tokens: between the spectral and temporal index in various regimes (cooling, density regimes, or an injection from the central engine). These relations present tests without delving into details of the models (e.g., Zhang Mészáros 2004 ; Gao et al. 2013 ). Using the conventional notation, F ν ∝ t − α ν − β , we obtained α X , β X for GRB 190829A afterglow in the X-ray bands. In Table 3 , we present the indices of the flux and flux density (@ 10 keV) for the segments of the light curve. We particularly analyze segments III (flare) and IV (break) regions in detail, starting with phase IV. Table 3 The Best-fit Values of Spectral and Temporal Indices for Episodes Marked in Figure 4 Notes. We use a power-law or a smooth-broken-power-law a function to model the XRT light curves for different segments using the python module emcee (Foreman-Mackey et al. 2013 ). All quoted errors on spectral parameters correspond to the 16th and 84th percentiles. a s : smoothness parameter, α 1 : index before break t b , α 2 : index after break (Wang et al. 2018 ), log( L ): log-likelihood, n : number of data points, and k : number of the free parameters in the fit. b Excluding 3 × 10 5 –2 × 10 6 s. The segment in the flux light curve shows a shallow change (0.3 ± 0.3) in the temporal decay index. Contrary to this, in the flux density (@10 keV), α X changes by 1.1 ± 0.2. Naively, one may tend to recognize the break with a jet break, however, upon closer examination the photon index softens during ∼3 × 10 5 –2 × 10 6 s (vertical dashed lines in Figure 4 (b)). This is also reflected in the softening of the hardness ration (vertical dashed lines in Figure 4 (c)). Since after this period, the photon index settles down to its previous value before the spectral change, it suggests a rebrightening within the low-energy Swift-XRT band. The passage of some spectral break frequency is also less likely due to the same reason, because any frequency crossover will cause an irreversible change in the spectral index. Phases IV and V (excluding the region between the black dashed lines) is consistent with a typical decay with α X ∼ 1.22 ± 0.03. The UVOT data in this phase is possibly dominated by the contribution of the host. The observation in the i -band shows the rising part of a supernova (Perley Cockeram 2019c ) contemporaneous with the break t b . Consider adiabatic cooling without energy injection from the central engine. The inferred value of α X (1.31 ± 0.15) from observed β X (1.21 ± 0.1) matches with the observed value (1.22 ± 0.03) within error bars for the spectral regime ν > ν c and the interstellar or Wind mediums (Table 3 ). We estimate the value of the electron distribution index p = 2.42 ± 0.2 from p = 2 β . We calculate the kinetic energy in the jet E K,iso = 1.7 × 10 52 erg according to Equation (17) of Wang et al. ( 2015 ), which is valid for the case ν X > ( ν m , ν c ). We took a prebreak segment from phase IV (0.27–1.9 days) with a mean photon arrival time ∼0.7 day.
ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-Wavelength O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O B-Model O O O O O B-Telescope O O O O O O O B-Software O B-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Telescope O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O B-Mission O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O