3 Detectability of GRB afterglows

GRB afterglows fade like t^-1.2 so one should start observation as soon as possible to obtain data with good statistics. However, the observational gap of several hours after GRB is inevitable in the observation network currently available (i.e., the WFC/BeppoSAX, BATSE/CGRO, ASM/RXTE with other telescopes for the follow-up observations). Although HETE2 can considerably shorten this period in optical/radio band, followups in X-rays will remain difficult in an inerval several minutes to a few hours after GRBs. MAXI scans the entire sky with the arc-shape FOVs. The FOV is small so that only a small number of GRBs could be caught by chance. However it could detect an afterglow if it is still brighter than the GSC's 5-$\sigma$ detection limit, $F^{\rm lim}_{\rm GSC}$, of 7 mCrab for one dwell (= 30 seconds) (Rubin et al. 1997) when the GSC's FOVs pass over its direction. The SSC is less sensitive than the GSC; its 5-$\sigma$ detection limit is $\approx20$ mCrab for one dwell. So, we concentrate on the GSC in the following discussions.

From the BATSE 4B catalog (Paciesas et al. 1997), the number of GRB with the Fluence in 50-300 keV $F_{50-300} \gt 1\ 10^{-6}$ erg cm^-2 is 688 out of 1292 for the net exposure time of 2.595 years. The expected observation rate is N_>10^-6=258.4 yr^-1. One could expect the X-ray flux of $\gt 1\ 10^{-8}$ erg cm^-2 s^-1 $\sim 500$ mCrab for these GRBs assuming a duration of $\sim 10$ s and 10% of $\gamma$-ray energy being emitted in the X-ray band. Although the X-ray flux of afterglow scatters from burst to burst, we assume the decay $\propto t^{-1.2}$ and $(t/10~{\rm s})^{-1.2} \sim$ ($F^{\rm lim}_{\rm GSC}$/500 mCrab). Then we have $t\sim$350 seconds after the burst, in which the GSC could detect an afterglow. During $\sim$350 s two FOVs of the GSC can sweep $\sim$7/54 of the entire sky. Since the BATSE exposure is roughly 4$\pi$, the number of afterglows expected to be detected a year with the GSC may be estimated to be $R = N_{\gt 10^{-6}} \cdot \varepsilon_{\rm obs} \cdot \Omega/4\pi$. Here $\varepsilon_{\rm obs}$, MAXI's observational efficiency, is estimated to be $\sim0.75$ taking account of the SAA in which GSC cannot be operated due to high charged particle background. $\Omega/4\pi$ is an effective solid angle for the detection of afterglows, which is $\sim$7/54 for $t\sim$350 s as mentioned above. Then one could estimate that $R\sim 25$ yr^-1. In addtion to afterglows, GRBs themselves possibly occur in the GSC FOV of $\approx0.16$ str. Its 5-$\sigma$ detection limit is $\approx20$ mCrab for an event with $\sim 10$ s duration. Therefore, one may expect a detection of a burst with the fluence of >10^-7 erg cm^-2. A similar estimation gives the chance detection rate of $\sim5$ yr^-1 for GRBs.

In conclusion, the MAXI-GSC has the capability not only to observe daily variation of weak sources such as AGNs, but also to detect GRB afterglows in the very early phase. It could bring the first opportunity to detect afterglows within about 350 seconds after GRBs.