Black Hole Growth in a Cosmological Context and the Associated Cosmic Star Formation History

Abstract

Listen

Translate article

Based on a co-evolution scenario of massive black holes (MBH) and their host spheroids, we trace the BH growth and the joint cosmic star formation history by ROSAT X-ray All sky surveys. We found: 1) the total amount of star formation associated with MBH growth is at least half of the net star formation at high redshift, which probably missed by the current UV/opt. deep surveys; 2) an upper limit of the abundance ratio of type 2 to type 1 QSOs is about 2, within the constraints of the local BH density, the Chandra hard x-ray deep surveys and the SCUBA counts; 3)the peak redshift of the massive spheroid formation in this case is around 1.5-2. 1 Modelling strategies and the results The set of cosmological parameters (Ωm, ΩΛ) = (0.3, 0.7) and H0 = 50 km/s/Mpc is adopted throughout the calculation. The BH mass is derived from the X-ray luminosity by Mbh = β Lx 0.013 , with an assumption of the Eddington ratio = η ṁ c2 LEdd . The AGN luminosity Lx at 0.5 − 2 KeV and Mbh are in units of 1040 erg s−1 and M ; We adopt the bolometric correction at soft x-ray β = 20 based on the mean type 1 AGN SED and assume each AGN shines for a constant time scale tQ = 5 × 108 yrs, close to the e-folding time [3]. The “duty cycle” of AGN active phase is defined as fon = tQ/tHub(z), tHub(z) is the Hubble time. We approximate = 10 (logL − 49), γ ≈ 0.2 is a scaling factor from various AGN observations. Considering all AGNs in Miyaji et al. (2000) sample as unobscured type 1 [5], the BH mass function could be derived from the observed XLF by: d Φ(z, Mbh) d Mbh = 0.013 β fon d Φ(z, Lx) d Lx (1) The abundance ratio of type 2 to type 1 AGNs is described as R2−1 = 4 e− Lx Ls +α (1+ z)p (1− e− Lx Ls ). Ls = 1044.3 erg s−1 is the e-folding luminosity. α and p are free parameters within the model constraints of local BH density and the SCUBA number counts. The mass function of spheroids may have a similar form to the BH mass function according to a BH-bulge co-evolution scheme: ESO Symposia: Growing Black Holes, pp. 472–474, 2005. © Springer-Verlag Berlin Heidelberg 2005 BH Growth and the Associated Cosmic Star Formation History 473 d Φ(z, Msph) d Msph = d Φ(z, Mbh) d Mbh × R (2) R is the BH to bulge mass ratio, a mean value of ∼ 0.002 is adopted as the first approximation ([7]; [4]). Assuming a star formation time scale tsf = 5 × 108 yrs and SFR = Msph tsf for spheroid formation, we give similar to eq.1 the 850μm luminosity function at different redshift as below, with a mean value LFIR/L = 3.8 × 109 SFR (M yr−1) and a mean color ratio Rc = LFIR/L850 ∼ 5 × 103 from IRAS, ISO and SCUBA surveys [2]: d Φ(z, L850) d L850 = fon d Φ(z, Msph) d Msph d Msph d L850 (3) where fon = tsf/tHub reflects the fraction of galaxies with intensive star formation ongoing. d Msph d L850 = ν850 Rc tsf 3.8 × 109 L . The model results are shown in Fig.1.