Impact of Primordial Black Hole population on 21 cm observables at high redshift

This paper utilizes a semi-numerical model to demonstrate that primordial black holes, acting as seeds for early AGNs, significantly alter high-redshift 21-cm observables by shallowing the global signal depth and suppressing power spectrum amplitudes, with the specific impact heavily dependent on the chosen PBH mass function.

The Gist

Imagine the early Universe as a giant, dark room filled with a thick, invisible fog. This fog is made of neutral hydrogen gas. For a long time, astronomers thought this room was completely silent and dark, lit only by the very first stars turning on like lightbulbs.

But recently, the James Webb Space Telescope (JWST) peeked into this room and found something unexpected: tiny, glowing "red dots." These are ancient, super-bright galaxies powered by black holes that formed almost instantly after the Big Bang. These are called Primordial Black Holes (PBHs).

This paper asks a big question: How do these early black holes change the "sound" of the Universe?

Here is the breakdown of the research using simple analogies:

1. The "21-cm Signal": The Universe's Radio Whisper

Astronomers can't just "see" this early fog with a normal camera. Instead, they listen to a specific radio frequency called the 21-cm signal.

• The Analogy: Imagine the hydrogen fog is a giant choir. When the Universe is cold, the choir sings a deep, low note (a strong "absorption" signal). When the fog gets heated up, the choir's voice changes, and the note becomes quieter or disappears.
• The Goal: Scientists want to record this "song" to understand how the Universe warmed up and how the first lights turned on.

2. The Old Story vs. The New Twist

• The Old Story: For years, models assumed the only things heating up the fog were the first stars (Star-Forming galaxies). In this story, the "choir" sings a very deep, loud note because the fog stays cold for a long time.
• The New Twist: The JWST found those early black holes (PBHs). Black holes are like cosmic heaters. As they eat gas, they spit out massive amounts of X-rays.
• The Effect: These X-rays act like a giant space heater turning on early. They warm up the hydrogen fog before the stars even get a chance to do it. This makes the "choir's" note much shallower (less deep) than we expected.

3. The Experiment: Testing Different "Heater" Recipes

The authors didn't just assume all black holes are the same. They tested three different "recipes" for how these black holes might have been distributed in the early Universe:

1. The Log-Normal Recipe: Most black holes are roughly the same size, with a few very small or very large ones (like a bell curve).
2. The Power-Law Recipe: There are tons of tiny black holes, but also a few massive giants (like a pyramid).
3. The Critical Recipe: A very specific, sharp distribution where black holes form at a very specific "critical" mass.

The Results:

• The "Critical" Recipe was the most aggressive heater. It warmed the fog so much that the 21-cm signal barely showed any absorption at all. It was like turning the space heater to "High" immediately.
• The "Power-Law" and "Log-Normal" recipes still warmed the fog, but not as drastically. They made the signal shallower than the "Star-Only" model, but not as flat as the Critical model.
• The "Star-Only" model (No Black Holes): This produced the deepest, coldest signal.

4. The "Leaky Bucket" Problem

The researchers also wondered: How much of that heat actually escapes the black hole's neighborhood to warm the rest of the Universe?

• The Analogy: Imagine the black hole is a heater in a room with a leaky door. If the door is wide open (100% escape), the whole house warms up fast. If the door is mostly closed (low escape), the heat stays trapped, and the rest of the house stays cold.
• The Finding: If the "door" is closed (low escape fraction), the signal looks like the old "Star-Only" model. If the door is wide open, the signal changes dramatically. This tells us that measuring the 21-cm signal could help us figure out how "leaky" these early black holes are.

5. Why This Matters

The paper uses a sophisticated computer simulation (called SCRIPT) to map out these changes. They found that:

• Black holes change the "texture" of the Universe. It's not just about the average temperature; it changes how the temperature fluctuates across space (the "power spectrum").
• The shape of the black hole distribution matters. Depending on which "recipe" (mass function) is correct, the radio signal we will see in the future could look completely different.
• Future telescopes can tell the difference. Upcoming radio telescopes (like the SKA) will be sensitive enough to detect these differences. If they see a shallow signal, it might mean our Universe was seeded by these early black holes. If they see a deep signal, maybe the black holes weren't as influential as we thought.

The Bottom Line

This paper is like a detective story. The clues (JWST images) suggest early black holes exist. The authors built a model to see how these black holes would "heat up" the early Universe. They found that if these black holes are real, they would have turned up the thermostat of the early Universe much earlier than we thought, changing the radio "song" of the hydrogen fog in a way that future telescopes will be able to hear.

It's a reminder that the early Universe wasn't just a quiet place waiting for stars; it might have been a chaotic, heated-up environment driven by mysterious, ancient black holes.

Technical Summary

1. Problem Statement

The 21-cm signal from neutral hydrogen is a primary probe for the Cosmic Dawn (CD) and Epoch of Reionization (EoR) ($z \sim 30-5$). Historically, models of this signal have assumed that astrophysical sources were exclusively star-forming (SF) galaxies, with Active Galactic Nuclei (AGN) becoming relevant only at lower redshifts ($z \lesssim 6$).

However, recent observations by the James Webb Space Telescope (JWST) have detected AGNs at remarkably high redshifts ($z \sim 6-10$), often referred to as "Little Red Dots." The origin of these early supermassive black holes is hypothesized to be Primordial Black Holes (PBHs). Previous work (Chatterjee 2026, "C26") established that PBH-seeded AGNs could impact the global 21-cm signal but suffered from two critical limitations:

1. Analytic Nature: It could only predict the sky-averaged global signal, not spatial fluctuations (the power spectrum).
2. Mass Function Assumption: It assumed a specific log-normal PBH mass function, ignoring other physically motivated distributions.

This paper addresses these gaps by investigating how different PBH mass functions influence both the global 21-cm signal and its power spectrum.

2. Methodology

The authors developed a unified semi-numerical framework to model the intergalactic medium (IGM) evolution from $z \sim 30$ to $z \sim 5$.

A. PBH Mass Functions

The study evaluates three physically motivated PBH mass functions, normalized to match JWST constraints at $z \sim 10$ (specifically a number density of $10^{-5.27} \text{ cMpc}^{-3}$ for a seed mass of $10^{4.65} M_\odot$):

1. Log-normal: Arising from primordial space-time fluctuations.
2. Power-law: Arising from density fluctuations in a matter-dominated epoch ($\alpha = 2$).
3. Critical: Arising from phase transitions and scalar field collapse.

B. The SCRIPT Framework

The authors extended the Semi-numerical Code for ReIonization with PhoTon Conservation (SCRIPT) model (Maity & Choudhury 2022a). Key extensions include:

• Cosmic Dawn Physics: Incorporation of X-ray heating and Ly-$\alpha$ coupling.
• PBH Integration: The model calculates contributions from PBH-seeded AGNs alongside standard star-forming galaxies.
• Photon Conservation: Explicitly tracks ionizing photons, inhomogeneous recombinations, and radiative feedback (modifying the minimum halo mass for star formation based on local temperature).
• Simulation Setup: Uses a $256 h^{-1} \text{ cMpc}$ box with $8 h^{-1} \text{ cMpc}$ resolution, generating 251 coeval boxes ($\Delta z = 0.1$) across $z=5-30$.

C. Physical Calculations

• AGN Evolution: Uses the PHANES framework to model PBH growth (linear DM accretion followed by gas accretion) and luminosity.
• Heating & Coupling:
  • X-ray Heating: Calculated for both SF and PBH sources. The global X-ray emissivity is integrated over the mass function.
  • Ly-$\alpha$ Coupling: Calculated for both sources to determine the spin temperature ($T_S$).
  • 21-cm Signal: Computed the differential brightness temperature ($\delta T_b$) and the dimensionless power spectrum ($\Delta^2_{21}$).

3. Key Contributions

1. Extension to Power Spectrum: Successfully extended the C26 analytic formalism into the semi-numerical SCRIPT framework, enabling the prediction of 21-cm power spectra (spatial fluctuations) alongside global signals.
2. Mass Function Sensitivity: Demonstrated that the choice of PBH mass function is not merely a normalization issue but fundamentally alters the shape and amplitude of the 21-cm observables.
3. Parameter Space Exploration: Investigated the sensitivity of the signal to the X-ray escape fraction ($f_{X,esc}^{PBH}$), a highly uncertain parameter, showing how it modulates the heating efficiency.

4. Key Results

A. X-ray Emissivity and Heating

• Early Onset: PBH-seeded systems produce significant X-ray emission at $z \ge 15$, much earlier than standard star-forming galaxies.
• Mass Function Dependence:
  • Critical Mass Function: Produces the highest X-ray emissivity at $z \sim 10-15$ due to a sharp peak in the mass distribution.
  • Power-law: Dominated by low-mass black holes but has an extended high-mass tail, leading to significant emission at lower redshifts ($z \lesssim 8$).
  • Log-normal: Produces the lowest X-ray emission among the PBH models in the relevant redshift range.

B. Global 21-cm Signal

• Absorption Trough Depth: The depth of the global absorption trough is inversely proportional to X-ray heating.
  • SF-only: Deepest trough ($\sim -60$ mK) due to lack of early heating.
  • Log-normal & Power-law: Produce shallower troughs ($\sim -30$ mK) at $z \sim 18$.
  • Critical: Produces the shallowest signal, eliminating the absorption trough entirely due to intense early X-ray heating that keeps the IGM temperature high.
• Conclusion: The presence of PBHs, particularly those following a critical mass function, can significantly suppress the depth of the 21-cm absorption feature.

C. 21-cm Power Spectrum

• Suppression: PBH heating suppresses the power spectrum amplitude during the Cosmic Dawn.
  • Log-normal/Power-law: Reduce the power amplitude by a factor of $>2$ (from $\sim 100$ mK$^2$ in SF-only to $\sim 20-30$ mK$^2$).
  • Critical: Suppresses the amplitude by more than two orders of magnitude.
• Reionization: PBHs do not significantly affect the power spectrum during the EoR ($z < 10$) in this model, as they do not contribute significantly to ionization compared to stars.

D. Sensitivity to X-ray Escape Fraction

• Varying the X-ray escape fraction ($f_{X,esc}^{PBH}$) for the log-normal model from $1.0$ to $0.2$ causes the signal to transition from a shallow trough (heated) to a deep trough (unheated, approaching the SF-only case).
• This suggests that future interferometers (e.g., HERA, SKA-low) could distinguish between high and low escape fractions.

5. Significance and Implications

• Interpretation of Future Data: The results imply that the absence of a deep 21-cm absorption trough in future observations (e.g., by SKA-low or HERA) could be a signature of a PBH population, specifically one following a critical or power-law mass function.
• JWST Synergy: The findings provide a theoretical link between JWST's detection of high-redshift AGNs and the 21-cm background, suggesting these early AGNs are likely seeded by PBHs.
• Model Constraints: The study highlights that assuming a single mass function (e.g., log-normal) can lead to incorrect predictions. The diversity of PBH formation scenarios must be accounted for when interpreting 21-cm data.
• Caveats: The authors note that they did not include radio emission from early AGNs (which could deepen the trough) or Pop-III star feedback, which are planned for future work. However, current JWST data suggests early AGNs have weak radio emission, supporting the current X-ray dominated model.

In summary, this paper establishes that the Primordial Black Hole population is a critical variable in 21-cm cosmology. Depending on the mass function and X-ray escape efficiency, PBHs can drastically alter the thermal history of the early Universe, potentially erasing the expected absorption signal and suppressing power spectrum fluctuations.