Compact  neutron stars Theory & Observations

Hovik GrigorianYerevan State University

Summer School Dubna – 2012

Compact stars Physics

• physics of compact stars,• astrophysics of compact stars,• superdense matter,• neutrino physics,• astrochemistry,• gravitational waves from compact stars and• supernova explosions.

CompStar meeting in Tahiti 2012: http://compstar-esf.org/tahiti/Conference/home.html

NS is a remnant of Supernova explosion

The Astrophysical Journal V 749 N1 Chris L. Fryer et al. 2012 ApJ 749 91

COMPACT REMNANT MASS FUNCTION: DEPENDENCE ON THE EXPLOSION MECHANISM AND METALLICITY

Statistics of Compact stars

Formation of millisecond pulsars

Paulo C. C. Freire Solar and Stellar Astrophysics (astro-ph.SR) Cite as:arXiv:0907.3219v1

Demorest, P., Pennucci, T., Ransom, S., Roberts, M., & Hessels,J. 2010, Nature, 467, 1081

The mass of the millisecond pulsar PSR J1614-2230 to be M = 1.97 ± 0.04 M .⊙ This value, together with the mass of pulsar J1903+0327 of M = 1.667 ± 0.021 M ⊙ due to the prolonged accretion episode that is thought to be required to form a MSP.

A two-solar-mass neutron star measured using Shapiro delay

In binary systems with "Recycled" Millisecond Pulsar

The light traveler time difference

Surface Temperature & Age Data

COOLING OF MAGNETARS

MagnetarsAXPs, SGRsB = 10^14 -

10^15 GRadio-quiet

NSsB = 10^13 G

Radio-pulsar NSs

B = 10^12 G

Radio-pulsar NSs

B = 10^12 GH - spectrum

Cooling of Neutron Star in Cassiopeia A

• 16.08.1680 John Flamsteed, 6m star 3 Cas• 1947 re-discovery in radio

• 1950 optical counterpart• T 30 MK∼

• V exp 4000 − 6000 km/s∼• distance 11.000 ly = 3.4 kpc

picture: spitzer space telescope

D.Blaschke, H. Grigorian, D. Voskresensky, F. Weber, Phys. Rev. C 85 (2012) 022802 e-Print: arXiv:1108.4125 [nucl-th]

Cass A Cooling Observations

Cass A is a rapid cooling star – Temperature drop - 10% in 10 yr

W.C.G. Ho, C.O. Heinke, Nature 462, 71 (2009)

Phase Diagramm & Cooling Simulations

Description of the stellar matter - local propertiesModeling of the self bound compact star - including the gravitational fieldExtrapolations of the energy loss mechanisms to higher densities and temperatures Consistency of the approaches

Choice of metric tensor

HOW TO MAKE A STAR CONFIGURATION?

2 2 2 2 2 2 2 2sinds e dt e dr r d r dn l q q j= - - -

Einstein Equations

TOV

EoS- P( )Thermodynamicas of

dence matter (Energy Momentum Tensor)

External fieldsSchwarzschild Solution

Spherically Symetric case

e

1R 82 R GTn n nm m md p- =

( )1 2ln 12( ) 0

GMr

r R P R

n l= - = - -< ® =

Intrernal solution

SOLUTION FOR INTERNAL STRUCTURE

Cerntral conditions :

1 2 ( )( ) ln 12Gmrr rl æ ö÷ç= - ÷ç ÷çè ø

( 0)( 0)( 0) 0

c

c

rrr

e en nl

= == == =

( )( ) ( ) ( )dP rr P r rn e= - +ò ; -

STRUCTURE OF HYBRID STAR

EoS for Nuclear Matter

T. Kl¨ahn et al., Phys. Rev. C 74, 035802 (2006).

EoS for Quark Matter

Dynamical Chiral Quark Model

EoS for Hybrid Matter

EoS & Hybrid Configurations

Internal structure of HS

Hibrid Configurations for NJL type QM models

T. Kl¨ahn et al., Phys.Lett.B654:170-176,2007

HS Mass-Redius relations

Rotation of Hybrid StarsEvolution of LMXBs

Evolution of LMXBs

Cooling of Compact Stars

Cooling Equations Time Evolution of Temperature

(algorithm) Thermal Regulators, Crust, SC,

Gaps ... Results and Observations

(Cassiopeia A) Conclusions

Equations for Cooling Evolution

, ,, ,

,, ,

a az a z a

aa

a z a

z L

zL

a

A B

C

, log ,az a T

1 11 2

1 2 1 12i i i i

ii

za

C C zL

1 2 1 2

1

2 i ii

i i

L La a aL

BOUNDARY CONDITIONS

L_conductivity L_photons

L = 0 L

mT

sT

FINITE DIFFERENCE SCHEME

Z_i next step

Time direction

Z_i+1Z_i initial

Z_i-1

, 1 1, , 1 , , 1 1, , 1i j i j i j i j i j i i i jz z z

0, 1 0, 1 0, 1

1, 1 1, 1

1,

0,

1,

1 , 1 ,

1

, , 1

0* ** * * * *

* * *0

*

j j j

j j

N j

N j N j N j

j

j

N j

zz

z

Neutrino - Cooling in HM

Cooling Mechanism in QM

Crust Model

Time dependence of the light element contents in the crust

Blaschke, Grigorian, Voskresensky, A& A 368 (2001)561.

Page,Lattimer,Prakash & Steiner, Astrophys.J. 155,623 (2004)

Yakovlev, Levenfish, Potekhin, Gnedin & Chabrier , Astron. Astrophys , 417, 169 (2004)

DU constraint

DU Thresholds

SC pairing gaps

Influence of SC on luminosity

Critical temperature, Tc, for the proton 1S0 and neutron 3P2 gaps, used in PAGE, LATTIMER, PRAKASH, & STEINER Astrophys.J.707:1131 (2009)

Tc ‘measurement’ from Cas A

1.4 M star built⊙from the APR EoS rapid cooling at ages

∼ 30-100 yrs is due to the thermal relaxation of the crust

Mass dependence

PAGE, LATTIMER, PRAKASH, & STEINER Phys.Rev.Lett.106:081101,2011

Medium effects in cooling of neutron stars

Based on Fermi liquid theory ( Landau (1956), Migdal (1967), Migdal et al. (1990))

MMU – insted of MU

Main regulator in Minimal Cooling

Contributions to luminosity

Some Anomalies

The influence of a change of the heat conductivity on the scenario

Blaschke, Grigorian, Voskresensky, A& A 424, 979 (2004)

Temperature Profiles for Cas A

Cas A as an Hadronic Star

Cas A as an Hybrid star

Stability of the stars & Mass- Radius relationship

Cooling of Hybrid star with a DD2-NJL EoS model

Cooling of Hadronic star with a DDF2 EoS model

COOLING PROFILES

Conclusions

Cas A rapid cooling consistently described by the medium-modified superfluid cooling model

Both alternatives for the inner structure, hadronic and hybrid star, are viable for Cas A; a higher star mass favors the hybrid model

In contrast to the minimal cooling scenario, our approach is sensitive to the star mass and thermal conductivity of superfluid star matter

Thank You!!!!!

Temperature in the Hybrid Star Interior

THERMAL EVOLUTIONS OF NSS WITH STRONG MANETIC FIELDS

Phenomenological model of the field decay

Thermal evolution including the Joule heating QJ

D.N. Aguilera, J.A. Pons, J.A. Miralles, arXiv astro-ph 0803.0486v (2009)

COOLING OF MAGNETARS

MagnetarsAXPs, SGRsB = 10^14 -

10^15 GRadio-quiet

NSsB = 10^13 G

Radio-pulsar NSs

B = 10^12 G

Radio-pulsar NSs

B = 10^12 GH - spectrum