Ultra-long gamma-ray bursts and ultra-soft gamma-ray bursts

Ultra-long gamma-ray bursts (ULGRBs) are special gamma-ray bursts (GRBs) lasting for several hours. However, their released energy is comparable with that of typical long GRBs. The observed flux of ULGRBs is typically low, making them hard to detect, and therefore, only a small sample of ULGRBs have been collected. Observationally, it remains a question of whether ULGRBs are a new population or just a tail distribution of long GRBs. Ultra-soft gamma-ray bursts (USGRBs) refer to another type of special GRBs with soft energy spectra. USGRBs include X-ray flashes (XRFs) and Xray rich GRBs (XRRs). In this paper, we first review the observations and theoretical studies of ULGRBs and USGRBs and discuss their possible explosion mechanisms and progenitor models. We then consider the Gravitational wave highenergy Electromagnetic Counterpart All-sky Monitor (GECAM), which has some advantages in observing ULGRBs and USGRBs. The GECAM has a full-sky FOV, high sensitivity, good positioning accuracy, extensive energy range coverage (6 keV-5 MeV), and lower energy threshold, making it ideal to observe ULGRBs and USGRBs. Based on the provided GECAM response matrix and background simulation data, we simulate the energy spectrum of typical ULGRB (GRB 130925A) and USGRB (XRR 050525A). We then compare those spectra with those observed by Fermi/GBM and Swift/BAT. We found that the GECAM can provide a more accurate energy spectrum. Furthermore, we also discuss the detection rate of ULGRBs and USGRBs observed by GECAM. We found that GECAM should detect similar to 20 ULGRBs, similar to 50 XRFs, and similar to 300 XRRs per year.