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Dark Matter: Clues from the Supernovae and the Neutrino Oscillations

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Dark Matter: Clues from the Supernovae and the Neutrino Oscillations Alexander Kusenko (UCLA) NOON '04 Dark Matter: clues from the supernovae and the neutrino oscillations A. Kusenko, UCLA 1 Alexander Kusenko (UCLA) NOON '04 Dark Matter: clues from the supernovae and the neutrino oscillations Is nature giving us a hint about dark matter? Pulsar kicks and possible explanations ² Sterile neutrinos: the minimal extension of the Standard Model consistent ² with dark matter. Pulsar kicks from active to sterile neutrino conversions ² [AK, Segr`e, Fuller, Pascoli, Mocioiu, Semikoz] 2 Alexander Kusenko (UCLA) NOON '04 Pulsar velocities Pulsars have large velocities, v 250 450 km=s. h i ¼ ¡ [Cordes et al.; Hansen, Phinney; Kulkarni et al.; Lyne et al. ] A signi¯cant population with v > 700 km=s, about 15 % have v > 1000 km=s, up to 1600 km=s. [Arzoumanian et al.; Thorsett et al.; ] The high-velocity population is so large that some suggested the distribution is two-component, with average velocities v 90km/s and 1 ¼ v 500km/s [Cordes, Cherno®] 2 ¼ 3 Alexander Kusenko (UCLA) NOON '04 4 Alexander Kusenko (UCLA) NOON '04 Proposed explanations: asymmetric collapse [Shklovskii] (small kick) ² evolution of close binaries [Gutt, Gunn, Ostriker] (not enough) ² acceleration by EM radiation [Harrison, Tademaru] (kick small, predicted ² polarization not observed) asymmetry in EW processes that produce neutrinos [Chugai; Dorofeev, ² Rodinov, Ternov] (asymmetry washed out) \cumulative" parity violation [Lai, Qian; Janka] (it's not cumulative ) ² 5 Alexander Kusenko (UCLA) NOON '04 Asymmetric collapse \...the most extreme asymmetric collapses do not produce ¯nal neutron star velocities above 200km/s" [Fryer '03] 6 Alexander Kusenko (UCLA) NOON '04 Supernova neutrinos Excellent discussion by Hix, Suzuki this morning 7 Alexander Kusenko (UCLA) NOON '04 Supernova neutrinos Nuclear reactions in stars lead to a formation of a heavy iron core. When it reaches M 1:4M , the pressure can no longer support gravity. ¯ ) collapse. ¼ Energy released: 2 GN M ¢E Fe core 1053erg » R » 99% of this energy is emitted in neutrinos 8 Alexander Kusenko (UCLA) NOON '04 Pulsar kicks from neutrino emission? Pulsar with v 500 km/s has momentum » M v 1041 g cm/s ¯ » SN energy released: 1053 erg in neutrinos. Thus, the total neutrino momentum is ) P 1043 g cm/s º; total » ¶ ³ a 1% asymmetry in the distribution of neutrinos is su±cient to explain the pulsar kick velocities ´ But what can cause the asymmetry?? 9 Alexander Kusenko (UCLA) NOON '04 Magnetic ¯eld? Neutron stars have large magnetic ¯elds. A typical pulsar has surface magnetic ¯eld B 1012 1013 G. » ¡ Recent discovery of soft gamma repeaters and their identi¯cation as magnetars some neutron stars have surface magnetic ¯elds as high as ) 1015 1016 G. ¡ magnetic ¯elds inside can be 1015 1016 G. ) ¡ Neutrino magnetic moments are negligible, but the scattering of neutrinos o® polarized electrons and nucleons is a®ected by the magnetic ¯eld. 10 Alexander Kusenko (UCLA) NOON '04 Core collapse supernova Onset of the collapse: t = 0 core Fe 11 Alexander Kusenko (UCLA) NOON '04 Core collapse supernova Shock formation and \neutronization burst": t = 1 10 ms ¡ shock ν PNS burst Protoneutron star formed. Neutrinos are trapped. The shock wave breaks up nuclei, and the initial neutrino come out (a few %). 12 Alexander Kusenko (UCLA) NOON '04 Core collapse supernova Thermal cooling: t = 10 15 s ¡ ν PNS thermal Most of the neutrinos emitted during the cooling stage. 13 Alexander Kusenko (UCLA) NOON '04 Electroweak processes producing neutrinos (urca), + p + e¡ )* n + ºe and n + e )* p + º¹e have an asymmetry in the production cross section, depending on the spin orientation. σ( e¡; º) = σ( e¡; º) " " 6 " # The asymmetry: g2 g2 V A ²~ = ¡ k0 0:4 k0; g2 + 3g2 ¼ V A where k0 is the fraction of electrons in the lowest Landau level. 14 Alexander Kusenko (UCLA) NOON '04 In a strong magnetic ¯eld, 0.7 16 0.6 B=3x10 G 0.5 0.4 K 0 16 0.3 B=10 G 0.2 15 0.1 B=3x10 G 0 20 30 40 50 60 20 30 40 50 60 µ, MeV k0 is the fraction of electrons in the lowest Landau level. Pulsar kicks from the asymmetric production of neutrinos? [Chugai; Dorofeev, Rodionov, Ternov] 15 Alexander Kusenko (UCLA) NOON '04 Can the weak interactions asymmetry cause an anisotropy in the flux of neutrinos due to a large magnetic ¯eld? No ν e ν ν e ν e e ν e ν ν e e ν ν e e ν e ν e ν ν e ν e e ν e Neutrinos are trapped at high density. 16 Alexander Kusenko (UCLA) NOON '04 Can the weak interactions asymmetry cause an anisotropy in the flux of neutrinos due to a large magnetic ¯eld? No Rescattering washes out the asymmetry [Vilenkin; AK,Segr`e, Vilenkin]. In approximate thermal equilibrium the asymmetries in scattering amplitudes do not lead to an anisotropic emission. Only the outer regions, near neutrinospheres, contribute (a negligible amount). However, if a weaker-interacting sterile neutrino was produced in these processes, the asymmetry would, indeed, result in a pulsar kick! 17 Alexander Kusenko (UCLA) NOON '04 Sterile neutrinos leave the star without scattering. Hence, they give the pulsar a kick. ν B ν s s ν e ν e ν ν ν e e e ν ν ν s s s 18 Alexander Kusenko (UCLA) NOON '04 Sterile neutrinos with a small mixing to active neutrinos º = cos θ º sin θ º j 1i j ei ¡ j si (1) º = sin θ º + cos θ º ½ j 2i j ei j si The almost-sterile neutrino, º was never in equilibrium. Production of j 2i º2 could take place through oscillations. The coupling of º to weak currents is also suppressed, and σ sin2 θ. 2 / The probability of º º conversion in presence of matter is e ! s 1 2 ¡ 1 ¸osc 2 Pm = 1 + sin 2θm; (2) h i 2 2¸ " µ s ¶ # where ¸osc is the oscillatino length, and ¸s is the scattering length. 19 Alexander Kusenko (UCLA) NOON '04 Sterile neutrinos in cosmology: dark matter Sterile neutrinos are produced in primordial plasma through oscillations. The resulting density of relic sterile neutrinos: 2 2 sin 2θ ms ­º 0:3 2 » 10 8 keV à ¡ ! µ ¶ [Dodelson, Widrow; Dolgov, Hansen; Fuller, Shi; Abazajian, Fuller, Patel] 20 sup explain A Alexander sterile ernova. the Kusenk neutrino observed o (UCLA) m s [keV] in 10 1 velo 1e-11 this dark matter cities Ω = 0.3 ν range, 1e-10 of ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ pulsa ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ consistent ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ sin ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ dark matter dark ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ 1e-09 2 ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ θ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ rs ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ though ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ 2 ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ 1e-08 ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ Ω > 0.3 with ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ν ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ º ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ e ¡ da ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ 1e-07 ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ! ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ rk º s matter, oscillations can NOON in also '04 21 a Alexander Kusenko (UCLA) NOON '04 Active-sterile conversions in a neutron star In matter, there is a potential Vm for ºe, but not for ºs: V (ºs) = 0 V (º ) = V (º¹ ) = V (3 Y 1 + 4 Y ) e ¡ e 0 e ¡ ºe V (º ) = V (º¹ ) = V (Y 1 + 2 Y ) ¹;¿ ¡ ¹;¿ 0 e ¡ ºe The di®erence V V (º ) V (º ) m ´ e ¡ s 22 Alexander Kusenko (UCLA) NOON '04 Mixing angle in matter is di®erent from vacuum: 2 2 2 2 (¢m =2p) sin 2θ sin 2θm = ; (3) (¢m2=2p)2 sin2 2θ + (¢m2=2p cos 2θ V )2 ¡ m GF ½ Vm = (3Ye 1 + 4Yºe + 2Yº¹ + 2Yº¿ ) (4) p2mn ¡ ( 0:2::: + 0:5)V ; (5) ' ¡ 0 where V = G ½=p2m 3:8eV(½=1014gcm¡3) 0 F n ' Mixing is suppressed when V (¢m2=2k). m À 23 Alexander Kusenko (UCLA) NOON '04 º = cos θ º sin θ º j 1i mj ei ¡ mj si (6) º = sin θ º + cos θ º ½ j 2i mj ei mj si The coupling of º to weak currents is also suppressed, and σ sin2 θ. 2 / The probability of º º conversion in presence of matter is e ! s 1 2 ¡ 1 ¸osc 2 Pm = 1 + sin 2θm; (7) h i 2 2¸ " µ s ¶ # where ¸osc is the oscillatino length, and ¸s is the scattering length. 24 Alexander Kusenko (UCLA) NOON '04 However, the matter potential can evolve on short time scales. GF ½ Vm = (3Ye 1 + 4Yºe + 2Yº¹ + 2Yº¿ ): (8) p2mn ¡ V > 0 Transitions º º V decreases m ) e ! s ) m V < 0 Transitions º¹ º V increases m ) e ! s ) m Therefore, [Abazajian, Fuller, Patel] V 0 m ! sin θ sin θ m ! 0 production of ºs is unsuppressed 25 Alexander Kusenko (UCLA) NOON '04 Electroweak processes (urca) producing neurtrinos, including sterile neutrinos, + p + e¡ )* n + ºe and n + e )* p + º¹e have asymmetry in the production cross section, depending on the spin orientation. In polarized medium, the asymmetry is of the order 0:4 k0: 0.7 £ 16 0.6 B=3x10 G 0.5 0.4 K 0 16 The asymmetry in sterile neutrinos 0.3 B=10 G 0.2 is not a®ected by rescattering. 15 B=3x10 G 0.1 Sterile neutrinos escape 0 20 30 40 50 60 20 30 40 50 60 µ, MeV 26 Alexander Kusenko (UCLA) NOON '04 Sterile neutrinos leave the star without scattering. Hence, they give the pulsar a kick. ν B ν s s ν e ν e ν ν ν e e e ν ν ν s s s 27 Alexander Kusenko (UCLA) NOON '04 If the fraction of energy emitted in sterile neutrinos is s r = E 0:05 0:7; (9) E » ¡ µEtot¶ (as it can easily be), then the resulting momentum asymmetry is k0 r ² 0:02 E ; (10) » 0:3 0:5 µ ¶ µ ¶ which is su±cient to explain the pulsar kick velocities.
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