Some constraints on quasar progenitors and quasar evolution
Authors: Sivaram C. 
Published: July 2016

There is strong evidence that quasars are powered by the gravitational energy released by in fall of matter into a compact supermassive object which is most likely a black hole with mass M>106 to 109MO. The question then arises as to how such massive black holes came to be formed. What sort of objects were the progenitors? While looking for an answer we have to bear in mind another bit of intriguing evidence that even high Z quasars show lines of heavier elements (Oxygen, magnesium, etc) with solar abundances, strongly suggesting that matter had already undergone nuclear processing at even earlier epochs. Again even the oldest stars in our galaxy show evidence of metal content. All this suggests that atleast part of the metal content could have been generated by pregalactic supermassive stars, sometimes referred to as Pop.III objects. Such stars with masses ranging from 102–106 M⊙ could have formed in clusters consisting of about a few hundred or thousand of these objects at Z ⋍ 10. Now objects >106 M⊙ would have central temperatures not high enough for nuclear reactions the reason being a well known instability of general relativistic origin which is reached when GM/R⋍9c2/16 (M⊙/M)½; MO ⋍M⊙ giving rise to a maximum central temperature Tc reached at the instability, i.e. just before collapse. This is given by Tc = 2×1013/(M/MO) giving Tmax = 107K (necessary for CNO reactions) for M ⋍ 106M⊙ and for M> 106 M⊙, Tc is too low. It is believed that 10−5 of the primordial material might have been processed in Pop III objects which would have undergone nuclear reactions and evolved over some fraction of a Salpeter time, cσT/4πGmp ⋍ 108 yrs; (σT = Thompson cross section, mp is proton mass)., producing heavier elements in the process. It turns out that objects of mass M <300 M⊙ can explode and scatter the heavy elements. For instance a 116 M⊙ oxgen core of a 200MO object can completely disrupt and the evolution of such objects can explain anomalies like the O/Fe enrichment in metal poor stars and the G dwarf problem. Again there can be substantial mass loss from these superstars (a typical empirical relation like M ⋍ (tD/tKH)¼. L/GM/R (where tD is the dynamical time, and tKH is the Kelvin-Helmholtz scale, L is the luminosity) predicting · ≈ 10−3MO/yr) again leading to enrichment of the medium. Stars >300 MO do not explode but would collapse. The relaxation time scale for a cluster of these objects is again 5×108 to 109 yrs, so that they would all collapse to form a central black hole of M ∼ 108 −109 MO, the surrounding earlier ejected matter enriched in heavier elements being now accreted onto it. There would have been atleast a few times 108 of these black holes formed. Assuming near Eddington luminosity the rate of accretion given by ·(t) ⋍ 8πGM(t)/kc⋍16πG2M2(t)X ρ(t)V/c4, ρ(t) being a function of Z) would put a constraint on when Pop III stars formed and accreted enough matter to trigger quasar activity as quasars do not seem to be present before z = 4. This gives the result that they could not have formed before z ⋍8–10. Another possibility of forming a central black hole is by the collapse of a dense star cluster (consisting mainly of neutron stars or white dwarfs), the central relaxation time is tR∼VC3 / mc21n(0.4 Nc) ∼109yr. One obtains the result that for a core of compact stars to evolve to a relativistic state in a Hubble time it should have a minimal velocity dispersion given by Vc (min)⋍ 103(mc) (1-A/B) (7-3A/B)km/s, A, B are constants. This corresponds to clusters roughly having 107–109 compact stars and the gravitational collapse of such a cluster would then lead to black holes in the required mass range. An observed example is the central 3.5 pc core of NGC 4151 which has a mean stellar density of 2×108 M pc−3 corresponding to V ⋍ 103 km/s. As the central black hole grows the relative tidal force decreases and quasar activity can stop when the hole can no longer break up stars. (Tidal break up is also producing and scattering heavy elements.) For a central black hole accreting white dwarfs M <106MO and for it to break up neutron stars M <2 · 103MO. The break up of a neutron star by such a hole would give a burst of energy ∼1052ergs/sec which has so far not been recorded in any quasar or AGN, the upper limit to the luminosity being ∼1049 ergs/s. This may be indirect evidence that the mass of the central black hole is well above 104 MO in all cases. It is a pleasure to thank Professor Martin Rees for valuable discussions.