Black hole mass and growth rate at z ≃ 4.8: A short episode of fast growth followed by short duty cycle activity

We present new H-band spectroscopy for a flux-limited sample of 40 z ≃ 4.8 active galactic nuclei, selected from the Sloan Digital Sky Survey. The sample probably contains the most massive active black holes (BHs) at this redshift and spans a broad range in bolometric luminosity, 2.7 × 10 ⁴⁶ erg s^-1 < L _bol < 2.4 × 10 ⁴⁷ erg s^-1. The high-quality observations and the accurate fitting of the Mg IIλ2798 line enable us to study, systematically, the distribution of BH mass (M _BH) and normalized accretion rate (L/L _Edd) at z ≃ 4.8. We find that 10⁸ M _⊙ ≲ M _BH ≲ 6.6 × 10⁹ M _⊙ with a median of 8.4 × 10⁸ M _⊙. We also find that 0.2 ≲ L/L _Edd ≲ 3.9 with a median of 0.6. Most of these sources had enough time to grow to their observed mass at z ≃ 4.8 from z = 20, assuming a range of seed BH masses, with 40% that are small enough to be stellar remnants. Compared to previously studied samples at z ≃ 2.4 and ≃3.3, the masses of the z ≃ 4.8 BHs are typically lower by 0.5 dex and their L/L _Edd is higher by a similar factor. The new z ≃ 4.8 sample can be considered as the progenitor population of the most massive BHs at z ≃ 2.4 and ≃3.3. Such an evolutionary interpretation requires that the growth of the BHs from z ≃ 4.8 to z ≃ 3.3 and z ≃ 2.4 proceeds with short duty cycles, of about 10%-20%, depending on the particular growth scenario.