⚛️ general relativity

Constraining spinning primordial black holes with interstellar dust heating

This paper extends constraints on the abundance of spinning primordial black holes (PBHs) in the $10^{15}$ – $10^{17}$ g mass range by modeling their Hawking radiation-induced heating of interstellar dust, revealing that higher spin parameters lead to tighter, albeit still less stringent than existing, upper limits on the PBH dark matter fraction.

Original authors: Qianyong Li, Yupeng Yang

Published 2026-09-11

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CC BY 4.0

Original authors: Qianyong Li, Yupeng Yang

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

Dark matter is the invisible scaffolding of the universe, a substance that outweighs all the stars and galaxies we can see but refuses to reveal itself through light or touch. For decades, scientists have proposed many candidates to explain what this missing mass might be, ranging from exotic subatomic particles to ancient, collapsed stars. Among these candidates are primordial black holes, objects that would have formed in the first fraction of a second after the Big Bang, long before the first stars ignited. Unlike the black holes we observe today, which are born from the death of massive stars, these primordial ones could exist in a vast range of sizes. Some would be so small that they are currently evaporating, releasing energy in a process known as Hawking radiation. This evaporation is not just a theoretical curiosity; it is a mechanism that could leave a detectable fingerprint on the cosmos, potentially allowing us to weigh the invisible dark matter that surrounds us.

A team of researchers at Qufu Normal University in China has taken a fresh look at how to detect these elusive objects by focusing on the dust that drifts between the stars. Interstellar dust, composed mostly of tiny grains of silicate and graphite, acts as a cosmic thermometer. These grains are constantly bathed in radiation from stars and other sources, which heats them up, causing them to glow in infrared light. The temperature of this dust is a delicate balance: it heats up when it absorbs energy and cools down when it radiates that energy away. If there were too many primordial black holes floating through the galaxy, their evaporation would pump extra energy into the dust, making it hotter than it actually is. By measuring how hot the dust really is, scientists can set a limit on how many of these black holes can exist without overheating the galaxy.

In their new study, the researchers refined this method by considering two factors that previous investigations had largely overlooked: the spin of the black holes and the full complexity of the particles they emit. While many earlier models assumed these black holes were stationary, the new work accounts for the possibility that they are spinning rapidly. A spinning black hole is more efficient at emitting radiation than a non-spinning one, much like a spinning top that sheds energy differently than a stationary stone. The team also updated their calculations to include a wider variety of particles produced during evaporation, specifically those that arise when the initial particles break apart into smaller fragments. By feeding these more realistic conditions into their models, they calculated exactly how much heat a population of spinning primordial black holes would add to the interstellar dust.

The results of this detailed accounting provide a new, independent way to constrain the abundance of dark matter. The researchers found that the limits depend heavily on both the mass of the black holes and how fast they are spinning. For the smallest black holes they considered, those with a mass of 10^15 grams, the constraints become significantly tighter if the black holes are spinning near their maximum speed. In the most extreme scenario they tested, where the black holes spin at nearly the fastest possible rate, the fraction of dark matter that could be made up of these objects drops to roughly 1.5 in 10,000. This means that if dark matter were composed entirely of these specific spinning black holes, the interstellar dust would be glowing far more brightly than astronomers actually observe.

While these new limits are not as strict as some other methods that use gamma-ray telescopes or cosmic microwave background data, they offer a distinct and complementary perspective. The study highlights that the spin of a black hole is a critical variable; ignoring it could lead to an underestimation of how much energy these objects inject into the universe. The researchers also noted that their calculations are conservative, meaning they likely underestimate the true constraints. If they were to include the heating from stars, which is the dominant source of warmth for the dust, the allowable number of black holes would have to be even lower to keep the dust at its observed temperature. Furthermore, the study suggests that looking at environments with less background radiation, such as the outskirts of our galaxy or distant dwarf galaxies, could yield even stronger limits in the future.

Ultimately, this work demonstrates that the quiet, cold dust of the interstellar medium serves as a sensitive detector for the most energetic processes in the universe. By carefully listening to the thermal whisper of dust grains, scientists can rule out vast populations of hypothetical black holes. The study confirms that while primordial black holes remain a viable candidate for dark matter, their properties—specifically their mass and spin—must fall within a narrow window to avoid cooking the galaxy's dust. This approach adds a valuable piece to the puzzle, proving that even the smallest, coldest specks of matter in the cosmos can help us solve the mystery of the universe's greatest invisible mass.

Technical Summary: Constraining Spinning Primordial Black Holes with Interstellar Dust Heating

Problem Statement
Primordial Black Holes (PBHs) remain a compelling dark matter candidate that does not require physics beyond the Standard Model. While PBHs in the mass range $10^{15} \text{ g} < M_{\text{PBH}} < 10^{18} \text{ g}$ are currently evaporating via Hawking radiation, their abundance is constrained by various observational probes. Recent studies have utilized the heating of interstellar dust by PBH radiation to place limits on non-spinning PBHs. However, existing constraints often neglect two critical factors: the influence of PBH spin on the Hawking radiation spectrum and the contribution of secondary photons arising from the fragmentation and decay of primary quarks and gluons. This paper addresses the gap in understanding how PBH spin and a more complete treatment of the photon spectrum affect the constraints on the fraction of dark matter composed of PBHs ( $f_{\text{PBH}}$ ).

Methodology
The authors extend the dust-heating constraint framework by incorporating the effects of PBH spin and a comprehensive photon spectrum.

PBH Radiation Modeling: The study utilizes the public code BlackHawk v2.3 to compute the Hawking radiation spectra. Unlike previous works focusing on non-spinning (Schwarzschild) black holes, this analysis considers spin parameters $a^* = 0, 0.5, 0.9,$ and $0.9999$. The total photon spectrum includes both primary photons emitted directly and secondary photons resulting from the decay of gauge bosons and the fragmentation of primary quarks and gluons (hadronization).
Interstellar Dust Physics: The authors model interstellar dust using the Mathis-Rumpel-Nordsieck (MRN) power-law size distribution ( $n(a) \propto a^{-3.5}$ ) for silicate and graphite grains with radii $0.01 \le a \le 0.25 \, \mu\text{m}$ . They focus on the smallest grains ( $a = 0.01 \, \mu\text{m}$ ) to derive conservative limits, as these possess the lowest heat capacity.
Thermal Balance Constraint: The core constraint is derived by equating the heating rate of dust grains due to isotropic PBH radiation with the maximum radiative cooling rate of the grains. The condition requires that the heating rate ( $dE/dt|_{\text{heat}}$ ) induced by PBHs must not exceed the cooling rate ( $dE/dt|_{\text{rad}}$ ) determined by the grain's absorption efficiency and temperature. The analysis assumes a monochromatic PBH mass distribution and integrates the radiation flux over the cosmological history from redshift $z \approx 1100$ to the present.

Key Contributions

Spin Dependence: The paper systematically investigates how the spin parameter $a^*$ influences the photon emission rate, demonstrating that higher spin leads to enhanced emission and consequently tighter constraints on $f_{\text{PBH}}$ .
Secondary Photon Inclusion: The authors explicitly account for secondary photons generated via hadron fragmentation, a component often omitted or simplified in earlier dust-heating analyses.
Dust Composition Comparison: The study provides comparative constraints for both silicate and graphite dust, noting that silicate grains yield stronger limits due to their lower equilibrium temperatures.
Model Robustness: The authors assess the impact of alternative dust models (e.g., those with higher abundances of very small carbonaceous grains/PAHs) and estimate that the choice of dust model introduces a systematic uncertainty of roughly a factor of 2–3 in the derived limits.

Results
The analysis yields new upper limits on the fraction of dark matter in the form of PBHs ( $f_{\text{PBH}}$ ) across the mass range $10^{15} \text{ g} \le M_{\text{PBH}} \le 10^{17} \text{ g}$ .

Strongest Constraint: The most stringent limit obtained is $f_{\text{PBH}} \sim 1.5 \times 10^{-4}$ for a PBH mass of $10^{15} \text{ g}$ and a spin parameter of $a^* = 0.9999$ (assuming silicate dust).
Spin and Mass Trends: Constraints become more stringent as the spin parameter increases and as the PBH mass decreases within the considered range.
Comparison with Existing Limits: When compared to other probes (e.g., the isotropic gamma-ray background, 21 cm differential brightness temperature, and Galactic center 511 keV lines), the dust-heating constraints derived here are generally weaker than the tightest existing limits for the same mass and spin range. For instance, limits from the 21 cm signal and isotropic gamma-ray background are orders of magnitude tighter for high-spin PBHs.

Significance and Claims
The authors position this work as providing a "distinct and complementary approach" to constraining PBH abundance. While the derived limits are less stringent than those from other established probes, the dust-heating method offers an independent physical mechanism for testing PBH models. The paper emphasizes that its results are conservative; they assume a uniform dust distribution, neglect local halo contributions (which would strengthen limits), and consider only the cosmological background. The authors note that future work targeting environments with lower interstellar radiation fields (e.g., high-latitude diffuse clouds or dwarf galaxies) could yield even stronger constraints. Ultimately, the study demonstrates that PBH spin and secondary photon production are non-negligible factors that must be included in accurate abundance estimations, even if the current dust-heating bounds do not yet rule out PBHs as the dominant dark matter component.

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