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


The origin of neutron star

http://www.seasky.org/celestial-objects/stars.html


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


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


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


Outline

Introduction


Numerical results



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


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


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


✓ 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


Outline

Introduction


Numerical results



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


The critical density of Direct Urca process at T=0

0Fp Fe Fnk k k


Reduction factors Mij at finite temperature 1/3 1/3 **

ji

p p pnijij

sat sat N N

MMM M

M M

NLδ


DD-MEδ

Reduction factors Mij at finite temperature

1/3 1/3 **

ji

p p pnijij

sat sat N N

MMM M

M M


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


Reduction factors: NLδ VS DD-Meδ

T=0


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


The effective proton and neutron masses:

DD-ME2 VS DD-MEδ

npeNM


Outline

Introduction


Numerical results



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

……


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Stellar neutrino emission at finite temperature in relativistic mean field theory

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