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Abstract <p>In this work, we investigate the problem of gravitational instability in a generalized model of a nonlinearly radially pulsating disk with an anisotropic velocity diagram relative to sectoral modes of perturbations. This model is a nonstationary generalization of the equilibrium self-gravitating disk by Bisnovatyi-Kogan and Zel’dovich. Exact expressions are obtained for the main physical characteristics of the generalized model, such as the components of the kinetic energy of the pulsating disk, velocity dispersions in the radial and transverse directions, the global anisotropy parameter, and others. We also found nonstationary analogs of dispersion equations (NADE) against the background of this generalized model for sectoral modes of perturbations. Based on the results of numerical calculations of NADE, graphs comparing the instability increments depending on the initial virial ratio of the system for various values of the parameters <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11444_2025_1664_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <!--AstEng2570164Mirtadzhieva-m1--> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11444_2025_1664_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <!--AstEng2570164Mirtadzhieva-m2--> </InlineEquation>, characterizing the difference and degree of anisotropy of nonlinearly nonstationary models of the self-gravitating disk, were constructed. In particular, it is shown that the development of bar-like mode instability will be the same for all anisotropic models, as the NADE of this mode does not depend on the parameters <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11444_2025_1664_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <!--AstEng2570164Mirtadzhieva-m3--> </InlineEquation> and <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11444_2025_1664_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <!--AstEng2570164Mirtadzhieva-m4--> </InlineEquation>. It is also established that the anisotropy parameters <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11444_2025_1664_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <!--AstEng2570164Mirtadzhieva-m5--> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11444_2025_1664_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <!--AstEng2570164Mirtadzhieva-m6--> </InlineEquation> of the generalized model have opposite effects during the evolution of sectoral modes of perturbations. The work is partially based on a talk presented at the Modern Stellar Astronomy 2024 conference.</p>

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Behavior of Sectoral Instabilities Depending on the Parameters of the Generalized Model of a Self-Gravitating Disk

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • K. T. Mirtadjieva,
  • S. N. Nuritdinov

摘要

Abstract

In this work, we investigate the problem of gravitational instability in a generalized model of a nonlinearly radially pulsating disk with an anisotropic velocity diagram relative to sectoral modes of perturbations. This model is a nonstationary generalization of the equilibrium self-gravitating disk by Bisnovatyi-Kogan and Zel’dovich. Exact expressions are obtained for the main physical characteristics of the generalized model, such as the components of the kinetic energy of the pulsating disk, velocity dispersions in the radial and transverse directions, the global anisotropy parameter, and others. We also found nonstationary analogs of dispersion equations (NADE) against the background of this generalized model for sectoral modes of perturbations. Based on the results of numerical calculations of NADE, graphs comparing the instability increments depending on the initial virial ratio of the system for various values of the parameters \(\alpha \) and \(\beta \) , characterizing the difference and degree of anisotropy of nonlinearly nonstationary models of the self-gravitating disk, were constructed. In particular, it is shown that the development of bar-like mode instability will be the same for all anisotropic models, as the NADE of this mode does not depend on the parameters \(\alpha \) and \(\beta \) . It is also established that the anisotropy parameters \(\alpha \) and \(\beta \) of the generalized model have opposite effects during the evolution of sectoral modes of perturbations. The work is partially based on a talk presented at the Modern Stellar Astronomy 2024 conference.