Probing Primordial Black Holes with upcoming Radio Telescopes: a case study for LOFAR2.0, FAST Core Array and BINGO

This paper forecasts that upcoming radio telescopes, specifically LOFAR2.0, FAST Core Array, and BINGO, will significantly enhance the ability to constrain the fraction of dark matter composed of Primordial Black Holes by detecting or ruling out lensed Fast Radio Bursts across various mass ranges.

The Gist

Imagine the universe is a giant, dark ocean. Most of this ocean is made of "dark matter," an invisible substance that holds galaxies together, but we can't see it or touch it. For decades, scientists have been trying to figure out what this dark matter is made of. One popular theory suggests it's made of Primordial Black Holes (PBHs)—tiny, ancient black holes formed in the very first split-second of the Big Bang.

This paper is like a detective story. The authors are asking: "Can we catch these invisible black holes in the act?"

Here is the simple breakdown of their plan, using some everyday analogies.

1. The "Flashlight" in the Dark: Fast Radio Bursts (FRBs)

To find these invisible black holes, the scientists need a flashlight. That flashlight is a Fast Radio Burst (FRB).

• What is it? Imagine a cosmic camera flash that happens in outer space. It's a burst of radio waves that lasts for just a tiny fraction of a second (milliseconds or microseconds).
• Why use them? They are incredibly bright and come from very far away. As they travel across the universe to reach Earth, they pass through everything in their path.

2. The "Cosmic Magnifying Glass": Gravitational Lensing

This is the core trick of the paper. According to Einstein, massive objects (like black holes) bend space and time.

• The Analogy: Imagine you are looking at a streetlight through a wine glass. The glass bends the light, and you might see two images of the light instead of one, or the light might arrive slightly later than expected.
• The Science: If a Fast Radio Burst passes near a Primordial Black Hole, the black hole acts like a cosmic magnifying glass. It splits the radio signal into two paths.
  • One path is shorter, the other is longer.
  • This creates a time delay. One "echo" of the signal arrives a tiny bit later than the other.
  • If we can detect this "echo" (the time delay), we know a black hole is hiding there, even if we can't see the black hole itself.

3. The "Super-Ears": The New Radio Telescopes

To hear these tiny echoes, we need incredibly sensitive ears. The paper focuses on three upcoming radio telescopes that are getting major upgrades:

• LOFAR2.0 (Europe): Think of this as a massive net of antennas in the Netherlands. It's getting a "speed boost" to catch signals faster and clearer.
• FAST Core Array (China): This is the world's largest single-dish telescope (a giant metal bowl in the mountains). It's adding a "surround sound" system (an array of smaller dishes) to pinpoint exactly where signals are coming from.
• BINGO (Brazil): A new telescope being built in Brazil, designed to listen to the "hum" of the early universe. It's getting help from a team of other telescopes to become a super-detective.

4. The Prediction: What Will They Find?

The authors ran simulations (computer forecasts) to see what these telescopes could achieve in the next few years.

• The Goal: They want to see if these telescopes can spot the "echoes" caused by Primordial Black Holes.
• The Result:
  • If they do find echoes, they can measure exactly how many of these black holes exist.
  • If they don't find echoes (which is what they are betting on), they can set a strict limit. They can say, "Okay, if there were this many black holes, we would have seen them. Since we didn't, there must be fewer than X amount."

The Specific Numbers:

• LOFAR2.0 might prove that Primordial Black Holes make up less than 16% of all dark matter for black holes the size of our Sun.
• FAST and BINGO could prove they make up less than 39% for heavier or lighter black holes.

5. Why Does This Matter?

Currently, we have other ways to hunt for dark matter (like looking at stars or the Cosmic Microwave Background), but those methods have blind spots.

• The "New Angle": This paper argues that using radio bursts is a completely independent way to check. It's like checking your bank account balance by looking at your credit card statement and your cash drawer. If both methods agree, you are sure of the number.
• The Future: Even if these telescopes don't find the black holes immediately, the fact that they can rule out certain possibilities helps scientists narrow down the search. As the telescopes get better and we find more FRBs (the "flashes"), our ability to solve the dark matter mystery will get sharper.

Summary

Think of the universe as a dark room. We suspect there are invisible ghosts (Primordial Black Holes) floating around. We can't see them, but we have a new, super-sensitive camera (the radio telescopes) that takes pictures of lightning flashes (FRBs) coming from outside.

If a ghost stands in front of the lightning, the flash will look weird (split or delayed). This paper calculates exactly how good our new cameras need to be to spot those ghosts. The conclusion? We are getting very close to being able to see the invisible.

Technical Summary

1. Problem Statement

The nature of Dark Matter (DM) remains one of the most significant unsolved problems in cosmology. Primordial Black Holes (PBHs), formed from the collapse of large density fluctuations in the early universe, are a viable candidate for DM. While various observational methods (microlensing of stars, gravitational wave mergers, CMB distortions) have placed constraints on the fraction of DM composed of PBHs ($f_{PBH}$), gaps remain, particularly in specific mass ranges.

Fast Radio Bursts (FRBs) offer a unique, independent probe. If PBHs constitute a significant fraction of DM, they can act as gravitational lenses for FRBs, creating time delays and magnification between multiple images of the same burst. The paper addresses the question: Can the upcoming generation of radio telescopes (LOFAR2.0, FAST Core Array, and BINGO) detect or constrain PBHs via FRB lensing, and how do their specific instrumental capabilities (time resolution, sensitivity, survey volume) impact these constraints?

2. Methodology

The authors employ a forecasting framework based on the work of Muñoz et al. [20], adapted to the specific design parameters of three upcoming radio telescopes.

• Data Foundation: The analysis utilizes a catalog of 131 confirmed FRBs (from Jia et al. [2] and other sources) to model the redshift distribution of FRB sources. The authors fitted this distribution using a Gamma function ($N(z) = N_0 z^{a_1} e^{-a_2 z}$) to estimate the expected number of lensing events.
• Gravitational Lensing Formalism:
  • PBHs are treated as point-mass lenses.
  • The optical depth ($\tau$) is calculated, representing the probability of an FRB being lensed. This depends on the comoving number density of lenses ($n_L$), the lensing cross-section ($\sigma$), and the cosmological parameters (using Planck 2018 best-fit values).
  • The cross-section is determined by the maximum magnification ratio ($\mu_{max}$) detectable, which is linked to the telescope's Signal-to-Noise Ratio (SNR) via $\mu_{max} = 1/3 \text{SNR}$.
  • The time delay ($\Delta t$) between lensed images is calculated. Crucially, the minimum detectable time delay is constrained by the time resolution of each telescope.
• Forecasting Constraints:
  • The study assumes a monochromatic mass function for PBHs (all PBHs have the same mass $M_{PBH}$).
  • Constraints are derived under the assumption of a null-detection (no lensed events found). In the optically thin regime, the maximum allowed fraction is $f_{PBH}^{max} \approx (N_{FRB} \cdot \bar{\tau})^{-1}$.
  • The analysis varies the PBH mass ($M_{PBH}$) from $10^{-2} M_\odot$ to $3 \times 10^4 M_\odot$ and calculates the resulting upper limits on $f_{PBH}$.

3. Key Contributions

• Instrument-Specific Forecasts: Unlike previous generic studies, this paper provides concrete forecasts based on the specific design upgrades of LOFAR2.0, the FAST Core Array, and BINGO (including the BINGO/ABDUS joint operation).
• Time Resolution Analysis: The paper explicitly quantifies how the time resolution of a telescope dictates the lower mass limit of PBHs it can probe. Higher time resolution allows the detection of smaller time delays, thereby constraining lower-mass PBHs.
• Redshift Distribution Modeling: The authors provide a rigorous Gamma distribution fit to the current 131 FRB dataset to serve as the baseline for predicting future event rates.
• Comparative Sensitivity: The study compares the projected sensitivity of these three distinct facilities, highlighting their complementary roles in covering different mass ranges of the PBH spectrum.

4. Key Results

The authors forecast the upper limits on the PBH fraction ($f_{PBH}$) for different mass ranges based on the expected number of FRB detections ($N_{FRB}$) and instrumental capabilities:

• LOFAR2.0:

  • Capabilities: High time resolution (down to $\sim 5.12 \mu s$), SNR = 7, expected $N_{FRB} \approx 4500$.
  • Constraint: Can constrain $f_{PBH} < 0.16$ for PBH masses $M_{PBH} > 1 M_\odot$.
  • Significance: Its superior time resolution makes it sensitive to lower-mass PBHs compared to the other telescopes in this study.

• FAST Core Array:

  • Capabilities: High sensitivity, SNR = 10, time resolution range $270 \mu s - 128 ms$, expected $N_{FRB} \approx 900$.
  • Constraint: Can constrain $f_{PBH} < 0.39$ for $M_{PBH} > 10 M_\odot$.
  • Limitation: The coarser time resolution (minimum $\sim 270 \mu s$) limits its ability to detect lensing by lower-mass PBHs.

• BINGO (and BINGO/ABDUS):

  • Capabilities: SNR = 10, time resolution $1 \mu s - 1 ms$, expected $N_{FRB} \approx 900$ (in joint operation).
  • Constraint: Can constrain $f_{PBH} < 0.39$ for $M_{PBH} > 10^{-2} M_\odot$.
  • Significance: BINGO offers a unique combination of wide sky coverage and fine time resolution, allowing it to probe the sub-solar mass range ($10^{-2} M_\odot$) effectively.

• Event Rate Projections:

  • For $N_{FRB} = 4500$ (LOFAR), the study predicts $\sim 6$ lensing events for $M_{PBH} \sim 1 M_\odot$ if $f_{PBH}=1$.
  • For $N_{FRB} = 900$ (FAST/BINGO), $\sim 3$ events are expected for higher masses.
  • The study notes that to reach competitive constraints comparable to microlensing ($f_{PBH} < 10^{-2}$), the number of detected FRBs would need to increase to $\sim 2 \times 10^4$ to $2 \times 10^5$.

5. Significance and Conclusion

• Independent Probe: While current constraints from CMB and microlensing are often stricter (e.g., $f_{PBH} < 10^{-8}$ for intermediate masses), FRB lensing provides a completely independent and complementary method. It is insensitive to the specific astrophysical assumptions required for stellar microlensing or CMB spectral distortions.
• Future Potential: The paper demonstrates that upcoming telescopes will significantly improve the landscape of PBH searches. Even if no lensed FRBs are detected, the null results will tighten the upper bounds on $f_{PBH}$ in the $0.01 - 100 M_\odot$ range.
• Methodological Robustness: The study highlights that the time resolution is the critical bottleneck for probing low-mass PBHs. As telescopes improve their backend processing to achieve microsecond resolution, their ability to constrain the PBH mass function will expand dramatically.
• Broader Impact: The methodology developed here can be applied to other transient surveys and can be extended to test alternative gravity theories or include plasma dispersion effects, making it a foundational work for the next decade of radio astronomy cosmology.

In summary, this paper establishes that while current FRB catalogs are too small to rival the tightest existing PBH constraints, the LOFAR2.0, FAST Core Array, and BINGO upgrades will transform FRB lensing into a powerful, independent tool for testing the Primordial Black Hole dark matter hypothesis, particularly in the sub-solar to stellar mass regimes.