some aspects of neutron stars cooling evolutionsome aspects of neutron stars cooling evolution max...
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Some aspects of Neutron Stars Cooling Evolution
Max Born 40 Symp. October 9 -12, 2019
Wroclaw, Polandmy co-authors: D.Blaschke, D.Voskresensky, A. Ayriyan E. Kolomeitsev, K. Maslov
Hovik Grigorian: JINR LIT (Dubna),
Yerevan State University, AANL CP&IT
(Yeravan, Armenia)
The research was carried out under financial support of the Russian Science Foundation (project #17-12-01427)
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Simulation of Cooling Evolution of Neutron Stars
▪ Introduction ▪ Neutron Stars cooling problem▪ Simulations algorithm▪ Results for NS cooling
H. Grigorian, D. N. Voskresensky and D. Blaschke Eur. Phys. J. A 52: 67 (2016).
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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 profiles✓Extrapolations of the energy loss mechanisms to higher densities and temperatures✓ Consistency of the approaches✓Comparison with observational data
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Structure Of Hybrid Star
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Stability of stars HDD, DD2 & DDvex-NJL EoS model
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Different Configurationswith the same NS mass
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High Mass Twin CS
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Different Configurationswith the same NS mass
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Surface Temperature & Age Data
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Cooling Mechanism
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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.
Cooling Evolution
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Equations for Cooling Evolution
( ) ( ) ( ) ( )
( ) ( ) ( )
, ,, ,
,, ,
a az a z a
aa
a z a
z L
zL
a
A B
C
τ τ
ττ
τ
∂ ∂⎧= +⎪⎪ ∂ ∂
⎨∂⎪ =
⎪ ∂⎩( ) ( ), log ,az a Tτ τ=
( )
1 11 2
1 2 1 12i i i i
ii
za
C C zL ± ±±
−
+ −= ±
Δ!
1 2 1 2
1
2 i ii
i i
L La a aL + −
−
−∂=
∂ Δ + Δ
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Finite difference scheme
• Z_i next step
• Time direction
• Z_i+1
• Z_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 zα β γ δ− + − − − −+ + =
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
β α δ
γ δ
α
γ β δ
− − −
− −
− −
− − −
⎛ ⎞⎛ ⎞ ⎛ ⎞⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟=⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠⎝ ⎠ ⎝ ⎠
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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)
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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:
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•Direct Urca (DU) the most efficient processes
• Modified Urca (MU) and Bremsstrahlung
• Suppression due to the pairing
•Enhanced cooling due to the pairing
Neutrino emissivities in hadronic matter:
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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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Medium Effects In Cooling Of Neutron Stars
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MKVORHp – Gap models
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HDD – AV18 , Yak.ME nc = 3 n0
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DD2 – EEHOrME-nc=1.5,2.0,2.5n0
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MKVOR – BCLL, TN-FGAME-nc=3.0n0
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MKVOR Hyp – EEHOr, TN-FGAME-nc=3.0n0
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Cooling of Twin CS
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Results produced with use of MPI Technology
142 configurations has been calculated in 0m49s on the 142 processes. On 1 process it takes 36m14s – acc is ~ 44 times
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Program Algorithm
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Model parameters – DD2
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Calculation Time and efficiency
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Distribution of Evolution tracks via Temperature at given Time
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Distribution of Evolution tracks via Temperature at
given Time
LogT
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Evolution tracks for different NS Masses
LogT
Logt
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Weighting of Data point on the Temperature - Age Diagram
log t
Log
T
Log
T
log t
w(T,t) = Exp{(logT-logTD)2/σT + (log t -logtD)2/σt }
WM = ʃ w(T
M (t),t) dt
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Expected Mass value for the Data points on the T - t
Diagram
WM
Mass value
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Expected Mass value for the Data points on the T - t
Diagram
Mass value
EoS: DD2; Proton Gap : BCLL Medium Eff : nc = 3.0 n0
with π –cond.
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Conclusions
▪ All known cooling data including the Cas A rapid cooling consistently described by the “nuclear medium cooling” scenario
▪ Influence of stiffness on EoS and cooling can be balanced by the choice of corresponding gap model.
▪ In case of existence of III CSF high-mass twin stars could show different cooling behavior depending on core superconductivity
▪ Parallelization allowed to make the calculations for statistical analyses of models in reasonable time
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Thank YOU!!!!!
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Highmass Twins: QM SC Effect
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Possible internal structure of CasA
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Cas A as an Hadronic Star
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Cas A As An Hybrid Star
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MKVOR – EoS model