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

Unveiling Extragalactic Star Formation Using Radio Recombination Lines: An Expanded Very Large Array Pilot Study With Ngc 253

Radio recombination lines (RRLs) are powerful, extinction-free diagnostics of the ionized gas in young, star-forming regions. Unfortunately, these lines are difficult to detect in external galaxies. We present the results of Expanded Very Large Array (EVLA) observations of the RRL and radio continuum emission at 33 GHz from NGC 253, a nearby nuclear starburst galaxy. We detect the previously unobserved H58{alpha} and H59{alpha} RRLs and make simultaneous sensitive measurements of the continuum. We measure integrated line fluxes of 44.3 {+-} 0.7 W m{sup -2} and 39.9 {+-} 0.8 W m{sup -2} for the H58{alpha} and H59{alpha} lines, respectively. The thermal gas in NGC 253 is kinematically complex with multiple velocity components. We constrain the density of the thermal gas to (1.4-4) x 10{sup 4} cm{sup -3} and estimate an ionizing photon flux of 1 x 10{sup 53} s{sup -1}. We use the RRL kinematics and the derived ionizing photon flux to show that the nuclear region of NGC 253 is not gravitationally bound, which is consistent with the outflow of gas inferred from the X-ray and H{alpha} measurements. The line profiles, fluxes, and kinematics of the H58{alpha} and H59{alpha} lines agree with those of RRLs at different frequencies confirming themore » accuracy of the previous, more difficult, high-frequency observations. We find that the EVLA is an order of magnitude more efficient for extragalactic RRL observations than the Very Large Array. These observations demonstrate both the power of the EVLA and the future potential of extragalactic RRL studies with the EVLA.« les

Unveiling Extragalactic Star Formation Using Radio Recombination Lines: An EVLA Pilot Study with NGC 253

Radio recombination lines (RRLs) are powerful, extinction-free diagnostics of the ionized gas in young, star-forming regions. Unfortunately, these lines are difficult to detect in external galaxies. We present the results of EVLA observations of the RRL and radio continuum emission at 33 GHz from NGC 253, a nearby nuclear starburst galaxy. We detect the previously unobserved H58a and H59a RRLs and make simultaneous sensitive measurements of the continuum. We measure integrated line fluxes of $44.3 \pm 0.7$ W m$^{-2}$ and $39.9 \pm 0.8$ W m$^{-2}$ for the H58a and H59a lines, respectively. The thermal gas in NGC 253 is kinematically complex with multiple velocity components. We constrain the density of the thermal gas to $1.4 - 4 \times 10^4$ cm$^{-3}$ and estimate an ionizing photon flux of $1 \times 10^{53}$ s$^{-1}$. We use the RRL kinematics and the derived ionizing photon flux to show that the nuclear region of NGC 253 is not gravitationally bound, which is consistent with the outflow of gas inferred from the X-ray and Halpha measurements. The line profiles, fluxes, and kinematics of the H58a and H59a lines agree with those of RRLs at different frequencies confirming the accuracy of the previous, more difficult, high frequency observations. We find that the EVLA is an order of magnitude more efficient for extragalactic RRL observations than the VLA. These observations demonstrate both the power of the EVLA and the future potential of extragalactic RRL studies with the EVLA.Comment: Accepted for publication in the ApJL EVLA Special Issue. Version with high resolution figures at http://www.astro.virginia.edu/~aak8t/data/rrl/ms.p

Rank rigidity for CAT(0) cube complexes

We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube complexes. We derive a number of other consequences for CAT(0) cube complexes, including a purely geometric proof of the Tits Alternative, an existence result for regular elements in (possibly non-uniform) lattices acting on cube complexes, and a characterization of products of trees in terms of bounded cohomology.Comment: 39 pages, 4 figures. Revised version according to referee repor

Analytic geometry of semisimple coalescent Frobenius structures

We present some results of a joint paper with Dubrovin (see references), as exposed at the Workshop "Asymptotic and Computational Aspects of Complex Differential Equations" at the CRM in Pisa, in February 2017. The analytical description of semisimple Frobenius manifolds is extended at semisimple coalescence points, namely points with some coalescing canonical coordinates although the corresponding Frobenius algebra is semisimple. After summarizing and revisiting the theory of the monodromy local invariants of semisimple Frobenius manifolds, as introduced by Dubrovin, it is shown how the definition of monodromy data can be extended also at semisimple coalescence points. Furthermore, a local Isomonodromy theorem at semisimple coalescence points is presented. Some examples of computation are taken from the quantum cohomologies of complex Grassmannians

Radio Recombination Lines in Galactic HII Regions

We report radio recombination line (RRL) and continuum observations of a sample of 106 Galactic HII regions made with the NRAO 140 Foot radio telescope in Green Bank, WV. We believe this to be the most sensitive RRL survey ever made for a sample this large. Most of our source integration times range between 6 and 90 hours which yield typical r.m.s. noise levels of 1.0--3.5 milliKelvins. Our data result from two different experiments performed, calibrated, and analyzed in similar ways. A CII survey was made at 3.5 cm wavelength to obtain accurate measurements of carbon radio recombination lines. When combined with atomic (CI) and molecular (CO) data, these measurements will constrain the composition, structure, kinematics, and physical properties of the photodissociation regions that lie on the edges of HII regions. A second survey was made at 3.5 cm wavelength to determine the abundance of 3He in the interstellar medium of the Milky Way. Together with measurements of the 3He+ hyperfine line we get high precision RRL parameters for H, 4He, and C. Here we discuss significant improvements in these data, with both longer integrations and newly observed sources.Comment: LaTeX, 50 pages with 11 figures. Accepted for publication in The Astrophysical Journal Supplement Serie

Sensitive Observations of Radio Recombination Lines in Orion and W51: The Data and Detection of Systematic Recombination Line Blueshifts Proportional to Impact Broadening

Sensitive spectral observations made in two frequency bands near 6.0 and 17.6 GHz are described for Orion and W51. Using frequency switching we were able to achieve a dynamic range in excess of 10,000 without fitting sinusoidal or polynomial baselines. This enabled us to detect lines as weak as T$_{A} ~1mK in these strong continuum sources. Hydrogen recombination lines with$\Delta n$ as high as 25 have been detected in Orion. In the Orion data, where the lines are stronger, we have also detected a systematic shift in the line center frequencies proportional to linewidth that cannot be explained by normal optical depth effects.Comment: 22 pages, 13 figures. Accepted for publication in Astrophysics and Space Scienc