Asteroseismology of the Nearby K-Dwarf $\sigma$ Draconis using the Keck Planet Finder and TESS

Asteroseismology of dwarf stars cooler than the Sun is very challenging due to the low amplitudes and rapid timescales of oscillations. Here, we present the asteroseismic detection of solar-like oscillations at 4-minute timescales ($\nu_{\mathrm{max}}\sim4300\mu$Hz) in the nearby K-dwarf $\sigma$ Draconis using extreme precision Doppler velocity observations from the Keck Planet Finder and 20-second cadence photometry from NASA's Transiting Exoplanet Survey Satellite. The star is the coolest dwarf star to date with both velocity and luminosity observations of solar-like oscillations, having amplitudes of $5.9\pm0.8\,$cm$\,\text{s}^{-1}$ and $0.8\pm0.2$ ppm, respectively. These measured values are in excellent agreement with established luminosity-velocity amplitude relations for oscillations and provide further evidence that mode amplitudes for stars with $T_{\mathrm{eff}}