Collisions of Terrestrial Worlds: The Occurrence of Extreme Mid-infrared Excesses around Low-mass Field Stars

We present the results of an investigation into the occurrence and properties (stellar age and mass trends) of low-mass field stars exhibiting extreme mid-infrared (MIR) excesses ({L}_{IR}/{L}_* ≳ 0.01). Stars for the analysis were initially selected from the Motion Verified Red Stars (MoVeRS) catalog of photometric stars with Sloan Digital Sky Survey, 2MASS, and WISE photometry and significant proper motions. We identify 584 stars exhibiting extreme MIR excesses, selected based on an empirical relationship for main-sequence W1-W3 colors. For a small subset of the sample, we show, using spectroscopic tracers of stellar age (Hα and Li I) and luminosity class, that the parent sample is most likely comprised of field dwarfs (≳ 1 Gyr). We also develop the Low-mass Kinematics (LoKi) galactic model to estimate the completeness of the extreme MIR excess sample. Using Galactic height as a proxy for stellar age, the completeness-corrected analysis indicates a distinct age dependence for field stars exhibiting extreme MIR excesses. We also find a trend with stellar mass (using r - z color as a proxy). Our findings are consistent with the detected extreme MIR excesses originating from dust created in a short-lived collisional cascade (≲100,000 years) during a giant impact between two large planetismals or terrestrial planets. These stars with extreme MIR excesses also provide support for planetary collisions being the dominant mechanism in creating the observed Kepler dichotomy (the need for more than a single mode, typically two, to explain the variety of planetary system architectures Kepler has observed), rather than different formation mechanisms.