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I was wondering how many Ultra-massive black holes can be added to the list of 8 known black holes with mass over 10 billion solar masses within 1 billion light years.

Looking at our current maps, the main super and ultra massive black holes are located on almost opposite sides of the sky where matter is grouped in superclusters or along filaments with further out massive black holes being on the other sides of our surrounding voids, so the locations of where or if I will add new massive black holes isn't an issue but how many more to add is what I am unsure of.

Denser areas seem to be where the largest black holes and their galaxies are located but some are isolated as their galaxy has merged with or thrown out their neighbour galaxies.

An interested video I watched recently was about "Shadow galaxies". These are very large but dim galaxies that have remained un noticed until recently, as there has been no interactions for these galaxies with others due to their isolation they have not had new starburst stages so they remain very dim and full of ancient and relic stars. It is believed at least 25% of our galaxies are this type of galaxy.

There are estimations of how many super massive black holes can exist in the universe by looking at how many stars of higher mass capable of dying and turning into a supermassive black hole but ultra massive black holes are generally thought due to many galactic mergers.

Using 8 as the current known value and as we have many known large galaxies who's nucleus is too bright to estimate the mass of their central black hole and as we have many more local galaxies to observe, What would be a good true number of ultra massive black holes over 10 billion solar masses to be considered when making a map of local universe within 1 billion light-years?

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The true number of ultramassive black holes

Natarajan & Treister 2008, when exploring the mass distribution of very massive black holes, determined from x-ray emissions of populations of active galactic nuclei (AGN) that over cosmological distances, the mean ultramassive black hole density should be at least $\sim3\times10^{-6}$ per cubic megaparsec. If we simply multiple this by your desired volume, we find that a sphere 1 billion light-years in radius should host $$N=3\times10^{-6}\;\text{Mpc}^{-3}\times\frac{4\pi}{3}(10^6\;\text{light-years})^3\approx360\;\text{UMBHs}$$ This is two or three orders of magnitude higher than Nip Dip's estimate. Note that UMBHs are expected to be rarer in the local universe, i.e. at lower redshifts and much closer to the Milky Way than gigaparsec distances. Locally, the authors derive a density of $\sim7\times10^{-7}$ per cubic megaparsec.

I should also note that the authors describe their density as a "conservative" estimate based on predictions of supermassive black hole accretion rates. On the other hand, it's possible that they overestimated the behavior of high-mass UMBHs, but they claim that this is unlikely.

The number of ultramassive black holes on your map

Now, how many UMBHs should you include on your map? Well, it could be all of them, if you want. An omnipotent civilization capable of traveling far enough to need such a big map might very well have found and mapped all of these ultramassive black holes. On the other hand, keep in mind that this encompasses an area 2 billion light-years in diameter. That's a lot of space! In reality, it's unlikely that the mapmakers will have found all of them. So you have some leeway; you could put only 100 or 200, and make it clear that the map only includes known UMBHs.

The distribution of ultramassive black hole masses

It seems that SMBH and UMBH masses follows a double power law. The point where the mass distribution breaks from one of those power laws to the other appears to happen around a mass of $M_{\text{BH}}\approx10^{8.5}$, at which point it dips sharply. Here's a plot from Natarajan & Treister, showing the quantity $M_{\text{BH}}\frac{dN}{dM_{\text{BH}}}$ as a function of black hole mass, with four different curves representing the distribution from galactic velocity distributions (solid line) and three different values of accretion efficiency (dotted lines, $\epsilon=0.1, 0.05, 0.5$):

Plot of UMBH mass distributions

I did a little bit of playing around, and eyeballed a fit to a double power law distribution over the entire mass range the authors considered ($10^6M_{\odot}<M_{\text{BH}}<10^{10}M_{\odot}$). The result looks like $$M_{\text{BH}}\frac{dN}{dM_{\text{BH}}}=\frac{1}{\left(f_{\text{low}}(M_{\text{BH}})^{-1/\alpha}+f_{\text{high}}(M_{\text{BH}})^{-1/\alpha}\right)^{\alpha}}$$ where $$f_{\text{low}}(M_{\text{BH}})=0.03\left(\frac{M_{\text{BH}}}{10^6M_{\odot}}\right)^{-0.44},\quad f_{\text{high}}(M_{\text{BH}})=10^{-8}\left(\frac{M_{\text{BH}}}{10^{9.78}M_{\odot}}\right)^{-9}$$ and $\alpha=4$.

Plot of my fit to the SMBH and UMBH mass distribution

From this, you can find $\frac{dN}{dM_{\text{BH}}}$ and then numerically integrate to find the fraction of UMBHs that lie in a given range.

Miscellaneous notes

There are a couple of other points I wanted to mention.

  • Supermassive black holes never result from the collapse of a single star. Astronomers are divided between the top-down (the collapse of a very massive primordial cloud) and bottom-up (the coalescence of smaller black holes) models, but even in the early universe, you couldn't find stars a million times the mass of the Sun!
  • I'd be surprised if there are many cases where a galactic nucleus is dominated by emission not caused by the central supermassive black hole. LINERs may be a counterexample, if the intense emission is due to star formation, but that would presumably be an edge case.
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    $\begingroup$ Brilliant, thank you. Is the 360 UMBH for over 1 million solar masses as you mentioned earlier or is it for billions of solar masses black hole? $\endgroup$
    – user78658
    Aug 29 '20 at 17:37
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    $\begingroup$ @Orochi Ah, it was just referring to the mass range of black holes the authors were studying; they used the same UMBH definition as you: at least $10^{10}M_{\odot}$. Sorry about that - I see that it was a bit confusing. $\endgroup$
    – HDE 226868
    Aug 29 '20 at 17:38
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    $\begingroup$ Oh wow, that helps. Do you think I can use the rough numbers we have already to come up with all their masses? For example we have 3 over 30 billion within that range and we estimate 50 to 250 billion being the highest natural mass possible (i have chose the less generous number of 50, i'm not sure if that is right) Do you think building the numbers off our known ratios make sense? $\endgroup$
    – user78658
    Aug 29 '20 at 17:56
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    $\begingroup$ @Orochi You likely could, with a bit of work. The paper doesn't do an excellent job of making the relevant information clear, though. $\endgroup$
    – HDE 226868
    Aug 29 '20 at 19:40
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I'd say somewhere between three and fifteen. After all, I think there is that number within 1 billion lightyears of the Sun. Holmberg 15A and NGC 1281 are good examples. But since you're worldbuilding, you could do any number, and even place an ultramassive black hole within your galaxy.

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    $\begingroup$ Are you saying to add between 3 and 15? any reason for those numbers or is it more of a safe guess? $\endgroup$
    – user78658
    Aug 29 '20 at 16:38
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    $\begingroup$ It's sort of a safe guess. The number of confirmed ultramassive black holes within 1 billion lightyears of the solar system is near the lower estimate though. $\endgroup$
    – Nip Dip
    Aug 29 '20 at 16:41
  • $\begingroup$ Ok thanks, I did have a number for made up UMBH's that needed to be added which included ones located in voids, shadow galaxies and galaxies we cant see inside and it was around your higher number, I just wasnt sure if mass distribution in the universe and possible merger volumes would allow those numbers. $\endgroup$
    – user78658
    Aug 29 '20 at 16:55

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