A new study, that doesn't rely on the micro-lensing and Hawking radiation exclusions which are the primary methods for constraining primordial black hole frequency, places very strict limitations on the maximum potential abundance of "supermassive" primordial black holes.
It limits them to less than 0.1% of dark matter in a dark matter particle hypothesis for "supermassive" primordial black holes (i.e. primordial black holes that are 10,000 times more massive than the Sun or more). This had already been ruled out long ago, albeit not quite so strictly.
The main focus on primordial black holes as a dark matter candidate has been on asteroid sized primordial black holes in the range of 3.5 × 10^−17 to 4 × 10^−12 solar masses (i.e. twelve to seventeen orders of magnitude smaller in mass than the Sun), which by definition cannot arise from stellar collapse. Non-detection of Hawking radiation (which is a net emission for primordial black holes up to about 10^-8 solar masses), and micro-lensing, has largely ruled out larger primordial black holes as a significant component of dark matter (if it exists).
Also, while the paper frames its constraints in terms of primordial black holes, it would seem to apply to any dark matter candidate in that mass range, such as ordinary black holes and MACHOs (massive compact halo objects).
We present updated constraints on the abundance of primordial black holes (PBHs) dark matter from the high-redshift Lyman-α forest data from MIKE/HIRES experiments. Our analysis leverages an effective field theory (EFT) description of the 1D flux power spectrum, allowing us to analytically predict the Lyman-α fluctuations on quasi-linear scales from first principles. Our EFT-based likelihood enables robust inference across redshifts z = 4.2−5.4 and down to scales of 100 kpc, within previously unexplored regions of parameter space for this dataset.
We derive new bounds on the PBH fraction with respect to the total dark matter fPBH, excluding populations with fPBH≳10^−3 for masses MPBH ∼ 10^4−10^16 M⊙. This offers the leading constraint for PBHs heavier than 10^9 M⊙ and highlights the Lyman-α forest as a uniquely sensitive probe of new physics models that modify the structure formation history of our universe.
Mikhail M. Ivanov, Sokratis Trifinopoulos, "Effective Field Theory Constraints on Primordial Black Holes from the High-Redshift Lyman-α Forest" arXiv:2508.04767 (August 6, 2025).
Additional Context
The Ordinary Matter Budget Of The Universe
Most of the ordinary matter in the universe is found in stars (about half) and the intergalactic/interstellar medium (mostly interstellar gas and dust) which is also about half, with planets and asteroids accounting for less than 1% of the total amount of ordinary mass in the universe.
Stellar-mass black holes (formed from dying stars) account for not more than about 0.1% of the universe's ordinary matter, and supermassive black holes, found at the centers of galaxies, account for not more than about 0.01% of the universe's ordinary matter.
Contributions to the mass-energy of the universe from photons and neutrinos are also very small (even though both kinds of particles are extremely numerous).
Planets, Asteroids, and Comets
Self-gravity forces planet-like objects of more than 0.5 x 10^21 kg (about one four billionth of the mass of the Sun) and more than 400 km in radius, to become approximately spherical, and this is the lower floor for dwarf planets, regular planets, and planet-sized moons. The mass of the Earth is about 3 x 10^-6 solar masses.
Objects smaller than this (but larger than dust or interstellar gas) tend to form non-spherical asteroids and comets, although some are approximately spherical due to random chance.
Star and Brown Dwarves
As an aside, anything other than a star or a black hole, can't have more than about 1.24% of the mass of the Sun (i.e. 13 Jupiter masses), because then gravity causes unstable nuclear fusion to commence in its core, turning it into a "sub-brown dwarf" although NASA conservatively assumes that planets could be as large as 30 Jupiter masses (about 2.86% of the mass of the Sun). In ideal conditions, a sub-brown dwarf can form at masses as low as one Jupiter mass (about 1/1024th of the mass of the Sun). Sub-brown dwarves and true brown dwarves, which range from 13 to 80 Jupiter masses (i.e. up to about 7.8% of the mass of the Sun) fill a liminal space between true planets with no gravity induced nuclear fusion and the smallest "main-sequence" stars.
While brown dwarves are an order of magnitude or two heavier than large gas giant planets, like Jupiter and Saturn, they aren't much larger: "most brown dwarfs are slightly larger in volume than Jupiter (15–20%), but are still up to 80 times more massive due to greater density." Jupiter's radius is 11 times that of Earth, and the Sun's radius is 10 times that of Jupiter.
The theoretical maximum mass of a star is on the order of 200 solar masses. Of the billions and billions of stars that astronomers have observed, only 11 of them are potentially more than 150 solar masses, and only 5 of them have an upper end of their two sigma mass range (given the uncertainty of the mass measurement) above 200 solar masses. Only 2 stars have a best fit mass estimate above 200 solar masses, and realistically, given the uncertainty in these mass measurements (which is stated for one of the two and is not stated for the other), a mass of 200 solar masses of less is probably within the two sigma uncertainty range of the observation for both cases (particularly if one considers look elsewhere effects which are significant given the very large number of star masses measured).
The theoretically largest radius star is about 1700 times the radius of the Sun (by comparison, the orbit of Saturn is about 2,048 times the radius of the Sun). The largest radius star ever observed has a radius of 1530 ± 370 times the radius of the Sun.
Thus, any compact object with a mass of more than about 2 * 10^2 solar masses, or a radius more than about 1700 times the radius of the Sun (the Sun has a radius of about 700,000 km) is a supermassive black hole.
Black Holes
An ordinary stellar collapse black hole has a minimum mass which is more than two times the mass of the Sun, but this minimum mass is a bit under three times the mass of the Sun. This mass, in the non-spinning case is called the Tolman-Oppenheimer-Volkoff limit. In theory, this threshold mass may vary modestly based upon the spin of the neutron star. The mass limit is 18%-20% higher for a very rapidly spinning neutron star that is on the brink of becoming a black hole. A stellar mass black hole has an event horizon radius (i.e. Schwarzschild radius radius) of about 6-9 km to 300 km.
The maximum density of anything ever observed in astronomy or high energy physics or nuclear physics is a neutron star/black hole right at the high end of the Tolman-Oppenheimer-Volkoff limit.
Pinning down the exact threshold more precisely is a matter of ongoing astronomy research. The least massive object definitively classified as a black hole has a mass of 3.04 ± 0.06 solar masses. A handful of observations of objects close to the limit have suggested a limit somewhere on the order of 2.01 to 2.9 solar masses.
Between stellar mass black holes (many of which have been indirectly observed) and supermassive black holes at the core of galaxies (many of which have been indirectly observed) are intermediate-mass black holes, which were first observed with gravitational wave telescopes:
An intermediate-mass black hole (IMBH) is a class of black hole with mass in the range of one hundred to one hundred thousand (10^2–10^5) solar masses: significantly higher than stellar black holes but lower than the hundred thousand to more than one billion (10^5–10^9) solar mass supermassive black holes.
An intermediate-mass black hole has an event horizon radius of 300 km to 300,000 km (which is smaller than the radius of the Sun).
In theory, it would have been possible shortly after the Big Bang and predominantly in the first second after the Big Bang, for matter to be dense enough to form a black hole with less mass than necessary to form an ordinary stellar collapse black hole (even though the density needed to form a black hole increases as the mass which collapses into a black hole gets smaller). These hypothetical black holes are called primordial black holes.
But no primordial black holes have ever been observed, despite the fact that they are predicted to emit intense Hawking radiation (a.k.a. Bekenstein-Hawking radiation after Jacob Bekenstein, who died at age 68 in 2015, and Stephen Hawking, who died at age 76 in 2018, who both proposed it) which has never been detected:
Depending on the model, primordial black holes could have initial masses ranging from 10^−8 kg (the so-called Planck relics) to more than thousands of solar masses. However, primordial black holes originally having masses lower than 10^12 kg would not have survived to the present due to Hawking radiation, which causes complete evaporation in a time much shorter than the age of the Universe. . . . Primordial black holes are also good candidates for being the seeds of the supermassive black holes at the center of massive galaxies, as well as of intermediate-mass black holes.
The smaller the black hole, the more rapidly it evaporates due to Hawking radiation. A primordial black hole which initially had the mass of the Sun (2 * 10^30 kg) would now have a mass of something on the order of 10^23 kg (about one 10,000,000th the mass of the Sun) due to Hawking radiation (although accretion of new matter could counteract Hawking radiation and slow down the rate at which a primordial black hole's mass declines).
A hypothetical stable mass primordial black hole has an event horizon radius of at least 24 meters. Evaporating primordial black holes would have a smaller event horizon radius. An asteroid sized black hole would have an event horizon radius of about 0.03 millimeters to 3 meters and would emit significant Hawking radiation.
For black holes formed by stellar mass collapse (about 3 solar masses) or more, the mass loss due to Hawking radiation would be almost completely offset by accretion of mass-energy from its absorption of cosmic background radiation alone, setting aside interstellar dust and other objects that could fall into the black hole. Specifically:
Since the universe contains the cosmic microwave background radiation, in order for the black hole to dissipate, the black hole must have a temperature greater than that of the present-day blackbody radiation of the universe of 2.7 K. The relationship between mass and temperature for Hawking radiation then implies the mass must be less than 0.8% of the mass of the Earth [i.e. about 2.4 * 10^-8 solar masses]. This in turn means any black hole that could dissipate cannot be one created by stellar collapse. Only primordial black holes might be created with this little mass.
The theoretical maximum size of a black hole (with maximal spin) is 2.7 x 10^11 solar masses, and the most massive black hole ever observed has an estimated mass of up to 1 x 10^11 solar masses. The largest theoretically possible black hole has an event horizon radius of about 800 billion (i.e. 800,000,000,000) km.
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