2.6. Stellar Collisions

There is a tight analogy between the tidal disruption of stars by the black hole and the disruption of two stars during a head-on collision. The factor = v_coll / v_* (v_* = 500km/s for a solar mass star) regulates the fate of collisions, and is equivalent to the factor of penetration of the star inside the tidal radius R_T / r_peri, where r_peri is the pericenter of the stellar orbit.

• if = 1, the collision occurs near the collision radius R_coll, there is coalescence of the two stars; the result may quickly explodes as a supernova.

• if > 1 a fraction of the mass is lost, and fuels the black hole.

• if >> 1 (well inside R_coll), a deformation in pancakes occurs, very similar to the tidal disruption, when R_T / r_peri >> 1. Gas and debris are bound to the black hole.

Stellar collisions help to refill the loss-cone, although they flatten the stellar cusp (Rauch 1999). The collisions rate is comparable to the diffusion rate, that refill the central core.

It is now generally accepted that for low density nuclei, stellar evolution and tidal disruption is the main mechanism to bring matter to the black hole, and for high density nuclei, stellar collisions dominate the gas fueling. The evolution of the stellar density through these processes is then opposite, and accentuates the differences: - for n < 10⁷ / pc³ the core then expands, due to heating that results from the settling of a small population of stars into orbits tightly bound to the black hole; - for n > 10⁷ / pc³, the core shrinks due to the removal of kinetic energy by collisions. To give an order of magnitude, the nuclear density in our own Galaxy is estimated at 10⁸ M / pc³ (Eckart et al 1993).

These mechanisms produce differing power-law slopes in the resulting stellar density cusp surrounding the black hole, -7/4 and -1/2 for low- and high-density nuclei, respectively (Murphy et al 1991, Rauch 1999). In simulations however (Rauch 1999), collisions tend to produce a flat core, instead of r^-1/2 law in Fokker-PLank studies, which imply isotropy (and are unable to treat sparse regions).

Finally, stellar collisions could explain both the high luminosities (up to 10⁴⁵ ergs/s, Spitzer & Saslaw 1966, Colgate 1967), and the variability of some QSOs (~ 10yr scale) according to Courvoisier et al (1996), see figure 3.

Figure 3. Light curve produced by the energy released in star collisions, with a collision rate of = 12 collisions per yr, provided for instance by a star cluster of mass 107 M, a core radius of Rc = 0.001 pc, surrounding a black hole of mass 109 M (from Torricelli-Campioni et al 2000).

But still, even with collisions, the most active quasars requiring 100 M / yr remain to be fueled. May be the gas from stars disruption can be stored in a disk, and suddenly poured in a burst of activity ? (Shields & Wheeler 1978). There might be tight relations with nuclear starbursts (Norman & Scoville 1988, Perry 1992, Williams et al 1999).