We derive the energy asymmetry given the proto-neutron star during the time when the neutrino sphere is near the surface of the proto-neutron star , using the modified URCA process .
The electrons produced with the anti-neutrinos are in Landau levels due to the strong magnetic field , and this leads to asymmetry in the neutrino momentum , and a pulsar kick .
The magnetic field must be strong enough for a large fraction of the eletrons to be in the lowest Landau level , however , there is no direct dependence of our pulsar velocity on the strength of the magnetic field .
Our main prediction is that the large pulsar kicks start at about 10 s and last for about 10 s , with the corresponding neutrinos correlated in the direction of the magnetic field .
We predict a pulsar velocity of 1.03 \times 10 ^ { -4 } ( T / 10 ^ { 10 } K ) ^ { 7 } km/s , which reaches 1000 km/s if T \simeq 9.96 \times 10 ^ { 10 } K .