🔭 astrophysics

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

By analyzing millimeter-wave absorption spectra of molecular transitions toward the quasar B0218+357 at redshift $z=0.68$ , the authors determined the Cosmic Microwave Background temperature to be $4.50 \pm 0.17$ K, marking the first and most precise measurement at this redshift that strongly supports the standard Big Bang cosmological model.

Original authors: Tatsuya Kotani, Tomoharu Oka, Rei Enokiya

Published 2026-02-27

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Tatsuya Kotani, Tomoharu Oka, Rei Enokiya

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the universe as a giant, expanding balloon. When the balloon was first inflated (the Big Bang), it was incredibly hot and dense. As it expanded over billions of years, it cooled down, leaving behind a faint, chilly "afterglow" that fills all of space. This is the Cosmic Microwave Background (CMB). It's like the residual heat from a campfire that has long since burned out, but you can still feel the warmth if you stand close enough.

Scientists have a very specific prediction: as the universe expands, this background "temperature" should drop in a precise, predictable way, just like a cup of coffee cooling down on a table. The formula is simple: the further back in time you look (which means looking at objects that are very far away), the hotter the universe should be.

The Mission: Taking the Universe's Temperature

In this paper, a team of astronomers led by Tatsuya Kotani set out to take the universe's temperature at a specific moment in its history. They wanted to check if the universe was cooling exactly as the "Big Bang theory" predicts.

To do this, they didn't look at a star or a galaxy directly. Instead, they looked at a quasar (a super-bright, distant lighthouse powered by a black hole) named B0218+357.

The Cosmic "Shadow" Trick

Here is the clever part of their method:

The Light Source: The quasar is shining brightly in the background.
The Cloud: Between us and the quasar, there is a galaxy (a "cosmic cloud") that happened to drift right in front of the quasar's light.
The Absorption: As the quasar's light passes through this cloud, the molecules inside the cloud (like HCN and HNC) act like a sponge. They "soak up" specific colors of light, creating dark lines in the spectrum.

Think of it like holding a piece of stained glass up to a bright streetlamp. The glass absorbs certain colors, leaving a shadow. By studying the shape and depth of these "shadows" (absorption lines), the scientists can figure out the temperature of the gas in that cloud.

Why is this cloud special?

Usually, gas in space is heated by nearby stars or collisions between particles. But this specific cloud is very diffuse (thin) and far away from any bright stars. It's so isolated that the only thing heating it up is the Cosmic Microwave Background itself.

It's like a thermometer placed in a room with no heaters, no sunlight, and no people. The only thing warming it up is the ambient heat of the room itself. If the thermometer reads 4.5 degrees, then the room is 4.5 degrees.

The Detective Work

The team used the ALMA telescope (a massive array of radio dishes in the Chilean desert) to listen to the "whispers" of these molecules. They had to solve a few tricky puzzles:

The "Covering" Problem: Imagine trying to measure the temperature of a room, but your thermometer is only touching a small patch of the wall, not the whole room. The scientists had to calculate exactly how much of the background light was blocked by the cloud to get an accurate reading. They used a statistical method called "Monte Carlo sampling" (basically running a million computer simulations) to account for this uncertainty.
The "Uneven" Problem: The cloud isn't a perfect, uniform sheet; it's clumpy. Some parts are thick, some are thin. The scientists had to correct their math to account for these clumps, ensuring they didn't get a false reading.
The "Noise" Filter: They looked at several different types of molecules. Some were influenced by collisions (like people bumping into each other in a crowded room), which would mess up the temperature reading. They realized that HCO+ was getting "too hot" from collisions, so they threw that data out. They focused on HCN and HNC, which were the most reliable thermometers.

The Result: A Perfect Match

After all the calculations, the team found the temperature of the universe at that specific moment in time (6 billion years ago, when the universe was about half its current age) to be 4.50 Kelvin (about -449°F).

The standard Big Bang model predicted it should be 4.59 Kelvin.

The verdict? The measurement is incredibly close to the prediction. The difference is tiny—smaller than the margin of error.

Why Does This Matter?

This is like checking the speedometer of a car that has been driving for 13 billion years. If the speedometer says you are going 60 mph, but the laws of physics say you should be going 65 mph, you might suspect the car's engine is broken or the laws of physics are wrong.

In this case, the "speedometer" (the temperature measurement) matches the "laws of physics" (the Big Bang model) perfectly. This confirms that our understanding of how the universe expands and cools is correct. It also sets a very strict rule for any "weird" new theories that try to change how the universe works; they now have to explain why they don't mess up this perfect temperature match.

In short: The scientists looked at a distant cosmic shadow, corrected for all the messy details, and confirmed that the universe is cooling down exactly as we thought it would. The Big Bang theory passes another test with flying colors.

1. Problem Statement

The Cosmic Microwave Background (CMB) temperature ( $T_{CMB}$ ) is a fundamental prediction of the standard Big Bang cosmological model, which posits that $T_{CMB}$ evolves with redshift ( $z$ ) according to the relation $T_{CMB}(z) = T_0(1+z)$ . While this relationship has been tested at various redshifts, measurements at intermediate redshifts ( $0.5 \lesssim z \lesssim 1$ ) have historically suffered from large uncertainties or relied on specific methods like the thermal Sunyaev–Zel'dovich (SZ) effect.

There was a lack of high-precision, independent measurements of $T_{CMB}$ at $z \approx 0.68$ . Previous attempts using molecular absorption lines in this redshift range were limited by uncertainties in the continuum covering factor ( $f_c$ ), column density non-uniformity, and potential contamination from collisional excitation. This study aims to provide the first precise determination of $T_{CMB}$ at $z = 0.68$ using quasar absorption lines, specifically targeting the B0218+357 system.

2. Methodology

Observational Data:

Target: The quasar B0218+357 ( $z_{em} = 0.944$ ) and its intervening absorber at $z_{abs} = 0.68466$ . The system is gravitationally lensed into two images (A and B). The study focuses on the A component, which exhibits a rich molecular absorption system.
Instrument: Atacama Large Millimeter/submillimeter Array (ALMA).
Data: Band 3 and Band 4 observations (Project 2016.1.00031.S) covering rotational transitions $J=2–1$ and $J=3–2$ of highly polar molecules: HCN, HCO+, HNC, and their isotopologues H $^{13}$ CN and H $^{13}$ CO $^+$ .

Analysis Pipeline:

Data Reduction: Standard CASA procedures were used for calibration. Spectra for components A and B were extracted using the UVMULTIFIT package by fitting visibilities directly in the Fourier plane to resolve the two lensed images.
Optical Depth Calculation:
- The optical depth ( $\tau_\nu$ ) was derived from the absorption depth relative to the continuum ( $I_c$ ) using $\tau_\nu = -\ln(1 - \Delta I / f_c I_c)$ .
- Continuum Covering Factor ( $f_c$ ): To address the uncertainty in $f_c$ (previously estimated between 0.77 and 1.0), the authors employed Monte Carlo sampling. They assumed $f_c$ follows a uniform distribution between 0.77 and 1.0 and propagated this uncertainty, along with statistical noise in the absorption depth, to derive the probability distribution of $\tau_\nu$ .
Column Density Correction:
- Recognizing that absorbing clouds are not uniform, the authors corrected for biases where high-density regions saturate absorption, leading to underestimated optical depths.
- They assumed a lognormal column-density probability distribution function (N-PDF), utilizing parameters derived from the Orion A giant molecular cloud (Ma et al. 2020) as a proxy, to convert observed optical depths ( $\tau_{obs}$ ) to real optical depths ( $\tau_{real}$ ).
Excitation Temperature ( $T_{ex}$ ) Derivation:
- $T_{ex}$ was calculated by fitting the Boltzmann distribution (Equation 3) to the optical depths of the $J=2–1$ and $J=3–2$ transitions.
- Optically Thin Regime: Analysis was restricted to velocity bins where $\tau < 1$ to minimize photon trapping and collisional effects.
- Collisional Excitation Check: The authors used RADEX simulations with physical conditions of the absorber ( $T_{kin} \approx 55$ K, $n(H_2) \sim 10^2-10^4$ cm $^{-3}$ ) to verify that radiative excitation by the CMB dominates over collisional excitation for the selected species.

3. Key Contributions

First Measurement at $z=0.68$ : This is the first determination of the CMB temperature at this specific redshift using a quasar absorption line system.
Rigorous Error Propagation: The study introduces a robust Monte Carlo framework to propagate uncertainties in the continuum covering factor ( $f_c$ ), a major source of systematic error in previous studies.
Non-Uniformity Correction: The application of a lognormal N-PDF correction to account for column density inhomogeneity, refining the optical depth estimates.
Species Selection Strategy: The authors demonstrated that while HCO+ is a common tracer, its lower critical density makes it susceptible to collisional excitation and velocity component contamination. Consequently, they excluded HCO+ from the final $T_{CMB}$ determination, relying instead on the more robust HCN and HNC data.

4. Results

Absorption Components: Two distinct velocity components were identified in HCN, HCO+, and HNC spectra (centered at $+5$ km s $^{-1}$ and $-6$ km s $^{-1}$ relative to the systemic velocity). The $+5$ km s $^{-1}$ component showed saturation in HCN, allowing for a constraint on $f_c$ .
Excitation Temperatures:
- HCN: $T_{ex} = 4.42^{+0.20}_{-0.20}$ K
- HNC: $T_{ex} = 4.71^{+0.35}_{-0.32}$ K
- HCO+: $T_{ex} = 5.62^{+0.26}_{-0.25}$ K (Excluded from final average due to evidence of collisional bias and contamination from a third velocity component).
- Isotopologues (H $^{13}$ CN, H $^{13}$ CO $^+$ ): Results were consistent with the standard model but had larger uncertainties due to low signal-to-noise ratios.
Final Determination:
By taking the weighted mean of the excitation temperatures from HCN and HNC (the most reliable tracers in the optically thin regime), the authors derived:
$T_{CMB}(z=0.68) = 4.50 \pm 0.17 \text{ K}$

5. Significance

Validation of Standard Cosmology: The measured value of $4.50 \pm 0.17$ K is in excellent agreement with the standard Big Bang model prediction of $T_{CMB} = T_0(1+z) \approx 4.59$ K at $z=0.68$ .
Precision: This result represents the most precise determination of $T_{CMB}$ at this redshift to date, significantly improving upon previous SZ-based measurements at similar redshifts (e.g., Hurier et al. 2014; Saro et al. 2014) which had uncertainties of $\sim 0.3$ K.
Constraints on Non-Standard Models: The result places tight constraints on deviations from the standard adiabatic expansion law. When combined with other measurements in a phenomenological model $T_{CMB}(z) = T_0(1+z)^{1-\beta}$ , the derived parameter $\beta = (3.9^{+7.4}_{-8.2}) \times 10^{-3}$ is consistent with zero, reinforcing the standard model.
Methodological Foundation: The study establishes a refined methodology for future high-precision $T_{CMB}$ measurements, emphasizing the importance of correcting for covering factors and column density inhomogeneities, and carefully selecting molecular tracers with high critical densities to avoid collisional biases.

In conclusion, this paper provides a landmark measurement confirming the evolution of the CMB temperature in the intermediate-redshift universe, utilizing advanced ALMA data and rigorous statistical corrections to achieve unprecedented precision.