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Equilibrium Configurations of Classical Polytropic Stars with a Multi-Parametric Differential Rotation Law: A Numerical Analysis

Published online by Cambridge University Press:  06 July 2017

Federico Cipolletta ,
Christian Cherubini ,
Simonetta Filippi ,
Jorge A. Rueda  and
Remo Ruffini
Federico Cipolletta*
Affiliation:
Dipartimento di Fisica and ICRA, Sapienza Università di Roma, P.le Aldo Moro 5, I–00185 Rome, Italy ICRANet, Piazza della Repubblica 10, I–65122 Pescara, Italy
Christian Cherubini*
Affiliation:
Unit of Nonlinear Physics and Mathematical Modeling, University Campus Bio-Medico of Rome, Via A. del Portillo 21, I–00128 Rome, Italy International Center for Relativistic Astrophysics-ICRA, University Campus Bio-Medico of Rome, Via A. del Portillo 21, I–00128 Rome, Italy
Simonetta Filippi*
Affiliation:
Unit of Nonlinear Physics and Mathematical Modeling, University Campus Bio-Medico of Rome, Via A. del Portillo 21, I–00128 Rome, Italy International Center for Relativistic Astrophysics-ICRA, University Campus Bio-Medico of Rome, Via A. del Portillo 21, I–00128 Rome, Italy
Jorge A. Rueda*
Affiliation:
Dipartimento di Fisica and ICRA, Sapienza Università di Roma, P.le Aldo Moro 5, I–00185 Rome, Italy ICRANet, Piazza della Repubblica 10, I–65122 Pescara, Italy ICRANet-Rio, Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, RJ, 22290–180, Brazil
Remo Ruffini*
Affiliation:
Dipartimento di Fisica and ICRA, Sapienza Università di Roma, P.le Aldo Moro 5, I–00185 Rome, Italy ICRANet, Piazza della Repubblica 10, I–65122 Pescara, Italy ICRANet-Rio, Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, Rio de Janeiro, RJ, 22290–180, Brazil
*
*Corresponding author. Email addresses:[email protected] (F. Cipolletta), [email protected] (C. Cherubini), [email protected] (F. Filippi), [email protected] (J. A. Rueda), [email protected] (R. Ruffini)
*Corresponding author. Email addresses:[email protected] (F. Cipolletta), [email protected] (C. Cherubini), [email protected] (F. Filippi), [email protected] (J. A. Rueda), [email protected] (R. Ruffini)
*Corresponding author. Email addresses:[email protected] (F. Cipolletta), [email protected] (C. Cherubini), [email protected] (F. Filippi), [email protected] (J. A. Rueda), [email protected] (R. Ruffini)
*Corresponding author. Email addresses:[email protected] (F. Cipolletta), [email protected] (C. Cherubini), [email protected] (F. Filippi), [email protected] (J. A. Rueda), [email protected] (R. Ruffini)
*Corresponding author. Email addresses:[email protected] (F. Cipolletta), [email protected] (C. Cherubini), [email protected] (F. Filippi), [email protected] (J. A. Rueda), [email protected] (R. Ruffini)
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Abstract

In this paper we analyze in detail the equilibrium configurations of classical polytropic stars with a multi-parametric differential rotation law of the literature using the standard numerical method introduced by Eriguchi and Mueller. Specifically we numerically investigate the parameters’ space associated with the velocity field characterizing both equilibrium and non-equilibrium configurations for which the stability condition is violated or the mass-shedding criterion is verified.

Keywords

Free boundary problemsself-gravitating systemsnumerical methods for partial differential equations
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 3 , September 2017 , pp. 863 - 888
Copyright
Copyright © Global-Science Press 2017 

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References

[1] Chandrasekhar, S., 1967: An Introduction to the Study of Stellar Structure, Dover.Google Scholar
[2] Chandrasekhar, S., 1987: Ellipsoidal Figures of Equilibrium, Dover.Google Scholar
[3] James, R. A., 1964: The Structure and Stability of Rotating Gas Masses, Astrophys. J., 140, 552–582.Google Scholar
[4] Busarello, G., Filippi, S. and Ruffini, R., 1988: Anisotropic tensor virial models for elliptical galaxies with rotation or vorticity, Astron. Astrophys., 197, 91–104.Google Scholar
[5] Busarello, G., Filippi, S. and Ruffini, R., 1989: Anisotropic and inhomogeneous tensor virial models for elliptical galaxies with figure rotation and internal streaming, Astron. Astrophys., 213, 80–88.Google Scholar
[6] Busarello, G., Filippi, S. and Ruffini, R., 1990: ‘b-type’ spheroids, Astron. Astrophys., 227, 30–32.Google Scholar
[7] Filippi, S., Ruffini, R. and Sepulveda, A., 1990: Generalized Riemann configurations and Dedekind's theorem - The case of non-linear internal velocities, Astron. Astrophys., 231, 30–40.Google Scholar
[8] Filippi, S.; Ruffini, R.; Sepulveda, A. 1990: On the generalization of Dedekind-Riemann sequences to nonlinear velocities., Europhys. Lett., 12, 735–740.Google Scholar
[9] Filippi, S.; Ruffini, R.; Sepulveda, A., 1990: Nonlinear velocities in generalized Riemann ellipsoids., Nuovo Cim. B, 105, 1047–1054.CrossRefGoogle Scholar
[10] Filippi, S., Ruffini, R. and Sepulveda, A., 1991: Generalized Riemann ellipsoids - Equilibrium and stability, Astron. Astrophys., 246, 59–70.Google Scholar
[11] Filippi, S., Ruffini, R. and Sepulveda, A., 1996: On the Implications of the nth-Order Virial Equations for Heterogeneous and Concentric Jacobi, Dedekind, and Riemann Ellipsoids, Astrophys. J., 460, 762 Google Scholar
[12] Filippi, S., Ruffini, R. and Sepulveda, A., 2002: Functional approach to the problem of self-gravitating systems: Conditions of integrability, Phys. Rev. D, 65, 044019.Google Scholar
[13] Eriguchi, Y. and Sugimoto, D. 1981: Another Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluid, Prog. Theor. Phys., 65, 1870–1875.CrossRefGoogle Scholar
[14] Sugimoto, D., Nomoto, K. and Eriguchi, Y. 1981: Stable Numerical Method in Computing of Stellar Evolution, Prog. Theor. Phys. Supp., 70, 115–131.Google Scholar
[15] Eriguchi, Y. and Hachisu, I., 1982: New Equilibrium Sequences Bifurcating from Maclaurin Sequence, Prog. Theor. Phys., 67, 844–851.Google Scholar
[16] Eriguchi, Y., Hachisu, I. and Sugimoto, D., 1982: Dumb-Bell Shape Equilibrium and Mass Shedding Pear-Shape of Self-Gravitating Incompressible Fluid, Prog. Theor. Phys., 67, 1068–1075.Google Scholar
[17] Hachisu, I., Eriguchi, Y., and Sugimoto, D. 1982: Rapidly Rotating Polytropes and Concave Hamburger Equilibrium, Prog. Theor. Phys., 68, 191–205.Google Scholar
[18] Hachisu, I. and Eriguchi, Y., 1982: Bifurcation and Fission of Three Dimensional, Rigidly Rotating and Self-Gravitating Polytropes, Prog. Theor. Phys., 68, 206–221.Google Scholar
[19] Eriguchi, Y. and Hachisu, I., 1983: Two Kinds of Axially Symmetric Equilibrium Sequences of Self-Gravitating and Rotating Incompressible Fluid, Prog. Theor. Phys., 69, 1131–1136.Google Scholar
[20] Hachisu, I. and Eriguchi, Y., 1983: Bifurcation and Phase Transitions of Self-Gravitating and Uniformly Rotating Fluid, Mon. Not. R. Astron. Soc., 204, 583–589.Google Scholar
[21] Eriguchi, Y. and & Mueller, E.: 1985, A general computationalmethod for obtaining equilibria of self-gravitating and rotating gases, Astron. Astrophys., 146, 260–268.Google Scholar
[22] Stoeckly, R., 1965: Polytropic Models with Fast, Non-Uniform Rotation, Astrophys. J., 142, 208–228.Google Scholar
[23] Fujisawa, K., 2015: A versatile numerical method for obtaining structures of rapidly rotating baroclinic stars: self-consistent and systematic solutions with shellular-type rotation, Mon. Not. R. Astron. Soc., 454, 3060–3072.Google Scholar
[24] Galeazzi, F., Yoshida, S. and Eriguchi, Y., 2012: Differentially-rotating neutron star models with a parametrized rotation profile, Astron. Astrophys., 541, A156.Google Scholar
[25] Cherubini, C., Filippi, S., Ruffini, R., Sepulveda, A. and Zuluaga, J. I., 2008: Non-Homogeneous Axisymmetric Models of Self-Gravitating Systems. The Eleventh Marcel Grossmann Meeting On Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories, 2340-2342.Google Scholar
[26] Tassoul, J.-L., 1978: Theory of rotating stars. Princeton Series in Astrophysics, Princeton University Press.Google Scholar
[27] Horedt, G. P., 2004: Polytropes - Applications in Astrophysics and Related Fields. Kluwer Academic Publishers.Google Scholar
[28] Maeder, A., 2009: Physics, Formation and Evolution of Rotating Stars. Astronomy and Astrophysics, Springer, Berlin.Google Scholar
[29] Press, W. H., Teukolsky, S. A., Vetterling, W. T. and Flannery, B. P., 1992: Numerical recipes in C. The art of scientific computing. Cambridge University Press, 2nd ed.Google Scholar
[30] Chandrasekhar, S., 1933: The equilibrium of distorted polytropes. I. The rotational problem, Mon. Not. R. Astron. Soc., 93, 390–406.Google Scholar
[31] Chandrasekhar, S., 1961: Hydrodynamic and hydromagnetic stability. Dover Publications.Google Scholar
[32] Ostriker, J. P. and Bodenheimer, P., 1968: Rapidly Rotating Stars. II. Massive White Dwarfs, Astrophys. J., 151, 1089–1098.Google Scholar
[33] Uryū, K., Limousin, F., Friedman, J.L., Gourgoulhon, E. and Shibata, M., 2009: Nonconformally flat initial data for binary compact objects, Phys. Rev. D, 80, 124004.Google Scholar