The Mass Assembly Of High-Redshift Black Holes

We use the Delphi semi-analytic model to study the mass assembly and properties of high-redshift (z>4) black holes over a wide mass range, 10(3) < M-bh/M-circle dot < 10(10). Our black hole growth implementation includes a critical halo mass (M-h(crit)) below which the black hole is starved and above which it is allowed to grow either at the Eddington limit or proportionally to the gas content of the galaxy. As a consequence, after an initial growth phase dominated by black hole mergers down to z similar to 7 (9), supermassive black holes in z = 4 halo masses of M-h vertical bar z=4 similar to 10(11.75) (10(13.4)) M-circle dot mainly grow by gas accretion from the interstellar medium. In particular, we find that (i) while most of the accretion occurs in the major branch for M-h vertical bar z=4 similar to 10(11-12)M(circle dot) haloes, accretion in secondary branches plays a significant role in assembling the black hole mass in higher mass haloes ( M-h vertical bar z=4 greater than or similar to 10(12)M(circle dot)); (ii) while the Eddington ratio increases with decreasing redshift for low-mass (M-bh < 10(5) M-circle dot) black holes, it shows the opposite trend for larger masses. In addition, since the accretion rate depends on the gas mass present in the host halo, the duty cycle of the Eddington-limited accretion phase - which can last up to approximate to 650 Myr - is crucially linked to the joint assembly history of the black hole and its host halo.