Kicks of magnetized strange quarks stars induced by anisotropic emision of neutrinos Daryel Manreza Paret, ICN-UNAM dmanreza@gmail.com Collaborators Alejandro Ayala, ICN-UNAM México, A. Perez Martinez, ICIMAF La Habana Cuba, G. Piccinelli, FES Aragón-UNAM, México, A. Sanchez, Facultad de Ciencias UNAM México, J. Salvador Ruiz Montaño, Universidad Autónoma de Sinaloa, México. (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 1 / 22
Introduction Compact Objects Neutron Stars M ∼ 1 . 4M ⊙ R ∼ 12 km ρ ∼ 10 14 g / cm 3 B ∼ 10 12 − 10 15 G Figure: Artist’s illustration of an isolated neutron star. Author: Casey Reed - Penn State University (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 2 / 22
Introduction Compact Objects traditional neutron star quark−hybrid star N+e N+e+n n,p,e, µ n superfluid hyperon n d o u c c t r neutron star with i star e n p g pion condensate u n , p s , e p µ , r u,d,s o quarks t ∆ o 2SC − , Ξ n π CFL , Λ s , H crust Σ Fe K − color−superconducting 10 6 g/cm 3 strange quark matter (u,d,s quarks) 10 11 g/cm 3 2SC CFL g/cm 3 10 14 CSL CFL−K+ gCFL CFL−K0 LOFF π 0 Hydrogen/He CFL− atmosphere strange star nucleon star R ~ 10 km † F. Weber. doi:10.1016/j.ppnp.2004.07.001. (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 3 / 22
Introduction Observational evidences for NSs kicks Pulsar kicks refers to peculiar translational velocities observed on pulsars with respect to surrounding stars and with respect to their progenitors. Kicks can be natal or post-natal: a natal kick is imparted to the NS at birth while post-natal kicks is due to some inner process of the pulsar. Hobbs et al. † have studied the data from the proper motion of 233 pulsars, obtaining velocities as high as 1000 km s − 1 and that the mean velocity of young pulsar is 400 km s − 1 . † Hobbs, G., Lorimer, D., Lyne, A., & Kramer, M. 2005, Mon. Not. R. Astron. Soc., 360, 974. (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 4 / 22
Introduction Models to describe NSs kicks Some mechanism to explain the kicks are: Hydrodynamically Driven Kicks: This mechanism explain a natal kick 1 during the core collapse and supernova explosion due to hydrodynamical perturbations that could lead to asymmetric matter ejection. Electromagnetic rocket effect: Electromagnetic radiation from an 2 off-centered rotating magnetic dipole imparts a kick to the pulsar along its spin axis. Neutrino–Magnetic Field Driven Kicks: Asymmetric neutrino emission 3 induced by strong magnetic fields. (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 5 / 22
Introduction Models to describe NSs kicks Some mechanism to explain the kicks are: Hydrodynamically Driven Kicks: This mechanism explain a natal kick 1 during the core collapse and supernova explosion due to hydrodynamical perturbations that could lead to asymmetric matter ejection. Electromagnetic rocket effect: Electromagnetic radiation from an 2 off-centered rotating magnetic dipole imparts a kick to the pulsar along its spin axis. Neutrino–Magnetic Field Driven Kicks: Asymmetric neutrino emission 3 induced by strong magnetic fields. Neutrino emissivity from the process d → u + e + ¯ ν e , u + e → d + ν e , (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 5 / 22
Introduction Models to describe NSs kicks Some mechanism to explain the kicks are: Hydrodynamically Driven Kicks: This mechanism explain a natal kick 1 during the core collapse and supernova explosion due to hydrodynamical perturbations that could lead to asymmetric matter ejection. Electromagnetic rocket effect: Electromagnetic radiation from an 2 off-centered rotating magnetic dipole imparts a kick to the pulsar along its spin axis. Neutrino–Magnetic Field Driven Kicks: Asymmetric neutrino emission 3 induced by strong magnetic fields. Neutrino emissivity from the process d → u + e + ¯ ν e , u + e → d + ν e , The polarisation of the electron spin will fix the neutrino emission in one direction along the magnetic field (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 5 / 22
Introduction Models to describe NSs kicks Some mechanism to explain the kicks are: Hydrodynamically Driven Kicks: This mechanism explain a natal kick 1 during the core collapse and supernova explosion due to hydrodynamical perturbations that could lead to asymmetric matter ejection. Electromagnetic rocket effect: Electromagnetic radiation from an 2 off-centered rotating magnetic dipole imparts a kick to the pulsar along its spin axis. Neutrino–Magnetic Field Driven Kicks: Asymmetric neutrino emission 3 induced by strong magnetic fields. Neutrino emissivity from the process d → u + e + ¯ ν e , u + e → d + ν e , The polarisation of the electron spin will fix the neutrino emission in one direction along the magnetic field The neutrinos work as a propulsion mechanism for the neutron star (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 5 / 22
Pulsar kick velocity The idea that neutrinos can be the cause for the kick is easily understood with the following estimation: Energy released in the emission of neutrinos ∼ 10 53 erg. Kinetic energy of a 1 . 4 M ⊙ NS moving at 1000 km s − 1 ∼ 10 49 erg. The momentum of neutrinos ( p ν ) and the NS ( p NS ) are E ν ∼ 10 43 erg · s p ν = c cm M NS · v kick ∼ 2 . 8 × 10 41 erg · s p NS = ∼ 0 . 03 p ν cm (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 6 / 22
Pulsar kick velocity To compute the kick velocity of the NS we have to take into account that the acceleration of the NS is due to the luminosity of the fraction of asymmetric emitted neutrinos: dv dt M NS = χL L = 4 3 πR 3 ǫ c , where χ is the electron polarization, L is the neutrino luminosity and ǫ the neutrino emissivity. The cooling equation give a relation between the emissivity and the specific heat C v dT = − ǫdt. In this way we have for the kick velocity dv = − χ e 4 3 πR 3 C v dT. M NS We have to compute the electron polarization and the specific heat in a magnetic field! (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 7 / 22
Pulsar kick velocity Electron polarization in a magnetic field The energy spectrum of electrons in a magnetic field is quantized by the so called Landau Levels E 2 l = m 2 e + p 2 3 + 2 leB, and the number density reads � ∞ ∞ n e = d e m 3 B 1 � e (2 − δ l 0 ) dp 3 e ( E l − µ e ) /T + 1 , 2 π 2 B e c 0 l =0 where l = ν + 1 2 + s , are the Landau level quantum numbers, e /e = 4 . 41 × 10 13 G. s = ± 1 / 2 and B e c = m 2 ν = 0 , 1 , 2 , . . . , (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 8 / 22
Pulsar kick velocity Electron polarization in a magnetic field The electron spin polarization χ is given by χ = n − − n + , n − + n + where n ± are the number densities of electrons with spin parallel ( s = +1 ) or anti–parallel ( s = − 1 ) to the magnetic field direction respectively, given by � ∞ ∞ n − = d e m 3 B 1 e � dx 3 , √ 2 π 2 B e e ( me c − x e ) + 1 x 2 3 +1+2 νB/B e c 0 T ν =0 � ∞ ∞ n + = d e m 3 B 1 e � dx 3 , √ 2 π 2 B e e ( me c − x e ) + 1 x 2 3 +1+2 νB/B e c 0 T ν =1 where x e = µ e /m e and we have used the relation between l , ν and s , changing the summation over l by the summation over ν (its important to noticed that the change is � ∞ � ∞ l =0 (2 − δ l 0 ) → � ν =0 ). s = ± 1 (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 9 / 22
Pulsar kick velocity Electron polarization in a magnetic field We can numerically compute the dependence of χ with the parameters B, T, and µ from the following expression − 1 ∞ � ∞ 1 � 2 dx 3 √ 0 ( me x 2 3+1+2 νB/Be c − xe ) +1 ν =1 e T χ e = 1 + . � ∞ 1 dx 3 √ 0 ( me x 2 3+1 − xe ) +1 e T (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 10 / 22
Pulsar kick velocity Electron polarization in a magnetic field 1.0 T=0.1 MeV T=1.0 MeV T=10 MeV 0.8 0.6 χ 0.4 0.2 0.0 -1 0 1 2 3 4 5 10 10 10 10 10 10 10 e B/B c Figure: Polarization of electrons χ as function of the magnetic field and temperature, for a fixed chemical potential x e = 10 . (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 11 / 22
Pulsar kick velocity Electron polarization in a magnetic field 1.0 0.8 0.6 χ e 5 0.4 B/B c =10 e 4 B/B c =10 0.2 e 3 B/B c =10 e 2 B/B c =10 0.0 0.1 1 10 T [MeV] Figure: Polarization of electrons χ as function of the temperature for several values of the magnetic field and fixed chemical potential x e = 10 . (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 12 / 22
Pulsar kick velocity Electron polarization in a magnetic field Figure: Polarization of electrons χ as function of the chemical potential for several values of the magnetic field and fixed temperature. (ISMD2017 Daryel Manreza Paret, ICN/UNAM ) September 14, 2017 13 / 22
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