Constraints on the abundance of supermassive primordial black holes from lensing of compact radio sources

ABSTRACT The possibility that primordial black holes (PBHs) form a part of dark matter has been considered over a wide mass range from the Planck mass ($10^{-5}~\rm g$) to the level of the supermassive black hole in the center of the galaxy. Primordial origin might be one of the most important formation channel of supermassive black holes. We use the non-detection of lensing effect of very long baseline interferometer observations of compact radio sources with extremely high angular resolution as a promising probe to constrain the abundance of intergalactic PBHs in the mass range ∼104–109 M⊙. For a sample of well-measured 543 flat-spectrum compact radio sources, no milli-lensed images are found with angular separations between 1.5 and 50 milli-arcsec. From this null search result, we derive that the fraction of dark matter made up of supermassive PBHs in the mass range ∼106–108 M⊙ is $\lesssim 1.48{{\ \rm per\, cent}}$ at $95{{\ \rm per\, cent}}$ confidence level. This constraints would be significantly improved due to the rapid increase of the number of measured compact radio sources. For instance, on the basis of none confirmed milli-lensing candidate in the latest ∼14 000 sources, we derive the abundance of supermassive PBHs and obtain that it is $\lesssim 0.06{{\ \rm per\, cent}}$ at $95{{\ \rm per\, cent}}$ confidence level.