ALMA Observation of a $z\gtrsim10$ Galaxy Candidate Discovered with JWST

We report the ALMA observation of a $z\gtrsim10$ galaxy candidate (GHZ1) discovered from the GLASS-JWST Early Release Science Program. Our ALMA program aims to detect the [OIII] emission line at the rest-frame 3393.0062 GHz ($88.36\mu$m) and far-IR continuum emission with the spectral window setup seamlessly covering a 26.125 GHz frequency range ($10.10<z<11.14$). A total of 7 hours of on-source integration was employed, using four frequency settings to cover the full range (1.7 hours per setting), with $0''.7$ angular resolution. No line or continuum is clearly detected, with a 5$\sigma$ upper limit of the line emission of 0.93 mJy beam$^{-1}$ at 25 km s$^{-1}$ channel$^{-1}$ and of the continuum emission of 30$\mu$Jy beam$^{-1}$. We report marginal spectral (at 225 km s$^{-1}$ resolution) and continuum features ($4.1\sigma$ and $2.6\sigma$ peak signal-to-noise ratio, respectively), within $0''.17$ from the JWST position of GHZ1. This spectral feature implies $z=10.38$ and needs to be verified with further observations. Assuming that the best photometric redshift estimate ($z=10.60^{+0.52}_{-0.60}$) is correct, the broadband galaxy spectral energy distribution model for the $3\sigma$ upper limit of the continuum flux from GHZ1 suggests that GHZ1 has a small amount of dust ($M_d\lesssim10^4 M_{\odot}$) with high temperature ($T_d\gtrsim90$K). The $5\sigma$ upper limit of the [OIII]$_{88\mu m}$ line luminosity and the inferred star formation rate of GHZ1 is consistent with the properties of the low metallicity dwarf galaxies. We also report serendipitous clear detections of six continuum sources at the locations of the JWST galaxy counterparts in the field.