The Electron Temperature Gradient in the Galactic Disk

We derive the electron temperature gradient in the Galactic disk using a sample of HII regions that spans Galactocentric distances 0--17 kpc. The electron temperature was calculated using high precision radio recombination line and continuum observations for more than 100 HII regions. Nebular Galactocentric distances were calculated in a consistent manner using the radial velocities measured by our radio recombination line survey. The large number of nebulae widely distributed over the Galactic disk together with the uniformity of our data provide a secure estimate of the present electron temperature gradient in the Milky Way. Because metals are the main coolants in the photoionized gas, the electron temperature along the Galactic disk should be directly related to the distribution of heavy elements in the Milky Way. Our best estimate of the electron temperature gradient is derived from a sample of 76 sources for which we have the highest quality data. The present gradient in electron temperature has a minimum at the Galactic Center and rises at a rate of 287 +/- 46 K/kpc. There are no significant variations in the value of the gradient as a function of Galactocentric radius or azimuth. The scatter we find in the HII region electron temperatures at a given Galactocentric radius is not due to observational error, but rather to intrinsic fluctuations in these temperatures which are almost certainly due to fluctuations in the nebular heavy element abundances. Comparing the HII region gradient with the much steeper gradient found for planetary nebulae suggests that the electron temperature gradient evolves with time, becoming flatter as a consequence of the chemical evolution of the Milky Way's disk.Comment: 43 pages, 9 figures (accepted for publication in the ApJ

Deformations with a resonant irregular singularity

I review topics of my talk in Alcal\ue1, inspired by the paper [1]. An isomonodromic system with irregular singularity at z= 1e (and Fuchsian at z=0) is considered, such that z= 1e becomes resonant for some values of the deformation parameters. Namely, the eigenvalues of the leading matrix at z= 1e coalesce along a locus in the space of deformation parameters. I give a complete extension of the isomonodromy deformation theory in this case

High-Mass Star Formation in the Outer Scutum-Centaurus Arm

The Outer Scutum-Centaurus (OSC) spiral arm is the most distant molecular spiral arm in the Milky Way, but until recently little was known about this structure. Discovered by Dame and Thaddeus (2011), the OSC lies $\sim$15 kpc from the Galactic Center. Due to the Galactic warp, it rises to nearly 4$^{\circ}$ above the Galactic Plane in the first Galactic quadrant, leaving it unsampled by most Galactic plane surveys. Here we observe HII region candidates spatially coincident with the OSC using the Very Large Array to image radio continuum emission from 65 targets and the Green Bank Telescope to search for ammonia and water maser emission from 75 targets. This sample, drawn from the WISE Catalog of Galactic HII Regions, represents every HII region candidate near the longitude-latitude (l,v) locus of the OSC. Coupled with their characteristic mid-infrared morphologies, detection of radio continuum emission strongly suggests that a target is a bona fide HII region. Detections of associated ammonia or water maser emission allow us to derive a kinematic distance and determine if the velocity of the region is consistent with that of the OSC. Nearly 60% of the observed sources were detected in radio continuum, and over 20% have ammonia or water maser detections. The velocities of these sources mainly place them beyond the Solar orbit. These very distant high-mass stars have stellar spectral types as early as O4. We associate high-mass star formation at 2 new locations with the OSC, increasing the total number of detected HII regions in the OSC to 12.Comment: 14 pages text and tables + 10 pages supplemental figure

Hyperasymptotic solutions for certain partial differential equations

We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel summability, which allows us to find integral representations of solutions for such PDEs.Comment: 17 page

Riemann-Hilbert problem for Hurwitz Frobenius manifolds: regular singularities

In this paper we study the Fuchsian Riemann-Hilbert (inverse monodromy) problem corresponding to Frobenius structures on Hurwitz spaces. We find a solution to this Riemann-Hilbert problem in terms of integrals of certain meromorphic differentials over a basis of an appropriate relative homology space, study the corresponding monodromy group and compute the monodromy matrices explicitly for various special cases.Comment: final versio