Revealing nature of GRB 210205A, ZTF21aaeyldq (AT2021any), and follow-up observations with the 4K$\times$4K CCD Imager+3.6m DOT

Optical follow-up observations of optical afterglows of gamma-ray bursts are crucial to probe the geometry of outflows, emission mechanisms, energetics, and burst environments. We performed the follow-up observations of GRB 210205A and ZTF21aaeyldq (AT2021any) using the 3.6m Devasthal Optical Telescope (DOT) around one day after the burst to deeper limits due to the longitudinal advantage of the place. This paper presents our analysis of the two objects using data from other collaborative facilities, i.e., 2.2m Calar Alto Astronomical Observatory (CAHA) and other archival data. Our analysis suggests that GRB 210205A is a potential dark burst once compared with the X-ray afterglow data. Also, comparing results with other known and well-studied dark GRBs samples indicate that the reason for the optical darkness of GRB 210205A could either be intrinsic faintness or a high redshift event. Based on our analysis, we also found that ZTF21aaeyldq is the third known orphan afterglow with a measured redshift except for ZTF20aajnksq (AT2020blt) and ZTF19abvizsw (AT2019pim). The multiwavelength afterglow modelling of ZTF21aaeyldq using the afterglowpy package demands a forward shock model for an ISM-like ambient medium with a rather wider jet opening angle. We determine circumburst density of $n_{0}$ = 0.87 cm$^{-3}$, kinetic energy $E_{k}$ = 3.80 $\times 10^{52}$ erg and the afterglow modelling also indicates that ZTF21aaeyldq is observed on-axis ($θ_{obs} < θ_{core}$) and a gamma-ray counterpart was missed by GRBs satellites. Our results emphasize that the 3.6m DOT has a unique capability for deep follow-up observations of similar and other new transients for deeper observations as a part of time-domain astronomy in the future.