Direct Imaging Constraints on the Putative Exoplanet 14 Her c

We present results of deep direct imaging of the radial velocity (RV) planet-host star 14 Her (=GJ 614, HD 145675), obtained in the \lprime ~band with the Clio-2 camera and the MMT adaptive optics system. This star has one confirmed planet and an unconfirmed outer companion, suggested by residuals in the RV data. The orbital parameters of the unconfirmed object are not well constrained since many mass/semimajor axis configurations can fit the available data. The star has been directly imaged several times, but none of the campaigns has ruled out sub-stellar companions. With \about 2.5 hrs of integration, we rule out at 5$\sigma$ confidence $\gtrsim$ 18 \mj ~companions beyond \about 25 AU, based on the \cite{baraffe} COND mass-luminosity models. Combining our detection limits with fits to the RV data and analytic dynamical analysis, we constrain the orbital parameters of 14 Her c to be: $3 \lesssim m/$\mj ~$\lesssim 42$, $7 \lesssim a/$AU $\lesssim 25$, and $e \lesssim 0.5$. A wealth of information can be obtained from RV/direct imaging overlap, especially with deep imaging as this work shows. The collaboration between RV and direct imaging will become more important in the coming years as the phase space probed by each technique converges. Future studies involving RV/imaging overlap should be sure to consider the effects of a potential planet's projected separation, as quoting limits assuming face-on orientation will be misleading.