The central finding is a possibility, not an identification: an analytic calculation finds that Punctum’s reported millimeter properties can be compatible with a primordial black hole surrounded by a concentrated dark-matter spike. The authors present the scenario as a way to explain the source and estimate dark-matter annihilation parameters, not as a detection of a black hole, dark matter or annihilation products.
Punctum is a millimeter continuum source in the central region of NGC 4945. Reported observations place it at about 100 GHz, with roughly 50% polarization, millimeter luminosity near 2 × 10^35 erg/s and a size below 2 parsecs. No counterpart is listed in other radio, infrared, optical or X-ray bands.
How the proposal is tested
The preprint, posted on arXiv on 26 Aug 2026, builds an analytic model around that single source. It links hypothetical annihilation-produced electrons and positrons to synchrotron radio emission and tests whether the resulting radiation can reproduce the millimeter signal. The calculation also includes synchrotron self-absorption at low frequencies, meaning the model allows some of the source’s own radiation to be absorbed within the emitting region.
To keep the calculation concrete, it adopts a dark-matter density spike whose density scales with radius as r to the power of minus nine-fourths. For illustration, it assumes annihilation mainly into electrons and positrons, with a yield factor of about 2. The paper notes that changing the annihilation channel would require changing that yield, so the numerical results are tied to this choice.
The observational input was limited but specific. Two reported measurements taken 14 days apart gave fluxes of 0.104 ± 0.018 mJy and 0.125 ± 0.016 mJy, in the 90.5 to 104.5 GHz range. The model uses those measurements alongside the reported polarization, luminosity and compactness.
What the numbers show
One illustrative solution sets the primordial black hole mass at 10 solar masses and the dark-matter particle mass at 25 MeV, with a velocity-weighted annihilation cross section of about 10^-33 cubic centimetres per second. Under those assumptions, the calculated core radius is about 0.00001 parsec, consistent with Punctum’s upper size limit of 2 parsecs. Those values are an example from the model, not a measured mass or cross section.
Across the benchmark magnetic-field range of about 1 to 1,000 gauss, the model estimates a velocity-weighted annihilation cross section of roughly 10^-33 cubic centimetres per second. In the 1-gauss case, it reports lower bounds of at least 146 MeV for the dark-matter mass and 16 solar masses for the primordial black hole. For black hole masses of about 10 to 100 solar masses, the constrained dark-matter mass range is roughly 10 to 1,000 MeV.
A separate check focuses on self-absorption. Matching the self-absorption radius to the model’s core radius at about 100 GHz gives a reported constraint of 0.0016 when the magnetic field is below the paper’s equipartition benchmark, and 0.0090 when it equals that benchmark. These are outputs of the matching calculation, not independent measurements of the source.
A fit that still needs testing
The analysis remains a one-object exercise. It uses reported observations of one unresolved astronomical source, has no empirical comparison group, and reports analytic equations, illustrative spectra and parameter-relation plots rather than formal hypothesis tests, regression or interval estimates. That design can show that a set of assumptions is compatible with the observations, but it cannot establish that Punctum is a primordial black hole.
The inferred values are therefore sensitive to the choices built into the model, including the magnetic-field strength, primordial black hole mass, density-spike profile and treatment of self-absorption. The polarization part of the explanation also relies on the possibility of an ordered magnetic field, and the analysis does not report a quantitative polarization fit. Other annihilation channels could change the assumed particle yield.
The authors say future millimeter observations could provide a way to look for more objects with similar properties and constrain dark-matter properties. Independent observations would need to check the predicted self-absorbed spectrum and polarization, while separate estimates of Punctum’s mass, magnetic field and density-spike structure would help distinguish this proposal from alternatives. Until then, the paper offers parameter scales for a speculative interpretation rather than a confirmed astrophysical identity.
The document is an arXiv preprint, version 1, dated 26 Aug 2026. The authors say the underlying data will be shared on reasonable request. The work was partially supported by the Research Grants Council of the Hong Kong Special Administrative Region, China, under Project No. EdUHK 18300324.
Paper data and sources
Original title: Is the mysterious {\it Punctum} a primordial black hole?
Authors: Man Ho Chan
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text