proto-neutron star evolution and gravitational wave emission
TRANSCRIPT
Proto-neutron star evolutionand gravitational wave emission
MORGANE FORTIN1
in collaboration withV. FERRARI2, L. GUALTIERI2, O. BENHAR1 & F. Burgio3
1Italian Institute for Nuclear Physics (INFN), Rome division, Italy2Sapienza University of Rome, Italy
3Italian Institute for Nuclear Physics, Catania division, Italy
YKIS2013 conferenceJune 6, 2013
M. FORTIN (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission
Formation of a proto-neutron star (PNS)
Lattimer & Prakash et al., Phys. Rep. (2007)
Stage 0
◮ collapse of a massive starand bounce;
◮ birth of a PNS;
◮ outward propagation of ashock wave.
M. FORTIN (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission
Formation of a proto-neutron star (PNS)
Lattimer & Prakash et al., Phys. Rep. (2007)
Stage I : t = 0
◮ stagnation of the shockwave at ∼ 200 km;
◮ unshocked, low entropycore in which the neutrinosare trapped;
◮ high entropy, low densitymantle losing energy due toelectron captures andthermally-producedneutrino emission;
◮ accretion of matter throughthe shock wave.
M. FORTIN (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission
Formation of a proto-neutron star (PNS)
Lattimer & Prakash et al., Phys. Rep. (2007)
Stage II : t = 0.5 s
◮ the shock is revived(neutrinos and/orconvection) and lifts off theenvelope;
◮ extensive neutrino lossesand deleptonization in theenvelope → loss ofpressure;
◮ the PNS shrinks from aradius of 200 km to 20 km;
◮ the core is left unchanged.
M. FORTIN (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission
Formation of a proto-neutron star (PNS)
Lattimer & Prakash et al., Phys. Rep. (2007)
Stage III : t ∼ 15 sThe diffusion of the neutrinosfrom the core up to the surfacedominates :
◮ deleptonization of the core;
◮ neutrino-matter interactions→ heating of the PNS up to∼ 50 MeV;
◮ decrease of the entropygradient between the coreand the envelope.
M. FORTIN (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission
Formation of a proto-neutron star (PNS)
Lattimer & Prakash et al., Phys. Rep. (2007)
Stage IV : t ∼ 50 s
◮ lepton-poor PNS but
◮ thermal production ofneutrinos that diffuse up tothe surface;
◮ cooling down of the PNS.
M. FORTIN (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission
Formation of a proto-neutron star (PNS)
Lattimer & Prakash et al., Phys. Rep. (2007)
Stage V : t & 50 s
◮ the PNS becomesneutrino-transparent;
◮ birth of a NS;
◮ cooling of the whole NS bythe emission of neutrinosfrom the interior and ofphotons from the surface.
M. FORTIN (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission
Formation of a proto-neutron star (PNS)
Lattimer & Prakash et al., Phys. Rep. (2007)
Kelvin-Helmholtz (KH)phase
◮ stages III and IV,
◮ quasi-stationary evolution→ sequence of equilibriumconfigurations.
PurposeModelling of KH phase :
◮ up-to-date description ofthe microphysicalproperties of PNSs;
◮ study of their oscillationsand the associatedgravitational wave (GW)emission .
M. FORTIN (INFN-Rome) Proto-neutron star evolution, 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 (INFN-Rome) Proto-neutron star evolution, 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 = 0.16fm−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⊙ .
M. FORTIN (INFN-Rome) Proto-neutron star evolution, 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 (INFN-Rome) Proto-neutron star evolution, 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 (INFN-Rome) Proto-neutron star evolution, 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 (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission
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 takes 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
.
M. FORTIN (INFN-Rome) Proto-neutron star evolution, 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 (INFN-Rome) Proto-neutron star evolution, 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 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.
M. FORTIN (INFN-Rome) Proto-neutron star evolution, 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 (INFN-Rome) Proto-neutron star evolution, 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 : 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
M. FORTIN (INFN-Rome) Proto-neutron star evolution, 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 ν thanfor no rotation.
PurposeConstraining the microphysical properties of PNSs, and ultimately the nuclearinteraction, by the observation of their GW emission . . .
M. FORTIN (INFN-Rome) Proto-neutron star evolution, and gravitational wave emission