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The First Short GRB Millimeter Afterglow: The Wide-Angled Jet of the Extremely Energetic SGRB 211106A

We present the discovery of the first millimeter afterglow of a short-duration $γ$-ray burst (SGRB) and the first confirmed afterglow of an SGRB localized by the GUANO system on Swift. Our Atacama Large Millimeter/Sub-millimeter Array (ALMA) detection of SGRB 211106A establishes an origin in a faint host galaxy detected in Hubble Space Telescope (HST) imaging at $0.7\lesssim z\lesssim1.4$. From the lack of a detectable optical afterglow, coupled with the bright millimeter counterpart, we infer a high extinction, $A_{\rm V}\gtrsim2.6$ mag along the line of sight, making this the one of the most highly dust-extincted SGRBs known to date. The millimeter-band light curve captures the passage of the synchrotron peak from the afterglow forward shock and reveals a jet break at $t_{\rm jet}=29.2^{+4.5}_{-4.0}$~days. For a presumed redshift of $z=1$, we infer an opening angle, $θ_{\rm jet}=(15.5\pm1.4)$~degrees, and beaming-corrected kinetic energy of $\log(E_{\rm K}/{\rm erg})=51.8\pm0.3$, making this one of the widest and most energetic SGRB jets known to date. Combining all published millimeter-band upper limits in conjunction with the energetics for a large sample of SGRBs, we find that energetic outflows in high density environments are more likely to have detectable millimeter counterparts. Concerted afterglow searches with ALMA should yield detection fractions of 24-40% on timescales of $\gtrsim2$~days at rates $\approx0.8$-1.6 per year, outpacing the historical discovery rate of SGRB centimeter-band afterglows.