tokens: ( 2010 ), 8 8 The quantity f end is set to avoid higher PN tidal effects and nonlinear hydrodynamical coupling. In Hinderer et al. ( 2010 ), the fitting formula was obtained by choosing 400 Hz ≥ f end ≥ 500 Hz. The end frequency adopted in Abbott et al. ( 2017c ) is the frequency of the innermost stable circular orbit, which is above 1 kHz. and an equal mass binary with M ∼ 2.7 M ⊙ , we obtain an estimate on the tidal deformability of a star: ΔΛ 1 (1.35 M ⊙ ) ∼ 2.9 × 10 3 . Assuming a low-spin prior, GW170817 places on upper bound Λ 1 (1.4 M ⊙ ) ≤ 800 at the 90% confidence level, and an upper bound of ≤1400 if the prior is relaxed to allow for high spin (Abbott et al. 2017c ). Such constraints on Λ 1 also limit the allowed radius of NS, given the family of EOS assumed in this paper. In Figure 3 , we compare this uncertainty in the tidal deformability to the amount by the tidal deformability that has to be changed in order for a BH–NS binary to have the same leading order tidal effects as a corresponding NS–NS binary with the same masses. Figure 3. Amount by which the dimensionless tidal deformability Λ has to be increased, relative to the quantity of the corresponding NS in an NS–NS binary with the same masses, for a BH–NS binary to have the same leading order tidal effects. This is shown as a function of the mass ratio. In all of the cases, one NS is assumed have a mass of M NS1 = 1.4 M ⊙ . The different curves correspond to different choices of EOS for the NS–NS binary, and hence the different values of the radius of 1.4 M ⊙ NS in the NS–NS, as shown in the legend. For comparison, we also show the Fupper bound constraints on Λ from GW170817 assuming either a high-spin prior or a low-spin prior on the source. The highest NS radius shown (dotted red curve) saturates the former constraint on Λ, while the middle value for the NS radius (dotted blue curve) saturates the latter constraint. With N identical detections, and under the same high-spin prior, such uncertainty scales as Δ N Λ 1 (1.4 M ⊙ ) ∼ 1.4 × 10 3 N −1/2 . In reality, the component masses and source distances are different for different events, and it is possible that the best event of previous N detections dominates the constraint of NS EOS. In the above discussion, we have not accounted for the effect of spin, which is particularly important for LMBHs formed through hierarchical mergers, as they are expected to have relatively high spin ( a ∼ 0.7; Fishbach et al. 2017 ; Gerosa Berti 2017 ). 9 9 The effective spin of a most rapidly spinning pulsar known so far is ∼0.4 (Hessels et al. 2006 ). Such a spin magnitude will generate ∼0.15 mismatch between a nonspinning BH–NS waveform and a generic pretcessing waveform if the mass ratio is around 2 (see Figure 8 of Harry et al. 2014 ). The relation between distinguishable mismatch and S/N is discussed in Baird et al. ( 2013 ). 5. Multi-messenger Detection An important question is whether multi-messenger signals can help us identify an
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