Eddington-limited accretion and the black hole mass function at redshift 6 (1006.1342v1)

Abstract: We present discovery observations of a quasar in the Canada-France High-z Quasar Survey (CFHQS) at redshift z=6.44. We also use near-IR spectroscopy of nine CFHQS quasars at z~6 to determine black hole masses. These are compared with similar estimates for more luminous Sloan Digital Sky Survey (SDSS) quasars to investigate the relationship between black hole mass and quasar luminosity. We find a strong correlation between MgII FWHM and UV luminosity and that most quasars at this early epoch are accreting close to the Eddington limit. Thus these quasars appear to be in an early stage of their life cycle where they are building up their black hole mass exponentially. Combining these results with the quasar luminosity function, we derive the black hole mass function at z=6. Our black hole mass function is ~10^4 times lower than at z=0 and substantially below estimates from previous studies. The main uncertainties which could increase the black hole mass function are a larger population of obscured quasars at high-redshift than is observed at low-redshift and/or a low quasar duty cycle at z=6. In comparison, the global stellar mass function is only ~10^2 times lower at z=6 than at z=0. The difference between the black hole and stellar mass function evolution is due to either rapid early star formation which is not limited by radiation pressure as is the case for black hole growth or inefficient black hole seeding. Our work predicts that the black hole mass - stellar mass relation for a volume-limited sample of galaxies declines rapidly at very high redshift. This is in contrast to the observed increase at 4<z<6 from the local relation if one just studies the most massive black holes.

• The paper measures SMBH masses using near-IR spectroscopy with the MgII emission line and a virial method.
• It finds that z~6 quasars predominantly accrete near the Eddington limit, indicating rapid early growth of black holes.
• The derived black hole mass function is significantly lower than prior estimates, providing new insights into early galaxy evolution.

Eddington-Limited Accretion and the Black Hole Mass Function at Redshift 6

The paper by Willott et al. addresses the properties of supermassive black holes (SMBHs) at the extreme end of cosmic history, specifically at redshift $z \approx 6$. The paper leverages data from the Canada-France High-z Quasar Survey (CFHQS) and Sloan Digital Sky Survey (SDSS) to explore the connection between black hole mass and quasar luminosity, resulting in valuable insights into the accretion processes during this early epoch.

Black Hole Accretion at $z \sim 6$

The authors examine quasar samples to measure SMBH masses using the virial method with near-IR spectroscopy focusing on the $[{\rm MgII}]$ emission line. The black hole masses for these quasars are estimated to lie within the range of $10^8$ to $10^{10}$ $M_\odot$. A crucial finding is that most quasars in this redshift range appear to be accreting close to the Eddington limit, marking them as young systems undergoing rapid black hole mass build-up.

Black Hole Mass Function

By combining these observations with the quasar luminosity function, the paper derives a black hole mass function for $z = 6$. They report the black hole mass density is roughly $10^{-4}$ times the density observed today. The derived function is significantly lower than previous estimates, which is attributed to better constraints from quasar luminosity and accretion efficiencies. Such a lower mass function suggests a limited early build-up of black holes compared to stellar mass formations, which are approximately 100 times lower at $z=6$ versus present conditions.

Implications for Galaxy Evolution

The evolutionary trajectory of the black hole mass function informs us about galaxy formation processes in the young universe. The stark difference in the evolution of black holes relative to that for stellar masses (a factor of $10^4$ versus $10^2$ from $z = 6$ to today) suggests the presence of efficient early star formation mechanisms that are less hindered by feedback effects than black hole growth.

Theoretical Implications and Future Research

The observation that quasars at $z = 6$ are predominantly accreting near the Eddington limit implies that these systems are in the exponential growth phase. The discrepancy between the black hole and stellar mass functions could indicate the need for massive black hole seeds or points to a potentially slower early growth of black holes due to radiation pressure limits.

The prospects for future research are clear: high-resolution simulations that incorporate detailed modeling of early galaxy dynamics, black hole seeds, and feedback mechanisms are needed to refine our understanding of mass distributions in the early universe. Additionally, upcoming observations with facilities like the James Webb Space Telescope will be crucial in probing fainter AGNs and dissecting the dusty environments of early galaxy hosts.

Overall, this paper provides a robust framework for understanding black hole growth within the first billion years after the Big Bang, laying ground for further theoretical and observational work aimed at uncovering the complex interplay between black hole accretion and galaxy evolution during the reionization era.