...

On leave from Astro Space Center of the P.N. Lebedev Physical Institute, Moscow, Russia.

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...$j_{\theta}$

Let the velocity components at the orbit apastron be $v_{\phi}$ and $v_{\theta}$ and the apastron distance be $r_{\rm a}$. Then, $j_{\phi}=r_{\rm a}v_{\theta}$and $j_{\theta}=r_{\rm a}v_{\phi}$.

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...1983)

Technically, it follows from the fact that the radius of periastron of a parabolic orbit does not depend on $\theta_{\infty}$.

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... models

See Ivanov $\&$ Novikov (2001) for an overview of works on tidal disruption and astrophysical applications.

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...1997)

Note misprints in the Diener et al. (1997) expression for the components of the tidal tensor. The sign of all components should be opposite.

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... units

In physical units the characteristic size of the tidal cross section $\propto$M^2/3 and the characteristic size of the capture cross section $\propto$M.

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... allowed

Note that these inequalities are also valid for the angle $\Theta(\tau)$ that changes during the fly-by around the black hole: $\Theta_{-}\leq \Theta (\tau) \leq \Theta_{+}$.

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... hole

Note that the fraction of stellar gas eventually accreted onto the black hole may differ from the fraction of gravitationally bound gas lost by the star. The physical processes occurring in the gas after the tidal disruption event have been discussed by e.g. Evans $\&$ Kochanek (1989).

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