Download - Compact neutron stars Theory & Observations
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