The potential-energy tensors for subsystems. IV. Homeoidally striated density profiles with a central cusp

Abstract

A general theory of homeoidally striated density profiles where no divergence occurs, is adapted to cuspy density profiles, with a suitable choice of the scaling density and the scaling radius. A general formulation of some physical parameters, such as angular-momentum vector, rotational-energy tensor (both calculated in connection with a special class of rotational velocity fields), inertia tensor, and self potential-energy tensor, is performed. Other potential-energy tensors involving two density profiles where the boundaries are similar and similarly placed, are also expressed. Explicit results are attained for three special cases of physical interest which fit to a good extent the results of high-resolution simulations for dark matter haloes, and a class of density profiles, which closely approximate the de Vaucouleurs $r^{1/4}$ law for elliptical galaxies. The virial theorem in tensor form for two-component systems is written for each subsystem, and applied to giant elliptical galaxies. The predicted velocity dispersion along the line of sight, in the limiting case where a principal axis points towards the observer, is found to be consistent with observations except for (intrinsic) $E7$ configurations where the major axis points towards the observer. If dark matter haloes host an amount of undetected baryons about twice as massive as the stellar subsystem, and undetected baryons trace non baryonic matter therein, two main consequences arise, namely (i) velocity dispersions along the line of sight are lower than in absence of undetected baryons, and (ii) dark matter haloes are dynamically ``hotter'' than stellar ellipsoids, the transition occurring when the amount of undetected baryons is about one and a half times that of the stellar subsystem.

New Astronomy, accepted

References in corpus (9)

• Triaxial Modeling of Halo Density Profiles with High-resolution N-body Simulations
• Dynamical family properties and dark halo scaling relations of giant elliptical galaxies
• Modeling Angular-Momentum History in Dark-Matter Halos
• The properties of field elliptical galaxies at intermediate redshift. III: the Fundamental Plane and the evolution of stellar populations from z~0.4 to z=0
• The phase-diagram of cosmological baryons
• Models of Cuspy Triaxial Galaxies
• Infrared Mass-to-Light Profile Throughout the Infall Region of the Coma Cluster
• Radial orbital anisotropy and the Fundamental Plane of elliptical galaxies
• Dark matter halos around elliptical galaxies: how reliable is the stellar kinematical evidence ?

Cited by in corpus (10)

• Clausius' Virial vs. Total Potential Energy in the dynamics of a two-component system
• R3 fluids
• Homeoidally striated density profiles. II. Anisotropy and rotation
• On the tilt of Fundamental Plane by Clausius' virial maximum theory
• Why there are no elliptical galaxies more flattened than E7: thirty years later
• Homeoidally striated density profiles: sequences of virial equilibrium configurations with constant anisotropy parameters
• An application of the tensor virial theorem to hole + vortex + bulge systems
• A necessary condition for best fitting analytical to simulated density profiles in dark matter haloes
• A numerical fit of analytical to simulated density profiles in dark matter haloes
• Holes within galaxies: the egg or the hen?