Transcript NUCLEAR MATTER EQUATIONS OF STATE AND THE NEUTRON STARS M. Urbanec

NUCLEAR MATTER
EQUATIONS OF STATE
AND THE NEUTRON STARS
M. Urbanec1, E. Běták1,2, Z. Stuchlík1
1 Fac.
of Philos. & Sci., Silesian Univ., Opava, Czech Rep.
2 Inst. of Physics, Slovak Acad. Sci., Bratislava, Slovakia
([email protected]
http://www.fu.sav.sk/~betak)
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Parametrized description of asymmetric nuclear matter corresponding to the
relativistic mean field theory – fitting of results of Dirac-Brueckner-Hartree-Fok.
nucleons (n, p), iso-scalar mesons (σ, ω), iso-vector mesons (ρ, δ)
vector cross-interactions included
Lagrangian
L(  , , ,  , )   [   ( i   g     M  g  )]
1
1
1 2


2 2
 (     m  )      m    
2
4
2
1
1
1
3
4
 b M ( g  )  c ( g  )  c ( g 2    ) 2
3
4
4
1
1
1
 (       m 2 2 )  m 2         
2
2
4
1
 V ( g  2     )( g 2    )  g       g 
2
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Parameters
(fitted by Gmuca & Bunta to DBHF calculations of Huber et al.)
with
without
gσ2
90.532
86.432
gω2
108.95
106.89
gρ2
gδ2
bσ
cσ
cω
ΛV
36.681
28.739
0.0043852
-0.0052045
-0.0001421
0.10647
28.795
25.170
0.0033779
-0.0037762
-0.001050
-
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vector cross interaction
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Contruction of static configuration
Space-time interval given by Schwarzschild metric (c=G=1)
ds 2  e 2 0 dt 2  e 20 dr 2  r 2 ( d 2  sin 2 d 2 )
where
e 2 0 
r
r  2m( r )
Hydrostatic equilibrium is given by Tolman-Oppenheimer-Volkov eq.
dp0
m( r )  4p0
 (  0  p0 )
dr
r( r  2m( r ))
r
and
m( r )  4   ( r1 ) r12 dr1
is the mass inside the sphere of radius r
0
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Neutron star radii:
Our calculations: 11.5 to 13 km
Neutron star masses:
Compilation of experimental data (Lattimer & Prakash 2007):
Typically very close to 1.4 MSun, but two most massive objects
reported with (2.44±0.27) MSun and (2.1±0.2) MSun.
Our calculations: not more than 2.46 MSun fo pure neutron matter
(or 2.41 MSun for proton fraction 0.1)
Causality limit
Not reached with inclusion of the vector cross interaction and not
narrowing permissible ranges of masses.
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CONCLUSIONS
• INPUTS:
- Relativistic man-field Brueckner-Hartree-Fock in
parametrized form with vector cross interaction for set of
proton fractions from 0 (pure neutron matter) up to 0.18
- σ, ω, ρ and δ mesons
- Tolman-Oppenheimer-Volkov eq.
• OUTPUT:
radius and mass of the neutron star
• CHECK for possible causality violation
• RESULTS:
possible masses and radii of neutron stars
- upper mass limit: 2.46 MSun
- radii: 11.5 to 13 km
(in good agreement with both other calculations and masses
obtained from observed data)
Masses and radii somewhat smaller with than without vector cross
interaction; more sensitivity to the proton fraction.
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Thank you for
your attention
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