Phase-space consistency of stellar dynamical models determined by separable augmented densities

Assuming the separable augmented density, it is always possible to construct a distribution function of a spherical population with any given density and anisotropy. We consider under what conditions the distribution constructed as such is in fact non-negative everywhere in the accessible phase-space. We first generalize known necessary conditions on the augmented density using fractional calculus. The condition on the radius part R(r^2) (whose logarithmic derivative is the anisotropy parameter) is equivalent to the complete monotonicity of R(1/w)/w. The condition on the potential part on the other hand is given by its derivative up to any order not greater than (3/2-beta) being non-negative where beta is the central anisotropy parameter. We also derive a specialized inversion formula for the distribution from the separable augmented density, which leads to sufficient conditions on separable augmented densities for the non-negativity of the distribution. The last generalizes the similar condition derived earlier for the generalized Cuddeford system to arbitrary separable systems.Comment: accepted for the publication in MNRAS, 12 journal pages (7pp in main body + 4 appendices

Dynamical models with a general anisotropy profile

Both numerical simulations and observational evidence indicate that the outer regions of galaxies and dark matter haloes are typically mildly to significantly radially anisotropic. The inner regions can be significantly non-isotropic, depending on the dynamical formation and evolution processes. In an attempt to break the lack of simple dynamical models that can reproduce this behaviour, we explore a technique to construct dynamical models with an arbitrary density and an arbitrary anisotropy profile. We outline a general construction method and propose a more practical approach based on a parameterized anisotropy profile. This approach consists of fitting the density of the model with a set of dynamical components, each of which have the same anisotropy profile. Using this approach we avoid the delicate fine-tuning difficulties other fitting techniques typically encounter when constructing radially anisotropic models. We present a model anisotropy profile that generalizes the Osipkov-Merritt profile, and that can represent any smooth monotonic anisotropy profile. Based on this model anisotropy profile, we construct a very general seven-parameter set of dynamical components for which the most important dynamical properties can be calculated analytically. We use the results to look for simple one-component dynamical models that generate simple potential-density pairs while still supporting a flexible anisotropy profile. We present families of Plummer and Hernquist models in which the anisotropy at small and large radii can be chosen as free parameters. We also generalize these two families to a three-parameter family that self-consistently generates the set of Veltmann potential-density pairs. (Abridged...)Comment: 18 pages, accepted for publication in A&

Radial stability of a family of anisotropic Hernquist models with and without a supermassive black hole

We present a method to investigate the radial stability of a spherical anisotropic system that hosts a central supermassive black hole (SBH). Such systems have never been tested before for stability, although high anisotropies have been considered in the dynamical models that were used to estimate the masses of the central putative supermassive black holes. A family of analytical anisotropic spherical Hernquist models with and without a black hole were investigated by means of N-body simulations. A clear trend emerges that the supermassive black hole has a significant effect on the overall stability of the system, i.e. an SBH with a mass of a few percent of the total mass of the galaxy can prevent or reduce the bar instabilities in anisotropic systems. Its mass not only determines the strength of the instability reduction, but also the time in which this occurs. These effects are most significant for models with strong radial anisotropies. Furthermore, our analysis shows that unstable systems with similar SBH but with different anisotropy radii evolve differently: highly radial systems become oblate, while more isotropic models tend to form into prolate structures. In addition to this study, we also present a Monte-Carlo algorithm to generate particles in spherical anisotropic systems.Comment: 16 pages, 12 figures, accepted for publication in MNRAS (some figures have a lowered resolution

Analytical properties of Einasto dark matter haloes

Recent high-resolution N-body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matter haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the S\'ersic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.Comment: 10 pages, 2 figures. Accepted for publication in Astronomy and Astrophysic

A critical reassessment of particle Dark Matter limits from dwarf satellites

Dwarf satellite galaxies are ideal laboratories for identifying particle Dark Matter signals. When setting limits on particle Dark Matter properties from null searches, it becomes however crucial the level at which the Dark Matter density profile within these systems is constrained by observations. In the limit in which the spherical Jeans equation is assumed to be valid for a given tracer stellar population, we study the solution of this equation having the Dark Matter mass profile as an output rather than as a trial parametric input. Within our new formulation, we address to what level dwarf spheroidal galaxies feature a reliable mass estimator. We assess then possible extrapolation of the density profiles in the inner regions and -- keeping explicit the dependence on the orbital anisotropy profile of the tracer population -- we derive general trends on the line-of-sight integral of the density profile squared, a quantity commonly dubbed J-factor and crucial to estimate fluxes from prompt Dark Matter pair annihilations. Taking Ursa Minor as a study case among Milky Way satellites, we perform Bayesian inference using the available kinematical data for this galaxy. Contrary to all previous studies, we avoid marginalization over quantities poorly constrained by observations or by theoretical arguments. We find minimal J-factors to be about 2 to 4 times smaller than commonly quoted estimates, approximately relaxing by the same amount the limit on Dark Matter pair annihilation cross section from gamma-ray surveys of Ursa Minor. At the same time, if one goes back to a fixed trial parametric form for the density, e.g. using a NFW or Burkert profile, we show that the minimal J can hardly be reduced by more than a factor of 1.5. \ua9 2016 IOP Publishing Ltd and Sissa Medialab srl

A lower bound on the mass of Dark Matter particles

We discuss the bounds on the mass of Dark Matter (DM) particles, coming from the analysis of DM phase-space distribution in dwarf spheroidal galaxies (dSphs). After reviewing the existing approaches, we choose two methods to derive such a bound. The first one depends on the information about the current phase space distribution of DM particles only, while the second one uses both the initial and final distributions. We discuss the recent data on dSphs as well as astronomical uncertainties in relevant parameters. As an application, we present lower bounds on the mass of DM particles, coming from various dSphs, using both methods. The model-independent bound holds for any type of fermionic DM. Stronger, model-dependent bounds are quoted for several DM models (thermal relics, non-resonantly and resonantly produced sterile neutrinos, etc.). The latter bounds rely on the assumption that baryonic feedback cannot significantly increase the maximum of a distribution function of DM particles. For the scenario in which all the DM is made of sterile neutrinos produced via non-resonant mixing with the active neutrinos (NRP) this gives m_nrp > 1.7 keV. Combining these results in their most conservative form with the X-ray bounds of DM decay lines, we conclude that the NRP scenario remains allowed in a very narrow parameter window only. This conclusion is independent of the results of the Lyman-alpha analysis. The DM model in which sterile neutrinos are resonantly produced in the presence of lepton asymmetry remains viable. Within the minimal neutrino extension of the Standard Model (the nuMSM), both mass and the mixing angle of the DM sterile neutrino are bounded from above and below, which suggests the possibility for its experimental search.Comment: 20 pages, published in JCA

Comparison of predicted and real propofol and remifentanil concentrations in plasma and brain tissue during target-controlled infusion: a prospective observational study

Target-controlled infusion systems are increasingly used to administer intravenous anaesthetic drugs to achieve a user-specified plasma or effect-site target concentration. While several studies have investigated the ability of the underlying pharmacokinetic-dynamic models to predict plasma concentrations, there are no data on their performance in predicting drug concentrations in the human brain. We assessed the predictive performance of the Marsh propofol model and Minto remifentanil model for plasma and brain tissue concentrations. Plasma samples were obtained during neurosurgery from 38 patients, and brain tissue samples from nine patients. Propofol and remifentanil concentrations were measured using gas chromatography mass spectrometry and liquid chromatography tandem mass spectrometry. Data were analysed from the nine patients in whom both plasma and brain samples were simultaneously obtained. For the Minto model (five patients), the median performance error was 72% for plasma and -14% for brain tissue concentration predictions. The model tended to underestimate plasma remifentanil concentrations, and to overestimate brain tissue remifentanil concentrations. For the Marsh model (five patients), the median prediction errors for plasma and brain tissue concentrations were 12% and 81%, respectively. However, when the data from all blood propofol assays (36 patients) were analysed, the median prediction error was 11%, with overprediction in 15 (42%) patients and underprediction in 21 (58%). These findings confirm earlier reports demonstrating inaccuracy for commonly used pharmacokinetic-dynamic models for plasma concentrations and extend these findings to the prediction of effect-site concentrations.status: publishe