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2 ROSAT all-sky survey data and expectations

The ROSAT satellite performed the first all-sky survey in the 0.1-2.4 keV band during 1990 August 1 - 1991 January 25 with short additional exposures ("repairs'') in February 16-18 and August 4-12, 1991. During the satellites orbital period of 96 min the telescope with a field of view of nearly 2$^\circ$ diameter scans a full 360$^\circ$ circle on the sky. Thus, the exposure per scan on a given sky location is between 10-30 s. Due to the orbital plane rotation (together with Earth's motion) these full circles move with 1$^\circ$/day perpendicular to the scan direction, covering the whole sky in 6 months. Thus, a sky location at the ecliptic equator is covered by the telescope scans over two days, and this coverage rises to 180 days at the ecliptic poles. Similarly, the typical sky exposure is a function of ecliptic latitude and amounts to 200 s at the equator and up to 40 ksec at the poles.

ROSAT is sensitive enough to detect a GRB X-ray afterglow for a few hours within its 10-30 s exposure time per sky location per scan. Figure 1 shows the one-scan sensitivity of ROSAT relative to the measured X-ray afterglow decay curves. The fraction f of afterglows detectable during the RASS depends on three critical parameters. First, the fraction of GRBs displaying X-ray afterglows: Previous observations suggest this fraction to be close to one. Second, the possible relation of X-ray flux to $\gamma$-ray peak flux or fluence: So far, the observed X-ray afterglow fluxes at about 100 s after the GRB are spread within a factor of 10 only, while the GRB fluxes range over a factor of > 1000. Third, the slope of the X-ray intensity decay: observed values range between t-1.8... t-2.5. The effect of the combination of the latter two factors is difficult to assess in an accurate manner given the low statistics at present, so we base our estimate of f on the observed X-ray afterglow intensities. A comparison with the ROSAT PSPC sensitivity suggests that we would detect practically all GRB afterglows in 3 subsequent scans, and $\sim$80% in 5 scans (see Fig. 1). Thus, we conservatively adopt f=0.8 in the following.

\includegraphics [width=8.8cm]{}
\vspace*{-3mm}\vspace*{-3mm} \end{figure} Figure 1: Decay light curves of some observed GRB X-ray afterglows in the 2-10 keV range (GRB 970111: Feroci et al. 1998; GRB 970228: Costa et al. 1997; GRB 970402: Nicastro et al. 1998; GRB 970508: Piro et al. 1998; GRB 980329: in 't Zand et al. 1998) and their corresponding brightness extrapolated into the ROSAT band (scale on the right; assuming a power law with photon index of -2 and no absorption). The horizontal line gives the sensitivity of the ROSAT PSPC during one scan, and the vertical lines mark the time windows for the possible coverage of a GRB location by ROSAT during its scanning mode. Thus, one may expect an afterglow at an intensity of up to several hundred cts/s during the first scan, between 0.3-8 cts/s during the second scan, <2 cts/s during the third scan and so on

The number of detectable X-ray afterglows from a GRB beamed towards us (based on the BATSE detection rate) during the RASS is
f \times S_{\rm R}^{\rm agl} \times R_{\rm GRB} \end{eqnarraystar}
where $R_{\rm GRB}$ is the rate of beamed GRBs per time and area on the sky and $S_{\rm R}^{\rm agl}$ is the effectiveness of ROSAT for afterglows in units of time$\times$area. We adopt $R_{\rm GRB} =$ 900 GRBs/sky/yr = 1 GRB/(16628$\Box ^{\circ}\times$ days). $S_{\rm R}^{\rm agl}$ would be 122296.5 $\Box ^{\circ}\times$ days for a 100% perfect survey. With a temporal completeness of the RASS of 62.5% we use $S_{\rm R}^{\rm agl}$ = 76435 $\Box ^{\circ}\times$ days in the following. Thus, we would expect $4.6\times f$ afterglows of beamed GRBs to be detected during the RASS.

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