Galaxy Distances - convert Distance Modulus to Distance!

[madbadgalaxyman]

HOW TO CONVERT THE DISTANCE MODULUS OF A GALAXY INTO ITS DISTANCE:

In the Catalog of Galaxy Distances [R.B. Tully et al.(2008) ] mentioned in my previous post in this Science Forum, each individual distance measurement for a specific galaxy is expressed as a single number; the distance modulus.
This is a logarithmic measure of the distance of an astronomical object, with no units of measurement (such as light years or parsecs) attached to it. It is not an actual distance in units of light years or parsecs.

How to convert the Distance Modulus of a galaxy to the actual distance of a galaxy:

Firstly, I note that, in this post, the distance to a galaxy is expressed in units of Megaparsecs (= millions of parsecs). But how big is one megaparsec; it is a long way, even if you are riding on a light beam………

One megaparsec = 1 million parsecs = 3.26 million light years......so to convert a specific Galaxy Distance of a certain number of megaparsecs into a certain number of millions of light years, just multiply the number of megaparsecs by 3.26

Here are a few technicalities, which can, if you wish, be left out of your conversion of a distance modulus to an actual distance:

Distance modulus is, when precisely expressed:
m - M
which is the mathematical expression for the apparent magnitude of a galaxy minus its absolute magnitude. This expression is actually a logarithmic restatement of the ratio of the intrinsic (absolute) brightness of an astronomical object to its observed brightness, which we can then use to calculate the distance of the object.

The distance moduli that are given in data tables and in catalogs of galaxies, usually have (already included within them) a numerical value for the dust extinction (from the foreground dust screen within the Milky Way) in front of a galaxy. In addition, a distance modulus as quoted in a galaxy catalog also includes a measure of the dust extinction of the light of a galaxy by the dust within that galaxy. This second type of extinction is sometimes called ‘internal extinction.’

So……… m - M – A (with each of these three numbers expressed in magnitudes) is the distance modulus which you actually find in the galaxy catalogs. This mathematical expression is actually:
apparent magnitude of a galaxy MINUS absolute magnitude of that galaxy MINUS total of the absorption (by dust)

Some more technicalities, for those who want to know more;
(1) apparent magnitudes and absolute magnitudes, and extinction, have to all be measured using the same band-pass and sensitivity (the same filter with the same transmission curve).
(2) The estimated ‘internal extinction’ (measured in magnitudes) from the dust within a spiral galaxy corrects its magnitude only to what the magnitude would be if the galaxy were in a “face on” orientation, but does not take into account the effect of the entire dust screen within the disk of the spiral galaxy.

Here is how to convert the Distance Modulus of a galaxy into to its actual Distance:

So now we have defined what a distance modulus actually is! By convention, the algebraic symbol normally used for a distance modulus is the lower-case greek letter mu

Galaxy Distance (expressed in Megaparsecs)
= 10 to the power of [[ (Distance Modulus minus 25) divided by 5 ]]

An easy way to calculate this is firstly to evaluate the expression within the square brackets, and than to use a calculator to calculate 10 to the power of x, where x is the expression in the square brackets.
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As one example, supposing the Distance Modulus of a galaxy in the Virgo Cluster of Galaxies is given as 31 in a catalog of galaxies, then the above expression becomes:
10 to the power of [ (31-25) / 5 ]
which when evaluated yields a physical distance of 15.84 megaparsecs for this galaxy. This is equivalent to 51.6 million light years.

As a second example, F.Thim et al. (in the reference 2003 , ApJ, 590, 256) used the 8.2 meter VLT to observe Cepheid Variable stars in the galaxy M83, and they estimated the distance of this galaxy as being a Distance Modulus of 28.25
So to convert this Distance Modulus to the distance of M83 :
10 to the power of [ (28.25 - 25) / 5 ]
yields a distance of 4.47 megaparsecs for M83. This is the same as 14.7 million light years.

Professional astronomers really love to give distances to astronomical objects by using distance moduli, but this is a headache for amateur astronomers. However, converting them to actual distances is “as easy as eating a piece of Nanna’s apple pie”!
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[PeterM]

Hi Robert,
Thank you indeed for going to the trouble of presenting such very useful information in your last 2 posts in the science forum. We are indeed fortunate to have someone with your knowledge and ability to present in such an manner that I am sure many here appreciate. I sure do!
Peter.

[madbadgalaxyman]

Thanks, Pete!

Further galaxy distances can be found in Tully's "Extragalactic Distance Database":
http://edd.ifa.hawaii.edu (http://edd.ifa.hawaii.edu/)
It should be noted that a good fraction of the individual distance determinations in this database are of low accuracy, and therefore mainly suitable for the averaging of multiple distances in order to find the distance of a galaxy cluster, or for statistical and cosmological work. However, the EDD (Extragalactic Distance Database) is also a very major source of all kinds of data, not just distances, about galaxies.

I am glad you found my posts about galaxy distances useful and understandable. It takes some work to get them right. As you have noticed, I am good at presenting technical information.

A lot of what I know about extragalactic astronomy is just from:
- reading scientific papers, and putting up with the fact that I won't understand everything in them.
- having very numerous reference books in my personal library (I have most everything about galaxies up to the upper undergraduate level)
- having learnt background information: such as the jargon, the conventions, the mathematical symbols, and the arcane language of professional astronomy. This gets you into the "world and mindset" of professional astronomy.
- knowing where to look for specific needed information about some aspect of astronomy
- understanding the detailed concepts about galaxies in a "physical" or "structural" sense of knowing the intricate details; but this need not involve really heavy maths!
- working on problems that do not necessarily need an extensive knowledge of physics, e.g. the extragalactic distance scale and the morphology of galaxies.

Best regards,
Robert

[Weltevreden SA]

Robert, thanks very much for the d.m. conversion formula. Your explanation makes me wonder if there is a comprehensive online-viewable list of the commonly used maths symbols and abbreviations in astrophysics. You mentioned the Gr. l.c. mu being the conventional term for distance modulus. Others I see are Greek l.c. lambda for wavelength, YSO = young stellar object, IMF = initial mass function, dSph - dwarf spheroidal galaxy. Sometimes an author defines a term early on then may not use it again for many pages. Also, I can't always readily recall what a l.c. delta or theta or phi usually represents. Wolfram Alpha sometimes defines a term as it is used in geophysics, which doesn't translate to astrophysics.

[madbadgalaxyman]

Dana,

Twenty years ago, it might have been possible to make a list of abbreviations, acronyms, symbols and conventions in astronomy and astrophysics, but it is probably not possible anymore...... because each of the specialized sub-fields within astronomy (e.g. X-ray astronomy ; high-z primeval galaxies ; stellar populations ; star formation ; the interstellar medium ; spectroscopy and photometry ; galaxy classification and morphology ; stellar astrophysics ; galaxy clusters ; the Large-Scale structures ; AGNs ; galaxy formation ; cosmology ; etc. etc. etc. etc.) now has its own specialized vocabulary.....
and each of these specialized areas of research even has its own "clique" of workers who barely communicate with workers in other sub-fields!!

To give an example, there now exist two very distinct groups of extragalactic astronomers who have little in common in terms of vocabulary, and who sometimes communicate very poorly;
- those who study elliptical galaxies
- those who study disk galaxies (spirals, S0 galaxies, irregulars)
Twenty years ago, there would not have been this division, because a lot less was known about each type of galaxy.

In fact, as I often say, the inability to decipher all of the acronyms, symbols, very elementary formulae , and obscure conventions, is in fact a gigantic barrier to understanding for non-professional astronomers and for non-astronomical physicists.
Examples:
- radio astronomers use Jansky as a unit of flux density, but optical astronomers use magnitudes, and people who study quasars use ergs per second!! (and lighting technicians use still other units and conventions!!)
- the people who study primeval galaxies at large look-back times use an obscure magnitude system which you don't find in the textbooks
- I recently bought a theoretical textbook on galaxy formation and this book uses a completely different set of abbrevations and mathematical formalisms to the general textbooks about galaxies.

That said, the only glossary of astrophysics and astronomy that I know of, which really defines an appreciable fraction of the terms in use, is:
"Glossary of Astronomy and Astrophysics"(2nd edition)
by Jeanne Hopkins
(2nd Revised and Enlarged Edition)
(University of Chicago Press, Published 1980)
(ISBN: 0226351718)
I have seen some cheap copies, mainly found using various 'book price comparison' engines on the internet.

I also keep a very large number of astronomy textbooks on my bookshelf, and even with all these references at hand, I still find it impossible to find a definition or a simple equation, from time to time!!

cheers, Robert