# Boötes Void numbers, 2016

As a general science (hence Wikipedia!) reader, the latest information I have is that 60 galaxies "have been found and counted" inside the Boötes void, this of 1997.

(1) What is the latest count of galaxies "known" inside the Boötes void?

The Boötes void is a ball 250 million light-years across. (Say, .002 of the width of the visible universe?) It seems - unbelievable - it has only 60 galaxies.

The "60" value (or some new number since 1997), maybe I am misunderstanding it, or it is misreported, or has a different meaning? Galaxies are counted in the thousands or tens of thousands, it seems hard to believe in a cosmological space, the number "60" would come up.

So, what is (2) the thinking on how many galaxies there likely are in the Boötes Void? An order of magnitude. Is it "about 100," or "about a trillion," or what?

What do you (3) normally quote galaxy density in? Galaxies per Gpc3, or?

Indeed, I am trying to get a (4) comparative sense of galactic density in the Boötes void versus elsewhere. What is the galaxy density in the Boötes void, versus the universe in general, or if it's more meaningful versus perhaps superclusters, walls, or?

Is it "one tenth as dense"? One zillionth? One half? Just how void is that sucker?

Further...

BruceS below has usefully pointed out that, indeed, the "60" galaxies are anyway only in a small tube which apparently cuts through the Boötes Void.

Does this mean that, incredibly, the actual main body of the Boötes Void - putting aside that tube - is literally empty, no galaxies at all??

That seems totally incredible. I feel we really need a galaxy-counting astronomer to clarify the nature of the Boötes Void.

An ADS search on refereed astronomical papers including the words "Boötes Void" in the title returns only two papers in this millennium, in 2001 and 2002, and even these do not report any new data, but use data from the beginning of the 1990's. I can't find any newer references for the number density of galaxies in the Boötes Void in particular, but a typical value is roughly one-tenth of the average number density in the Universe.

## Theoretical approach

I previously answered the similar question of the number of galaxies in an overdensity. This answer is based on an anlytical fit to (observationally calibrated) simulations of galaxy halo formation, giving the so-called halo mass function, i.e. the number of galaxy halos per halo mass. The total number $N_\mathrm{gal}$ of galaxies in a volume $V$ can be expressed as $$N_\mathrm{gal} = n_\mathrm{gal} \times V \times \delta,$$ where $n_\mathrm{gal}$ is the average number density of galaxies in the Universe, and $\delta$ is the relative density in the volume. As I wrote in the other answer, $n_\mathrm{gal}$ is a number that impels you to define a lower threshold of galaxy size. The reason is that the lower you go, the more there are, and there is no formal threshold for how larger a clump of stars you need before you call it a galaxy. But as in the other answer, for the sake of this discussion we may use Small Magellanic Cloud-sized galaxies as our lower minimum. In that case, with $\delta\sim0.1$ and $V\sim236,\!000\,\mathrm{Mpc}^3$, the total number becomes $$N_\mathrm{gal,Böotes} = 0.17\,\mathrm{Mpc}^{-3} \, \times \, 236,\!000\,\mathrm{Mpc}^3 \, \times \, 0.1 \, \simeq \, 4000\,\mathrm{galaxies}.$$

Units of galaxy number density

The way I write this result also answers your question 3: Galaxy number densities are almost always written in $\mathrm{Mpc}^{-3}$. In theoretical/numerical work, you'll often see the factor $h^3$ in front of the unit. This is simply the Hubble constant divided by 100 (i.e. $h=0.7$ for $H_0 = 70\,\mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$), allowing people to compare results more easily without knowing the exact value of $H_0$.

## Observational approach

The observations of the Boötes Void are old, and seem to have been carried out on 1m-class telescopes. Hence, they won't be able to observe the smallest galaxies. In addition to telescope specifications, weather, etc., the exact detection limit (in terms of a limiting magnitude $m_\mathrm{lim}$) depends on how long they integrate (i.e. expose). Without reading the old papers in detail, I can't say what this is, but a typical value for such surveys would be, very approximately, $m_\mathrm{lim} \sim 20$ (if someone has a more realistic value than this, please edit). That is, objects fainter (i.e. larger values due to the backward astronomical system) than $m=20$ would be missed.

The distance to the Boötes Void implies a distance modulus of $\mu\sim37$, so the minimum absolute magnitude is $$M_\mathrm{lim} = m_\mathrm{lim} - \mu \simeq -17,$$ which is somewhere between the Small and the Large Magellanic Cloud.

The figure below (from Wyder et al. 2005) shows the local-Universe luminosity function for UV-selected galaxies. That is, it shows the number density of galaxies at a given magnitude. For instance, it shows (with the green dashed line) that the number density (here called $\Phi$) of galaxies with magnitudes around $M=-17$ is roughly $10^{-2.5}\sim0.003\,\mathrm{Mpc}^{-3}\,\mathrm{mag}^{-1}$.

Integrating over magnitudes from the $M=-17$ doesn't change the 0.003 much, since the density of brighter galaxies quckly declines. I get 0.004, i.e. the number density of galaxies at least as bright as $M=-17$ is $0.004\,\mathrm{Mpc}^{-3}$, smaller than the theoretical result above by 1.5 orders of magnitude. Multiplying this by the volume $V$ and the relative density $\delta$ yields $N_\mathrm{gal,Böotes} \simeq 100$ galaxies, not far from the 60 you quote.

To conclude, the number 60 seems in rough accordance with what is expected observationally, but theoretically, we'd expect there to be many more galaxies (although they're very small).

Location of the galaxies

They detected galaxies seem to be lying in a "tube" extending across the void. In general, galaxies and the underlying dark matter mass field tend not to be evenly distributed, but to form knots, sheets and filaments, separated by voids. My guess is that this "tube" is such a filament. Outside this filament, the void is voidier, but not completely void. There will still be galaxies, although few and small.

• Wait - tbc 0.17 Mpc-3 is indeed "typical galactic density of the universe" {at the "Small Magellanic Cloud" metric level}, is that right? Thanks for this! – Fattie Jun 6 '16 at 13:03
• Thanks again for this. Is brilliant. My immediate question: I'm bamboozled by the "60" figure. If there's on the order of 4000 galaxies "in the Boötes Void", it seems to me nonsensical, on a number of levels, that "60" were found, and indeed, apparently those 60 happened to be "in the tube". If we interpret "the tube" as indeed an overdensity amongst the 4000 - something is confused. {Or, is the idea that the BV is utterly empty, except for, 4000 in a tube?} {Indeed, is it actually correct that the 60 are "in the tube", or is this some misquote along the way?} – Fattie Jun 6 '16 at 13:08
• @JoeBlow: The 0.17 Mpc$^{-3}$ was calculated under certain assumptions, e.g. the cosmological parameters. Observational constraints on the number are challinging, since all observations probe only a subset of galaxies corresponding to the selection criteria. But I'd say that the 0.17 is a good estimate. – pela Jun 6 '16 at 14:36
• But since the void is so far away, you won't be able to see so small galaxies as the SMC, only the brighter ones. As far as I can see, the detected galaxies actually lie in a "tube". It is probably a filament extending across the void, hosting the largest galaxies which are then the only ones we can see. – pela Jun 6 '16 at 14:37
• As far as I can see, all the places that quote "a few hundred billion galaxies" all point to an extrapolation to the full sky of observational number counts in the Hubble Ultra Deep Field's small patch of the sky. But since this is flux-limited, it will miss the smallest galaxies. This article discusses exactly this — and says that taking into account the galaxies that Hubble can't see, the number may be closer to $10^{12}$. – pela Jun 7 '16 at 7:22

First, notice that the distribution of galaxies in the universe is not uniform. Not only they are located mostly along filaments or walls, but also the density among them varies.

So far 60 (up to 2013 http://asd.gsfc.nasa.gov/blueshift/index.php/2013/07/30/jasons-blog-next-stop-voids/) galaxies have been discovered in the Boötes Void and all of those are found in a tube shape running through the void. If we are to use a rough estimate of about 1 galaxy every 10 million light years (4 times farther than Andromeda) there should be approximately 2,000 galaxies in the Boötes Void. So a good order of magnitude estimate would be that the galaxy density is about 3% that of a "typical" region.

• Just BTW. If a 3D space is 250 units, and there is a dot every 10 units, it would contain around 20,000 dots (not 2,000). (It could be the 2000 in the answer refers to "just the tube".) – Fattie Jun 6 '16 at 11:40
• Note that the linked blog post (which was written in 2013) seems to just quote the ancient, 20-year old "60" figure from wikipedia; the odd "2000" calculation also comes from that blog post. It's difficult to believe that more galaxies haven't been "found and counted" since 1997. – Fattie Jun 6 '16 at 11:53