On the effect of gas drag on the dust dynamics

We investigate in this paper the effect of gas drag on the dynamics of the dust particles in the edge-on β Pictoris disc in order to derive an upper limit on the mass of gas in this system. Our study is motivated by the large uncertainties on the amount of gas in the β Pictoris disc currently found in the literature. The dust particles are assumed to originate from a colliding annulus of planetesimals peaked around 100AU from the central star as proposed by Augereau et al. (2001). We consider the various gas densities that have been inferred from independent observing techniques and we discuss their impact on the dust dynamics and on the disc profile in scattered light along the midplane. We show that the observed scattered light profile of the disc cannot be properly reproduced if the hygrogen gas number density at 117AU exceeds 10 cm. This corresponds to an upper limit on the total gas mass of about 0.4M⊕ assuming the gas density profile inferred by Brandeker et al. (2004) and thus to a gas to dust mass ratio smaller than 1. Our approach therefore provides an independent diagnostic for a gas depletion in the β Pictoris system relative to the dust disc. Such an approach could also be used to constrain the gas content of recently identified systems like the edge-on disc around AUMic.