Dynamical Packing in the Habitable Zone: The Case of Beta CVn

Uncovering the occurrence rate of terrestrial planets within the Habitable Zone (HZ) of their host stars has been a particular focus of exoplanetary science in recent years. The statistics of these occurrence rates have largely been derived from transiting planet discoveries, and have uncovered numerous HZ planets in compact systems around M dwarf host stars. Here we explore the width of the HZ as a function of spectral type, and the dynamical constraints on the number of stable orbits within the HZ for a given star. We show that, although the Hill radius for a given planetary mass increases with larger semi-major axis, the width of the HZ for earlier-type stars allows for more terrestrial planets in the HZ than late-type stars. In general, dynamical constraints allow $\sim$6 HZ Earth-mass planets for stellar masses $\gtrsim 0.7 M_\odot$, depending on the presence of farther out giant planets. As an example, we consider the case of Beta CVn, a nearby bright solar-type star. We present 20 years of radial velocities (RV) from the Keck/HIRES and APF instruments and conduct an injection-recovery analysis of planetary signatures in the data. Our analysis of these RV data rule out planets more massive than Saturn within 10~AU of the star. These system properties are used to calculate the potential dynamical packing of terrestrial planets in the HZ and show that such nearby stellar targets could be particularly lucrative for HZ planet detection by direct imaging exoplanet missions.