Primordial magnetic fields generated by the non-adiabatic fluctuations at pre-recombination era

In the pre-recombination era, cosmological density fluctuations can naturally generate magnetic fields through Thomson scatterings. In previous studies, only the magnetic field generation from the initially- adiabatic fluctuations has been considered. Here we investigate the generation of cosmological magnetic fields sourced by the primordial non-adiabatic fluctuations based on the cosmological perturbation theory, using the tight-coupling approximations between photon and baryon fluids. It is found that the magnetic fields from the non-adiabatic fluctuations can arise at the first-order expansion of the tight coupling approximation. This result is in contrast to the case of adiabatic initial fluctuations, where the magnetic fields can be generated only at the second-order. In a general case where the primordial density perturbations contain small non-adiabatic fluctuations on the top of the dominant adiabatic ones, we show that the leading source of magnetic fields is given by the second-order coupling of the adiabatic and non-adiabatic fluctuations. We calculate the power spectrum of the generated magnetic fields when the non-adiabatic fluctuations have a blue power spectrum, which has been suggested by recent cosmological observations