Implications of \textit{SARAS3} data for Coulomb-like interacting dark matter

This paper analyzes SARAS3's non-detection of the 21-cm signal in the 55.5–84.4 MHz band to constrain Coulomb-like interacting dark matter by self-consistently modeling both gas cooling and structure formation suppression, ultimately finding no statistically significant preference for interacting dark matter over standard cold dark matter while establishing a meaningful upper bound on the global 21-cm signal amplitude.

The Gist

The Big Picture: Listening to the Universe's "Baby Cry"

Imagine the early universe as a giant, dark nursery. About 100 to 200 million years after the Big Bang, the first stars were just starting to be born. These stars emitted light that interacted with the hydrogen gas filling the universe, creating a specific radio signal known as the 21-cm signal.

Think of this signal like a "baby cry" from the cosmic dawn. If we can hear it clearly, it tells us how hot or cold the gas was and how fast the first stars were forming.

For a long time, scientists hoped to hear this cry. However, the signal is incredibly faint, like trying to hear a whisper in a hurricane. The "hurricane" is made of radio noise from our own galaxy, the Earth's atmosphere, and our radio telescopes themselves.

The Mystery: Dark Matter's Secret Conversation

We know that most of the universe is made of Dark Matter, an invisible substance that doesn't emit light. The standard theory says Dark Matter is "cold" and "lazy"—it just sits there and only interacts with normal matter (like gas) through gravity.

But what if Dark Matter is more like a "social butterfly"? What if it bumps into normal gas particles and exchanges heat, like two people shaking hands and sharing body warmth? This is the idea of Interacting Dark Matter (IDM).

The authors of this paper wanted to test a specific type of "social" Dark Matter that interacts like Coulomb force (similar to how electric charges attract or repel). They asked: If Dark Matter does this, how would it change the "baby cry" (the 21-cm signal)?

The Two-Step Effect: Cooling and Delay

The paper explains that if Dark Matter interacts with gas, it causes two major changes, which the authors modeled carefully:

1. The "Ice Pack" Effect (Cooling):
   Normally, gas cools down slowly as the universe expands. But if Dark Matter is colder than the gas, it acts like an ice pack, sucking heat out of the gas. This makes the gas much colder than expected.

   • Result: A colder gas creates a deeper, louder "cry" (a stronger absorption signal).

2. The "Traffic Jam" Effect (Delayed Stars):
   When Dark Matter bumps into gas, it creates friction (drag). This slows down the gas, making it harder for it to collapse and form stars.

   • Result: Star formation gets delayed. Since stars provide the heat and light that eventually warm up the gas, the "cry" happens later and is weaker than it would be if stars formed on time.

The authors realized that previous studies often only looked at the "Ice Pack" (cooling) and ignored the "Traffic Jam" (delayed stars). This paper is the first to model both effects happening at the same time to see the full picture.

The Detective Work: The SARAS3 Experiment

To test this theory, the team looked at data from the SARAS3 experiment.

• The Setup: Unlike other telescopes on the ground, SARAS3 is a floating antenna on a lake. The water acts as a perfect, uniform background, helping to filter out some of the "noise" from the ground.
• The Result: SARAS3 looked for the "baby cry" in a specific frequency range but did not find it. They saw nothing but static.

The Investigation: What Does "Nothing" Tell Us?

Usually, when scientists say "we didn't find it," it feels like a dead end. But the authors treated this "null result" (finding nothing) as a clue.

They built a complex computer model that simulated:

1. The "baby cry" (the 21-cm signal) based on their Dark Matter theories.
2. The "noise" (foregrounds like galactic radio waves).

They then used a statistical method (Bayesian inference) to see if their "Dark Matter + Noise" model could explain the SARAS3 data.

The Findings:

• The Signal is Hidden: The data is too noisy to pin down the exact values of the Dark Matter's mass or how strongly it interacts. It's like trying to guess the exact weight of a feather while standing in a windstorm; the wind (noise) is too strong to tell.
• The "Too Loud" Rule: However, they can say what the signal isn't. The data proves that the "baby cry" cannot be extremely deep or loud in the frequency range they observed. Specifically, at a certain point in time (redshift 23.6), the signal cannot be deeper than -277.6 millikelvin. If the Dark Matter interaction were strong enough to make the signal that deep, SARAS3 would have seen it. Since they didn't, those specific strong interactions are ruled out.
• Dark Matter vs. Standard Model: The authors compared their "Social Dark Matter" model against the standard "Lazy Dark Matter" model. They asked: Does the data prefer the social version?
  • The Verdict: No. The data is inconclusive. It's a toss-up. The "betting odds" slightly favor the social version (1.7 to 1), but not enough to say it's definitely true. It's essentially a draw.

The Conclusion

This paper is a lesson in how to listen to silence. Even though SARAS3 didn't find the signal, the authors learned that:

1. We cannot yet rule out the idea that Dark Matter interacts with gas, but we know it can't interact too strongly (otherwise the signal would have been too loud to miss).
2. To solve this mystery, we need better data (less wind, clearer signal) from future experiments like REACH.
3. The "Social Dark Matter" theory is still alive, but it hasn't been proven yet.

In short: The universe is still whispering, and we are still trying to figure out if the whisper is coming from a standard ghost or a chatty one. SARAS3 told us the ghost isn't shouting, but it hasn't told us exactly what it's whispering yet.

Technical Summary

1. Problem Statement

The nature of Dark Matter (DM) remains one of the most significant open questions in cosmology. While the standard Cold Dark Matter (CDM) model assumes DM is collisionless, various anomalies (e.g., dwarf galaxy dynamics, cosmic ray positron excess) suggest the possibility of non-gravitational interactions between DM and baryons. Specifically, Coulomb-like Interacting Dark Matter (IDM) models propose that DM particles carry a tiny fractional charge or interact via a force scaling inversely with the fourth power of relative velocity ($\sigma \propto v^{-4}$).

The 21-cm signal from Cosmic Dawn (the epoch of first star formation) is a sensitive probe of the thermal history of the Intergalactic Medium (IGM). Previous studies, often relying on the controversial EDGES detection, suggested that IDM could explain an anomalously deep absorption trough via excess baryon cooling. However, the SARAS3 experiment (Shaped Antenna Measurement of the Background Radio Spectrum) reported a non-detection of such a deep feature in the 55.5–84.4 MHz band, ruling out the EDGES profile at 95% confidence.

The Core Challenge: Previous constraints on IDM using 21-cm data were often incomplete, focusing primarily on the baryon cooling effect while neglecting the momentum exchange effect. Momentum exchange suppresses structure formation (halo formation), thereby delaying star formation and reducing the Ly$\alpha$, X-ray, and ionizing backgrounds. This paper aims to provide the first self-consistent analysis of IDM using SARAS3 data, simultaneously modeling both the cooling and the delayed star formation effects within a rigorous Bayesian framework.

2. Methodology

A. Theoretical Framework

The authors utilize the ECHO21 Python package to model the global 21-cm signal, incorporating two distinct physical mechanisms of IDM:

1. Excess Baryon Cooling: Heat exchange between DM and baryons cools the gas ($T_k$) below the adiabatic limit, deepening the 21-cm absorption trough.
2. Delayed Star Formation: Momentum exchange suppresses the matter power spectrum ($P(k)$), reducing the halo mass function (HMF). This delays the onset of star formation, which in turn delays Ly$\alpha$ coupling and X-ray heating. This effect tends to shift the absorption trough to lower redshifts and reduce its depth.

The model solves coupled differential equations for:

• Gas kinetic temperature ($T_k$)
• DM temperature ($T_\chi$)
• Relative velocity between DM and baryons ($v_{b\chi}$)
• Ionization fraction ($x_e$)

B. Parameter Space

The model is defined by 7 free parameters:

• IDM Physics: DM particle mass ($m_\chi$) and interaction cross-section parameter ($\sigma_{45}$).
• Astrophysics: Ly$\alpha$ background scaling ($f_{Ly}$), X-ray background scaling ($f_X$), X-ray spectral index ($w$), ionizing photon escape fraction ($f_{esc}$), and minimum virial temperature for star formation ($T_{vir}^{min}$).
• Note: Star formation efficiency ($f_*$) is fixed at 0.1 due to degeneracy with other parameters.

C. Data and Inference

• Dataset: SARAS3 antenna temperature data (55.5–84.4 MHz).
• Foreground Modeling: A 6th-order log-log polynomial (7 coefficients) is used to model galactic/extragalactic foregrounds and systematics.
• Statistical Approach: A Joint Bayesian Inference is performed using the Polychord nested sampling algorithm.
  • The total model is 14-dimensional (7 signal parameters + 7 foreground coefficients).
  • Priors: Uniform (uninformative) priors are used for all parameters to avoid bias.
  • Likelihood: Gaussian likelihood based on the difference between observed and modeled antenna temperatures, weighted by SARAS3 noise levels.
• Analysis Metrics:
  • Bayesian Evidence: To compare IDM vs. CDM models (via Bayes Factor).
  • Kullback-Leibler (KL) Divergence: To measure information gain (constraining power) from prior to posterior.
  • Gaussian Model Dimensionality (GMD): To quantify the effective number of constrained parameters.

3. Key Contributions

1. Self-Consistent IDM Modeling: This is the first study to jointly constrain IDM parameters by simultaneously including both the cooling effect (which deepens the signal) and the momentum-transfer effect (which suppresses star formation and weakens the signal).
2. Rigorous Bayesian Framework: Unlike previous approximate analyses, this work performs a full marginalization over foregrounds and astrophysical uncertainties using nested sampling.
3. Functional Constraints: Instead of just constraining individual parameters, the authors translate parameter posteriors into functional constraints on the 21-cm signal amplitude ($T_{21}$) across redshift.
4. Model Comparison: A direct Bayesian evidence comparison between the IDM scenario and the standard CDM scenario using SARAS3 data.

4. Results

A. Parameter Constraints

• Weak Constraints on Parameters: The SARAS3 data, given its noise level and the degeneracy between the foregrounds and the cosmological signal, does not significantly constrain the individual IDM or astrophysical parameters.
  • The KL divergence for the 7D signal parameter space is extremely low ($D_{KL} \approx 0.007$).
  • The Gaussian Model Dimensionality is negligible ($d_G \approx 0.01$).
  • Posterior distributions for $m_\chi$, $\sigma_{45}$, and astrophysical parameters remain largely consistent with the priors.

B. Signal Amplitude Bounds

While individual parameters are unconstrained, the data does rule out deep absorption features within the observed band:

• The strongest constraint occurs at $z = 23.6$ ($\nu \approx 57.7$ MHz), where the KL divergence peaks ($0.52$).
• At this redshift, the data places a $3\sigma$ lower bound on the signal amplitude:
  $$T_{21}(z=23.6) \gtrsim -277.6 \text{ mK}$$
• This effectively rules out IDM models that predict absorption features deeper than this limit within the SARAS3 frequency band.

C. IDM vs. CDM Preference

• The authors computed the Bayesian evidence for both the IDM and standard CDM models.
• Log Bayes Factor: $\ln B = \ln Z_{IDM} - \ln Z_{CDM} \approx 0.53$.
• Bayes Factor: $B \approx 1.7$.
• Conclusion: According to the Jeffreys scale, this represents inconclusive evidence. There is no statistically significant preference for IDM over CDM based on the current SARAS3 data.

5. Significance and Implications

• Null Results are Informative: Even though SARAS3 did not detect a signal, the non-detection provides a meaningful upper bound on the amplitude of the global 21-cm signal for Coulomb-like IDM models. It rules out the most extreme cooling scenarios that would produce deep absorption troughs.
• Importance of Momentum Exchange: The study highlights that neglecting the momentum exchange (delayed star formation) leads to an overestimation of the cooling effect. A self-consistent model shows that momentum suppression can counteract the cooling, making the signal shallower and harder to distinguish from CDM.
• Future Prospects: The current constraints are limited by the noise level of SARAS3 and the large uncertainty in high-redshift astrophysics (e.g., X-ray and Ly$\alpha$ backgrounds). The authors suggest that future experiments with wider bandwidths (e.g., REACH) and the combination of datasets (e.g., 21-cm power spectra, UV luminosity functions) will be necessary to break degeneracies and place tighter constraints on IDM parameters.
• Tool Release: The authors have updated and released the ECHO21 Python package to include Coulomb-like IDM modeling, facilitating future research in this domain.

In summary, this paper establishes a robust framework for testing interacting dark matter against global 21-cm data, demonstrating that while current data cannot distinguish between CDM and IDM, it successfully excludes models predicting extremely deep absorption features.