Metal enrichment of the intergalactic medium and production of massive black holes

A model for the chemical evolution of the intergalactic medium (IGM) is presented using theoretical yields of very massive stars (VMSs; M_VMS > 100 M_⊙) and Type II supernovae (SNe II). It is shown that if [Si/C] is indeed as high as ∼0.7 in the IGM, then VMSs (M_VMS ≈ 140-260 M_⊙) associated with pair-instability supernovae (PI-SNe) in low-mass (∼ 10⁵ M_⊙) halos at high redshift must produce at least 50% of the Si. The remainder is from later galactic outflows of SN II debris, which also provide most of the C and O. Both sources are required to account for the metal inventory in the IGM. The early VMS production must continue until redshift z ∼ 15 so that the efficiency of VMS formation per low-mass halo is significantly below unity. Contributions from the later galactic outflows mainly occur at z ∼ 4-6. Using a Salpeter initial mass function, we infer that the number of V_VMS ≈ 260-2000 M_⊙) producing massive black holes (MBHs) with an average mass (M_MBH) ∼ 270-550 M_⊙ is ≈0.72 times the number of VMSs associated with PI-SNe. The amount of metals (particularly Si) in the IGM that is attributable to PI-SNe is thus closely coupled with the total mass of MBHs produced in epochs prior to galaxy formation. Production of ∼50% of the Si in the IGM by PI-SNe corresponds to an early inventory of MBHs that constitutes a fraction ∼(4-8) × 10^-5 of the total baryonic mass in the universe. This is comparable to the global mass budget of the central supermassive black holes (SMBHs) in present-day galaxies. The corresponding occurrence rates in each halo of ∼ 10⁵ M_odot; during the epoch of VMS formation at z ≳ 15 are ∼0.9 Gyr^-1 for VMSs associated with PI-SNe and ∼0.6 Gyr^-1 for the concomitant more massive stars producing MBHs. These rates may be of use to studies of H₂ dissociation and reionization and to models of SMBH formation.