Predictions on the Abundance of Primordial Black Holes: Results from the SMILE VLBI Milli-lensing Sample

Primordial black holes (PBHs) formed in the early Universe represent a well-motivated dark matter candidate. However, their abundance in the intermediate-to-high mass range (10 6 –10 9 M ⊙ ) remains relatively less constrained. In this mass regime, the corresponding Einstein radii on the milliarcsecond scale make very long baseline interferometry (VLBI) the most direct observational probe via milli-lensing of compact radio sources. In this paper, we present predictions for the abundance of PBH dark matter ( f PBH ) using the large Search for MIlli-LEnses (SMILE) sample of ∼5000 flat-spectrum compact radio sources. Under the optimistic observational conditions (with an angular resolution of 1.5 mas, a maximum image separation of 100 mas, and a maximum detectable flux ratio of 40), assuming that no milli-lensing events are confirmed, we obtain the projected 95% upper limit of f PBH ≲ 0.12% in the intermediate-to-high mass range, which would be approximately an order of magnitude tighter than previous VLBI milli-lensing limits. Broader lognormal mass functions yield correspondingly weaker projected limits. Generalizing the optical depth to account for magnification bias and finite-core resolvability changes these projected limits by only about 5%. Moreover, we show that the predicted limits are highly sensitive to a small number of confirmed events, i.e., even one confirmed milli-lensing event would relax the projected upper limit to 0.20%, highlighting the critical importance of robust candidate confirmation in the SMILE sample. Finally, under the optimistic baryonic accretion scenario, the PBH mass growth changes the projected limits by ≲1% within the VLBI-sensitive mass range, confirming the robustness of our results.