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Cooling of CasAWith&without Quark Matter
CSQCD-IV- Prepow- 2014
my ‘cool’ co-authors: D. Blaschke, D. Voskresensky
Hovik Grigorian: Yerevan State University,JINR - Dubna
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Cooling Of Neutron StarsCooling Of Neutron Stars
Introduction to Cooling Simulation Cooling regulators Time Evolution of Surface
Temperature Influence of super conductivity Explanations for Cas A rapid
cooling Influence of heat conductivityD. Blaschke, H. Grigorian and D. N. Voskresensky, Phys. Rev. C 88, 065805 (2013).
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Phase Diagramm & Cooling Simulation
Phase Diagramm & Cooling Simulation
Description of the stellar matter - local properties (EoS of super-dense matter)Modeling of the gravitationally self bound compact star - including the density profilesExtrapolations of the energy loss mechanisms to higher densities and temperatures Consistency of the approachesComparison with observational data
Description of the stellar matter - local properties (EoS of super-dense matter)Modeling of the gravitationally self bound compact star - including the density profilesExtrapolations of the energy loss mechanisms to higher densities and temperatures Consistency of the approachesComparison with observational data
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The energy flux per unit time l(r) through a spherical slice at distance r from the center is:
The equations for energy balance and thermal energy transport are:
where n = n(r) is the baryon number density, NB = NB(r) is the total baryon number in the sphere with radius r
F.Weber: Pulsars as Astro. Labs ... (1999);
D. Blaschke Grigorian, Voskresensky, A& A 368 (2001)561.
The energy flux per unit time l(r) through a spherical slice at distance r from the center is:
The equations for energy balance and thermal energy transport are:
where n = n(r) is the baryon number density, NB = NB(r) is the total baryon number in the sphere with radius r
F.Weber: Pulsars as Astro. Labs ... (1999);
D. Blaschke Grigorian, Voskresensky, A& A 368 (2001)561.
Cooling EvolutionCooling Evolution
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Choice of metric tensorChoice of metric tensor
How to make a star configuration?
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 8
2R GTn n n
m m md p- =
( )1 2ln 1
2( ) 0
GMr
r R P R
n l= - = - -
< ® =
Intrernal solution
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Solution for Internal structureSolution for Internal structure
Cerntral conditions :
1 2 ( )( ) ln 1
2Gm r
rr
læ ö÷ç= - ÷ç ÷çè ø
( 0)
( 0)
( 0) 0
c
c
r
r
r
e e
n n
l
= =
= =
= =
( )( )
( ) ( )dP r
rP r r
ne
= -+ò ; -
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Modification of HHJ parameterization of EoS
Modification of HHJ parameterization of EoS
Introduction of the excluded volume
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The Mass constraint and DU - onsets
The Mass constraint and DU - onsets
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1
1
Structure Of Hybrid StarStructure Of Hybrid Star
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Surface Temperature & Age Data
Surface Temperature & Age Data
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Data of NS on Magnetic Field
Data of NS on Magnetic Field
MagnetarsAXPs, SGRsB = 10^14 -
10^15 G
Radio-quiet NSs
B = 10^13 G
Radio-pulsar NSs
B = 10^12 G
Radio-pulsar NSs
B = 10^12 GH - spectrum
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Neutron Star in Cassiopeia ANeutron 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]
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Cass A Cooling Observations 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)
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Heat Transport In Magnetized NS
Heat Transport In Magnetized NS
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2D- Equations In A “Canonical” Form
2D- Equations In A “Canonical” Form
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Alternate-direction method
, 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
z
z
z
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Cooling MechanismCooling Mechanism
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•Quark direct Urca (QDU) the most efficient processes
Compression n/n0 ≃ 2 , strong coupling αs ≈ 1
• Quark Modified Urca (QMU) and Quark Bremsstrahlung
• Suppression due to the pairing
•Enhanced cooling due to the pairing
Neutrino emissivities in quark matter:Neutrino emissivities in quark matter:
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Crust ModelCrust 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)
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DU constraintDU constraint
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DU Problem & ConstraintDU Problem & Constraint
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SC Pairing GapsSC Pairing Gaps•2SC phase: 1 color (blue) is unpaired (mixed superconductivity)Ansatz 2SC + X phase:
Pairing gaps for hadronic phase(AV18 - Takatsuka et al. (2004))
Popov, Grigorian, Blaschke, PRC 74 (2006)
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Influence Of SC On LuminosityInfluence 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)
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Tc ‘Measurement’ From Cas A Tc ‘Measurement’ From Cas A
Assumed to be a star with mass = 1.4 M⊙
from the APR EoS Rapidly cools at ages
∼ 30-100 yrs due to the thermal relaxation of the crust
Mass dependence
Page, Lattimer, Prakash, & Steiner Phys.Rev.Lett.106:081101,2011
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Medium Effects In Cooling Of Neutron Stars
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
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AV18 gaps, pi-condensate, without suppression of 3P2 neutron pairing - Enhanced PBF process
Anomalies Because Of PBF Proccess
Anomalies Because Of PBF Proccess
The gaps from Yakovlev at al. (2003)
Grigorian, Voskresensky Astron.Astrophys. 444 (2005)
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Contributions To LuminositiesContributions To Luminosities
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Temperature In The Hybrid Star Interior
Temperature In The Hybrid Star Interior
Blaschke, Grigorian, Voskresensky, A& A 368 (2001) 561
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The Influence Of A Change Of The Heat Conductivity On The ScenarioThe Influence Of A Change Of The Heat Conductivity On The Scenario
Blaschke, Grigorian, Voskresensky, A& A 424, 979 (2004)
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Cas A as an Hadronic StarCas A as an Hadronic Star
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Cas A As An Hybrid StarCas A As An Hybrid Star
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Stability of stars within DDF2,DDF2-NJL and DDF2-MNJL
EoS model
Stability of stars within DDF2,DDF2-NJL and DDF2-MNJL
EoS model
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Cooling of Hadronic star with a DDF2
EoS model
Cooling of Hadronic star with a DDF2
EoS model
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Cooling Of Hybrid Star With A DD2-NJL
Eos Model
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Cooling of Hybrid star with DDF2-MNJL EoS model
Cooling of Hybrid star with DDF2-MNJL EoS model
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Cooling ProfilesCooling Profiles
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Conclusions Conclusions
All known cooling data including the 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 (as well 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
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Thank YOU!!!!!
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