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Pseudo-viscous modeling of self-gravitating discs and the formation of low mass ratio binaries

We present analytic models for the local structure of self-regulated self-gravit ating accretion discs that are subject to realistic cooling. Such an approach can be used to predict the secular evolution of self-gravitating discs (which can usefully be compared with future radiation hydrodynamical simulations) and to define various physical regimes as a function of radius and equivalent steady state accretion rate. We show that fragmentation is inevitable, given realistic rates of infall into the disc, once the disc extends to radii $> 70$ A.U. (in the case of a solar mass central object). Owing to the outward redistribution of disc material by gravitational torques, we also predict fragmentation at $> 70$ A.U. even in the case of low angular momentum cores which initially collapse to a much smaller radius. We point out that 70 A.U. is close to the median binary separation and propose that such delayed fragmentation, at the point that the disc expands to $> 70$ A.U., ensures the creation of low mass ratio companions that can avoid substantial further growth and consequent evolution towards unit mass ratio. We thus propose this as a promising mechanism for producing low mass ratio binaries, which, while abundant observationally, are severely underproduced in hydrodynamical models.