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 $\gamma$-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 solidifies an origin in a faint host galaxy detected in Hubble Space Telescope (HST) imaging at a projected separation of $\approx0.8$ kpc. The millimeter-band light curve captures the passage of the synchrotron peak from the afterglow forward shock, constraining the afterglow kinetic energy, $\log(E_{\rm K,iso}/{\rm erg})=53.2\pm0.3$ and density, $\log(n_0/{\rm cm}^{-3})=-0.6\pm0.2$ at a presumed redshift of $z=1$. We identify a jet break at $t_{\rm jet}=29.2^{+4.5}_{-4.0}$ days in the millimeter-band data and infer an opening angle of $\theta_{\rm jet}=(15.5\pm1.4)$ degrees and beaming-corrected kinetic energy of $\log(E_{\rm K}/{\rm erg})=54.3\pm0.3$, which are the widest and highest ever measured for an SGRB, respectively. 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. Combining all published millimeter-band upper limits in conjunction with the energetics for a large sample of SGRBs, we find that energetic, wide-angled 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 $>2$ days at rates $\approx0.8$--1.6 per year, outpacing the historical discovery rate of SGRB centimeter-band afterglows.Comment: 18 pages, 8 figures, 4 tables. Submitted to ApJ Letter