Gamma Ray Bursts Spectral--Energy correlations: recent results

The correlations between the rest frame peak of the EF_E spectrum of GRBs Epeak and their isotropic energy (E_iso) or luminosity (L_iso) could have several implications for the understanding of the GRB prompt emission. These correlations are presently founded on the time-averaged spectral properties of a sample of 95 bursts, with measured redshifts, collected by different instruments in the last 13 years (pre-Fermi). One still open issue is wether these correlations have a physical origin or are due to instrumental selection effects. By studying 10 long and 14 short GRBs detected by Fermi we find that a strong time-resolved correlation between E_peak and the luminosity L_iso is present within individual GRBs and that it is consistent with the time-integrated correlation. This result is a direct proof of the existence in both short and long GRBs of a similar physical link between the hardness and the luminosity which is not due to instrumental selection effects. The origin of the E_peak-L_iso correlation should be searched in the radiation mechanism of the prompt emission.Comment: 5 pages, 3 figures, to appear in the proceedings of the 275 IAU Symp: "Jets at all scales", Buenos Aires, Sept. 201

Extremely energetic Fermi Gamma-Ray Bursts obey spectral energy correlations

The extremely energetic Fermi GRBs 080916C, with its Eiso of ~ 10^{55} erg in 1 keV - 10 GeV and intense GeV emission, and 090323 give us a unique opportunity to test the reliability and extension of spectral energy correlations. Based on Konus/WIND and Fermi spectral measurements, we find that both events are fully consistent with the updated (95 events as of April 2009) Ep,i - Eiso correlation, thus further confirming and extending it and pointing against a possible flattening or increased dispersion at very high energies. This also suggests that the physics behind the emission of peculiarly bright and hard GRBs is the same as for softer and weaker ones. In addition, we find that the normalization of the correlation obtained by considering these two GRBs and the other long ones for which Ep,i was measured with high accuracy by the Fermi/GBM are fully consistent with those obtained by other instruments (e.g., BeppoSAX, Swift, Konus-WIND), thus indicating that the correlation is not affected significantly by detectors limited thresholds and energy bands. Prompted by the extension of the spectrum of GRB 080916C up to several GeVs without any excess or cut-off, we also investigated if the evaluation of Eiso in the commonly adopted 1 keV - 10 MeV energy band may bias the Ep,i - Eiso correlation contributing to its scatter. By computing Eiso from 1 keV to 10 GeV, the slope of the correlation becomes slightly flatter, while its dispersion does not change significantly. Finally, we find that GRB 080916C is also consistent with most of the other spectral energy correlations derived from it, with the possible exception of the Ep,i - Eiso - tb correlation.Comment: 9 pages, 5 figures, final revised version accepted for pubblication in Astronomy & Astrophysics (main Journal

Retrospective revaluation as simple associative learning

Backward blocking, unovershadowing and backward conditioned inhibition are examples of "retrospective revaluation" phenomena, that have been suggested to involve more than simple associative learning. Models of these phenomena have thus employed additional concepts, e.g. appealing to attentional effects or more elaborate learning mechanisms. I show that a suitable representation of stimuli, paired with a careful analysis of the discriminations faced by animals, leads to an account of these and other phenomena in terms of a simple "elemental" model of associative learning, with essentially the same learning mechanism as the Rescorla and Wagner (1972) model. I conclude with a discussion of some implications for theories of learning

GRB 060218 and the outliers with respect to the Ep-Eiso correlation

GRB 031203 and GRB 980425 are the two outliers with respect to the Ep-Eiso correlation of long GRBs. Recently Swift discovered a nearby extremely long GRB 060218 associated with a SN event. The spectral properties of this bursts are striking: on the one hand its broad band SED presents both thermal and non-thermal components which can be interpreted as due to the emission from the hot cocoon surrounding the GRB jet and as standard synchrotron self absorbed emission in the GRB prompt phase, respectively; on the other hand it is its long duration and its hard--to--soft spectral evolution which make this underluminous burst consistent with the Ep-Eiso correlation of long GRBs. By comparing the available spectral informations on the two major outliers we suggests that they might be twins of 060218 and, therefore, only apparent outliers with respect to the Ep_Eiso correlation. This interpretation also suggests that it is of primary importance the study the broad band spectra of GRBs in order to monitor their spectral evolution throughout their complete duration.Comment: To appear in the conference proceeding of the IV workshop on "Science with the new generation of high energy Gamma-Ray Experiment", 20-22 June 2006, Isola d'Elb

Modeling Society with Statistical Mechanics: an Application to Cultural Contact and Immigration

We introduce a general modeling framework to predict the outcomes, at the population level, of individual psychology and behavior. The framework prescribes that researchers build a cost function that embodies knowledge of what trait values (opinions, behaviors, etc.) are favored by individual interactions under given social conditions. Predictions at the population level are then drawn using methods from statistical mechanics, a branch of theoretical physics born to link the microscopic and macroscopic behavior of physical systems. We demonstrate our approach building a model of cultural contact between two cultures (e.g., immigration), showing that it is possible to make predictions about how contact changes the two cultures

The Geometry of Stimulus Control

Many studies, both in ethology and comparative psychology, have shown that animals react to modifications of familiar stimuli. This phenomenon is often referred to as generalisation. Most modifications lead to a decrease in responding, but to certain new stimuli an increase in responding is observed. This holds for both innate and learned behaviour. Here we propose a heuristic approach to stimulus control, or stimulus selection, with the aim of explaining these phenomena. The model has two key elements. First, we choose the receptor level as the fundamental stimulus space. Each stimulus is represented as the pattern of activation it induces in sense organs. Second, in this space we introduce a simple measure of `similarity' between stimuli by calculating how activation patterns overlap. The main advantage we recognise in this approach is that the generalisation of acquired responses emerges from a few simple principles which are grounded in the recognition of how animals actually perceive stimuli. Many traditional problems that face theories of stimulus control (e.g. the Spence-Hull theory of gradient interaction or ethological theories of stimulus summation) do not arise in the present framework. These problems include the amount of generalisation along different dimensions, peak-shift phenomena (with respect to both positive and negative shifts), intensity generalisation, and generalisation after conditioning on two positive stimuli

Artificial neural networks as models of stimulus control

We evaluate the ability of artificial neural network models (multi-layer perceptrons) to predict stimulus-­response relationships. A variety of empirical results are considered, such as generalization, peak-shift (supernormality) and stimulus intensity effects. The networks were trained on the same tasks as the animals in the considered experiments. The subsequent generalization tests on the networks showed that the model replicates correctly the empirical results. It is concluded that these models are valuable tools in the study of animal behaviour

Possible existence of Ep-Lp and Ep-Eiso correlations for Short Gamma-Ray Bursts with a factor 5 to 100 dimmer than those for Long Gamma-Ray Bursts

We analyzed correlations among the rest frame spectral peak energy $E_{\rm p}$, the observed frame 64ms peak isotropic luminosity $L_{\rm p}$ and the isotropic energy $E_{\rm iso}$ for 13 Short Gamma Ray Burst (SGRB) candidates having the measured redshift $z$, $T_{\rm 90}^{\rm obs}/(1+z)<2$ sec and well determined spectral parameters. A SGRB candidate is regarded as a misguided SGRB if it is located in the 3-$\sigma_{\rm int}$ dispersion region from the best-fit function of the $E_{\rm p}$--$E_{\rm iso}$ correlation for Long GRBs (LGRBs) while the others are regarded as secure SGRBs possibly from compact star mergers. Using 8 secure SGRBs out of 13 SGRB candidates, we tested whether $E_{\rm p}$--$E_{\rm iso}$ and $E_{\rm p}$--$L_{\rm p}$ correlations exist for SGRBs. We found that $E_{\rm p}$--$E_{\rm iso}$ correlation for SGRBs($E_{\rm iso} =10^{51.42 \pm 0.15}{\rm erg s^{-1}} ({E_{\rm p}}/{\rm 774.5 keV})^{1.58 \pm 0.28}$) seems to exist with the correlation coefficeint $r=0.91$ and chance probability $p=1.5\times10^{-3}$. We found also that the $E_{\rm p}$--$L_{\rm p}$ correlation for SGRBs($L_{\rm p} = 10^{52.29 \pm 0.066}{\rm erg s^{-1}} ({E_{\rm p}}/{\rm 774.5 keV})^{1.59 \pm 0.11}$) is tighter than $E_{\rm p}$--$E_{\rm iso}$ correlation since $r=0.98$ and $p=1.5\times10^{-5}$. Both correlations for SGRBs are dimmer than those of LGRBs for the same $E_{\rm p}$ by factors $\sim$100 ($E_{\rm p}$--$E_{\rm iso}$) and $\sim$ 5($E_{\rm p}$--$L_{\rm p}$). Applying the tighter $E_{\rm p}$--$L_{\rm p}$ correlation for SGRBs to 71 bright BATSE SGRBs, we found that pseudo redshift $z$ ranges from 0.097 to 2.258 with the mean $$ of 1.05. The redshifts of SGRBs apparently cluster at lower redshift than those of LGRBs ($\sim 2.2$), which supports the merger scenario of SGRBs.Comment: 8 pages, 6 figures, Accepted for publication in MNRA

Cosmological constraints with GRBs: homogeneous medium vs wind density profile

We present the constraints on the cosmological parameters obtained with the $E_{\rm peak}$--$E_{\gamma}$ correlation found with the most recent sample of 19 GRBs with spectroscopically measured redshift and well determined prompt emission spectral and afterglow parameters. We compare our results obtained in the two possible uniform jet scenarios, i.e. assuming a homogeneous density profile (HM) or a wind density profile (WM) for the circumburst medium. Better constraints on $\Omega_{M}$ and $\Omega_{\Lambda}$ are obtained with the (tighter) $E_{\rm peak}$--$E_{\gamma}$ correlation derived in the wind density scenario. We explore the improvements to the constraints of the cosmological parameters that could be reached with a large sample, $\sim$ 150 GRBs, in the future. We study the possibility to calibrate the slope of these correlations. Our optimization analysis suggests that $\sim 12$ GRBs with redshift $z\in(0.9,1.1)$ can be used to calibrate the $E_{\rm peak}$--$E_{\gamma}$ with a precision better than 1%. The same precision is expected for the same number of bursts with $z\in(0.45,0.75)$. This result suggests that we do not necessarily need a large sample of low z GRBs for calibrating the slope of these correlations.Comment: 7 pages, 7 figures, submitted to A&