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Evolution of proto-neutron starsand gravitational wave emission

MORGANE FORTIN1,2,3

1 Italian Institute for Nuclear Physics, Rome1 division, Italy

2N. Copernicus Astronomical Center, Polish Academy of Sciences, Poland

3Laboratory Universe and Theories, Paris-Meudon Observatory, France

TEONGRAV meeting 2014

M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission

Formation of a proto-neutron star (PNS)

T

∼ 2 × 1010 KR ∼ 200 km

ν

Stage 0

◮ collapse of a massive star andbounce;

◮ outward propagation of a shock wave;

◮ birth of a PNS.

Stage I : t = 0

◮ stagnation of the shock wave at ∼200 km;

◮ unshocked, low entropy core in whichthe neutrinos are trapped;

◮ high entropy, low density mantlelosing energy due to electroncaptures and thermally-producedneutrino emission.



T

∼ 2 × 1010 KR ∼ 30 km

Stage II : t = 0.5 s

◮ the shock is revived (neutrinos and/orconvection) and lifts off the envelope;

◮ extensive neutrino losses anddeleptonization in the envelope →

loss of pressure;

◮ the PNS shrinks from a radius of 200km to 30 km;

◮ the core is left unchanged.



T

∼ 2 × 1010 KR ∼ 30 km

ν

Stage III : t ∼ 15 sThe diffusion of the neutrinos from the coreup to the surface dominates :

◮ deleptonization of the core;

◮ neutrino-matter interactions →

heating of the PNS up to ∼ 50 MeV;

◮ decrease of the entropy gradientbetween the core and the envelope.



T

∼ 5 × 1010 KR ∼ 15 km

ν

Stage IV : t ∼ 50 s

◮ lepton-poor PNS but

◮ thermal production of neutrinos thatdiffuse up to the surface;

◮ cooling down of the PNS.



T

∼ 5 × 109 KR ∼ 12 km

ν γ

Stage V : t & 50 s

◮ the PNS becomesneutrino-transparent;

◮ birth of a NS;

◮ cooling of the whole NS by theemission of neutrinos from the interiorand of photons from the surface.



ν ν

T

∼ 2 × 1010 KR ∼ 30 km

T

∼ 5 × 1010 KR ∼ 15 km

Kelvin-Helmholtz (KH) phase

◮ stages III and IV,

◮ quasi-stationary evolution →

sequence of equilibriumconfigurations.

PurposeModelling of KH phase :

◮ up-to-date description of themicrophysical properties of PNSs;

◮ study of their oscillations and theassociated gravitational wave (GW)emission .


Overview

Equation of stateP = P (n

b

, T ,YL

)

Evolution equations :• Transport equations• Structure equations

Profiles in P, nb

, T and YL

Oscillations and GW emissionFrequency and damping time of

the quasinormal modes

Diffusion coefficientD = D (n

b

,T ,YL

)


Equation of state (EoS)Describes the properties and composition of the interior of the PNS.

PropertiesInclude the dependence on :

◮ the density nb

: up to few times n0, the nuclear saturation density (n0 = 0.16fm−3),

◮ the temperature : 0 . T . 50 MeV,

◮ the lepton fraction : 0 . YL

= nν+nenp+nn

. 0.4, ie. the composition.

ModelBurgio & Schulze, A&A (2010)

◮ High-density part :

◮ finite temperature many-body approach (Brueckner-Hartree-Fock),◮ nucleon-nucleon potential : Argonne V18,◮ three body forces : phenomenological Urbana model,◮ for neutrino-trapped β-stable nuclear matter ie. νe, e−, n, p.

◮ Low-density part : EoS by Shen et al., Nuc. Phys. A (1998).◮ consistent with the mass measurements of PSR J1614-2230 and J0348+0432

(Demorest et al., Nature, 2010 & Antoniadis et al., Science, 2013) :

Mmax(T = 0) = 2.03 M⊙ .


Overview


b

, T ,YL

)


Profiles in P, nb

, T and YL




b

,T ,YL

)


Evolution equations

Pons et al., ApJ (1999)

Hypothesis

◮ spherically symmetric PNS,

◮ with a constant baryon mass (no accretion),

◮ stationary evolution,

◮ in the framework of general relativity.

Transport equationsDiffusion approximation :

◮ neutrinos in thermal and chemical equilbrium with the ambient matter,

◮ Boltzmann equation becomes a system of two diffusion equations :

◮ one for the energy-integrated lepton flux,◮ another one for the energy-integrated energy flux,◮ in terms of the neutrino diffusion coefficient . . .

Structure equations

◮ Tolman Oppenheimer Volkoff equations.


Overview


b

, T ,YL

)


Profiles in P, nb

, T and YL




b

,T ,YL

)


Diffusion coefficientDescribes the interactions of the neutrinos with the ambient matter during theirdiffusion.

ProcessesFor nuclear matter :

◮ Neutral current (scattering) :

νe + e−→ νe + e−

νe + n → νe + n

νe + p → νe + p

◮ Charged current (absorption):

νe + n → e− + p

Mean free path of a given reaction : λiReddy et al., PRD (1998)Calculations take into account the effects of the strong interaction by :

◮ being consistent with the model for nuclear interaction so with the EoS,

◮ depending on the composition in addition to the temperature and density.

Diffusion coefficient

D−1 =∑

all pro esses

1λi

.


Overview


b

, T ,YL

)


Profiles in P, nb

, T and YL




b

,T ,YL

)


Oscillations and GW emissionBurgio et al., PRD (2011)

Quasinormal modes◮ Solution of the equations describing the nonradial perturbations of a star that

behave as a pure outgoing wave at infinity.

◮ Use of Lindblom & Detweiler formulation.

◮ Solution characterized by a pulsation frequency ν of the given mode and itsdamping time due to gravitational wave emission τ

GW

.

Mode classificationAccording to the restoring force dominating when a fluid element is displaced, eg. :

◮ the f -mode (fundamental mode) : global oscillation of the star,

◮ the g-modes (gravity-modes) : due thermal and composition gradients,

◮ the p-modes (pressure-modes) : the restoring force is due to a pressuregradient,. . .

GW emissionComparison between :

◮ the damping time of a given mode τGW

,

◮ the time scale associated with dissipative processes competing with GW emission(eg. neutrino diffusion) τ

diss

.

If τdiss

> τGW

, the GW emission is the main source of dissipation.


Overview


b

, T ,YL

)


Profiles in P, nb

, T and YL




b

,T ,YL

)


Previous modellingsQNM propertiesFerrari et al., MNRAS (2003); Burgio et al., PRD (2011)

◮ stronger dependence of the QNM frequencies on the temperature profile than onthe lepton fraction profile;

◮ modes properties different from the ones of cold NSs;

◮ f -mode : ν does not scale as ρ̄ → doubles during the PNS evolution; efficientsource of GW emission after few seconds;

◮ g-modes : smaller ν than the f -mode, increases for t . 1 s and then decreases;efficient source in the first few seconds.

Detectability

Andersson et al., GRG (2011)

◮ Results for a SNR of 8 withET : at 10 kpc, radiation of10−11

− 10−12 M⊙c2

through the modes.

◮ Note that the oscillationspectrum evolves during theobservation.

EoS : relativistic mean field (cf. Pons etal. 1998).

1 10 100 1000 10000f [Hz]

1e-25

1e-24

1e-23

1e-22

1e-21

Sh1/

2 , f

1/2 h(

f)

[Hz-1

/2]

Advanced LIGOETf-modeg-mode


Perspectives

◮ Calculation of the evolution of a PNS and the GW emission due to oscillations forthe Burgio & Schulze EoS.

◮ Influence of the microphysical properties on the QNMs properties :

◮ use of different EoSs, including ones with a phase transition;◮ use of recent works on the treatment of neutrino-nucleon interactions for the

calculation of diffusion coefficients : in-medium correlation (eg. Reddy et al.PRC 1999), . . .

◮ Inclusion of rotation in the model : generation of two branches of modes(co-rotating and counter-rotating with the star). The latter would have lower ν thanfor no rotation.

PurposeConstraining the microphysical properties of PNSs, and ultimately the nuclearinteraction, by the observation of their GW emission . . .
