A question about primordial black holes

Primordial black holes (PBHs) are theorized to have been created in great numbers in the radiation era shortly after the Big Bang. Due to a formation process not related to stellar collapse, they could have had essentially any range of masses: from an atomic nucleus to thousands of solar masses.

If PBHs were really abundant, one must have collided with a star by now. Let’s say a wandering PBH with 1 Earth mass collides with the Sun at a relatively low velocity: it would oscillate through the Sun and eventually settle at the core. It would eat the Sun’s fusing mass at the core without contributing anything to energy production. (The pressure at the Sun’s core would essentially force-feed the PBH.)

As the PBH feeds on the superdense matter in the core, the Sun would contract and brighten in an effort to maintain hydrostatic equilibrium. A vicious cycle would follow as the PBH grows and grows; the Sun would get brighter and brighter until it… explodes as a supernova? collapses into a BH itself?

But there is no observational evidence for any star meeting this fate. No supernova has ever been observed in low-mass Sun-like stars. Nor has any Sun-like star been observed collapsing into a BH.

Not one instance in the all the galaxies surveyed so far.

Does this not essentially rule out the existence of PBHs?

It sets an upper bound on their abundance. But as space goes, a star is a very small target, and you’d need a direct hit to even have a chance of what you’re describing happening. And for us to be able to tell that it’d happened, we’d have to not only observe the supernova, but to know what sort of star it was before the supernova, which means that first, it’d have to have been in our Galaxy or one of its satellites, and second, we’d have to have lucked out to have observations of that star before it blew.

Put it all together, and while it is an upper bound, it’s probably not a very strong one. I haven’t run the numbers, but probably, the bounds from microlensing surveys are stronger.