NEUTRINO EMISSION FROM A STRONGLY MAGNETIZED DEGENERATE ELECTRON GAS: THE COMPTON MECHANISM VIA A NEUTRINO MAGNETIC MOMENT

Abstract

We derive relative upper bounds on the effective magnetic moment of Dirac neutrinos from comparison of the standard weak and electromagnetic mechanisms of the neutrino luminosity due to the Compton-like photoproduction of neutrino pairs in a degenerate gas of electrons on the lowest Landau level in a strong magnetic field. These bounds are close to the known astrophysical and laboratory ones. 1. Neutrino emission is the main source of energy losses of stars in the late stages of their evolution [1]. As is well known, neutron stars (NSs) can have strong magnetic fields H >∼ 10 12 G, the NSs with H ∼ 10− 10 G are called magnetars [2]. In this report, we consider one of the main processes of neutrino emission in the outer regions of NSs (for a review of various neutrino processes, see [3]) that is photoproduction of neutrino pairs (γe → eνν) in a degenerate gas of electrons through two mechanisms: the weak one via standard charged and neutral weak currents and the electromagnetic one via neutrino electromagnetic dipole moments arising in extended versions of the Standard Model [1,4] (for a recent review, see [5]). By comparison of the neutrino luminosities due to these two mechanism, Lw and Lem, we derive relative upper bounds on the neutrino effective magnetic moment (NEMM) μν = (μ 2 ν + d 2 ν) , (1) restricting ourselves to the case of Dirac neutrinos. Here μν and dν are the neutrino magnetic and electric dipole moments, respectively. 2. We assume that the electron gas is degenerate and strongly magnetized: T ≪ μ−m, H > ((μ/m) − 1)H0/2, (2) where T and μ ≃ μ(T = 0) ≡ eF = (m 2 + p F ) are the temperature and chemical potential of the gas, eF and pF are the Fermi energy and momentum, H0 = m /e ≃ 4.41×10 G, m and −e are the electron mass and charge (we use the units with h = c = kB = 1). Under the conditions (2), electrons occupy only the lowest Landau level in the magnetic field with pF = 2π 2ne/(eH), where ne is the electron concentration, and the effective photon mass is generated which e-mail: borisov@phys.msu.ru late e-mail: mstranger@list.ru is equal to the plasmon frequency ωp = ((2α/π)(pF/eF)H/H0) m, α is the fine-structure constant. For the nonrelativistic case, pF ≪ m and ωp ≪ T , the neutrino luminosities are expressed as follows: Lw = 3.49× 10 H 13 ρ 6 T 9 8 erg cm s, (3) Lem = 4.06× 10 30(μν/μB) 2ρ26T 3 8 erg cm −3 s, (4) where H13 = H/(10 13 G), ρ6 = ρ/ (