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https://en.wikipedia.org/wiki/List_of_largest_galaxies

says galaxy ESO 383-76 has a MA diameter of 1,764,000 light years based on information from

https://ned.ipac.caltech.edu/cgi-bin/objsearch?objname=ESO+383-G+076&extend=no&hconst=67.74&omegam=0.3089&omegav=0.6911&corr_z=1&out_csys=Equatorial&out_equinox=J2000.0&obj_sort=RA+or+Longitude&of=pre_text&zv_breaker=30000.0&list_limit=5&img_stamp=YES

NED. I see the NED page says that the galaxy has a diameter of 2.3. Using this as an example, how can I convert 2.3 to 1.764 million. I am after the formula that they used to convert, can someone provide me with a non-scientific calculator version.

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    $\begingroup$ To convert you will also need the distance of the galaxy. Ideally the angular size distance (which may be significantly different from other measures of distance for very distant galaxies.) $\endgroup$
    – James K
    Sep 25, 2022 at 18:40
  • $\begingroup$ Where does 1.764 million light years come from? There is a section in NED on physical diameters for this object and they don;t agree with you. $\endgroup$
    – ProfRob
    Sep 27, 2022 at 15:08

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A simple, non-scientific calcultor method is to multiply the angular size in radians by the distance.

I get a different and much smaller value.

2.3 /60 *pi/180  * 417000000 = 278990 ly
     ^    ^        ^
     |    |        multiply by distance in light years
     |    convert to radians
     convert to degrees

The distance I found from the Ned "redshift independent distance". You could also use redshift of z= 0.0386 and Ned Wrights calculator to give a distance of 538000000 ly.

The angular size of 2.3 arc min is evidently too small. Even a general glance at aladin shows that the galaxy is much larger than this. But it is very hard to define the edge of such a galaxy, it just tends to get less and less bright towards the edge with no clear edge.

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    $\begingroup$ I don't think the 2.3' is wrong, it's probably the half-light radius, and the surface brightness is much higher in the center. But the distance is uncertain, since it's determined using the Tully-Fisher relation which has some scatter. The redshift distance may be more precise since its radial velocity is ~11,000 km/s, but peculiar velocities may still give 10–20% uncertainty, in principle. $\endgroup$
    – pela
    Sep 25, 2022 at 20:12
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    $\begingroup$ Yes, by "wrong" I mean it's not the right number to put into this formula. It may very well be a half light radius, but the we would want the full major axis length, to the "edge" And the distance isn't very well constrained, somewhere between 400 and 550 million light-years seems a reasonable estimate. However to get the 1764000 ly radius for the galaxy you will need to use a different value for the angular diameter. $\endgroup$
    – James K
    Sep 25, 2022 at 22:27
  • $\begingroup$ Right, okay. Yes, if you use the redshift distance and add ±1500 km/s uncertainty, you get a distance of ~550±70 million lightyears. To get those 1,764,000 lyr would then require an angular diameter of $11.4_{-1.2}^{+1.6}$ arcmin. Very odd… $\endgroup$
    – pela
    Sep 26, 2022 at 8:16
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I am one of the editors of Wikipedia's "List of largest galaxies."

We chose not to use the input from the "Basic Data", which gave an apparent diameter of 2.3 arcminutes. This is an unreferenced value, intended to take a quick look upon a galaxy's characteristics. As stated by NED on the "Notes":

This information is indicative only. With the exception of the redshift they are unreferenced and highly inhomogeneous as to their origin. The Radial Velocity (when available) is computed from the listed redshift. The remaining values are designed to orient the user with a quick-look, overall assessment of the general properties of the object in question. They are not averages nor are they standardized in any way.

What we did is to look at the section "Quick-Look Angular and Physical Diameters", which is at the very bottom of the NED search results that you just linked. Unlike the Basic Data, this one is referenced; in the case of ESO 383-76 it was this paper from 1989 by Lauberts et al.

Here, they used 90% of the galaxy's total B-light (this was also stated in the "List of largest galaxies" in the "Estimation" part of the table). In this procedure you use a sensitive, long-exposure B-band photographic plate (which can detect light far better than a plain look at a telescope). They gave its major and minor axis diameters of 555.9 arcseconds and 277.95 arcseconds, respectively, and in the Physical diameter they gave its size: 344.97 kpc for the major axis and 172.48 kpc for the minor one.

That is 1.125 million light-years and 562,554 light-years on the major and minor axes. So, where does the 1.764 million light-years came from?

Well, you have to look at the distance. In the "Note" they stated this:

Physical diameters are derived using a scale of 0.6206 kpc/arcsec based on Average NED-D Metric Distance of (128.000 +/- 35.355) Mpc.

But the galaxy is actually further than this. This estimate is old and uses the Tully-Fischer relation, but the distance estimated using redshift is 200.6 Mpc away (about 654 million light-years). You can see this at "Quantities Derived from Redshift" section and at "Virgo + GA + Shapley".

So you have to adjust it for this newer distance. The apparent diameters are raw data and independent variables so they cannot be changed. Fortunately, you can easily calculate the size by multiplying the apparent diameters of 555.9 arcseconds and 277.95 arcseconds with the given scale at "Scale (Virgo + GA + Shapley)", which is 973 pc/arcsec.

555.9 arcsec × 973 pc/arcsec = 540,890.7 pc 277.95 arcsec × 973 pc/arcsec = 270,445.35 pc

540,890.7 pc is approximately 1.764 million light-years. 270,445.35 pc is about 882,000 light-years. The exact numbers listed in Wikipedia. There you go.

I hope this clarifies everything for you. :)

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