Euler Integration of Gaussian Random Fields and Persistent Homology

In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to compute the expected Euler integral of a Gaussian random field using the Gaussian kinematic formula and obtain a simple closed form expression. This results in the first explicitly computable mean of a quantitative descriptor for the persistent homology of a Gaussian random field.Comment: 21 pages, 1 figur

The Keck Lyman Continuum Spectroscopic Survey (KLCS): The Emergent Ionizing Spectrum of Galaxies at z∼3z\sim3

We present results of a deep spectroscopic survey designed to quantify the statistics of the escape of ionizing photons from star-forming galaxies at z~3. We measure the ratio of ionizing to non-ionizing UV flux density _obs, where f900 is the mean flux density evaluated over the range [880,910] A. We quantify the emergent ratio of ionizing to non-ionizing UV flux density by analyzing high-S/N composite spectra formed from sub-samples with common observed properties and numbers sufficient to reduce the statistical uncertainty in the modeled IGM+CGM correction to obtain precise values of _out, including a full-sample average _out=$0.057\pm0.006$. We further show that _out increases monotonically with Ly$\alpha$ rest equivalent width, inducing an inverse correlation with UV luminosity as a by-product. We fit the composite spectra using stellar spectral synthesis together with models of the ISM in which a fraction f_c of the stellar continuum is covered by gas with column density N(HI). We show that the composite spectra simultaneously constrain the intrinsic properties of the stars (L900/L1500)_int along with f_c, N(HI), E(B-V), and $f_{esc,abs}$, the absolute escape fraction of ionizing photons. We find a sample-averaged $f_{esc,abs} =0.09\pm0.01$, and that subsamples fall along a linear relation $\langle f_{esc,abs}\rangle \sim 0.75[W(Ly\alpha)/110 A]$. We use the FUV luminosity function, the distribution function $n[W(Ly\alpha)]$, and the relationship between $W(Ly\alpha)$ and _out to estimate the total ionizing emissivity of $z\sim3$ star-forming galaxies with Muv < -19.5: $\epsilon_{LyC}\sim 6\times10^{24}$ ergs/s/Hz/Mpc$^3$, exceeding the contribution of QSOs by a factor of $\sim 3$, and accounting for $\sim50$% of the total $\epsilon_{LyC}$ at $z\sim3$ estimated using indirect methods.Comment: 45 pages, 31 figures, ApJ, in pres

Instabilities and Clumping in Type Ia Supernova Remnants

We present two-dimensional high-resolution hydrodynamical simulations in spherical polar coordinates of a Type Ia supernova interacting with a constant density interstellar medium. The ejecta are assumed to be freely expanding with an exponential density profile. The interaction gives rise to a double-shocked structure susceptible to hydrodynamic instabilities. The Rayleigh-Taylor instability initially grows, but the Kelvin-Helmholtz instability takes over, producing vortex rings. The nonlinear instability initially evolves toward longer wavelengths and eventually fades away when the reverse shock front is in the flatter part of the supernova density distribution. Based on observations of X-ray knots and the protrusion in the southeast outlin of Tycho's supernova remnant, we include clumping in the ejecta. The clump interaction with the reverse shock induces Rayleigh-Taylor and Kelvin-Helmholtz instabilities on the clump surface that facilitate fragmentation. In order to survive crushing and to have a bulging effect on the forward shock, the clump's initial density ratio to the surrounding ejecta must be at least 100 for the conditions in Tycho's remnant. The 56Ni bubble effect may be important for the development of clumpiness in the ejecta. The observed presence of an Fe clump would then require a non-radioactive origin for this Fe, possibly 54Fe. The large radial distance of the X-ray emitting Si and S ejecta from the remnant center indicates that they were initially in clumps.Comment: 27 pages, 4 postscript figures, 5 GIF figures submitted to Astrophysical Journa

GRB 030329: 3 years of radio afterglow monitoring

Radio observations of gamma-ray burst (GRB) afterglows are essential for our understanding of the physics of relativistic blast waves, as they enable us to follow the evolution of GRB explosions much longer than the afterglows in any other wave band. We have performed a three-year monitoring campaign of GRB 030329 with the Westerbork Synthesis Radio Telescopes (WSRT) and the Giant Metrewave Radio Telescope (GMRT). Our observations, combined with observations at other wavelengths, have allowed us to determine the GRB blast wave physical parameters, such as the total burst energy and the ambient medium density, as well as investigate the jet nature of the relativistic outflow. Further, by modeling the late-time radio light curve of GRB 030329, we predict that the Low-Frequency Array (LOFAR, 30-240 MHz) will be able to observe afterglows of similar GRBs, and constrain the physics of the blast wave during its non-relativistic phase.Comment: 5 pages, 2 figures, Phil. Trans. R. Soc. A, vol.365, p.1241, proceedings of the Royal Society Scientific Discussion Meeting, London, September 200

Multifrequency VLA observations of the FR I radio galaxy 3C 31: morphology, spectrum and magnetic field

We present high-quality VLA images of the FR I radio galaxy 3C 31 in the frequency range 1365 to 8440 MHz with angular resolutions from 0.25 to 40 arcsec. Our new images reveal complex, well resolved filamentary substructure in the radio jets and tails. We also use these images to explore the spectral structure of 3C 31 on large and small scales. We infer the apparent magnetic field structure by correcting for Faraday rotation. Some of the intensity substructure in the jets is clearly related to structure in their apparent magnetic field: there are arcs of emission where the degree of linear polarization increases, with the apparent magnetic field parallel to the ridges of the arcs. The spectral indices are significantly steeper (0.62) within 7 arcsec of the nucleus than between 7 and 50 arcsec (0.52 - 0.57). The spectra of the jet edges are also slightly flatter than the average for their surroundings. At larger distances, the jets are clearly delimited from surrounding larger-scale emission both by their flatter radio spectra and by sharp brightness gradients. The spectral index of 0.62 in the first 7 arcsec of 3C 31's jets is very close to that found in other FR I galaxies where their jets first brighten in the radio and where X-ray synchrotron emission is most prominent. Farther from the nucleus, where the spectra flatten, X-ray emission is fainter relative to the radio. The brightest X-ray emission from FR I jets is therefore not associated with the flattest radio spectra, but with a particle-acceleration process whose characteristic energy index is 2.24. The spectral flattening with distance from the nucleus occurs where our relativistic jet models require deceleration, and the flatter-spectra at the jet edges may be associated with transverse velocity shear. (Slightly abridged)Comment: 17 pages, 13 figures, accepted for publication in MNRA

Fragmentation and Evolution of Molecular Clouds. I: Algorithm and First Results

We present a series of simulations of the fragmentation of a molecular cloud, leading to the formation of a cluster of protostellar cores. The purpose of these simulations is to address a specific numerical problem called artificial fragmentation, that plagues SPH simulations of cloud fragmentation. We argue that this is a serious problem that needs to be addressed, and that the only reasonable and practical way to address it is to use a relatively new technique called particle splitting. Our largest simulation has an effective resolution of 256^3 particles (much higher than most previous SPH simulations of cloud fragmentation) and results in the formation of a dense cluster containing ~3000 protostellar cores. It is the first simulation of this kind to properly resolve the Jeans mass throughout the entire system, at all times, thus preventing artificial fragmentation.Comment: 47 pages, 15 figures (2 grayscale, one color), ApJ Suppl, in pres