[C ii] Properties and Far-infrared Variability of a z = 7 Blazar

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We present millimeter observations of the host galaxy of the most distant blazar known, VLASS J041009.05−013919.88 (hereafter J0410–0139) at z = 7, using Atacama Large Millimeter/submillimeter Array (ALMA) and NOrthern Extended Millimeter Array (NOEMA) observations. The ALMA data reveal a (2.02 ± 0.36) × 1042 erg s−1 [C ii] 158 μm emission line at z = 6.9964 with a [C ii]-inferred star formation rate (SFR) of 58 ± 9 M ⊙ yr−1. We estimate a dynamical mass of M dyn,[C ii] = (4.6 ± 2.0) × 109 M ⊙, implying a black hole mass to host a dynamical mass ratio of 0.15 − 0.05 + 0.08 . The 238 GHz continuum (rest-frame IR) decreased by ∼33% from the NOEMA to the ALMA observations taken ∼10 months apart. The Very Large Array 3–10 GHz radio flux densities showed a ∼37% decrease in a similar time frame, suggesting a causal connection. At face value, J0410–0139 would have the lowest [C ii]-to-IR luminosity ratio of a z > 5.7 quasar reported to date (∼10−4). However, if only <20% of the measured IR luminosity was due to thermal emission from dust, the [C ii]-to-IR luminosity ratio would be typical of (U)LIRGs, and the SFRs derived from [C ii] and IR luminosities would be consistent. These results provide further evidence that synchrotron emission significantly contributes to the observed rest-frame IR emission of J0410–0139, similar to what has been reported in some radio-loud active galactic nuclei at z < 1.