Chemical abundances in the inner 5 kpc of the Galactic disk

High-resolution, high signal-to-noise spectral data are presented for four young B-type stars lying towards the Galactic Centre. Determination of their atmospheric parameters from their absorption line profiles, and uvby photometric measurement of the continua indicate that they are massive objects lying slightly out of the plane, and were probably born in the disk between 2.5-5 kpc from the Centre. We have carried out a detailed absolute and differential line-by-line abundance analyses of the four stars compared to two stars with very similar atmospheric parameters in the solar neighbourhood. The stars appear to be rich in all the well sampled chemical elements (C, N, Si, Mg, S, Al), except for oxygen. Oxygen abundances derived in the atmospheres of these four stars are very similar to that in the solar neighbourhood. If the photospheric composition of these young stars is reflective of the gaseous ISM in the inner Galaxy, then the values derived for the enhanced metals are in excellent agreement with the extrapolation of the Galactic abundance gradients previously derived by Rolleston et al. (2000) and others. However, the data for oxygen suggests that the inner Galaxy may not be richer than normal in this element, and the physical reasons for such a scenario are unclear.

Molecular Hydrogen Emission from Protoplanetary Disks: Effects of X-ray Irradiation and Dust Evolution

Detailed models for the density and temperature profiles of gas and dust in protoplanetary disks are constructed by taking into account X-ray and UV irradiation from a central T Tauri star, as well as dust size growth and settling toward the disk midplane. The spatial and size distributions of dust grains are numerically computed by solving the coagulation equation for settling dust particles, with the result that the mass and total surface area of dust grains per unit volume of the gas in the disks are very small, except at the midplane. The H2 level populations and line emission are calculated using the derived physical structure of the disks. X-ray irradiation is the dominant heating source of the gas in the inner disk and in the surface layer, while the UV heating dominates otherwise. If the central star has strong X-ray and weak UV radiation, the H2 level populations are controlled by X-ray pumping, and the X-rayinduced transition lines could be observable. If the UV irradiation is strong, the level populations are controlled by thermal collisions or UV pumping, depending on the dust properties. As the dust particles evolve in the disks, the gas temperature at the disk surface drops because the grain photoelectric heating becomes less efficient. This makes the level populations change from LTE to non-LTE distributions, which results in changes to the line ratios. Our results suggest that dust evolution in protoplanetary disks could be observable through the H2 line ratios. The emission lines are strong from disks irradiated by strong UV and X-rays and possessing small dust grains; such disks will be good targets in which to observe H2 emission.

Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.