Where can we really find the First Stars' Remnants today?

A number of recent numerical investigations concluded that the remnants of rare structures formed at very high redshift, such as the very first stars and bright redshift z~6 QSOs, are preferentially located at the center of the most massive galaxy clusters at redshift z=0. In this paper we readdress this question using a combination of cosmological simulations of structure formation and extended Press-Schechter formalism and we show that the typical remnants of Population III stars are instead more likely to be found in a group environment, that is in dark matter halos of mass ~2x10^{13} h^{-1}M_sun. Similarly, the descendants of the brightest z~6 QSOs are expected to be in medium-sized clusters (mass of a few 10^{14} h^{-1}M_sun), rather than in the most massive superclusters (M>10^{15} h^{-1}M_sun) found within the typical 1 Gpc^3 cosmic volume where a bright z~6 QSO lives. The origin of past claims that the most massive clusters preferentially host these remnants is rooted in the numerical method used to initialize their numerical simulations: Only a small region of the cosmological volume of interest was simulated with sufficient resolution to identify low-mass halos at early times, and this region was chosen to host the most massive halo in the cosmological volume at late times. The conclusion that the earliest structures formed in the entire cosmological volume evolve into the most massive halo at late times was thus arrived at by construction. We demonstrate that, to the contrary, the first structures to form in a cosmological region evolve into relatively typical objects at later times. We propose alternative numerical methods for simulating the earliest structures in cosmological volumes.