Active and Sterile Neutrino Emission and SN1987A Pulsar Velocity
aa r X i v : . [ a s t r o - ph . C O ] J un Active and Sterile Neutrino Emission and SN1987A Pulsar Velocity
Leonard S Kisslinger, Department of Physics, Carnegie Mellon University, Pittsburgh, PA 15213Sandip Pakvasa, Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822
Recently estimates have been made of the velocities of pulsars produced by the emission of sterileneutrinos during the first 10 seconds and by active neutrinos during the second 10 seconds aftera supernova event reaches thermal equilibrium. Neutrinos produced with electrons in the lowestLandau level are emitted in the direction of the magnetic field, and the resulting pulsar velocitydepends mainly on the temperature. Using measurements of the neutrino energies emitted fromSN1987A, the temperature can be estimated, and from this we estimate the velocity of the resultingpulsar from both active and large mixing-angle sterile neutrinos.
PACS Indices:97.60.Bw,97.60.Gb,97.60.JdA supernova event, which is the gravitational col-lapse of a massive star, often leads to the formationof a rapidly rotating neutron star, a pulsar. It hasbeen observed that many pulsars move with linearvelocities of 1000 km/s or greater, the pulsar kick.See Ref.[1] for a review.Electrons in very strong magnetic fields, such asthose found at the surface of a protoneutron starcreated by a supernova, are in Landua levels [2, 3].If the electron is in the lowest Landau level, n=0,it has only negative helicity with respect to the di-rection of the magnetic field, say in the z direction.This leads to neutrinos produced with the electronsby URCA or modified URCA processes to have mo-menta strongly correlated with the magnetic fields,which could produce pulsar kicks.It was shown in a recent work on pular kicks[4]that if electrons created by the modified URCA pro-cesses, which dominate neutrino emission after 10seconds[5], are in the n=0 level, only those movingin the z (B) direction will contribute to neutrino emi-sion. Therefore, even though only one or two percentof the neutrino emissivity occurs during the periodof approximately 10 to 20 seconds after the super-nova collapse, since almost all emission is correlatedin the z direction this can account for the observedlarge pulsar velocities, the pulsar kicks. The result-ing pulsar velocity, v ns , is proportional to the tem-perature, T, of the protoneutron star surface to theseventh power, and one must be able to estimate Tin order to predict v ns .The largest neutrino emission after the super-nova collapse takes place during the first 10 sec-onds, when the neutrinosphere starts at about 40km, with the URCA process dominating neutrinoproduction. However, due to the high opacity forstandard model neutrinos in the dense region withinthe neutrinosphere, few neutrinos are emitted, andthe large pulsar kick is not obtained[6]. This has led to studies of pulsar kicks coming from sterile neu-trinos to which the active neutrinos oscillate. In astudy using sterile neutrinos with a very small mix-ing angle and a large mass (mass > R ν , is a lit-tle smaller that the radius of the protoneutron star, R ns , so all the created neutrinos correlated with thez direction are emitted. In ref[4] it was shown thatwith the probability of the electron being in the n=0Landau level ≃ . R ν ≃ .
96 km, the velocitygiven to the neutron star during this period by ac-tive neutrinos, for a neutron star with the mass ofour sun is v active ns = 1 . × − ( T K ) kms . (1)During the first 10 seconds, using the model of[11, 12] with two light large mixing angle neutrinos,it was shown that the velocity given to a pulsar is v sterile ns ≃ . × − ( T K ) sin (2 θ ) kms , (2)where the mixing angles of the two sterile neutrinosgive sin (2 θ ) = 0 .
004 and 0 . kT = E ν / . . +1 . − . . Since then there have beenmany analyses. See references [18, 19]. Althoughthere are discrepancies, the general agreement is thatthe neutrino energy at 10 seconds is in the range 9-14Mev, giving a temperature range: T ≃ (3 ↔ .
5) MeV = (3 . ↔ . × K , (3)which results in our prediction from Eq.(1) that v active , SN1987A ns ≃ (0 . → .
6) kms , (4)which is too small in comparison with other sources of pulsar kicks to be significant. Note that if theneutrino energy were 30 MeV, v ns would be greaterthan 1000 km/s,for high-luminoscity pulsars.From Eq(2) the velocity of the a pulsar producedvia SN1987A by large mixing angle sterile neutrinoshas the range given by T and sin (2 θ ) v sterile , SN1987A ns ≃ (1 . × − → .
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