Constraining primordial black hole abundance with Insight-HXMT

Primordial black holes (PBHs) are a major candidate for dark matter and they have been extensively constrained across most mass ranges. However, PBHs in the mass range of $10^{17}$ - $10^{21}$ g remain a viable explanation for all dark matter. In this work, we use observational data from the Hard X-ray Modulation Telescope (Insight-HXMT) to refine constraints on PBHs within the mass range of $2\times10^{16}$ - $5\times10^{17}$ g. Our analysis explores three scenarios: directly using observational data, incorporating the astrophysical background model (ABM), and employing the power-law spectrum with an exponential cutoff. Our results indicate that although Insight-HXMT does not have an advantage in the first two scenarios, when considering the power-law model, its exceptional sensitivity in the hard X-ray regime and sufficiently high upper energy limit significantly strengthen the constraints on PBHs with masses greater than $10^{17}$ g compared to previous limits. Furthermore, the exclusion limit for PBHs as dark matter has reached $4\times10^{17}$ g, which is comparable to the current threshold.

💡 Research Summary

This paper investigates the abundance of primordial black holes (PBHs) in the largely unconstrained mass window of $10^{17}$–$10^{21}$ g, focusing specifically on the narrower range $2\times10^{16}$ g to $5\times10^{17}$ g. The authors exploit diffuse X‑ray background measurements from the Chinese Hard X‑ray Modulation Telescope (Insight‑HXMT), which offers a broad energy coverage (1–250 keV), large effective area, and high sensitivity in the hard X‑ray band.

The theoretical framework starts from Hawking radiation, using the BlackHawk code to compute the spectra of primary photons, secondary photons from hadron decays, and photons arising from positron–electron annihilation (both the 511 keV line from para‑positronium and the continuum from ortho‑positronium). The total photon flux from PBHs, $\psi_{\rm PBH}(E)$, is obtained by summing contributions from Galactic PBHs (using a Navarro‑Frenk‑White dark‑matter profile and a line‑of‑sight J‑factor) and extragalactic PBHs (integrated over redshift up to $z_{\rm max}\gtrsim10$). The authors also include the positron annihilation component, which dominates the flux in the 1–250 keV band for the masses considered.

Three distinct analysis strategies are pursued:

1. Direct use of observational data – The PBH flux is required not to exceed any measured data point (including a 2σ observational uncertainty) from Insight‑HXMT’s Low‑Energy (LE) and High‑Energy (HE) instruments. This conservative approach yields limits that are weaker than previous constraints because the available high‑energy points are sparse and no background subtraction is performed.

2. Incorporation of an astrophysical background model (ABM) – Known contributors to the diffuse X‑ray background, such as star‑forming galaxies and active galactic nuclei, are modeled and subtracted. The resulting residual flux is then used to set PBH limits. The improvement over the first method is modest, reflecting the fact that the ABM does not dramatically change the residual in the limited HXMT energy window.

3. Power‑law extrapolation model – The observed spectrum is fitted with a power‑law, and the fit is extrapolated to the theoretical upper energy limit of Insight‑HXMT (≈250 keV) and beyond (up to ∼10 MeV). Because HXMT’s sensitivity is excellent in the hard X‑ray regime, the extrapolated high‑energy tail provides a stringent ceiling on any additional PBH‑induced photons. In this scenario the constraints become substantially tighter, especially for $M_{\rm PBH}\gtrsim10^{17}$ g where the positron‑annihilation component dominates. The derived upper bound on the PBH dark‑matter fraction, $f_{\rm PBH}$, reaches $f_{\rm PBH}=1$ only at $M\approx4\times10^{17}$ g, effectively closing the window for PBHs of that mass to constitute all of dark matter.

The analysis assumes a monochromatic, non‑spinning PBH mass function, which yields the most conservative limits. The authors note that broader (e.g., log‑normal) mass distributions or rotating PBHs would only strengthen the constraints, as shown in previous works.

Overall, the study demonstrates that while Insight‑HXMT does not improve PBH limits when raw data or simple background subtraction are used, its exceptional hard X‑ray sensitivity combined with a power‑law spectral model can significantly tighten constraints for PBHs heavier than $10^{17}$ g. The work highlights the importance of high‑energy coverage and accurate background modeling for future PBH searches, and suggests that forthcoming instruments with even broader energy ranges (MeV–GeV) could further probe the remaining viable mass window.