Measuring individuals' response quality in self-administered psychological tests : an introduction to Gendre's functional method

The functional method is a new test theory using a new scoring method that assumes complexity in test structure, and thus takes into account every correlation between factors and items. The main specificity of the functional method is to model test scores by multiple regression instead of estimating them by using simplistic sums of points. In order to proceed, the functional method requires the creation of hyperspherical measurement space, in which item responses are expressed by their correlation with orthogonal factors. This method has three main qualities. First, measures are expressed in the absolute metric of correlations; therefore, items, scales and persons are expressed in the same measurement space using the same single metric. Second, factors are systematically orthogonal and without errors, which is optimal in order to predict other outcomes. Such predictions can be performed to estimate how one would answer to other tests, or even to model one's response strategy if it was perfectly coherent. Third, the functional method provides measures of individuals' response validity (i.e., control indices). Herein, we propose a standard procedure in order to identify whether test results are interpretable and to exclude invalid results caused by various response biases based on control indices

Detection of a very bright optical flare from a gamma-ray burst at redshift 6.29

In this letter we discuss the flux and the behavior of the bright optical flare emission detected by the 25 cm TAROT robotic telescope during the prompt high-energy emission and the early afterglow. We combine our data with simultaneous observations performed in X-rays and we analyze the broad-band spectrum. These observations lead us to emphasize the similarity of GRB 050904 with GRB 990123, a remarkable gamma-ray burst whose optical emission reached 9th magnitude. While GRB 990123 was, until now, considered as a unique event, this observation suggests the existence of a population of GRBs which have very large isotropic equivalent energies and extremely bright optical counterparts. The luminosity of these GRBs is such that they are easily detectable through the entire universe. Since we can detect them to very high redshift even with small aperture telescopes like TAROT, they will constitute powerful tools for the exploration of the high-redshift Universe and might be used to probe the first generation of stars.Comment: 9 pages, 3 figures. Accepted in ApJ

Fall back accretion and energy injections in gamma-ray bursts

Intense flares that occur at late times relative to the prompt phase have been observed by the $Swift$ satellite in the X-ray afterglows of gamma-ray bursts (GRBs). Here, we present a detailed analysis on the fall back accretion process to explain the intense flare phase in the very early X-ray afterglow light curves. To reproduce the afterglow at late times, we resort to the external shock by engaging energy injections. By applying our model to GRBs 080810, 081028 and 091029, we show that their X-ray afterglow light curves can be reproduced well. We then apply our model to the ultra-long $Swift$ GRB 111209A, which is the longest burst ever observed. The very early X-ray afterglow of GRB 111209A showed many interesting features, such as a significant bump observed at around 2000 s after the $Swift$/BAT trigger. We assume two constant energy injection processes in our model. These can explain the observed plateau at X-ray wavelength in the relatively early stage ($8.0\times10^{3}$ s) and a second X-ray plateau and optical rebrightening at about $10^{5}$ s. Our analysis supports the scenario that a significant amount of material may fall back toward the central engine after the prompt phase, causing an enhanced and long lived mass accretion rate powering a Poynting-flux-dominated outflow.Comment: 2 tables, 3 figures, accepted by MNRA

Luminosity Functions of Gamma-Ray Burst Afterglows

Aims: Use the standard fireball model to create virtual populations of gamma-ray burst afterglows and study their luminosity functions. Methods: We randomly vary the parameters of the standard fireball model to create virtual populations of afterglows. We use the luminosity of each burst at an observer's time of 1 day to create a luminosity function and compare our results with available observational data to assess the internal consistency of the standard fireball model. Results: We show that the luminosity functions can be described by a function similar to a log normal distribution with an exponential cutoff. The function parameters are frequency dependent but not very dependent on the model parameter distributions used to create the virtual populations. Comparison with observations shows that while there is good general agreement with the data, it is difficult to explain simultaneously the X-ray and optical data. Possible reasons for this are discussed and the most likely one is that the standard fireball model is incomplete and that decoupling of the X-ray and optical emission mechanism may be needed.Comment: 5 pages, 4 figures; accepted for publication in A&

The ultra-long GRB 111209A - II. Prompt to afterglow and afterglow properties

The "ultra-long" Gamma Ray Burst GRB 111209A at redshift z=0.677, is so far the longest GRB ever observed, with rest frame prompt emission duration of ~4 hours. In order to explain the bursts exceptional longevity, a low metallicity blue supergiant progenitor has been invoked. In this work, we further investigate this peculiar burst by performing a multi-band temporal and spectral analysis of both the prompt and the afterglow emission. We use proprietary and publicly available data from Swift, Konus Wind, XMM-Newton, TAROT as well as from other ground based optical and radio telescopes. We find some peculiar properties that are possibly connected to the exceptional nature of this burst, namely: i) an unprecedented large optical delay of 410+/-50 s is measured between the peak epochs of a marked flare observed also in gamma-rays after about 2 ks from the first Swift/BAT trigger; ii) if the optical and X-ray/gamma-ray photons during the prompt emission share a common origin, as suggested by their similar temporal behavior, a certain amount of dust in the circumburst environment should be introduced, with rest frame visual dust extinction of AV=0.3-1.5 mag; iii) at the end of the X-ray "steep decay phase" and before the start of the X-ray afterglow, we detect the presence of a hard spectral extra power law component never revealed so far. On the contrary, the optical afterglow since the end of the prompt emission shows more common properties, with a flux power law decay with index alpha=1.6+/-0.1 and a late re-brightening feature at 1.1 day. We discuss our findings in the context of several possible interpretations given so far to the complex multi-band GRB phenomenology. We also attempt to exploit our results to further constrain the progenitor nature properties of this exceptionally long GRB, suggesting a binary channel formation for the proposed blue supergiant progenitor.Comment: ApJ accepted. Revised version with substantial adjustments, the main results remain unchange

Studying the WHIM with Gamma Ray Bursts

We assess the possibility to detect and characterize the physical state of the missing baryons at low redshift by analyzing the X-ray absorption spectra of the Gamma Ray Burst [GRB] afterglows, measured by a micro calorimeters-based detector with 3 eV resolution and 1000 cm2 effective area and capable of fast re-pointing, similar to that on board of the recently proposed X-ray satellites EDGE and XENIA. For this purpose we have analyzed mock absorption spectra extracted from different hydrodynamical simulations used to model the properties of the Warm Hot Intergalactic Medium [WHIM]. These models predict the correct abundance of OVI absorption lines observed in UV and satisfy current X-ray constraints. According to these models space missions like EDGE and XENIA should be able to detect about 60 WHIM absorbers per year through the OVII line. About 45 % of these have at least two more detectable lines in addition to OVII that can be used to determine the density and the temperature of the gas. Systematic errors in the estimates of the gas density and temperature can be corrected for in a robust, largely model-independent fashion. The analysis of the GRB absorption spectra collected in three years would also allow to measure the cosmic mass density of the WHIM with about 15 % accuracy, although this estimate depends on the WHIM model. Our results suggest that GRBs represent a valid, if not preferable, alternative to Active Galactic Nuclei to study the WHIM in absorption. The analysis of the absorption spectra nicely complements the study of the WHIM in emission that the spectrometer proposed for EDGE and XENIA would be able to carry out thanks to its high sensitivity and large field of view.Comment: 16 pages, 16 figures, accepted for publication by Ap

GRB 130427A Afterglow: A Test for GRB Models

Gamma-ray Burst 130427A had the largest fluence for almost 30 years. With an isotropic energy output of 8.5×1053 erg and redshift of 0.34, it combined a very high energy release with a relative proximity to Earth in an unprecedented fashion. Sensitive X-ray facilities such as {\it XMM-Newton} and {\it Chandra} detected the afterglow of this event for a record-breaking baseline of 90 Ms. We show the X-ray light curve of GRB 130427A of this event over such an interval. The light curve shows an unbroken power law decay with a slope of α=1.31 over more than three decades in time. In this presentation, we investigate the consequences of this result for the scenarios proposed to interpret GRB 130427A and the implications in the context of the forward shock model (jet opening angle, energetics, surrounding medium). We also remark the chance of extending GRB afterglow observations for several hundreds of Ms with {\it Athena}