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First Determination of the Cosmic Microwave Background Radiation Temperature at $z\!=\!0.68$ Using Molecular Absorption Lines

Tatsuya Kotani, Tomoharu Oka, Rei Enokiya

Abstract

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, H$^{13}$CN, and H$^{13}$CO$^{+}$ 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 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 cosmic microwave background (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 ${4.50\pm0.17\,\mathrm{K}}$. 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.

First Determination of the Cosmic Microwave Background Radiation Temperature at $z\!=\!0.68$ Using Molecular Absorption Lines

Abstract

We analyzed millimeter-wave data toward the quasar B0218+357 observed with the Atacama Large Millimeter/submillimeter Array and obtained absorption spectra of the =2-1 and =3-2 rotational transitions of HCN, HCO, HNC, HCN, and HCO at the cosmological redshift of . 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 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 cosmic microwave background (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 to be . This constitutes the first measurement of the CMB temperature at 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.
Paper Structure (16 sections, 9 equations, 3 figures)

This paper contains 16 sections, 9 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Data Processing
  3. Analyses
  4. Fundamentals
  5. $T_{\rm CMB}$ Calculations
  6. Uncertainty
  7. Continuum Covering Factor
  8. Time Variability
  9. Correction for Nonuniformity
  10. Results and Discussion
  11. Optical Depth
  12. Excitation Temperature
  13. HCN, HCO$^{+}$, and HNC
  14. $^{13}$C isotopologues
  15. Redshift Dependence of $T_\mathrm{CMB}$
  16. ...and 1 more sections

Figures (3)

  • Figure 1: Continuum-normalized absorption spectra of the rotational transitions of HCN, HCO$^{+}$, HNC, H$^{13}$CN, and H$^{13}$CO$^{+}$ detected toward the A image of B0218+357. The velocities are shown as offsets from the systemic velocity, using the barycentric reference frame.
  • Figure 2: Profiles of HCN, HCO$^{+}$, and HNC obtained after accounting for the uncertainty in the continuum covering factor and the bias due to column-density inhomogeneity. (Top) Corrected optical depth profiles of the $J$=2--1 and $J$=3--2 transitions toward the A image of B0218+357, shown in blue and orange, respectively. Thin vertical lines indicate the boundaries of the velocity bins. (Bottom) Excitation temperature profiles calculated for velocity bins in which the optical depths of both the $J$=2--1 and $J$=3--2 transitions are smaller than unity. The purple dashed line marks the CMB temperature at $z\!=\!0.68$ predicted by the standard Big Bang model, $T_{\rm ex}\!=\!4.59\,\mathrm{K}$.
  • Figure 3: Plot of the measured CMB temperature ($T_\mathrm{CMB}$) versus redshift ($z$). The values of previous measurements were taken from existing literature Battistelli_2002Luzzi_2009Muller_2013Klimenko_2020Riechers_2022Kotani_2025. A star indicates the measurement at $z\!=\!0$Fixsen_2009. Each plot symbol represents a measurement method at $z>0$. The black dashed line denotes the relationship expected from the standard model (Equation (\ref{['eq:tcmb']})). The blue curve shows the best-fit result by the Equation (\ref{['eq:btcmb']}), $\beta=(3.9^{+7.4}_{-8.2})\times10^{-3}$, with the 1$\sigma$ uncertainty area (blue shadow).