on Recent Developments on Theoretical and Experimental General Relativity, Astrophysics, and Relativistic Field Theories

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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.

A. Rueda,

Rueda,

Remo

Ruffini

and

Ivan

Siutsou

Dipartimento di Fisica, Universita' di Roma La Sapienza, Piazzale Aldo Moro 5, I-00185 Roma, Italy

ICRANet, Piazzale della Repubblica 10, I-65122 Pescara, Italy

Stockholm July 1-7 2012

Stockholm, July 1-7, 2012

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Outline



Introduction;



Motivations;



The Hartle-Thorne formalism;

St bilit it i

E

ti

f t t



Stability criteria, Equation of state;



Results applications and conclusions



Results, applications and conclusions.

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Introduction

•Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011, Phys. Rev. D, 84, 084007

R t d M R d J A R ffi i R & X S S 2011 •Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011,

Phys. Rev. C, 83, 045805

•Malheiro, M., Rueda, J. A., & Ruffini, R. 2011, PASJ, in press; Xi 1102 0653

arXiv:1102.0653

•Maximum mass of rotating white dwarfs

The

aim

of

the

work

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).

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Motivations

3 2 4 P P I E      P rot

R=10 km, R=10_{0 km,} 3 _km,

I=1045_[g×_cm2_]

0 km,

I=1049_[g×_cm2_]

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 0418+5729 using respectively the upper and the lower limit of Pdot given by the Eq above The blue squares are 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_rotdot when described as neutron stars.

R=10 km, I=1045_[g

×

_cm2_{] according to the magnetar model}

R 103 _k _{I 10}49_[

×

2_] _di _h _hi _d _{f (RHMWD)} _{d l}

M=1 4Msun

Malheiro, M., Rueda, J. A., & Ruffini, R. 2011, PASJ, in press; arXiv:1102.0653

R=103 _{km, I=10}49_[g

×

_cm2_{] according to the white dwarf (RHMWD) model}

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The

Hartle

‐

Thorne

formalism,

solutions

•Hartle, J. B. 1967, Astrophys. J., 150, 1005

•Hartle, J. B. & Thorne, K. S. 1968, Astrophys. J., 153, 807Hartle, 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

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Stability criteria for NRWDs

General Relativity instability

, , 0 stable M _         , , 0 , , max M M _                 . , 0 unstable M _               

Newtonian Physics General Relativity

Inverse

β

-decay instability



  Newtonian Physics General Relativity

,

n

e

p









_e

).

,

1 (

)

,

(

Z

A



Z



A

R t d M R d J A R ffi i R & X S S 2011 Ph R D 84 084007

•Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011, Phys. Rev. D, 84, 084007

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Stability criteria for RWDs

Mass shedding

Secular and dynamical instabilities

•Bini, D., Boshkayev, K., Ruffini, R., & Siutsou, I. 2012, (in press) NCC

e=0.81267, T/W=0.14

e=0.952887, T/W=0.25

y

Chandrasekhar

(1969)

for

Maclaurin

spheroids

95 7,

5 _{Chandrasekhar}

₍₁₉₆₉₎

Axisymmetric secular instability

.

,

0 ;

,

0 ;

,

0 stable

M

_max

M

unstable

M

J J J



















































_

_J

_

_

_J

_

_

_J





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Equation of state

q

•Rotondo, M., Rueda, J. A., Ruffini, R., & Xue, S.-S. 2011, Phys. Rev. D, 84, 084007

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Surface Pressure for different EoS

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Results: Mass vs central density

y

Carbon WD for RFMT EoS.

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Eccentricity versus

central density

T/W

(kinetic

energy/binding

energy)

versus

central

density

central density

energy)

versus

central

density

e=0.81267, e=0.952887.

T/W=0.14 T/W=0.25

•Boshkayev, K., Rueda, J. A. & Ruffini, R., IJMPE, 2011, 20, 136 •Boshkayev, K., Rueda, J. A. & Ruffini, R., IJMPCS, (in press) 2012

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Non-rotating case

General Relativity!

Rotating

case

Is this period minimum?

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Constant J sequence

C

J

q

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Stability region: M vs rho

•Boshkayev K Rueda J A Ruffini R & Siutsou I ApJ 2012 •Boshkayev, K., Rueda, J. A., Ruffini, R., & Siutsou, I. ApJ , 2012,

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Stability region: M vs rho

Oxygen WD for RFMT EoS.

•Boshkayev, K., Rueda, J. A., Ruffini, R., & Siutsou, I. ApJ , 2012, submitted; arXiv:1204.2070

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Stability region: M vs Req

P_min

•Boshkayev K Rueda J A Ruffini R & Siutsou I ApJ 2012 •Boshkayev, K., Rueda, J. A., Ruffini, R., & Siutsou, I. ApJ , 2012,

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Minimum

periods

p

The

minimum

p

period

is

determined

at

the

crossing

g p

point

between

Keplerian

p

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:1102 0653 •Malheiro, M., Rueda, J. A., & Ruffini, R. 2011, PASJ, in press; arXiv:1102.0653

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Conclusion

• We have investigated the behaviour of general relativistic uniformlyWe 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, 045805 and Rotondo, Rueda, Ruffini, Xue, 2011, PRD,

84, 084007

• 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