How Bad or Good Are the External Forward Shock Afterglow Models of Gamma-Ray Bursts?

Abstract

The external forward shock models have been the standard paradigm to interpret the broadband afterglow data of gamma-ray bursts (GRBs). One prediction of the models is that some afterglow temporal breaks at different energy bands should be achromatic; that is, the break times should be the same in different frequencies. Multiwavelength observations in the Swift era have revealed chromatic afterglow behaviors at least in some GRBs, casting doubts on the external forward shock origin of GRB afterglows. In this paper, using a large sample of GRBs with both X-ray and optical afterglow data, we perform a systematic study to address the question: how bad or good are the external forward shock models? Our sample includes 85 GRBs up to 2014 March with well-monitored X-ray and optical light curves. Based on how well the data abide by the external forward shock models, we categorize them into five grades and three samples. The first two grades (Grade I and II) include 45 of 85 GRBs. They show evidence of, or are consistent with having, an achromatic break. The temporal and spectral behaviors in each afterglow segment are consistent with the predictions (the "closure relations") of the forward shock models. These GRBs are included in the Gold sample. The next two grades (Grade III and IV) include 37 of 85 GRBs. They are also consistent with having an achromatic break, even though one or more afterglow segments do not comply with the closure relations. These GRBs are included in the Silver sample. Finally, Grade V (3/85) shows direct evidence of chromatic behaviors, suggesting that the external shock models are inconsistent with the data. These are included in the Bad sample. We further perform statistical analyses of various observational properties (temporal index α, spectral index β, break time t b ) and model parameters (energy injection index q, electron spectral index p, jet opening angle j q , radiative efficiency η γ , and so on) of the GRBs in the Gold sample, and derive constraints on the magnetization parameter ϵ B in the forward shock. Overall, we conclude that the simplest external forward shock models can account for the multiwavelength afterglow data of at least half of the GRBs. When more advanced modeling (e.g., long-lasting reverse shock, structured jets, arbitrary circumburst medium density profile) is invoked, up to >90% of the afterglows may be interpreted within the framework of the external shock models.

GRB 110530a: Peculiar Broad Bump and Delayed Plateau in Early Optical Afterglows

“…6 Some recent statistical analysis suggests a low ǫ B , i.e., [10 −6 , 10 −3 ] (e.g., Wang et al 2015;Gao et al 2015;Japelj et al 2014). Therefore, we set ǫ B ∈ [10 −7 , 10 −2 ].…”

“…Statistical analysis of the optical afterglow lightcurves observed from Feb, 1997to Nov., 2011 shows that about 1/3 of the optical afterglow lightcurves well agree with the prediction of the external shock model in the thin shell case, and another 1/3 may require an extra energy injection to the external shocked medium (Li et al 2012;Liang et al 2013). An extensive analysis of the X-ray and optical afterglow data by Wang et al (2015) shows that the standard external shock models are good for explaining the data by elaborately considering various effects, such as long-lasting reverse shock, structured jets, circumburst medium density profile.…”

The extension of variability properties in gamma-ray bursts to blazars

“…With the MTS values derived by and Golkhou et al (2015), we find a similar MTS − Γ anti-correlation for the 22 GRBs with estimated Lorentz factors, with no evidence of the shallow-plateau (GRB 100621A is an outlier, see Figure 1). After excluding GRB 100621A, a best straight-line fit to GRB data with errors 1 in both Γ and MTS gives (solid line in Figure 1) log MTS 1 + z = −(4.8 ± 1.5) log Γ + (11.1 ± 3.2), References: 1) and 2) represent the references for MTS measurements that selected from and Golkhou et al (2015) where a 50% error is adopted for Γ considering uncertainties of the model parameters in deriving them (e.g., one order of magnitude uncertainty in the density of ambient medium and radiative efficiency of the blast wave, Wang et al 2015;Zhang et al 2015) and 0.2 dex is adopted for MTS considering that the MTS measurements are derived from different telescopes with different wavebands (e.g.,MTS derived from Swift at 15-350 keV maybe 1-1.5 times longer than that derived from Fermi at 8-1000 keV, see Golkhou et al 2015, for more details). We find that this anticorrelation as found in GRBs can be extended to blazars, where 20 blazars roughly stay on the best-fit line of GRBs (solid line in Figure 1).…”

On the Late-Time Spectral Softening Found in X-Ray Afterglows of Gamma-Ray Bursts

“…The light curves of most normal non-softening GRBs have been exclusively explained by the well-studied external shock models (e.g., Liang et al 2007Liang et al , 2008Liang et al , 2009Li et al 2015;Wang et al 2015). In principle the dust scattering takes place at a distance of approximately a hundred parsecs, while the internal and external shocks would be produced at less than a parsec.…”

“…To successfully interpret the seemingly very complicated afterglow light curves, it would take great effort to develop the external shock models (e.g., Li et al 2015;Wang et al 2015). Alternatively, for the X-ray afterglows that have shallow decay in the light curves and softening in the spectra, an X-ray scattering scenario (Shao & Dai 2007) has been proposed to nicely reproduce both the light curves and spectral evolution (Shao et al 2008;Holland et al 2010;Evans et al 2014;Zhao & Shao 2014).…”