A decade or more ago, the debate about dark matter was, is it due to WIMPs (weakly interacting massive particles) or MACHOs (massive compact halo objects)? WIMPs would be new exotic particles, while MACHOs are objects formed from ordinary matter but very hard to detect due to their limited electromagnetic radiation emission.

Schwarzenegger (MACHO), not Schwarzschild (Black Holes)

Image credit: Georges Biard, CC BY-SA 3.0

Candidates in the MACHO category such as white dwarf or brown dwarf stars have been ruled out by observational constraints. Black holes formed in the very early universe, dubbed primordial black holes, were thought by many to have been ruled out as well, at least across many mass ranges, such as between the mass of the Moon and the mass of the Sun.

The focus during recent years, and most of the experimental searches, has shifted to WIMPs or other exotic particles (axions or sterile neutrinos primarily). But the WIMPs, which were motivated by supersymmetric extensions to the Standard Model of particle physics, have remained elusive. Most experiments have only placed stricter and stricter limits on their possible abundance and interaction cross-sections. The Large Hadron Collider has not yet found any evidence for supersymmetric particles.

Have primordial black holes (PBHs) as the explanation for dark matter been given short shrift? The recent detections by the LIGO instruments of two gravitational wave events, well explained by black hole mergers, have sparked new interest. A previous blog entry addressed this possibility:

https://darkmatterdarkenergy.com/2016/06/17/primordial-black-holes-as-dark-matter/.

The black holes observed in these events have masses in a range from about 8 to about 36 solar masses, and they could well be primordial.

There are a number of mechanisms to create PBHs in the early universe, prior to the very first second and the beginning of Big Bang nucleosynthesis. At any era, if there is a total mass M confined within a radius R, such that

2*GM/R > c^2 ,

then a black hole will form. The above equation defines the Schwarzschild limit (G is the gravitational constant and c the speed of light). A PBH doesn’t even have to be formed from matter whether ordinary or exotic; if the energy and radiation density is high enough in a region, it can also result in collapse to a black hole.

Cosmic Strings

Image credit: David Daverio, Université de Genève, CSCS supercomputer simulation data

The mechanisms for PBH creation include:

1. Cosmic string loops – If string theory is correct the very early universe had very long strings and many short loops of strings. These topological defects intersect and form black holes due to the very high density at their intersection points. The black holes could have a broad range of masses.
2. Bubble collisions from symmetry breaking – As the very early universe expanded and cooled, the strong force, weak force and electromagnetic force separated out. Bubbles would nucleate at the time of symmetry breaking as the phase of the universe changed, just as bubbles form in water as it boils to the surface. Collisions of bubbles could lead to high density regions and black hole formation. Symmetry breaking at the GUT scale (for the strong force separation) would yield BHs of mass around 100 kilograms. Symmetry breaking of the weak force from the electromagnetic force would yield BHs with a mass of around our Moon’s mass ~ 10^25 kilograms.
3. Density perturbations – These would be a natural result of the mechanisms in #1 and #2, in any case. When observing the cosmic microwave background radiation, which dates from a time when the universe was only 380,000 years old, we see density perturbations at various scales, with amplitudes of only a few parts in a million. Nevertheless these serve as the seeds for the formation of the first galaxies when the universe was only a few hundred million years old. Some perturbations could be large enough on smaller distance scales to form PBHs ranging from above a solar mass to as high as 100,000 solar masses.

For a PBH to be an effective dark matter contributor, it must have a lifetime longer than the age of the universe. BHs radiate due to Hawking radiation, and thus have finite lifetimes. For stellar mass BHs, the lifetimes are incredibly long, but for smaller BHs the lifetimes are much shorter since the lifetime is proportional to the cube of the BH mass. Thus a minimum mass for PBHs surviving to the present epoch is around a trillion kilograms (a billion tons).

Carr et al. (paper referenced below) summarized the constraints on what fraction of the matter content of the universe could be in the form of black holes. Traditional black holes, of several solar masses, created by stellar collapse and detectable due to their accretion disks, do not provide enough matter density. Neither do supermassive black holes of over a million solar masses found at the centers of most galaxies. PBHs may be important in seeding the formation of the supermassive black holes, however.

Limits on the PBH abundance in our galaxy and its halo (which is primarily composed of dark matter) are obtained from:

1. Cosmic microwave background measurements
2. Microlensing measurements (gravitational lensing)
3. Gamma-ray background limits
4. Neutral hydrogen clouds in the early universe
5. Wide binaries (disruption limits)

Microlensing surveys such as MACHO and EROS have searched for objects in our galactic halo that act as gravitational lenses for light originating from background stars in the Magellanic Clouds or the Andromeda galaxy. The galactic halo is composed primarily of dark matter.

A couple of dozen of objects with less than a solar mass have been detected.  Based on these surveys the fraction of dark matter which can be PBHs with less than a solar mass is 10% at most. The constraints from 1 solar mass up to 30 solar masses are weaker, and a PBH explanation for most of the galactic halo mass remains possible.

Similar studies conducted toward distant quasars and compact radio sources address the constraint in the supermassive black hole domain, apparently ruling out an explanation due to PBHs with from 1 million to 100 million solar masses.

Lyman-alpha clouds are neutral hydrogen clouds (Lyman-alpha is an important ultraviolet absorption line for hydrogen) that are found in the early universe at redshifts above 4. Simulations of the effect of PBH number density fluctuations on the distribution of Lyman-alpha clouds appear to limit the PBH contribution to dark matter for a characteristic PBH mass above 10,000 solar masses.

Distortions in the cosmic microwave background are expected if PBHs above 10 solar masses contributed substantially to the dark matter component. However these limits assume that PBH masses do not change. Merging and accretion events after the recombination era, when the cosmic microwave background was emitted, can allow a spectrum of PBH masses that were initially less than a solar mass before recombination evolve to one dominated by PBHs of tens, hundreds and thousands of solar masses today. This could be a way around some of the limits that appear to be placed by the cosmic microwave background temperature fluctuations.

Thus it appears could be a window in the region 30 to several thousand solar masses for PBHs as an explanation of cold dark matter.

As the Advanced LIGO gravitational wave detectors come on line, we expect many more black hole merger discoveries that will help to elucidate the nature of primordial black holes and the possibility that they contribute substantially to the dark matter component of our Milky Way galaxy and the universe.

References

B. Carr, K. Kohri, Y. Sendouda, J. Yokoyama, 2010 arxiv.org/pdf/0912.5297v2 “New cosmological constraints on primordial black holes”

S. Cleese and J. Garcia-Bellido, 2015 arxiv.org/pdf/1501.07565v1.pdf “Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the Seeds of Galaxies”

P. Frampton, 2015 arxiv.org/pdf/1511.08801.pdf “The Primordial Black Hole Mass Range”

P. Frampton, 2016 arxiv.org/pdf/1510.00400v7.pdf “Searching for Dark Matter Constituents with Many Solar Masses”

Green, A., 2011 https://www.mpifr-bonn.mpg.de/1360865/3rd_WG_Green.pdf “Primordial Black Hole Formation”

P. Pani, and A. Loeb, 2014 http://xxx.lanl.gov/pdf/1401.3025v1.pdf “Exclusion of the remaining mass window for primordial black holes as the dominant constituent of dark matter”

S. Perrenod, 2016 https://darkmatterdarkenergy.com/2016/06/17/primordial-black-holes-as-dark-matter/

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