BE Lyncis: A Pulsating Star in the Most Eccentric Binary with a Massive Unseen Companion

We report the discovery of an exceptionally eccentric binary system, BE Lyncis (BE~Lyn), which might host a compact companion with mass $\gtrsim 2.5~M_{\odot}$. By combining TESS photometry with an extensive set of times of maximum light spanning 39~years, we identify BE~Lyn as a high-amplitude $\delta$ Scuti star in a binary with an orbital period of $\approx15.9$~years and an extraordinary eccentricity of $e=0.9989^{+0.0008}_{-0.0021}$ ($>0.9968$ at 95% confidence) -- the most extreme eccentricity reliably measured for any binary system. Dynamical constraints limit the orbital inclination to $i \lesssim 10.1^{\circ}$, implying a companion mass $M_2 \gtrsim 2.5~M_{\odot}$, which identifies the companion as a compact object. This mass points to it most likely being a black hole; if instead it is a rapidly rotating neutron star, it would be the most massive known. If the black hole interpretation holds, it would be the closest such object to Earth. This system provides a unique laboratory for studying asteroseismology in strong gravitational fields, as well as the formation and evolution of extremely eccentric binaries. Our work demonstrates the use of the light-travel time effect in a pulsating star to reveal a compact companion, offering a novel method for detecting black holes in non-interacting binaries.