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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

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.

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

Formation of a proto-neutron star (PNS)

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.

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

Formation of a proto-neutron star (PNS)

T

2 1010 KR 30 km

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.

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

Formation of a proto-neutron star (PNS)

T

5 1010 KR 15 km

Stage IV : t 50 s

lepton-poor PNS but

thermal production of neutrinos thatdiffuse up to the surface;

cooling down of the PNS.

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

Formation of a proto-neutron star (PNS)

T

5 109 KR 12 km

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.

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

Formation of a proto-neutron star (PNS)

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.

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

)

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

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 = 0.16fm3),

the temperature : 0 . T . 50 MeV,

the lepton fraction : 0 . YL

= n+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 -stable nuclear matter ie. e, 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 .

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

)

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

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.

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

)

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

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

ProcessesFor nuclear matter :

Neutral current (scattering) :

e + e e + e

e + n e + n

e + p e + p

Charged current (absorption):

e + n e + p

Mean free path of a given reaction : iReddy 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

D1 =

all proesses

1i

.

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

)

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

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 of the given mode and itsdamping time due to gravitational wave emission

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 GW

,

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

diss

.

If diss

> GW

, the GW emission is the main source of dissipation.

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

)

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

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 : does not scale as doubles during the PNS evolution; efficientsource of GW emission after few seconds;

g-modes : smaller 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 of1011 1012 Mc2

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,

f1/

2 h(f

) [

Hz-

1/2 ]

Advanced LIGOETf-modeg-mode

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

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 thanfor no rotation.

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

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