Random Primordial Magnetic Fields and the Gas Content of Dark Matter Halos

We recently predicted the existence of random primordial magnetic fields (RPMF) in the form of randomly oriented cells with dipole-like structure with a cell size $L_0$ and an average magnetic field $B_0$. Here we investigate models for primordial magnetic field with a similar web-like structure, and other geometries, differing perhaps in $L_0$ and $B_0$. The effect of RPMF on the formation of the first galaxies is investigated. The filtering mass, $M_F$, is the halo mass below which baryon accretion is severely depressed. We show that these RPMF could influence the formation of galaxies by altering the filtering mass and the baryon gas fraction of a halo, $f_g$. The effect is particularly strong in small galaxies. We find, for example, for a comoving $B_0=0.1\muG$, and a reionization epoch that starts at $z_s=11$ and ends at $z_e=8$, for $L_0=100\,\text{pc}$ at $z=12$, the $f_g$ becomes severely depressed for $M<10^7\msun$, whereas for $B_0=0$ the $f_g$ becomes severely depressed only for much smaller masses, $M<10^5\msun$. We suggest that the observation of $M_F$ and $f_g$ at high redshifts can give information on the intensity and structure of primordial magnetic fields.