Astron. Astrophys. 344, 433–449 (1999) ASTRONOMY AND ASTROPHYSICS Star formation and evolution in accretion disks around massive black holes Star formation and evolution in accretion disks Suzy Collin1,2 and Jean-Paul Zahn1 1 Observatoire de Paris, Section de Meudon, F-92195 Meudon, France 2 Research Associate at Institut d’Astrophysique, Paris Received 23 October 1998 / Accepted 4 January 1999 Abstract. We develop an exploratory model for the outer, grav- mass transport in the intermediate region of the disk where itationally unstable regions of accretion disks around massive global instabilities do not work. As a first consequence, it could 6 10 black holes. We consider black holes of mass 10 to 10 M , explain the high velocity metal enriched outflows implied by and primeval or solar abundances. In a first step we study star the presence of the broad absorption lines in quasars. As a sec- formation and evolution in a purely gaseous marginally unsta- ond consequence it could account for a pregalactic enrichment ble disk, and we show that unstable fragments should collapse of the intergalactic medium, if black holes formed early in the rapidly and give rise to compact objects (planets or protostars), Universe. Finally it could provide a triggering mechanism for which then accrete at a high rate and in less than 106 years starbursts in the central regions of galaxies. A check of the model acquire a mass of a few tens of M , according to a mecha- would be to detect a supernova exploding within a few parsecs nism first proposed by Artymowicz et al. (1993). When these from the center of an AGN, an observation which can be per- stars explode as supernovae, the supernova shells break out of formed in the near future. the disk, producing strong outflows. We show that the gaseous disk is able to support a large number of massive stars and su- Key words: accretion, accretion disks – black hole physics – pernovae while staying relatively homogeneous. An interesting stars: supernovae: general – galaxies: active – galaxies: nuclei aspect is that the residual neutron stars can undergo other accre- – galaxies: quasars: general tion phases, leading to other (presumably powerful) supernova explosions. In a second step we assume that the regions at the periphery of the disk provide a quasi stationary mass inflow dur- 1. Introduction ing the lifetime of quasars or of their progenitors, i.e. 108 yrs, and that the whole mass transport is ensured by the supernovae,∼ It is now a paradigm to state that quasars and Active Galac- which induce a transfer of angular momentum towards the ex- tic Nuclei (AGN) harbour massive black holes in their centers terior, as shown by the numerical simulations of Rozyczka et (Rees 1984). Massive black holes exist also at the center of qui- al. (1995). Assuming that the star formation rate is proportional escent galaxies like ours. In quasars and AGN the accretion rate to the growth rate of the gravitational instability, we solve the amounts to a fraction of the critical one. This rate of accretion disk structure and determine the gas and the stellar densities, of this black hole must be sustained during at least 108 yrs to the heating being provided mainly by the stars themselves. We account for the total mass of the black holes locked in quasars find self-consistent solutions in which the gas is maintained in and for the fraction of AGN among all galaxies (cf. for instance a state very close to gravitational instability, in a ring located Cavaliere & Padovani 1988 and 1989). Since the gas fueling 6 between 0.1 and 10 pc for a black hole mass of 10 M , and the black hole at such a high rate cannot be produced inside the 8 between 1 and 100 pc for a black hole mass of 10 M or larger, central parsec (except if there is a preexisting dense star cluster, whatever the abundances, and for relatively low accretion rates through star collisions, tidal disruptions, or ablation) a process ( 10% of the critical accretion rate). For larger accretion rates for supplying gas from larger distances is necessary, whatever the≤ number of stars becomes so large that they inhibit any fur- it is. This will be a prerequisite of our study. ther star formation, and/or the rate of supernovae is so high that There is a large concensus that AGN are fueled via accretion they distroy the homogeneity and the marginal stability of the disks. Moreover the observation of the “UV bump” (Shields disk. We postpone the study of this case. 1978, Malkan & Sargent 1982, and many subsequent papers) Several consequences of this model can be envisioned, be- argues in favor of geometrically thin and optically thick disks, sides the fact that it proposes a solution to the problem of the possibly embedded in a hot X-ray emitting corona. Generally these disks are studied using the α prescription for viscosity Send offprint requests to: Suzy Collin (Observatoire de Meudon) introduced by Shakura and Sunayev (1973). It is well known 434 S. Collin & J.-P. Zahn: Star formation and evolution in accretion disks that these “α-disks” have two serious problems at large radii: In this case the disk would probably be made of discrete in- they are not able to transport rapidly enough the gas from regions teracting clouds. In order that the disk stays homogeneous, the located at say one parsec, and they are gravitationally unstable mechanism providing the heating and the angular momentum beyond about 0.1 parsec. They should therefore give rise to transport should not perturb too much the gaseous component. star formation, and as a consequence evolve rapidly towards An important part of this paper is devoted to verify that this stellar systems whose properties are quite different from gaseous condition is fulfilled in our model. accretion disks. Second we stress that the assumption of stationarity is not The suggestion of star formation in the self-gravitating re- constraining, as the properties of marginally unstable disks de- gion of such an accretion disk has been first made by Kolykhalov pend very little on the accretion rate (in particular the density & Sunayev (1980). Begelman et al. (1989) and Shlosman & profile depends only on the central mass), and moreover the Begelman (1989) discussed in more details the conditions for model is a local one (i.e. the different rings are independent). star formation at about 1–10 pc from the black hole, and its con- Variations of the accretion rate with radius, due for instance to sequences on the disk. They concluded that unless the disk can infall of gas, should simply induce small variations of the surface be maintained in a hot or highly turbulent state, it should trans- density and of the midplane temperature. The only assumption form rapidly into a flat stellar system which will be unable to linked to stationarity in Paper 1 was to take the luminosity of build a new gaseous accretion disk and to fuel a quasar (note the central source as given by the accretion rate in the gravi- that they apparently did not take into account the influence of tationally unstable region. But it was shown that this external self-gravity on the scale height, which would even strengthen radiation has not a strong influence on the radial structure. this conclusion). It is why they finally adopt the picture of a disk It is also worth noting that in Paper 1 the disk was actually made of marginally unstable randomly moving clouds, where not supposed to be exactly marginally unstable, since all results the “viscosity” of the disk is provided by cloud collisions. Here were parametrized with ζ, the ratio of the disk self-gravity to we adopt the opposite view that if a marginally unstable frag- the vertical component of the central attraction. The results are ments begin to collapse owing to a local increase of density for valid provided that this quantity is not much larger than unity instance, the collapse will continue until a protostar is formed, (for marginal stability, ζ =4.83, cf. later). Again we stress that unless the collapse time is larger than the characteristic time for it is a local quantity, which can vary from place to place in the mass transport in the disk. disk. Farther from the center the supply of gas can be achieved In Paper 1 the heating of the disk was assumed due to dis- by gravitational torques or by global non axisymmetric gravita- sipation of the gravitational energy of the accreting flow (for tional instabilities. However this does not solve the problem of which we use the word “viscous heating”, although it might the mass transport in the intermediate region where the disk is not be due to viscosity) and to the external radiative heating. locally but not globally self-gravitating, and one cannot avoid For a disk made of stars and gas, other sources of heating can appealing for a mechanism to transport angular momentum. play a role, and one should take them into account. Note finally This can be achieved by magnetic torques if large scale mag- that the mechanism for momentum and mass transport was not netic fields are anchored in the disk. We shall assume here that specified in Paper 1. neither turbulent nor large scale magnetic fields are important Here our approach will be as follows. First we assume the in accretion disks, and examine whether it is possible to find a existence of a marginally unstable gaseous disk, and discuss the solution to the problem of the existence of a quasi continuous formation of stars, their evolution, and the feedback of the stars.