THE SPECTACULARITY OF DEEP SKY OBJECTS
------------------------------------
John Pazmino
NYSkies Astronomy Inc
www.nyskies.org
nyskies@nyskies.org
1981 March 1 initial
2009 September 11 current
[This article was published in three parts in Eyepiece on January 1,
February 1, and March 1 of 1981. The issue date in the neader is for
the concluding part. It is here consolidated into one piece with
touchup. Newsletter editor Jack Dittrick explains:
"Ed. Note: John Pazmino's SPECTACULARITY treatise was presented at
the 68th annual AAVSO meeting in Cambridge, Mass., October 1979. Here
begins a verbatim serialization. Chopping John's paper into parts is a
rather violent act, as it is made of whole cloth. Even the most
erudite readers who miss the beginning or middle of the paper are
likely to find the parts they do read entirely unintelligible.
Observers who can stay with the tract from beginning to end should
find it an invaluable aid in the telescopic observation of deep sky
objects."]
= = = = =
It has always been for deep sky objects -- nebulae, galaxies, and
clusters -- that there was no single, simple rating by which the
observer could assess the object's impressiveness, conspicuousness, or
ease-of-finding prior to searching out the object in the sky. All the
observer had to go by were verbal commentaries, haphazard brightness
values, and illrepresentative pictures. For the beginning stargazer,
interpretation of such notes can be uncertain, hesitant, even
downright frustrating. This leads to huge waste of time and effort at
the telescope and, frequently, to abandonment of stargazing
altogether.
About two years ago, when fellow AAAer Frances McCool and I began
to observe together regularly, this lack of a descriptive figure-of-
merit for deep sky objects became a severely acute situation. Frances,
having the typical stargazer's telescope and other equipage, was first
starting out in deep sky observing. And she frittered away her
valuable hours looking for a this or that nebula because she had no
sure way of ascertaining beforehand how hard it would be to find or
what to expect of its appearance when found. True, we two could work
together to share the frustrations, but what was really needed was an
index -- a spectacularity index -- for deep sky objects.
Now, there are two elemental properties of deep sky objects of
concern to the observer, the angular size and the total magnitude. The
visual impact of the object, based on physiological grounds, depends
on both how much total illumination is sends to the observer and how
much this illumination is spread out by the object's angular extent on
the sky.
So I began by setting down directly the definition of angular
illumination from ordinary photometry:
ANGULAR ILLUMINATION = (TOTAL ILLUMINATION)/(ANGULAR AREA)
Then, I converted this into the magnitude system by which all good
observers are brought up:
ANGULAR MAGNITUDE = -2.5*LOG(TOT ILLUM/((ANG AREA)*(BASE ILLUM)))
The units here are magnitude per square radian above whatever base
illumination one cares to use. I calibrated the magnitudes to the
standard stellar photometry so the base illurnination is 2.65E-6
lumens per square meter. Factoring this last equation results in two
terms:
ANGULAR MAGNITUDE = (-2.5*LOG((TOT ILLUM)/(BASE ILLUM)))
+(-2.5*LOG((1)/(ANJULAR AREA)))
= (TOTAL MAGNITllQE)+(2.5*LOG(NAGULAR AREA))
The second term is a function only of area and can be pretabulated for
convenient intervals over the size range of astronomical interest. I
call this term the dilution modulus because it acts to spread out the
total illumination over the angular extent of the object.
With such a prepared table I can look up an object's dilution
modulus, knowing the size, and add it directly to the total magnitude.
The algebraic sum is immediately the object's angular magnitude,
tantamount to one of the two determiants of the object's
spectacularity. The other, the total magnitude, I already had all
along.
Having now in hand the determinants of impressiveness and ease-of-
finding, I sought a function of the two which would generate a simple,
easily evaluated spectacularity index. There heretofore never having
been such a function, I could define one myself. Obviously, tho, the
index must follow the spectacularity in a single-valued, monotonic
manner. I chose a straight addition function:
SPECTACULARITY INDEX = (TOTAL MAGNITUDE)+(ANGULAR MAGNITUDE)
= (2)*(TOT MAGN)+(DILUTION MODULUS)
That is to say, the spectacularity index of an object is twice its
total magnitude plus its dilution modulus.
All this reasoning took an evening or two of deskwork, but far
more was to come. In the course of calculating spectacularity indices
for the objects in the usual observing lists, hideous aberrations
reared up. Objects known to be impressive received poor indices and
vice-versa. The same object taken from different lists got discordant
indices.
The cause was in the values cited for total magnitude and angular
size. It seemed as if some compilers were truly on the weed! Sizes
were copied from previous authors, measured in outsized instruments,
enclosed dim outlaying areas, taken from hearsay. Same thing with
total magnitudes with the added complication that photographic and
visual values were often mixed together without distinction.
In many cases the numbers were so misleading that I had to just go
outside and examine the object for myself in the sky.
It took the better part of two years to card the entangled
litterature and assemble (at least for the more prominent objects) a
uniform and consistent set of magnitudes and sizes from which valid
spectacularity indices could be worked up.
The end results are presented here in two tables. Table 1 gives
the spectacularity index versus total magnitude and angular size. This
eliminates even the simple mathematics described above; the index can
be read out directly from this table by entering it with the object's
magnitude and size.
Table I is divided into two zones, the left one for objects of
index +1.5 and better and the right one for objects of index worse
than +1.5. [The zones are demarcated by '#'.] The left zone embraces
those objects suitable for the novice telescope user in an urban
setting to work with when just starting out in deep sky observing.
The right zone takes in objects for the more practiced observer.
The breakpoint of index +1.5 is based on my own experience with many
tens of observers of assorted skill working under the skies of New
York City.
By and large, novice telescope users in the City (transparency
averaging +3.5 [in 1981]) spend overly and frustratingly long times
looking for objects of index worse than +1.5. Some difficulty is
experienced at index +1.5, but only enough to present a realistic
challenge repaid by a pleasing impact from the object once found.
By going to skies of better transparency the boundary between the
two zones shifts to the right by one column in Table 1 for each 0.5
magnitude improvement in transparency, unveiling ever dimmer, more
diffuse objects to view. For poorer skies the boundary migrates
leftward at the same rate, leaving fewer and fewer objects of merit to
look at. Thus, for our country friend, if just starting out in deep
sky stargazing, the breakpoint index is +4.5; this includes most of
the Messier objects and a good number of objects in the NGC catalog.
TABLE 1
------------------------------------------------------------
SPECTACULARITY INDEX VERSUS TOTAL MAGH[TUDE AND ANGULAR SIZE
---------------------------------------------------------------------
MAGN +4.5 +5.0 +5.5 +0.0 +0.5 +7.0 +7.5 +8.0 +B.5 +9.0 +9.5 10.0 10.5
DIAM ----------------------------------------------------------------
I' -9.0 -8.0 -7.0 -6.0 -5.0 -4.0 -3.0 -2.O -1.0 0.0 +1.0#+2.0 +3.0
2' -7.5 -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 +0.5 +1.5#+2.5 +3.5 +4.5
3' -6.5 -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 +0.5#+1.5 +2.5 +3.5 +4.5 +5.5
4' -0.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0
5' -5.5 -4.5 -3.5 -2.5 -1.5 -0.5 +0.5 +I.5#+2.5 +3.5 +4.5 +5.5 +6.5
6' -5.0 -4.0 -3.0 -2.0 -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0 +6.0
7' -4.5 -3.5 -2.5 -1.5 -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +6.5 +7.5
8' -4.5 -3.5 -2.5 -1.5 -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +6.5 +7.5
9' -4.0 -3.0 -2.0 -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0 67.0 +8.0
10' -4.0 -3.0 -2.0 -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0 67.0 +8.0
12' -3.5 -2.~ -1.5 -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +6.5 +7.5 +8.5
14' -3.0 -2.0 -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0 +7.0 +8.0 +9.0
16' -3.0 -2.0 -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0 +7.0 +8.0 +9.0
I8' -2.5 -1.5 -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +6.5 +7.5 +8.5 +9.5
20' -2.5 -1.5 -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +6.5 +7.5 +8.5 +9.5
24' -2.0 -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0 +7.0 +8.0 +9.0 10.0
28' -1.5 -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +0.5 +7.5 +8.5 +9.5 10.5
32' -1.5 -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +0.5 +7.5 +8.5 +9.5 10.5
36' -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +0.0 +7.0 +8.0 +9.0 10.0 11.0
40' -1.0 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +u.O +7.0 +8.0 +9.0 10.0 11.0
45' -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +0.5 +7.5 +8.5 +9.5 10.5 11.5
50' -0.5 +0.5 +1.5#+2.5 +3.5 +4.5 +5.5 +6.5 +7.5 +8.5 +9.5 10.5 11.5
55' 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0 +7.0 +8.0 +9.0 10.0 11.0 12.0
60' 0.0 +1.0#+2.0 +3.0 +4.0 +5.0 +6.0 +7.0 +8.0 +9.0 10.0 11.0 12.0
--------------------------------------------------------------------
Table 2 gives all the deep sky objects visible in the latitude of
New York whose indices are +1.5 or better; which is to say, all
objects which the novice observer should choose from for starting out
in looking for deep sky objects under a city sky.
Because, despite my concerted efforts, there may yet be further
adjustments in an object's adopted magnitude and size, In the table I
list those I finally settled on and from which the indices are
derived. [There are many more such deep sky objects, but I didn't
catch them when I wrote this article.] Should other values prove more
appropriate, Table 1 can be used to obtain the new index for the
object.
However, contemplated adjustments to either the total magnitude or
the angular size ought to be founded where ever possible on actual
recourse to the object in the sky, not on quotations from compiled
lists. It is essential to enclose in the magnitude and size only the
principal seats of light in the object and no more.
Taking in the faint peripheral territories will only increase the
angular size with no real increase in illumination; this will unfairly
depress the object's spectacularity index.
Use of the spectacularity index is quite easy and direct. Just
think of it as an ordinary magnitude rating. The algebraicly smaller
indices denote the more showy, easier-to-find, objects.
Take, by way of a simplified example, a sky of uniform
transparency. We've just looked at M 80 Scorpii, an old favorite. Now
we want to look for M 56 Lyrae which we haven't seen before. Turning
to Table 2 we see that both M 80 and M 56 have an index of -0.5. While
M 56 is half a magnitude fainter than M 80, it is also less than half
as large areawise. The two factors compensate to yield equal
spectacularity indices.
Thus, overall, we would have just as much ease (or trouble)
locating M 56 as M 80 and we would be about equally impressed with its
aspect. But if instead we wanted to look for M 12 in Ophiuchus we
would have quite a bit harder a time finding it than M 80 and it would
seem significantly more mediocre. M 12's index is +1.0, as read out
from Table 2.
Suppose, tho, the sky is not of uniform transparency. Usually the
transparency decreases toward the horizon and there may be regions of
poor transparency due to local circumstances. Take the same two
clusters, M 80 and M 56, again.
M 80 is, say, in a part of the sky whose transparency is one
magnitude worse than M 56's part. So instead of M 80's magnitude
being +7.5, it is equivalently only +8.5. Look up in Table 1 under
+8.5 magnitude, 3 arcminute diameter, and take out the equivalent index
of +1.5. M 80's equivalent index of +1.5 compared to M 56's index of -
0.5 indicates that we should locate M 56 much more easily than M 80
(which we have already appreciated) and it would look much more
conspicuous.
The spectacularity index enables us to assess the visibility of
objects in different skies. Let us already from our city location have
appreciated M 3 in Canes Venatici. Could we try for M 51, also in
Canes Venatici, during a visit .to our country friend? The sky in the
city was overall of transparency +3 and we can reasonably expect an
overall transparency of +5 where our friend lives. M 3's index is 0.0
from Table 2. We adopt magnitude +8.5, diameter 8 arcminutes, for M 51.
Since the difference in transparency is 2 magnitudes in favor of M 51,
we look in Table 1 under +6.5 and 8' and read out the equivalent index
of -0.5.
We under our friend's sky would find M 51 a somewhat easier object
to pick up than M 3 is under our own sky.
TABLE 2
---------------------------------------------------------------
DEEP SKY OBJECTS WITH SPECTACULARITY INDEX OF +1.5 AND GREATER
SORTED BY CATALOG NAME
----------------------------------------------------------
CATALOG RA (1950) DEC DIM TOT. SPEC. PROPER
NAME TYPE CONST HR MN DEG MIN MAGN INDEX NAME
------- ---- ----- -- -- ---- --- ---- ----- --------
M 2 GC AQR 21 31 -01.1 8 +6.5' -0.5 AQR CLUS
M 3 GC CVN 13 40 +28.6 10 +6.5 0.0 CVN CLUS
M 4 GC SCO 16 21 -26.4 14 +6.0 0.0
M 5 OC SER 15 16 + 2.3 13 +6.0 0.0 SER ClUS
M 6 OC SCO 17 37 -32.2 25 +5.0 -1.0
M 7 OC SCO 17 51 -34.8 60 +3.0 -3.0 SCO CLUS
M 8 ON SGR 18 02 -24.3 10 +4.5 -4.0 LAGOON NEB
M 9 OC OPH 17 16 -18.5 2 +6.0 +0.5
M 10 GC OPH 16 55 - 4.0 8 +7.0 +0.5
M 11 OC SCT 18 48 - 6.3 10 +6.0 -1.0 SCT ClUS
M 12 GC OPH 16 45 - 1.9 9 +7.0 +1.0
M 13 GC HER 16 40 +36.6 10 +6.0 -1.0 HER CLUS
M 14 OC OPH 17 35 - 3.2 3 +7.5 -0.5
M 15 GC PEG 21 23 +12.0 7 +6.5 -0.5 PEG CLUS
M 16 ON SER 18 16 -13.8 8 +5.5 -2.5 EAGLE NEB
M 17 ON SGR 18 18 -16.2 10 +5.0 -3.0 OMEGA NEB
M 18 OC SGR 18 17 -17.2 7 +7.5 +1.5
M 19 GC OPH 17 00 -26.2 4 +7.0 -1.0
M 20 ON SGR 17 59 -23.0 8 +5.5 -2.5 TRIFID NEB
M 21 OC SGR 18 02 -22.5 10 +6.0 -1.0
M 22 GC SGR 18 33 -24.0 17 +5.0 -2.0
M 24 OC SGR 18 13 -18.5 30 +4.5 -1.5 SGR CLUS
M Z7 GN VUL 19 57 +22.6 6 +7.0 0.0 BUMBBELL NEB
M 28 GC SGR 18 22 -24.9 5 +7.0 -0.5
M 29 OC CYG 20 22 +38.4 12 +7.0 +1.5
M 30 GC CAP 21 38 -23.4 6 +7.5 +1.0 CAP CLUS
M 31 GX AND 0 40 +41.0 40 +3.5 -3.0 AND GALAXY
M 32 GX AND 0 40 +40.6 2 +8.0 -0.5
M 34 OC PER 2 39 +42.6 18 +6.0 +0.5
M 35 OC GEM 6 6 +24.3 30 +5.5 +0.5 GEM CLUS
M 36 OC AUR 5 32 +34.1 16 +6.5 +1.0
M 37 OC AUR 5 49 +32.6 24 +6.0 +1.0
M 39 OC CYG 21 30 +48.2 30 +5.5 +0.5 CYG CLUS
M 41 OC CMA 6 45 -20.5 20 +5.0 -1.5 CNA CLUS
H 42 ON ORI 5 33 - 5.4 15 +3.0 -6.0 ORI NEB
M 43 ON ORI 5 33 - 5.3 5 +5.0 -4.5
M 44 OC CNC 8 38 +19.9 90 +3.5 -1.0 PRAESEPE
M 45 OC TAU 3 44 +24.0 100 +1.5 -5.0 PLEIADES
M 46 OC PUP 7 40 -14.7 24 +6.0 +1.0
M 47 OC PUP 7 34 -14.4 2S +4.5 -2.0 PUP CLUS
M 48 OC HYA 8 11 -05.6 30 +5.5 +0.5
M 50 OC MON 7 1 - 8.3 10 +6.5 O.Q
M 53 GC COM 13 11 +18.4 3 +8.0 +0.5
M 54 GC SGR 18 52 -30.5 2 +7.5 -1.5
M 55 GC SGR 19 37 -31.1 10 +6.5 0.0
M 56 GC LYR 19 15 +30.1 2 +8.0 -0.5 LYR CLUS
M 57 GN LYR 18 52 +33.0 1 +8.5 -1.0 RING NEB
M 62 GC SCO 16 58 -30.1 4 +6.5 -2.0
M 67 OC CNC 8 43 +12.0 15 +6.5 +1.0
M 68 GC HYA 12 37 -26.5 3 +8.5 +1.5
M 69 GC SGR 18 28 -32.4 3 +7.5 -0.5
M 70 GC SGR 18 40 -32.4 3 +8.0 +0.5
M 73 OC AQR 20 56 -12.8 3 +8.5 +1.5
M 75 GC SGR 20 03 -22.1 2 +8.5 +0.5
M 79 GC LEP 5 22 -24.6 3 +8.5 +1.5
M 80 GC SCO 16 14 -22.9 3 +7.5 -0.5
M 81 GX UMA 9 52 +69.3 13 +7.0 +1.5
M 82 GX UMA 9 52 +69.9 3 +8.5 +1.5
M 92 GC HER 17 16 +43.2 8 +6.5 -0.5
M 93 OC PUP 7 42 -23.8 25 +6.0 +1.0
M 103 OC CAS 1 30 +60.5 5 +7.0 -0.5 CAS CLUS
M 107 GC OPH 16 30 -13.0 2 +8.0 -0.5
M 110 GX AND 0 40 +41.0 5 +8.0 +1.5
NEL 25 OC TAU 4 17 +15.5 240 +1.0 -4.0 HYADES
MEL 111 OC COM 12 23 +26.4 360 +3.0 +1.0 COM CLUS
N 869 OC PER 2 16 +56.9 30 +4.0 -2.5 DOUBLE CLUS
N 884 OC PER 2 20 +56.9 30 +4.0 -2.5 DOUBLE CLUS
N 1980 OC ORI 5 33 - 6.0 14 +4.0 -4.0 lOT ORI
N Z237 OC MON 6 30 + 4.7 10 +6.5 0.0
N 2244 OC MON 6 30 + 4.9 27 +5.0 -0.5 ROSETTE
N 2264 OC MON 6 38 +10.0 30 +4.5 -1.5 15 MON
N 5128 GX CEN 13 22 -42.8 9 +7.0 +1.O CEN GALAXY
N 5139 GC CEN 13 24 -47.1 23 +3.5 -4.0 OME CEN
N 6356 GC OPH 17 21 -17.8 2 +8.5 +0.5
N 6638 GC SGR 18 28 -25.5 1 +9.0 0.0
M 6642 GC SGR 18 29 -23.5 1 +9.5 +1.0
M 6712 GC SCT 18 50 - 8.8 2 +8.0 -0.5
PAZ 1 OC CAM 3 13 +59.7 10 +6.0 -1.0 PAZMINO'S CLUS
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