Can gas in young debris disks be constrained by their radial brightness profiles ?

Disks around young stars are known to evolve from optically thick, gas-dominated protoplanetary disks to optically thin, almost gasfree debris disks. It is thought that the primordial gas is largely removed at ages of ∼ 10 Myr and indeed, only little amounts of gas have been deduced from observations for debris disks at ages of >∼ 10 Myr. However, gas detections are difficult and often indirect, not allowing one to discern the true gas densities. This suggests using dynamical arguments: it has been argued that gas, if present with higher densities, would lead to flatter radial profiles of the dust density and brightness than those actually observed. In this paper, we systematically study the influence of gas on the radial profiles of brightness. We assume that dust is replenished by planetesimals orbiting in a “birth ring” and model the dust distribution and scattered-light brightness profile in the outer part of the disk exterior to the birth ring, under different assumptions about the gas component. Our numerical simulations, supported with an analytic model, show that the radial profile of dust density and the surface brightness are surprisingly insensitive to variation of the parameters of a central star, location of the dust-producing planetesimal belt, dustiness of the disk and — most importantly — the parameters of the ambient gas. The radial brightness slopes in the outer disks are all typically in the range −3...−4. This result holds for a wide range of gas densities (three orders of magnitude), for different radial profiles of the gas temperature, both for gas of solar composition and gas of strongly non-solar composition. The slopes of −3...−4 we find are the same that were theoretically found for gas-free debris disks, and they are the same as actually retrieved from observations of many debris disks. Our specific results for three young (10–30 Myr old), spatially resolved, edge-on debris disks (β Pic, HD 32297, and AU Mic) show that the observed radial profiles of the surface brightness do not pose any stringent constraints on the gas component of the disk. We cannot exclude that outer parts of the systems may have retained substantial amounts of primordial gas which is not evident in the gas observations (e.g. as much as 50 Earth masses for β Pic). However, the possibility that gas, most likely secondary, is only present in little to moderate amounts, as deduced from gas detections (e.g. ∼ 0.05 Earth masses in the β Pic disk or even less), remains open, too.