  Eps Ind A is one of the nearest sun-like stars, located only 3.6 pc away. It
is known to host a binary brown dwarf companion, Eps Ind Ba/Bb, at a large
projected separation of 6.7", but radial velocity measurements imply that an
additional, yet unseen component is present in the system, much closer to Eps
Ind A. Previous direct imaging has excluded the presence of any stellar or
high-mass brown dwarf companion at small separations, indicating that the
unseen companion may be a low-mass brown dwarf or high-mass planet. We present
the results of a deep high-contrast imaging search for the companion, using
active angular differential imaging (aADI) at 4 micron, a particularly powerful
technique for planet searches around nearby and relatively old stars. We also
develop an additional PSF reference subtraction scheme based on locally
optimized combination of images (LOCI) to further enhance the detection limits.
No companion is seen in the images, although we are sensitive to significantly
lower masses than previously achieved. Combining the imaging data with the
known radial velocity trend, we constrain the properties of the companion to
within approximately 5-20 Mjup, 10-20 AU, and i > 20 deg, unless it is an
exotic stellar remnant. The results also imply that the system is probably
older than the frequently assumed age of ~1 Gyr.
