A. V. Kolesnichenko

Modification of the jeans instability criterion for fractal-structure astrophysical objects in the framework of nonextensive statistics

Unlike classical studies in which the gravitational instability criterion for astrophysical disks is derived in the framework of traditional kinetics or hydrodynamics, we propose to consider the totality of fluffy dust clusters of various astrophysical objects, in particular, protoplanetary subdisks, as a special type of continuous medium, i.e., fractal medium for which there are points and areas not filled with its components. Within the deformed Tsallis statistics formalism, which is intended to describe the behavior of anomalous systems with strong gravitational interaction and fractal nature of phase space, we derive, on the basis of the modified kinetic equation (with the collision integral in the Bhatnagar-Gross-Krook form), the generalized hydrodynamic Euler equations for a medium with the fractal mass dimension. Considering the linearization of the q-hydrodynamics equations, we investigate the instability of an infinitely homogeneous medium to obtain a simplified version of the modified gravitational instability criterion for an astrophysical disk with fractal structure.

Modeling of aggregation of fractal dust clusters in a laminar protoplanetary disk

The evolutionary hydrodynamic model for the formation and growth of loose dust aggregates in the aerodisperse medium of a laminar disk, which was originally comprised of the gas and solid (sub)micrometer particles, is considered as applied to the problem of the formation of planetesimals in the Solar protoplanetary cloud. The model takes into account the fractal properties of dust clusters. It is shown that the clusters partly merge in the process of cluster-cluster coagulation, giving rise to the formation of large fractal aggregates that are the basic structure-forming elements of loose protoplanetesimals arising as a result of physicochemical and hydrodynamic processes similar to the processes of growth of the fractal clusters. Earlier, the modeling was conventionally performed in an “ordinary” continuous medium without considering the multifractional structure of the dust component of the protoplanetary cloud and the fractal nature of the dust clusters being formed during its evolution. Instead, we propose to consider a complex of loose dust aggregates as a special type of continuous medium, namely, the fractal medium for which there exist points and regions that are not filled with its particles. We suggest performing the hydrodynamic modeling of this medium, which has a noninteger mass dimensionality, in a fractional integral model (its differential form) that takes the fractality into account using fractional integrals whose order is determined by a fractal dimensionality of the disk medium.

Thermodynamic Model of MHD Turbulence and Some of Its Applications to Accretion Disks

Within the framework of the main problem of cosmogony related to the reconstruction of the evolution of the protoplanetary gas-dust cloud that surrounded the proto-Sun at an early stage of its existence, we have derived a closed system of magnetohydrodynamic equations for the scale of mean motion in the approximation of single-fluid magnetohydrodynamics designed to model the shear and convective turbulent flows of electrically conducting media in the presence of a magnetic field. These equations are designed for schematized formulations and the numerical solution of special problems to interconsistently model intense turbulent flows of cosmic plasma in accretion disks and associated coronas, in which the magnetic field noticeably affects the dynamics of astrophysical processes. In developing the model of a conducting turbulized medium, apart from the conventional probability-theoretical averaging of the MHD equations, we systematically use the weighted Favre averaging. The latter allows us to considerably simplify the writing of the averaged equations of motion for a compressible fluid and the analysis of the mechanisms of macroscopic field amplification by turbulent flows. To clearly interpret the individual components of the plasma and field-energy balance, we derive various energy equations that allow us to trace the possible energy conversions from one form into another, in particular, to understand the transfer mechanisms of the gravitational and kinetic energies of the mean motion into magnetic energy. Special emphasis is placed on the method for obtaining the closure relations for the total (with allowance made for the magnetic field) kinetic turbulent stress tensor in an electrically conducting medium and the turbulent electromotive force (or the so-called magnetic Reynolds tensor). This method also makes it possible to analyze the constraints imposed on the turbulent transport coefficients by the entropy growth condition. As applied to the problem of numerically simulating the structure and evolution of a protoplanetary accretion disk differentially rotating around the proto-Sun, we suggest a technique for modeling the turbulent transport coefficients, in particular, the coefficient of kinematic turbulent viscosity that allows us to take into account the magnetic field effect and the inverse effect of the heat transfer on the development of turbulence in a rotating electrically conducting disk. Our study is ultimately aimed at improving several representative hydrodynamic models of natural cosmic turbulized media, including the birth of stars from the diffuse medium of gas-dust clouds, the formation of accretion disks, and the subsequent accumulation of planetary systems. It is a continuation of the stochastic-thermodynamic approach to the synergetic description of the turbulence of astrophysical and geophysical systems that we have developed in a series of papers (Kolesnichenko, 2003; 2004; 2005; Kolesnichenko and Marov, 2006; 2007; Marov and Kolesnichenko, 2002; 2006).

On the Simulation of Helical Turbulence in an Astrophysical Nonmagnetic Disk

The problem of the influence of vortex helicity on the synergic structuring of cosmic matter in it, as well as the appearance of the effect of negative viscosity in three-dimensional gyrotropic turbulence, were studied in the framework of the fundamental problem of simulating the evolution of a rotating astrophysical nonmagnetic disk—in particular, the accretion disk—surrounding the Sun at the early stage of its existence. The evolution equations for averaged vorticity and vortex helicity, as well as rheological relations for the turbulent flow of heat and asymmetrical tensor of the turbulent stress in helical turbulence, were obtained. The demonstrative dependence of helicity on the rotation velocity, density (temperature) gradients, and turbulent energy of the disk gas was established. The role of helicity in the appearance of the inverse Richardson-Kolmogorov energy cascade from small vortices to larger ones and the related process of the generation of the power-consuming macroscale coherent vortex formations appearing in gyrotropic turbulence at high Reynolds number were discussed. The results of the numerical experiments confirming the real existence of the inverse energy cascade in helical turbulence were analyzed. It was assumed that the relatively long-term decay of turbulence in the solar protoplanet cloud can be due to the absence of the reflective symmetry of the anisotropic field of the turbulent velocities with respect to its equatorial plane. As the concept of the inverse energy cascade in three-dimensional helical turbulence is more and more reliably confirmed in numerical experiments, accounting for this effect affecting the structure and dynamics of the astrophysical nonmagnetic disk becomes important during its simulation.

On the thermodynamic derivation of differential equations for turbulent flow transfer in a compressible heat-conducting fluid

This paper considers the modern approach to the thermodynamic modeling of developed turbulent flows of a compressible fluid based on the systematic application of the formalism of extended irreversible thermodynamics (EIT) that goes beyond the local equilibrium hypothesis, which is an inseparable attribute of classical nonequilibrium thermodynamics (CNT). In addition to the classical thermodynamic variables, EIT introduces new state parameters—dissipative flows and the means to obtain the respective evolutionary equations consistent with the second law of thermodynamics. The paper presents a detailed discussion of a number of physical and mathematical postulates and assumptions used to build a thermodynamic model of turbulence. A turbulized liquid is treated as an indiscrete continuum consisting of two thermodynamic sub-systems: an averaged motion subsystem and a turbulent chaos subsystem, where turbulent chaos is understood as a conglomerate of small-scale vortex bodies. Under the above formalism, this representation enables the construction of new models of continual mechanics to derive cause-and-effect differential equations for turbulent heat and impulse transfer, which describe, together with the averaged conservations laws, turbulent flows with transverse shear. Unlike gradient (noncausal) relationships for turbulent flows, these differential equations can be used to investigate both hereditary phenomena, i.e., phenomena with history or memory, and nonlocal and nonlinear effects. Thus, within EIT, the second-order turbulence models underlying the so-called invariant modeling of developed turbulence get a thermodynamic explanation. Since shear turbulent flows are widespread in nature, one can expect the given modification of the earlier developed thermodynamic approach to developed turbulence modeling (see Kolesnichenko, 1980; 1998; 2002–2004; Kolesnichenko and Marov, 1985; Kolesnichenko and Marov, 2009) to be used in research on a broad class of dissipative phenomena in various astro- and geophysical applications. In particular, a major application of the proposed approach is the reconstruction of the processes in the preplanetary circumsolar disk, which might help solve the fundamental problems of stellar-planetary cosmogony.

The thermophob experiment: Direct investigations of the thermophysical properties of the regolith of phobos

The methodology and the main features of the Thermophob experiment developed for the direct analysis of the thermophysical properties of the surface of the Martian satellite Phobos from the Phobos-Grunt lander are considered. The methodical and engineering aspects of the measurements are discussed, and the design of the instrument and the potential of the interpretation of the measurement results with accounting for the theoretical estimates and the data of the laboratory tests are discussed.

Magnetohydrodynamic simulation of the protoplanetary disk of the Sun

In the framework of the basic cosmogony problem related with the reconstruction of the solar protoplanetary disk at the early stages of its existence, a closed system of magnetohydrodynamic equations with the scale of average motion is formulated in the approximation of single-fluid magnetic hydrodynamics; this system is designated for setting and numerically solving various problems on the self-consistent simulation of the structure and evolution of the disk and related corona. The influence of both the axially symmetric magnetic field of the proto-Sun and the large-scale field generated by the turbulent dynamo mechanism on the disk structure formation is analyzed. A new approach to the simulation of the turbulent transport coefficient in the weakly ionized disk is developed. This approach provides an account of the effects of the influence of the generated magnetic field and the processes of convective heat transport on turbulence development in the stratified layer with finite thickness and, thus, rejects the Shakura-Sunyaev α formalism widely used in astrophysical literature. The mathematical model of a thin (but optically thick) non-Keplerian disk taking into account the turbulence dissipation due to kinematical and magnetic viscosity, medium opacity, accretion from ambient space, the action of a turbulent αω dynamo on the magnetic field generation, the magnetic force and energy interaction between the disk and its corona, etc., is discussed. This study is the continuation of the stochastic-thermodynamic approach to the description of turbulence of astro-geophysical systems developed by us in a number of papers [Kolesnichenko 2000, 2001, 2003, 2004, 2005; Kolesnichenko, Marov 2006, 2007, 2008; Marov, Kolesnichenko 2002, 2006].

Modification of the Jeans and Toomre Instability Criteria for Astrophysical Fractal Objects Within Nonextensive Statistics

Within the formalism of Tsallis nonextensive statistics designed to describe the behavior of anomalous systems, systems with a strong gravitational interaction between their individual parts and the fractal nature of phase space, we have obtained linearized equations for the oscillations of a rigidly rotating disk by taking into account dissipative effects and give a derivation of the dispersion equation in the WKB approximation. Based on the previously derived modified Navier—Stokes hydrodynamic equations (the so-called equations of q-hydrodynamics), we have analyzed the axisymmetric oscillations of an astrophysical, differentially rotating gas—dust cosmic object and obtained modified Jeans and Toomre gravitational instability criteria for disks with a fractal phase-space structure.

Power distributions for self-gravitating astrophysical systems based on nonextensive Tsallis kinetics

The long-time development of self-gravitating gaseous astrophysical systems (in particular, the evolution of the protoplanet accretion disk) is mainly determined by relatively fast processes of the collision relaxation of particles. However, slower dynamical processes related to force (Newton or Coulomb) interactions between particles should be included (as q-collisions) in the nonextensive kinetic theory as well. In the present paper, we propose a procedure to include the Newton self-gravity potential and the centrifugal potential in the near-equilibrium power-like q-distribution in the phase space, obtained (in the framework of nonextensive statistics) by means of the modified Boltzmann equation averaged with respect to an unnormalized distribution. We show that if the power distribution satisfies the stationary q-kinetic equation, then the said equation imposes clear restrictions on the character of the long-term force field and on the possible dependence of hydrodynamic parameters of the coordinates: it determines those parameters uniquely. We provide a thermodynamic stability criterion for the equilibrium of the nonextensive system. The results allow us to simulate the evolution of gaseous astrophysical systems (in particular, the gravitational stability of rotating protoplanet accretion disks) more adequately.

Stochastic-thermodynamic modeling of turbulent chaos with nonzero memory using fractional Fokker—Planck—Kolmogorov equations

A stochastic-thermodynamic approach to the derivation of the generalized fractional Fokker—Planck—Kolmogorov (FFPK) equations is considered. The equations describe turbulent transfer processes in a subsystem of turbulent chaos on the basis of fractional dynamics, which takes into account the structure and metric of fractal time. The actual turbulent motion of a fluid is known to be intermittent, since it demonstrates the properties that are intermediate between the properties of regular and chaotic motions. On the other hand, the process of the flow turbulization may be non-Markovian because of the multidimensional spatiotemporal correlations of pulsating parameters; in a physical language, this means that the process has a memory. The introduction of fractional time derivatives into the FFPK kinetic equations, used to find the probability distribution functions for different statistical characteristics of structured turbulence, makes it possible to use an unified mathematical formalism in considering the effects of memory, nonlocality, and time intermittence, with which we usually associate the presence of turbulent bursts against the background of less intense low-frequency oscillations in the background turbulence. This study is aimed at creating representative models of space and natural media. It is a development of the synergetic approach to the modeling of structured turbulence in astrogeophysical systems, which has been developed by the author in a series of papers (Kolesnichenko, 2002–2005).