Transcript Moment of Inertia of Neutron Star Crust Calculations vs

Moment of Inertia
of Neutron Star Crust
Calculations vs. Glitches Observations
Joanna Porębska
Jagiellonian University – prof. Marek Kutschera
& Nuclear Physics Institute (Polish Academy of Sciences)
- collaboration with dr Sebastian Kubis,
Cracow
Dense Matter in HIC and Astrophysics, Dubna, 18.07.2008
General structure of NS
crust
core
Equations of Internal Structure
1)Tolman-Oppenheimer-Volkoff (TOV), rSch~4km → GR
2) mass=f(r)
3) Equation of State (EoS)
EoS… in more details
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only some analytical solutions
energy density (APR model)
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energy per particle (nucleon)
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derivatives of E,ε
masses
EoS… density & pressure
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density and pressure - full expressions
leptons
Neutrality & β equilibrium
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β equilibrium
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electrical neutrality
Compressibility K
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stability considerations
V(n) - isoscalar potential
Es(n) – symmetry energy corresponding
to the interactions isovector channel
EoS again... two regimes
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APR - Akmal, Pandharipande & Ravenhall (npe)
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SLy - Skyrme, Lion
SLy
APR
nlimit
ncc
nsat
nmax
0.01
0.08
0.16
~15 nsat
low density
n
baryon
density
high density
saturation of nuclear interactions
Calculations
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the fourh-order Runge-Kutta integration method (rk4)
output:
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Moment of Inertia (Pethick, Ravenhall formulae)
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Results…
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ρ_0 [g/cm3]
7.00E+14
8.00E+14
9.00E+14
1.00E+15
1.30E+15
M_tot [sol.mass]
0.98
1.20
1.40
1.57
1.93
Ic/Itot
5.7%
3.4%
2.2%
1.4%
0.5%
Glitches staff
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What are they…?
Glitch - sudden spin-up of pulsar produced by angular
momentum transfer from the superfluid component of
the stellar interior to the normal crust
frequency jump
spin-down rate jump
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What do they say about crust Moment of Inertia? …
Icrust from glitches
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Ic - solid crust + tightly coupled rest (90% of all the star)
Ires - angular mom. reservoir
A - pulsar activity parameter
G - coupling parameter – minimum fraction of the star
mom. of in. that stores angular momentum and imparts
it to the crust in glitches
Alpar ’93 >2.4% , Datta&Alpar ’93 >3.4% for 1.4MΘ
Conclusions..
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Hybrid approach (calculative-observational)
Verification/falsification
Quite nice confirmation..
Still under construction
Considerations.. to be continued
References
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M.Camenzind, Compact Objects in Astrophysics (WD, NS & BH)
(Springer-Verlag, Berlin Heidelberg, 2007)
N.K.Glendenning, Compact Stars: Nuclear Physics, Particle Physics
and GR (Springer-Verlag, New York, 1997)
P.Haensel , A.Y.Potekhin, D.G.Yakovlev, Neutron Stars 1: Equation
of State and Structure (Springer, 2007)
S.Kubis, Phys. Rev. C 76, 025801(2007)
C.P.Lorenz, D.G.Ravenhall, C.J.Pethick Phys. Rev. Lett. 70, 4
(1993)
B.Link, R.I.Epstein, J.M.Lattimer, Phys. Rev. Lett. 83, 17 (1999)
D.G.Ravenhall, C.J.Pethick, ApJ 424:846-851 (1994)
Dziękuję bardzo Thank you