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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