<p>The article references a paper by Huo et al. (2004; that's the reference number "33" in your quoted text). Huo et al. merely list a redshift of "0.0103" for Arp 299 in their Table 1 (without any apparent sources); combined with the fact that the authors of the <i>Science</i> paper say what Hubble constant they assumed (73 km/s/Mpc), this tells us that the distance is redshift-based. That is, they used the redshift plus the Hubble constant to derive the (comoving) distance.</p>

<p>If you look up Arp 299 in the <a href="http://ned.ipac.caltech.edu" rel="noreferrer">NASA Extragalactic Database</a> and scroll down <a href="http://ned.ipac.caltech.edu/cgi-bin/objsearch?objname=arp%20299&amp;extend=no&amp;list_limit=5" rel="noreferrer">the resulting page</a>, you can see a list of possible redshifts ("Calculated and Corrected Velocities") for this galaxy, ranging from 3088 km/s (which is in fact $z = 0.0103$) to 3511 km/s. Immediately below that, you can see the derived distances ("Hubble Flow Distance"), assuming $H_0 = 73$, the same value the authors say they used. The closest number to their value is the 44.4 Mpc, assuming "3K CMB" correction (which seems to match the authors' description). Why this isn't exactly the same as the authors' value of 44.8 Mpc I don't know; possible a slightly different value of the redshift was used.</p>

<p>At this relatively small redshift, the differences between the different distances that pela mentions are pretty minor. E.g., plugging $z = 0.0108$ (NED's "3K CMB" corrected redshift) and $H_0 = 73$ into Ned Wright's cosmology calculator gives you a comoving distance of 44.2 Mpc, a luminosity distance of 44.7 Mpc, and an angular-diamter distance of 43.8 Mpc. The differences between these are all smaller than any plausible uncertainty based on using the redshift.[*]</p>

<p>So, to summarize, the distance in the paper is (as pela says) the comoving distance; the method used to derive it was the redshift of the galaxy (corrected to a CMB-relative value) plus a Hubble constant of 73 km/s/kpc.</p>

<p>[*] E.g., if we assume a redshift uncertainty of 300 km/s, based on possible peculiar motion of Arp 299, then the distances are uncertain by +/- 4 Mpc.</p>

CC BY-SA 4.0
2018-06-16T15:50:02.657Z
Redshift! I was looked by for a $z$ but didn’t find one. Thank you for solving this riddle!
Charles
CC BY-SA 4.0
2018-06-17T06:09:47.067Z
I found it surprising that reference 33 was supposedly to support the cited distance, but the paper by Huo et al is entirely unrelated to distance. Poor academic rigour.
Chappo Hasn't Forgotten
CC BY-SA 4.0
2018-06-16T10:59:32.280Z
2018-06-16T10:59:32.280Z
Peter Erwin
<p>It's the good old physical distance — also called <em>proper distance</em> — i.e. what you'd measure if you stopped the expansion of the Universe and patiently laid out meter sticks from us to Arp 299. It's also the <a href="https://en.wikipedia.org/wiki/Comoving_and_proper_distances" rel="nofollow noreferrer">comoving distance</a> — i.e. the distance measured in coordinates that expand with the Universe and hence don't change with time — since that distance is defined to coincide the physical distance today. </p>

<p><a href="https://en.wikipedia.org/wiki/Luminosity_distance" rel="nofollow noreferrer">Luminosity distances</a> are used mostly in relations between flux, magnitudes, and distances, and are rarely quoted as a distance without explicitly saying that it's the luminosity distance. This distance is defined such that it satisfies the inverse-square law, and takes into account the expansion of the Universe and the redshift of light.</p>

<p>The same goes for <a href="https://en.wikipedia.org/wiki/Angular_diameter_distance" rel="nofollow noreferrer">angular diameter distances</a>, which is defined such that it takes into account the fact that an observed object spanned a larger angle on the sky when it emitted the light we observe.</p>

<p>In popular science, the physical distance is usually what is quoted. Sometimes, however, journalists use the <a href="https://en.wikipedia.org/wiki/Distance_measures_(cosmology)#Light-travel_distance" rel="nofollow noreferrer">light travel distance</a>, which is the time the light has traveled, divided by the speed of light. That means that a photon emitted at the Big Bang, 13.8 billion years ago, has a light travel distance of 13.8 billion lightyears. But that's sort of a misleading number, since in fact the particle that emitted the photon is now much farther away, due to the expansion of the Universe (in fact 46.3 billion lightyears), and as <a href="http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html" rel="nofollow noreferrer">Ned Wright says</a> the term should be avoided.</p>

CC BY-SA 4.0
2018-06-15T21:39:03.027Z
2018-06-16T07:19:06.560Z
2018-06-16T07:19:06.560Z
pela
<p><a href="http://chandra.harvard.edu/photo/2017/arp299/" rel="nofollow noreferrer">Arp 299</a> is in the news, with most sources reporting it as 140 or 150 million light-years away. But what kind of distance is this?</p>

<p><a href="http://science.sciencemag.org/content/early/2018/06/13/science.aao4669" rel="nofollow noreferrer">The paper</a> which is trhe source for the news item has <a href="http://www.sciencemag.org/cgi/content/full/science.aao4669/DC1" rel="nofollow noreferrer">Supplementary Materials</a> which mention the distance but don't appear to say what kind or give details:</p>

<blockquote>
  <p>The merging pair of galaxies Arp 299 (Fig. 1) at a 44.8 Mpc distance (33; corrected to the cosmic microwave background reference frame; H0 = 73 km s^-1 Mpc^-1) is one of the brightest nearby LIRGs with an IR luminosity LIR ~ 7x10^11 L_⊙ (34; L_⊙ = 3.833×10^26 W).</p>
</blockquote>

<p>Is it obvious what method is used (and thus what type of distance this is) to measure the distance to this galaxy? Is there a standard reference/database/etc. giving basic information like distances of astronomical objects like galaxies? I'd like to know the answer for this galaxy, but answers that generalize will naturally be more interesting.</p>

<hr>

<p>Edward L. Wright has <a href="http://www.astro.ucla.edu/~wright/CosmoCalc.html" rel="nofollow noreferrer">a cosmology calculator</a> that is useful in converting between different types of distances. His <a href="http://www.astro.ucla.edu/~wright/distance.htm" rel="nofollow noreferrer">page on distances</a> gives many methods for measuring distances; I feel that if I knew which type (if any) of these methods was used to find the distance I'd have a decent chance of figuring out what kind of distance it was (and could find the other distances by bisection).</p>

<light><cosmology><distances><redshift><mathematics>
How far away is this galaxy?
Charles
# How far away is this galaxy?

(Asked by: username_0 on 2018-06-15)

[Arp 299](http://chandra.harvard.edu/photo/2017/arp299/) is in the news, with most sources reporting it as 140 or 150 million light-years away. But what kind of distance is this?

[The paper](http://science.sciencemag.org/content/early/2018/06/13/science.aao4669) which is trhe source for the news item has [Supplementary Materials](http://www.sciencemag.org/cgi/content/full/science.aao4669/DC1) which mention the distance but don't appear to say what kind or give details:

> The merging pair of galaxies Arp 299 (Fig. 1) at a 44.8 Mpc distance (33; corrected to the cosmic microwave background reference frame; H0 = 73 km s^-1 Mpc^-1) is one of the brightest nearby LIRGs with an IR luminosity LIR ~ 7x10^11 L\_⊙ (34; L\_⊙ = 3.833×10^26 W).

Is it obvious what method is used (and thus what type of distance this is) to measure the distance to this galaxy? Is there a standard reference/database/etc. giving basic information like distances of astronomical objects like galaxies? I'd like to know the answer for this galaxy, but answers that generalize will naturally be more interesting.

---

Edward L. Wright has [a cosmology calculator](http://www.astro.ucla.edu/~wright/CosmoCalc.html) that is useful in converting between different types of distances. His [page on distances](http://www.astro.ucla.edu/~wright/distance.htm) gives many methods for measuring distances; I feel that if I knew which type (if any) of these methods was used to find the distance I'd have a decent chance of figuring out what kind of distance it was (and could find the other distances by bisection).

**Tags:** light, cosmology, distances, redshift, mathematics


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## 2 answers

### Answer by username_1 on 2018-06-16. Score: 4 | Accepted answer

The article references a paper by Huo et al. (2004; that's the reference number "33" in your quoted text). Huo et al. merely list a redshift of "0.0103" for Arp 299 in their Table 1 (without any apparent sources); combined with the fact that the authors of the *Science* paper say what Hubble constant they assumed (73 km/s/Mpc), this tells us that the distance is redshift-based. That is, they used the redshift plus the Hubble constant to derive the (comoving) distance.

If you look up Arp 299 in the [NASA Extragalactic Database](http://ned.ipac.caltech.edu) and scroll down [the resulting page](http://ned.ipac.caltech.edu/cgi-bin/objsearch?objname=arp%20299&extend=no&list_limit=5), you can see a list of possible redshifts ("Calculated and Corrected Velocities") for this galaxy, ranging from 3088 km/s (which is in fact $z = 0.0103$) to 3511 km/s. Immediately below that, you can see the derived distances ("Hubble Flow Distance"), assuming $H\_0 = 73$, the same value the authors say they used. The closest number to their value is the 44.4 Mpc, assuming "3K CMB" correction (which seems to match the authors' description). Why this isn't exactly the same as the authors' value of 44.8 Mpc I don't know; possible a slightly different value of the redshift was used.

At this relatively small redshift, the differences between the different distances that username_3 mentions are pretty minor. E.g., plugging $z = 0.0108$ (NED's "3K CMB" corrected redshift) and $H\_0 = 73$ into Ned Wright's cosmology calculator gives you a comoving distance of 44.2 Mpc, a luminosity distance of 44.7 Mpc, and an angular-diamter distance of 43.8 Mpc. The differences between these are all smaller than any plausible uncertainty based on using the redshift.[\*]

So, to summarize, the distance in the paper is (as username_3 says) the comoving distance; the method used to derive it was the redshift of the galaxy (corrected to a CMB-relative value) plus a Hubble constant of 73 km/s/kpc.

[\*] E.g., if we assume a redshift uncertainty of 300 km/s, based on possible peculiar motion of Arp 299, then the distances are uncertain by +/- 4 Mpc.

> **Comments:**
> **username_0**: Redshift! I was looked by for a $z$ but didn’t find one. Thank you for solving this riddle!  
> **username_2**: I found it surprising that reference 33 was supposedly to support the cited distance, but the paper by Huo et al is entirely unrelated to distance. Poor academic rigour.  

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### Answer by username_3 on 2018-06-15. Score: 3

It's the good old physical distance — also called *proper distance* — i.e. what you'd measure if you stopped the expansion of the Universe and patiently laid out meter sticks from us to Arp 299. It's also the [comoving distance](https://en.wikipedia.org/wiki/Comoving_and_proper_distances) — i.e. the distance measured in coordinates that expand with the Universe and hence don't change with time — since that distance is defined to coincide the physical distance today.

[Luminosity distances](https://en.wikipedia.org/wiki/Luminosity_distance) are used mostly in relations between flux, magnitudes, and distances, and are rarely quoted as a distance without explicitly saying that it's the luminosity distance. This distance is defined such that it satisfies the inverse-square law, and takes into account the expansion of the Universe and the redshift of light.

The same goes for [angular diameter distances](https://en.wikipedia.org/wiki/Angular_diameter_distance), which is defined such that it takes into account the fact that an observed object spanned a larger angle on the sky when it emitted the light we observe.

In popular science, the physical distance is usually what is quoted. Sometimes, however, journalists use the [light travel distance](https://en.wikipedia.org/wiki/Distance_measures_(cosmology)#Light-travel_distance), which is the time the light has traveled, divided by the speed of light. That means that a photon emitted at the Big Bang, 13.8 billion years ago, has a light travel distance of 13.8 billion lightyears. But that's sort of a misleading number, since in fact the particle that emitted the photon is now much farther away, due to the expansion of the Universe (in fact 46.3 billion lightyears), and as [Ned Wright says](http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html) the term should be avoided.


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