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## Neutrino Cooling of Neutron Stars

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**Neutrino Cooling of Neutron Stars**D.N. Voskresensky NRNU MEPhI, Moscow**General information on NS**“Standard” scenario. “Minimal” cooling. Neutrino reaction rates in normal nuclear matter in superfluid nuclear matter “Nuclear medium cooling” scenario. Medium effects on reaction rates in normal nuclear matter in superfluid nuclear matter conclusions Plan**Neutron stars are forming in supernova II explosions**(M~Msol, R~10 km, initialT~30-50 MeV) «Простираю свою персону ниц: я наблюдал в созвездии Твен-Куан явление звезды-гостьи.» Янг-Вэй-Тэ Pulsar in Crab cancellationis remnantSN 1052 observed in 1968**Double neutron star binaries**1,4414(2) M☉,1,3867(2) M☉ majority of measured NS masses are focused near the value 1.4 Msol**New data: masses are essentially different**Pulsar J1614-2230 Measured Shapiro delay with high precision P.Demorest et al., Nature 467 (2010) Time signal is getting delayed when passing near massive object. Pulsar J0348-04232 M = (2.01± 0.04 ) Msol J. Antoniadis et al., Science (2013) Highest well-known masses of NS there are heavier, but far less precisely measured candidates) Lowest well-known mass of NS 1.18 ±0.02 Мsol**NS mass-central density diagram for different EoS**Klähn et al. PRC 74, 035802 (2006) If M>2.4 Msol ( ) were observed, all these EoS would be invalid! Central densities in various NS are different! Studying various NS we may test density dependences of EoS and NN interaction**HEAVY ION COLLISIONS MEET NEUTRON STARS**(common constraints) Danielewicz, Lacey, Lynch (2002) - Boltzmann kinetic equation fitted to directed & elliptic flow Stiffest EoS do not satisfy the HIC constraint. Only EoS near the upper boundary of the box satisfy both the HIC and NS mass constraints yielding Mmax>1.93 Msol**Aim: to construct a phenomenological EoS and apply it to**calculations of neutron stars and hydro. calculations of HIC reactions a RMF-based (KVOR, Mmax~2 Msol ) quasiparticle model with scaled hadron masses and couplings Kolomeitsev,D.V.Nucl.Phys. (2005); T.Klahn, et al. Phys.Rev. (2006) following constraints from chiral symmetry restoration, SU(3) multiplet particle species are included Khvorostukhin,Toneev,D.V. Nucl. Phys. (2007,2008)**1) age of the associated SNR**3) historical events Crab : 1054 AD Cassiopeia A: 1680 AD Tycho’s SN: 1572 AD 2) pulsar speed and position w.r. to the geometric center of the associated SNR rotation frequency period for non-accreting systems, period increases with time power-law spin-down braking index for magnetic dipole spin-down n=3 “spin-down age"**Explosion ofSN1987A**Registration of 20 neutrinosEν~ 10-40 МэВ If Supernova will be exploded in our Galaxy (frequency 1/(30-100 yr)), Superkamiokandewill register ~103 neutrinos! certainly, if not too close to our Sun !!!**Cooling of neutron stars**After passing a minute, during 105 years a neutron star cools down by neutrino emission, than by photon emission from the surface (except first minutes after NS formation during which NS cools down up to few MeV) White-body radiation problem (at low T<T ~1-few MeV): direct reactions: Similar to di-lepton radiation problem in HIC opac bring information straight from the dense interior Tsurf (t) is related to Tin (t); problem to compute Tin (t)**emissivity**For T> min., T<Topac~ MeV neutron star is transparent for neutrino cV - specific heat density, εv – neutrino emissivity, Ф, λ – metric coefficients for t>300-500yr CV – specific heat, L-luminosity ~60 MeV each fermion leg on a Fermi surface ~ T neutrino phase space ´ neutrino energy**slow cooling**Neutron star cooling data 3 groups+Cas A: >103 in emissivity CaS A intermediate cooling rapid cooling How to describe all groups within one cooling scenario?**(where baryon density**Cooling: crust is light and interior is massive most important are reactions in dense interior n0 is the nuclear saturation density) G.Gamov Phase-space separation direct Urca (DU) one-nucleon reactions: modified Urca (MU) two-nucleon reactions: nucleon bremsstrahlung (NB) (less important) • URCA “Un-Recordable Coolant Agent” (by Gamov) Casino da Urca in Brazil-waist of money; pilferer, thief in Odessa**the weak interaction constant**lepton current nucleon current ~v (Fermi velocity) corrections are important Note 1/2 in neutral channel, since Z boson is neutral and W is charged!**For**bare vertices ! emissivity: Counting powers ofT: each external nucleon and electron line ~T neutrino phase space ´ neutrino energy • one-nucleon phase-space volume (» 1027-1028 factor) • T6dependence • threshold behavior (n>ncDU , ncDU depends on EoS) • very moderate density dependence**D.V., Senatorov Yad.Fiz.(1987)**self-energy with free non-equilibrium Green’s functions Cut of the diagram means removing of dE integration due to -function**Pion Urca processes**PU is also one-nucleon process (if the model permits pion condensation) For pion Urca (PU) processes: All “exotic” one-nucleon processes start only when the density exceeds some critical density**energy-momentum conservation**requires processes on neutral currents are forbidden!**Friman & Maxwell AJ (1979)**FOPE model of NN interaction (no medium effects) (1) (3) k (2) (4) Additionally one should take into account exchange reactions (identical nucleons) FOPE model continues to be used by different groups, e.g. by Page et. All, Yakovlev et al.**Emissivity:**s=2 is symmetry factor. Reactions with the electron in an initial state yield extra factor 2. Finally due to exchange reactions Coherence:only axial-vector term contributes (!)**+**- + - + - + - + - + + - - + - - + + - + - + - + - - + - + + - + - + - thick pion line (here up to 2nd order): one-nucleon process with pion two-nucleon process**Nucleon-nucleon pairing in NS(for T<Tc ~109-1010 K)**A.B. Migdal 1959**Pairing in NS matter**A.B.Migdal (1959) model I model II 3P2 gap is <10 keV**Standard scenario + exotics**standard MU: exotics DU: PU:**DU constraint:**DU process schould be „exotics“(if DU starts it is dificult to stop it) since in reality masses of NS are not close to each other EoS should produce a large DU threshold in NS matter ! MDU>1.35-1.5 Msol Otherwise why many masses have M~1.3-1.5 Msol ? [Kolomeitsev, D.V. (2005), Klahn et al. (2006)]**DU -- information about nuclear EoS**should be modified Information about density dependence of the symmetry energy 3 n0 Klähn et al. PRC 74, 035802 (2006) L>80 MeV are excluded by the DU constraint**-**+ normal matter with free vertices and Green’s functions are forbidden new “quasi”-one-nucleon-like processes (one-nucleon phase space volume) become permitted superfluid matter [Flowers, Ruderman, Sutherland, AJ 205 (1976), D.V.& Senatorov, Sov. J. Nucl. Phys. 45 (1987) ] Diagrams with normal and anomalous Green func. - - + + Naive generalization: are allowed**In superfluid (T<Tc<0.1-1 MeV) all two-nucleon processes are**suppressed by factor exp(-2/T) un-paired nucleon paired nucleon D.V., Senatorov (1987) nn is neutron gap and nn=exp(-nn/T)**strongly depending on Δ(n)**pair breaking and formation (PBF) processes are important for cooling! D.V.& Senatorov, (1987) Schaab et al. (1996) [Page, Geppert, Weber , NPA 777, 497 (2006)]**Minimal cooling paradigmD.Page et al., D.G.**Yakovlev et al. Reactions in presence of pairing MU: PBF: (at least) and for Δ> 0.1 MeV attempts to fit cooling data by fitting Δ (n) dependencies and using different Ts-Tin for different NS • Minimal cooling paradigm does not allow to explain all available data • (problems or with slow coolers or with Cas A, + with rapid coolers).**Minimal (+exotics) scenario**for T<Tc standard minimal MU: PBF: (at least) exotics DU: PU:**Minimal cooling +exoticsD.Page et al., D.G. Yakovlev et al.**• Minimal cooling +exotics cannot appropriately explain all available modern data(either precision Cas A data or all others, with deficiency of the DU mentioned above).**The only diagram in FOPE model which contributes to the MU**and NB is Free one-pion exchange For consistency one needs to calculate corrections of the second-order in f NN in other values. Otherwise -- problems with unitarity. Pion polarization operator in dispersion relation at order f NN2 : measure of pion softening Pion condensation already at n>0.3 n0 But there is no pion condensation in atomic nuclei**One should replace FOPE by the full NN interaction,**essential part of which is due to MOPE with vertices corrected by NN correlations. NN-1 part of the pion polarization operator is Another inconsistency of standard scenario: it uses FOPE but adds PU processes for n > ncPU> n0: Pion condensation arises only due to pion softening!**Dressed Green’s functions**Dressed interactions Dressed vertices**Direct reactions from piece of matter (v in NS, e+e-, γ,**K+ in HIC) white body radiation problem General consideration: Knoll, D.V. Ann. Phys. 249 (1996) expansion in full non-equilibrium G - + Only for low T<<εF, quasiparticle approximation is valid (each G- + yields T2, allows to cut diagrams over G -+ ) For soft radiation: quasiclassics (all graphs in first line are of the same order):LPM effect**Landau-Pomeranchuk-Migdal effect**on example of the soft photon radiation ω~T>>Ѓ~T2/εF QPA region**Part of the interaction involving isobar is analogously**constructed: pion with residual (irreducible in NN-1 and N-1) s-wave N interaction and scattering`` Fermi liquid approach explicit nucleon-nucleon hole and Delta-nucleon hole degrees of freedom small**full pion propagator:**enhancement of the amplitude dressed vertex: suppression Low energy excitations in nuclear Fermi liquid (Landau-Migdal approach) based on a separation of long and short scales Re-summed NN interaction provided short-scale interaction can be reduced to the local one Similar to Debye screening in plasma Landau-Migdal parameters of short-range interaction are extracted from atomic nuclei Poles yield zero-sound modes in scalar and spin channels known phenomena in Fermi liquid see Migdal et al., Phys.Rep. (1990)**similar for π0 in neutron matter**free π Kolomeitsev,D.V. (1996) the smaller collision energy, the larger is in-medium effect 2 : ω <0 for n>n cr A.B. Migdal ZhETF (1971)**Charged pion spectra in neutron matter and pion condensation**[Migdal,Markin,Mishustin,JETP (1974)] variational calculations [Akmal, Pandharipande, Ravenhall, PRC58 (1998)]: pion condensate: neutral pion condensate:**Pion softening with increase of the density**reconstruction of pion spectrum on top of the pion condensate pion gap for n<ncPU no pion condensate |*|~ amplitude of the condensate 1st-order phase transition possibility of no π-cond. Г –vertex suppression factor From the cooling fit nc >2.5 n0**MEDIUM EFFECTS IN NEUTRINO PRODUCTION**In the medium many reaction channels are opened up**The weak coupling vertex is renormalized in medium:**wavy line corresponds to weak current For the -decay: For processes on the neutral currents with the correlation functions [D.V., Senatorov, Sov. J. Nucl. Phys. 45 (1987)]