1. Neutrino Cooling of Neutron Stars D.N. Voskresensky NRNU MEPhI, Moscow

2.  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

3. Pulsar in Crab cancellation is remnant SN 1052 observed in 1968 Neutron stars are forming in supernova II explosions (M~M sol, R~10 km, initial T~30-50 MeV ) «Простираю свою персону ниц: я наблюдал в созвездии Твен-Куан явление звезды-гостьи.» Янг-Вэй-Тэ

5. Double neutron star binaries 1,4414(2) M ☉, 1,3867(2) M ☉M ☉M ☉ majority of measured NS masses are focused near the value 1.4 M sol

6. Pulsar J1614-2230 J. Antoniadis et al., Science (2013) Measured Shapiro delay with high precision Time signal is getting delayed when passing near massive object. Highest well-known masses of NS there are heavier, but far less precisely measured candidates) Lowest well-known mass of NS1.18 ±0.02 М sol Pulsar J0348-04232 P.Demorest et al., Nature 467 (2010) M = (2.01± 0.04 ) M sol New data: masses are essentially different

7. Klähn et al. PRC 74, 035802 (2006) If M>2.4 M sol ( ) 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 NS mass-central density diagram for different EoS

8. 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 M max >1.93 M sol Danielewicz, Lacey, Lynch (2002) - Boltzmann kinetic equation fitted to directed & elliptic flow HEAVY ION COLLISIONS MEET NEUTRON STARS (common constraints)

9. a RMF-based (KVOR, M max ~2 M sol ) quasiparticle model with scaled hadron masses and couplings Khvorostukhin,Toneev,D.V. Nucl. Phys. (2007,2008) Aim: to construct a phenomenological EoS and apply it to calculations of neutron stars and hydro. calculations of HIC reactions following constraints from chiral symmetry restoration, SU(3) multiplet particle species are included Kolomeitsev,D.V.Nucl.Phys. (2005); T.Klahn, et al. Phys.Rev. (2006 )

10. rotation frequency for non-accreting systems, period increases with time power-law spin-down braking index for magnetic dipole spin-down n=3 period “spin-down age" 2) pulsar speed and position w.r. to the geometric center of the associated SNR 1) age of the associated SNR 3) historical events Crab : 1054 AD Cassiopeia A: 1680 AD Tycho’s SN: 1572 AD

11. Yakovlev et al

12. Explosion of SN1987A Registration of 20 neutrinos E ν ~ 10-40 МэВ If Supernova will be exploded in our Galaxy (frequency 1/(30-100 yr)), Superkamiokande will register ~10 3 neutrinos! certainly, if not too close to our Sun !!!

13. White-body radiation problem (at low T<T ~1-few MeV): direct reactions: Similar to di-lepton radiation problem in HIC Cooling of neutron stars After passing a minute, during 10 5 years a neutron star cools down by neutrino emission, than by photon emission from the surface opac T surf (t) is related to T in (t); problem to compute T in (t) (except first minutes after NS formation during which NS cools down up to few MeV) bring information straight from the dense interior

14. For T> min., T<T opac ~ MeV neutron star is transparent for neutrino c V - specific heat density, ε v – neutrino emissivity, Ф, λ – metric coefficients each fermion leg on a Fermi surface ~ T neutrino phase space  neutrino energy emissivity for t>300-500 yr C V – specific heat, L-luminosity ~60 MeV

15. intermediate cooling rapid cooling How to describe all groups within one cooling scenario? slow cooling 3 groups+Cas A: Neutron star cooling data >10 3 in emissivity CaS A

16. Cooling: crust is light and interior is massive most important are reactions in dense interior (where baryon density one-nucleon reactions: two-nucleon reactions: direct Urca (DU) modified Urca (MU) nucleon bremsstrahlung (NB) (less important) Casino da Urca in Brazil-waist of money; pilferer, thief in Odessa URCA “Un-Recordable Coolant Agent” (by Gamov) n 0 is the nuclear saturation density) Phase-space separation G.Gamov

17. the weak interaction constant lepton current nucleon current Note 1/2 in neutral channel, since Z boson is neutral and W is charged! ~v (Fermi velocity) corrections are important

18. For bare vertices ! emissivity: Counting powers of T: each external nucleon and electron line ~ T neutrino phase space  neutrino energy one-nucleon phase-space volume (» 10 27 -10 28 factor) T 6 dependence threshold behavior ( n>n c DU, n c DU depends on EoS) very moderate density dependence

19. self-energy with free non- equilibrium Green’s functions Cut of the diagram means removing of dE integration due to  -function D.V., Senatorov Yad.Fiz.(1987)

20. pion Urca (PU) processes:For All “exotic” one-nucleon processes start only when the density exceeds some critical density Pion Urca processes PU is also one-nucleon process (if the model permits pion condensation)

21. energy-momentum conservation requires processes on neutral currents are forbidden!

23. Friman & Maxwell AJ (1979) (3) (1) (4)(2) k Additionally one should take into account exchange reactions (identical nucleons) FOPE model of NN interaction (no medium effects) FOPE model continues to be used by different groups, e.g. by Page et. All, Yakovlev et al.

24. Emissivity: s=2 is symmetry factor. Reactions with the electron in an initial state yield extra factor 2. Finally Coherence: only axial-vector term contributes (!) due to exchange reactions

25. + - + - + - + - + - + - - + +- + - - + thick pion line (here up to 2 nd order): - + +- + - + - ++++---- one-nucleon process with pion two-nucleon process

26. Nucleon-nucleon pairing in NS (for T<T c ~10 9 -10 10 K) A.B. Migdal 1959

27. Pairing in NS matter 3P 2 gap is <10 keV model I model II A.B.Migdal (1959)

29. standard exotics MU: DU: PU: Standard scenario + exotics

30. DU process schould be „exotics“ (if DU starts it is dificult to stop it) EoS should produce a large DU threshold in NS matter ! [Kolomeitsev, D.V. (2005), Klahn et al. (2006)] DU constraint: M DU >1.35-1.5 M sol since in reality masses of NS are not close to each other Otherwise why many masses have M~1.3-1.5 M sol ?

31. Klähn et al. PRC 74, 035802 (2006) should be modified Information about density dependence of the symmetry energy 3 n 0 DU -- information about nuclear EoS L>80 MeV are excluded by the DU constraint

32. superfluid matter normal matter with free vertices and Green’s functions Diagrams with normal and anomalous Green func. Naive generalization: ++ -- are forbidden are allowed new “quasi”-one-nucleon-like processes (one-nucleon phase space volume) become permitted [Flowers, Ruderman, Sutherland, AJ 205 (1976), D.V.& Senatorov, Sov. J. Nucl. Phys. 45 (1987) ] + -

33. In superfluid ( T<T c <0.1-1 MeV ) all two-nucleon processes are suppressed by factor exp(-2  /T) paired nucleon un-paired nucleon D.V., Senatorov (1987)  nn is neutron gap and  nn =exp(-  nn /T)

34. [Page, Geppert, Weber, NPA 777, 497 (2006)] pair breaking and formation (PBF) processes are important for cooling! strongly depending on Δ(n) Schaab et al. (1996) D.V.& Senatorov, (1987)

35. Minimal cooling paradigm D.Page et al., D.G. Yakovlev et al. Reactions in presence of pairing MU: PBF: (at least) and for Δ> 0.1 MeV Minimal cooling paradigm does not allow to explain all available data (problems or with slow coolers or with Cas A, + with rapid coolers). attempts to fit cooling data by fitting Δ (n) dependencies and using different T s -T in for different NS

36. standard exotics minimal MU: PBF: DU: PU: (at least) Minimal (+exotics) scenario for T<T c

37. Minimal cooling +exotics D.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).

38. The only diagram in FOPE model which contributes to the MU and NB is 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  NN 2 : Pion condensation already at n>0.3 n 0 Free one-pion exchange measure of pion softening But there is no pion condensation in atomic nuclei

39. 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 > n c PU > n 0 : Pion condensation arises only due to pion softening!

40. Dressed Green’s functions Dressed interactions Dressed vertices

41. white body radiation problem General consideration: Knoll, D.V. Ann. Phys. 249 (1996) Only for low T<< ε F, quasiparticle approximation is valid (each G - + yields T 2, allows to cut diagrams over G -+ ) For soft radiation: quasiclassics (all graphs in first line are of the same order):LPM effect Direct reactions from piece of matter ( v in NS, e+e-, γ, K + in HIC) expansion in full non-equilibrium G - +

42. Landau-Pomeranchuk-Migdal effect on example of the soft photon radiation QPA region ω~T>> Ѓ~T 2 /ε F

43. pion with residual (irreducible in NN -1 and  N -1 ) s-wave  N interaction and  scattering`` Part of the interaction involving  isobar is analogously constructed: explicit nucleon-nucleon hole and Delta-nucleon hole degrees of freedom small Fermi liquid approach

44. full pion propagator: enhancement of the amplitude dressed vertex: suppression Poles yield zero-sound modes in scalar and spin channels Low energy excitations in nuclear Fermi liquid (Landau-Migdal approach) based on a separation of long and short scales Re-summed NN interaction Landau-Migdal parameters of short-range interaction are extracted from atomic nuclei known phenomena in Fermi liquid Similar to Debye screening in plasma provided short-scale interaction can be reduced to the local one see Migdal et al., Phys.Rep. (1990)

46. A.B. Migdal ZhETF (1971) free π the smaller collision energy, the larger is in-medium effect : ω n 2 cr similar for π 0 in neutron matter Kolomeitsev,D.V. (1996)

47. [Migdal,Markin,Mishustin, JETP (1974)] variational calculations [Akmal, Pandharipande, Ravenhall, PRC58 (1998)]: pion condensate: neutral pion condensate: Charged pion spectra in neutron matter and pion condensation

48. pion gap for n<n c PU no pion condensate reconstruction of pion spectrum on top of the pion condensate |  *|~ amplitude of the condensate 1 st -order phase transition Г –vertex suppression factor Pion softening with increase of the density possibility of no π-cond. From the cooling fit n c >2.5 n 0

49. MEDIUM EFFECTS IN NEUTRINO PRODUCTION In the medium many reaction channels are opened up

50. The weak coupling vertex is renormalized in medium: [D.V., Senatorov, Sov. J. Nucl. Phys. 45 (1987)] wavy line corresponds to weak current For the  -decay: For processes on the neutral currents with the correlation functions

51. ONE-NUCLEON PROCESSES DIRECT URCA (DU), PION URCA (PU) etc. require n>n c

53. TWO-NUCLEON PROCESSES MEDIUM-MODIFIED URCA (MMU)

54. Very strong density dependence emissivity: largersmaller Very important in our scenario! Straight generalization of MU

55. The Ward identity is fulfilled and the current is conserved superfluid matter normal matter free vertices and Green’s functions free vertices and non-interacting quasi-particles with a gapped spectrum Gap appears due to a non-trivial self-energy Vertex must be modified accordingly. Otherwise the current is not conserved Diagrams with normal and anomalous Green func. Problem! Naive generalization: -+ + + --

56. A.B. Migdal A.I. Larkin A.J. Leggett

57. Cannot be written in matrix form in Nambu-Gor’kov space since U ≠ V taken into account earlier

58. Main contribution is due to the axial current. Suppression is of the order ~0.1 moderate suppressionstrong suppression Leinson,Perez (2006),Kolomeitsev,D.V. (2008) Kolomeitsev,D.V. (2008) with free vertices

59. D.V., Senatorov JETP 1986 all the data known to that time were explained by MMU process assuming different masses (here different average densities) of NS upper limits on surface temperatures that time most of researches believed that all NS have the very same masses ~1.4 M sol

60. Nuclear medium cooling scenario [ D.Blaschke, H. Grigorian, D.V., AA 424 (2004)] 1S 0 Gaps model I, heat conductivity from Baiko et al. 2001(left), varied (right). If we suppress Baiko result by k~0.3 we are able to describe CaS A data 2010. All data are explained by different masses of objects DU Model I for pairing

61. Thermal conductivity with taking into account of medium effects lepton term with inclusion of Landau damping nn- term with inclusion of pion softening Blaschke, Grigorian, D.V. 2013 yields suppression of Baiko result

62. NS Mass-central density for EoS that we use We incorporated excluded volume effect: resulting HDD EoS is very close to KVOR, APR EoS for n 4n 0 increasing M max. Blaschke, Grigorian, D.V. 2013

63. Cas A data (observations 2000-2010) show very sharp temperature drop minimal cooling ( Page et al. 2011, Yakovlev et al.2011 ) requires 3Р 2 pairing T c ~0.05MeV (but some other data are not explained within the same scenario). Nuclear medium cooling (Blaschke, Grigorian, Weber, D.V. 2012, Blaschke, Grigorian,D.V. 2013)

64. Nuclear medium cooling scenario important age region Blaschke, Grigorian, D.V. 2013

65. Pulsar period-age diagram

66. Region of r-mode instability Coriolis driving force Kolomeitsev,D.V. preliminary Stable owing to shear viscosity bulk visc. Unstable region Max. rotating young pulsar Within nucl.medium cooling we are able to explain low frequencies of young pulsars

67. Theoretically medium effects and pion dressing are necessary, otherwise calculations become inconsistent. Cooling data motivate strong density (neutron star mass) dependence of neutrino emissivities. (Supported by new measurements of different neutron star masses in supernova remnants.) Within our nuclear medium cooling scenario we explain precision Cas A data (for that we used tiny 3P 2 pairing gaps). Models of EoS with a strong density dependence of the symmetry energy (low DU threshold) have problems with description of NS cooling. DU constraint: M DU crit >1.3-1.5 M sol. Our new EoS is compatible with NS mass measurements and flow constraint. Statement of some works that fit of Cas A allows to measure the value of 3P 2 pairing gap (T c ~0.5 MeV) seems as misleading. Within nuclear medium cooling scenario we may explain absence of rapidly rotating young pulsars