Hot accretion disks with electron-positron pair winds

It is well known that optically thick, geometrically thin accretion disks in black hole systems are unstable in their inner region. Evolving into hot, optically thin configurations, these environments can easily account for the gross features of the X-ray and γ-ray emission from sources such as Cygnus X-1 and 1E 1740.7-2942. Recent analysis of the stability criteria for such disks, however, have pointed to a critical accretion rate ṁ_cr above which electron-positron pair creation exceeds annihilation, and a runaway ensues, rendering the two-temperature corona unstable. On the assumption that they are 10 solar mass black holes, both these sources appear to be close to ṁ_cr - indeed, 1E 1740.7-2942 seems to exceed it. Knowing where objects such as this lie with respect to the stability cutoff is essential not only in terms of understanding the physical conditions near the central black hole, but because these systems are also prodigious sources of outflowing, energetic positrons the contribution to the pair flux from particles escaping the corona can be substantial when ṁ is close to ṁ_cr. However, drawing definite conclusions from the currently available analysis is premature given the approximate nature of the earlier studies. In this paper, we refine these analyses by employing a more accurate treatment of the Comptonization process throughout the corona, and we also include the energy loss associated with the escaping pairs in the overall energy balance equation. The pair outflux depends critically on the velocity of the escaping particles, which we here consider in the two extreme values of zero and the thermal velocity. We find that the combined effect of these improvements results in an overall increase in ṁ_cr by a factor of ∼0.5-3 when the pairs escape with the thermal velocity, but that the improved treatment of the Comptonization actually decreases ṁ_cr by about 30% when this velocity is zero. An application to Cygnus X-1 (assuming a mass of 10 M_⊙) shows that this source is supercritical if the velocity of the escaping pairs is zero, but it is subcritical when the escaping pair flux is maximal. In the latter case, as much as ∼50% of the power emitted by the corona is carried off by escaping electron-positron pairs. Under some conditions, this positron number flux can account for the annihilation line radiation and the extended radio jets observed in 1E 1740.7-2942.