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Register a new userDensity Profiles of Collisionless Equilibria. I. Spherical Isotropic Systems
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Eric I. Barnes
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We investigate the connection between collisionless equilibria and the phase-space relation between density $rho$ and velocity dispersion $sigma$ found in simulations of dark matter halo formation, $F=psd propto r^{-alpha}$. Understanding this relation will shed light on the physics relevant to collisionless collapse and on the subsequent structures formed. We show that empirical density profiles that provide good fits to N-body halos also happen to have nearly scale-free psd distributions when in equilibrium. We have also done a preliminary investigation of variables other than $r$ that may match or supercede the correlation with $F$. In the same vein, we show that $rho/sigma^m$, where $m=3$ is the most appropriate combination to use in discussions of the power-law relationship. Since the mechanical equilibrium condition that characterizes the final systems does not by itself lead to power-law $F$ distributions, our findings prompt us to posit that dynamical collapse processes (such as violent relaxation) are responsible for the radial power-law nature of the psd distributions of virialized systems.
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Mass modelling of spherical systems through internal motions is hampered by the mass/velocity anisotropy (VA) degeneracy inherent in the Jeans equation, as well as the lack of techniques that are both fast and adaptable to realistic systems. A new fast method, called MAMPOSSt, which performs a maximum likelihood fit of the distribution of observed tracers in projected phase space, is developed and thoroughly tested. MAMPOSSt assumes a shape for the gravitational potential, but instead of postulating a shape for the distribution function in terms of energy and angular momentum, or supposing Gaussian line-of-sight velocity distributions, MAMPOSSt assumes a VA profile and a shape for the 3D velocity distribution, here Gaussian. MAMPOSSt requires no binning, differentiation, nor extrapolation of the observables. Tests on cluster-mass haloes from LambdaCDM cosmological simulations show that, with 500 tracers, MAMPOSSt is able to jointly recover the virial radius, tracer scale radius, dark matter scale radius and outer or constant VA with small bias (<10% on scale radii and <2% on the two other quantities) and inefficiencies of 10%, 27%, 48% and 20%, respectively. MAMPOSSt does not perform better when some parameters are frozen, and even worse when the virial radius is set to its true value, which appears to be the consequence of halo triaxiality. The accuracy of MAMPOSSt depends weakly on the adopted interloper removal scheme, including an efficient iterative Bayesian scheme that we introduce here, which can directly obtain the virial radius with as good precision as MAMPOSSt. Our tests show that MAMPOSSt with Gaussian 3D velocities is very competitive with, and up to 1000x faster than other methods. Hence, MAMPOSSt is a very powerful and rapid tool for the mass and anisotropy modeling of systems such as clusters and groups of galaxies, elliptical and dwarf spheroidal galaxies.
In the mean field limit, isolated gravitational systems often evolve towards a steady state through a violent relaxation phase. One question is to understand the nature of this relaxation phase, in particular the role of radial instabilities in the establishment/destruction of the steady profile. Here, through a detailed phase-space analysis based both on a spherical Vlasov solver, a shell code and a $N$-body code, we revisit the evolution of collisionless self-gravitating spherical systems with initial power-law density profiles $rho(r) propto r^n$, $0 leq n leq -1.5$, and Gaussian velocity dispersion. Two sub-classes of models are considered, with initial virial ratios $eta=0.5$ (warm) and $eta=0.1$ (cool). Thanks to the numerical techniques used and the high resolution of the simulations, our numerical analyses are able, for the first time, to show the clear separation between two or three well known dynamical phases: (i) the establishment of a spherical quasi-steady state through a violent relaxation phase during which the phase-space density displays a smooth spiral structure presenting a morphology consistent with predictions from self-similar dynamics, (ii) a quasi-steady state phase during which radial instabilities can take place at small scales and destroy the spiral structure but do not change quantitatively the properties of the phase-space distribution at the coarse grained level and (iii) relaxation to non spherical state due to radial orbit instabilities for $n leq -1$ in the cool case.
The collisionless expansion of spherical plasmas composed of cold ions and hot electrons is analyzed using a novel kinetic model, with special emphasis on the influence of the electron dynamics. Simple, general laws are found, relating the relevant expansion features to the initial conditions of the plasma, determined from a single dimensionless parameter. A transition is identified in the behavior of the ion energy spectrum, which is monotonic only for high electron temperatures, otherwise exhibiting a local peak far from the cutoff energy.
We perform a systematic study of the impact of the J^2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate both from zero-range central and tensor forces. We build a set of 36 parameterizations, which covers a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants, with a fit protocol very similar to that of the successful SLy parameterizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of charge radii. Our main conclusion is that the currently used central and spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the presence of large tensor terms.
In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. Applying these results to a given rotational-transform profile in cylindrical geometry, we find magnetic field and current density profiles compatible with the fractal pressure.
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