arXiv subjects

Luca Ciotti

Publications and source records attributed to Luca Ciotti.

At least 19 recordsLinked to original sources

arXiv2025

Anisotropy ansatz for the Jeans equations: oblate galaxies

In the solution of the Jeans equations for axisymmetric galaxy models the ``$b$-ansatz" is often adopted to prescribe the relation between the vertical and radial components of the velocity dispersion tensor, and close the equations. However, $b$ affects the resulting azimuthal velocity fields quite indirectly, so that the analysis of the model kinematics is usually performed after numerically solving the Jeans equations, a time consuming approach. In a previous work we presented a general method to determine the main properties of the kinematical fields resulting in the $b$-ansatz framework before solving the Jeans equations; results were illustrated by means of disk galaxy models. In this paper we focus more specifically on realistic ellipsoidal galaxy models. It is found that how and where $b$ affects the galaxy kinematical fields is mainly dependent on the flattening of the stellar density distribution, moderately on the presence of a Dark Matter halo, and much less on the specific galaxy density profile. The main trends revealed by the numerical exploration, in particular the fact that more flattened systems can support larger $b$-anisotropy, are explained with the aid of simple ellipsoidal galaxy models, for which most of the analysis can be conducted analytically. The obtained results can be adopted as guidelines for model building and in the interpretation of observational data.

astro-ph.GA↗

arXiv2025

A (very) simple proof of the gravitational energy formula of polytropic spheres

It is shown how the well-known formula for the gravitational energy of self-gravitating regular polytropes of finite mass can be obtained in an elementary way by using Gauss's divergence theorem and the Chandrasekhar virial tensor, without resorting to lengthy algebra, to specific properties of Lane-Emden functions, and to thermodynamics arguments, as is instead commonly found in standard treatises and in astrophysical literature. The present approach, due to its simplicity, can be particularly useful to students and researchers, and it can be easily applied to the study of more complicated polytropic structures.

astro-ph.SR↗

arXiv2025

X-ray Halos of Early-Type Galaxies with AGN Feedback and Accretion from a Circumgalactic Medium: models and observations

The knowledge of the X-ray properties of the hot gas halos of early-type galaxies has significantly advanced in the past years, for large and homogeneously investigated samples. We compare these results with the X-ray properties of an exploratory set of gas evolution models in realistic early-type galaxies, produced with our high-resolution 2D hydrodynamical code MACER that includes AGN feedback and accretion from a circumgalactic medium. The model X-ray emission and absorption are integrated along the line of sight, to obtain maps of the surface brightness Sigma_X and temperature Tx. The X-ray diagnostics considered are the luminosity and average temperature for the whole galaxy (Lx and ) and within 5 optical effective radii (Lx5 and ), and the circularized profiles Sigma_X(R) and Tx(R). The values for Lx, Lx5, , and compare very well with those observed. The Sigma_X(R) and Tx(R) also present qualitative similarities with those of the representative galaxy NGC5129, and of ETGs with the most commonly observed shape for Tx(R): Sigma_X(R) matches the observed profile over many optical effective radii Re, and Tx(R) reproduces the characteristic bump that peaks at R=(1 - 3)Re. Inside the peak position, Tx(R) declines towards the center, but the explored models are systematically hotter by ~30%; possible explanations for this discrepancy are discussed. Interestingly, Sigma_X(R) and Tx(R) as large as observed outside of R~Re are reproduced only with significant accretion from a circumgalactic medium, highlighting its importance.

astro-ph.GA↗

arXiv2024

Rotation curves of disk galaxies and General Relativity

It has been proposed that the flat rotation curves observed at large radii in disk galaxies can be interpreted as an effect of General Relativity (GR) instead of the presence of dark matter (DM) halos in Newtonian gravity. In Ciotti (2022) the problem is rigorously explored in the special setting of the weak-field, low-velocity gravitomagnetic limit of GR. The rotation curves are obtained for purely baryonic disk models with realistic density profiles, and compared with the predictions of Newtonian gravity for the same disks, in absence of DM. The rotation curves are indistinguishable, with percentual GR corrections at all radii of the order of $\approx 10^{-6}$ or less, so that DM halos are required in gravitomagnetism as in Newtonian gravity. From a more general point of view, a list of the most urgent problems that must be addressed by any proposed GR-based alternative to the existence of DM, is given.

astro-ph.GA↗

arXiv2024

Anisotropy ansatz for the axisymmetric Jeans equations

The Jeans equations do not form a closed system, and to solve them a parametrization relating the velocity moments is often adopted. For axisymmetric models, a phenomenological choice (the "$b$-ansatz") is widely used for the relation between the vertical ($\sigma_z^2$) and radial ($\sigma_R^2$) components of the velocity dispersion tensor, thus breaking their identity present in two-integral systems. However, the way in which the ansatz affects the resulting kinematical fields can be quite complicated, so that the analysis of these fields is usually performed only after numerically computing them. We present here a general procedure to study the properties of the ansatz-dependent fields $\overline{v_{\varphi}^2}$, $\Delta = \overline{v_{\varphi}^2} - \sigma_z^2$ and $\Delta_R = \overline{v_{\varphi}^2} - \sigma_R^2$. Specifically, the effects of the $b$-ansatz can be determined before solving the Jeans equations once the behaviour over the ($R,z$)-plane of three easy-to-build ansatz-independent functions is known. The procedure also constrains the ansatz to exclude unphysical results (as a negative $\overline{v_{\varphi}^2}$). The method is illustrated by discussing the cases of three well-known galaxy models: the Miyamoto & Nagai and Satoh disks, and the Binney logarithmic halo, for which the regions and the constraints on the ansatz values can be determined analytically; a two-component (Miyamoto & Nagai plus logarithmic halo) model is also discussed.

astro-ph.GA↗

arXiv2023

Jeans modelling of weakly flattened stellar systems

In the homoeoidal expansion, a given ellipsoidally stratified density distribution, and its associated potential, are expanded in the (small) density flattening parameter $\eta$, and usually truncated at the linear order. The truncated density-potential pair obeys exactly the Poisson equation, and it can be interpreted as the first-order expansion of the original ellipsoidal density-potential pair, or as a new autonomous system. In the first interpretation, in the solutions of the Jeans equations the quadratic terms in $\eta$ must be discarded (``$\eta$-linear'' solutions), while in the second (``$\eta$-quadratic'') all terms are retained. In this work we study the importance of the quadratic terms by using the ellipsoidal Plummer model and the Perfect Ellipsoid, which allow for fully analytical $\eta$-quadratic solutions. These solutions are then compared with those obtained numerically for the original ellipsoidal models, finding that the $\eta$-linear models already provide an excellent approximation of the numerical solutions. As an application, the $\eta$-linear Plummer model (with a central black hole) is used for the phenomenological interpretation of the dynamics of the weakly flattened and rotating globular cluster NGC 4372, confirming that this system cannot be interpreted as an isotropic rotator, a conclusion reached previously with more sophisticated studies.

astro-ph.GA↗

arXiv2023

The face-on projection of the Miyamoto & Nagai disks

The face-on projected density profile of the Miyamoto & Nagai disks of arbitrary flattening is obtained analytically in terms of incomplete elliptic integrals of first and second type, by using two complementary approaches, and then checked against the results of numerical integration. As computer algebra systems do not seem able to obtain the resulting formula in any straightforward way, the relevant mathematical steps are provided. During this study, three wrong identities in the Byrd & Friedman tables of elliptic integrals have been identified, and their correct expression is given.

astro-ph.GA↗

arXiv2023

Rotation curves of galaxies in GR

It has been suggested that the observed flat rotation curves of disk galaxies can be a peculiar effect of General Relativity (GR) rather than evidence for the presence of dark matter (DM) halos in Newtonian gravity. In Ciotti (2022) the problem has been quantitatively addressed by using the well known weak-field, low-velocity gravitomagnetic limit of GR, for realistic exponential baryonic (stellar) disks. As expected, the resulting GR and Newtonian rotation curves are indistinguishable, with GR corrections at all radii of the order of $v^2/c^2\approx 10^{-6}$. Here we list some astrophysical problems that must be faced if the existence of DM halos is attributed to a misinterpretation of weak field effects of GR.

astro-ph.GA↗

arXiv2023

Active galactic nuclei feedback in an elliptical galaxy (III): the impacts and fate of cosmological inflow

The cosmological inflow of a galaxy is speculated to be able to enter the galaxy and enhance the star formation rate (SFR) and black hole accretion rate (BHAR). In this paper, by performing high-resolution hydrodynamic simulations in the framework of {\it MACER}, we investigate the fate of the inflow and its impacts on the evolution of a massive elliptical galaxy. The inflow properties are adopted from the cosmological simulation IllustrisTNG. We find that, the inflow gas hardly enters but is blocked beyond $\sim 20$ kpc from the central galaxy and becomes part of the circumgalactic medium (CGM). The gas pressure gradient, mainly contributed by the thermalized stellar wind and subdominantly by the energy input from the AGN, balances gravity and prevents the inflow from entering the galaxy. The SFR and BHAR are almost not affected by the normal inflow. However, if the rate of cosmological inflow were increased by a factor of 3, a small fraction of the inflow would enter the galaxy and contribute about 10\% of the gas in the galaxy. In this case, the gas density in the galaxy would increase by a factor of $\ga$ 20. This increase is not because of the additional gas supply by the inflow but the increase of gas density in the CGM caused by the inflow. Consequently, the SFR and BHAR would increase by a factor of $\sim$ 5 and $\sim 1000$ respectively. Finally, AGN feedback can perturb the motion of the inflow and heat the CGM through its intermittent outbursts.

astro-ph.GA↗

arXiv2022

Chemical evolution of elliptical galaxies I: supernovae and AGN feedback

We study the formation and evolution of elliptical galaxies and how they suppress star formation and maintain it quenched. A one-zone chemical model which follows in detail the time evolution of gas mass and its chemical abundances during the active and passive evolution, is adopted. The model includes both gas infall and outflow as well as detailed stellar nucleosynthesis. Elliptical galaxies with different infall masses, following a down-sizing in star formation scenario, are considered. In the chemical evolution simulation we include a novel calculation of the feedback processes. We include heating by stellar wind, core-collapse SNe, Type Ia SNe (usually not highlighted in galaxy formation simulations) and AGN feedback. The AGN feedback is a novelty in this kind of models and is computed by considering a Bondi-Eddington limited accretion onto the central supermassive black hole. We successfully reproduce several observational features, such as the [$\alpha$/Fe] ratios increasing with galaxy mass, mass-metallicity, $\rm M_{BH}-\sigma$ and $\rm M_{BH}-M_{*}$ relations. Moreover, we show that stellar feedback and in particular Type Ia SNe, has a main role in maintaining quenched the star formation after the occurrence of the main galactic wind, especially in low-mass ellipticals. For larger systems, the contribution from AGN to thermal energy of gas appears to be necessary. However, the effect of the AGN on the development of the main galactic wind is negligible, unless an unreasonable high AGN efficiency or an extremely low stellar feedback are assumed. We emphasize the important role played by Type Ia SNe in the energy budget of early-type galaxies.

astro-ph.GA↗

arXiv2022

Star formation inefficiency and Kennicutt-Schmidt laws in early-type galaxies

Star formation in disk galaxies is observed to follow the empirical Kennicutt-Schmidt law, a power-law relationship between the surface density of gas ($\Sigma_{gas}$) [$\textrm{M}_{\odot}\; \textrm{kpc}^{-2}$] and the star formation rate ($\Sigma_{SFR}$) [$\textrm{M}_{\odot}\; \textrm{kpc}^{-2} \; \textrm{Gyr}^{-1}$]. In contrast to disk galaxies, early-type galaxies (ETGs) are typically associated with little to no star formation and therefore no Kennicutt-Schmidt law; recent observations, however, have noted the presence of massive gaseous cold disks in ETGs, raising the question as to why the conversion of gas into stars is so inefficient. With our latest simulations, performed with our high-resolution hydrodynamic numerical code MACER, we reevaluate the traditional classification of ETGs as quiescent, dead galaxies. We predict the inevitable formation of stellar disks following cooling episodes of the ISM of the host galaxy in the presence of galactic rotation via a simple but robust star formation model combining local Toomre instabilities and local gas cooling timescales. We find that resolved Kennicutt-Schmidt star formation laws for our simulated ETGs, in both surface density and volumetric forms, reproduce the observed threshold, slope, and normalization observed in disk galaxies. At the same time, through analysis of global Kennicutt-Schmidt laws, we suggest that increased star formation and high gaseous outflows offers a partial remedy to the observed star formation inefficiency problem. Observational checks of our star formation predictions are thus essential for confirming the form of local star formation laws and reassessing star formation inefficiency in ETGs.

astro-ph.GA↗

arXiv2022

On the rotation curve of disk galaxies in General Relativity

Recently, it has been suggested that the phenomenology of flat rotation curves observed at large radii in the equatorial plane of disk galaxies can be explained as a manifestation of General Relativity instead of the effect of Dark Matter halos. In this paper, by using the well known weak field, low velocity gravitomagnetic formulation of GR, the expected rotation curves in GR are rigorously obtained for purely baryonic disk models with realistic density profiles, and compared with the predictions of newtonian gravity for the same disks in absence of Dark Matter. As expected, the resulting rotation curves are indistinguishable, with GR corrections at all radii of the order of $v^2/c^2\approx 10^{-6}$. Next, the gravitomagnetic Jeans equations for two-integral stellar systems are derived, and then solved for the Miyamoto-Nagai disk model, showing that finite-thickness effects do not change the previous conclusions. Therefore, the observed phenomenology of galactic rotation curves at large radii requires Dark Matter in GR exactly as in newtonian gravity, unless the cases here explored are reconsidered in the full GR framework with substantially different results (with the surprising consequence that the weak field approximation of GR cannot be applied to the study of rotating systems in the weak field regime). In the paper, the mathematical framework is described in detail, so that the present study can be extended to other disk models, or to elliptical galaxies (where Dark Matter is also required in newtonian gravity, but their rotational support can be much less than in disk galaxies).

astro-ph.GA↗

arXiv2022

On the polytropic Bondi accretion in two-component galaxy models with a central massive BH

In many investigations involving accretion on a central point mass, ranging from observational studies to cosmological simulations, including semi-analytical modelling, the classical Bondi accretion theory is the standard tool widely adopted. Previous works generalised the theory to include the effects of the gravitational field of the galaxy hosting a central black hole, and of electron scattering in the optically thin limit. Here we apply this extended Bondi problem, in the general polytropic case, to a class of new two-component galaxy models recently presented. In these models, a Jaffe stellar density profile is embedded in a dark matter halo such that the total density distribution follows a $r^{-3}$ profile at large radii; the stellar dynamical quantities can be expressed in a fully analytical way. The hydrodynamical properties of the flow are set by imposing that the gas temperature at infinity is proportional to the virial temperature of the stellar component. The isothermal and adiabatic (monoatomic) cases can be solved analytically, in the other cases we explore the accretion solution numerically. As non-adiabatic accretion inevitably leads to an exchange of heat with the ambient, we also discuss some important thermodynamical properties of the polytropic Bondi accretion, and provide the expressions needed to compute the amount of heat exchanged with the environment, as a function of radius. The results can be useful for the subgrid treatment of accretion in numerical simulations, as well as for the interpretation of observational data.

astro-ph.GA↗

arXiv2022

A Parameter Space Exploration of High Resolution Numerically Evolved Early Type Galaxies Including AGN Feedback and Accurate Dynamical Treatment of Stellar Orbits

An extensive exploration of the model parameter space of axisymmetric Early-Type Galaxies (ETGs) hosting a central supermassive Black Hole (SMBH) is conducted by means of high resolution hydrodynamical simulations performed with our code MACER. Global properties such as 1) total SMBH accreted mass, 2) final X-ray luminosity and temperature of the X-ray emitting halos, 3) total amount of new stars formed from the cooling gas, 4) total ejected mass in form of supernovae and AGN feedback induced galactic winds, are obtained as a function of galaxy structure and internal dynamics. In addition to the galactic dark matter halo, the model galaxies are also embedded in a group/cluster dark matter halo; finally cosmological accretion is also included, with amount and time dependence derived from cosmological simulations. Angular momentum conservation leads to the formation of cold HI disks; these disks further evolve under the action of star formation induced by disk instabilities, of the associated mass discharge onto the central SMBH, and of the consequent AGN feedback. At the end of the simulations, the hot (metal enriched) gas mass is roughly $10\%$ the mass in the old stars, with twice as much having been ejected into the intergalactic medium. The cold gas disks are a $\approx$ kpc in size, and the metal rich new stars are in $0.1$ kpc disks. The masses of cold gas and new stars are roughly $0.1\%$ the mass of the old stars. Overall, the final systems appear to reproduce quite successfully the main global properties of real ETGs.

astro-ph.GA↗

arXiv2020

A family of Exponential Integrals suggested by Stellar Dynamics

While investigating the generalization of the Chandrasekhar (1943) dynamical friction to the case of field stars with a power-law mass spectrum and equipartition Maxwell-Boltzmann velocity distribution, a pair of 2-dimensional integrals involving the Error function occurred, with closed form solution in terms of Exponential Integrals (Ciotti 2010). Here we show that both the integrals are very special cases of the family of (real) functions $$ I(λ,μ,ν; z) :=\int_0^zx^λ\,\Enu(x^μ)\,dx= {γ\left({1+λ\overμ},z^μ\right) + z^{1+λ}\Enu(z^μ)\over 1+λ+ μ(ν-1)}, \quad μ>0,\quad z\geq 0, \eqno (1) $$ where $\Enu$ is the Exponential Integral, $γ$ is the incomplete Euler gamma function, and for existence $λ>\max \left\{-1,-1- μ(ν-1)\right\}$. Only in one of the consulted tables a related integral appears, that with some work can be reduced to eq.~(1), while computer algebra systems seem to be able to evaluate the integral in closed (and more complicated) form only provided numerical values for some of the parameters are assigned. Here we show how eq.~(1) can in fact be established by elementary methods.

math-ph↗

arXiv2020

Infra-Red Emission from Cold Gas Dusty Disks in Massive Ellipticals

What is the expected infrared output of elliptical galaxies? Here we report the latest findings obtained in this high time resolution (~10 years) and high spatial resolution (2.5 parsec at center) study. We add a set of grain physics to the MACER code, including (a) dust grains made in passive stellar evolution; (b) dust grain growth due to collision and sticking; (c) grain destruction due to thermal sputtering; (d) dust cooling of hot gas via inelastic collisions; and (e) radiation pressure on dust grains. The code improvements enable us to analyze the effects of dust on metal depletion and AGN obscuration, and also to assess the infrared output of the modeled galaxies. We simulate a representative massive elliptical galaxy of a central stellar velocity dispersion ~ 260 km/s and modest rotation. We find that: (1) the circumnuclear disk (of a size <~ 1 kpc) is dusty in its outer region where most of the metals are in dust grains, while in the inner disk most of the dust grains are destroyed by the AGN irradiation; (2) the dusty disk is optically thick to both the starlight within the disk and the radiation from the central AGN. Thus the AGN will be obscured behind the disk, and the latter is of a covering factor ~ 0.2; (3) the dust infrared emission is mainly due to the AGN irradiation. The median infrared luminosity is ~ 2e44 erg/s, and it can reach >~ 1e46 erg/s during outbursts; (4) the duty cycles of the AGN activities, star formation, and the dust infrared luminosity roughly match observations, e.g., in most of its lifetime, the simulated galaxy is a stereotypical "quiescent" elliptical galaxy with L_{IR} ~ 1e11*L_{solar}, while the star formation rate can exceed 250 M_{solar}/yr during central outbursts.

astro-ph.GA↗

arXiv2019

On a family of curious integrals suggested by Stellar Dynamics

While investigating the properties of a galaxy model used in Stellar Dynamics, a curious integral identity was discovered. For a special value of a parameter, the identity reduces to a definite integral with a very simple symbolic value; but, quite surprisingly, all the consulted tables of integrals, and computer algebra systems, do not seem aware of this result. Here I show that this result is a special case ($n=0$ and $z=1$) of the following identity (established by elementary methods): $$ I_n(z)\equiv\int_0^1{{\rm K}(k) k\over (z+k^2)^{n+3/2}}dk = {(-2)^n\over (2n+1)!!} {d^n\over dz^n} {{\rm ArcCot}\sqrt{z}\over\sqrt{z(z+1)}},\quad z>0,$$ where $n=0,1,2,3...$, and ${\rm K}(k)$ is the complete elliptic integral of first kind.

math.CA↗

arXiv2019

Dynamical models of spheroidal multi-component stellar systems

We present a significantly improved version of our numerical code JASMINE, that can now solve the Jeans equations for axisymmetric models of stellar systems, composed of an arbitrary number of stellar populations, a Dark Matter halo, and a central Black Hole. The stellar components can have different structural (density profile, flattening, mass, scale length), dynamical (rotational support, velocity dispersion anisotropy), and population (age, metallicity, Initial Mass Function, mass-to-light ratio) properties. These models, when combined with observations, will allow to investigate important issues, such as quantifying the systematic effects of IMF variations, of mass-to-light ratio gradients, and of different stellar kinematic components (e.g. counter rotating disks, kinematically decoupled cores) on luminosity-weighted properties. The developed analytical and numerical framework aims at modeling Early-Type Galaxies, but it can also be applied to dwarf Spheroidal galaxies and Globular Clusters.

astro-ph.GA↗