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Forest without Trees is still Fruitful: Constraints on the thermal state of the neutral IGM at $z\approx5.6$ with the 21-cm forest power spectrum

By analyzing archival uGMRT observations of the high-redshift quasar J352-15, this study utilizes the non-detection of the 21-cm forest power spectrum to constrain the thermal state of the neutral intergalactic medium at $z\approx5.6$ , ruling out cold, substantially neutral models and demonstrating the 21-cm forest's potential as a statistically informative probe of the Epoch of Reionization.

Original authors: Tomáš Šoltinský (INAF-OATs), Arnab Chakraborty (McGill University), Girish Kulkarni (TIFR), Matteo Viel (SISSA), Cathryn M. Trott (Curtin University), Rashmi Sagar (IIT Indore), Nithyanandan Thyagaraj

Published 2026-07-20

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Original authors: Tomáš Šoltinský (INAF-OATs), Arnab Chakraborty (McGill University), Girish Kulkarni (TIFR), Matteo Viel (SISSA), Cathryn M. Trott (Curtin University), Rashmi Sagar (IIT Indore), Nithyanandan Thyagarajan (CSIRO), James S. Bolton (University of Nottingham), Benedetta Ciardi (MPA), Emma V. Ryan-Weber (Swinburne University of Technology), Soumak Maitra (TIFR), Abhirup Datta (IIT Indore), Nirupam Roy (IISc Bangalore)

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, invisible ocean. For most of its history, this ocean was made of cold, quiet gas, mostly hydrogen, drifting silently between the stars. Then, about 13 billion years ago, the first stars and galaxies ignited like massive lighthouses. Their intense light began to boil the ocean, turning the cold, neutral gas into a hot, ionized soup. This dramatic transformation is called the "Epoch of Reionization." Scientists are desperate to understand exactly how and when this happened, but there's a problem: the cold, neutral gas that existed before it was fully boiled away is incredibly hard to see. It's like trying to find a specific type of invisible fish in a dark, foggy lake using only a flashlight that shines on the water's surface. Traditional tools can see the clear, ionized water, but they struggle to peek into the dense, neutral fog where the real action was happening. To solve this mystery, astronomers are looking for a new kind of clue hidden in the light of distant, bright radio beacons.

This paper is about a clever new way to listen to that invisible fog. The researchers used a giant radio telescope called the uGMRT to stare at the brightest known radio-loud quasar from that ancient era, a cosmic lighthouse named J352–15. They weren't looking for a single, clear signal; instead, they were hunting for a "forest" of tiny, invisible absorption marks that the neutral gas would leave on the quasar's radio light. Think of it like shining a flashlight through a forest of trees. If the trees are there, the light gets blocked in specific, tiny patterns. By analyzing the statistical "noise" or the pattern of these blocks, the team tried to figure out how cold and how thick the fog was.

The team didn't find the forest. In fact, they found nothing at all. But in the world of science, a "null result" can be just as powerful as a discovery. By proving that the forest wasn't there, they were able to rule out a whole bunch of theories about what the early universe looked like. Specifically, they showed that the neutral gas couldn't have been as cold and as thick as some scientists had hoped. If the gas had been that cold, the "forest" would have been loud and obvious. Since it was silent, the gas must have been warmer than expected.

The researchers analyzed 17.5 hours of data, which, after cleaning out radio interference, left them with about 11.73 hours of good listening time. They achieved a sensitivity of 3.62 mJy beam⁻¹ per 6.1 kHz channel. Even though they didn't detect the 21-cm forest signal, their analysis allowed them to set strict limits on the temperature of the neutral gas. They found that models where the gas was colder than about 27 K (for a neutral fraction of 0.1) are now disfavoured. In simpler terms, the "fog" of the early universe wasn't a freezing, solid block; it had been pre-heated by something, likely X-rays from early black holes or stars, raising its temperature well above the absolute minimum.

The paper also looked at data from another telescope, the MWA, but it wasn't sensitive enough to compete with the uGMRT results. However, the authors are optimistic about the future. They ran simulations showing that if they could observe the same quasar for a total of about 71.73 hours (combining old data with new, deeper observations), they could push the temperature limits even higher, potentially ruling out gas temperatures below 159 K for very neutral gas. This would be a massive step forward.

Ultimately, this study proves that the "21-cm forest" is no longer just a theoretical idea; it has entered the realm of real, useful observation. Even without finding the signal, the silence of the data tells us that the early universe was warmer and more energetic than the coldest models predicted. It's a bit like walking into a room and not hearing a whisper; you might not know who is there, but you definitely know the room isn't as quiet as you thought. This work opens the door to using these ancient radio beacons to map the thermal history of the universe, turning the invisible fog of the past into a measurable, warm reality.

Technical Summary: Constraints on the thermal state of the neutral IGM at z ≈5.6 with the 21-cm forest power spectrum

Problem and Motivation
The thermal and ionization state of the predominantly neutral intergalactic medium (IGM) during the final stages of the Epoch of Reionization (EoR, $z \gtrsim 5.5$ ) remains poorly constrained. Traditional probes like the Ly $\alpha$ forest are insensitive to substantially neutral regions due to rapid saturation, while global-signal and tomographic 21-cm emission experiments face severe contamination from bright astrophysical foregrounds. The 21-cm forest—narrow absorption features imprinted on the spectra of bright radio-loud quasars (RLQSOs) by the neutral IGM—offers a differential absorption probe that is largely immune to these foregrounds. However, despite theoretical predictions, the 21-cm forest has not yet been statistically detected, primarily due to the low redshift of previously targeted sources and insufficient sensitivity. This study addresses the challenge of constraining the IGM state in the absence of a direct detection by utilizing the one-dimensional (1D) power spectrum of the forest as a statistical observable.

Methodology
The authors analyzed archival data from the upgraded Giant Metrewave Radio Telescope (uGMRT) targeting J352–15 (PSO J352.4034–15.3373), the brightest known RLQSO at $z > 5.5$ ( $z=5.82$ ).

Observations: A total of 17.5 hours of on-source time (across Band-2 receivers) was reduced, resulting in an effective integration time of 11.73 hours after Radio Frequency Interference (RFI) flagging and calibration. The data were processed using advanced direction-dependent calibration techniques (DDFacet and CUBICAL) to mitigate sidelobe artifacts, followed by continuum subtraction and wavelet-based residual bandpass removal.
Data Product: The analysis yielded a radio spectrum spanning 209.0–222.5 MHz ( $5.4 \le z \le 5.82$ ) with a per-channel RMS noise of 3.62 mJy beam $^{-1}$ (6.1 kHz resolution). The primary observable is the 1D power spectrum ( $P_{21}$ ) of the normalized flux fluctuations ( $\delta F_{21}$ ), calculated using a Lomb–Scargle periodogram to handle irregularly sampled data due to RFI excision.
Forward Modeling: Synthetic 21-cm forest spectra were generated using the semi-numerical code 21cmFAST (v3.3.1) across a grid of 534 IGM models. These models varied the mean neutral hydrogen fraction ( $\langle x_{\text{HI}} \rangle$ ) and the X-ray heating efficiency ( $f_X$ ), which determines the mean temperature of the neutral IGM ( $\langle T_{\text{HI}} \rangle$ ). The simulations assumed a saturated coupling between spin temperature ( $T_S$ ) and kinetic temperature ( $T_K$ ).
Inference: A Bayesian Markov Chain Monte Carlo (MCMC) analysis was performed using a Gaussian likelihood. The observed power spectrum was compared against the forward-modeled synthetic spectra, accounting for a covariance matrix derived from both instrumental noise (estimated from off-source sightlines) and sample variance. The analysis treated the non-detection as a constraint, excluding regions of the $\langle T_{\text{HI}} \rangle$ – $\langle x_{\text{HI}} \rangle$ parameter space where the predicted signal would exceed the observed residuals.

Key Results

Null Detection: The measured 1D power spectrum of J352–15 is consistent with instrumental noise. Statistical tests (Kolmogorov–Smirnov and Anderson–Darling) comparing the target spectrum distribution to off-source noise distributions yielded no significant evidence for a 21-cm forest detection ( $p$ -value = 0.353).
Thermal Constraints: Despite the null detection, the analysis places joint constraints on the IGM state at $z \approx 5.6$ $z \approx 5.6$ . At the 68% credible level, the data disfavor models with cold and substantially neutral IGM. Specifically:
- For $\langle x_{\text{HI}} \rangle = 0.1$ , models with $\langle T_{\text{HI}} \rangle \lesssim 26.9$ K are excluded.
- For $\langle x_{\text{HI}} \rangle = 0.2, 0.5, 0.8$ , the lower limits on temperature are $\langle T_{\text{HI}} \rangle > 39.8, 64.7, 79.9$ K, respectively.
- Models with $\langle x_{\text{HI}} \rangle \gtrsim 0.05$ and $\langle T_{\text{HI}} \lesssim 18$ K are excluded.
Comparison with Other Probes: These constraints are complementary to Ly $\alpha$ forest limits (which constrain ionization but not temperature in neutral regions) and existing 21-cm tomography limits (which are currently limited to higher redshifts or marginalize over many parameters). The 21-cm forest results suggest the neutral IGM has undergone substantial pre-heating above the adiabatic cooling floor.
MWA Analysis: An independent analysis of archival Murchison Widefield Array (MWA) data was performed. Due to lower sensitivity and a larger field of view (leading to higher sidelobe contamination), the MWA data yielded significantly weaker constraints and was not included in the final inference.

Significance and Claims
The paper claims that the 21-cm forest has entered the regime of "observationally informative statistics." The primary significance lies in demonstrating that meaningful constraints on the thermal and ionization state of the neutral IGM can be derived even in the absence of a statistical detection, provided the power spectrum is used as the observable.

The study provides the first observational estimate of the 21-cm forest 1D power spectrum during the EoR.
It establishes that current-generation radio facilities (uGMRT) can probe parameter spaces allowed by existing Ly $\alpha$ and 21-cm tomography observations, specifically ruling out very cold, neutral IGM scenarios.
The authors emphasize that future deeper observations (e.g., a hypothetical 100-hour campaign) would either lead to a statistical detection or significantly tighten these constraints, potentially excluding models with temperatures 30–100% higher than current limits.

Limitations
The authors acknowledge several limitations in their modeling:

Proximate Effects: Radiative feedback from the quasar and potential host galaxy absorption were not modeled, though regions close to the quasar were excluded from the analysis.
Small-scale Structure: Unresolved minihalos and dense structures were not included due to resolution constraints in the semi-numerical simulations.
Redshift Evolution: The analysis assumes a coeval IGM, neglecting the evolution of the IGM state across the observed redshift interval ( $5.4 < z < 5.8$ ).
Ionization Modeling: The 21cmFAST excursion-set formalism produces predominantly fully ionized or neutral cells, lacking a detailed treatment of partially ionized structures at ionization fronts.
Systematics: The noise model assumes uncorrelated Gaussian noise for forecasts, which may not hold if residual systematics or calibration errors dominate in deeper observations.

In conclusion, the work validates the 21-cm forest as a viable probe for the thermal history of the neutral IGM, moving the field from theoretical prediction to observational constraint.

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