Peak Energy Correlations for Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are the most powerful explosions in the universe. Over the past two decades, several GRB energy and luminosity correlations were discovered. These correlations typically involve an observable parameter, like the observed peak energy, Ep,obs, and a non-observable quantity, like the equivalent isotropic energy, Eiso. This paper provides a brief review of GRB peak energy correlations. Specifically, it focuses on the Amati relation, which correlates Ep,obs and Eiso, and the Ghirlanda relation, which correlates Ep,obs and Ey, the total energy corrected for beaming. The paper also discusses the physical interpretation of these relations in the context of the internal shock model.

The correlations among variability,optical peak time and spectral time lag of long gamma-ray bursts

Statistical relations are useful tools to comprehend the intrinsic physics processes of gamma-ray bursts(GRBs). In this work we collect spectral lag(τ), variability(V) and optical peak time(tp,o). We find that there is a correlation between variabilities and spectral lags, reading as V =-0.0075(±0.0007) ×log10τ +0.0351(±0.0024). There may also exist a relatively weak positive tendency between GRBs optical band peak times and their spectral time lags. Its Pearson coefficient is 0.398, which indicates a weak linear correlation. If we contain some "negative spectral lag" samples, then the latter relation would be worse due to two outlying points. The τ-V relation is consistent with previous studies, and the positive trend betweenτ and tp,oindicates the spectral lag of GRB might be caused by the curvature effect, but this conclusion is not significant.

Gamma-ray bursts with extended emission:classifications, energy correlations and radiation properties

Thanks to more and more gamma-ray bursts with measured redshift and extended emission detected by the recent space telescopes,it is urgent and possible to check whether those previous energy correlations still satisfy the particular sample involving only the bursts accompanied by tail radiations.Using 20 long and 22 short bursts with extended emission,we find that the popular γ-ray energy correlations of the intrinsic peak energy versus the isotropic energy(Amati relation) and the intrinsic peak energy versus the peak luminosity(Yonetoku relation) do exist in both short and long bursts.However,it is much better if these gamma-ray bursts with extended emissions are reclassified into two subgroups of E-Ⅰ and E-Ⅱ that make the above energy correlations more tight.As proposed by Zhang et al.,the energy correlations can be utilized to distinguish these kinds of gamma-ray bursts in the plane of bolometric fluence versus peak energy as well.Interestingly,the peculiar short GRB 170817 A belongs to the E-Ⅰ group in the fluence versus peak energy plane,but it is an outlier of both the Amati and Yonetoku relations even though the off-axis effect has been corrected.Furthermore,we compare the radiation features between the extended emissions and the prompt gamma-rays in order to search for their possible connections.Taking into account all these factors,we conclude that gamma-ray bursts with extended emission are still required to model with dichotomic groups,namely E-Ⅰ and E-Ⅱ classes,which hint that they might have different origins.

An Amati-Like Correlation for Short Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are by far the most powerful explosions in the universe. Over the past two decades, several GRB energy and luminosity correlations were discovered for long gamma-ray bursts, which are bursts whose observed duration exceeds 2 seconds. One important correlation, the Amati relation, involves the observed peak energy, Ep,obs, in the vFv spectrum and the equivalent isotropic energy, Eiso. For many years, it was believed that the Amati correlation applied only to long GRBs. In this paper, we use a recent data sample that includes both long and short GRBs to re-examine the issue of whether the Amati correlation applies to long GRBs only. Our results indicate that although short bursts do not follow the Amati relation in the strict sense, they do exhibit a correlation between the intrinsic peak energy, Ep,i, and Eiso that is very similar to the Amati relation but with a different normalization and slope. The paper also discusses the physical interpretation of this correlation in the context of the internal shock model.

The Eiso-Liso Plane for Gamma-Ray Bursts

Gamma-ray bursts (GRBs) are the most intense and powerful explosions in the universe. Based on their observed duration, they are traditionally divided into long bursts whose observed duration equals or exceeds 2 s, and short bursts whose observed duration is less than 2 s. Several GRB energy and luminosity correlations have been discovered for long gamma-ray bursts. Two important correlations are the Amati relation and the Yonetoku relation. The Amati relation is a correlation between the intrinsic peak energy, Ep,i, obtained from the νFν spectrum and the equivalent isotropic energy, Eiso, while the Yonetoku relation is a correlation between Ep,i and the peak isotropic luminosity, Liso. In this paper, we use a recent data sample that includes both long and short GRBs to compare these two correlations for the two groups of bursts. We also compare the Eiso-Liso plane for these two types of bursts. Our results indicate that both long and short bursts adhere to these two correlations but with different normalizations. We also find that the Eiso-Liso plane is similar for both types of GRBs but is shifted to lower values of Eiso for short GRBs.

Relationships between Relative Spectral Lags and Relative Widths of Gamma-ray Bursts

The phenomenon of gamma-ray burst （GRB） spectral lags is very common, but a definitive explanation has not yet been given. From a sample of 82 GRB pulses we find that the spectral lags are correlated with the pulse widths, however, there is no correlation between the relative spectral lags and the relative pulse widths. We suspect that the correlations between spectral lags and pulse widths might be caused by the Lorentz factor of the GRBs concerned. Our analysis on the relative quantities suggests that the intrinsic spectral lag might reflect other aspect of pulses than the aspect associated with the dynamical time of shocks or that associated with the time delay due to the curvature effect.

A Close Correlation between the Spectral Lags and Redshifts of Gamma-Ray Bursts

Based on nine BATSE GRBs with known redshifts, we found that the maximum spectral lag of all the pulses in a gamma-ray burst （GRB） appears to be anti-correlated with the redshift of the burst. In order to confirm this finding, we analyzed 10 GRBs detected by HETE-2 with known redshifts and found a similar relation. Using the relation, we estimated the redshifts of 878 long GRBs in the BATSE catalog, then we investigated the distributions of the redshifts and 869 Eiso of these GRBs. The distribution of the estimated redshifts is concentrated at z = 1.4 and the distribution of Eiso peaks at 10^52.5 erg. The underlying physics of the correlation is unclear at present.

A Test on Different Types of the Time Curve of Hardness Ratio of Gamma-Ray Bursts based on the Curvature Effect

We analyzed a sample of 66 gamma-ray bursts （GRBs） and statistically confirmed the prediction on the time curve of the hardness ratio of GRBs made by Qin et al. based on the curvature effect. In their analysis, GRB pulses are divided into three types according to the shape of their raw hardness ratio （RHR） time curves, defined as to include the background counts to the signal counts, so as to make use of counts within small time intervals. Of the three types, very hard sources exhibit a perfect pulse-like profile （type 1）, hard bursts possess a pulse-like profile with a dip in the decay phase （type 2）, and soft bursts show no pulse-like profile but have only a dipped profile （type 3）. In terms of the conventional hardness ratio, type 3 sources are indeed generally softer than those of type 1 and type 2, in agreement with the prediction. We found that the minimum value of RHR is sensitive in distinguishing the different types. We propose that GRB pulses can be classified according to the minimum value of RHR and that the different type sources may be connected with different strengths of the shock or/and the magnetic field.

Origins of short gamma-ray bursts deduced from offsets in their host galaxies revisited

The spatial distribution of short Gamma-ray bursts (GRBs) in their host galaxies provides us with an opportunity to investigate their origins. Based on the currently observed distribution of short GRBs relative to their host galaxies, we obtain the fraction of the component that traces the mergers of binary compact objects and the one that traces star formation rate (such as massive stars) in earlyand late-type host galaxies. From the analysis of projected offset distribution and only based on population synthesis and massive star models, we find that the fraction of massive stars is 0.37+-00..4327 with an error at the 1σ level for a sample with 22 short GRBs in the literature. From these results, it is hard to accept that the origin of short GRBs with observed statistics is well described by current models using only the offset distribution. The uncertainties in observational localizations of short GRBs also strongly affect the resulting fraction.

Spectral properties of Fermi/GBM gamma-ray bursts and the GeV emission detection rate with Fermi/LAT

With a sample of 58 Fermi/GBM GRBs detected before 2009 May,we compare the spectral properties of GBM GRBs with those detected by CGRO/BTASE and HETE-2.Our results show that the spectral index distributions are very consistent with those observed by BATSE.However,the Ep distribution is quite different from that observed with BATSE and HETE-2.The GBM GRBs tend to be softer than the BATSE sample,but harder than the HETE-2 sample.This may be due to the instrumental selection effects and artificial sample effect on the BATSE sample.The distribution of the pseudo redshifts derived from the luminosity indicator based on the Amati-relation shows rough consistency with the spectroscopic redshifts of Swift GRBs.We estimate the detection rate of GBM GRBs with LAT based on the observed spectrum in the GBM band,and the inferred burst ratio of LAT detection with over 5 photons to GBM detection is 6%,yielding a detection rate pf 12 GRBs/yr with over 5 photons in the 1-300 GeV band.This is roughly consistent with the results in the first half year of Fermi operation.The low detection rate compared with theoretical predictions is a key for revealing the radiation mechanisms and particle acceleration of the prompt gamma-rays.

Duration distributions for different softness groups of gamma-ray bursts

Gamma-ray bursts(GRBs) are divided into two classes according to their durations.We investigate if the softness of bursts plays a role in the conventional classification of the objects.We employ the BATSE(Burst and Transient Source Experiment) catalog and analyze the duration distributions of different groups of GRBs associated with distinct softness.Our analysis reveals that the conventional classification of GRBs with the duration of bursts is influenced by the softness of the objects.There exists a bimodality in the duration distribution of GRBs for each group of bursts and the time position of the dip in the bimodality histogram shifts with the softness parameter.Our findings suggest that the conventional classification scheme should be modified by separating the two well-known populations in different softness groups,which would be more reasonable than doing so with a single sample.According to the relation between the dip position and the softness parameter,we get an empirical function that can roughly set apart the short-hard and long-soft bursts:SP =(0.100 ± 0.028) T-(0.85 0.18) 90,± where SP is the softness parameter adopted in this paper.

Self-organized criticality in multi-pulse gamma-ray bursts

The variability in multi-pulse gamma-ray bursts(GRBs)may help to reveal the mechanism of underlying processes from the central engine.To investigate whether the self-organized criticality(SOC)phenomena exist in the prompt phase of GRBs,we statistically study the proper ties of GRBs with more than 3 pulses in each burst by fitting the distributions of several observed physical variables with a Markov Chain Monte Carlo approach,including the isotropic energy E_(iso),the duration time T,and the peak count rate P of each pulse.Our sample consists of 454 pulses in 93 GRBs observed by the CGRO/BATSE satellite.The best-fitting values and uncertainties for these power-law indices of the differential frequency distributions are:α_(E)^(d)=1.54±0.09,α_(T)^(d)=1.82_(-0.15)^(+0.14)andα_(P)^(d)=2.09_(-0.19)^(0.18),while the power-law indices in the cumulative frequency distributions are:α_(E)^(c)=1.44_(-0.10)^(+0.08),α_(T)^(c)=1.75_(-0.13)^(0.11)andα_(P)^(c)=1.99_(-0.19)^(+0.16).We find that these distributions are roughly consistent with the physical framework of a Fractal-Diffusive,Self^Organized Criticality(FD-SOC)system with the spatial dimension S=3 and the classical diffusionβ=1.Our results support that the jet responsible for the GRBs should be magnetically dominated and magnetic instabilities(e.g.,kink model,or tearing-model instability)lead the GRB emission region into the SOC state.

Luminosity-peak energy relation in the decay phases of gamma-ray burst pulses

Using time-resolved spectral data for a sample of 30 pulses in 27 bright GRBs detected with CGRO/BATSE, we investigate the luminosity-peak energy relation (L-E p relation) in the decay phases of these pulses. A tight L-E p relation is found for most of the pulses, but its power law index is various among pulses, which is normally distributed at 1.84±0.60(1σ) for the pulses in our sample, roughly consistent with the L-E p relation within a GRB and the isotropic gamma-ray energy-E p relation among GRBs. The large scatter of the power law index cannot be explained with both the statistical or observational effects and it may be an intrinsic feature, indicating that no universal L-E p relation would be expected among GRBs/pulses. This may strongly weaken the cosmological use of this relation.

共动系中伽玛暴峰值能量的分布及其与光度的关系

伽玛暴νfν谱的峰值能量E_p是伽玛暴的一个很重要的观测物理量,观测系中伽玛暴νf_ν谱的峰值能量Ep分布很宽.根据各向同性光度L_(iso)、初始洛伦兹因子Γ_0和暴源系中峰值能量E_p,z之间的关系式估算伽玛暴的初始洛伦兹因子Γ_0,再把伽玛暴νf_ν谱的峰值能量E_p和光度L_(iso)修正到共动坐标系,发现共动系中峰值能量的分布还是很宽.这意味着观测系中E_p的宽分布可能是伽玛暴的真实物理分布.检验了共动坐标系中光度和峰值能量之间的关系,发现它们之间仍然存在相关性.最后,进一步对伽玛暴的辐射物理进行限制,认为共动坐标系中峰值能量分布很宽可能是由于辐射电子的洛伦兹因子γ_e分布很宽.