A numerical method for efficient 3D inversions using Richards equation

Fluid flow in the vadose zone is governed by Richards equation; it is parameterized by hydraulic conductivity, which is a nonlinear function of pressure head. Investigations in the vadose zone typically require characterizing distributed hydraulic properties. Saturation or pressure head data may include direct measurements made from boreholes. Increasingly, proxy measurements from hydrogeophysics are being used to supply more spatially and temporally dense data sets. Inferring hydraulic parameters from such datasets requires the ability to efficiently solve and deterministically optimize the nonlinear time domain Richards equation. This is particularly important as the number of parameters to be estimated in a vadose zone inversion continues to grow. In this paper, we describe an efficient technique to invert for distributed hydraulic properties in 1D, 2D, and 3D. Our algorithm does not store the Jacobian, but rather computes the product with a vector, which allows the size of the inversion problem to become much larger than methods such as finite difference or automatic differentiation; which are constrained by computation and memory, respectively. We show our algorithm in practice for a 3D inversion of saturated hydraulic conductivity using saturation data through time. The code to run our examples is open source and the algorithm presented allows this inversion process to run on modest computational resources

The star-formation history of the universe - an infrared perspective

A simple and versatile parameterized approach to the star formation history allows a quantitative investigation of the constraints from far infrared and submillimetre counts and background intensity measurements. The models include four spectral components: infrared cirrus (emission from interstellar dust), an M82-like starburst, an Arp220-like starburst and an AGN dust torus. The 60 $\mu$m luminosity function is determined for each chosen rate of evolution using the PSCz redshift data for 15000 galaxies. The proportions of each spectral type as a function of 60 $\mu$m luminosity are chosen for consistency with IRAS and SCUBA colour-luminosity relations, and with the fraction of AGN as a function of luminosity found in 12 $\mu$m samples. The luminosity function for each component at any wavelength can then be calculated from the assumed spectral energy distributions. With assumptions about the optical seds corresponding to each component and, for the AGN component, the optical and near infrared counts can be accurately modelled. A good fit to the observed counts at 0.44, 2.2, 15, 60, 90, 175 and 850 $\mu$m can be found with pure luminosity evolution in all 3 cosmological models investigated: $\Omega_o$ = 1, $\Omega_o$ = 0.3 ($\Lambda$ = 0), and $\Omega_o$ = 0.3, $\Lambda$ = 0.7. All 3 models also give an acceptable fit to the integrated background spectrum. Selected predictions of the models, for example redshift distributions for each component at selected wavelengths and fluxes, are shown. The total mass-density of stars generated is consistent with that observed, in all 3 cosmological models.Comment: 20 pages, 25 figures. Accepted for publication in ApJ. Full details of models can be found at http://astro.ic.ac.uk/~mrr/countmodel

Detections and Constraints on White Dwarf Variability from Time-Series GALEX Observations

We search for photometric variability in more than 23,000 known and candidate white dwarfs, the largest ultraviolet survey compiled for a single study of white dwarfs. We use gPhoton, a publicly available calibration/reduction pipeline, to generate time-series photometry of white dwarfs observed by GALEX. By implementing a system of weighted metrics, we select sources with variability due to pulsations and eclipses. Although GALEX observations have short baselines (< 30 min), we identify intrinsic variability in sources as faint as Gaia G = 20 mag. With our ranking algorithm, we identify 49 new variable white dwarfs (WDs) in archival GALEX observations. We detect 41 new pulsators: 37 have hydrogen-dominated atmospheres (DAVs), including one possible massive DAV, and four are helium-dominated pulsators (DBVs). We also detect eight new eclipsing systems; five are new discoveries, and three were previously known spectroscopic binaries. We perform synthetic injections of the light curve of WD 1145+017, a system with known transiting debris, to test our ability to recover similar systems. We find that the 3{\sigma} maximum occurrence rate of WD 1145+017-like transiting objects is < 0.5%.Comment: 17 pages, 13 figure

Shocks, cooling and the origin of star formation rates in spiral galaxies

Understanding star formation is problematic as it originates in the large scale dynamics of a galaxy but occurs on the small scale of an individual star forming event. This paper presents the first numerical simulations to resolve the star formation process on sub-parsec scales, whilst also following the dynamics of the interstellar medium (ISM) on galactic scales. In these models, the warm low density ISM gas flows into the spiral arms where orbit crowding produces the shock formation of dense clouds, held together temporarily by their external pressure. Cooling allows the gas to be compressed to sufficiently high densities that local regions collapse under their own gravity and form stars. The star formation rates follow a Schmidt-Kennicutt \Sigma_{SFR} ~ \Sigma_{gas}^{1.4} type relation with the local surface density of gas while following a linear relation with the cold and dense gas. Cooling is the primary driver of star formation and the star formation rates as it determines the amount of cold gas available for gravitational collapse. The star formation rates found in the simulations are offset to higher values relative to the extragalactic values, implying a constant reduction, such as from feedback or magnetic fields, is likely to be required. Intriguingly, it appears that a spiral or other convergent shock and the accompanying thermal instability can explain how star formation is triggered, generate the physical conditions of molecular clouds and explain why star formation rates are tightly correlated to the gas properties of galaxies.Comment: 13 pages, 12 figures. MNRAS in pres

The Global Star Formation Rate from the 1.4 GHz Luminosity Function

The decimetric luminosity of many galaxies appears to be dominated by synchrotron emission excited by supernova explosions. Simple models suggest that the luminosity is directly proportional to the rate of supernova explosions of massive stars averaged over the past 30 Myr. The proportionality may be used together with models of the evolving 1.4 GHz luminosity function to estimate the global star formation rate density in the era z < 1. The local value is estimated to be 0.026 solar masses per year per cubic megaparsec, some 50% larger than the value inferred from the Halpha luminosity density. The value at z ~ 1 is found to be 0.30 solar masses per year per cubic megaparsec. The 10-fold increase in star formation rate density is consistent with the increase inferred from mm-wave, far-infrared, ultra-violet and Halpha observations.Comment: 10 pages, 2 figures, Astrophysical Journal Letters (in press); new PS version has improved figure placemen

The Redshift of GRB 970508

GRB 970508 is the second gamma-ray burst (GRB) for which an optical afterglow has been detected. It is the first GRB for which a distance scale has been determined: absorption and emission features in spectra of the optical afterglow place GRB 970508 at a redshift of z >= 0.835 (Metzger et al. 1997a, 1997b). The lack of a Lyman-alpha forest in these spectra further constrains this redshift to be less than approximately 2.3. I show that the spectrum of the optical afterglow of GRB 970508, once corrected for Galactic absorption, is inconsistent with the relativistic blast-wave model unless a second, redshifted source of extinction is introduced. This second source of extinction may be the yet unobserved host galaxy. I determine its redshift to be z = 1.09^{+0.14}_{-0.41}, which is consistent with the observed redshift of z = 0.835. Redshifts greater than z = 1.40 are ruled out at the 3 sigma confidence level.Comment: Accepted to The Astrophysical Journal (Letters), 10 pages, LaTe