The use of genetic algorithms to model protoplanetary discs

The protoplanetary discs of T Tauri and Herbig Ae/Be stars have previously been studied using geometric disc models to fit their spectral energy distribution (SED). The simulations provide a means to reproduce the signatures of various circumstellar structures, which are related to different levels of infrared excess. With the aim of improving our previous model, which assumed a simple flat-disc configuration, we adopt here a reprocessing flared-disc model that assumes hydrostatic, radiative equilibrium. We have developed a method to optimize the parameter estimation based on genetic algorithms (GAs). This paper describes the implementation of the new code, which has been applied to Herbig stars from the Pico dos Dias Survey catalogue, in order to illustrate the quality of the fitting for a variety of SED shapes. The star AB Aur was used as a test of the GA parameter estimation, and demonstrates that the new code reproduces successfully a canonical example of the flared-disc model. The GA method gives a good quality of fit, but the range of input parameters must be chosen with caution, as unrealistic disc parameters can be derived. It is confirmed that the flared-disc model fits the flattened SEDs typical of Herbig stars; however, embedded objects (increasing SED slope) and debris discs (steeply decreasing SED slope) are not well fitted with this configuration. Even considering the limitation of the derived parameters, the automatic process of SED fitting provides an interesting tool for the statistical analysis of the circumstellar luminosity of large samples of young stars.     

Spectral analysis of Swift long gamma-ray bursts with known redshift

We study the spectral and energetics properties of 47 long-duration gamma-ray bursts (GRBs) with known redshift, all of them detected by the Swift satellite. Due to the narrow energy range (15–150 keV) of the Swift -BAT detector, the spectral fitting is reliable only for fitting models with two or three parameters. As high uncertainty and correlation among the errors is expected, a careful analysis of the errors is necessary. We fit both the power law (PL, two parameters) and cut-off power law (CPL, three parameters) models to the time-integrated spectra of the 47 bursts, and we present the corresponding parameters, their uncertainties and the correlations among the uncertainties. The CPL model is reliable only for 29 bursts for which we estimate the  ν f _ν  peak energy E _pk. For these GRBs, we calculate the energy fluence and the rest-frame isotropic-equivalent radiated energy,   E _γ,iso  , as well as the propagated uncertainties and correlations among them. We explore the distribution of our homogeneous sample of GRBs on the rest-frame diagram   E '_pk  versus   E _γ,iso  . We confirm a significant correlation between these two quantities (the 'Amati' relation) and we verify that, within the uncertainty limits, no outliers are present. We also fit the spectra to a Band model with the high-energy PL index frozen to −2.3, obtaining a rather good agreement with the 'Amati' relation of non- Swift GRBs.     

An expanding Universe with constant pressure and no cosmological constant

Thanks to its fitting triumph, the ΛCDM paradigm is assumed to be the most powerful model, for describing the Universe dynamics, over much the myriad of cosmological models. Unfortunately, the quest of a self-consistent model remains not well explained, because it is not clear how to solve the problems of fine-tuning and coincidence, afflicting the ΛCDM framework; as a matter of fact, these theoretical drawbacks do not allow to consider the ΛCDM model, as the final picture of the modern cosmological scenario. Here, we show that the simplest model, which provides a constant equation of state for the pressure, leads to a generalization of ΛCDM, reducing to it in a particular case. Moreover, we highlight the physical mechanisms of this model, describing the thermodynamical reasons why a constant pressure should be negative in an expanding Universe. In addition, we fit the free parameters of our model by minimizing the chi square through the age differential method, involving a direct measurement of H.     

Stokes imaging of AM Her systems using 3D inhomogeneous models – I. Description of the code and an application to V834 Cen

Polars (or AM Her systems) are cataclysmic variables without a disc due to the strong magnetic field of the white dwarf. Most of their emission comes from the region where the accretion column impacts the white dwarf and cools through cyclotron and bremsstrahlung processes. We present a new code, cyclops , to model the optical emission from these systems including the four Stokes parameters. It considers a three-dimensional region with the electronic density and temperature varying following a shock-like profile and a dipolar magnetic field. The radiative transfer is solved in steps considering the solution with non-null input radiation. The footprint of the column in the white dwarf surface is determined by the threading region in the equatorial plane, i.e. the region from where the flow follows the magnetic lines. The extinction caused by the Thomson scattering above the emitting region is optionally included. The search for the model parameters that best fit an observational data set is carried out using a hybrid approach: a genetic algorithm is used to seek for the regions of the parameter space having the best models and then an amoeba code refines the search. An example of the application to multi-wavelength data of V834 Cen is presented. The fit found is consistent with previous parameter estimates and is able to reproduce the features of V834 data in three wavebands.     

Rhessi Images and Spectra of Two Small Flares

We studied the evolution of two small flares (GOES class C2 and C1) that developed in the same active region with different morphological characteristics: one is extended and the other is compact. We analyzed the accuracy and the consistency of different algorithms implemented in Reuven Ramaty High-Energy Spectroscopic Imager (RHESSI) software to reconstruct the image of the emitting sources, for energies between 3 and 12 keV. We found that all tested algorithms give consistent results for the peak position, while the other parameters can differ at most by a factor 2. Pixon and Forward-fit generally converge to similar results but Pixon is more reliable for reconstructing a complex source. We investigated the spectral characteristics of the two flares during their evolution in the 3–25 keV energy band. We found that a single thermal model of the photon spectrum is inadequate to fit the observations and we needed to add either a non-thermal model or a hot thermal one. The non-thermal and the double thermal fits are comparable. If we assume a non-thermal model, the non-thermal energy is always higher than the thermal one. Only during the very final decay phase a single thermal model fits the observed spectrum fairly well.     

Initial-Condition Influences on CME Expansion and Propagation

A general-purpose melon-seed-overpressure-expansion (MSOE) model is used to examine the dependence of the expansion and propagation of fast CMEs on average initial values of the magnetic field inside the CME, the magnetic field outside the CME, and the CME mass. The MSOE model extracts from the real situation only features that are essential in determining the expansion and propagation processes and idealizes them to obtain an adaptable “minimalist” set of equations that governs these processes yet retains enough relevant physics to give useful results. This minimalist set is used to carry out a systematic comparison of solutions against four sets of observed correlations between CME and ICME parameters in which the input parameters to the MSOE model are varied to achieve simultaneous fits to all four correlations. The fits impose relations between the three independent input variables: initial internal field strength, initial external field strength, and initial density. For example, light CMEs (e.g., those with no prominences) require the external field strength to nearly equal the internal field strength. However, heavy CMEs (e.g., those with prominences) require the external field strength to be much weaker than the internal field strength.     

Dynamical modelling of the elliptical galaxy NGC 2974

In this paper we analyse the relations between a previously described oblate Jaffe model for an ellipsoidal galaxy and the observed quantities for NGC 2974, and obtain the length and velocity scales for a relevant elliptical galaxy model. We then derive the finite total mass of the model from these scales, and finally find a good fit of an isotropic oblate Jaffe model by using the Gauss-Hermite fit parameters and the observed ellipticity of the galaxy NGC 2974. The model is also used to predict the total luminous mass of NGC 2974, assuming that the influence of dark matter in this galaxy on the image, ellipticity and Gauss-Hermite fit parameters of this galaxy is negligible within the central region, of radius 0.5R _e.     

Orbit of an Astrometric Binary System

We present a new method to solve the problem of initial orbit determination of any binary system. This method is mainly based on the material available for an observer, for example relative positions at a given time of the couple in the “plane of sky”, namely the tangent plane to the celestial sphere at the position of the primary component. The problem of orbit determination is solved by splitting in successive stages in order to decorrelate the parameters of each other as much as possible. On one hand, the geometric problem is solved using the first Kepler’s law from a single observing run and, on the other hand, dynamical parameters are then inferred from the fit of the Kepler’s equation. At last, the final stage consists in determining the main physical parameters involved in the secular evolution of the system, that is the spin axis and the J₂ parameter of the primary if we assume that it is a quasi-spherical body. As a matter of fact there is no need to make too restrictive initial assumptions (such as circular orbit or zero eccentricity) and initial guesses of parameters required by a non-linear least-squares Levenberg–Marquardt algorithm are finally obtained after each stage. Such a protocol is very useful to study systems like binary asteroids for which all of the parameters should be considered a priori as unknowns. As an example of application, we used our method to estimate the set of the Pluto–Charon system parameters from observations collected in the literature since 1980.     

Testing the Hapke photometric model: Improved inversion and the porosity correction

In conjunction with a companion paper (Shepard, M.K., Helfenstein, P. [2011]. Icarus, submitted for publication), we derive, test, and apply a detailed approach for visualizing the phase angle dependence of light scattering in particulate soils from both whole-disk and disk-resolved observations. To reduce the number of model parameters and provide stronger constraints on model fits, we combine Hapke’s (Hapke, B. [2008]. Icarus 195, 918-926) recent correction for effects of porosity with his (Hapke, B. [1986]. Icarus 67, 264-280) model of the shadow hiding opposition effect. We further develop our method as a tool for least-squares fitting of Hapke’s model to photometric data. Finally, we present an improved method for estimating uncertainties in retrieved values of Hapke model parameters. We perform a preliminary test of the model on spectrogoniometric measurements from three selected laboratory samples from Shepard and Helfenstein (Shepard, M.K., Helfenstein, P. [2007]. J. Geophys. Res. 112 (E03001), 17). Our preliminary suite of test samples is too small and selective to permit the drawing of general conclusions. However, our results suggest that Hapke’s porosity correction improves the fidelity of fits to samples composed of low- and moderate-albedo particles and may allow for more reliable retrieval of porosity estimates in these materials. However, we find preliminary evidence that in high-albedo surfaces, the effects of porosity may be difficult to detect.     

The point spread function of the soft X-ray telescope aboard Yohkoh

The point spread function of the SXT telescope aboardYohkoh has been measured in flight configuration in three different X-ray lines at White Sands Missile Range. We have fitted these data with an elliptical generalization of the Moffat function. Our fitting method consists of ² minimizationin Fourier space, especially designed for matching of sharply peaked functions. We find excellent fits with a reduced ² of order unity or less for single exposure point spread functions over most of the CCD. Near the edges of the CCD the fits are less accurate due to vignetting. From fitting results with summation of multiple exposures we find a systematic error in the fitting function of the order of 3% near the peak of the point spread function, which is close to the photon noise for typical SXT images in orbit. We find that the full width to half maximum and fitting parameters vary significantly with CCD location. However, we also find that point spread functions measured at the same location are consistent to one another within the limit determined by photon noise. A best analytical fit to the PSF as function of position on the CCD is derived for use in SXT image enhancement routines. As an aside result we have found that SXT can determine the location of point sources to about a quarter of a 2.54 arc sec pixel.This paper is dedicated to the memory of our friend and colleague Kermit Smith, who died in June 1993, after a valient fight with leukemia.     

Simulated Annealing and Bayesian Posterior Distribution Analysis Applied to Spectral Emission Line Fitting

Spectral-line fitting problems are extremely common in all remote-sensing disciplines, solar physics included. Spectra in solar physics are frequently parameterized by using a model for the background and the emission lines, and various computational techniques are used to find values to the parameters given the data. However, the most commonly-used techniques, such as least-squares fitting, are highly dependent on the initial parameter values used and are therefore biased. In addition, these routines occasionally fail because of ill-conditioning. Simulated annealing and Bayesian posterior distribution analysis offer different approaches to finding parameter values through a directed, but random, search of the parameter space. The algorithms proposed here easily incorporate any other available information about the emission spectrum, which is shown to improve the fit. Example algorithms are given and their performance is compared to a least-squares algorithm for test data – a single emission line, a blended line, and very low signal-to-noise-ratio data. It is found that the algorithms proposed here perform at least as well or better than standard fitting practices, particularly in the case of very low signal-to-noise ratio data. A hybrid simulated annealing and Bayesian posterior algorithm is used to analyze a Mg x line contaminated by an O IV triplet, as observed by the Coronal Diagnostic Spectrometer onboard SOHO. The benefits of these algorithms are also discussed.     

Galaxy cluster masses without non-baryonic dark matter

We apply the modified acceleration law obtained from Einstein gravity coupled to a massive skew symmetric field,   F _μνλ  , to the problem of explaining X-ray galaxy cluster masses without exotic dark matter. Utilizing X-ray observations to fit the gas mass profile and temperature profile of the hot intracluster medium (ICM) with King 'β-models', we show that the dynamical masses of the galaxy clusters resulting from our modified acceleration law fit the cluster gas masses for our sample of 106 clusters without the need of introducing a non-baryonic dark matter component. We are further able to show for our sample of 106 clusters that the distribution of gas in the ICM as a function of radial distance is well fitted by the dynamical mass distribution arising from our modified acceleration law without any additional dark matter component. In a previous work, we applied this theory to galaxy rotation curves and demonstrated good fits to our sample of 101 low surface brightness, high surface brightness and dwarf galaxies including 58 galaxies that were fitted photometrically with the single-parameter mass-to-light ratio ( M / L )_stars. The results obtained there were qualitatively similar to those obtained using Milgrom's phenomenological Modified Newtonian Dynamics (MOND) model, although the determined galaxy masses were quantitatively different, and MOND does not show a return to Keplerian behaviour at extragalactic distances. The results obtained here are compared to those obtained using Milgrom's phenomenological MOND model which does not fit the X-ray galaxy cluster masses unless an auxiliary dark matter component is included.     

A NLTE model atmosphere analysis of the pulsating sdO star SDSS J1600+0748

We started a program to construct several grids of suitable model atmospheres and synthetic spectra for hot subdwarf O stars computed, for comparative purposes, in LTE, NLTE, with and without metals. For the moment, we use our grids to perform fits on our spectrum of SDSS J160043.6+074802.9 (J1600+0748 for short), this unique pulsating sdO star. Our best fit is currently obtained with NLTE model atmospheres including carbon, nitrogen and oxygen in solar abundances, which leads to the following parameters for SDSS J1600+0748 : T _eff=69060±2080 K, log?g=6.00±0.09 and log?N(He)/N(H)=?0.61±0.06. Improvements are needed, however, particularly for fitting the available He ii lines. It is hoped that the inclusion of Fe will help remedy the situation.     

Benchmarking a Light-Curve Model at Low-z

A set of well-measured, {low-z}, type Ia supernovae from the Calán/Tololo SNe data sets is used to determine benchmark parameters in our hydrodynamics-based, light-curve model. The light-curve data fit fairly well in B, V, and R passbands but not as well in the I passband. The fitting procedure, extracted best-fit model parameters, and their connection to type Ia SN parameters are presented. Our benchmarked light-curve model represents an alternative to empirical template methods for the analysis of light-curve data.     

On model selection forecasting, dark energy and modified gravity

The Fisher matrix approach allows one to calculate in advance how well a given experiment will be able to estimate model parameters, and has been an invaluable tool in experimental design. In the same spirit, we present here a method to predict how well a given experiment can distinguish between different models, regardless of their parameters. From a Bayesian viewpoint, this involves computation of the Bayesian evidence. In this paper, we generalize the Fisher matrix approach from the context of parameter fitting to that of model testing, and show how the expected evidence can be computed under the same simplifying assumption of a Gaussian likelihood as the Fisher matrix approach for parameter estimation. With this 'Laplace approximation' all that is needed to compute the expected evidence is the Fisher matrix itself. We illustrate the method with a study of how well upcoming and planned experiments should perform at distinguishing between dark energy models and modified gravity theories. In particular, we consider the combination of 3D weak lensing, for which planned and proposed wide-field multiband imaging surveys will provide suitable data, and probes of the expansion history of the Universe, such as proposed supernova and baryonic acoustic oscillations surveys. We find that proposed large-scale weak-lensing surveys from space should be able readily to distinguish General Relativity from modified gravity models.     

Spitzer and ISO galaxy counts in the mid-infrared

Galaxy source counts that simultaneously fit the deep mid-infrared surveys at 24 microns and 15 microns made by the Spitzer Space Telescope and the Infrared Space Observatory ( ISO ), respectively, are presented for two phenomenological models. The models are based on starburst and luminous infrared galaxy dominated populations. Both models produce excellent fits to the counts in both wavebands and provide an explanation for the high-redshift population seen in the longer Spitzer 24-micron band supporting the hypothesis that they are luminous–ultraluminous infrared galaxies at   z = 2–3  , being the mid-infrared counterparts to the submillimetre galaxy population. The source counts are characterized by strong evolution to redshift unity, followed by less drastic evolution to higher redshift. The number–redshift distributions in both wavebands are well explained by the effect of the many mid-infrared features passing through the observation windows. The sharp upturn at around a millijansky in the 15-μm counts in particular depends critically on the distribution of mid-infrared features around 12 μm, in the assumed spectral energy distribution.     

Power law relating 10.7 cm flux to sunspot number

To investigate the relation between observations of the 10.7 cm flux and the international sunspot number so that a physical unit may be ascribed to historical records, both polynomial and power law models are developed giving the radio flux as a function of sunspot number and vice versa. Bayesian data analysis is used to estimate the model parameters and to discriminate between the models. The effect on the parameter uncertainty and on the relative evidence of normalizing the measure of fit is investigated. The power law giving flux as a function of sunspot number is found to be the most plausible model and may be used to estimate the radio flux from historical sunspot observations.     

Test of a geometric model for the modification stage of simple impact crater development

Abstract— Small terrestrial hypervelocity impact craters have a bowl-shaped form and are partially filled by an interior breccia lens, roughly parabolic in cross-section, of allochthonous material. This interior breccia volume is geometrically modelled as the volume of material slumped off the interior wall of the transient cavity during late stage crater modification. This model is tested by comparing the estimated volume of the breccia lens based on observational data with the calculated volume of slump material based on known dimensional parameters. The model fits well for Meteor Crater and Brent and is highly sensitive to changes in input parameters (e.g., a 10% increase in the input diameter for Meteor Crater produces an almost 200% increase in the model breccia lens volume). Further testing of the model with less constrained data from West Hawk Lake and Lonar leads to reasonable fits, given the sensitivity of the model to input parameters. Fits to other craters: Aouelloul, Tenoumer and Wolf Creek, where previous depth data are constrained only by gravity data, are unsatisfactory. However, revised depths can be obtained that fit both the gravity data and the model. While these tests do not provide unqualified support for the model, they do suggest that it may represent a good first order approximation. More and better quality dimensional data are required for more rigorous testing.     

Cycloidal cracks on Europa: Improved modeling and non-synchronous rotation implications

Cycloidal crack patterns on Europa are influenced by tides induced by orbital eccentricity, which in turn is driven by the Laplace orbital resonance. Their shapes potentially record the location of their formation (relative to the direction of Jupiter), as well as the parameters of crack formation. Hoppa et al. [Hoppa, G., Tufts, B.R., Greenberg, R., Geissler, P., 1999a. Icarus 141, 287-298] modeled several cycloid chains using a fixed set of material parameters, but some details did not fit. We now allow material parameters to vary for each arc of an observed cycloid. In general, with minimal variation of model parameters between the arcs, fits are greatly improved. Furthermore, accounting for tidal stress accumulated during non-synchronous rotation, in addition to diurnal stress, allows even better fits. Even with the added freedom in the model our fits allow us to better constrain the location where each cycloid may have formed. Our results support Hoppa et al.'s finding that only a few cracks form ridges per cycle of non-synchronous rotation in the region examined, probably because cracking relieves built up stress until further substantial rotation occurs.