Self-regulating the early growth of black holes through global warming

A decade after their first discovery, the origin of giant supermassive black holes (SMBHs), with masses in excess of 109 Msolar, at redshifts as early as z > 6, remains a puzzle. One possibility is that stellar-mass ``seed'' BHs, left behind by the first stars, accrete gas at close to the Eddington limit during a large fraction (>~ 50%) of the time. While maintaining such a high accretion rate may itself be difficult, here we focus on another, less commonly discussed problem in this scenario: unless BH seed formation and growth are preferentially suppressed in less massive protogalaxies, the mass density in M~106Msolar SMBHs at z ~ 6 already exceeds the locally observed SMBH mass density by several orders of magnitude. We show that the X-rays from the earliest accreting BHs themselves can cause a self-regulation, by partially ionizing and heating the intergalactic medium (IGM). This ``global warming'' suppresses the formation and growth of subsequent generations of BHs in low-mass halos, and can produce excellent agreement with recent estimates of the z = 6 SMBH mass function, without impeding the growth of the largest (M>~109Msolar) holes, which reside in the most massive galaxies that formed first. The proposed gravitational-wave observatory eLISA could detect several tens of major mergers between SMBHs at z > 6.