On the Fundamental Properties of Dynamically Hot Galaxies

A two-component isothermal equilibrium model is applied to reproduce basic structural properties of dynamically hot stellar systems immersed in their massive dark haloes. The origin of the fundamental plane relation for giant ellipticals is naturally explained as a consequence of dynamical equilibrium in the context of the model. The existence of two galactic families displaying different behaviour in the luminosity--surface-brightness diagram is shown to be a result of a smooth transition from dwarfs, dominated by dark matter near the centre, to giants dominated by the luminous stellar component. The comparison of empirical scaling relations with model predictions suggests that probably a unique dissipative process was operating during the violent stage of development of stellar systems in the dark haloes, and the depth of the potential well controlled the observed luminosity of the resulting galaxies. The interpretation also provides some restrictions on the properties of dark haloes implied by the fundamental scaling laws.Comment: 9 pages, 7 PostScript figures, uses MNRaS LaTeX style file; accepted for publication in MNRaS (Aug 1996

Adaptive Mesh Refinement for Supersonic Molecular Cloud Turbulence

We performed a series of three-dimensional numerical simulations of supersonic homogeneous Euler turbulence with adaptive mesh refinement (AMR) and effective grid resolution up to 1024^3 zones. Our experiments describe non-magnetized driven supersonic turbulent flows with an isothermal equation of state. Mesh refinement on shocks and shear is implemented to cover dynamically important structures with the highest resolution subgrids and calibrated to match the turbulence statistics obtained from the equivalent uniform grid simulations. We found that at a level of resolution slightly below 512^3, when a sufficient integral/dissipation scale separation is first achieved, the fraction of the box volume covered by the AMR subgrids first becomes smaller than unity. At the higher AMR levels subgrids start covering smaller and smaller fractions of the whole volume, which scale with the Reynolds number as Re^{-1/4}. We demonstrate the consistency of this scaling with a hypothesis that the most dynamically important structures in intermittent supersonic turbulence are strong shocks with a fractal dimension of two. We show that turbulence statistics derived from AMR simulations and simulations performed on uniform grids agree surprisingly well, even though only a fraction of the volume is covered by AMR subgrids. Based on these results, we discuss the signature of dissipative structures in the statistical properties of supersonic turbulence and their role in overall flow dynamics.Comment: 5 pages, 5 figures, revised versio

Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids

Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by S. Banerjee and S. Galtier (Phys. Rev. E,93, 033120, 2016) and S. Banerjee and S. Galtier (J. Phys. A, Math. and Theor.,50, 015501, 2017), an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be non-trivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.Comment: 8 page

Scaling Laws and Intermittency in Highly Compressible Turbulence

We use large-scale three-dimensional simulations of supersonic Euler turbulence to study the physics of a highly compressible cascade. Our numerical experiments describe non-magnetized driven turbulent flows with an isothermal equation of state and an rms Mach number of 6. We find that the inertial range velocity scaling deviates strongly from the incompressible Kolmogorov laws. We propose an extension of Kolmogorov's K41 phenomenology that takes into account compressibility by mixing the velocity and density statistics and preserves the K41 scaling of the density-weighted velocity v=rho^{1/3}u. We show that low-order statistics of 'v' are invariant with respect to changes in the Mach number. For instance, at Mach 6 the slope of the power spectrum of 'v' is -1.69 and the third-order structure function of 'v' scales linearly with separation. We directly measure the mass dimension of the "fractal" density distribution in the inertial subrange, D_m=2.4, which is similar to the observed fractal dimension of molecular clouds and agrees well with the cascade phenomenology.Comment: 7 pages, 3 figures; in press, AIP Conference Proceedings: "Turbulence and Nonlinear Processes in Astrophysical Plasmas", Waikiki Beach, Hawaii, March 21, 200