Radiation drag driven mass accretion in a clumpy interstellar medium: implications for the supermassive black hole-to-bulge relation

Nozomu KawakatuP 0 Masayuki UmemuraP 0 0 Centre for Computational Physics, University of Tsukuba , Tsukuba, Ibaraki 305 , Japan We quantitatively scrutinize the effects of the radiation drag arising from the radiation fields in a galactic bulge in order to examine the possibility that the radiation drag could be an effective mechanism to extract angular momentum in a spheroidal system like a bulge and allow plenty of gas to accrete on to the galactic centre. For this purpose, we numerically solve the relativistic radiation hydrodynamical equation coupled with accurate radiative transfer, and quantitatively assess the radiation drag efficiency. As a result, we find that in an optically thick regime the radiation drag efficiency is sensitively dependent on the density distributions of the interstellar medium (ISM). The efficiency drops according to t22 in an optically thick T uniform ISM, where tT is the total optical depth of the dusty ISM, whereas the efficiency remains almost constant at a high level if the ISM is clumpy. Hence, if bulge formation begins with a star formation event in a clumpy ISM, the radiation drag will effectively work to remove the angular momentum and the accreted gas may form a supermassive black hole. As a natural consequence, this mechanism reproduces a putative linear relation between the mass of a supermassive black hole and the mass of a galactic bulge, although further detailed modelling for stellar evolution is required for a more precise prediction. I N T R O D U C T I O N Recently, Kormendy & Richstone (1995) have pioneeringly suggested that the mass of a supermassive black hole (BH) does correlate linearly with the mass of the host bulge. (It is noted that the term bulge is used to mean a whole galaxy for an elliptical galaxy in this paper, as is often so.) Further high-quality observations of the galactic centre using stellar dynamics, gas dynamics and maser dynamics (Miyoshi et al. 1995; Magorrian et al. 1998; Richstone et al. 1998; Ho 1999; Wandel 1999; Kormendy & Ho 2000; Gebhardt et al. 2000b; Ferrarese et al. 2001; Sarzi et al. 2001; Merritt & Ferrarese 2001a) allow us to make a detailed demography of supermassive BHs. The recent findings are the following. (1) The BH mass exhibits a linear relation to the bulge mass for a wide range of BH mass with a median BH mass fraction of f BH ; MBH=Mbulge 0:001 0:006 (Kormendy & Richstone 1995; Richstone et al. 1998; Magorrian et al. 1998; Gebhardt et al. 2000b; Ferrarese & Merritt 2000; Merritt & Ferrarese 2001a). (2) The BH mass correlates with the velocity dispersion of bulge stars with a power-law relation as MBH / s n, n 3:75 (Gebhardt et al. 2000a) or 4.72 (Ferrarese & Merritt 2000; Merritt & Ferrarese 2001a,b). (3) fBH tends to grow with the age of the youngest stars in a bulge until 109 yr (Merrifield, Forbes & Terlevich 2000). (4) In disc galaxies, the mass ratio is significantly smaller than 0.001 if the disc stars are included (Salucci et al. 2000; Sarzi et al. 2001). (5) For quasars, fBH is on a similar level to that for elliptical galaxies (Laor 1998; Mclure & Dunlop 2001a; Wandel 2001). (6) fBH in Seyfert 1 galaxies is under debate, and may be considerably smaller than 0.001 (Wandel 1999; Gebhardt et al. 2000b) or similar to that for ellipticals (McLure & Dunlop 2001a,b; Wandel 2001), while the BH mass-to-velocity dispersion relation in Seyfert 1 galaxies seems to hold good in a similar way to elliptical galaxies (Gebhardt et al. 2000a; Nelson 2000; Ferrarese et al. 2001). These BH-to-bulge correlations suggest that the formation of a supermassive BH is physically connected with the formation of a galactic bulge. So far, very little is understood about the physical mechanism to produce such correlations, although some theoretical models have been proposed (Silk & Rees 1998; Ostriker 2000; Adams, Graff & Richstone 2001). Recently, as a possible mechanism to work in a spheroidal system, Umemura (2001) has considered the effects of radiation drag. The radiation drag is a relativistic effect, which may extract angular momentum effectively in a spheroidal system like a bulge, so that plenty of interstellar medium (ISM) could accrete on to the galactic centre. Obviously, the radiation drag is inefficient in present-day elliptical galaxies or galactic bulges, since they possess little ISM. If the contents of a supermassive BH are initially in the form of ISM, however, the bulge must have been optically thick in the early stage: t < xrrb Mgas where x is the mass extinction coefficient due to dust opacity of the ISM, Mgas is the mass of the ISM, and rb is the bulge radius. If a considerable amount of gas is expelled by a galactic wind at some stage, the optical depth should be still larger before the wind. If the radiation drag works efficiently in an optically thick medium, the rate of mass accretion induced by the radiation drag is maximally Lbol=c 2 (Umemura, Fukue & Mineshige 1997, 1998; Fukue, Umemura & Mineshige 1997), where Lbol is the bolometric luminosity. Umemura (2001) has found that, if the maximal drag efficiency is achieved, the resultant BH-to-bulge mass ratio is basically determined by the energy conversion efficiency of the nuclear fusion from hydrogen to helium, i.e. 0.007. However, it is not very clear whether this mechanism really works efficiently in realistic situations. In this paper, we investigate in detail the efficiency of the radiation drag in an optically thick ISM to test whether the radiation drag model is promising to account for the putative BHto-bulge correlations. In particular, we concentrate our attention on the effects of the inhomogeneity in the ISM. The model for the chemical evolution of elliptical galaxies suggests that an elliptical galaxy is initiated by a starburst in its early stages (107 yr) and evolves passively after a galactic wind event at a few 108 yr (Arimoto & Yoshii, 1986, 1987; Kodama & Arimoto, 1997; Mori et al. 1997). Also, in nearby starburst galaxies that have been studied, the ISM is highly clumpy (Sanders et al. 1988; Gordon, Calzetti & Witt 1997). Thus, if we consider the radiation drag in the early phase of bulge evolution, we should consider an inhomogeneous optically thick ISM. In this paper, to elucidate the mutual effect between the clumpiness of the ISM and the optical depth on the radiation drag efficiency, we build up a simple model of the bulge system and accurately solve the radiation transfer in a clumpy ISM. The paper is organized as follows. In Section 2, we construct the model of a galactic bulge. In Section 3, the basic equations for the ISM are provided. In Section 4, the angular momentum transfer efficiency is assessed in a uniform ISM. In Section 5, we investigate the angular momentum transfer efficiency by solving the radiation transfer in a clumpy ISM, and elucidate the relationship between the clumpiness of the ISM and the angular momentum transfer efficiency. In Section 6, we give implicati (...truncated)