  Recent observations have detected top-heavy IMFs in dense star forming
regions like the Arches cluster. Whether such IMFs also exist in old dense
stellar systems like globular clusters is difficult to constrain, because
massive stars already became black holes (BHs) and neutron stars (NSs).
However, studies of stellar dynamics find that BHs/NSs influence the long-term
evolution of star clusters. Following Breen & Heggie (2013) and by carrying out
two-component $N$-body simulations, we demonstrate how this dynamical impact
connects with the shape of IMFs. By investigating the energy balance between
the BH subsystem and the global, we find that to properly describe the
evolution of clusters, a corrected two-body relaxation time, $T_{rh,p} =
T_{rh}/\psi$, is necessary. Because $\psi$ depends on the total mass fraction
of BHs, $M_2 / M$, and the mass ratio, $m_2 / m_1$, the cluster dissolution
time is sensitive to the property of BHs or IMFs. Especially, the escape rate
of BHs via ejections from few-body encounters is linked to mass segregation. In
strong tidal fields, top-heavy IMFs easily lead to the fast dissolution of star
clusters and the formation of BH-dominant dark clusters, which suggests that
the observed massive GCs with dense cores are unlikely to have extreme
top-heavy IMFs. With the future observations of gravitational waves providing
unique information of BHs/NSs, it is possible to combine the multi-message
observations to have better constrains on the IMFs of old star clusters.
