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 !