Kompaneets equation for neutrinos: Application to neutrino heating in supernova explosions
Abstract
We derive a "Kompaneets equation" for neutrinos, which describes how the distribution function of neutrinos interacting with matter deviates from a Fermi-Dirac distribution with zero chemical potential. To this end, we expand the collision integral in the Boltzmann equation of neutrinos up to the second order in energy transfer between matter and neutrinos. The distortion of the neutrino distribution function changes the rate at which neutrinos heat matter, as the rate is proportional to the mean square energy of neutrinos, E_ν^2. For electron-type neutrinos the enhancement in E_ν^2 over its thermal value is given approximately by E_ν^2/E_{ν,thermal}^2=1+0.086(V/0.1)^2, where V is the bulk velocity of nucleons, while for the other neutrino species the enhancement is (1+δ_v)^3, where δ_v=mV^2/3k_BT is the kinetic energy of nucleons divided by the thermal energy. This enhancement has a significant implication for supernova explosions, as it would aid neutrino-driven explosions.
- Publication:
-
Progress of Theoretical and Experimental Physics
- Pub Date:
- August 2019
- DOI:
- 10.1093/ptep/ptz087
- arXiv:
- arXiv:1904.05047
- Bibcode:
- 2019PTEP.2019h3E04S
- Keywords:
-
- Astrophysics - High Energy Astrophysical Phenomena;
- Astrophysics - Cosmology and Nongalactic Astrophysics;
- Astrophysics - Solar and Stellar Astrophysics
- E-Print:
- 14 pages, 1 figure, matched to published version