OF THE ROGER N. CLARK

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APPENDIX F: OPTIMUM DETECTION MAGNIFICATIONS FOR DEEP-SKY OBJECTS
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Table F.1. Magnification causing a given suiface brightness reduction
Appendix F
Optimum detection magnifications
for deep-sky objects
Appendix E listed the minimum optimum detection
magnification (MDM) for each of the
611 deep-sky objects catalogued. But that
magnification is the best for an object only if
it is the lowest your telescope can give. No
one will be viewing each object at this power
optimally, unless they happen to be using a
whole battery of different-sized telescopes.
For your particular instrument, what is the
best power for detecting each galaxy, cluster,
or nebula This appendix suggests answers.
It lists the optimum detection magnification,
which we will call the OD M, fo r each catalogued
object in a range of telescopes under a
dark country sky.
Of course, if an object is bright enough and
the sky dark enough, it will be easy to see at
many magnifications and no calculation is
needed. But if the object is a challenging one
near the limit of detection, it's very helpful to
know the ODM.
HOW THE COMPUTATION IS DONE
again. By following some simple rules the
solution can be found quickly.
First check that the object's total magnitude
is within reach of your telescope. Use
Table 4.1 or equation 4.2 to find your telescope's
limiting magnitude. If the object
should be detectable at all, then you can do a
computation to find the ODM.
The ODM depends on three things. First is
the surface brightness of the background (Mo).
As in Appendix E we will use Mo = 24.25
magnitudes per square arc-second for a dark
coun try sky. Second is the size of the object
you wish to study. Use the smaller dimension
that describes the object. For example, if you
are examining an elliptical galaxy, use the
minor axis size. If you are examining a wisp
of nebulosity, use its width, not its length.
Third is the reduction in surface brightness
due to the telescope's transmission factor and
magnification.
The first step is to make a guess at the
ODM. You can use any number you wish
here. To generate the entries in this appendix
I simply made a first guess of lOOX. You
For those who want to know how these values could use the MDM value from Appendix E.
were calculated, or who wish to perform their To get close you might try using Figure 2.7b
own calculations for light-polluted conditions in the following way. Add about one to the
or for objects not listed in the table, the next background surface brightness Mo (for examfew
pages explain the method. Other readers pie for a dark country sky try 25), then find
may wish to skip this section. the angle corresponding to this value from
The computation of the optimum detection Figure 2.7b (at Mo = 25 we find about 7 armagnification
is a complex iterative proce- minutes). This angle divided by the object s
dure ideal for a computer. The goal is to find size gives the first guess.
the power that magnifies the object to the Now that we have made a guess at the
optimum magnified visual angle. This sounds magnification, we need to see whether it is
simple, but each time you change the tele- close. We must determine what effect the
scope's magnification, the surface brightness magnification has on the object's brightn ss .
of everything you are viewing also changes. Recall from Chapter 4 that magnification
So to find the correct magnification you simp- dims the apparent surface brightness of anyly
make a guess and then compute if that is thing seen through a telescope. To get a parcorrect.
If not, you make a new guess and try ticular surface brightness reduction Mb ID a
318
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Reduction in magnitudes/sq. arc-sec
Telescope 0.38 2.12 3.62 4.73 6.24 7.1 2
aperture
-
Magnification per inch of aperture
15.0 25.0 50.0 75.0
Inches mm 3.4 7.5
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2 51 7 15
4 102 14 30
6 152 20 45
8 203 27 60
10 254 34 75
12 305 41 90
14 356
105
16 406 54 120
18
61 135
20 508 68 150
24 610 81 180
30 762 101 225
457
47
36 914 121 270
40 1016 135 300
given telescope means using a particular
magnification m. The relation can be easily
derived by rearranging equation 4.3:
m = 0. 1116 D 10 (Mtl5) , or
Mb = 5 10g(m / (0.1116 D)) ,
(equation F.l)
(equation F.2)
where D is the telescope aperture in millimeters
and Mb is in magnitudes per square
arc-second. (If you wish to give D in inches,
change the constant 0.1116 to 2.833.) Table
F. l uses this formula to list the magnifications
that yield certain surface-brightness reductions
in various telescopes.
Now compute the background surface
brightness as viewed by the eye through the
telescope at this power. It is found by adding
the surface brightness reduction Mb from
equation F.2 to the initial background Mo:
Bo = Mo + Mb. (equation F.3)
ow read the OMV A from Figure 2.7b
Usmg this new Bo as the background surface
brightness. (If you extrapolate the OMV A
ey nd 27.0 mag. per square arc-sec., do not
et It become greater than 360 arc-minutes,
because the object is then spread over too
large an area in the eye.)
319
30 50 100 150
60 100 200 300
90 150 300 450
120 200 400 600
150 250 500 750
180 300 600 900
210 350 700 1050
240 400 800 1200
270 450 900 1350
300 500 1000 1500
360 600 1200 1800
450 750 1500 2250
540 900 1800 2700
600 1000 2000 3000
A new guess for the optimum detection
magnification, which for now we will simply
call m, is given by
m = OMVA/size (equation F.4)
where "size" is the object's smallest dimension,
as discussed above. If m turns out to be
the same magnification that was used to compute
Mb, then m is the optimum detection
magnification (ODM), and you're done.
More likely m will be somewhat different. In
this case use the m just computed and try
again until the two results match within
reason. With a computer, a few iterations can
quickly narrow in on a good solution.
For those wishing to program this procedure
into a computer you must be able to
compute the curve in Figure 2.7b. Table F.2
lists specific values along that curve. Other
values can be found by interpolation. If you
do interpolation, you should interpolate the
10g(OMV A) values because the line curves
too much using normal OMVA values.
Let's work through an example. Suppose
we intend to hunt for NGC 134 in an 8-inch
telescope. What is the best magnification
Look at Table F.3, which shows computations
for this object. At iteration 1 an initial