Observational Strategies

It is fifty years since Stephen Hawking laid out the physics of primordial black holes (PBHs) and fifty years since the cold dark matter paradigm became the standard model for the formation of structure in the universe. It is time to see if they can be linked. There is one overwhelming obstacle: no PBH has yet been detected and confirmed. Theoretically, PBHs have a mass range from the Planck mass at 21 $\mathsf{\mu }$g to supermassive black holes at 10⁷ M_⊙. Their gravitational radiation would arise from a density in some cases far into the quantum gravity regime. It is time to systematically review their detectability across the electromagnetic and gravitational wave spectra.

1. Introduction

It is interesting to compare the mass–radius relation of PBHs to the observed density sequences of stars and planets in the cosmos. All resemble power laws not very different from constant density. The region −9 < log M/M_⊙ < 3; 4 < log R [km] < 7 is occupied by main sequence stars, rocky planets, electron-degenerate white dwarfs and neutron stars at nuclear density. Each is supported hydrostatically by different physics. The event horizon of 1 M_⊙ PBHs is actually somewhat less than an order of magnitude below neutron stars in radius. PBHs of 1 M_♁ would be two orders of magnitude lower than that. We shall not know how Nature accomplishes the density change from nuclear to black hole until the next Galactic supernova, if our laser interferometers are turned on.

The very small radius of these putative objects and their correspondingly low luminosity suggests detection of their mass rather than their radiation. The search for the 80% of the Universe’s matter that is dark was the motivation for beginning this quest [1].

This paper is written in three parts. In Section 2, the discoveries of high-density objects in the previous century are reviewed for clues as to how to proceed. Section 3 lists some of the unknowns about PBHs. We need to know what we are looking for. Section 4 summarizes the evidence for and against the roles PBHs may have played in the evolution of the Universe.

2. 20th Century Discoveries of Objects of Unfamiliar Densities

Discovery of new entities in the cosmos during the twentieth century did not all fit the same pattern. According to Wikipedia1, in 1910, Russell, Pickering and Fleming noted that, despite its low luminosity, 40 Eridani B was of spectral type A, or white2. This would become known as the first white dwarf [2,3], the name white dwarf being coined by Luyten [4]. In 1931, Chandrasekhar [5] developed a physical model of white dwarfs and won the 1983 Nobel Prize in Physics for his work in stellar evolution.

The discovery of quasars followed the development of useful sensitivity [6] of a new technology, radio astronomy, two of whose sources, 3C273 and 3C48 were found to have luminosities far in excess of that generated by stars [7,8], heralded by Sandage [9] as a major new constituent of the Universe. Again, the physics followed later, with the identification of the source of their energy as, not stars, but a supermassive black hole [10].

The discovery of the neutron star occurred in a rather different way. The neutron was discovered in the laboratory [11]. Zwicky’s inspiration [12] seems to have been that Nature finds a way to form all things that are not physically impossible. Baade and Zwicky [13] proposed a theory that supernovae represent the dramatic end of a massive star’s life [14], culminating in an explosive event that leads to the formation of neutron stars or black holes. Their theory suggests that during the supernova explosion, the unopposed gravitational force fuses protons and electrons into neutrons, resulting in the formation of a neutron star.

The subsequent discovery of pulsars in 1967 by Bell and Hewish [15], again through radio astronomy, provided the first observational support for Zwicky and Baade’s ideas. Pulsars, rapidly spinning neutron stars emitting radio waves from their magneto spheres, initially sparked speculation about extraterrestrial intelligence before their true nature was understood. These results were not only a boon to the understanding of the lifecycle of stars, but also pointed to the important role of supernovae in enriching the cosmos with elements necessary for planet formation.

Hawking [16] proposed that black holes were not necessarily all formed by the gravitational collapse of stars. Arbitrarily small ones might have been formed when the density and overdensities in the cosmos were at the critical level. These ideas developed [17], and MacGibbon [18] speculated about the cosmological significance of small primordial black holes, as they evaporated into Planck mass relics. Extrapolation of the densities of white dwarfs and neutron stars in Zwicky’s sense makes a case for their existence, and microlensing observations have resulted in claims of their discovery (e.g., [19,20,21]), but the jury is still out on the uniqueness of a primordial black hole assignment.

The technique of microlensing is now sufficiently mature that the Rubin and $Roman$ telescopes will be able to distinguish PBHs from interstellar planets with the aid of optical depth predictions [22]. The 21st century technology of gravitational wave mass measurement needs more than the present sensitivity to reach interesting subsolar masses [23] with the Einstein telescope.

3. Uncertain Properties of PBHs

The more we know about PBHs, the more chance there is of recognizing them. These are some of the questions that, if answered, would focus the search.

• Do PBHs form during inflation?
• Do they form during a radiation-dominated era?
• What is their initial mass function?
• How is it related to the primordial spectrum of fluctuations?
• Do PBHs always emit Hawking radiation?
• Do the small ones evaporate completely or leave a relic?
• Do the large ones accrete mass?
• What accreted fraction is turned into radiation?
• SMBHs have magnetospheres; do PBHs have them too?
• Do they cluster significantly?
• Is there a large or small dispersion in the PBH-to-baryon ratio?
• Are there processes by which they gain or lose angular momentum?

Some of these properties are discussed in this Special Issue of $Universe$.

4. Evidence For and Against Detection

There are many ways in which PBHs may play a part in the ionization history of the Universe, galaxy formation and life. None of these is uncontested, as

Table 1. Evidence for PBHs and alternative theories.

Reference	Possible Role	Alternative	Ref.
[24]	PBHs as dark matter	WIMPs *	[25]
[19]	Microlensing	Interstellar planets	[26]
[27]	Triggering SNeIa	No trigger required	[28]
[29]	Binary inspiral	Low S/N detections	-
[30]	Hubble tension	Early dark energy	[31]
[32]	Bulk flow tension	Rare event	[33]
[34]	Early galaxy formation	Population III	[35]
[36,37]	JWST Little Red Dots	Direct collapse black holes	[38]
[39]	Pre-galactic globular clusters	Blue colour metallicity, not age-related	-
[40]	Initiating comets	Tidal disruption	[41]

* Weakly Interacting Massive Particles. SNeIa = type Ia supernovae.

shows.

5. Conclusions

It is to be hoped that this Special Issue will help focus efforts to obtain unequivocal results on PBH existence.