Gravitational waves from proto-neutron star evolution
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1 Gravitational waves from proto-neutron star evolution Giovanni Camelio in collaboration with: Leonardo Gualtieri, Alessandro Lovato, Jose A. Pons, Omar Benhar, Morgane Fortin & Valeria Ferrari PhD University of Rome Sapienza work supported by an STSM through the COST Action NewCompStar September 14, 2016
2 Supernovae (SNe) 8 M M 25 M neutron star (NS); E γ = erg (L SN L galaxy ); E ν = erg (matter opaque to neutrinos!); GWs from PNS evolution: Introduction 1 / 9
3 Supernovae (SNe) 8 M M 25 M neutron star (NS); E γ = erg (L SN L galaxy ); E ν = erg (matter opaque to neutrinos!); Fe core supported by electrons Fermi pressure; when M core > M Ch = 1.44 M core collapse; GWs from PNS evolution: Introduction 1 / 9
4 Supernovae (SNe) 8 M M 25 M neutron star (NS); E γ = erg (L SN L galaxy ); E ν = erg (matter opaque to neutrinos!); Fe core supported by electrons Fermi pressure; when M core > M Ch = 1.44 M core collapse; increasing density nucleons Fermi pressure n B n 0 ; outer-core bounce shock wave; GWs from PNS evolution: Introduction 1 / 9
5 Proto-neutron star (PNS) PNSs are the SN contracting cores: very early evolution (PHASE I): core bounce 0.2 s: fully relativistic, highly dynamical codes; mass accretion; PNS contraction 150 km 30 km; high-temperature PNS envelope; neutrinos are trapped in the low-temperature PNS core. GWs from PNS evolution: Introduction 2 / 9
6 Proto-neutron star (PNS) PNSs are the SN contracting cores: very early evolution (PHASE I): core bounce 0.2 s: fully relativistic, highly dynamical codes; mass accretion; PNS contraction 150 km 30 km; high-temperature PNS envelope; neutrinos are trapped in the low-temperature PNS core. early evolution (PHASE II): 0.2 s minutes: relativistic, quasi-stationary evolution; beta equilibrium; deleptonization stage (heating of the inner core); cooling stage. GWs from PNS evolution: Introduction 2 / 9
7 Proto-neutron star (PNS) PNSs are the SN contracting cores: very early evolution (PHASE I): core bounce 0.2 s: fully relativistic, highly dynamical codes; mass accretion; PNS contraction 150 km 30 km; high-temperature PNS envelope; neutrinos are trapped in the low-temperature PNS core. early evolution (PHASE II): 0.2 s minutes: relativistic, quasi-stationary evolution; beta equilibrium; deleptonization stage (heating of the inner core); cooling stage. minutes: birth of a mature neutron star (neutrino transparent). We are interested in the gravitational wave emission (from rotation or stellar oscillations) of the PNS in PHASE II. GWs from PNS evolution: Introduction 2 / 9
8 PNS evolution: general facts in a cold NS the EoS is barotropic: P (n B, ɛ,...) in a PNS the T 40 MeV E F 10 MeV and therefore the EoS is non-barotropic (s, Y L, P) (n B, ɛ, T, Y ν,...) GWs from PNS evolution: Introduction 3 / 9
9 PNS evolution: general facts in a cold NS the EoS is barotropic: P (n B, ɛ,...) in a PNS the T 40 MeV E F 10 MeV and therefore the EoS is non-barotropic (s, Y L, P) (n B, ɛ, T, Y ν,...) PNS structure from general relativistic TOV equations (spherical metric) with a given finite-temperature EoS ɛ(s, Y L, P); ν transport (Boltzmann Lindquist Eqs, BLE) with β-equilibrium to evolve the profiles of entropy s and lepton number Y L ; GWs from PNS evolution: Introduction 3 / 9
10 PNS evolution: general facts in a cold NS the EoS is barotropic: P (n B, ɛ,...) in a PNS the T 40 MeV E F 10 MeV and therefore the EoS is non-barotropic (s, Y L, P) (n B, ɛ, T, Y ν,...) PNS structure from general relativistic TOV equations (spherical metric) with a given finite-temperature EoS ɛ(s, Y L, P); ν transport (Boltzmann Lindquist Eqs, BLE) with β-equilibrium to evolve the profiles of entropy s and lepton number Y L ; the neutrino number and energy fluxes depend on the EoS and on the neutrino diffusion coefficients; neutrino diffusion coefficients depend on the neutrino cross sections (and therefore on the EoS...); GWs from PNS evolution: Introduction 3 / 9
11 PNS evolution: general facts in a cold NS the EoS is barotropic: P (n B, ɛ,...) in a PNS the T 40 MeV E F 10 MeV and therefore the EoS is non-barotropic (s, Y L, P) (n B, ɛ, T, Y ν,...) PNS structure from general relativistic TOV equations (spherical metric) with a given finite-temperature EoS ɛ(s, Y L, P); ν transport (Boltzmann Lindquist Eqs, BLE) with β-equilibrium to evolve the profiles of entropy s and lepton number Y L ; the neutrino number and energy fluxes depend on the EoS and on the neutrino diffusion coefficients; neutrino diffusion coefficients depend on the neutrino cross sections (and therefore on the EoS...); For now, only mean-field EoSs have been used (e.g., GM3 Glendenning & Moszkowski, Reconciliation of Neutron-Star Masses and Binding of the Λ in Hypernuclei, PRL 67: [1991]). GWs from PNS evolution: Introduction 3 / 9
12 PNS evolution: our code Our code reproduces the results of Pons, Reddy, Prakash, Lattimer & Miralles, Evolution of proto-neutron stars, ApJ 513: [1999]: Y ν [#] T [MeV] s 01.0 s 05.0 s 10.0 s 20.0 s 30.0 s low T core; high T envelope; trapped ν; inner core heating; cooling; deleptonization r [km] Figure: PNS evolution, GM3 EoS (our code). GWs from PNS evolution: Results 4 / 9
13 Effective inclusion of rotation: the procedure We have extended the work of Villain, Pons, Cerdá-Durán & Gourgoulhon, Evolutionary sequences of rotating protoneutron stars, A&A 418: [2004]: Camelio, Gualtieri, Pons & Ferrari, Spin evolution of a proto-neutron star, PRD 94, (2016), arxiv: [astro-ph.he]. GWs from PNS evolution: Results 5 / 9
14 Effective inclusion of rotation: the procedure We have extended the work of Villain, Pons, Cerdá-Durán & Gourgoulhon, Evolutionary sequences of rotating protoneutron stars, A&A 418: [2004]: Camelio, Gualtieri, Pons & Ferrari, Spin evolution of a proto-neutron star, PRD 94, (2016), arxiv: [astro-ph.he]. First, evolve the non-rotating star: fix the total baryon mass M b ; the finite-temperature EoS is ɛ(s, Y L, P); the (non-rotating) evolution gives s(t, a), Y L (t, a). GWs from PNS evolution: Results 5 / 9
15 Effective inclusion of rotation: the procedure We have extended the work of Villain, Pons, Cerdá-Durán & Gourgoulhon, Evolutionary sequences of rotating protoneutron stars, A&A 418: [2004]: Camelio, Gualtieri, Pons & Ferrari, Spin evolution of a proto-neutron star, PRD 94, (2016), arxiv: [astro-ph.he]. First, evolve the non-rotating star: fix the total baryon mass M b ; the finite-temperature EoS is ɛ(s, Y L, P); the (non-rotating) evolution gives s(t, a), Y L (t, a). To effectively include the rotation: 1. fix an initial angular momentum J in = J(t = 0); 2. effective EoS at time t: ɛ t(a, P) = ɛ(s(t, a), Y L (t, a), P); 3. using ɛ t, solve Hartle-Torne (structure equations of a slowly rigidly rotating PNS) at time t with fixed M b and J(t); 4. determine J(t + dt) using the Epstein formula; 5. t t + dt, back to point 2. GWs from PNS evolution: Results 5 / 9
16 Effective inclusion of rotation: results M b =1.6 M O km erg s J (km 2 ) J in =2.00 km 2 J in =J max =0.92 km 2 J in =0.50 km t (s) Camelio, Gualtieri, Pons & Ferrari, Spin evolution of a proto-neutron star, PRD 94, (2016), arxiv: [astro-ph.he] GWs from PNS evolution: Results 6 / 9
17 Effective inclusion of rotation: results 1000 M b =1.6 M O ν ms J in =2.00 km 2 J in =J max J in =0.50 km ν (Hz) t (s) Camelio, Gualtieri, Pons & Ferrari, Spin evolution of a proto-neutron star, PRD 94, (2016), arxiv: [astro-ph.he] GWs from PNS evolution: Results 6 / 9
18 Effective inclusion of rotation: results h(ν) ν 1/ ε=10-4 r=10 kpc SNR: avirgo = 1.4 ET = 22 aligo = 2.2 Advanced Virgo ET Advanced LIGO J in =J max ν (Hz) Camelio, Gualtieri, Pons & Ferrari, Spin evolution of a proto-neutron star, PRD 94, (2016), arxiv: [astro-ph.he] GWs from PNS evolution: Results 6 / 9
19 EoS dependence: general facts previous PNS evolution studies used relativistic mean-field EoSs; we want to use a general EoS, e.g. a nuclear many-body theory EoS (Lovato & Benhar, An effective interaction from Argonne-Urbana nuclear forces, in preparation); GWs from PNS evolution: Results 7 / 9
20 EoS dependence: general facts previous PNS evolution studies used relativistic mean-field EoSs; we want to use a general EoS, e.g. a nuclear many-body theory EoS (Lovato & Benhar, An effective interaction from Argonne-Urbana nuclear forces, in preparation); from the free energy per baryon f (T, n b, Y p ) you can obtain all the other thermodynamical quantities with derivatives! GWs from PNS evolution: Results 7 / 9
21 EoS dependence: general facts previous PNS evolution studies used relativistic mean-field EoSs; we want to use a general EoS, e.g. a nuclear many-body theory EoS (Lovato & Benhar, An effective interaction from Argonne-Urbana nuclear forces, in preparation); from the free energy per baryon f (T, n b, Y p ) you can obtain all the other thermodynamical quantities with derivatives! we want to obtain the EoS from the fit of the interacting part of the baryon free energy f EoS (T, n b, Y p ) = f free gas (T, n b, Y p ) + f I (T, n b, Y p ), f I (T, n b, Y p ) = 4Y p (1 Y p )f SNM (T, n b ) + (1 2Y p ) 2 f PNM (T, n b ), f NM (T, n b ) = polynomial in T and n b, that is similar to how the bulk nuclear matter has been treated in Lattimer & Swesty, A generalized equation of state for hot, dense matter, Nucl.Phys.A 535:331 [1991]. GWs from PNS evolution: Results 7 / 9
22 EoS dependence: results (preliminary!) time: 00.2 s PRELIMINARY!!! GM3 bulk CBFEI T [MeV] Y ν [#] r [km] Camelio, Lovato, Gualtieri, Benhar, Pons, Fortin & Ferrari, GW and neutrino luminosity from proto-neutron stars with a nuclear many-body EoS, in preparation. GWs from PNS evolution: Results 8 / 9
23 EoS dependence: results (preliminary!) GM3 bulk CBFEI 5000 p ν [Hz] f 1000 g t [s] Camelio, Lovato, Gualtieri, Benhar, Pons, Fortin & Ferrari, GW and neutrino luminosity from proto-neutron stars with a nuclear many-body EoS, in preparation. GWs from PNS evolution: Results 8 / 9
24 EoS dependence: results (preliminary!) GM3 bulk CBFEI 1000 g τ [s] 10 p 1 1 f t [s] Camelio, Lovato, Gualtieri, Benhar, Pons, Fortin & Ferrari, GW and neutrino luminosity from proto-neutron stars with a nuclear many-body EoS, in preparation. GWs from PNS evolution: Results 8 / 9
25 Conclusions Done: new PNS evolution code; GW emission from a rotating PNS and its angular momentum evolution (effective inclusion of rotation), Camelio+[2016]; generalization to other EoSs (in particular the nuclear many-body theory EoS of Lovato&Benhar [in preparation]); GWs from PNS evolution: Conclusions 9 / 9
26 Conclusions Done: new PNS evolution code; GW emission from a rotating PNS and its angular momentum evolution (effective inclusion of rotation), Camelio+[2016]; generalization to other EoSs (in particular the nuclear many-body theory EoS of Lovato&Benhar [in preparation]); Work in progress: GW from quasi-normal modes (stellar perturbation theory), Camelio+[in preparation]; GWs from PNS evolution: Conclusions 9 / 9
27 Conclusions Done: new PNS evolution code; GW emission from a rotating PNS and its angular momentum evolution (effective inclusion of rotation), Camelio+[2016]; generalization to other EoSs (in particular the nuclear many-body theory EoS of Lovato&Benhar [in preparation]); Work in progress: GW from quasi-normal modes (stellar perturbation theory), Camelio+[in preparation]; Outlooks: convection (mixing length theory); accretion; evolution in 1+1.5D (consistent inclusion of rotation). GWs from PNS evolution: Conclusions 9 / 9
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