Spectro-Perfectionism: An Algorithmic Framework for Photon Noise-Limited Extraction of Optical Fiber Spectroscopy

We describe a new algorithm for the "perfect" extraction of one-dimensional spectra from two-dimensional (2D) digital images of optical fiber spectrographs, based on accurate 2D forward modeling of the raw pixel data. The algorithm is correct for arbitrarily complicated 2D point-spread functions (PSFs), as compared to the traditional optimal extraction algorithm, which is only correct for a limited class of separable PSFs. The algorithm results in statistically independent extracted samples in the 1D spectrum, and preserves the full native resolution of the 2D spectrograph without degradation. Both the statistical errors and the 1D resolution of the extracted spectrum are accurately determined, allowing a correct chi-squared comparison of any model spectrum with the data. Using a model PSF similar to that found in the red channel of the Sloan Digital Sky Survey spectrograph, we compare the performance of our algorithm to that of cross-section based optimal extraction, and also demonstrate that our method allows coaddition and foreground estimation to be carried out as an integral part of the extraction step. This work demonstrates the feasibility of current- and next-generation multi-fiber spectrographs for faint galaxy surveys even in the presence of strong night-sky foregrounds. We describe the handling of subtleties arising from fiber-to-fiber crosstalk, discuss some of the likely challenges in deploying our method to the analysis of a full-scale survey, and note that our algorithm could be generalized into an optimal method for the rectification and combination of astronomical imaging data.Comment: 9 pages, 4 figures, emulateapj; minor corrections and clarifications; to be published in the PAS

A study of methods to predict and measure the transmission of sound through the walls of light aircraft

The objectives are: measurement of dynamic properties of acoustical foams and incorporation of these properties in models governing three-dimensional wave propagation in foams; tests to measure sound transmission paths in the HP137 Jetstream 3; and formulation of a finite element energy model. In addition, the effort to develop a numerical/empirical noise source identification technique was completed. The investigation of a design optimization technique for active noise control was also completed. Monthly progress reports which detail the progress made toward each of the objectives are summarized

A Note on the Morse Index Theorem for Geodesics between Submanifolds in semi-Riemannian Geometry

The computation of the index of the Hessian of the action functional in semi-Riemannian geometry at geodesics with two variable endpoints is reduced to the case of a fixed final endpoint. Using this observation, we give an elementary proof of the Morse Index Theorem for Riemannian geodesics with two variable endpoints, in the spirit of the original Morse's proof. This approach reduces substantially the effort required in the proofs of the Theorem given in previous articles on the subject. Exactly the same argument works also in the case of timelike geodesics between two submanifolds of a Lorentzian manifold. For the extension to the lightlike Lorentzian case, just minor changes are required and one obtains easily a proof of the focal index theorems of Beem, Ehrlich and Kim.Comment: 12 pages, LaTeX2e, amsart style. To appear on the Journal of Mathematical Physic

Cosmic Variance In the Transparency of the Intergalactic Medium After Reionization

Following the completion of cosmic reionization, the mean-free-path of ionizing photons was set by a population of Ly-limit absorbers. As the mean-free-path steadily grew, the intensity of the ionizing background also grew, thus lowering the residual neutral fraction of hydrogen in ionization equilibrium throughout the diffuse intergalactic medium (IGM). Ly-alpha photons provide a sensitive probe for tracing the distribution of this residual hydrogen at the end of reionization. Here we calculate the cosmic variance among different lines-of-sight in the distribution of the mean Ly-alpha optical depths. We find fractional variations in the effective post-reionization optical depth that are of order unity on a scale of ~100 co-moving Mpc, in agreement with observations towards high-redshift quasars. Significant contributions to these variations are provided by the cosmic variance in the density contrast on the scale of the mean-free-path for ionizing photons, and by fluctuations in the ionizing background induced by delayed or enhanced structure formation. Cosmic variance results in a highly asymmetric distribution of transmission through the IGM, with fractional fluctuations in Ly-alpha transmission that ar larger than in Ly-beta transmission.Comment: 7 pages 3 figures. Replaced with version accepted for publication in Ap

Possible evidence for an inverted temperature-density relation in the intergalactic medium from the flux distribution of the Lyman-alpha forest

We compare the improved measurement of the Lya forest flux probability distribution at 1.7<z<3.2 presented by Kim et al. (2007) to a large set of hydrodynamical simulations of the Lya forest with different cosmological parameters and thermal histories. The simulations are in good agreement with the observational data if the temperature-density relation for the low density intergalactic medium (IGM), T=T_0 Delta^{gamma-1}, is either close to isothermal or inverted (gamma<1). Our results suggest that the voids in the IGM may be significantly hotter and the thermal state of the low density IGM may be substantially more complex than is usually assumed at these redshifts. We discuss radiative transfer effects which alter the spectral shape of ionising radiation during the epoch of HeII reionisation as a possible physical mechanism for achieving an inverted temperature-density relation at z~3.Comment: 16 pages, 6 figures, accepted for publication in MNRAS following minor revision. The accepted version includes an expanded discussion of the flux power spectru

How neutral is the intergalactic medium surrounding the redshift z=7.085 quasar ULAS J1120+0641?

The quasar ULAS J1120+0641 at redshift z=7.085 has a highly ionised near zone which is smaller than those around quasars of similar luminosity at z~6. The spectrum also exhibits evidence for a damping wing extending redward of the systemic Lya redshift. We use radiative transfer simulations in a cosmological context to investigate the implications for the ionisation state of the inhomogeneous IGM surrounding this quasar. Our simulations show that the transmission profile is consistent with an IGM in the vicinity of the quasar with a volume averaged HI fraction of f_HI>0.1 and that ULAS J1120+0641 has been bright for 10^6--10^7 yr. The observed spectrum is also consistent with smaller IGM neutral fractions, f_HI ~ 10^-3--10-4, if a damped Lya system in an otherwise highly ionised IGM lies within 5 proper Mpc of the quasar. This is, however, predicted to occur in only ~5 per cent of our simulated sight-lines for a bright phase of 10^6--10^7 yr. Unless ULAS J1120+0641 grows during a previous optically obscured phase, the low age inferred for the quasar adds to the theoretical challenge of forming a 2x10^9 M_sol black hole at this high redshift.Comment: 5 pages, 4 figures, accepted to MNRAS letter

The ontogeny, palaeobiology and systematic palaeontology of some lower liassic belemnitida

The Belemnite Marls of the Dorset coast constitute the jamesoni and ibex Zones of that area. This study is essentially a revision of the total belemnite fauna of these beds, with a preliminary appraisal of the belemnites from the overlying basal Green Ammonite Beds (davoei Zone). Twelve morphospecies are described which are defined by their rostral ontogeny and other morphometric data. Probable sexual dimorphism into relatively stout and slender rostra is demonstrated for Four species (Belemnites longissimus Miller, B. charmouthensis Mayer, B. imus (Lang) and B. cricki (Lissajous)). It is recognised that, at different localities and horizons, single species may be represented by assemblages that vary with respect to age and sex of individuals, and it is concluded that such belemnite assemblages are at least partly due to local population structures analagous to those that are found in modern cephalopods. Early ontogeny, rostral form and function, epirostra and surface ornamentation are briefly discussed with reference to the species described

A study of methods to predict and measure the transmission of sound through the walls of light aircraft

Several research investigations are discussed. The development of a numerical/empirical noise source identification procedure using boundary element techniques, the identification of structure-borne paths using structural intensity and finite element methods, the development of a design optimization numerical procedure to be used to study active noise control in three-dimensional geometries, and the measurement of the dynamic properties of acoustical foams and the incorporation of these properties in models governing three-dimensional wave propagation in foams are discussed

Thermal constraints on the reionisation of hydrogen by population-II stellar sources

Measurements of the intergalactic medium (IGM) temperature provide a potentially powerful constraint on the reionisation history due to the thermal imprint left by the photo-ionisation of neutral hydrogen. However, until recently IGM temperature measurements were limited to redshifts 2 < z < 4.8, restricting the ability of these data to probe the reionisation history at z > 6. In this work, we use recent measurements of the IGM temperature in the near-zones of seven quasars at z ~ 5.8 - 6.4, combined with a semi-numerical model for inhomogeneous reionisation, to establish new constraints on the redshift at which hydrogen reionisation completed. We calibrate the model to reproduce observational constraints on the electron scattering optical depth and the HI photo-ionisation rate, and compute the resulting spatially inhomogeneous temperature distribution at z ~ 6 for a variety of reionisation scenarios. Under standard assumptions for the ionising spectra of population-II sources, the near-zone temperature measurements constrain the redshift by which hydrogen reionisation was complete to be z > 7.9 (6.5) at 68 (95) per cent confidence. We conclude that future temperature measurements around other high redshift quasars will significantly increase the power of this technique, enabling these results to be tightened and generalised.Comment: 15 pages, 8 figures, accepted for publication in MNRA