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In the November-December 1992 issue of STAR's newsletter SPECTROGRAM a very interesting and useful article was written by Frank Loso with the title of this Note. In this article Frank pointed out the important difference between the so-called visual magnitude (mv) and the "extended" magnitude (me) of deep sky objects, that is, galaxies, globular clusters and planetary nebulae. As Frank correctly pointed out the published magnitudes of objects given by (mv) can be quite misleading for observers. The more suitable and meaningful magnitude is the extended magnitude, (me). For example, the visual magnitude of the Helix nebula is listed as 6.5. Because the nebula extends over 16 minutes of arc (about half the size of the moon) the observed image is much dimmer and is observed to actually appear to be 13.5 magnitude. Thus, if one began to search for the Helix nebula on the belief that its magnitude was 6.5, a relatively bright object in an 8" telescope, one would miss it completely. Its low brightness as represented by an observed magnitude is at the limit of an 8" telescope. Consequently, before one begins an observing session for these deep sky objects if will save hours of searching if the "extended" magnitude is known beforehand.

Frank gave an excellent discussion of the steps required to determine the extended magnitude, (me), and provided a table of some of the most interesting objects. In practice, it would be preferable to have a formula which relates the extended magnitude to the visual magnitude and the dimensions of the object. Following Frank's verbal description the corresponding mathematical formula is found to be

(me) = (mv) + (5log10 ^d)-(5log10 ^70")

where

(me) = the extended, or observed magnitude of the object.

(mv) = the visual (the usual published value).

d = the diameter of the object measured in arc seconds (").

The appearance of 70" in the formula is due to the fact that Frank based his table on the brightness of the Ring Nebula (M57, Lyra) as the "standard". Note that for any object whose diameter (d) is 70" the extended magnitude (me) is equal to the visual magnitude (mv). If d is expressed in arc minutes (') it must be converted to arc seconds by multiplying by 60 (60" = 1'). For example, if d is 5' then in arc seconds the diameter is 5' x 60"/1 = 300". As an example of the formula Frank lists the visual magnitude and the diameter of the Rosette Nebula as (mv) = 7 and d = 70'. In terms of arc seconds d = 70' x 60" / 1' = 4200". Substuting these values into the formula we find

(me) = 7 + (5log10 ^4200")-(5log10 ^70") = 15.9

Thus, the Rosette Nebula certainly cannot be seen in an 8" telescope.

Another example is the Crab Nebula (M1) in Taurus. Its parameters are

(mv) = 8.4 and d = 5' = 300". We then have

(me) = 8.4 + (5log10 ^300") - (5log10 ^70") = 11.6

In general, one finds that most objects are listed not in terms of a single dimension but as a product of dimensions, that is, in terms of their length times their width. For example, the dimensions of the galaxy NGC253 in Sculptor is given as 22' x 5'. Which dimension should be used in the formula? I get around this problem by determining the area of this object and then taking the square root of the area. For this problem the area is 22' x 5' = 110 square arcminutes ('). The square root is then 10.5' = (630"). The visual magnitude of NGC253 is 7.0 so the extended magnitude according to the formula is

(me) = 7.0 + (5log10 ^630") - (5log10 ^70") = 11.8

which can be seen in an 8" telescope. However, this object which is a very beautiful spiral edgewise galaxy is located at declination - 25.6 deg, a very low declination as seen in our 40 deg N latitude. Factoring in another two magnitude decrease due to atmospheric absorption at this latitude the expected magnitude is around (me) = 13.8. Indeed, this is what it appears to be as observed in my 25" telescope.

Two other examples are of interest. We normally assume that the Messier objects are relatively bright, certainly visible in an 8" telescope. In general, this is true. But there are exceptions. For example, consider M33, a spiral galaxy in the constellation of Triangulum. Its parameters are (me) = 6.4 and its dimensions are 60' x 40'. This dimension is converted to 2400 square arcminutes (') and its square root is then 49.0 square arcminutes (') = 2940 square arcseconds ("). Using the formula we then find

(me) = 6.4 + (5log10 ^2940") - (5log10 ^70") = 14.5

Thus this Messier object is very faint and its observed magnitude is confirmed by the fact that it appears very faint even in a 25" telescope. As a final example we take M74, another spiral galaxy located in Pisces. Its parameters are (mv) = 10.5 and 10' x 9'. Its dimension is then found to be 570 square arcminutes (") and the extended magnitude is then found to be

(me) = 10.5 + (5log10 ^570") - (5log10 ^70") = 15.1

which is very faint, indeed. It would be extremely doubtful if this could be seen even on the best of nights with an 8" telescope, It is barely visible in my 25" telescope.

The conclusion which can be reached is that not only the visual magnitude is of importance but equally important is its dimension. Before carrying out an observing session it is highly advisable to determine the extended magnitudes (me) of the evening's objects. You may discover that a "simple" object such as M74 with a listed magnitude of 10.4 is actually 15.1 and so will be very difficult to find. Knowing this kind of informnation beforehand can save hours of fruitless searching. Most of all, you will have a very good idea if an object will actually be very faint and, hence, prepared for a difficult search.

© Edward Collett 1992. All rights reserved.

This page last updated 25 Feb 1996