tokens: plot the branching ratio as a function of the NSC density (, β = 2.3); in the bottom panel, we show as a function of the the slope of the BH mass function ( and ). The general trend with a hard discussed previously is in part smeared out by the fact that we sample the binary semimajor axis in the range ( a GW , a hard ), rather than having it fixed to a hard . Moreover, BHs do not have a fixed mass, as in Mod1 and Mod2 in equal-mass binaries, but their masses are sampled from a distribution. Additionally, we find that SBH–SBH binaries produce the largest branching ratio, while IMBH–IMBH lead to the lowest one. This can again be ascribed to the fact that hard binaries of two SBHs have typically smaller semimajor axes than binaries comprised of two IMBHs. As a consequence, stars that undergo a resonant encounter with an SBH–SBH binary are more likely to pass within the tidal radius of one of the two BHs and get tidally disrupted. Branching ratios of binary IMBH–SBHs are in between the SBH–SBH and IMBH–SBH cases. Figure 2. Top panel: branching ratio as a function of the NSC mass (, β = 2.3) for SBH–SBH (orange), IMBH–SBH (red), and IMBH–IMBH (green). Central panel: branching ratio as a function of the NSC density (, β = 2.3) for SBH–SBH (orange), IMBH–SBH (red), and IMBH–IMBH (green). Bottom panel: branching ratio as a function of the the slope of the BH mass function (, ) for SBH–SBH (orange), IMBH–SBH (red), and IMBH–IMBH (green). 3.3 Orbital properties of binaries that exhibit tidal disruption events The semimajor axis of the binaries that undergo a TDE depends on the host NSC mass and density, and on the slope of the BH mass function β. We illustrate in Fig. 3 the distribution of semimajor axes of the SBH–SBH binaries that undergo a TDE. In the top panel, we show the case for and different values of the NSC mass (Mod3), while in the bottom panel, we plot the case for and different values of the NSC density (Mod4). The slope of the SBH mass function is fixed at β = 2.3. We find that the NSC mass has only a modest effect in shaping the semimajor axis of the binaries that undergo a TDE, unlike the host NSC density. The reason for this trend can be explained considering that binaries have orbital semimajor axis in the range ( a GW , a hard ), where Larger densities correspond to smaller values of a GW , thus a wider range of possible binary semimajor axes, while the NSC mass does not have a significant effect. Figure 3. Distribution of semimajor axis ( a ) of the SBH–SBH binaries that undergo a TDE. Top panel: and different values of the NSC mass; and bottom panel: and different values of the NSC density. The slope of the SBH mass function is fixed to β = 2.3. Fig. 4 shows the distribution of semimajor axes ( a ) of the SBH–SBH binaries (top) and masses ( m SBH ) of the SBHs (bottom) that undergo a TDE, for different values of the slope of the SBH mass function. The mass and density of the NSC are fixed to and , respectively. We find that the
ner_tags: O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O