Constraining the dark cusp in the Galactic Center by long-period
  binaries
  Massive black holes (MBHs) in galactic nuclei are believed to be surrounded
by a high density stellar cluster, whose mass is mostly in hard-to-detect faint
stars and compact remnants. Such dark cusps dominate the dynamics near the MBH:
a dark cusp in the Galactic center (GC) of the Milky Way would strongly affect
orbital tests of General Relativity there; on cosmic scales, dark cusps set the
rates of gravitational wave emission events from compact remnants that spiral
into MBHs, and they modify the rates of tidal disruption events, to list only
some implications. A recently discovered long-period massive young binary (P_12
<~ 1 yr, M_12 ~ O(100 M_sun), T_12 ~ 6x10^6 yr), only ~0.1 pc from the Galactic
MBH (Pfuhl et al 2013), sets a lower bound on the 2-body relaxation timescale
there, min t_rlx ~ (P_12/M_12)^(2/3)T_12 ~ 10^7 yr, and correspondingly, an
upper bound on the stellar number density, max n ~ few x 10^8/<M_star^2>
1/pc^3, based on the binary's survival against evaporation by the dark cusp.
However, a conservative dynamical estimate, the drain limit, implies t_rlx >
O(10^8) yr. Such massive binaries are thus too short-lived and tightly bound to
constrain a dense relaxed dark cusp. We explore here in detail the use of
longer-period, less massive and longer-lived binaries (P_12 ~ few yr, M_12 ~
2-4 M_sun, T_12 ~ 10^8-10^10 yr), presently just below the detection threshold,
for probing the dark cusp, and develop the framework for translating their
future detections among the giants in the GC into dynamical constraints.
