Post on 27-Sep-2020
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Evolution of Protoneutron Stars
Marcelo D. Alloy1 Débora P. Menezes2
1,2Departamento de FísicaUniversidade Federal de Santa Catarina
October - 2009 / Maresias
Motivation
1 Study protoneutron star evolution2 Understand the formation of neutron star remnants after
the shock1 Deleptonization process2 Cooling process
Star formation
Boltzmann transport equations
Boltzmann equation:
pβ
(
∂f∂xβ
− Γαβγpγ ∂f
∂pα
)
=
(
dfdτ
)
coll,
Metric:
ds2 = −e2φdt2 + e2Λdr2 + r2dθ2 + r2sen2θdφ2,
Number transport equation
et0∂Nν
∂t+ er
0∂Nν
∂r+ et
1∂Fν
∂t+ er
1∂Fν
∂r+ (Γ1
10 + 2Γ220)Nν + (Γ1
00 − 2Γ122)Fν = SN ,
Energy transport equation
et0∂Jν
∂t+ er
0∂Jν
∂r+ et
1∂Hν
∂t+ er
1∂Hν
∂r+ (Γ1
10 + 3Γ220)Jν + (2Γ1
00 − 2Γ122)Hν + (Γ1
10 − Γ220)Pν = SE ,
Boltzmann transport equations
Boltzmann equation:
pβ
(
∂f∂xβ
− Γαβγpγ ∂f
∂pα
)
=
(
dfdτ
)
coll,
Metric:
ds2 = −e2φdt2 + e2Λdr2 + r2dθ2 + r2sen2θdφ2,
Number transport equation
et0∂Nν
∂t+ er
0∂Nν
∂r+ et
1∂Fν
∂t+ er
1∂Fν
∂r+ (Γ1
10 + 2Γ220)Nν + (Γ1
00 − 2Γ122)Fν = SN ,
Energy transport equation
et0∂Jν
∂t+ er
0∂Jν
∂r+ et
1∂Hν
∂t+ er
1∂Hν
∂r+ (Γ1
10 + 3Γ220)Jν + (2Γ1
00 − 2Γ122)Hν + (Γ1
10 − Γ220)Pν = SE ,
Boltzmann transport equations
Boltzmann equation:
pβ
(
∂f∂xβ
− Γαβγpγ ∂f
∂pα
)
=
(
dfdτ
)
coll,
Metric:
ds2 = −e2φdt2 + e2Λdr2 + r2dθ2 + r2sen2θdφ2,
Number transport equation
et0∂Nν
∂t+ er
0∂Nν
∂r+ et
1∂Fν
∂t+ er
1∂Fν
∂r+ (Γ1
10 + 2Γ220)Nν + (Γ1
00 − 2Γ122)Fν = SN ,
Energy transport equation
et0∂Jν
∂t+ er
0∂Jν
∂r+ et
1∂Hν
∂t+ er
1∂Hν
∂r+ (Γ1
10 + 3Γ220)Jν + (2Γ1
00 − 2Γ122)Hν + (Γ1
10 − Γ220)Pν = SE ,
Boltzmann transport equations
Boltzmann equation:
pβ
(
∂f∂xβ
− Γαβγpγ ∂f
∂pα
)
=
(
dfdτ
)
coll,
Metric:
ds2 = −e2φdt2 + e2Λdr2 + r2dθ2 + r2sen2θdφ2,
Number transport equation
et0∂Nν
∂t+ er
0∂Nν
∂r+ et
1∂Fν
∂t+ er
1∂Fν
∂r+ (Γ1
10 + 2Γ220)Nν + (Γ1
00 − 2Γ122)Fν = SN ,
Energy transport equation
et0∂Jν
∂t+ er
0∂Jν
∂r+ et
1∂Hν
∂t+ er
1∂Hν
∂r+ (Γ1
10 + 3Γ220)Jν + (2Γ1
00 − 2Γ122)Hν + (Γ1
10 − Γ220)Pν = SE ,
Protoneutron star evolution transport equations
∂YL
∂t+
∂eφ4πr2Fν
∂a= 0,
T∂s∂t
− µν∂YL
∂t+ e−2φ∂e2φ4πr2Hν
∂a= 0,
1 Fν is flux number.2 Hν is flux energy.3 YL is lepton fraction.4 T is temperature.5 s is entropy.6 a is baryon number.
Diffusion Coefficients
Information about neutrino interactions in dense matter for
Neutrinos
Dn =
∫
∞
0dEνEn
ν λν(Eν)fν(Eν)(1 − fν(Eν)),
Anti-neutrinos
Dn =
∫
∞
0dEνEn
ν λν(Eν)fν(Eν)(1 − fν(Eν)),
Neutrino interactions with dense matter
1 Neutral current scattering of neutrinos:
νe + n → νe + n, νe + p → νe + p.
2 Charged current absortion:
νe + n → e− + p, νe + p → e+ + n.
3 Neutrinos mean free path:
λν(Eν) =1
nB(Ynσn(Eν) + Ypσp(Eν) + (Yn + Yp)σa(Eν)).
General scheme
RESULTS
1 2 3 4 5
0.1
1
10np) m
nB/n0
T=10 MeV T=20 MeV T=30 MeV T=40 MeV T=50 MeV
1 2 3 4 50.5
1.0
1.5
2.0
T=25 MeV
np) m
nB/n0
1 2 3 4 50.00
0.05
0.10
0.15
0.20
0.25
0.30
T=50 MeV
np m
nB/n0
RESULTS
Neutrino degenerescence parameter and neutrino chemicalpotential evolution:
RESULTS
Temperature and entropy evolution:
RESULTS
Neutrino fraction evolution:
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.350
2
4
6
8
10
12
14
16
Tempo
Y 1
0-3 (f
raçã
o de
neu
trin
os)
MB (M )
t = 0 s t = 1.67 s t = 3.35 s t = 5.02 s t = 6.65 s t = 7.94 s t = 9.20 s t = 10.44 s t = 22.00 s t = 42.62 s
RESULTS
Electron fraction evolution:
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.350.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
Tempo
Y e (fra
ção
de e
létr
ons)
MB (M )
t = 0 s t = 1.67 s t = 3.35 s t = 5.02 s t = 6.65 s t = 7.94 s t = 9.20 s t = 10.44 s t = 22.00 s t = 42.62 s
RESULTS
Neutron fraction evolution:
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.350.70
0.75
0.80
0.85
Tempo
t = 0 s t = 1.67 s t = 3.35 s t = 5.02 s t = 6.65 s t = 7.94 s t = 9.20 s t = 10.44 s t = 22.00 s t = 42.62 s
Y n (fra
ção
de n
êutr
ons)
MB (M )
RESULTS
Diffusion coefficient D2 evolution:
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.3575
100
125
150
175
200
225
250
TempoD2 (M
eV3 k
m)
MB (M )
t = 0 s t = 1.67 s t = 3.35 s t = 5.02 s t = 6.65 s t = 7.94 s t = 9.20 s t = 10.44 s t = 22.00 s t = 42.62 s
RESULTS
Diffusion coefficient D3 evolution:
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.350
4
8
12
16
20
24
Tempo
D3 1
03 (MeV
4 km
)
MB (M )
t = 0 s t = 1.67 s t = 3.35 s t = 5.02 s t = 6.65 s t = 7.94 s t = 9.20 s t = 10.44 s t = 22.00 s t = 42.62 s
RESULTS
Diffusion coefficient D4 evolution:
0.30 0.45 0.60 0.75 0.90 1.05 1.20 1.350
1
2
3
4
Tempo
D4 1
06 (MeV
5 km
)
MB (M )
t = 0 s t = 1.67 s t = 3.35 s t = 5.02 s t = 6.65 s t = 7.94 s t = 9.20 s t = 10.44 s t = 22.00 s t = 42.62 s
Next step
ImprovementsEoS with hyperons.EoS with nuclear pasta.
Obtain luminosity to compare with observationalresults.
Collaboration
Marcelo D. Alloy
German Lugonesour source of inspiration
See you next IWARA
THANK YOU FOR YOUR ATTENTION !