with cosmic time), 2) linearly proportional to the stellar mass of the host spheroid, 3) summing up to a total gas mass that is >100 times larger than the currently observed SMBH masses, 4) available independently of merging events. The main results of numerical simulations of Es with central SMBH, in which a physically based implementation of radiative and mechanical feedback effects is considered, are presented., Comment: 1 page, no figures. Invited talk to Joint Discussion 08 "Hot Interstellar Matter in Elliptical Galaxies". To appear in Highlights of Astronomy, Vol. 15, Proc. of the XXVIIth IAU General Assembly, Rio de Janeiro, Brazil, August 2009, eds. D.-W. Kim and S. Pellegrini, Cambridge University Press

The effects of dry and wet merging on the Scaling Laws (SLs) of elliptical galaxies (Es) are discussed. It is found that the galaxy SLs, possibly established at high redshift by the fast collapse of gas-rich and clumpy stellar distributions in preexisting dark matter halos following the cosmological SLs, are compatible with a (small) number of galaxy mergers at lower redshift., Comment: 1 page, no figures. Invited talk to Joint Discussion 01 "Dark Matter in Early-Type Galaxies". To appear in Highlights of Astronomy, Vol. 15, Proc. of the XXVIIth IAU General Assembly, Rio de Janeiro, Brazil, August 2009, eds. L.V.E. Koopmans and T. Treu, Cambridge University Press

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 galaxy 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 spectrum's 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 $\sim 1.3\times 10^6 L_{\odot}$ at the frequency 5 GHz (radio band), of $\sim 1.1\times 10^6 L_{\odot}$ at $4.3\times10^{14}$ Hz (R band, corresponding to the absolute magnitude -10.4), and of $\sim 1.5\times 10^{7} L_{\odot}$ at $2.4\times10^{17}$ Hz (soft X-ray, 0.5 -- 2.0 keV band)., Comment: 15 pages, 11 figures, resubmitted to ApJ, add one more figure, typos corrected

The centers of elliptical galaxies host supermassive black holes that significantly affect the surrounding interstellar medium through feedback resulting from the accretion process. The evolution of this gas and of the nuclear emission during the galaxies' lifetime has been studied recently with high-resolution hydrodynamical simulations. These included gas cooling and heating specific for an average AGN spectral energy distribution, a radiative efficiency declining at low mass accretion rates, and mechanical coupling between the hot gas and AGN winds. Here we present a short summary of the observational properties resulting from the simulations, focussing on 1) the nuclear luminosity; 2) the global luminosity and temperature of the hot gas; 3) its temperature profile and X-ray brightness profile. These properties are compared with those of galaxies of the local universe, pointing out the successes of the adopted feedback and the needs for new input in the simulations., Comment: 15 pages, 6 figures, accepted for publication in Advances in Space Research

Whereas considerable effort has been afforded in understanding the properties of galaxies, a full physical picture, connecting their baryonic and dark-matter content, super-massive black holes, and (metric) theories of gravity, is still ill-defined. Strong gravitational lensing furnishes a powerful method to probe gravity in the central regions of galaxies. It can (1) provide a unique detection-channel of dark-matter substructure beyond the local galaxy group, (2) constrain dark-matter physics, complementary to direct-detection experiments, as well as metric theories of gravity, (3) probe central super-massive black holes, and (4) provide crucial insight into galaxy formation processes from the dark matter point of view, independently of the nature and state of dark matter. To seriously address the above questions, a considerable increase in the number of strong gravitational-lens systems is required. In the timeframe 2010-2020, a staged approach with radio (e.g. EVLA, e-MERLIN, LOFAR, SKA phase-I) and optical (e.g. LSST and JDEM) instruments can provide 10^(2-4) new lenses, and up to 10^(4-6) new lens systems from SKA/LSST/JDEM all-sky surveys around ~2020. Follow-up imaging of (radio) lenses is necessary with moderate ground/space-based optical-IR telescopes and with 30-50m telescopes for spectroscopy (e.g. TMT, GMT, ELT). To answer these fundamental questions through strong gravitational lensing, a strong investment in large radio and optical-IR facilities is therefore critical in the coming decade. In particular, only large-scale radio lens surveys (e.g. with SKA) provide the large numbers of high-resolution and high-fidelity images of lenses needed for SMBH and flux-ratio anomaly studies., Comment: White paper submitted to the 2010 Astronomy & Astrophysics Decadal Survey

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], Comment: 42 pages, 4 figures (low resolution), ApJ accepted

After the discovery that supermassive black holes (SMBHs) are ubiquitous at the center of stellar spheroids and that their mass Mbh, in the range 10^6-10^9 Msun, is tightly related to global properties of the host stellar system, the idea of the co-evolution of elliptical galaxies and of their SMBHs has become a central topic of modern astrophysics. Here, I summarize some consequences that can be derived from the galaxy Scaling Laws (SLs) and present a coherent scenario for the formation and evolution of elliptical galaxies and their central SMBHs, focusing in particular on the establishment and maintenance of their SLs. In particular, after a first observationally based part, the discussion focuses on the physical interpretation of the Fundamental Plane. Then, two important processes in principle able to destroy the galaxy and SMBH SLs, namely galaxy merging and cooling flows, are analyzed. Arguments supporting the necessity to clearly distinguish between the origin and maintenance of the different SLs, and the unavoidable occurrence of SMBH feedback on the galaxy ISM in the late stages of galaxy evolution (when elliptical galaxies are sometimes considered as ``dead, red objects''), are then presented. At the end of the paper I will discuss some implications of the recent discovery of super-dense ellipticals in the distant Universe. In particular, I will argue that, if confirmed, these new observations would lead to the conclusion that at early epochs a relation between the stellar mass of the galaxy and the mass of the central SMBH should hold, consistent with the present day Magorrian relation, while the proportionality coefficient between Mbh and the scale of velocity dispersion of the hosting spheroids should be significantly smaller than that at the present epoch., Comment: La Rivista del Nuovo Cimento, accepted (invited paper, 72 pages, some low-quality figure)

In a previous paper the complex-shift method has been applied to self-gravitating spherical systems, producing new analytical axisymmetric density-potential pairs. We now extend the treatement to the Miyamoto-Nagai disc and to the Binney logarithmic halo, and we study the resulting axisymmetric and triaxial analytical density-potential pairs; we also show how to obtain the surface density of shifted systems from the complex-shift of the surface density of the parent model. In particular, the systems obtained from Miyamoto-Nagai discs can be used to describe disc galaxies with a peanut-shaped bulge or with a central triaxial bar, depending on the direction of the shift vector. By using a constructive method that can be applied to generic axisymmetric systems, we finally show that the Miyamoto-Nagai and the Satoh discs, and the Binney logarithmic halo, cannot be obtained from the complex-shift of any spherical parent distribution. As a by-product of this study we also found two new generating functions in closed form for even and odd Legendre polynomials, respectively., Comment: 10 pages, 2 figures, MNRAS, accepted

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 profile 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)., Comment: 14 pages, 7 figures, MNRAS, accepted

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 in 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., Comment: Accepted for publication in MNRAS. 6 pages, 3 figures. Corrected typo in eq. (8), added panel to Fig. 1, added references and discussion. Results unchanged

We computed the chemical evolution of spiral bulges hosting Seyfert nuclei, based on updated chemical and spectro-photometrical evolution models for the bulge of our Galaxy, made predictions about other quantities measured in Seyferts, and modeled the photometry of local bulges. The chemical evolution model contains detailed calculations of the Galactic potential and of the feedback from the central supermassive black hole, and the spectro-photometric model covers a wide range of stellar ages and metallicities. We followed the evolution of bulges in the mass range 10^9 - 10^{11} Msun by scaling the star formation efficiency and the bulge scalelength as in the inverse-wind scenario for elliptical galaxies, and considering an Eddington limited accretion onto the central supermassive black hole. We successfully reproduced the observed black hole-host bulge mass relation. The observed nuclear bolometric luminosity is reproduced only at high redshift or for the most massive bulges; in the other cases, at z = 0 a rejuvenation mechanism is necessary. The black hole feedback is in most cases not significant in triggering the galactic wind. The observed high star formation rates and metal overabundances are easily achieved, as well as the constancy of chemical abundances with redshift and the bulge present-day colours. Those results are not affected if we vary the index of the stellar IMF from x=0.95 to x=1.35; a steeper IMF is instead required in order to reproduce the colour-magnitude relation and the present K-band luminosity of the bulge., Comment: 17 pages, 15 figures, 3 tables, accepted for publication in A&A

We computed the chemical evolution of Seyfert galaxies, residing in spiral bulges, based on an updated model for the Milky Way bulge with updated calculations of the Galactic potential and of the feedback from the central supermassive black hole (BH) in a spherical approximation. We followed the evolution of bulges of masses $2\times 10^{9}-10^{11}M_{\odot}$ by scaling the star-formation efficiency and the bulge scalelenght as in the inverse-wind scenario for ellipticals. We successfully reproduced the observed relation between the BH mass and that of the host bulge, and the observed peak nuclear bolometric luminosity. The observed metal overabundances are easily achieved, as well as the constancy of chemical abundances with the redshift., Comment: 2 pages, 1 figure, to appear the proceedings of IAUS245 "Formation and Evolution of Galaxy Bulges"

The importance of the radiative feedback from massive black holes 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. We show how this AGN radiative output affects the hot ISM of an isolated elliptical galaxy with the aid of a high-resolution hydrodynamical code, where the cooling and heating functions include photoionization plus Compton heating. We find that radiative heating is a key factor in the self-regulated coevolution of massive black holes and their host galaxies and that 1) the mass accumulated by the central black hole is limited by feedback to the range observed today, and 2) relaxation instabilities occur so that duty cycles are small enough (~0.03) to account for the very small fraction of massive ellipticals observed to be in the "on" -QSO- phase, when the accretion luminosity approaches the Eddington luminosity. The duty cycle of the hot bubbles inflated at the galaxy center during major accretion episodes is of the order of 0.1-0.4. Major accretion episodes caused by cooling flows in the recycled gas produced by normal stellar evolution trigger nuclear starbursts coincident with AGN flaring. During such episodes the central sources are often obscured; but overall, in the bursting phase (1

Dissipationless collapses in Modified Newtonian Dynamics (MOND) have been studied by using our MOND particle-mesh N-body code, finding that the projected density profiles of the final virialized systems are well described by Sersic profiles with index m<4 (down to m~2 for a deep-MOND collapse). The simulations provided also strong evidence that phase mixing is much less effective in MOND than in Newtonian gravity. Here we describe "ad hoc" numerical simulations with the force angular components frozen to zero, thus producing radial collapses. Our previous findings are confirmed, indicating that possible differences in radial orbit instability under Newtonian and MOND gravity are not relevant in the present context., Comment: 10 pages, 3 figures. To appear in the Proceedings of the International Workshop "Collective Phenomena in Macroscopic Systems", G. Bertin, R. Pozzoli, M. Rome, and K.R. Sreenivasan, eds., World Scientific, Singapore