Chromatic Afterglow of GRB 200829A

GRB 200829A was detected as a bright GRB of duration $\sim 30$ s with the BAT instrument onboard the Swift space observatory; the report on its detection was distributed via the GCN/TAN¹¹1https://gcn.nasa.gov automated alert system (Siegel et al., 2020). The Swift observatory also detected an X-ray component of GRB 200829A with the XRT (0.3–10 keV). The X-ray source was found on August 29, 2020, at 14:01:43.1 UT, i.e., 128.7 s after the BAT trigger at $27^{\prime\prime}$ from the center of the error circle for the gamma-ray component (Siegel et al., 2020; Goad et al., 2020).

The Swift Ultraviolet/Optical Telescope (UVOT) began to observe the GRB 200829A field almost immediately after the XRT. It detected a bright optical afterglow with a magnitude $white=14.28\pm 0.14$ (Siegel et al., 2020) at coordinates (J2000) R.A. = 16:44:49.14 and Dec. = +72:19:45.63 with a statistical error of $\pm 0.35^{\prime\prime}$ (90% confidence; Kuin et al. 2020). In the subsequent UVOT observations the source continued to fade (Kuin et al., 2020).

The ground-based optical observations of the fading afterglow of GRB 200829A began $\sim$ 1 hr after the BAT trigger (Pozanenko et al., 2020) with the 1-meter Zeiss-1000 telescope of the Tien-Shan Astronomical Observatory (TShAO) as the part of GRB-IKI-FuN network (Volnova et al. 2021). One hour after the trigger the magnitude of the source was $R=16.8\pm 0.1$ in a single image (Fig.1) with an exposure time of 60 s.

The observations for 2.83 h, beginning from September 29, 2022, 14:49:05 UT, with the Zeiss-1000 telescope at TShAO allowed a detailed R-band light curve with a time resolution $\sim 60$ s to be constructed. Other instruments of the GRB-IKI-FuN network were additionally used to observe the fading afterglow. For example, the observations with the RC-36 telescope of the Kitab Observatory were carried out without a filter quasi-synchronously with TShAO. Beginning from August 29, 2020, 17:25 UT, telescopes on the Crimean Peninsula joined the observations: Zeiss-1000 at the observatory on Mount Koshka in the R and I filters, AZT-11 at the Crimean Astrophysical Observatory (CrAO) in the R filter. Owing to the coordinated work of several telescopes, a detailed light curve was constructed over 12 h of observations. One day after the trigger the optical transient was observed with the AS-32 telescope of the Abastumani Astrophysical Observatory (AbAO) in the R filter and the Zeiss-1000 telescopes (Mount Koshka and the Special Astrophysical Observatory of the Russian Academy of Sciences (SAO RAS) in the R and I filters). Upper limits in the R filter were also obtained on the third and fifth days after the trigger in the observations with the AZT-33IK telescope at the Mondy observatory of the Institute of Solar-Terrestrial Physics, the Siberian Branch of the Russian Academy of Sciences. When the afterglow could no longer be observed with other telescopes due to the source brightness decline, $R\gtrsim 22^{m}.5$, the AZT-22 telescope of the Maidanak Astronomical Observatory (MAO) was used. MAO is located in a unique climatic region and, for this reason, the seeing (angular resolution) here reaches $0^{\prime\prime}.7$. A total of four deep upper limits were obtained in the $R$ filter: three in the period from 13 to 45 days after the burst.

In our analysis of GRB 200829A we used the publicly accessible data of the GBM/Fermi experiment²²2ftp://legacy.gsfc.nasa.gov/fermi/data/.

As has been shown above, GRB 200829A is characterized by a fairly hard energy spectrum with $E_{p}>350$ keV located outside the effective BAT/Swift sensitivity range, 15 – 150 keV. Therefore, in this section devoted to analyzing the burst based on BAT/Swift data, we restricted our study only to its light curve.

As the data source we used the publicly accessible service⁴⁴4https://www.swift.ac.uk/burst_analyser/. Although the trigger time in the BAT/Swift experiment differs by 79.74 s from that in GBM/Fermi, as the trigger time $T_{0}$ we will use the trigger time of the latter, since it corresponds more closely to the start time of the burst prompt phase (Fig.2).

The light curve constructed in the 15 – 50 keV energy band is presented in Fig.6. After binning the light curve by the signal accumulation method until a certain statistical significance was reached, we detected a weak, but statistically significant extended emission with a duration $\sim 1000$ s that is a separate component of the light curve.

The light curves of individual pulses at the prompt phase of GRBs are usually characterized by the so- called FRED shape (fast rise – exponential decay, see, e.g., Norris et al. 2005; Hakkila & Preece 2011; Minaev et al. 2014). The light curve of GRB 200829A has a complex shape and is a superposition of several significantly overlapping FRED pulses, making it difficult to fit the light curve of the entire prompt phase. Therefore, when jointly fitting the component of the prompt phase and the extended emission, we used only the decay stage of the last pulse of the prompt phase that was described by an exponential model.

The light curve of the extended emission is characterized by an initial quasi-plateau stage followed by a power-law flux decline. To describe this component of the light curve, we used a broken power law (Beuermann et al., 1999).

The results of jointly fitting the decay stage of the prompt phase and the extended emission component by the above models are presented in Fig.6. At the initial stage the index of the light curve for the extended emission is $\alpha=0.34\pm 0.27$, which does not rule out the plateau stage ($\alpha=0$), the break in the light curve is observed at $t_{br}=143\pm 38$ s, and the index after the break is $\beta=-1.28\pm 0.18$. The index after the break is close to a value typical for an afterglow ($\beta\sim-1$), suggesting a connection of the extended emission component with the afterglow, which is typical for bright GRBs (see, e.g., Mozgunov et al. 2021). In our further analysis of the X-ray and optical data this interpretation will be confirmed.

GRB 200829A was also detected by the anticoincidence shield (ACS) of the SPI gamma-ray spectrometer onboard the INTEGRAL observatory (von Kienlin et al., 2003).

The light curve of GRB 200829A at energies above 80 keV with a time resolution of 0.5 s constructed from the SPI-ACS/INTEGRAL data⁵⁵5http://isdc.unige.ch/s̃avchenk/spiacs-online/spiacs-ipnlc.pl is presented in Fig. 7. Despite the stable back-ground conditions in the time interval from -5000 to 5000 s around the GRB typical for the SPI- ACS detector (Minaev et al., 2010a; Mozgunov et al., 2021), no extended emission was detected by SPI-ACS/INTEGRAL, although it was recorded in the BAT/Swift experiment with great confidence.

This is probably due to the relatively soft energy spectrum (the small fraction of high-energy emission) of this component and the high lower sensitivity threshold of the ACS detector (80 keV). A possible precursor (Minaev & Pozanenko, 2017) was not detected either. Although several dim episodes with a total duration of about 15 s, from which the burst prompt phase begins, were recorded in the SPI-ACS experiment (Fig. 7), the duration parameters $T_{90}$ and $T_{50}$ cover only the main bright episode and are $T_{90}=5.5\pm 0.1$ s and $T_{50}=2.1\pm 0.1$ s, confirming the classification of this burst as type II (long).

According to the SPI-ACS/INTEGRAL data, the time-integrated flux from GRB 200829A was $F=(115.3\pm 0.3)\times 10^{4}$ counts. Using the cross-calibration of the SPI-ACS and GBM experiments for GRBs from Pozanenko et al. 2020, we obtain an estimate of the fluence in the energy range 10 – 1000 keV, $F\gtrsim 2.9\times 10^{-4}$ erg cm^-2.

Given the systematic calibration error for the SPI-ACS response to GRB energy spectra differing in shape, the estimated fluence can vary within the range $8.4\times 10^{5}$ – $9.8\times 10^{-4}$ erg cm^-2 (at $2\sigma$ confidence). The estimated fluence agrees well with the value obtained through our spectral analysis of the GBM/Fermi data (Table LABEL:tab:gbmspectra).

The afterglow of GRB 200829A was observed for the first $\sim 3$ days in the X-ray and optical bands. To construct the optical light curve of the GRB 200829A afterglow, we processed the GRB-IKI-FuN observational data and the publicly accessible Nordic Optical Telescope (NOT) data using the developed software pipeline (Pankov et al., 2022) based on the APEX package (Kouprianov, 2012; Devyatkin et al., 2010). The standard data processing procedure includes the calibration and quality control of the original images, their alignment and stacking (if required), the extraction of objects in the images, the astrometry and photometry, the construction of a local catalog, the search for and identification of transients in it. In addition to the software pipeline (Pankov et al., 2020), we used the PyRAF software package (Science Software Branch at STScI, 2012) in individual cases, for example, when an optical transient had a low signal-to-noise ratio, $S/N<5$. We performed the astrometry of images based on the USNO-B1.0 reference catalog (Monet et al., 2003). The photometric calibration stars were chosen by cross-matching the stars from USNO-B1.0 with the PanSTARRS PS1 catalog (Chambers et al., 2016). This allowed us to calibrate the source magnitudes in the images taken both in $R$, $I$, and in $r$ using the same stars. The photometry of images without a filter was performed relative to the R magnitude. A log of optical observations is given in Appendix A. Figure 8 presents a multicolor optical light curve; for clarity, the magnitudes in all filters, except $R$, were separated relative to their initial values.

A break in the $R$ filter, which may be related to the geometrical viewing angle effect typical for relativistic jets (Sari et al., 1999; Piran, 2004), is traceable in Fig.8. The magnitudes in the light curve were not corrected for the Galactic extinction characterized by the color excess $E(B-V)=0.0364$ (Schlegel et al., 1998) toward GRB 200829A. Since it is impossible to establish the spectral evolution at the entire optical afterglow stage due to insufficient quasisynchronous coverage in different filters, we assume its absence. Under this assumption the light curves in the $g$, $r$, $i$, $z$, $I$, $u$, $b$, $v$, $uvw1$, $uvw2$ filters and in $clear$ and $white$ light were reduced to the R light curve (the data are presented predominantly in this filter) by additionally multiplying the flux by the appropriate numerical coefficient at which the best agreement with the data from the $\chi^{2}$ test is achieved. In our subsequent analysis of the afterglow we will consider this monochromatic optical light curve.

The X-ray afterglow was also observed quasisynchronously with the optical one by the XRT/Swift instrument (Burrows et al., 2005a). The XRT is a Wolter I telescope with a focal length of $EFF=3500$ mm and a $FOV=23.6^{\prime}\times 23.6^{\prime}$. An E2V CCD detector with $600\times 600$ pixels and cooled to $-100$ ^∘C was mounted at the focal plane. As a result, an angular resolution of $\theta\sim 3^{\prime\prime}$ is achieved. The telescope operates in the 0.3 – 10 keV energy band in several modes, among which are Windowed Timing (WT), and Photon Counting (PC). In the WT mode a good time resolution ($\sim$ 1.8 ms) is achieved, but, at the cost of, the angular and spectral resolutions. In the PC mode the signal readout rate from the CCD is reduced to $\sim$ 2.5 s, but other characteristics do not change. The WT and PC modes are used at fluxes $F_{X}=1-600$, and $F_{X}<1$ mCrab, respectively (Burrows et al., 2005a).

The X-ray light curve of GRB 200829A was constructed from the data publicly available via the Swift Burst Analyzer¹⁰¹⁰10https://www.swift.ac.uk/burst_analyser/00993768/ service. The data contain the results of observations (time and flux) in the WT and PC modes and span a period $\sim 2$ days. The observed X-ray flux was grouped into bins whose duration increases on a logarithmic scale, starting from 60 s. The Galactic extinction on the line of sight was not taken into account. Thus, the light curve was smoothed, while the significance of individual measurements was improved. Fig.9 presents the X-ray light curve of the GRB 200829A afterglow.

According to Fig. 9, a break is traceable in the X-ray light curve, as in the optical one. Fitting the light curve by the Beuermann function (Beuermann et al., 1999) allowed us to determine the slope of the light curve and the position of the break on the time scale. For example, the slope is $\alpha_{1}=1.06\pm 0.03$ before the break and $\alpha_{2}=1.88\pm 0.06$ after the break. Note that the slope for the X-ray afterglow $\alpha_{1}=1.06\pm 0.03$ before the break agrees well with the slope for the extended emission in the soft 15 – 50 keV gamma-ray band $\beta=1.28\pm 0.18$ found previously. Hence a correlation of the observed extended emission and the afterglow can be assumed. According to this assumption, the gamma-ray light curve was rescaled to the X-ray light curve in the time interval 100 – 1000 s relative to $T_{0}$ (in which the data from both telescopes were obtained) assuming the afterglow to be achromatic in the X-ray and soft gamma-ray bands. According to the $\chi^{2}$ test, the conversion coefficient is $k=F_{XRT}/F_{BAT}=4.54$. Thus, we constructed the most complete light curve of the X-ray afterglow that will be used in our further analysis.

Let us investigate the previously constructed X-ray and optical light curves (presented together in Fig. 10) and fit and interpret them.

In Fig. 10 both X-ray and optical light curves consist of three episodes (not counting the burst prompt phase): a flare gradually decays into a power-law flux decline and then a break after which the flux fades according to a steeper law. At the same time, the leading edge of the flash looks rather steep against the background of the power-law decay. Since in the optical light curve the time of the peak cannot be unambiguously determined due to the absence of data, we assume that it coincides with that for the X-ray band.

To fit the light curves, we chose a function in the form of a sum of two power laws with a smooth break (Beuermann et al., 1999) defined by Eq.3:

where, $F_{i}=(\frac{t-T_{0}}{t_{b_{j}}})^{\alpha_{i}}$, $t$ – the time since trigger (days), $t_{b_{i}}$ – the break time (days), $\alpha_{i}$ – are the indices before and after the break, $n$ – the smoothing parameter ($n>0$), $i={1,2,3,4}$, $j=1$ at $i=1,2$, and $j=2$ at $i=3,4$. The fitting results are presented in the Table LABEL:table:ag_fit; the values marked by * were fixed. The fitting by the two-component model was performed in the intervals $\sim 50$ s – 3.66 days in the X-ray band and 283 s – 2.80 days in the optical band (relative to the GBM/Fermi trigger). Fig.10 (bottom) demonstrates the color evolution between the X-ray and optical bands.

To estimate the redshift, we used the technique of simultaneously fitting the spectral energy distribution in the optical and X-ray bands under absorption conditions (Schady et al., 2010). The time-sliced XRT X-ray spectrum and the UVOT optical images were retrieved via the Swift Burst Analyser service. The spectra span the time interval 1554 – 1638 s relative to $T_{0}$, where no significant color evolution is observed. The data were processed with the HEASOFT¹¹¹¹11https://heasarc.gsfc.nasa.gov/ftools (Blackburn, 1995) software package. Figure 11 presents a multiwavelength spectrum of the GRB 200829A afterglow fitted by the model curve (see below).

As the spectral model we use a power law and a broken power law. The model takes into account the optical extinction by interstellar dust grains and the photoelectric X-ray absorption and is represented by Eq. (4) in terms of XSPEC (HEASOFT), where the zdust components are responsible for the optical extinction.

These components are based on an empirical dust extinction law (Pei, 1992). Three extinction laws are available in XSPEC: the Milky Way (MW), the Large Magellanic Cloud (LMC), and the Small Magellanic Cloud (SMC). The extinction model is characterized by the color excess $E(B-V)$, the total-to-selective extinction ratio $R(V)=A(V)/E(B-V)$, where $A(V)$ is the extinction, and the redshift $z$. The phabs and zphabs components allow the absorption by hydrogen in the Galaxy and the burst host galaxy to be taken into account. Both components are defined by the column density $N_{H}$ in units of $10^{-22}$ cm^-2, while zphabs is also defined by the redshift $z$. The powerlaw component is responsible for the power law spectrum and is specified by the spectral index $\beta$ and the normalization $K$ (photons^-1 keV^-1 cm${-2}$ at 1 keV). During our fitting the Galactic extinction parameters were fixed: $E(B-V)=0.0364$ (Schlegel et al., 1998), $R(V)=3.08$ (Pei, 1992), $A(V)=R(V)E(B-V)=0.20$, and $N_{H}=0.039\times 10^{-22}$ cm^-2 (HI4PI Collaboration et al., 2016). The redshift of the Galaxy was also fixed ($z=0$). We found that the spectral data cannot be fitted with the broken power law and, therefore, this model was not considered. Table 3 presents the results of fitting the spectral data for the early afterglow of GRB 200829A by the model defined in Eq. (4). The best spectral fit from the standpoint of the $\chi^{2}/d.f.$ test is achieved when choosing the MW extinction law for the GRB host galaxy (see Table 3). The estimate of the photometric redshift $z=1.29\pm 0.04$ consistent with the independent estimate of $z=1.25\pm 0.02$ obtained previously by Oates et al. (2020) by the same method corresponds to it. However, in contrast to Oates et al. (2020), we also provide our estimates of the extinction parameters in the burst host galaxy. Note that in both cases the error is statistical. Below, $z=1.29\pm 0.04$ will be deemed to be the redshift of GRB 200829A.

The multiwavelength light curve (Fig. 10) of GRB 200829A has an asynchronous (chromatic) behavior in the early afterglow that encompasses the irregularity (flare) and continues up until the jet break. The chromaticity during the flare can be interpreted in terms of the model of a structured jet (see, e.g., Duque et al. 2022). According to this model, harder emission is observed closer to the jet axis and, for this reason, the X-ray emission corresponds to the part of the jet that is characterized by a larger gamma factor. Let us estimate the gamma factor of the jet from the following formula (see, e.g., Han et al. 2022):

where, $m_{p}$ – is the proton mass, $c$ – is the speed of light, $E_{\gamma}=2\pi(1-\cos{\theta_{j}})E_{iso}$ – is the gamma-ray energy of the jet corrected for its opening angle $\theta_{j}$, $\eta=E_{\gamma}/\xi E_{iso}$, $t_{p}=t_{b}-\alpha_{1}/\alpha_{2})^{1/{\omega(\alpha_{2}-\alpha_{1})}}$, $t_{b}$ – is the break time relative to $T_{0}$ (days), $\alpha_{1}$, $\alpha_{2}$ – are the power-law slopes of the light curve before and after the break, respectively, and $\omega=1$. Note that in the light curve the jet break cannot be unambiguously determined. Therefore, we will choose $t_{b}$ from Table LABEL:table:ag_fit in such a way that the open angle is not an extreme one. For example,

1. 1.

   $t_{b}=T_{0}+1.9\times 10^{-3}$ days corresponds to the flare peak in the early afterglow,

2. 2.

   $t_{b}=T_{0}+0.02$ days corresponds to the break of the second component in the X-ray band,

3. 3.

   $t_{b}=T_{0}+0.15$ days corresponds to the break of the second component in the optical band.

The opening angle of the jet cone can be determined from the formula given below (e.g. Sari et al., 1999; Zhang et al., 2007):

where, $t_{b}$ is the break time relative to $T_{0}$ (days), $z$ is the redshift, $E_{52}$ is the isotropic energy $E_{iso}$ in units of $10^{52}$ erg, $n=1$ cm^-3 is the ISM density, and the kinetic energy-to-radiation conversion factor is $\xi=0.1$ (e.g. Zhang et al., 2007). The jet opening angle will then be: $\theta_{j}(a)\approx 0.474^{+0.035}_{-0.039}$ ^∘, $\theta_{j}(b)\approx 1.15^{+0.47}_{-0.32}$ ^∘ or $\theta_{j}(c)\approx 2.44^{+0.71}_{-0.35}$ ^∘. The typical angle $\theta_{j}$determined for bursts with a jet break (e.g. Wang et al., 2018) is known to be $\theta_{j}\approx 2.5\pm 1.0$ ^∘. Thus, the inhomogeneity (flare) in the afterglow light curve is probably not connected with the jet break since the opening angle $\theta_{j}(a)\sim 0.5^{\circ}$ would be anomalously narrow. In cases b) and c) he values turn out to be appropriate. At the same time, the opening angle derived from the X-ray data is narrower than from the optical ones. In cases (b) and (c) we will estimate the energy contained within the jet from the formula $E_{\gamma}=2\pi(1-\cos{\theta_{j}})E_{iso}$. We will obtain, $E_{\gamma,O}=7.04^{+4.72}_{-1.85}\times 10^{51}$ erg when estimated from the optical light curve and $E_{\gamma,X}=1.55^{+1.51}_{-0.75}\times 10^{51}$ erg when estimated from the X-ray light curve. The gamma factors determined from the X-ray, $\Gamma_{X}=197^{+170}_{-99}$, and optical, $\Gamma_{O}=120^{+85}_{-34}$ light curves then formally coincide within the error limits.

Our previous analysis showed that the light curve of the GRB 200829A afterglow contains a flare-type inhomogeneity at the early phase. The flares in GRB light curves were considered, for example, in the following papers Piro et al. (2005); Perna et al. (2006); Swenson et al. (2013); Yi et al. (2017); Mazaeva et al. (2018). For instance, Swenson et al. (2013) investigated the duration as a function of the flare peak time $\Delta t/t_{peak}$ based on a sample of bursts from the second UVOT/Swift catalog. During the analysis it was established that $\Delta t/t_{peak}<0.5$ for more than 80% of the bursts from the sample. Yi et al. (2017) and Mazaeva et al. (2018) also established that the flares have a linear $FWHM$ – $t_{peak}$ correlation as well. Figure 14 presents the profile of the flare in the X-ray light curve of GRB 200829A obtained by subtracting the afterglow model.

The flare being investigated in this paper has $FWHM\approx 146$ s and $t_{peak}\approx 132$ s. The values obtained are consistent with the $FWHM$ – $t_{p}eak$ correlation (Yi et al., 2017; Mazaeva et al., 2018) and are probably further evidence for the unified physical nature of the flares in GRB light curves. The flares may arise at the shock fed by the burst central engine (Burrows et al., 2005b; de Pasquale et al., 2007; Barkov et al., 2021), from the simultaneous observation of different structured-jet zones (Beniamini et al., 2020; Duque et al., 2022), or a variable accretion rate $\dot{M}$ (e.g. Perna et al., 2006).

Our analysis of the first $\sim$ 250 s of the X-ray light curve for GRB 200829A (Fig. 6) does not reject the hypothesis about a plateau either. Owing to its strong magnetic field, the newly formed magnetar is believed to provide energy pumping and to maintain the luminosity at an approximately constant level for some time equal to the plateau duration (de Pasquale et al., 2007; Metzger et al., 2011; Rowlinson et al., 2013). Let us determine the energy release of the plateau in the X-ray light curve of GRB 200829A. First, we need to determine the plateau fluence in the 0.3–10 keV energy band ($\Delta\nu=7.3\times 10^{16}$ – $2.4\times 10^{18}$ Hz) from Eq. (8)

where the times $t_{1}=51.8$ s, and $t_{2}=86.4$ s specify the light curve segment with a power-law slope $\sim 0$, corresponding to the plateau, and $f_{\nu}(t)$ is the spectral flux density. Having substituted all of the necessary values, we obtain the plateau fluence $F_{plat}=1.3\times 10^{-10}$ erg cm^-2. The plateau energy in the 0.3 – 10 keV band calculated from Eq. (8), will then be $E_{plateu}=5.8\times 10^{47}$ erg. Note that such values are consistent with the $L_{X}$ – $T_{a}$, where $L_{x}$ – is the plateau luminosity in the 0.3 - 10 keV, and $T_{a}=t_{2}/(1+z)$ is the time at the end of the plateau stage in the source frame (Dainotti et al., 2008; Dainotti et al., 2021).