  The discovery of stellar-mass black holes (BHs) in globular clusters (GCs)
raises the possibility of long-term retention of BHs within GCs. These BHs
influence various astrophysical processes, including merger-driven
gravitational waves and the formation of X-ray binaries. They also impact
cluster dynamics by heating and creating low-density cores. Previous N-body
models suggested that Palomar 5, a low-density GC with long tidal tails, may
contain more than 100 BHs. To test this scenario, we conduct N-body simulations
of Palomar 5 with primordial binaries to explore the influence of BHs on binary
populations and the stellar mass function. Our results show that primordial
binaries have minimal effect on the long-term evolution. In dense clusters with
BHs, the fraction of wide binaries with periods >$10^5$ days decreases, and the
disruption rate is independent of the initial period distribution. Multi-epoch
spectroscopic observations of line-of-sight velocity changes can detect most
bright binaries with periods below $10^4$ days, significantly improving
velocity dispersion measurements. Four BH-MS binaries in the model with BHs
suggests their possible detection through the same observation method.
Including primordial binaries leads to a flatter inferred mass function because
of spatially unresolved binaries, leading to a better match of the observations
than models without binaries, particularly in Palomar 5's inner region. Future
observations should focus on the cluster velocity dispersion and binaries with
periods of $10^4-10^5$ days in Palomar 5's inner and tail regions to constrain
BH existence.
