  Using the Hamilton Echelle Spectrograph at Lick Observatory, we have obtained
precise radial velocities (RVs) of a sample of 373 G- and K-giant stars over
more than 12 years, leading to the discovery of several single and multiple
planetary systems. The RVs of the long-period (~53 years) spectroscopic binary
$\epsilon$ Cyg (HIP 102488) are found to exhibit additional regular variations
with a much shorter period (~291 days). We intend to improve the orbital
solution of the $\epsilon$ Cyg system and attempt to identify the cause of the
nearly periodic shorter period variations, which might be due to an additional
substellar companion. We used precise RV measurements of the K-giant star
$\epsilon$ Cyg from Lick Observatory, in combination with a large set of RVs
collected more recently with the SONG telescope, as well as archival data sets.
Our Keplerian model to the RVs characterizes the orbit of the spectroscopic
binary to higher precision than achieved previously, resulting in a semi-major
axis of $a = 15.8 \mathrm{AU}$, an eccentricity of $e = 0.93$, and a minimum
mass of the secondary of $m \sin i = 0.265 M_\odot$. Additional short-period RV
variations closely resemble the signal of a Jupiter-mass planet orbiting the
evolved primary component with a period of $291 \mathrm{d}$, but the period and
amplitude of the putative orbit change strongly over time. Furthermore, in our
stability analysis of the system, no stable orbits could be found in a large
region around the best fit. Both of these findings deem a planetary cause of
the RV variations unlikely. Most of the investigated alternative scenarios,
such as an hierarchical triple or stellar spots, also fail to explain the
observed variability convincingly. Due to its very eccentric binary orbit, it
seems possible, however, that $\epsilon$ Cyg could be an extreme example of a
heartbeat system.
