1 Thirteenth Marcel Grossman Meeting on Recent Developments on Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories ON GENERAL RELATIVISTIC UNIFORMLY ROTATING WHITE DWARFS Kuantay Boshkayev Jorge A. Rueda, Remo Ruffini and Ivan Siutsou Dipartimento di Fisica, Universita' di Roma La Sapienza, Piazzale Aldo Moro 5, I Roma, Italy ICRANet, Piazzale della Repubblica 10, I Pescara, Italy Stockholm, July 1-7, 2012
2 Outline Introduction; Motivations; The Hartle-Thorne formalism; Stability criteria, i Equation of state; t Results, applications and conclusions.
3 Introduction Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011, Phys. Rev. D, 84, Rotondo, R t d M., Rueda, J. A., Ruffini, i R., & Xue, S.-S. S 2011, Phys. Rev. C, 83, Malheiro, M., Rueda, J. A., & Ruffini, R. 2011, PASJ, in press; arxiv: The aim of the work Maximum mass of rotating white dwarfs. Stability (GR, Inverse beta decay, mass shedding and secular). Minimum period (Maximum angular velocity).
4 Motivations 2 P E 4 I 3 rot P R=10 0km, R=10 3 km, I=10 45 [g cm 2 ] I=10 49 [g cm 2 ] X-ray luminosity versus the loss of rotational energy describing SGRs and AXPs by rotation powered neutron stars and white dwarfs. The green star and the green triangle correspond to SGR using respectively the upper and the lower limit of Pdot given by the Eq. above. The blue squares are the only four sources that satisfy L X <E rot dot when described as neutron stars. R=10 km, I=10 45 [g cm 2 ] according to the magnetar model M=1 1.4Msun R=10 3 km, I=10 49 [g cm 2 ] according to the white dwarf (RHMWD) model Malheiro, M., Rueda, J. A., & Ruffini, R. 2011, PASJ, in press; arxiv:
5 The Hartle Thorne formalism, solutions Hartle, J. B. 1967, Astrophys. J., 150, 1005 Hartle, J. B. & Thorne, K. S. 1968, Astrophys. J., 153, 807 Stergioulas, N. 2003, Living Reviews in Relativity, 6, 3 N. K. Glendenning. Compact Stars: Nuclear Physics, Particle Physics & General Relativity
6 M 0, stable, M 0, Stability criteria for NRWDs General Relativity instability M max M 0, unstable., Newtonian Physics General Relativity Inverse β-decay instability p e n, e ( Z, A) ( Z 1, A). R t d M R d J A R ffi i R & X S S 2011 Ph R D Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011, Phys. Rev. D, 84, Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011, Phys. Rev. C, 83,
7 Stability criteria for RWDs Mass shedding Bini, D., Boshkayev, K., Ruffini, R., & Siutsou, I. 2012, (in press) NCC Secular and dynamical instabilities e= , T/W=0.14 for Maclaurin spheroids e= , T/W=0.25 Chandrasekhar (1969) Axisymmetric secular instability M J M M 0, stable; 0, M max; 0, unstable. J J Friedman, J. L., Ipser, J. R., & Sorkin, R. D. 1988, Astrophys. J., 325, 722
8 Equation of state Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011, Phys. Rev. D, 84, T. Hamada and E. E. Salpeter, Astrophys. J. 134, 683 (1961).
9 Surface Pressure for different EoS Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011, Phys. Rev. D, 84,
10 Results: Mass vs central density Carbon WD for RFMT EoS. Boshkayev, K., Rueda, J. A. & Ruffini, R., IJMPE, 2011, 20, 136
11 Eccentricity versus central density T/W (kinetic energy/binding energy) versus central density e= , e= T/W=0.14 T/W=0.25 Carbon WD for RFMT EoS. Boshkayev, K., Rueda, J. A. & Ruffini, R., IJMPE, 2011, 20, 136 Boshkayev, y, K., Rueda, J. A. & Ruffini, R., IJMPCS, (in press) 2012
12 Non-rotating case General Relativity! Rotating case Is this period minimum?
13 Constant J sequence Turning point method of Friedman, Ipser & Sorkin, 1988, ApJ, 325, 722
14 Stability region: M vs rho Carbon WD for RFMT EoS. Boshkayev K Rueda J A Ruffini R & Siutsou I ApJ 2012 Boshkayev, K., Rueda, J. A., Ruffini, R., & Siutsou, I. ApJ, 2012, submitted; arxiv:
15 Stability region: M vs rho Oxygen WD for RFMT EoS. Boshkayev, K., Rueda, J. A., Ruffini, R., & Siutsou, I. ApJ, 2012, submitted; arxiv:
16 Stability region: M vs Req P min Carbon WD for RFMT EoS. Boshkayev K Rueda J A Ruffini R & Siutsou I ApJ 2012 Boshkayev, K., Rueda, J. A., Ruffini, R., & Siutsou, I. ApJ, 2012, submitted; arxiv:
17 Minimum periods The minimum period is determined at the crossing point between Keplerian and inverse beta decay sequences! The minimum period is consistent with the observed periods of SGRs and AXPs! Malheiro, M., Rueda, J. A., & Ruffini, R. 2011, PASJ, in press; arxiv: Boshkayev, K., Rueda, J. A. & Ruffini, R., IJMPCS, 2012, in press
18 Conclusion We have investigated the behaviour of general relativistic uniformly rotating WDs for given values of the central density and rotation period on the basis Hartle-Thorne formalism using the EoS of Chandrasekhar, Salpeter and RFMT for WDs introduced in Rotondo, Rueda, Ruffini,Xue, 2011, PRC, 83, and Rotondo, Rueda, Ruffini, Xue, 2011, PRD, 84, We have shown that the minimum rotation periods are approximately 0.3, 0.5, 0.7 and 2.2 seconds for a rotating 4 He, 12 C, 16 O, and 56 Fe WDs (RFMT EoS), respectively. Corresponding maximum masses to the same chemical composition are 1.500, 1.474, and Solar mass. Below these minimum periods the configurations become unstable because of mass shedding, secular and dynamical instabilities. M J 0 max 1.06M We showed that WDs composed of light elements (Helium, Carbon) are unstable against axisymmetric secular instability, whereas WDs with heavy elements (Oxygen,.., Iron) are stable. J 0 max,
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