Exponentially growing bubbles around early supermassive black holes

Abstract

We address the as yet unexplored issue of outflows induced by exponentially growing power sources, focusing on early supermassive black holes (BHs). We assumed that these objects grow to 10 9 M by z=6 by Eddington-limited accretion and convert 5% of their bolometric output into a wind. We first considered the case of energy-driven and momentum-driven outflows expanding in a region where the gas and total mass densities are uniform and equal to the average values in the Universe at z > 6. We derived analytic solutions for the evolution of the outflow: for an exponentially growing power with e-folding time t S al , we find that the late time expansion of the outflow radius is also exponential, with e-folding time of 5t S al and 4t S al in the energy-driven and momentum-driven limit, respectively. We then considered energy-driven outflows produced by quasi-stellar objects (QSOs) at the centre of early dark matter halos of different masses and powered by BHs growing from different seeds. We followed the evolution of the source power and of the gas and dark matter density profiles in the halos from the beginning of the accretion until z = 6. The final bubble radius and velocity do not depend on the seed BH mass, but are instead smaller for larger halo masses. At z=6, bubble radii in the range 50-180 kpc and velocities in the range 400-1000 km s −1 are expected for QSOs hosted by halos in the mass range 3 × 10 11 − 10 13 M . These radius and velocity scales compare well with those measured for the outflowing gas in the z=6.4 QSO SDSS J1148+5251. By the time the QSO is observed, we found that the total thermal energy injected within the bubble in the case of an energy-driven outflow is E th ∼ 5 × 10 60 erg. This is in excellent agreement with the value of E th = (6.2 ± 1.7) × 10 60 erg measured through the detection of the thermal Sunyaev-Zeldovich effect around a large population of luminous QSOs at lower redshifts. This suggests that QSO outflows are closer to the energy-driven limit than to the momentum-driven limit. We investigated the stability of the expanding gas shell in the case of an energy-driven supersonic outflow propagating within a dark matter halo with M h = 3 × 10 11 M at z=6. We found that the shell is Rayleigh-Taylor unstable already at early times and, by means of a simple model, we investigated the fate of the fragments detaching from the shell. We found that these fragments should rapidly evaporate because of the extremely high temperature of the hot gas bubble if this does not cool. Since the only effective cooling mechanism for such a gas is inverse Compton by the cosmic microwave background (CMB) photons (IC-CMB), which is important only at z ≥ 6, we speculate that such shell fragments may be observed only around high-z QSOs, where IC-CMB cooling of the bubble gas can prevent their evaporation.

X-Ray Properties of AGN in Brightest Cluster Galaxies. I. A Systematic Study of the Chandra Archive in the 0.2 < z < 0.3 and 0.55 < z < 0.75 Redshift Range

“…During CCA, the clouds collide inelastically within r<500 pc, promoting rapid radial funneling down to a few tens gravitational radii, hence rapidly boosting the accretion rate, without the requirement of a thin disk. In addition, shells of gas lifted by powerful AGN outflows may fragment through Rayleigh-Taylor instabilities and produce clouds of cooling gas that may eventually fall back toward the black hole and contribute to its feeding (e.g., Gilli et al 2017). This process affects both the shape of the average nuclear luminosity of the BCG and its variance.…”

Active galactic nucleus outflows in galaxy discs

“…The accretion rate and hence the AGN luminosity oscillate by up to two orders of magnitude on time-scales of several thousand years, shorter than the lifetime of the AGN in our model. Gilli et al (2017) investigate galactic outflows driven by an AGN with exponentially increasing luminosity, i.e. they self-consistently account for the mass growth of the central BH at constant Eddington ratio.…”

Discovery of a galaxy overdensity around a powerful, heavily obscured FRII radio galaxy atz= 1.7: star formation promoted by large-scale AGN feedback?

“…Note that R 0 is not R(t = 0); seeGilli et al (2017).Article number, page 15 of 17 A&A proofs: manuscript no. 36121corr…”

“…As the cooling time of the shock-heated gas is expected to be longer than the AGN lifetime, we refer to the case of an energy-driven outflow, that is, to Eqs. 16 and 15 in Gilli et al (2017), which describe the temporal evolution of the bubble radius R(t) and its normalization R 0 , respectively 6 . These equations, which were derived for radio-quiet AGN, can be extended to jetted sources by considering that the gravitational energy of the matter falling toward the black hole is dissipated not only through radiation from the accretion disk (L rad ), but also through jet launching (P jet ).…”