Revealing the formation of stellar-mass black hole binaries: The need
  for deci-Hertz gravitational wave observatories
  The formation of compact stellar-mass binaries is a difficult, but
interesting problem in astrophysics. There are two main formation channels: In
the field via binary star evolution, or in dense stellar systems via dynamical
interactions. The Laser Interferometer Gravitational-Wave Observatory (LIGO)
has detected black hole binaries (BHBs) via their gravitational radiation.
These detections provide us with information about the physical parameters of
the system. It has been claimed that when the Laser Interferometer Space
Antenna (LISA) is operating, the joint observation of these binaries with LIGO
will allow us to derive the channels that lead to their formation. However, we
show that for BHBs in dense stellar systems dynamical interactions could lead
to high eccentricities such that a fraction of the relativistic mergers are not
audible to LISA. A non-detection by LISA puts a lower limit of about $0.005$ on
the eccentricity of a BHB entering the LIGO band. On the other hand, a
deci-Hertz observatory, like DECIGO or Tian Qin, would significantly enhance
the chances of a joint detection, and shed light on the formation channels of
these binaries.
