Relation Between Light Curves And Spectra Of Gamma-ray Bursts

Gamma-ray bursts(GRBs)are the events of gamma-ray flash from cosmological distances,which are the most violent explosion ever detected in space. The events were first detected in 1967.Modern astrophysical models have been challenged due to its extreme high energy photons,short time scales,and large amount of radiative energy.In this thesis,I give a brief review on both theoretical and observational progress of GRBs,and then present two investigations on the relation between GRB light curves and spectra from different aspects.Statistical analysis revealed that the observed FWHM of gamma-ray burst pulses is related to energy by a power-law with its index beingα=0.4.The first investigation is the analysis of the relationship between the local pulse width and the power-law indexα.What investigated in the past are pulses obtained from direct observation.However,as an influence of the curvature effect,what one observes is in fact a combination of various local pulses that are emission from different parts of the fireball surface.To reveal the relation between light curves and spectra,we should pay our attention to local pulses.For example,one might wish to know what quantities are related with local pulses.We focus our attention to single pulse sources for which the pulses are seen to comprise a fast rise and an exponential decay(FRED).We choose seven single pulse GRB sources which have been carefully studied elsewhere to perform the analysis.Local pulses for six of the seven sources have been presented vias the fit,of the flux density formulas which take into account the curvature effect,to the light curve data.For the other one,we fit its light curve data with the same method and obtain its local pulse.For these sources,the power-law indexαis calculated according to their light curve data.We find that,for this sample,the local pulse FWHM width is obviously anti-correlated with the indexα.This phenomenon has not been predicted by the curvature effect,nor has ever been predicted by other models. Since the number of the sample is small,one needs a sizable sample to check this new finding.Nevertheless,investigating the relation between the local pulse width and the power-law index provides us a new view on the relation between light curves and spectra of GRB pulses.What is new in this investigation is that we pay our attention to local pulses and investigate their relation with spectra. The anti-correlation between the local pulse width and the power-law indexαis a new finding which has not been revealed before.The second investigation is an statistical analysis which is using the Kocevski et al.(2003)sample to check the predictions on the hardness ratio curve of GRB pulses proposed recently by Qin et al.(2006).Compared with what discussed above,the relation between GRB light curves and spectra is investigated from another aspect.Qin et al.(2006)analyzed the evolutionary law of the hardness of spectra based on the scenario of the curvature effect,and they presented several predictions based on their research.They introduced a so-called raw hardness ratio(RHR)in order to reveal the details of the evolution of the hardness of spectra during the period of pulses.They found that the RHR curve shows different types of profile,with one having a perfect pulse shape without any sinkage,another possessing a pulse-like shape with a sinkage in its decaying phase, and the other showing no pulse-like shape but having only a sinkage shape.In their paper,they studied only few sources,and hence it is unclear whether their predictions are true if a sizable sample is employed.To check their predictions, we adopt the Kocevski et al.(2003)sample in which the light curves of GRBs are in agreement with what the curvature effect predicts.We get 66 GRB pulses from the sample.The light curve data,for which the background counts have been subtracted,are available in the BATSE website.According to the paper of Qin et al.(2006),we add to the signal data a certain background count(in this way,RHR can be well defined through out a pulse),and with these new data we calculate RHR.For two of the 66 sources their hardness ratio signals are too faint to be recognized,and for the rest their RHR curves show exactly what predicted in Qin et al.(2006).Following Qin et al.(2006),we classify the 64 sources into three types merely according to the profiles of their RHR curves:the first type contains sources with a perfect pulse-like profile,sources of the second type possess a pulse-like profile with a sinkage in its decaying phase,and for the third type the sources show no pulse-like profile but have only a sinkage profile.Qin et al.(2006)pointed out that among the three types, sources of the first type should be the hardest,those of the second type should be less hard,and sources of the third type should be the softest.To check this prediction,we calculate the conventional hardness ratio of sources of the three types.Different from RHR,the conventional hardness ratio HR is calculated with the time integral flux(the so-called fluence),which can roughly represent the hardness of sources.(Note that,in our classification,we relay only on the profiles of the RHR curves;no any RHR values such as the peak of RHR are used.)We analyze the HR distributions of the three types and perform K-S tests for these distributions.The analysis reveals that sources of the second type are indeed harder than those of the third type.The number of the first type is small(only three sources)and hence we cannot perform any statistical analysis.However, one can also notice from their HR values that they are relatively harder.Another prediction proposed in Qin et al.(2006)is also confirmed in our analysis:the peak of the RHR curves appears in advance of the peak of the corresponding light curves.A finding beyond our expectation is that in distinguishing sources of different hardness the minimum of the RHR curve is more sensitive than the conventional HR.We therefore suggest that GRB pulses be divided into three types according to their RHR profile and/or the minimum value of RHR(fm2). It is general believed that GRB pulses arise from inner(or outer)shocks.It is the shocks that convey parts of the kinetic energy into radiation.The hardness of a GRB pulse might probably be connected with the strength of the shock or/and the strength of the magnetic field.Such a classification might in some extent connect light curves of GRB pulses and the real physical process.The main contribution of this investigation is checking,in terms of statistics,the predicted profile of the hardness ratio curve of GRB pulses proposed previously based on the curvature effect.The fact that the minimum of the RHR curve is more sensitive than the conventional HR in distinguishing GRB pulses of different hardness is a new finding.