2026ApJ..1000..141K

We analyzed millimeter-wave data toward the quasar B0218+357 observed with the Atacama Large Millimeter/submillimeter Array and obtained absorption spectra of the J = 2-1 and J = 3-2 rotational transitions of HCN, HCO⁺, HNC, H¹³CN, and H¹³CO⁺ at the cosmological redshift of z = 0.68. For HCN, HCO⁺, and HNC, we identified two distinct absorption components that are common to both transitions, whereas a single component was detected in the isotopologue spectra. In this paper, we accurately evaluate the excitation temperatures and their uncertainties from the absorption strengths of these components and use them to determine the cosmic microwave background radiation (CMB) temperature. Uncertainties in the continuum covering factor were propagated into the excitation temperature via Monte Carlo sampling. We further corrected the observed optical depths for biases due to column-density nonuniformity by assuming a lognormal column-density distribution. Under the assumption that the rotational levels are in radiative equilibrium with the CMB, we derived excitation temperature profiles in the optically thin regime. Because the excitation of HCO⁺ is biased by an additional velocity component and partial collisional excitation, this species was excluded from the final determination of the CMB temperature. From a weighted mean of the excitation temperatures obtained from HCN and HNC, we determined the CMB temperature at z = 0.68 to be 4.50 ± 0.17 K. This constitutes the first measurement of the CMB temperature at z = 0.68 based on a quasar absorption line system and represents the most precise determination at this redshift, highly consistent with the standard Big Bang cosmological model.