Multiwavelength Observations of GRB 181201A and Detection of Its Associated Supernova

Abstract

Multicolor photometric observations in the optical band and a comprehensive study in the X-ray, gamma-ray, and radio bands are presented for GRB 181201A and its afterglow. The optical observations began ${\sim}0.5$ day after the burst and lasted almost continuously for ${\sim}24$ days. They were resumed after eight months, which allowed us to determine the contribution of the host galaxy to the measured fluxes and to estimate the related extinction. Such complete coverage of the light curve became possible owing to the coordinated work of a network of nine telescopes worldwide. Convincing evidence of an incipient supernova explosion at the location of the burst source was obtained at the end of the first series of observations. Thus, GRB 181201A became yet another event that confirmed the association of gamma-ray bursts with supernovae. Thirty such events based on photometric observations of burst afterglows were known before it. A comparison of the supernova-induced excess emission in the light curve of the afterglow from GRB 181201A with other events has allowed some of the supernova parameters to be determined.

APPENDIX

ANALYTICAL DESCRIPTION OF THE SN LIGHT CURVE

In this paper we estimated the parameters of the SN associated with GRB 181201A (the position of the light-curve peak and its amplitude) by fitting the model light curve of the previously well-studied SN 2013dx/GRB 130702A (Volnova et al. 2017) to the photometric data. In the case of a sufficient number of measurements (number of data points in the light curve), analytical functions can also be used to determine the SN parameters. Figure 15 shows the best fits to the bolometric light curve of SN 2013dx (Volnova et al. 2017) by various functions. The following functions were used:

• the Bazin function (Bazin et al. 2011)

  $$f_{1}(t)=A+B\frac{\exp[-(t-t_{0})/\tau_{\textrm{fall}}]}{1+\exp[-(t-t_{0})\tau_{\textrm{rise}}]};$$

• the quartic polynomial

  $$f_{2}(t)=A+Bt+Ct^{2}+Dt^{3}+Et^{4};$$

• the quadratic polynomial (Bianco et al. 2014)

  $$f_{3}(t)=A+Bt+Ct^{2};$$

• the lognormal function

  $$f_{4}(t)=A+\frac{B}{\omega}\left(\frac{2}{\pi}\right)^{1/2}\exp\left[-\frac{2\log^{2}(t/t_{0})}{\omega^{2}}\right].$$

From Fig. 15 we can understand how well these functions are able to fit the SN light curve. Table 11 additionally presents the parameters characterizing the quality of this fit. In particular, it can be seen that the Bazin function derived empirically to model the SN light curves allows the light curve of SN 2013dx to be fitted best over the entire period of its activity. The long-term SN light curve can also be described satisfactorily with the quartic polynomial. The functions with fewer parameters successfully describe only the immediate neighborhood of the light-curve peak in an interval of ${\pm}6.5$ days. They can be used only for an approximate (${\sim}0.5$ day) determination of the time of this peak.

Fig. 15

The best fit (green curves) of the bolometric light curve of SN 2013dx (black points; see Volnova et al. 2017) by various analytical functions: (a) a Bazin function (Bazin et al. 2011), (b) a quartic polynomial, (c) a parabola (Bianco et al. 2014), and (d) a lognormal distribution. The chosen model function is indicated by the solid line in the time interval where it fits well the light curve ($\chi^{2}$ normalized to the number of degrees of freedom is ${\lesssim}1.1$) and by the dashed line in the intervals where it fits the light curve unsatisfactorily.