Image Credit: Bill Saxton, ALMA (ESO/NAOJ/NRAO), NRAO/AUI/NSF In this image, from the Atacama Large Millimeter Array in Chile, we are seeing three stars forming from a dusty disk within our own Milky Way. The two objects in the center are separated by 61 astronomical units (Earth-Sun distance is one AU, astronomical unit). One sees evidence of the disk fragmenting to form additional protostars.
Dark Stars is the name given to hypothetical stars in the early universe that were overwhelmingly composed of ordinary matter (baryons [protons and neutrons] and electrons) but that also were ‘salted’ with a little bit of dark matter.
And stars in this category have not evolved to the point of achieving stellar nucleosynthesis in their cores, instead they are, again hypothetically, heated by the dark matter within.
In a paper from last year “Dark stars powered by self-interacting dark matter” authors Wu, Baum, Freese, Visinelli, and Yu propose a type of self-interacting dark matter (SIDM). The authors start with the consideration of overdense regions known as ‘halos’ at the epoch of 200 million years for the universe’s age, corresponding to redshift z ~ 20. These are expected due to gravitational instability of slightly overdense regions that we see in the cosmic microwave background maps, from an epoch of only 0.38 million years.
One starts out with these dark matter dominated halos, but the ordinary matter within is much more efficient at collapse since it can radiate energy away electromagnetically. Dark matter, by definition, does not interact electromagnetically, that is why we don’t see it except through its gravitational effects or if it were to decay into normal matter. That also minimizes its ability to cool and collapse, other than through decay processes.
As the normal matter radiates, cools, and collapses further it concentrates into the center, away from the dark matter halo overall, but would include some modest amount of dark matter. A dark star might be fueled by only 0.1% dark vs. ordinary matter.
New Particles χ, φ
This SIDM scenario requires two new particles that the authors refer to as χ and φ. The χ dark matter particle (a fermion) could have a mass of order 100 GeV, similar to that of the Higgs particle (but that is a boson, not a fermion), and some 100 times that of a proton or neutron.
The φ particle (a scalar field) is a low-mass mediator in the dark sector with a mass closer to that of an electron or muon (heavy electron), in the range of 1 to 100 MeV. This particle would mediate between the χ and ordinary matter, baryons and electrons.
The main mechanism for heating is the decay of the charged χ and its anti-particle into pairs of (neutral) φ particles that can then go on to decay to electron / positron pairs. These easily thermalize within the ionized hydrogen and helium gas cloud as the electrons and positrons annihilate to gamma rays when they meet their corresponding anti-particle.
The decay mean free path for the φ would need to be of order 1 AU or less (an astronomical unit, the Earth-Sun distance); in this way, the decays would deposit heat into the protostellar cloud. The clouds can heat up to thousands of degrees Kelvin such that they are very efficient radiators. And since they can be large, larger than 1 AU their luminosity can also be very large.
A Model Dark Star
In their paper, Wu and co-authors model a 10 solar mass dark star with a photosphere of 3.2 AU radius. Such a dark star if placed at the Sun’s location would have its photosphere beyond the orbits of Earth and Mars and reaching to the outer edge of the asteroid belt.
The temperature of their model star is 4300 Kelvin, or 3/4 that of the Sun. Despite the lower temperature, because of the large size, the total luminosity in this case is 150,000 times that of our Sun. It would be reddish in color at the source, but highly redshifted into the infrared light would reach us. This luminosity is 100 times more luminous than the most luminous red supergiant star, but not much brighter intrinsically than the (much hotter) blue supergiant Rigel.
Because such a star would be a first stellar generation, it would have no spectral lines from any elements other than hydrogen or helium. Only hydrogen and helium and a trace amount of lithium are formed in the Big Bang.
Black holes as a result?
Other dark stars might have temperatures of 10,000 Kelvin, and possibly accrete matter from the aforementioned halo until they reach luminosities as large as 10 million times that of the Sun. These might be visible with the James Webb Space Telescope (JWST).
Dark stars might last as long as half a billion years, or the annihilation might shut down sooner due to the collapse of ordinary matter in the protostellar envelope. Once the dark star phase ends, there could be a rapid collapse to high mass nucleosynthesis-powered stars that would end their short lives as black holes, or one could even have direct collapse to black holes of high masses. These would be interesting candidates as the seeds of the supermassive black holes of millions and billions of solar masses that we observe today in the centers of galaxies, both nearby and at high redshifts.
The James Webb Space Telescope is finding more early galaxies than expected within the first 500 million years of the universe. It is able to peer back that far because of its instruments’ sensitivity in the infrared portion of the spectrum. The light from such early galaxies is heavily shifted from optical to infrared frequencies, by order a factor of 10, due to the universe’s expansion over the past 13 billion plus years. Perhaps seeing more early-onset galaxies is in part because of the role that dark stars play in hastening the evolution of the stellar population.
We look forward to JWST detecting the earliest stars, that might be dark stars, or providing constraints on their visibility or viability.
Previously I have written about the possibility of primordial black holes as the explanation for dark matter, and on the observational constraints around such a possibility.
But maybe it is dark energy, not dark matter, that black holes explain. More precisely, it would be dark energy stars (or gravatars, or GEODEs) that are observationally similar to black holes.
Dark energy
Dark energy is named thusly because it has negative pressure. There is something known as an equation of state that relates pressure to energy density. For normal matter, or for dark matter, the coefficient of the relationship, w, is zero or slightly positive, and for radiation it is 1/3.
If it is non-zero and positive then the fluid component loses energy as the universe expands, and for radiation, this means there is a cosmological redshift. The redshift is in proportion to the universe’s linear scale factor, which can be written as the inverse of the cosmological redshift plus one, by normalizing it to the present-day scale. The cosmological redshift is a measure of the epoch as well, currently z = 0, and the higher the redshift the farther we look back into the past, into the earlier years of the universe. Light emitted at frequency ν is shifted to lower frequency (longer wavelength) ν’ = ν / (1 + z).
Since 1998, we have known that we live in a universe dominated by dark energy (and its associated dark pressure, or negative pressure). The associated dark pressure outweighs dark energy by a factor of 3 because it appears 3 times, once for each spatial component in Einstein’s stress-energy tensor equations of general relativity.
Thus dark energy contributes a negative gravity, or expansion acceleration, and we observe that our universe has been accelerating in its expansion for the past 4 or 5 billion years, since dark energy now provides over 2/3 of the universal energy balance. Dark matter and ordinary matter together amount to just less than 1/3 of the average rest-mass energy density.
If w is less than -1/3 for some pervasive cosmological component, then you have dark energy behavior for that component, and in our universe today over the past several billion years, measurements show w = -1 or very close to it. This is the cosmological constant case where dark energy’s negative pressure has the same magnitude but the opposite sign of the positive dark energy density. More precisely, the dark pressure is the negative of the energy density times the speed of light squared.
Non-singular black holes
There has been consideration for decades of other types of black holes that would not have a singularity at the center. In standard solutions of general relativity black holes have a central singular point or flat zone, depending on whether their angular momentum is zero or positive.
For example a collapsing neutron star overwhelms all pressure support from neutron degeneracy pressure once its mass exceeds the TOV limit at about 2.7 solar masses (depending on angular momentum), and forms a black hole that is often presumed to collapse to a singularity.
But when considering quantum gravity, and quantum physics generally, then there should be some very exotic behavior at the center, we just don’t know what. Vacuum energy is one possibility.
For decades various proposals have been made for alternatives to a singularity, but the problem has been observationally intractable. A Soviet cosmologist Gliner, who was born just 100 years ago in Kyiv, and who only passed away in 2021, proposed the basis for dark energy stars and a dark energy driven cosmology framework in 1965 (in English translation, 1966).
E. Gliner, early 1970s in St. Petersburg, courtesy Gliner family
He defended his Ph.D. thesis in general relativity including dark energy as a component of the stress-energy tensor in 1972. Gliner emigrated to the US in 1980.
The essential idea is that the equation of state for compressed matter changes to that of a material (or “stuff”) with a fully negative pressure, w = -1 and thus that black hole collapse would naturally result in dark energy cores, creating dark energy stars or gravatars rather than traditional black holes. The cores could be surrounded with an intermediate transition zone and a skin or shell of normal matter (Beltracchi and Gondolo 2019). The dark energy cores would have negative pressure.
Standard black hole solution is incomplete
Normally black hole physics is attacked with Kerr (non-zero angular momentum) or Schwarzschild (zero angular momentum) solutions. But these are incomplete, in that they assume empty surroundings. There is no matching of the solution to the overall background which is a cosmological solution. The universe tracks an isotropic and homogeneous (on the largest scales) Lambda-cold dark matter (ΛCDM) solution of the equations of general relativity. Since dark energy now dominates, it is approaching a de Sitter exponential runaway, whereas traditional black hole solutions with singularities are quite the opposite, known as anti-de Sitter.
We have no general solution for black hole equations including the backdrop of an expanding universe. The local Kerr solution for rotating black holes that is widely used ignores the far field. Really one should match the two solution regimes, but there has been no analytical solution that does that; black hole computations are very difficult in general, even ignoring the far field.
In 2019, Croker and Weiner of the University of Hawaii found a way to match a model of dark energy cores to the standard ΛCDM cosmology, and demonstrate that for w = -1 that dark energy stars (black holes with dark energy cores) would have masses that grow in proportion to the cube of the universe’s linear scale factora, starting immediately from their initial formation at high redshifts. In effect they are forced to grow their masses and expand (with their radius proportional to mass as for a black hole) by all of the other dark energy stars in the universe acting in a collective fashion. They call this effect, cosmological coupling of the dark energy star gravity to the long-range and long-term cosmological gravitational field.
This can be considered a blueshift for mass, as distinguished from the energy or frequency redshift we see with radiation in the cosmos.
Their approach potentially addresses several problems: (1) an excess of larger galaxies and their supermassive black holes seen very early on in the recent James Webb Space Telescope data, (2) more intermediate mass black holes than expected, as confirmed from gravitational wave observations of black hole mergers, (see Coker, Zevin et al. 2021 for a possible explanation via cosmological coupling), and (3) possibly a natural explanation for all or a substantial portion of the dark energy in the universe, which has been assumed to be highly diffuse rather than composed primarily of a very large number of point sources.
Inside dark energy stars, the dark energy density would be many, many orders of magnitude higher than it is in the universe at large. But as we will see below, it might be enough to explain all of the dark energy budget of the ΛCDM cosmology.
M87* supermassive black hole (or dark energy star) imaged in polarized radio waves by the Event Horizon Telescope collaboration; signals are combined from a global collection of radio telescopes via aperture synthesis techniques. European Southern Observatory, licensed under a Creative Commons Attribution 4.0 International License
A revolutionary proposal
Here’s where it gets weird. A number of researchers have investigated the coupling of a black hole’s interior to an external expanding universe. In this case there is no singularity but instead a vacuum energy solution interior to the (growing) compact stellar remnant.
And one of the most favored possibilities is that the coupling causes the mass for all black holes to grow in proportion to the universe’s characteristic linear size a cubed, just as if it were a cosmological constant form of dark energy. This type of “stuff” retains equal energy density throughout all of space even as the space expands, as a result of its negative pressure with equation of state parameter w = -1.
Just this February a very interesting pair of papers has been published in The Astrophysical Journal (the most prestigious American journal for such work) by a team of astronomers from 9 countries (US, UK, Canada, Japan, Netherlands, Germany, Denmark, Portugal, and Cyprus), led by the University of Hawaii team mentioned above.
They have used observations of a large number of supermassive black holes and their companion galaxies out to redshift 2.5 (when the universe was less than 3 billion years of age) to argue that there is observable cosmologicalcouplingbetween the cosmological gravitational field at large and the SMBH masses, where they suppose those masses are dominated by dark energy cores.
Figure 1 from Farrah, Croker, et al. shows their measured cosmological coupling parameter k based on 3 catalogs (5 samples using different emission lines) of supermassive black holes contained in elliptical galaxies at high redshifts, 0.7 < z < 2.5. If k =3, that corresponds to the cosmological constant case with equation of state parameter w = -1.
Their argument is that the black hole* (or *dark energy star) masses have grown much faster than could be explained by the usual mechanism of accretion of nearby matter and mergers.
In Figure 1 from their second paper of the pair (Farrah, Croker, et al. 2023), they present their measurements of the strength of cosmological coupling for five different galaxy surveys (three sets of galaxies but two sets were surveyed at two frequencies each). They observed strong increases in the measured SMBH masses from redshifts close to z =1 and extending above z = 2. They derive a coupling strength parameter k that measures the power law index of how fast the black hole masses grow with redshift.
Their reformulation of the black hole model to include the far field yields cosmological coupling of the dark energy cores. The mass of the dark energy core, coupled to the overall cosmological solution, results in a mass increase M ~ a^k , a power law of index k, depending on the equation of state for the dark energy. Here a is the cosmological linear scale factor of the universal expansion and is also equal to 1/(1+z) where z is the redshift at which a galaxy and its SMBH are observed. (The scale factor a is normalized to 1 presently, such that z = 0 now and is positive in the past).
And they are claiming that their sample of several hundred galaxies and supermassive black holes indicates k = 3, on average, more or less. So between z = 1 and z = 0, over the past 8 billion years, they interpret their observations as an 8-fold growth in black hole masses. And they say this is consistent with M growing by a^3 as the universe’s linear scale has doubled (a was 1/2 at z = 1). This implies they are measuring a different class of black holes than we normally think of, those don’t increase in mass other than by accretion and mergers. Normal black holes would yield k > 0 but not by much, based on expected accretion and mergers. The k = 0 case they state is excluded by their observations with over 99.9% confidence.
The set of upper graphs in Figure 1 is for the various surveys, and the large lower graph combines all of the surveys as a single data set. They find a near-Gaussian distribution, and k is centered near 3, with an uncertainty close to 1. There is a 2/3 chance that the value lies between 2.33 and 3.85, based on their total sample of over 400 active galaxy nuclei.
And they also suggest this effect would be for all dark energy dominated “black holes”, including stellar class and intermediate BHs, not just SMBHs. So they claim fast evolution in all dark energy star masses, in proportion to the volume growth of the expanding universe, and consistent with dark energy cores having an equation of state just like the observed cosmological constant.
Now it gets really interesting.
We already know that the dark energy density of the universe, unlike the ever-thinning mater and radiation density, is more or less constant in absolute terms. That is the cosmological constant, due to vacuumenergy, interpretation of dark energy for which the pressure is negative and causes acceleration of the universe’s expansion. Each additional volume of the growth has its own associated vacuum energy (around 4 proton masses’ worth of rest energy per cubic meter). This is the universe’s biggest free lunch since its original creation.
The authors focus on dark energy starts created during the earliest bursts of star formation. These are the so-called Pop III stars, never observed because all or mostly all have reached end of life long ago. When galaxy and star formation starts as early as about 200 million years after the Big Bang, there is only hydrogen and helium for atomic matter. Heavier elements must be made in those first Pop III stars. As a result of their composition, the first stars with zero ‘metallacity’ have higher stellar masses; high mass stars are the ones that evolve most rapidly and they quickly end up as white dwarfs, or more to the point here, black holes or neutron stars in supernovae events. Or, they end their lives as dark energy stars.
The number of these compact post supernova remnant stars will decrease in density in inverse proportion to the increasing volume of the expanding universe. But the masses of all those that are dark energy stars would increase as the cube of the scale factor, in proportion to the increasing volume.
And the net effect would be justright to create a cosmological constant form of dark energy as the total contribution of billions upon billions of dark energy stars. And dark energy would be growing as a background field from very early on. Regular matter and dark matter thin out with time, but this cohort would have roughly constant energy density once most of the first early rounds of star formation completed, perhaps by redshift z = 8, well within the first billion years. Consequently, dark energy cores, collectively, would dominate the universe within the last 4 or 5 billion years or so, as the ordinary and dark matter density fell off. And now its dominance keeps growing with time.
But is there enough dark energy in cores?
But is it enough? How much dark energy is captured in these dark energy stars, and can it explain the dominant 69% of the universe’s energy balance that is inferred from observations of distant supernovae, and from other methods?
The dark energy cores are presumably formed from the infall and extreme compression of ordinary matter, from baryons captured into the progenitors of these black hole like stars and being compressed to such a high degree that they are converted into a rather uniform dark energy fluid. And that dark energy fluid has the unusual property of negative pressure that prevents further compression to a singularity.
It is possible they could consume some dark matter, but ordinary matter clumps much more easily since it can radiate away energy via radiation, which dark matter does not do. Any dark matter consumption would only build their case here, but we know the overall dark matter ratio of 5:1 versus ordinary matter has not changed much since the cosmic microwave background emission after the first 380,000 years.
We know from cosmic microwave background measurements and other observations, that the ordinary matter or baryon budget of the universe is just about 4.9%, we’ll call it 5% in round numbers. The rest is 69% dark energy, and 26% dark matter.
So the question is, how much of the 5% must be locked up in dark energy stars to explain the 69% dark energy dominance that we currently see?
Remember that with dark energy stars the mass grows as the volume of the universe grows, that is in proportion to (1 + z)3. Now dark energy stars will be formed at different cosmological redshifts, but let’s just ask what fraction of baryons would we need to convert, assuming all are formed at the same epoch. This will give us a rough feel for the range of when and of how much.
Table 1 looks at some possibilities. It asks what fraction of baryons need to collapse into dark energy cores, and we see that the range is from only about 0.2% to 1% of baryons are required. Those baryons are just 5% of the mass-energy of the universe, and only 1% or less of those are needed, because the mass expansion factors range from about 1000 to about 10,000 — 3 to 4 orders of magnitude, depending on when the dark energy stars form.
Table 1. The first column has the redshift (epoch) of dark energy star formation. In actuality it will happen over a broad range of redshifts, but the earliest stars and galaxies seem to have formed from around 200 to 500 million years after the Big Bang started. The second column has the mass expansion factor (1+z)3; the DE star’s gravitational mass grows by that factor from the formation z until now. The third column is the age of the universe at DE star formation. The fourth column tells us what fraction of all baryons need to be incorporated into dark energy cores in those stars (they could be somewhat more massive than that). The fifth column is the lower bound on their current mass if they never experience a merger or accretion of other matter. All in all it looks as if less than 1% of baryons convert to dark energy cores.
The fifth column shows the current mass of a minimal 3 solar mass dark energy star at present, noting that 3 solar masses is the lightest known black hole. There may be lighter dark energy stars, but not very much lighter than that, perhaps a little less than 2 solar masses. And the number density should be highest at the low end according to everything we know about star formation.
Now to some degree these are underestimates for the final mass, as shown in the fifth column, since there will be mergers and accretion of other matter into these stars, and of the two effects, the mergers are more important, but they support the general argument. If a dark energy star merges with a neutron star, or other type of black hole, the dark energy core gains in relative terms. So all of this is a plausibility argument that says if the formation is of dark energy stars of a few solar masses in the epoch from 200 to 500 million years after the Big Bang, that less than 1% of all baryons are needed. And it says that the final masses are well into the intermediate range of thousands or tens of thousands of solar masses, and yet they can hide out in galaxies or between galaxies with hundreds of billions of solar masses, only contributing a few percent to the total mass.
Dark energy star cosmology
Dark energy star cosmology needs to agree with the known set of cosmological observations. It has to provide all or a significant fraction of the total dark energy budget in order to be useful. It appears from simple arguments that it can meet the budget by conversion of a small percentage of the baryons in the universe to dark energy stars.
It should exhibit an equation of state w = -1 or nearly so, and it appears to do that. It should not contribute too much mass to upset our galaxy mass estimates. It does that and it does not appear to explain dark matter in any direct way.
Dark energy stars collectively could potentially fill that role. In the model described above it is their collective effects that are being modeled as a dark energy background field that in turn drives dark energy star cores to higher masses over time. Dark energy (as a global field) feeds on itself (the dark energy cores)!
There are some differences with the normal ΛCDM cosmology assumption of a highly uniform dark energy background, not one composed of a very large number of point sources. In particular the ΛCDM cosmology has the dark energy background there from the very beginning, but it is not significant until,the universe has expanded sufficiently.
With the dark energy star case it has to be built up, one dark energy core at a time. So the dark energy effects do not begin until redshifts less than say z = 20 to 30 and most of it may be built up by z = 8 to 10, within the first billion years.
In the dark energy star case we will have accretion of nearby matter including stars, and mergers with neutron stars, other dark energy stars, and other black hole types.
A merger with a neutron star or non dark energy star only increases the mass in dark energy cores; it is positive evolution in the aggregate dark energy core component. A merger of two dark energy stars will lose some of the collective mass in conversion to gravitational radiation, and is a negative contribution toward the overall dark energy budget.
One way to distinguish between the two cosmological models is to push our measurement of the strength of dark energy as far back as we can and look for variations. Another is to identify as many individual intermediate scale black holes / dark energy stars as we can from gravitational wave surveys and from detailed studies of globular clusters and dwarf galaxies.
What about dark matter?
Dark matter’s ratio to ordinary matter at the time of the cosmic microwave background emission is measured to be 5:1 and currently in galaxies and their rotation curves and in clusters of galaxies in their intracluster medium it is also seen to be around 5:1 on average. Since the dark energy cores in the Croker et al. proposal are created hundreds of millions of years after the cosmic microwave background era, then these dark energy stars can not be a major contribution to dark matter per se.
The pair of papers just published by the team doesn’t really discuss dark matter implications. But a previous paper by Croker, Runburg and Farrah (2020) explored the interaction between the dark energy bulk behavior of the global population of dark energy stars with cold dark matter and found little or no affect.
Their process converts a rather small percentage of baryons (or even some dark matter particles) into dark energy and its negative pressure. Such material couples differently to the gravitational field than dark matter, which like ordinary matter is approximately dust-like with an equation of state parameter w = 0.
In the 2020 paper they find that GEODEs or dark energy stars can be spread out even more than dark matter that dominates galaxy halos, or the intracluster medium in rich clusters of galaxies.
Prizes ahead?
This concept of cosmological coupling is one of the most interesting areas of observational and theoretical cosmology in this century. If this work by Croker and collaborators is confirmed the team will be winning prizes in astrophysics and cosmology, since it could be a real breakthrough in both our understanding of the nature of dark energy and our understanding of black hole physics.
In any case, Dark Energy Star already has its own song.
Glossary
Black Hole: A dense collection of matter that collapses inside a small radius, and in theory, to a singularity, and which has sufficiently strong gravity that nothing, not even light, is able to escape. Black holes are characterized by three numbers: mass, angular momentum, and charge.
Cosmological constant: Einstein added this term, Λ, on the left hand side of the equations of general relativity, in a search for a static universe solution. It corresponds to an equation of state parameter w = -1. If the term is moved to the right hand side it becomes a dark energy source term in the stress-energy tensor.
Cosmological coupling: The coupling of local properties to the overall cosmological model. For example, photons redshift to lower energies with the expansion of the universe. It is argued that dark energy stellar cores would collectively couple to the overall Friedmann cosmology that matches the bulk parameters of the universe. In this case it would be a ‘blueshift’ style increase in mass in proportion to the growing volume of the universe, or perhaps more slowly.
Dark Energy: Usually attributed to energy of the vacuum, dark energy has a negative pressure in proportion to its energy density. It was confirmed by Nobel prize winning teams that dark energy is the dominant component of the universe’s mass-energy balance, some 69% of the critical value, and is driving an accelerated expansion with an equation of state w = -1 to within small errors.
Dark Energy Star: A highly compact object that should look like a black hole externally but has no singularity at its core. Instead it has a core of dark energy. If one integrates over all dark energy stars, it may add up to a portion or all of the universe’s dark energy budget. It should have a crust of ‘normal’ matter with anisotropic stress at the boundary with the core, or an intermediate transition zone with varying equation of state between the crust and the core.
Dark Matter: An unknown substance thought to reside in galactic halos, with 5 times as much matter density on average as ordinary matter. Dark matter does not interact electromagnetically and is typically considered to be particulate in nature, although primordial mini black holes have been suggested as one possible explanation.
Equation of state: The relationship between pressure and energy density, P = w * ρ * c^2 where P is pressure and can be negative, and ρ the energy density is positive. If w < -1/3 there is dark pressure, if w = -1 it is the simplest cosmological constant form. Dark matter or a collection of stars or galaxies can be modeled as w ~ 0.
GEODEs: GEneric Objects of Dark Energy, dark energy stars. Formation is thought to occur from Pop III stars, the first stellar generation, at epochs 30 > z > 8.
Gravastar: A stellar model that has a dark energy core and a very thin outer shell. With normal matter added there is anisotropic stress at the boundary to maintain pressure continuity from the core to the shell.
Non-singular black holes: A black hole like object with no singularity.
Primordial black holes: Black holes that may have formed in the very early universe, within the first second. Primordial dark energy stars in large numbers would be problematic, because they would grow in mass by (1 + z)^3 where z >> 1000.
Vacuumenergy: The irreducible energy of the vacuum state. The vacuum state is not empty, it is pervaded by fields and virtual particles that pop in and out of existence on very short time scales.
Croker, K.S., Nishimura, K.A., and Farrah D., 2020 https://arxiv.org/pdf/1904.03781.pdf, “Implications of Symmetry and Pressure in Friedmann Cosmology. II. Stellar Remnant Black Hole Mass Function”
Croker, K.S., Runburg, J., and Farrah D., 2020 https://doi.org/10.3847/1538-4357/abad2f “Implications of Symmetry and Pressure in Friedmann Cosmology. III. Point Sources of Dark Energy that tend toward Uniformity”
Croker, K.S., Zevin, M.J., Farrah, D., Nishimura, K.A., and Tarle, G. 2021, “Cosmologically coupled compact objects: a single parameter model for LIGO-Virgo mass and redshift distributions” https://arxiv.org/pdf/2109.08146.pdf
Farrah, D., Croker, K.S. et al. 2023 February, https://iopscience.iop.org/article/10.3847/2041-8213/acb704/pdf “Observational Evidence for Cosmological Coupling of Black Holes and its Implications for an Astrophysical Source of Dark Energy” (appeared in Ap.J. Letters 20 February, 2023)
Farrah, D., Petty S., Croker K.S. et al. 2023 February, https://doi.org/10.3847/1538-4357/acac2e “A Preferential Growth Channel for Supermassive Black Holes in Elliptical Galaxies at z <~ 2”
Gliner, E.B. 1965, Algebraic Properties of the Energy-momentum Tensor and Vacuum-like States of Matter. ZhTF 49, 542–548. English transl.: Sov. Phys. JETP 1966, 22, 378.
Harikane, Y., Ouchi, M., et al. arXiv:2208.01612v3, “A Comprehensive Study on Galaxies at z ~ 9 – 16 Found in the Early JWST Data: UV Luminosity Functions and Cosmic Star-Formation History at the Pre-Reionization Epoch”
Ancient Voyager Satellite Says No for the Smallest Possible
Hawking Radiation
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.
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 gm (smaller ones have evaporated already) up to 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 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.
Smaller black holes radiate at higher temperatures and have shorter lifetimes. The Hawking radiation temperature is
Thus for an 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 or 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 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 grams and above? Most mass regions are ruled out.
The mass region above grams and up to about 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 up to 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
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
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 Joules of energy, released in 0.2 seconds, or an average of 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:
LIGO Gravitational Wave Detection Postulated to be Due to Primordial Black Holes
Dark matter remains elusive, with overwhelming evidence for its gravitational effects, but no confirmed direct detection of exotic dark matter particles.
Another possibility which is being re-examined as an explanation for dark matter is that of black holes that formed in the very early universe, which in principle could be of very small mass, or quite large mass. And they may have initially formed at smaller masses and then aggregated gravitationally to form larger black holes.
Recently gravitational waves were discovered for the first time, by both of the LIGO instruments, located in Louisiana and in Washington State. The gravitational wave signal (GW150914) indicates that the source was a pair of black holes, of about 29 and 36 solar masses respectively, spiraling together into a single black hole of about 62 solar masses. A full 3 solar masses’ worth of gravitational energy was radiated way in the merger. Breaking news: LIGO has just this month announced gravitational waves from a second black hole binary of 22 solar masses total. One solar mass of energy was radiated away in the merger.
Most of the black holes that we detect (indirectly, from their accretion disks) are stellar-sized in the range of 10 to 100 solar masses and are believed to be the evolutionary endpoints of massive stars. We detect them when they are surrounded by accretion disks of hot luminous matter outside of their event horizons. The other main category of black holes exceeds a million solar masses and can even be more than a billion solar masses, and are known as supermassive black holes.
It is possible that some of the stellar-sized and even elusive intermediate black holes were formed in the Big Bang. Such black holes are referred to as primordial black holes. There are a variety of theoretical formation mechanisms, such as cosmic strings whose loops in all dimensions are contained within the event horizon radius (Schwarzschild radius). In general such primordial black holes (PBHs) would be distributed in a galaxy’s halo, would interact rarely and not have accretion disks and thus would not be detectable due to electromagnetic radiation. That is, they would behave as dark matter.
Dr. Simon Bird and coauthors have recently proposed that the gravitational wave event (GW150914) could be due to two primordial black holes encountering each other in a galactic halo, radiate enough of their kinetic energy away in gravity waves to become bound to each other and inspiral to a single black hole with a final burst of gravitational radiation. The frequency of events is estimated to be of order a few per year per cubic Gigaparsec (a Gigaparsec is 3.26 billion light years), if the dark matter abundance is dominated by PBHs.
While low-mass PBHs have been ruled out for the most part, except of a window around one one-hundred millionth of a solar mass, the authors suggest a window also remains for PBHs in the range from 20 to 100 solar masses.
Dr. A. Kashlinsky has gone further to suggest that the cosmic infrared background (CIB) of unresolved 2 to 5 micron near-infrared sources is due to PBHs. In this case the PBHs would be the dominant dark matter component in galactic halos and would mediate early star and galaxy formation. Furthermore there is an unresolved soft cosmic X-ray background which appears to be correlated with the CIB.
This would be a trifecta, with PBHs explaining much or most of the dark matter, the CIB and the soft-X-Ray CXB! But at this point it’s all rather speculative.
The LIGO instruments are now upgraded to Advanced LIGO and as more gravitational wave events are detected due to black holes, we can gain further insight into this possible explanation for dark matter, in whole or in part. Improved satellite born experiments to further resolve the CIB and CXB will also help to explore this possibility of PBHs as a major component to dark matter.
References:
S. Bird et al. arXiv:1603.00464v2 “Did LIGO detect Dark Matter”
A. Kashlinksy arXiv:1605.04023v1 “LIGO gravitational wave detection, primordial black holes and the near-IR cosmic infrared background anisotropies”
Video (artist’s representation) of inspiral and merger of binary black hole GW151226 (second gravitational wave detection): https://youtu.be/KwbXxzgAObU
NEW BOOK just released:
S. Perrenod, 2016, 72 Beautiful Galaxies (especially designed for iPad, iOS; ages 12 and up)
What does the discovery of gravitational waves imply about dark matter and dark energy?
The first detection of gravitational waves results from a pair of merging black holes, and is yet another magnificent confirmation of the theory of general relativity. Einstein’s theory of general relativity has passed every test thrown at it during the last 100 years.
While the existence of gravitational waves was fully expected to be confirmed, the discovery took several decades and represents a technological tour de force. Detected at the two LIGO sites, one in Louisiana and one in Washington State, the main event lasted only 0.2 seconds, and was seen as a change of length in the “arms” of the detector (laser interferometers) of only one part in a thousand billion billion.
The LIGO detection of gravitational waves. The blue curve is from the Louisiana site and the red curve from the Washington state site. The two curves are shifted by 7 milliseconds to account for the speed-of-light delay between the two sites. Note that most of the power in the signal occurs within less than 0.2 seconds. The strain is a measure of proportional change in length of the detector arm and is less than 1 part in 10²¹.
Nevertheless, this is the most energetic event ever seen by mankind. The merger of two large black holes totaling over 60 times the Sun’s mass resulted in the conversion of 3 solar masses of material into gravitational wave energy. Imagine, there were 3 Suns worth of matter obliterated in the blink of an eye. During this brief period, the generated power was greater than that from the light of all of the stars of all of the galaxies in our known universe.
What the discovery of gravitational waves has to say about dark matter and dark energy is essentially that it further confirms their existence.
Although there is as of now no direct detection of dark matter, we infer the existence of dark matter by using the equations of general relativity (GR), in a number of cases, including:
Gravitational lensing – Typically, a foreground cluster of galaxies distorts and magnifies the image of a background galaxy. GR is used to calculate the bending and magnification, primarily caused by the dark matter in the foreground cluster.
Cosmic microwave background radiation (CMBR) – The CMBR has spatial fluctuation peaks (harmonics) and the first peak tells us about ordinary matter and the third peak about the density of dark matter. A GR-based cosmological model is used to determine the dark matter average density.
Dark matter is also inferred from the way in which galaxies rotate and from the velocities of galaxies within galaxy clusters, but general relativity is not needed to calculate the dark matter densities in such cases. However, results from these methods are consistent with results from the methods listed above.
In the case of dark energy, it turns out to be a parameter in the equations of general relativity as first formulated by Einstein. The parameter, lambda, (Λ) is known as the cosmological constant, and represents the minimum energy of the vacuum. For many years astronomers and cosmologists thought it might take the value of zero. However in 1998 multiple teams confirmed that the value is positive and not zero, and it turns out that dark energy has more than twice the energy content of dark matter. Its non-zero value is actually another stunning success for general relativity.
Thus the detection of gravitational waves indirectly provides further support for the canonical cosmological model ΛCDM, with both dark matter and dark energy, and fully consistent with general relativity.
This blog is based on a recent talk on the Horizon supercomputer simulation for galaxy formation. The talk (in English) was given at the Ecole Normale Superieure by Julien Devrient, of the University of Oxford, available on YouTube here:
The background for the simulation of galaxy formation on supercomputers is the standard Lambda-Cold Dark Matter cosmology with 4.8% ordinary matter, 26.8% dark matter and 68.4% dark energy, which are the measured values from the Planck satellite and other observations. These are the proportions at present, but until the last few billion years, dark matter was dominant over dark energy. The ratio of dark matter to ordinary matter has stayed essentially fixed since the universe was 1 second old, with about 5 times or so as much dark matter as ordinary matter.
The collisionless components to consider are cold dark matter (CDM) and stars, as the stars form inside the simulation.
Then there is a collisional fluid composed of gas, in both atomic (neutral and ionized) and molecular forms and consisting primarily of hydrogen, helium and a small amount, up to around 1% by mass, of heavy elements including carbon, nitrogen, oxygen, silicon, iron and so forth. This fraction increases during the history of the universe as star formation and evolution proceeds. This ‘primordial’ gas is heated by falling into the gravitational potential determined primarily by the CDM (but also by the ordinary matter) and it cools via various radiative processes that depend on density, temperature and composition.
There are many complicating factors and feedback processes. This is an extremely messy problem to address. Dust, supernovae, turbulent gas dynamics, magnetic fields, and black holes that merge and grow into supermassive black holes (SMBH) are all things to consider. The SMBH are surrounded by accretion disks and also may emit jets and these components are visible as highly luminous AGN (active galactic nuclei). Not all of these can be included in simulations at present, or they are treated empirically.
Although the physics is well understood for the collisionless component behavior and for the atomic and molecular gas, including the cooling (radiative) functions, the modeling must occur over many, many orders of magnitude, since scales range from less than 1 parsec to 100s of Megaparsecs (a million parsecs, where 1 parsec = 3.26 light-years). This huge range in scale, plus complex physics, makes the calculation extremely computationally expensive.
The Horizon simulation had 7 billion grid cells and 1 billion dark matter particles. The highest resolution is down to 1 kiloparsec. Gas cooling, star formation, stellar winds, two types of supernovae are included and the abundances of C, N, O, Si, Mg, and Fe tracked. Black hole formation was included. Two million CPU core hours were required for the simulation.
Figure 1. The multi-scale problem
Many scales are involved in simulating galaxy formation – 11 or 12 orders of magnitude. Each tick mark in the above Figure 1 is 3 orders of magnitude (a factor of 1000) in linear scale. From the largest to the smallest objects (moving from right to left) we have LSS = large-scale structure: the universe has evolved into a web-like structure with filaments and sheets of galaxies and high-density and low-density regions. The scale is 100s of Megaparsecs to more than a Gigaparsec. Below this are the galaxy clusters, which are the largest gravitationally bound structures, at around 1 Megaparsec, and then galaxies which are found primarily in the 1 kiloparsec to 100 kiloparsec range.
Then within galaxies, star formation happens within molecular clouds and the scales are parsecs to 100s of parsecs. At the smallest scale, we have highly energetic active galactic nuclei (AGN), that are powered by SMBH (supermassive black holes), with millions to billions of solar masses, and have surrounding accretion disks, confined within a very small region of order 1/1000 of a parsec, reaching down towards the scale of our solar system.
Figure 2. The Dark Matter Halo mass function and the galaxy mass function
It is impossible with current supercomputers and techniques to directly model across all these scales, but the Horizon-AGN Simulation, one of the largest galaxy formation simulations today, spans around 5 orders of magnitude by using adaptive mesh refinement strategies. When and where the density of matter is high and the physics is interesting, an increasingly finer mesh is employed for the calculations. Without this method, it would be impossible to make progress.
Galaxies are formed within the gravitational potentials of dark matter halos (DMH). There is about 5 times as much mass in dark matter as in ordinary matter (baryons, e.g. protons and neutrons). So the ordinary matter falls into the gravitational potentials of DMH, is heated up, and cools by radiation which allows for further collapse, and so on until galaxies are formed.
The interesting scales for DMH are from about 100 billion to 1000 trillion solar masses. The size distribution for the density perturbations that self-collapse under their own gravity follows a power law (with an index of close to -1 in the inverse linear scale). This comes from the cosmic microwave background measurements and inflationary Big Bang theory. How these density perturbations evolve and collapse to DMH is now a well-studied problem in cosmology.
One might assume that each DMH results in a single galaxy, and in the mid-range, this matches observations fairly well. But at the low-end and the high-end, this simple model breaks down, when comparison is made to the observed galaxy mass function (which is simply a measurement of how many galaxies we see per unit volume with a given mass).
At the low end we see fewer galaxies than expected. These are very faint however more and more dwarf galaxies with low luminosity yet with significant mass dominated by dark matter are being detected, and this is helping to resolve this issue. An important factor is most likely feedback from supernovae. As supernovae explode they produce blast waves which drive gas out and prevent molecular cloud formation and star formation.
Supernova physics is tricky as it can result in gas compression which enhances the star formation rate but also can drive gas out of a galaxy, partcularly if it is smaller and has a lower gravitational field, and this suppresses star formation.
In the left panel of Figure 2 above, the first black line is the DMH mass function, and the second black line is just shifted to the left by the baryon to dark matter ratio. What is being plotted is the frequency of galaxies expected for a given mass.The actual observed curve for galaxy stellar masses is in red, and one sees fewer galaxies at the low end and especially at the very high end. The right panel shows the observational data which is replotted as the red line in the left panel.
At the high end of the mass function there are fewer galaxies with a rapid cutoff around 1 to 10 trillion solar masses for baryon content, which is about an order of magnitude lower than the DMHmass function would suggest. At the high end it is believed that feedback from AGN (SMBH) is the cause of inhibited star formation, placing a limit on the maximum size of an individual galaxy. Of course multiple galaxies may form out of a single halo as well.
Figure 3. The Horizon simulation without and with Active Galactic Nuclei included
The upper panel on the right in Figure 3 is the simulation without AGN, the lower one with AGN. The simulation including AGN is a better fit to observed galaxy properties.
The simulation had 7 billion grid cells and 1 billion dark matter particles. The highest resolution is down to 1 kiloparsec. Gas cooling, star formation, stellar winds, two types of supernovae are included and the abundances of C, N, O, Si, Mg, and Fe tracked. Black hole formation was included. Two million CPU core hours were required for the simulation.
Including modeling of AGN, the larger galaxies in the simulation are less massive and dimmer, and are more likely to be ellipticals than spiral galaxies. The high mass galaxies in the center of clusters are generally observed to be ellipticals, so this is a desired result.
There is much room for refining and improving galaxy simulation work, including adding additional physics and more small-scale resolution to the models. I encourage you to look at the YouTube video, there are many other interesting results discussed by Prof. Devrient from the Horizon-AGN simulation work.
Black holes can cause dark matter to annihilate in their vicinity by concentrating the dark matter and enhancing the collision rate between dark matter particles. The best observational candidates are supermassive black holes, such as the 4 million solar mass black hole found at the center of our Milky Way galaxy. Some galaxies have much larger supermassive black holes, reaching as high as several billion or even tens of billions of solar masses. Most massive galaxies appear to have supermassive black holes in their centers.
Artist’s conception of a supermassive black hole (public domain; courtesy NASA JPL)
We infer the existence of supermassive black holes through their effect on nearby stellar or molecular cloud orbits. And we more directly detect supermassive black holes (SMBHs) by the radiation emitted from ordinary matter that is near the black hole (BH), but has not yet fallen into the BH’s event horizon (from which nothing, not even light, can escape). Such matter will often form a hot accretion disk around the SMBH. The disk or other infalling matter can be heated to millions of degrees by the strong gravitational potential of the BH as the kinetic energy of infall is converted to thermal energy by frictional processes. Ordinary matter (OM) heated to such high temperatures will give off X-rays.
Now if OM is being pulled into a SMBH, so is dark matter, which pervades every galaxy. Dark matter (DM) responds to the same gravitational potential from the SMBH. The difference is that OM is collisional since it easily interacts with other OM via the electromagnetic force, whereas DM is generally collisionless, since it does not interact via electromagnetism.
Nevertheless DM – DM collisions can occur, rarely, via a ‘direct hit’ (as if two bullets hit each other in mid-air) and this leads to annihilation. Two DM particles meet directly and their entire energy content, from their rest mass as well as their kinetic energy of motion, is converted into other particles. The cross-section strength is not known, but it must be small due to observational limits, yet is expected to be non-zero. The most likely candidates for decay products are expected to be photons, neutrinos, and electrons.
The leading candidate for DM is some sort of weakly interacting massive particle with a mass of perhaps 5 to 300 GeV; this is the range where DM searches from satellites and on Earth are focused. (The proton mass is a little less than 1 GeV = billion electron Volts.) So if two DM particles mutually annihilate, there is of order 10 GeV to 600 GeV of available rest mass energy to produce highly energetic gamma rays.
The likelihood of a direct hit is proportional to the square of the density of the DM. A SMBH’s gravitational potential acts as a concentrator for DM, allowing the density to be high enough that there could be a significant number of annihilation events, resulting in a detectable flux of escaping photons reaching Earth. Relativistic effects work to further increase the annihilation rate. And it is possible that the annihilation signal could scale as M³ (mass of the SMBH cubed), and thus the most massive SMBHs would be very strong gamma ray emitters. These would be highly energetic gamma rays with well over 1 GeV of energy.
Movie from NASA Goddard showing Dr. Jeremy Schnittman’s simulation
Dr. Jeremy Schnittman of the NASA Goddard Space Flight Center has investigated possible annihilation rates and the nature of the observable gamma ray spectrum for some simple dark matter models. He used a compute cluster to simulate hundreds of millions of DM particles moving in the general direction of a SMBH. One of his remarkable findings is that much higher gamma ray energies can be produced than previously believed, in the case of SMBHs which are rapidly spinning.
This is a result of something known as the Penrose process, which allows energy to be extracted from a rotating BH. There is a region called the ergosphere outside of the event horizon and when two DM particles annihilate in this region and produce two gamma rays, one gamma ray photon would fall into the event horizon (into the BH), and the other photon would escape to infinity, possibly in the direction of Earth. Dr. Schnittman’s simulation indicates that the energy boost can be as high as 6 times or more. The faster the SMBH is spinning, the greater the potential energy boost.
He also has looked at DM particles on bound orbits, which are likely to form into a (donut-shaped) corotating torus around the SMBH, aligned with its spin vector. The bound DM particle annihilations lead to lower energy gamma ray production, as compared to the unbound particles.
One of the important considerations is that the influence radius of the BH is very large. The size of the BH itself (event horizon or Schwarzschild radius) is small, even for SMBHs. The radius is proportional to the mass, via the relation 2GM/R = c² (G is the gravitational constant, c the speed of light and M and R are the BH mass and radius, respectively). A SMBH with a mass of 10 million solarmasses will have a radius of only around 30 million kilometers, or about 1/5 of the Earth-Sun distance (an AU, or astronomical unit).
But the gravitational influence is much greater, since DM particles are typically expected to be moving at around only a couple of hundred kilometers per second far away from the SMBH. Thus DM particles that are 1 million times further away than the SMBH will have their orbits in their galaxy perturbed by the SMBH. And the scale of influence is thus parsecs (1 parsec = 3.26 light-years) or tens of parsecs or even hundreds of parsecs, depending on the SMBH mass.
The most energetic gamma rays can be produced by unbound DM particles. These are on orbits which can approach near to the SMBH after falling from far away (a “swan dive” toward the SMBH) and these DM particles would then typically head out away from the SMBH in the opposite direction. But before they are able to, they have a direct hit with another DM particle and annihilate into gamma rays or some other decay products.
The search for gamma rays from annihilating DM around SMBHs is already underway. There is in fact a possible detection by the Fermi telescope at 130 GeV in our Milky Way galaxy, from the direction of the Sagittarius A* SMBH. Future more sensitive gamma ray surveys may lead to many detections, helping us to better understand both dark matter and black holes.
References
J.D. Schnittman, 2015. “The Distribution and Annihilattion of Dark Matter around Black Holes”, http://arxiv.org/abs/1506.06728
J.D. Schnittman, 2014. Phys. Rev. Letters 113, 261102,“Revised Upper Limit to Energy Extraction from a Kerr Black Hole”
Globular clusters are highly compact star clusters containing hundreds of thousands or even millions of old stars. The stars found in a globular cluster can be up to almost 13 billion years old, and thus act as good tracers of the early history of our Milky Way Galaxy, or of other galaxies in which they are found.
Our Galaxy has about 150 or so globular clusters, and our neighbor the Andromeda Galaxy has over 500. Because they are so compact, they are tightly gravitationally bound, and tend to be very spherical, hence the description as globular. They also orbit our Galaxy in the halo and in various directions; they are not confined to the disk where most of the other stars of the Milky Way are found. This suggests a history for globulars (as they are also called) that predates the formation of the Milky Way’s disk and spiral arms. Many globulars may be remnants of dwarf galaxies that have been pulled into the Milky Way during its long lifetime, or have been captured by the Milky Way as it consumed another, smaller galaxy in its vicinity.
M13 globular cluster
The large majority of globular clusters are thought to contain little dark matter. They contain no dust or gas, their matter appears to be all in stars. Astronomers are able to measure the mass of globulars by determining how fast stars are moving around in the core, and by measuring the size of the globulars. Assuming the globulars are gravitationally relaxed, which most appear to be, then the mass within a certain radius is proportional to the radius and the square of the velocities of stars relative to the globular’s center and within that radius. Some assumptions need to be made about the falloff of matter density, and projection effects corrected, but these can be calculated and compared with observations to provide a self-consistent model.
Going through these steps, and also measuring the absolute brightness of the globular (which requires a distance measurement) allows something called a mass-to-light ratio for the globular to be determined. This is stated in terms of solar units, i.e., using the mass in relation to the Sun’s mass and the absolute brightness in relation to the Sun’s luminosity.
Typical mass-to-light ratios for most globulars are of order unity, say 1 or 2 or 3. This indicates little dark matter is present (we know the dark matter content of ordinary stars such as the Sun is low).
But now some possible dark matter-containing globular clusters have been found. To be more precise, some globular clusters with quite high mass-to-light ratios have been found around Centaurus A.
Centaurus A galaxy and globular clusters observed by the Very Large Telescope (ESO)
Centaurus A is a peculiar galaxy about 10 million light-years or so away, and is the fifth brightest galaxy in the sky by apparent magnitude. It is classified as a giant elliptical, or lenticular, galaxy with peculiar characteristics. It has a very prominent dust lane through the center as seen in the photograph above, and also possesses a large relativistic jet visible at radio and X-ray wavelengths. There is a black hole at the center of Centaurus A with a mass of over 50 million solar masses. Centaurus A may have as many as 2000 globular clusters.
A study of 125 of the brighter globular clusters in the Centaurus A galaxy, by Matthew Taylor and co-authors, was made at the European Southern Observatory’s Very Large Telescope in Chile. The locations of the globulars are indicated in the green, blue and red circles superimposed on Centaurus A’s image. A certain fraction of the globulars with masses above a million solar masses showed the characteristic that the mass-to-light ratio was abnormally high, and becomes higher nearly in proportion to the mass of the globular. This set of globulars is denoted in red circles in the image. The most massive of the red circle globulars have the highest mass-to-light ratios.
The authors find, quoting from their paper, “a distinct group of objects which require significant dark gravitating components such as central massive black holes and/or exotically concentrated dark matter distributions.” These objects have mass-to-light ratios above 6, and half a dozen have mass-to-light ratios over 15, including one object with a very high ratio of 67.
Several explanations are proposed. One is rotation of the globulars in question, but the authors are able to rule this explanation out since the stability of the cluster would be destroyed. Another is massive black holes in the centers of these globulars. This would require black holes with masses in the range 40,000 to over 1 million solar masses, and would be quite an exciting finding in its own right. There is evidence for intermediate mass black holes in a few other globular clusters found in the Milky Way and other galaxies. An additional possibility is the accumulation of many smaller stellar-sized black holes and/or neutron stars in the center of the cluster that would modify the cluster’s dynamical properties.
Yet another possibility is the presence of significant dark matter. If verified there would be important implications for globular cluster formation histories. This study should lead to a rush for other observations to ferret out high mass-to-light ratio globular clusters and to allow astronomers to distinguish between the black hole, dark stellar remnant, and dark matter possible scenarios.
Already there is a Wikipedia entry for “dark globular clusters”.
grams up to about 3 times the Earth’s mass. 
gm (smaller ones have evaporated already) up to 
gm as well, as the source of most dark matter. And it is because of the Hawking radiation that we do not detect.
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.)
or 
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.
grams and up to about 
up to 
Joules of energy, released in 0.2 seconds, or an average of 
during that interval. You know, a Tera Tera Tera Terawatt.
Dark Matter, Dark Energy, Dark Gravity 