Optimising optimal image subtraction

Difference imaging is a technique for obtaining precise relative photometry of variable sources in crowded stellar fields and, as such, constitutes a crucial part of the data reduction pipeline in surveys for microlensing events or transiting extrasolar planets. The Optimal Image Subtraction (OIS) algorithm of Alard & Lupton (1998) permits the accurate differencing of images by determining convolution kernels which, when applied to reference images with particularly good seeing and signal‐to‐noise (S/N), provide excellent matches to the point‐spread functions (PSF) in other images of the time series to be analysed. The convolution kernels are built as linear combinations of a set of basis functions, conventionally bivariate Gaussians modulated by polynomials. The kernel parameters, mainly the widths and maximal degrees of the basis function model, must be supplied by the user. Ideally, the parameters should be matched to the PSF, pixel‐sampling, and S/N of the data set or individual images to be analysed. We have studied the dependence of the reduction outcome as a function of the kernel parameters using our new implementation of OIS within the IDL‐based TRIPP package. From the analysis of noise‐free PSF simulations of both single objects and crowded fields, as well as the test images in the ISIS OIS software package, we derive qualitative and quantitative relations between the kernel parameters and the success of the subtraction as a function of the PSF widths and sampling in reference and data images and compare the results to those of other implementations found in the literature. On the basis of these simulations, we provide recommended parameters for data sets with different S/N and sampling. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the reliability of the VCV Matrix: A case study based on GAMIT and Bernese GPS Software

Commonly, the variance-covariance (VCV) matrix derived from GPS processing software underestimates the magnitude of the error, mainly due to the fact that physical correlations are normally neglected. The GAMIT and Bernese software packages serve the scientific community as important tools for GPS measurement processing and analyzing, especially in precise applications. Therefore, the reliability of the VCV matrices derived by the GAMIT and Bernese packages is of great importance. Formal accuracies derived from both software need to be scaled by applying a scaling factor (SF) that multiplies the software-derived formal errors. However, to the best of our knowledge, no standard approach approved by the GPS community exists. In this report, an analysis is carried out in order to test the reliability and the validity of the VCV matrices in both software, and to provide SFs needed to calculate the realistic accuracies reflecting the actual error levels. The method applied in this study allows deriving SFs for formal accuracies obtained from GAMIT and Bernese. The results attained from the time series of eight days for eight baselines (lengths of 20–415 km) indicate that the overall SF for GAMIT is more than 10 times smaller than for Bernese (1.9 and 23.0, respectively). Although no distance-dependent SF was detected in either case, the session-duration dependence was detected for the Bernese software, while no clear session-duration dependence was observed for the GAMIT. Furthermore, no receiver/antenna dependence could be deduced from the results of this analysis.     

Dynamic programming and the principle of optimality: A systematic approach

The dynamic programming recursive procedure has provided an efficient method for solving a variety of sequential decision problems related to water resources systems. In many investigations Bellman's principle of optimality is used as a proof for the optimality of the dynamic programming solutions. In this paper the dynamic programming procedure is systematically studied so as to clarify the relationship between Bellman's principle of optimality and the optimality of the dynamic programming solutions.Our main result is that although the principle is valid, in order to use it as a proof for the optimality of the dynamic programming solution certain modeling requirements should be met.The mathematical model presented in this paper provides a convenient framework for the modeling and analysis of dynamic programming problems encountered by in water resources management studies.The results derived here resolve few of the fundamental questions raised in the literature regarding the validity of Bellman's principle of oplimality and the optimality of the dynamic programming solutions.     

Molecular hydrogen in the central regions of southern infrared galaxies

An extensive set of molecular hydrogen observations of centers of southern infrared galaxies is presented. Our data are combined with published infrared and radio observations to investigate the relationship between nuclear and circumnuclear activity. We convert the observational data to absolute luminosities, by applying the known distances. The resulting dataset covers several decades in luminosity for the various parameters, which observe fairly tight correlations. The parameters of our (power law) fits are, at the level of accuracy achieved, not dependent on the type of nuclear activity: while the dataset comprises a mixture of alleged Seyfert, Liner & starburst galaxies, single fits match the complete sample well enough. In particular, non-thermal nuclei (AGN) present in some of the galaxies in the current sample, do not stand out in the parameters we investigated. The absence of a significant dependence on the nuclear type is consistent with the idea that the ever present starbursts energetically dominate a possible ‘AGN in a dusty environment’-component in most galaxy nuclei with infrared excesses.The size of the H₂ emitting region is found to be proportional to the square root of the 21 cm radio continuum luminosity. The excitation of the circumnuclear H₂ is dominated by shocks. If the H₂ extent marks the size of an inner cavity in the dense molecular material surrounding a galaxy nucleus and the radio luminosity is proportional to the mechanical luminosity of (circum)nuclear winds. This result then indicates that the cavity size occurs at constant pressure in the sample galaxies, in accordance with the superwind model by Heckman et al. (1990) [ApJS, 74, 833]. Our results, together with those obtained by others, thus suggest that luminosities and size scales of excited gas associated with active nuclei are dominated by the mechanical energy input. Given the difficulties of uniquely establishing the presence of an AGN, we cannot exclude that (a large fraction of the) infrared luminous galaxies procure part of their radiated energy through accretion onto a massive dark object.F. Duccio Macchetto     

Spectral Line and Continuum Radiation Propagation in a Clumpy Medium

We discuss the propagation of spectral line and continuum radiation in a clumpy medium and give general expressions for the observed absorption or emission from a cloud population. We show that the affect of the medium clumpiness can usually be characterised by a single number multiplying the mean column opacity. Our result provides a simpler proof and generalization of the result of Martin et al. (1984). The formalism provides a simple way to understand the effects of clumping on molecular line profiles and ratios; for example, how clumping effects the interpretation of ¹³CO(1–0) to ¹²CO(1–0) line ratios. It also can be used as a propagation operator in physical models of clumpy media where the incident radiation effects the spectral line emissivity. We are working to extend the formalism to the propagation of masers in a clumpy medium, but in this case, there are special difficulties because formal expectation values are not characteristic of observations because they are biased by rare events.     

X-ray intensity-hardness correlation and deep IR observations of the anomalous X-ray pulsar 1RXS J170849-400910

We report here on X-ray and IR observations of the Anomalous X-ray Pulsar (AXP) 1RXS J170849-400910. First, we report on new XMM-Newton, Swift-XRT and Chandra observations of this AXP, which confirm the intensity–hardness correlation observed in the long term X-ray monitoring of this source. These new X-ray observations show that the AXP flux is rising again, and the spectrum hardening. If the increase of the source intensity is indeed connected with the glitches and a possible bursting activity, we expect this source to enter in a bursting active phase around 2006–2007. Second, we report on deep IR observations of 1RXS J170849-400910, taken with the VLT-NACO adaptive optics, showing that there are many weak sources consistent with the AXP position. Neither star A or B, as previously proposed by different authors, might yet be conclusively recognised as the IR counterpart of 1RXS J170849-400910. Third, using Monte Carlo simulations, we re-address the calculation of the significance of the absorption line found in a phase-resolved spectrum of this source, and interpreted as a resonant scattering cyclotron feature.     

Post-stack velocity analysis in the dip-angle domain using diffractions

Interval velocity analysis in complex geological areas is often considered as an unresolved problem. A novel approach to improve the velocity analysis process is to perform the analysis in a non-conventional domain and to use seismic events that are usually ignored during standard data processing and imaging. In this study, a method to analyse diffraction data for migration velocity analysis in the time- or depth-domain is presented. The method is based on the clear distinction between diffractions and reflections in the post-migration dip-angle domain. The attractive possibility to perform the analysis, using only stacked data as an input, is demonstrated on synthetic and real data examples.     

New limits on the orbital parameters of 1E 1048.1–5937 and 1E 2259+586 from RXTE observations

We report on two Rossi X-ray Timing Explorer ( RXTE ) observations of the anomalous X-ray pulsars 1E 1048.1–5937 and 1E 2259+586. Both sources have continued their almost constant spin-down during 1995/96. We carried out a search for orbital Doppler shifts, in their observed spin frequencies, deriving stringent limits on the projected semi-axis. Unless these systems have unlikely small inclinations, main-sequence companions can be excluded. If 1E 1048.1–5937 and 1E 2259+586 are indeed binary systems, their companion stars must be either white dwarfs, or helium-burning stars with M ≲ 0.8 M⊙, possibly underfilling their Roche lobe.