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The impact of the streaming between baryons and dark matter on the firststructures has been actively explored by recent studies. We investigate how thekey results are affected by two popular approximations. One is to implement thestreaming by accounting for only the relative motion while assuming ``baryonstrace dark matter" spatially at the initialization of simulation. This neglectsthe smoothing on the gas density taking place before the initialization. In oursimulation initialized at $z_i=200$, it overestimates the gas density powerspectrum by up to 40\% at $k\approx10^2~h~\mbox{Mpc}^{-1}$ at $z=20$. Halo mass($M_h$) and baryonic fraction in halos ($f_{b,h}$) are also overestimated, butthe relation between the two remains unchanged. The other approximation testedis to artificially amplify the density/velocity fluctuations in the cosmic meandensity to simulate the first minihalos that form in overdense regions. Thisgives a head start to the halo growth while the subsequent growth is similar tothat in the mean density. The growth in a true overdense region, on the otherhand, is accelerated gradually in time. For example, raising $\sigma_8$ by 50\%effectively transforms $z\rightarrow\sqrt{1.5}z$ in the halo mass growthhistory while in 2-$\sigma$ overdensity, the growth is accelerated by aconstant in redshift: $z\rightarrow{z+4.8}$. As a result, halos have grown morein the former than in the latter before $z\approx27$ and vice versa after. The$f_{b,h}$-$M_h$ relation is unchanged in those cases as well, suggesting thatthe Pop III formation rate for a given $M_h$ is insensitive to the testedapproximations.

astrophysical journal/the astrophysical journal

First Structure Formation under the Influence of Gas-Dark Matter  Streaming Velocity and Density: Impact of the Baryons-trace-dark matter  Approximation