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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<ul><li><p>Evolution of proto-neutron starsand gravitational wave emission</p><p>MORGANE FORTIN1,2,3</p><p>1 Italian Institute for Nuclear Physics, Rome1 division, Italy</p><p>2N. Copernicus Astronomical Center, Polish Academy of Sciences, Poland</p><p>3Laboratory Universe and Theories, Paris-Meudon Observatory, France</p><p>TEONGRAV meeting 2014</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Formation of a proto-neutron star (PNS)</p><p>T</p><p> 2 1010 KR 200 km</p><p>Stage 0</p><p> collapse of a massive star andbounce;</p><p> outward propagation of a shock wave;</p><p> birth of a PNS.</p><p>Stage I : t = 0</p><p> stagnation of the shock wave at 200 km;</p><p> unshocked, low entropy core in whichthe neutrinos are trapped;</p><p> high entropy, low density mantlelosing energy due to electroncaptures and thermally-producedneutrino emission.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Formation of a proto-neutron star (PNS)</p><p>T</p><p> 2 1010 KR 30 km</p><p>Stage II : t = 0.5 s</p><p> the shock is revived (neutrinos and/orconvection) and lifts off the envelope;</p><p> extensive neutrino losses anddeleptonization in the envelope loss of pressure;</p><p> the PNS shrinks from a radius of 200km to 30 km;</p><p> the core is left unchanged.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Formation of a proto-neutron star (PNS)</p><p>T</p><p> 2 1010 KR 30 km</p><p>Stage III : t 15 sThe diffusion of the neutrinos from the coreup to the surface dominates :</p><p> deleptonization of the core;</p><p> neutrino-matter interactions heating of the PNS up to 50 MeV;</p><p> decrease of the entropy gradientbetween the core and the envelope.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Formation of a proto-neutron star (PNS)</p><p>T</p><p> 5 1010 KR 15 km</p><p>Stage IV : t 50 s</p><p> lepton-poor PNS but</p><p> thermal production of neutrinos thatdiffuse up to the surface;</p><p> cooling down of the PNS.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Formation of a proto-neutron star (PNS)</p><p>T</p><p> 5 109 KR 12 km</p><p>Stage V : t &amp; 50 s</p><p> the PNS becomesneutrino-transparent;</p><p> birth of a NS;</p><p> cooling of the whole NS by theemission of neutrinos from the interiorand of photons from the surface.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Formation of a proto-neutron star (PNS)</p><p>T</p><p> 2 1010 KR 30 km</p><p>T</p><p> 5 1010 KR 15 km</p><p>Kelvin-Helmholtz (KH) phase</p><p> stages III and IV,</p><p> quasi-stationary evolution sequence of equilibriumconfigurations.</p><p>PurposeModelling of KH phase :</p><p> up-to-date description of themicrophysical properties of PNSs;</p><p> study of their oscillations and theassociated gravitational wave (GW)emission.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Overview</p><p>Equation of stateP = P (n</p><p>b</p><p>, T ,YL</p><p>)</p><p>Evolution equations : Transport equations Structure equations</p><p>Profiles in P, nb</p><p>, T and YL</p><p>Oscillations and GW emissionFrequency and damping time of</p><p>the quasinormal modes</p><p>Diffusion coefficientD = D (n</p><p>b</p><p>,T ,YL</p><p>)</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Equation of state (EoS)Describes the properties and composition of the interior of the PNS.</p><p>PropertiesInclude the dependence on :</p><p> the density nb</p><p>: up to few times n0, the nuclear saturation density (n0 = 0.16fm3),</p><p> the temperature : 0 . T . 50 MeV,</p><p> the lepton fraction : 0 . YL</p><p>= n+nenp+nn. 0.4, ie. the composition.</p><p>ModelBurgio &amp; Schulze, A&amp;A (2010)</p><p> High-density part :</p><p> 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.</p><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</p><p>(Demorest et al., Nature, 2010 &amp; Antoniadis et al., Science, 2013) :</p><p>Mmax(T = 0) = 2.03 M .</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Overview</p><p>Equation of stateP = P (n</p><p>b</p><p>, T ,YL</p><p>)</p><p>Evolution equations : Transport equations Structure equations</p><p>Profiles in P, nb</p><p>, T and YL</p><p>Oscillations and GW emissionFrequency and damping time of</p><p>the quasinormal modes</p><p>Diffusion coefficientD = D (n</p><p>b</p><p>,T ,YL</p><p>)</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Evolution equations</p><p>Pons et al., ApJ (1999)</p><p>Hypothesis</p><p> spherically symmetric PNS,</p><p> with a constant baryon mass (no accretion),</p><p> stationary evolution,</p><p> in the framework of general relativity.</p><p>Transport equationsDiffusion approximation :</p><p> neutrinos in thermal and chemical equilbrium with the ambient matter,</p><p> Boltzmann equation becomes a system of two diffusion equations :</p><p> one for the energy-integrated lepton flux, another one for the energy-integrated energy flux, in terms of the neutrino diffusion coefficient . . .</p><p>Structure equations</p><p> Tolman Oppenheimer Volkoff equations.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Overview</p><p>Equation of stateP = P (n</p><p>b</p><p>, T ,YL</p><p>)</p><p>Evolution equations : Transport equations Structure equations</p><p>Profiles in P, nb</p><p>, T and YL</p><p>Oscillations and GW emissionFrequency and damping time of</p><p>the quasinormal modes</p><p>Diffusion coefficientD = D (n</p><p>b</p><p>,T ,YL</p><p>)</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Diffusion coefficientDescribes the interactions of the neutrinos with the ambient matter during theirdiffusion.</p><p>ProcessesFor nuclear matter :</p><p> Neutral current (scattering) :</p><p>e + e e + e</p><p>e + n e + n</p><p>e + p e + p</p><p> Charged current (absorption):</p><p>e + n e + p</p><p>Mean free path of a given reaction : iReddy et al., PRD (1998)Calculations take into account the effects of the strong interaction by :</p><p> being consistent with the model for nuclear interaction so with the EoS,</p><p> depending on the composition in addition to the temperature and density.</p><p>Diffusion coefficient</p><p>D1 =</p><p>all proesses</p><p>1i</p><p>.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Overview</p><p>Equation of stateP = P (n</p><p>b</p><p>, T ,YL</p><p>)</p><p>Evolution equations : Transport equations Structure equations</p><p>Profiles in P, nb</p><p>, T and YL</p><p>Oscillations and GW emissionFrequency and damping time of</p><p>the quasinormal modes</p><p>Diffusion coefficientD = D (n</p><p>b</p><p>,T ,YL</p><p>)</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Oscillations and GW emissionBurgio et al., PRD (2011)</p><p>Quasinormal modes Solution of the equations describing the nonradial perturbations of a star that</p><p>behave as a pure outgoing wave at infinity.</p><p> Use of Lindblom &amp; Detweiler formulation.</p><p> Solution characterized by a pulsation frequency of the given mode and itsdamping time due to gravitational wave emission </p><p>GW</p><p>.</p><p>Mode classificationAccording to the restoring force dominating when a fluid element is displaced, eg. :</p><p> the f -mode (fundamental mode) : global oscillation of the star,</p><p> the g-modes (gravity-modes) : due thermal and composition gradients,</p><p> the p-modes (pressure-modes) : the restoring force is due to a pressuregradient,. . .</p><p>GW emissionComparison between :</p><p> the damping time of a given mode GW</p><p>,</p><p> the time scale associated with dissipative processes competing with GW emission(eg. neutrino diffusion) </p><p>diss</p><p>.</p><p>If diss</p><p>&gt; GW</p><p>, the GW emission is the main source of dissipation.</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Overview</p><p>Equation of stateP = P (n</p><p>b</p><p>, T ,YL</p><p>)</p><p>Evolution equations : Transport equations Structure equations</p><p>Profiles in P, nb</p><p>, T and YL</p><p>Oscillations and GW emissionFrequency and damping time of</p><p>the quasinormal modes</p><p>Diffusion coefficientD = D (n</p><p>b</p><p>,T ,YL</p><p>)</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Previous modellingsQNM propertiesFerrari et al., MNRAS (2003); Burgio et al., PRD (2011)</p><p> stronger dependence of the QNM frequencies on the temperature profile than onthe lepton fraction profile;</p><p> modes properties different from the ones of cold NSs;</p><p> f -mode : does not scale as doubles during the PNS evolution; efficientsource of GW emission after few seconds;</p><p> g-modes : smaller than the f -mode, increases for t . 1 s and then decreases;efficient source in the first few seconds.</p><p>Detectability</p><p>Andersson et al., GRG (2011)</p><p> Results for a SNR of 8 withET : at 10 kpc, radiation of1011 1012 Mc2</p><p>through the modes.</p><p> Note that the oscillationspectrum evolves during theobservation.</p><p>EoS : relativistic mean field (cf. Pons etal. 1998).</p><p>1 10 100 1000 10000f [Hz]</p><p>1e-25</p><p>1e-24</p><p>1e-23</p><p>1e-22</p><p>1e-21</p><p>Sh1</p><p>/2, </p><p> f1/</p><p>2 h(f</p><p>) [</p><p>Hz-</p><p>1/2 ]</p><p>Advanced LIGOETf-modeg-mode</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li><li><p>Perspectives</p><p> Calculation of the evolution of a PNS and the GW emission due to oscillations forthe Burgio &amp; Schulze EoS.</p><p> Influence of the microphysical properties on the QNMs properties :</p><p> use of different EoSs, including ones with a phase transition; use of recent works on the treatment of neutrino-nucleon interactions for the</p><p>calculation of diffusion coefficients : in-medium correlation (eg. Reddy et al.PRC 1999), . . .</p><p> 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.</p><p>PurposeConstraining the microphysical properties of PNSs, and ultimately the nuclearinteraction, by the observation of their GW emission . . .</p><p>M. FORTIN Evolution of proto-neutron stars, and gravitational wave emission</p></li></ul>

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