Radiation-Pressure Driven Wind Model

During the period of super-Eddington accretion and possibly beyond, the radiation pressure from the central BH would be sufficient to drive a wind. If this wind is driven by radiation pressure of the central source, then equations similar to those of hot stars apply. For the case of a magnetic wind externally illuminated by the central engine, the detailed theory has already been developed in a series of papers by Murray and his collaborators (Murray and Chiang, 1995; Murray et al. 1995; Chiang and Murray, 1996). However, in our case we would like to consider the possibility that the radiatively driven wind is both dense, so that it is not heated to the Compton temperature, and is optically thick to the escape of X- and - ray photons from the central source so that the continuum observed is produced by a reprocessing photosphere dominated by electron scattering opacity. Such geometry may apply in the high accretion rate limit. In this case, the momentum flux in the wind is given by:

 
where is the solid angle covered by the optically-thick radiatively-driven wind, subtended at the BH, and is the effective number of scatterings per photon. In stars, this factor is greater than unity; typically however, in Wolf-Rayet stars it may rise even higher. In such radiatively-driven winds, the outflow velocity is similar to the escape velocity at the base of the outflow, which in this case will be at the inner edge of the region of super-Eddington flow:

 
where is the mass of the BH in units of 10 and is the inner radius in units of 10cm. In stars, 1 typically. From 7 the number density in the wind is given by:

 
which corresponds to cm where is the luminosity of the BH in units of 10 ergs.s, and is the radius in units of 10cm and is the velocity of the wind in units of 10 km.s. The photospheric radius is set by the point where the electron scattering optical depth in the outflowing wind is unity, which for a constant-velocity wind gives:

 
where is the electron scattering opacity. Such photospheric radii are consistent with limits produced by variability studies and reverberation mapping analysis of nearby Sy I galaxies. The effective temperature of the photosphere is then determined from Stefan's Law, remembering that electron scattering photospheres have their radiation density diluted by a factor 10 with respect to a Black-Body emitter;

 
Thus, when the wind velocity is of order 20,000 km.s as implied by eqn. (8), the effective photospheric temperature is high enough ( 10 K) to provide a ``big blue bump'' in the continuum spectrum which, thanks to the high outflow velocity and the electron scattering, should provide only weak and broad photospheric lines. In addition, such electron scattering dominated extended atmospheres should show only a weak Lyman Limit discontinuity. It should be noted that the spectral distribution of such an electron scattering photosphere is not characterised by a simple temperature; the temperature given in eqn. (11) is only representative of the hardness of the spectrum. In general, such atmospheres give a power-law below the peak in emergent flux, and roll off sharply above this peak. This is the result of the fact that the peak temperature, given roughly by eqn. (11) is seen in the line of sight to the centre of the structure where the deepest penetration occurs. The photosphere occurs further out in annuli around this point, and so is characterised by lower electron temperatures. The contribution from these annuli produce the power-law extension of the spectrum to lower frequencies. The slope of this power-law depends on the effective curvature of the atmosphere, i.e. on the ratio This effect is very familiar to those who work on Wolf-Rayet stellar atmospheres (e.g. Abbott and Conti, 1987). In AGN, the value of this ratio is much higher than in Wolf-Rayet stars, so we expect them to be characterised by little curvature, and a rather flat power-law ( 1) at energies below the peak.

Since the photosphere is extended both above, and below the accretion disk, it can illuminate and photoionise the surface layers of the accretion disk. This would give the broad-line region in our model. Since the effective temperature decreases for higher BH luminosities, we would expect that this photoionisation would provide lower ionisation conditions in the more luminous AGN. This is presumably the explanation of the Baldwin Effect in QSOs (Baldwin (1977), Baldwin et al. (1978), where the CIV equivalent width and the ratio of C IV/ Ly is observed to decrease with increasing luminosity. This effect has been most comprehensively studied by Kinney, Rivolo and Koratkar (1990).

Equations (7), (8) and (10) imply together that:

 
consistency therefore requires if the BH luminosity is to be of the same order as the Eddington Limit. Equation (7) also implies that the mechanical energy flux in the wind is simply related to the bolometric luminosity of the central object:

 
Finally, we can relate the mass flux in the wind to the mass flux onto the BH, using Eqns (5) and (7):

 
Thus, the mass flux into the radiatively driven wind will dominate over the mass flux into the BH until the accretion disk becomes thin (

The outflowing radiative wind interacts directly with the accretion flow. The condition that the accretion flow is not seriously dynamically modified by this interaction is that the ram pressure in the wind is less than the ram pressure in the accretion flow. From eqn. (7) this implies that the BH luminosity ( in units of 10erg.s; ) is below where is the rate of mass accretion in units of 200 yr is the velocity of infall in units of 300 km.s and is the solid angle covered by the accretion flow.

© Copyright Astronomical Society of Australia 1997