  We study the mass fallback rate of tidally disrupted stars on marginally
bound and unbound orbits around a supermassive black hole (SMBH) by performing
three-dimensional smoothed particle hydrodynamic (SPH) simulations with three
key parameters: the star is modeled by a polytrope with two different indexes
($n=1.5$ and $3$). The stellar orbital properties are characterized by five
orbital eccentricities ranging from $e=0.98$ to $1.02$ and five different
penetration factors ranging from $\beta=1$ to $3$, where $\beta$ represents the
ratio of the tidal disruption to pericenter distance radii. We derive analytic
formulae for the mass fallback rate as a function of the stellar density
profile, orbital eccentricity, and penetration factor. Moreover, two critical
eccentricities to classify tidal disruption events (TDEs) into five different
types: eccentric ($e<e_{\rm crit,1}$), marginally eccentric ($e_{\rm
crit,1}\lesssim{e}<1$), purely parabolic ($e=1$), marginally hyperbolic
($1<e<e_{\rm crit,2}$), and hyperbolic ($e\gtrsim{e_{\rm crit,2}}$) TDEs, are
reevaluated as $e_{\rm crit,1}=1-2q^{-1/3}\beta^{k-1}$ and $e_{\rm
crit,2}=1+2q^{-1/3}\beta^{k-1}$, where $q$ is the ratio of the SMBH to stellar
masses and $0<k\lesssim2$. We find the asymptotic slope of the mass fallback
rate varies with the TDE type. The asymptotic slope approaches $-5/3$ for
parabolic TDEs, is steeper for marginally eccentric TDEs, and is flatter for
marginally hyperbolic TDEs. The mass fallback rates of the marginally eccentric
TDEs are much larger than the parabolic TDE case, while those of marginally
hyperbolic TDEs are much smaller. Marginally unbound TDEs could be an origin of
a very low density gas disk around a dormant SMBH.
