Stellar neutrino emission at finite temperature in relativistic mean field theory
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Transcript of Stellar neutrino emission at finite temperature in relativistic mean field theory
111/20/13 120/10/2014 Jinniu Hu
Stellar neutrino emission at finite temperature
in relativistic mean field theory
Jinniu Hu
School of Physics, Nankai University
Quarks and Compact Stars 2014,
October, 20-22, 2014, Beijing, China
20/10/2014 Jinniu Hu
Outline
Introduction
Theoretical framework
Numerical results
Summary and perspective
20/10/2014 Jinniu Hu
Neutron star cooling
Direct Urca process
Modified Urca process
NN bremsstrahlung process
e en p e p e n
n N p N e
p N e n N
N N N N
D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, P. Haensel, Phys. Rep. 354(2001)1
20/10/2014 Jinniu Hu
The research status: from the point of neutron star matter Fermi gas model:
J. M. Lattimer, C. J. Pethick, M. Prakash, and P. Haensel, Phys. Rev. Lett. 66(1991)2701
Relativistic mean field theory (σ,ω,ρ): L. B. Leinson, and A. Pérez, Phys. Lett. B 518(2001)15 L. B. Leinson, Nucl. Phys. A 707(2002)543 G. Shen, J. Meng and, G. C. Hillhouse G. C. HEP&NP, Supp. 28(2004)99 W. B. Ding, G. Z. Liu, M. F. Zhu, Z. Yu, and E. G. Zhao, A&A 506 (2009) L13
Relativistic mean field theory (σ,ω,ρ,δ): Y. Xu, G. Z. Liu, C. Z. Liu, C. B. Fan, H. Y. Wang, M. F. Zhu and, E. G. Zhao, Chin. Phys. Lett. 30(2013)129501
Brueckner-Hartree-Fock theory: M. Baldo, G. F. Burgio, H.-J. Schulze, and G. Taranto, Phys. Rev. C 89(2014)048801
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Proton-neutron effective mass splitting in relativistic mean field (RMF) theory✓ Scalar isovector meson in Hartree
approximation
✓ Relativistic Hartree-Fock approximation
*
*
p N
n N
M M g g
M M g g
X. Roca-Maza, X. Vinas, M. Centelles, P. Ring, and P. Schuck, Phys. Rev. C 84(2011) 054309
σ,ω,ρ,π σ,ω,ρ,π
W. L. Long, N. Van Giai, J. Meng, Phys. Lett. B 604(2006) 150
20/10/2014 Jinniu Hu
Outline
Introduction
Theoretical framework
Numerical results
Summary and perspective
20/10/2014 Jinniu Hu
Direct Urca process
✓ Neutrino emissivity Q(D)
3 3 3 3
2(D) 412
1 1 (2 )(2 )
e p ne p n f i fi
d p d p d p d pQ f f f P P M E
✓ The matrix element of the neutron beta decay
5
5 5
12
1
2
Ffi e e
p p V M A q n n
G CM i u p u p
u p C C q C F q u pM
GF , C, CV , CM , CA are the coupling constants in weak interaction and Fq is the form factor
D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, P. Haensel, Phys. Rep. 354(2001)1
20/10/2014 Jinniu Hu
Direct Urca process✓ Fermi–Dirac distribution
1
( )exp ( ) / 1n n
n n
fT
✓ The Neutrino emissivity in non-relativistic limit
1/3 * *(D) 27 6 3 1
92
27 6 3 111 9
4.00 10 erg cm s
=4.00 10 erg cm s
p n pFp Fe Fn
sat N
Fp Fe Fn
M MQ T p p p
M
M T p p p
where, 1/3 1/3 **
ji
p p pnijij
sat sat N N
MMM M
M M
and 9
9 / 10
T T
20/10/2014 Jinniu Hu
The neutrino emissivity in other processes The modified Urca (MU) processes
( ) 21 8 3 1
31 9
( ) 21 8 3 113 9
8.1 10 erg cm s
8.1 10 1 / 3 erg cm s
Mnn n
Mpp p Fe Fp Fp Fe Fn
Q M T
Q M T k k k k k
The NN bremsstrahlung (BNN) processes
1/3( ) 20 8 3 140 9
( ) 20 8 3 122 9
( ) 20 8 3 104 9
2.3 10 / erg cm s
4.5 10 erg cm s
2.3 10 erg cm s
Bnnnn nn n p
Bnpnp pn
Bpppp pp
Q M T
Q M T
Q M T
20/10/2014 Jinniu Hu
✓ Lagrangian
RMF theory in finite temperature
,
2 2 3 42 3
2 2
2 2
1 1 1 1 +
2 2 3 41 1 1 1
4 2 4 21 1
2 2
a ai N a a i
i p n
a a a a
a a a
L i M g g g g
m g g
W W m R R m
m
✓ Effective nucleon mass in RMF theory
*
*
p N
n N
M M g g
M M g g
2 2 *22 0
,
2 2 3 42 3
2 2 2 2 2 2
1
1 1 1
2 3 41 1 1
+2 2 2
k ki i i
i n p
dkk k M f f
m g g
m m m
4
2 2 *20,
2 2 3 42 3
2 2 2 2 2 2
1
3
1 1 1
2 3 41 1 1
+2 2 2
k ki i
i n p i
kP dk f f
k M
m g g
m m m
✓ Pressure density
✓ Energy density
✓Fermion and antifermion distribution functions
*
*
1,
exp / 1
1
exp / 1
ki
i i
ki
i i
fE k T
fE k T
B. Liu, V. Greco, and V. Baran Phys. Rev. C 65(2002)045201
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Outline
Introduction
Theoretical framework
Numerical results
Summary and perspective
20/10/2014 Jinniu Hu
The properties of nuclear matter
Nuclear matter
Yp: proton fraction
npe neutron star matter
T=0
NLδ : B. Liu, V. Greco, and V. Baran Phys. Rev. C 65(2002)045201DD-MEδ : X. Roca-Maza, X. Vinas, M. Centelles, P. Ring, and P. Schuck, Phys. Rev. C
84(2011) 054309
ρ0 (fm-3) E/A (MeV) aasym (MeV) K (MeV) M*/M
NLδ 0.160 −16.00 30.50 240.0 0.75
DD-MEδ 0.152 −16.12 32.35 219.1 0.61
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Reduction factors Mij at finite temperature 1/3 1/3 **
ji
p p pnijij
sat sat N N
MMM M
M M
NLδ
20/10/2014 Jinniu Hu
DD-MEδ
Reduction factors Mij at finite temperature
1/3 1/3 **
ji
p p pnijij
sat sat N N
MMM M
M M
20/10/2014 Jinniu Hu
Proton fractions at npe neutron matter
L. W. Chen, F. S. Zhang, Z. H. Lu, W. F. Li, Z. Y. Zhu, and H. R. Ma, Jour. Phys. G 27 (2001)1799A. Li, X. R. Zhou, G. F. Burgio, and H. –J Schulze, Phys. Rev. C 81(2010)025806
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Reduction factors: δ meson effect
DD-ME2: G. A. Lalazissis, T. Niksi´, D. Vretenar, and P. Ring, Phys. Rev.C 71 (2005)024312 DD-MEδ: X. Roca-Maza, X. Vinas, M. Centelles, P. Ring, and P. Schuck, Phys. Rev. C 84(2011) 054309
M11
M31M13
M22M40 M04
20/10/2014 Jinniu Hu
Outline
Introduction
Theoretical framework
Numerical results
Summary and perspective
20/10/2014 Jinniu Hu
Summary1. We study the neutrino emissivity at finite temperature in relativistic mean field theory.2. The neutrino emissivity in non-relativistic limit is mainly determined by the nucleon effective masses.3. The neutrino emissivity becomes larger at high temperature and suppressed at large density.4. The isovector meson is very important in neutrino emission, which generates the proton-neutron mass splitting.
Perspectives1. The relativistic beta decay matrix elements2. The effective mass splitting from Fock term3. The neutrino emissivity in strangeness freedom
……