A Weyl-covariant tensor calculus

On a (pseudo-) Riemannian manifold of dimension n > 2, the space of tensors which transform covariantly under Weyl rescalings of the metric is built. This construction is related to a Weyl-covariant operator D whose commutator [D,D] gives the conformally invariant Weyl tensor plus the Cotton tensor. So-called generalized connections and their transformation laws under diffeomorphisms and Weyl rescalings are also derived. These results are obtained by application of BRST techniques.Comment: LaTeX, 10 pages. Minor corrections and a reference adde

Photoelectric effect on dust grains across the L1721 cloud in the rho Ophiuchi molecular complex

We present ISO-LWS measurements of the main gas cooling lines, C+ 158 mum and O 63 mum towards a moderate opacity molecular cloud (Av=3), L1721, illuminated by the B2 star nu Sco (X = 5-10). These data are combined with an extinction map and IRAS dust emission images to test our understanding of gas heating and cooling in photo-dissociation regions (PDRs). This nearby PDR is spatially resolved in the IRAS images; variations in the IRAS colors across the cloud indicate an enhanced abundance of small dust grains within the PDR. A spatial correlation between the gas cooling lines and the infrared emission from small dust grains illustrates the dominant role of small dust grains in the gas heating through the photoelectric effect. The photoelectric efficiency, determined from the observations by ratioing the power radiated by gas and small dust grains, is in the range 2 to 3% in close agreement with recent theoretical estimates. The brightness profiles across the PDR in the C+ 158 mum and O 63 mum lines are compared with model calculations where the density profile is constrained by the extinction data and where the gas chemical and thermal balances are solved at each position. We show that abundance variations of small dust grains across the PDR must be considered to account for the LWS observations.Comment: 10 pages, 15 figure