What fraction of the matter in the universe is in black holes?

[ohwilleke]

Conceptually, at least, this is a simple question, although I recognize that it might be hard to calculate in practice from available data.

The matter-energy budget of the universe is measured (in a model dependent way) to consist of a certain percentage of dark energy, a certain percentage of dark matter, and a certain percentage of ordinary matter.

Most of the ordinary matter is made up of stars and interstellar gas with a smidgen of planets, asteroids, comets, and neutrinos thrown in for good measure. Some of that ordinary matter is in the form of black holes. Photons also contribute slightly to the total.

(Black holes also gobble up dark matter like everything else and also dark energy if it is "stuff" rather than a default curvature of space or something. In truth, I don't really know in the Standard Model of Cosmology which part of the matter-energy budget for the universe black holes are assigned to. I have assumed that they are part of the ordinary matter budget, but feel free to correct me if this assumption is wrong.)

What estimates exist of the proportion of ordinary matter (or all matter or all matter-energy in the universe) that is in the form of black holes at this moment in time?

As I understand the matter, there is reasonably reliable estimates of how many galaxies of various types there are in the universe, and galaxies of each type of characteristic sized central supermassive black holes. So, estimating the share of the mass of the universe that is in the form of supermassive black holes shouldn't be an overwhelming task and surely someone has done that.

Stellar sized black holes have also been observed, and those observations ought to be capable of being converted into estimates of the number of stellar sized black holes in the universe, although probably with bigger error bars. I have no idea how the estimated mass of stellar black holes in the aggregate compares to the aggregate mass of supermassive black holes. I would think that someone has also estimated this in the scholarly literature.

This source suggests that the proportion of ordinary matter than is in the form of supermassive black holes or stellar sized black holes is about 11/10,000, but I have a hard time evaluating its credibility, and it doesn't consider two other possible kinds of black holes.

Even if the estimate for supermassive black hole mass (1/10,000th of the total galaxy mass) is order of magnitude correct (and that estimate really needs to be confirmed with better data), the estimate for the mass of stellar black holes must be too low.

This is true first, because even if 1/1000th of star mass is fated to end up as a stellar black hole based upon the size and type of the star, every stellar black hole will gobble up some mass including mass from other stars that were not on track to collapse into stellar black holes.

This is also true because some stars that are not fated to collapse into stellar black holes will nova, and some of the ejected material will either go directly into a black hole or will go into a star that is the right size and type to collapse into a stellar black hole eventually.

LIGO has shown us that there are also intermediate sized black holes out there, which hadn't been observed before even though almost all theories said that they had to exist. The error bars on how many of those there are in the universe is probably going to get much smaller as LIGO accumulates data, but surely there must be some theoretical estimates that exist already to get from stellar black holes to supermassive ones, and some of those theoretical estimates must be consistent with LIGO measurements to date even though that is a quite small data set so far.

If you make the assumption that supermassive black holes star as stellar black holes that merge until they become supermassive black holes, that alone bounds the potential aggregate mass of intermediate sized black holes, and we have decent estimates at both ends.

Some theorists think that there are sub-stellar sized primordial black holes as well. And, the theories that suppose that they exist seem very well suited to estimating their aggregate mass at any particular time in the history of the universe. Efforts to determine in primordial black holes could be dark matter from various kinds of observations have put some serious bounds on how much mass in the universe can be in that form.

BONUS: Has anyone estimated the change in the proportion of ordinary matter that is in the form of black holes over the history of the universe? And, if so what are those findings?

With very weak assumptions, the proportion of ordinary matter in the form of black holes will always rise over time. One need only assume that the aggregate mass of black hole matter due to existing black holes absorbing matter, and due to stars collapsing into black holes, is greater than the amount of new matter condensed out of radiation or other forms of energy, and this is almost surely true for the vast majority of the history of the universe (although the amount of primordial black hole mass could fall and balance that out somewhat due to Hawking radiation).

But, beyond that assumption it gets tricky. If lots of stars are formed at around the same time, there should be peaks and valleys in black hole formation from star collapse since stars that can collapse into black holes tend to have similar lifetimes.

Also, as the universe expands, matter is more spread out, so the average amount of matter near black holes that they can swallow up should fall over time. But, the fall shouldn't be as fast as in an analog to the ideal gas formula, because matter has clumped up as the universe has evolved with filaments of matter causing average distance from a black hole to other matter to fall much more slowly than the average mass per volume of space in the universe. Likewise, average distance from a black hole to other matter falls much more slowly in the core of a galaxy than in its periphery.

But, a black holes eat up the closest matter to them, the stream of matter into them should slow down because the "low hanging fruit" has already been eaten up.

 

[phinds]

This source suggests that the proportion of ordinary matter than is in the form of supermassive black holes or stellar sized black holes is about 11/10,000, but I have a hard time evaluating its credibility, and it doesn't consider two other possible kinds of black holes.

I was surprised to see that low a number since I was under the impression that the SMBH's at the heart of galaxies generally constituted 1% to 2% of the mass of the galaxy, BUT ... he's likely to know way more about this than I do and his estimates seem reasonable, based on his statement about the ratio of SMBH's to galaxies. I must be seriously mis-remembering what I've read about SMBH/galaxy ratios.

 

[kimbyd]

I was surprised to see that low a number since I was under the impression that the SMBH's at the heart of galaxies generally constituted 1% to 2% of the mass of the galaxy, BUT ... he's likely to know way more about this than I do and his estimates seem reasonable, based on his statement about the ratio of SMBH's to galaxies. I must be seriously mis-remembering what I've read about SMBH/galaxy ratios.

I think it's partially because most normal matter hasn't collapsed into galaxies. I think galaxies make up only about 10% of the normal matter.

Also, while there are some galaxies with truly massive SMBHs, most have quite small ones, such as our own Milky Way, whose SMBH has about 4 million solar masses, compared to a total galaxy mass of 600 billion solar masses.

 

[ohwilleke]

Also relevant (suggesting 10s of thousand of black holes swarming around the SMBH at the center of the Milky Way.

Charles J. Hailey, Kaya Mori, Franz E. Bauer, Michael E. Berkowitz, Jaesub Hong, Benjamin J. Hord. A density cusp of quiescent X-ray binaries in the central parsec of the Galaxy. Nature, 2018; 556 (7699): 70 DOI: 10.1038/nature25029

 

[Chronos]

Fraser Cain appears to agree the number is pretty small as discussed here https://www.universetoday.com/112500/how-much-of-the-universe-is-black-holes/.

 

[ohwilleke]

Fraser Cain appears to agree the number is pretty small as discussed here https://www.universetoday.com/112500/how-much-of-the-universe-is-black-holes/.

This is the article linked in the original post on this thread.

 

[JMz]

every stellar black hole will gobble up some mass including mass from other stars that were not on track to collapse into stellar black holes

I think you are placing far too much weight (so to speak) on this effect:

1. Most stars don't form BH's. This conversation works through some research to estimate ~ 4e-6 as the fraction of stars that are massive enough, or perhaps 4e-5 of the mass. (In fact, those are massive enough for supernovae, but many SNs don't form BHs, so even this tiny fraction is an over-estimate.)
   
2. Stars are so widely separated (roughly 1 per cubic light year) that, when one forms a BH, it typically has no nearby neighbors, nor any significant gas, to "gobble up".
   
3. Even if it's part of a binary system, most binaries aren't tight ones where the companion will "care" whether the primary turns into a BH. (E.g., for α Centauri, the pair never get closer than the Sun-Saturn distance, 11 AU. Even if the "A" component turned into a BH [which it won't], B's orbit wouldn't change, and even in its red-giant phase, B's outer atmosphere won't extend anywhere near A, not even as much as 1 AU closer than B's center does.)
   
4. And even if it's part of a tight binary system, it's going to gobble up only part of its companion, strictly less than a factor of two in its total mass. (That's because the BH is going to form first in whichever star is more massive.)

 

[ohwilleke]

I think you are placing far too much weight (so to speak) on this effect

I don't have a good intuition of the magnitude of these effects, only their direction. Basically, all of the estimates that I've seen are operating at the spherical cow level of approximation and I'm pretty comfortable that it would be possible do be much more accurate with only fairly modest research and calculation effort. I would think that a team of four post-docs working on the question for a year ought to be able to pin it down to perhaps +/- 10% or less with a high degree of confidence using very reliable and data rich methods.

While I don't have a good intuition for the magnitude of the potential factors, if an effect can only move in one direction as proportion of matter that is in black holes does, even very modest effects can add up over 13 billion plus years, so it makes sense to really be careful in evaluating every possibility. A very slow and infrequent process can easily make a factor of 2-4 difference over billions of years when the base number is already so small, and quantifying the frequency of very slow and infrequent processes is very difficult to do via direct measurement. That may be the difference between 0.2% and 0.6%, perhaps, but that's not nothing.

The annual percentage growth you need to double in mass over a billion years is really, really small (although the rule of 72 does not apply for numbers that extreme and is instead approximately linear at such a great extreme), specifically, about 0.7 parts per billion per year. Certainly, anything that causes mass growth at an average rate of one part per billion per year (about 4 * 10^21 kg per year for a small stellar black hole, which is less than five times the mass of dwarf planet Ceres) needs to be carefully considered. And, over 13 billion years, effects of less than one doubling per billion years can still be quite material, so the relevant threshold is quite a bit lower than that, more like 5* 10^17 kg per year, a bit bigger than asteroid Ida but smaller than asteroid Siwa). So it is easy to miss a potentially relevant effect.

In a spiral galaxy, stars at the core are closer to each other than those in the fringes, so an average distance between stars may not be a very accurate predictor, you'd really be more interested in knowing what percent are at a distance less than X at which the possibility of collision or formation of a gravitationally bound system is high and that percentage, even if only 1-5% say, that percentage might be quite a bit higher than what you would suspect making estimates of collision likelihood based upon mean distances even with a Gaussian distribution of distances around the mean. This would be of a piece with evidence that there are more black holes in the core of galaxies than in the fringes.

Also, the chance of stars absorbing substantial mass from other objects is probably greatest before a galaxy system is in equilibrium or when galaxies collider with each other, for example. A typical intermediate sized black hole, for example, might have a very punctuated history of mass acquisition with billions of years at a time of negligible change, in between several brief (by cosmological standards) periods of rapid mass acquisition when the gravitationally bound system that it is a part of goes out of equilibrium for some reason, leading to collisions of massive bodies.

I would think that indirect measurements - like inferring what sort of merger history you'd need to get the presently observed collection of supermassive black holes, are probably going to be more accurate than trying to estimate the numbers directly. The fact that we hadn't observed a single intermediate sized black hole ever until LIGO came on line, and now have observed not just several intermediate sized black holes, but several of them merging (which implies that this is the tip of the iceberg and that there must be far more that aren't merging and hence aren't seen by LIGO), at pretty modest distances from Earth as distances in the universe go, in just a few years, suggests to me that we may know less than we think we do about how many black holes there are out there. I'm not suggesting that intermediate size black holes make up 10% of the matter in the universe or anything like that, but intermediate sized black holes might very well be contributing more to the aggregate mass in black holes than supermassive ones do, and might be on the same order of magnitude or even a little bit more than the total population of stellar black holes. Whether that number is 0.02% or 0.1% or 0.3% of the matter in the universe has a pretty material effect on the total percentage of mass in the universe that is in black holes, given how low first order of magnitude estimates based upon direct collapse of stars into stellar black holes and supermassive black holes is to start with.

But, in principle, it doesn't seem like it would be so impossible to actually run numbers for a plausible merger history to produce the population of known supermassive black holes to get a much, much more accurate estimate of how much mass should be in intermediate sized black holes. Another useful endeavor might be to estimate how many intermediate black holes exist in the aggregate based upon the number of collisions that are observed by LIGO and other gravity wave detectors - figuring out how much total mass the observed tip of the iceberg implies does not seem like an impossibly ambitious enterprise.

I also haven't seen any really careful analyses of how much dark matter ends up in black holes, but, one often sees it described as interstellar matter streaming through many solar systems in a galaxy over time, rather than being rather static, and if this is the case, black holes should be absorbing a fairly steady flux of dark matter every single year. I don't have a good intuition of how that compares to the total volume of inferred dark matter (because a lot of dark matter is inferred to be in locations with dark matter halos that are far from any stars at all), but, in principle, it should be too hard to figure out by what percentage an average black hole grows every year by absorbing part of the passing flux of dark matter in its vicinity. In any given year, this has to be a tiny percentage of the total mass of a black hole. But, multiply that by a billion and maybe it adds up to something appreciable. I wouldn't be surprised to learn that a mature intermediate sized black hole has gained 20%-50% of its mass from absorbing dark matter (assuming that dark matter particles exist).

Similar estimates could be made for the mass-energy gain that a black hole receives from absorbing photons at various frequencies. Again, a small number no doubt, but not necessarily so small that it can be ignored until somebody has made a serious attempt to calculate it. The numbers I've seen for photon absorption by black holes suggest that even this tiny influx of mass-energy is sufficient to clearly exceed mass losses due to Hawking radiation for all stellar sized or larger black holes in the current universe.

Also, in addition to the actual percentage at any given time, I'm quite interested in the rate of change over time. On one hand, you have a percentage that is constantly increasing, but the rate of increase should be getting smaller with time as the expanding universe, in general, increases the average distance between masses and decreases the likelihood of events like colliding galaxies, and as local matter in the vicinity of existing black holes is exhausted. This is a classic asymptotic function. But, on the other hand, it can take billions of years for a star on a long term path towards a collapse into a black hole to get there, so to get the percentage change right you need to know something about how many stars of the right size were being formed X billion years earlier, so there might be pulses up and down around a purely asymptotic trend.

 

[JMz]

The title of this OP is in the present tense. It is true that, over (enormously) long periods of time, more mass will be added to BHs. But (1) cosmological measurements say that not much of the mass has been in BHs over most of the universe's history so far, and (2) astrophysical measurements and theory say that rather little has been going into BHs in more recent eons. So in the present tense, the title's answer is, "not much". In fact, probably much less than 1%.

 

[ohwilleke]

I think it's partially because most normal matter hasn't collapsed into galaxies. I think galaxies make up only about 10% of the normal matter.

Do you have a reference for that?

That percentage is lower than I had thought and I don't recall seeing the percentage of matter that is in galaxies ever states one way or the other in so many words.

 

[Chronos]

In theory, black holes come in 3 basic flavors - primordial, supermassive and stellar mass black holes. For purposes of this discussion, intermediate mass black holes will be considered a subset of stellar mass black holes. The first two categories can be fairly well accounted for with existing technology. The abundance of primordial black holes is constrained by the gamma ray background as discussed here; https://arxiv.org/abs/1612.07738. Planck Constraint on Relic Primordial Black Holes. The contribution by supermassive black holes is constrained by velocity dispersion measurements [m sigma ratio] and quasar formation models as discussed here; https://arxiv.org/abs/astro-ph/0311008, High redshift quasars and the supermassive black hole mass budget, constraints on quasar formation models. Stellar black hole mass contributions are the most difficult to constrain. We can safely rule them out as the principle component of the dark matter mass fraction, but, more stringent constraints are imposed by the low abundance of qualified progenitor stars.

 

[JMz]

more stringent constraints are imposed by the low abundance of qualified progenitor stars.

Exactly. That's the "4e-6" estimated fraction in This conversation. Most of the mass in any generation of stars goes into stars that will never evolve into BHs or be "eaten" by binary companions that turn into BHs.

 

[kimbyd]

Do you have a reference for that?

That percentage is lower than I had thought and I don't recall seeing the percentage of matter that is in galaxies ever states one way or the other in so many words.

I drew it from observations of the gas mass fraction in galaxy clusters. Here's one example:
https://arxiv.org/abs/1406.3709

The gas mass fraction appears to range from about 8% to about 12%.

The full picture is substantially more complicated than this, however, as only a minority of galaxies are in galaxy clusters. The warm-hot intergalactic medium (https://en.wikipedia.org/wiki/Warm–hot_intergalactic_medium) is a gas which comprises roughly half of the normal matter, spread diffusely across the observable universe.

Overall, think of the 10% number I floated as an extremely rough estimate in a very complex system, and the true number could be pretty substantially different.

 

[JMz]

only a minority of galaxies are in galaxy clusters

I assume you meant only a minority of the gas fraction? (My understanding is that truly isolated galaxies are rare -- though I recognize that there could be a strong selection effect there.)

 

[kimbyd]

I assume you meant only a minority of the gas fraction? (My understanding is that truly isolated galaxies are rare -- though I recognize that there could be a strong selection effect there.)

No, I did mean galaxies. Most galaxies are not in clusters at all. For instance, our own Milky Way is not in a galaxy cluster. At most it's in a galaxy pair with the Andromeda galaxy, with which it will eventually collide. If you included the dwarf galaxies around our two galaxies, you'd have a few more members (known as the Local Group), but ultimately this structure is tiny compared to a galaxy cluster, which is typically considered to be a grouping of more than a hundred galaxies.

Our galaxy is a part of the Virgo supercluster, which is a much more diffuse object than a galaxy cluster would be considered to be.

The key differentiator that matters for this discussion is the existence of a hot cluster gas. Galaxy clusters are large overdensities of matter in which there is a gravitational well so deep that when the intergalactic medium falls into the cluster, it heats up to x-ray temperatures. The ratio of mass between the normal matter in the galaxies of the cluster and this hot x-ray gas is the 10% I was referring to. Most galaxies do not exist in such deep potential wells that a hot x-ray gas forms.

 

[JMz]

No, I did mean galaxies. Most galaxies are not in clusters at all. For instance, our own Milky Way is not in a galaxy cluster. At most it's in a galaxy pair with the Andromeda galaxy, with which it will eventually collide. If you included the dwarf galaxies around our two galaxies, you'd have a few more members (known as the Local Group), but ultimately this structure is tiny compared to a galaxy cluster, which is typically considered to be a grouping of more than a hundred galaxies.

Our galaxy is a part of the Virgo supercluster, which is a much more diffuse object than a galaxy cluster would be considered to be.

The key differentiator that matters for this discussion is the existence of a hot cluster gas. Galaxy clusters are large overdensities of matter in which there is a gravitational well so deep that when the intergalactic medium falls into the cluster, it heats up to x-ray temperatures. The ratio of mass between the normal matter in the galaxies of the cluster and this hot x-ray gas is the 10% I was referring to. Most galaxies do not exist in such deep potential wells that a hot x-ray gas forms.

Ah, I see the distinction you are making. Quite right: Although the MW & M31 are not isolated, a cluster defined that way[*] is quite different from the Local Group. (Hey, doesn't Triangulum get any respect?) That hot gas is indeed massive, and it's specific to clusters.
* I.e., as the appropriate term of art. I misunderstood you, having thought you were using the term more informally.

BTW, this is a particularly well reasoned explanation, IMO.