<strong>Yes, for a given galaxy type…</strong>
<p>The term &quot;a distribution of number of galaxies per redshift interval&quot; <em>does</em> make sense, but usally we restrict ourselves to a certain type of galaxies, e.g. <a href="https://en.wikipedia.org/wiki/Lyman-alpha_emitter" rel="nofollow noreferrer">Lyman <span class="math-container">$\alpha$</span> emitters</a>, <a href="https://en.wikipedia.org/wiki/Lyman-break_galaxy" rel="nofollow noreferrer">Lyman break galaxies</a>, <a href="https://en.wikipedia.org/wiki/Submillimetre_astronomy" rel="nofollow noreferrer">sub-mm galaxies</a>, etc. The reason is that galaxies are detected in a number of different ways, and no single selection technique captures all types of galaxies.</p>
<strong>…and <em>comoving</em> volume…</strong>
<p>Because the Universe is expanding with time, the &quot;true&quot; (physical) number density of galaxies — and everything else (except dark energy) — decreases with time. To be able to compare densities at different times, it is useful to measure them in <a href="https://en.wikipedia.org/wiki/Comoving_distance" rel="nofollow noreferrer">comoving coordinates</a>, which is the coordinates that expand along with the Universe. In these coordinates, densities only change if some physical process happen. For instance, the  physical <em>energy</em> density of photons decreases both because the volume of the Universe increases <em>and</em> because the photons redshift. In comoving coordinates it <em>also</em> decreases, but only due to the redshifting since the volume change is factored out.</p>
<strong>…and luminosity.</strong>
<p>Moreover, since galaxies have no well-defined lower size/mass/luminosity threshold, we have to define a threshold above which we count them.
For this reason, rather than talking about &quot;the number density of galaxies per redshift&quot;, we usually use the very useful observable <a href="https://en.wikipedia.org/wiki/Luminosity_function_%28astronomy%29" rel="nofollow noreferrer">luminosity function</a> (LF) which measures the number of (a certain type of) galaxies <em>per luminosity bin</em>, and per comoving volume, at a given redshift.</p>
<p>LFs have been probed out to very high redshifts, at the times when galaxies were just beginning to form at <span class="math-container">$\sim$</span>half a gigayear after Big Bang (e.g. <a href="http://arxiv.org/abs/1212.4819" rel="nofollow noreferrer">Schenker et al. 2013</a>).</p>
<p>You end your question by asking about the number of galaxies at <span class="math-container">$z\le0.01$</span>, which would be considered very low redshift in the context of galaxies. You can find the answer by considering all kinds of selection criteria, checking for overlaps between surveys (most local galaxies will be detected by multiple techniques), and integrating over volume the LFs down to your chosen threshold (e.g. Small Magellanic Cloud-sized). Doable, but not trivial. An alternative is to integrate numerically calculated dark matter halo mass functions, using e.g. <a href="http://hmf.icrar.org/" rel="nofollow noreferrer">this online tool</a>, and assuming the every halo hosts a galaxy. I get a number density of <span class="math-container">$n\sim0.4$</span> halos per <span class="math-container">$h^{-3}\,\mathrm{Mpc}^{3}$</span>, or <span class="math-container">$1.2\,\mathrm{Mpc}^{-1}$</span>. The comoving volume out to <span class="math-container">$z=0.01$</span> is <span class="math-container">$V=3.3\times10^5$</span> Mpc, so the total number of (super-SMC-sized) galaxies is <span class="math-container">$N = n V \simeq 3.8\times10^5$</span>.</p>

CC BY-SA 3.0
2016-01-04T22:22:05.460Z
2017-09-06T07:23:16.597Z
2020-06-17T09:47:40.653Z
pela
<p>Does exist something like a distribution of number of galaxies per redshift interval? I'm studying galaxy formation and evolution, and I'm curious to know how many todays' galaxies (with redshift &lt;0.01 I would say) we see.</p>

<galaxy><redshift>
Number of galaxies per redshift
Federico Esposito
# Number of galaxies per redshift

(Asked by: username_0 on 2016-01-04)

Does exist something like a distribution of number of galaxies per redshift interval? I'm studying galaxy formation and evolution, and I'm curious to know how many todays' galaxies (with redshift <0.01 I would say) we see.

**Tags:** galaxy, redshift


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## 1 answers

### Answer by username_1 on 2016-01-04. Score: 5 | Accepted answer

**Yes, for a given galaxy type…**

The term "a distribution of number of galaxies per redshift interval" *does* make sense, but usally we restrict ourselves to a certain type of galaxies, e.g. [Lyman $\alpha$ emitters](https://en.wikipedia.org/wiki/Lyman-alpha_emitter), [Lyman break galaxies](https://en.wikipedia.org/wiki/Lyman-break_galaxy), [sub-mm galaxies](https://en.wikipedia.org/wiki/Submillimetre_astronomy), etc. The reason is that galaxies are detected in a number of different ways, and no single selection technique captures all types of galaxies.

**…and *comoving* volume…**

Because the Universe is expanding with time, the "true" (physical) number density of galaxies — and everything else (except dark energy) — decreases with time. To be able to compare densities at different times, it is useful to measure them in [comoving coordinates](https://en.wikipedia.org/wiki/Comoving_distance), which is the coordinates that expand along with the Universe. In these coordinates, densities only change if some physical process happen. For instance, the physical *energy* density of photons decreases both because the volume of the Universe increases *and* because the photons redshift. In comoving coordinates it *also* decreases, but only due to the redshifting since the volume change is factored out.

**…and luminosity.**

Moreover, since galaxies have no well-defined lower size/mass/luminosity threshold, we have to define a threshold above which we count them.
For this reason, rather than talking about "the number density of galaxies per redshift", we usually use the very useful observable [luminosity function](https://en.wikipedia.org/wiki/Luminosity_function_%28astronomy%29) (LF) which measures the number of (a certain type of) galaxies *per luminosity bin*, and per comoving volume, at a given redshift.

LFs have been probed out to very high redshifts, at the times when galaxies were just beginning to form at $\sim$half a gigayear after Big Bang (e.g. [Schenker et al. 2013](http://arxiv.org/abs/1212.4819)).

You end your question by asking about the number of galaxies at $z\le0.01$, which would be considered very low redshift in the context of galaxies. You can find the answer by considering all kinds of selection criteria, checking for overlaps between surveys (most local galaxies will be detected by multiple techniques), and integrating over volume the LFs down to your chosen threshold (e.g. Small Magellanic Cloud-sized). Doable, but not trivial. An alternative is to integrate numerically calculated dark matter halo mass functions, using e.g. [this online tool](http://hmf.icrar.org/), and assuming the every halo hosts a galaxy. I get a number density of $n\sim0.4$ halos per $h^{-3}\,\mathrm{Mpc}^{3}$, or $1.2\,\mathrm{Mpc}^{-1}$. The comoving volume out to $z=0.01$ is $V=3.3\times10^5$ Mpc, so the total number of (super-SMC-sized) galaxies is $N = n V \simeq 3.8\times10^5$.


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