Gravitational wave bursts from Primordial Black Hole hyperbolic
  encounters
  We propose that Gravitational Wave (GW) bursts with millisecond durations can
be explained by the GW emission from the hyperbolic encounters of Primordial
Black Holes in dense clusters. These bursts are single events, with the bulk of
the released energy happening during the closest approach, and emitted in
frequencies within the AdvLIGO sensitivity range. We provide expressions for
the shape of the GW emission in terms of the peak frequency and amplitude, and
estimate the rates of these events for a variety of mass and velocity
configurations. We study the regions of parameter space that will allow
detection by both AdvLIGO and, in the future, LISA. We find for realistic
configurations, with total mass $M\sim60\,M_\odot$, relative velocities $v\sim
0.01\,c$, and impact parameters $b\sim10^{-3}$ AU, for AdvLIGO an expected
event rate is ${\cal O}(10)$ events/yr/Gpc$^3$ with millisecond durations. For
LISA, the typical duration is in the range of minutes to hours and the
event-rate is ${\cal O}(10^3)$ events/yr/Gpc$^3$ for both $10^3\,M_\odot$ IMBH
and $10^6\,M_\odot$ SMBH encounters. We also study the distribution functions
of eccentricities, peak frequencies and characteristic timescales that can be
expected for a population of scattering PBH with a log-normal distribution in
masses, different relative velocities and a flat prior on the impact parameter.
