# Category Archives: primordial black holes

## Mini Black Holes as Dark Matter?

Ancient Voyager Satellite Says No for the Smallest Possible

Black holes can come in all sizes from about a billion tons up to billions of solar masses.

Because isolated black holes are difficult to detect, especially smaller mass ones, they have long been considered as candidates for dark matter, invoked to explain the extra gravitational accelerations measured at the outskirts of galaxies.

Stephen Hawking showed that black holes radiate low energy particles very slowly due to quantum thermodynamic effects. So the very lowest mass black holes evaporate away due to Hawking radiation during the life of the universe.

Voyager Satellites

The Voyager satellites were launched in 1977 and NASA has determined that Voyager 1 crossed the heliopause in 2012. This is the boundary for the solar wind, which holds back a large portion of galactic cosmic rays. Voyager 2 crossed the heliopause last year.

Forty-two years after launch, and having toured Jupiter, Saturn, Uranus, and Neptune, these remarkable satellites are still returning valuable data about the outer reaches of the Solar System.

What is the connection between black holes, dark matter, and Voyager 1?

In the early universe, large numbers of so-called primordial black holes (PBHs) of various sizes may have formed. The question arises, could these be the primary component of dark matter?

Primordial Black Holes as Dark Matter Candidates

The detection of gravitational waves from half a dozen mergers of black holes of intermediate mass has given new energy to this idea. Also, there is the continued failure to detect exotic particle candidates for dark matter in Earth-bound laboratory experiments.

A team of Japanese astronomers, searching for microlensing effects with stars in the Andromeda galaxy, have ruled out small black holes in the range of $10^{20}$ grams up to about 3 times the Earth’s mass. https://darkmatterdarkenergy.com/2017/12/07/primordial-black-holes-and-dark-matter has more detail.

Constraints from other lensing experiments (MACHO, EROS) and the cosmic microwave background appear to rule out more massive primordial black holes as the explanation for most dark matter.

What about the tiniest allowable black holes, from about $4 \cdot 10^{14}$ gm (smaller ones have evaporated already) up to $10^{20}$ gm?

Voyager 1 Constraints

With a recent analysis researchers at the Laboratoire de Physique Theorique et Hautes Energies (LPTHE) show that the Voyager 1 satellite now rules out primordial black holes with masses below $10^{17}$ gm as well, as the source of most dark matter. And it is because of the Hawking radiation that we do not detect.

Although Hawking radiation has never been detected, it is on very firm theoretical grounds that it should exist. Everything, including strange objects like black holes, has a quantum nature.

$T = 1.1 GeV / (m/10^{13} gm)$

Thus for an $m = 10^{16}$ gm black hole the Hawking temperature is about 1 MeV. (GeV or giga electron-Volt is a billion eV and around the rest mass energy of a proton, and an MeV or mega electron-Volt is a million eV and about twice the rest mass energy of an electron.)

Since these temperatures are in the MeV range, only very light particles such as neutrinos, electrons, and positrons would be emitted by the PBHs.

Figure 1 from the Boudaud and Cirelli paper shows the observed combined electron and positron cosmic ray flux from Voyager 1 in the energy range from 3 MeV to 50 MeV. It also shows results in the 1 to 10 GeV range from the Alpha Magnetic Spectrometer 2 experiment on the International Space Station (located well inside the heliopause). Two different models of how the energetic particles propagate through the galaxy are used.

Smallest possible Black Holes ruled out

PBHs with $10^{15}$ or $10^{16}$ grams are clearly ruled out; they would inject far too many energetic electron and positron cosmic rays into the interstellar medium that Voyager 1 has entered.

The authors state that no more than 0.1% of dark matter can be due to PBHs of mass less than $10^{16}$ grams (10 billion tons).

In Figure 1, a monotonic mass distribution was assumed (PBHs all have the same mass). They also consider various log-normal mass distributions and similar constraints on the allowable PBH mass were found.

What about at $10^{17}$ grams and above? Most mass regions are ruled out.

The mass region above $5 \cdot 10^{17}$ grams and up to about $10^{20}$ grams has been excluded as a primary source of dark matter from PBHs by a 2012* result from Barnacka, Glicenstein, and Moderski. They searched for gravitational lensing effects upon gamma ray burst sources due to intervening black holes.

So vast ranges of possible PBH masses are ruled out. However the mass region from $3 \cdot 10^{16}$ up to $5 \cdot 10^{17}$ grams remains a possibility as a dark matter hideout for PBHs.

*The same year that Voyager 1 crossed the heliopause, coincidentally

References

Boudaud, M. And Cirelli, M. 2019 “Voyager 1 electrons and positrons further constrain primordial black holes as dark matter” https://arxiv.org/abs/1807.03075

https://darkmatterdarkenergy.com/2017/12/07/primordial-black-holes-and-dark-matter/

Barnacka, A., Glicenstein, J.-F., Moderski, R. 2012 “New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts” http://arxiv.org/abs/1204.2056

## Primordial Black Holes and Dark Matter

Based on observed gravitational interactions in galactic halos (galaxy rotation curves) and in group and clusters, there appears to be 5 times as much dark matter as ordinary matter in the universe. The alternative is no dark matter, but more gravity than expected at low accelerations, as discussed in this post on emergent gravity.

The main candidates for dark matter are exotic, undiscovered particles such as WIMPs (weakly interacting massive particles) and axions. Experiments attempting direct detection for these have repeatedly come up short.

The non-particle alternative category is MACHOs (massive compact halo objects) composed of ordinary matter.  Planets, dwarf stars and neutron stars have been ruled out by various observational signatures. The one ordinary matter possibility that has remained viable is that of black holes, and in particular black holes with much less than the mass of the Sun.

The only known possibility for such low mass black holes is that of primordial black holes (PBHs) formed in the earliest moments of the Big Bang.

Gravitational microlensing, or microlensing for short, seeks to detect PBHs by their general relativistic gravitational effect on starlight. MACHO and EROS were experiments to monitor stars in the Large Magellanic Cloud. These were able to place limits on the abundance of PBHs with masses from about one hundred millionth of a the Sun’s mass up to 10 solar masses. PBHs from that mass range are not able to explain the total amount of dark matter determined from gravitational interactions.

LIGO has recently detected several merging black holes in the tens of solar mass range. However the frequency of LIGO detections appears too low by two orders of magnitude to explain the amount of gravitationally detected dark matter. PBHs in this mass range are also constrained by cosmic microwave background observations.

Extremely low mass PBHs, below 10 billion tons, cannot survive until the present epoch of the universe. This is due to Hawking radiation. Black holes evaporate due to their quantum nature. Solar mass black holes have an extremely long lifetime against evaporation. But very low mass black holes will evaporate in billions of years or much sooner, depending on mass.

The remaining mass window for possible PBH, in sufficient amount to explain dark matter, is from about 10 trillion ton objects up to those with ten millionths of the Sun’s mass.

Figure 5 from H. Niikura et al. “Microlensing constraints on primordial black holes with the Subaru/HSC Andromeda observation”, https://arxiv.org/abs/1701.02151

Here f is the fraction of dark matter which can be explained by PBHs. The red shaded area is excluded by the authors observations and analysis of Andromeda Galaxy data. This rules out masses above 100 trillion tons and below a hundred thousandth of the Sun’s mass. (Solar mass units used above and grams are used below).

Now, a team of Japanese astronomers have used the Subaru telescope on the Big Island of Hawaii (operated by Japan’s national observatory) to determine constraints on PBHs by observing millions of stars in the Andromeda Galaxy.

The idea is that a candidate PBH would pass in front of the line of sight to the star, acting as a lens, and magnifying the light from the star in question for a relatively brief period of time. The astronomers looked for stars exhibiting variability in their light intensity.

With only a single nights’ data they made repeated short exposures and were able to pick out over 15,000 stars in Andromeda exhibiting such variable light intensity. However, among these possible candidates, only a single one turned out to fit the characteristics expected for a PBH detection.

If PBHs in this mass range were sufficiently abundant to explain dark matter, then one would have expected of order one thousand events, and they saw nothing like this number. In summary, with 95% confidence, they are able to rule out PBHs as the main source of dark matter for the mass range from 100 trillion tons up to one hundred thousandth of the Sun’s mass.

The window for primordial black holes as the explanation for dark matter appears to be closing.

## Yet Another Intermediate Black Hole Merger

Another merger of two intermediate mass black holes has been observed by the LIGO gravitational wave observatories.

There are now three confirmed black hole pair mergers, along with a previously known fourth possible, that lacks sufficient statistical confidence.

These three mergers have all been detected in the past two years and are the only observations ever made of gravitational waves.

They are extremely powerful events. The lastest event is known as GW170104 (gravitational wave discovery of January 4, 2017).

It all happened in the wink of an eye. In a fifth of a second, a black hole of 30 solar masses approximately merged with a black hole of about 20 solar masses. It is estimated that the two orbited around one another six times (!) during that 0.2 seconds of their final existence as independent objects.

The gravitational wave generation was so great that an entire solar mass of gravitational energy was liberated in the form of gravitational waves.

This works out to something like $2 \cdot 10^{47}$ Joules of energy, released in 0.2 seconds, or an average of $10^{48} Watts$ during that interval. You know, a Tera Tera Tera Terawatt.

Researchers have now discovered a whole new class of black holes with masses ranging from about 10 solar masses (unmerged) to 60 solar masses (merged). If they keep finding these we might have to give serious consideration to intermediate mass black holes as contributors to dark matter.  See this prior blog for a discussion of primordial black holes as a possible dark matter contributor:

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

Image credit: LIGO/Caltech/MIT/Sonoma State (Aurore Simonnet)

## WIMPs or MACHOs or Primordial Black Holes

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:

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”

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S. Perrenod, 2016, 72 Beautiful Galaxies (especially designed for iPad, iOS; ages 12 and up)