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tokens: of higher-Γ EEs. We also estimate P k using declination-averaged effective area for IceCube, , shown as IC () in Table 2 , which shows slightly higher for EE-opt-dist. Although the declination dependence of does not change our conclusion much, the declination-dependent analysis is important for more quantitative evaluations. Table 2 The Detection Probabilities, , for d L = 300 Mpc Note. IC: IceCube, Gen2: IceCube-Gen2, up+hor: upgoing+horizontal events, down: downgoing events, all: covering-factor-weighted average over the up+hor and down, : using the declination-averaged effective area. Using the relation , we estimate as a function of d L , which is shown in Figure 2 . Here, we ignore the effects of cosmological redshift, since we focus on the local universe at Gpc. The vertical dotted lines show d L = 300 Mpc and d L = 600 Mpc, which corresponds to the sensitivity ranges of face-on NS–NS and NS–BH mergers by aLIGO, respectively. For NS–BH mergers, since the distance is longer, is lower than those for NS–NS mergers. The detection probability of nearby events is affected by , while that of distant events is not. Figure 2. Detection probability as a function of luminosity distance d L . The upper and lower panels are with IceCube and IceCube-Gen2, respectively. The vertical thin-dotted lines show d L = 300 Mpc and d L = 600 Mpc. We estimate the detection probability within a given time interval, , which is estimated to be , where N is the number of EEs for the time interval within the covering area of neutrino detectors. The local SGRB rate is (e.g., Nakar et al. 2006 ; Wanderman Piran 2015 ), so the event rate within the sensitivity range of aLIGO (300 Mpc) is . According to the Swift results, ∼25% of SGRBs are accompanied by EEs (Sakamoto et al. 2011 ), noting that softer instruments could detect more EEs (Nakamura et al. 2014 ). Here, we simply assume that half of SGRBs have EEs, leading to N ∼ 2–5 for years. Within the sensitivity range of NS–BH mergers by aLIGO (600 Mpc), the SGRB rate is , leading to ∼9–22 EEs for a 5 year operation. The estimated values of are tabulated in Table 3 . We find that the simultaneous detection of gamma-rays, neutrinos, and GWs is possible in the era of IceCube-Gen2 and aLIGO/aVirgo/KAGRA, assuming a cosmic-ray loading factor, . This will allow us to probe the physical conditions during EEs, including the cosmic-ray loading factor and the Lorentz factor (see Section 4 ). Table 3 The Detection Probabilities within a Given Time Interval, Note. The SGRB rate is assumed to be . In the near future, KM3NeT will be in operation. While IceCube is more suitable to observe the northern sky, KM3NeT will achieve a better sensitivity for the southern sky, helping us improve the possibility of detections. In reality, not only Γ but also the other parameters for EEs (, , , α , β , , , d L ) should be distributed in certain ranges. However, their distribution functions are quite uncertain, and detailed discussion of