Editing Stellar dynamics (section)

== Tidal disruption radius ==

A star can be tidally torn by a heavier black hole when coming within the so-called Hill's radius of the black hole, inside which a star's surface gravity yields to the tidal force from the black hole,<ref name="Galaxy Dynamics">{{cite web |last1=Binney |first1=James |title=Galaxy Dynamics |url=https://cds.cern.ch/record/1371794/files/9780691130279_TOC.pdf |publisher=Princeton University Press |access-date=4 January 2022}}</ref> i.e.,

<math display="block"> (1-1.5) \ge Q^\text{tide}
\equiv { G M_\odot /R_\odot^2 \over  [G M_\bullet/s^2_\text{Hill} - G M_\bullet/(s_\text{Hill}+R_\odot)^2] }, ~~~
s_\text{Hill}  \rightarrow  R_\odot \left({ (2-3) GM_\bullet  \over  GM_\odot}\right)^{1 \over 3},  </math>

For typical black holes of <math> M_\bullet = (10^0-10^{8.5}) M_\odot</math> the destruction radius <math display="block"> \max[s_\text{Hill}, s_\text{Loss}] = 400R_\odot \max\left[\left({M_\bullet \over 3 \times 10^7 M_\odot}\right)^{1/3}, {M_\bullet \over 3 \times 10^7 M_\odot}\right] = (1-4000) R_\odot \ll 0.001 \mathrm{pc},</math> where 0.001pc is the stellar spacing in the densest stellar systems (e.g., the nuclear star cluster in the Milky Way centre). Hence (main sequence) stars are generally too compact internally and too far apart spaced to be disrupted by even the strongest black hole tides in galaxy or cluster environment.