COol Companions ON Ultrawide orbiTS (COCONUTS). III. A Very Red L6 Benchmark Brown Dwarf around a Young M5 Dwarf

We present the third discovery from the COol Companions ON Ultrawide orbiTS (COCONUTS) program, the COCONUTS-3 system, composed of a young M5 primary star UCAC4 374-046899 and a very red L6 dwarf WISEA J081322.19$-$152203.2. These two objects have a projected separation of 61$''$ (1891 au) and are physically associated given their common proper motions and estimated distances. The primary star, COCONUTS-3A, has a mass of $0.123\pm0.006$ M$_{\odot}$ and we estimate its age as 100 Myr to 1 Gyr based on its kinematics and spectrophotometric properties. We derive its metallicity as $0.21 \pm 0.07$ dex using empirical calibrations established by older higher-gravity M dwarfs and find this [Fe/H] could be slightly underestimated according to PHOENIX models given COCONUTS-3A's younger age. The companion, COCONUTS-3B, has a near-infrared spectral type of L6$\pm$1 INT-G, and we infer physical properties of $T_{\rm eff} = 1362^{+48}_{-73}$ K, $\log{(g)}= 4.96^{+0.15}_{-0.34}$ dex, $R = 1.03^{+0.12}_{-0.06}$ R$_{\rm Jup}$, and $M = 39^{+11}_{-18}$ M$_{\rm Jup}$, using its bolometric luminosity, its host star's age, and hot-start evolution models. We construct cloudy atmospheric model spectra at the evolution-based physical parameters and compare them to COCONUTS-3B's spectrophotometry. We find this companion possesses ample condensate clouds in its photosphere with the data-model discrepancies likely due to the models using an older version of the opacity database. Compared to field-age L6 dwarfs, COCONUTS-3B has fainter absolute magnitudes and a 120 K cooler $T_{\rm eff}$. Also, the J-K color of this companion is among the reddest for ultracool benchmarks with ages older than a few 100 Myr. COCONUTS-3 likely formed in the same fashion as stellar binaries given the companion-to-host mass ratio of 0.3 and represents a valuable benchmark to quantify the systematics of substellar model atmospheres.