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

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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

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