Two New and Remarkable Sightlines through the Galactic Center's Molecular Gas

Until now the known sources in the Galactic center with sufficiently smooth spectra and of sufficient brightness to be suitable for high resolution infrared absorption spectroscopy of interstellar gas occupied a narrow range of longitudes, from the central cluster of hot stars to approximately 30 pc east of the center. In order to more fully characterize the gas within the r ~ 180 pc central molecular zone it is necessary to find additional such sources that cover a much wider longitudinal range. We are in the process of identifying luminous dust-embedded objects suitable for spectroscopy within 1.2 deg in longitude and 0.1 deg in latitude of Sgr A* using the Spitzer GLIMPSE and the 2MASS catalogues. Here we present spectra of H3+ and CO towards two such objects, one located 140 pc west of Sgr A*, and the other located on a line of sight to the Sgr B molecular cloud complex 85 pc to the east of Sgr A*. The sightline to the west passes through two dense clouds of unusually high negative velocities and also appears to sample a portion of the expanding molecular ring. The spectra toward Sgr B reveal at least ten absorption components covering over 200 km/s and by far the largest equivalent width ever observed in an interstellar H3+line; they appear to provide the first near-infrared view into that hotbed of star formation.Comment: 13 pages, incl. 4 figures - accepted by ApJ Letters Dec 14, 2009; minor typos correcte

Intersection numbers and twisted period relations for the generalized hypergeometric function m+1Fm{}_{m+1} F_m

We study the generalized hypergeometric function ${}_{m+1} F_m$ and the differential equation ${}_{m+1}E_m$ satisfied by it. We use the twisted (co)homology groups associated with an integral representation of Euler type. We evaluate the intersection numbers of some twisted cocycles which are defined as $m$-th exterior products of logarithmic $1$-forms. We also give twisted cycles corresponding to the series solutions to ${}_{m+1}E_m$, and evaluate the intersection numbers of them. These intersection numbers of the twisted (co)cycles lead twisted period relations which give relations for two fundamental systems of solutions to ${}_{m+1}E_m$.Comment: 13 page