OF THE ROGER N. CLARK

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--- VISUAL ASTRONOMY OF THE DEEP SKY -- Table F.2. The optimum magnified visual angle (in arc-minutes) for various surface brightnesses S.B. OMVA Log(OMVA) S.B. OMVA Log(OMVA) S.B. OMVA === Log(OMVA) 4.0 9 0.97 16.0 16 1.20 22.0 62 1.79 9.0 10 1.01 17.0 18 1.26 23.0 68 1.83 11.0 11 1.04 18.0 23 1.36 24.0 72 1.86 13.0 12 1.07 19.0 31 1.49 25.0 1.90 79 14.0 13 1.11 20.0 42 1.62 26.0 1.96 15.0 14 1.14 21.0 51 1. 71 27.0 117 2.07 S.B. is the surface brightness in magnitudes per square arc-second. guess fo r the magnification was made. In this case, 100x was selected (for no other reason than it is a starting point). Now compute the background surface brightness Eo through the 8-inch telescope at 100x using equations F.2 and F.3. We find that Eo is 27.5. Next estimate the OMVA from Figure 2.7b or interpolate it using Table F.2. In the table the last entry is at 27, so the OMVA must be found by extrapolation. After doing this we find the OMVA should be 132.4 arc-minutes. Using this guess for the optimum size, compute the magnification that would give that size using equation F.3. Because NGC 134 has a smaller dimension of 1.0 arcminutes we find the optimum magnification would be 132.4/1.0 or 132.4x. But we guessed 100 X. These do not match very well so use 132.4x as a new guess and start over. Examining each iteration in Table F.3 for the 8-inch we see that the guess and the computed magnification are getting closer. By iteration 9 the difference is less than I, so 186X is very close. At iteration 12 the difference is only 0.1 X so 187X is certainly better than one needs. In practice the final magnification is only approximate for reasons discussed below. Any value between 180 and 190 is accurate enough. Once the two magnifications agree you have converged on the ODM! Try the same exercise using a 24-inch telescope. Only 5 iterations are needed to converge on a value of 76x. Because 81X is already the lowest useful magnification on a 24-inch, a lower power could not be beneficially used, so 81x should be considered the OUM. 320 91 WHAT THE ODM MEANS - = By examining the entries in the catalog you will note that the optimum magnification on the large telescope is less than on the small one! The reason is that the larger a telescope is, the greater an object's surface brightness is at a given magnification, so it can be detected at a smaller apparent size. Examining the solutions for NGC 134 in the catalog, we see that the ODM on the 8-inch is 187x, and on the 24-inch 81x. Notice that for very small telescopes, the magnification must be higher still. A 4-inch needs about twice the power of an 8-inch to show NGC 134 best. Once an object has been found, and ifit is not at the very threshold of detection, try raising the power to enlarge any internal d : tail toward its ODM. Recall that the opnmum magnifications in the catalog are only approximate, because the entire object's mean surface brightness is used. Man y' objects show considerable variation in brIghtness across their surfaces. Spiral galaxies, for instance, typically have a bright central region and faint arm . The fainter parts may not be seen at all, whl!e the bright inner area is much smaller (tendm to raise the ODM) and much brighter (tendmg to lower it but usually not as much as e increase cused by the smaller size). ThIS . . b· n't be catalog is only a gmde; If an 0 ect ca . her detected at the listed ODM, try both hlg and lower powers. DM com- In the catalog, when the 0 was f, I Puted to be less than the minimum us , nuDlpower of the telescope, the telescope s _ APPENDIX F: OPTIMUM DETECTION MAGNIFICATIONS FOR DEEP-SKY OBJECTS - -::::==== Iteration Telescope Guess # size (inches) magnification - 8.0 100.0 2 8.0 132.4 3 8.0 154.6 4 8.0 168.3 5 8.0 176.3 6 8.0 180.9 7 8.0 183.5 8 8.0 184.9 9 8.0 185.7 10 8.0 186.2 11 8.0 186.4 12 8.0 186.5 I 1 24.0 100.0 2 24.0 80.4 3 24.0 76.7 4 24.0 75.9 5 24.0 75.8 mum was listed. If the total magnitude of the object is simply too faint for the telescope under any conditions whatsoever, the entry for that telescope is left blank. THE ROLE OF CONTRAST Even where an optimum magnification is listed, it does not necessarily mean the object will be seen at that power. The contrast must also be high enough, as described in Chapter 6. To check on the contrast, find the apparent size of the object's minimum dimension at the ODM, as well as its apparent surface brightness, as des cri bed earlier. For example: in a 12-inch telescope NGC 134 has an ODM of about 1 14 X , at which a dark country sky background is reduced 2.63 magmtudes to a value of 24.25 + 2.63 = 26.88 magnitudes per square arc-second. We can round this off to 27. The size of NGC 134's smaller dimension is 1.0 arc-minutes, which when magnified 114X is 114 arc-minutes. This is the object's OMV A. The smallest detectable contrast can be fOund from Figure 2.6 or interpolating the values in Table F.4. The Table lists the log threshold contrast for different values of Table F.3. Sample iterative calculationjor NGC 134 321 Possible OMV A Computed Bo (arc-min) magnification 27.5 132.4 132.4 28.1 154.6 154.6 28.4 168.3 168.3 28.6 176.3 176.3 28.7 180.9 180.9 28.8 183.5 183.5 28.8 184.9 184.9 28.8 185.7 185.7 28.8 186.2 186.2 28.8 186.4 186.4 28.8 186.5 186.5 28.8 186.6 186.6 25.1 80.4 80.4 24.6 76.7 76.7 24.5 75.9 75.9 24.5 75.8 75.8 24.5 75.8 75.8 background surface brightness and OMV A. The entries were used to plot the curves in Figure 2.6. Again you must use log contrast values for any interpolations. Figure 2.6 shows that, at an apparent size of 114 arc-minutes on the curve for background brightness 27, a contrast of about I is needed for detection. This is a log contrast of O. The Cl column gives a log contrast for NGC 134 of 1.0 (which equals 101 or a contrast of 10), well above the threshold. Thus, NGC 134 should be easily detectable. I have used the logarithm of the contrast because, as for brightness, the eye responds to contrast on a logarithmic scale. Just think of the Cl column as a contrast scale with a higher number meaning more contrast. The contrast of each object in the catalog was evaluated for each telescope to determine whether it is high enough for detection. Where the contrast is too low, the letter "u" (for undetectable) appears in front of the magnification entry. Once again, this does not necessarily mean all of the object is invisible, because the calculation was done using the mean surface brightness. If the object has a brighter region, like the nucleus of a galaxy,
------- VISUAL ASTRONOMY OF THE DEEP SKY Table F.4. Log threshold contrast as afunction of angle and suiface brightness --- A P PENDIX F: OPTIMUM DETECTION MAGNIFICATIONS FOR DEEP-SKY OBJECTS - Optimum Detection Magnification = size for a given telescope aperture Background Angle (arc-minutes) ID v mag arc -min S.B. Cl 2 4 6 8 12 16 24 surface 0.595 3.60 9.68 18.2 55.2 121 brightness 360 - - - - - - - - -1 - - - - - 1 - - - - - - - - - 1 - - - - 1 - - - -1 - - - - 1 - - - - 1 - - - -1 - - - -1 - - - - 1 - - - -1 - - _ _ NGC 7814 12 .0 1.0x5 .0 22 .4 0.7 360 360 265 187 114 87 81 (magnitudes per Log angle (arc-minutes) NGC 40 10 .5 1. OxO . 7 18 .7 2.2 514 514 514 412 251 177 122 sq. arc-second) -0.2255 0.5563 0.9859 1.260 1.742 2.083 NGC 45 12 .1 8.0x5 .5 24 .8 -0.2 23 u14 20 27 41 54 81 2.556 - NGC 55 7.8 25x40 23 .9 0.1 7 14 20 41 54 81 NGC ' 104 25x25 20 .1 1.7 7 14 20 27 41 81 4 -0.3769 -1.8064 -2.3368 -2.4601 -2.5469 -2.5610 -2.5660 5 -0.3315 -1.7747 -2.3337 -2.4608 -2.5465 -2.5607 -2.5658 6 -0.2682 -1.7345 -2.3310 -2.4605 -2.5467 -2.5608 NGC 128 12 .8 2.2xO .4 21 . 3 1.2 900 900 900 871 - 613 373 2.5658 NGC 134 11 .4 5. Ox1 . 0 7 -0. 1982 -1.6851 -2.3140 -2.4572 -2.5481 -2.5615 21 . 8 1.0 360 360 265 187 114 87 81 -2.5665 NGC 147 12 .1 6.5x3 .8 24 .2 0.0 52 23 20 27 41 8 -0. 1238 -1.6252 -2.279 1 -2.4462 -2.5463 -2.5597 81 - 54 2.5646 NGC 150 12 .2 2. Ox1 . 0 21 . 6 1.1 360 360 265 187 114 87 81 4.5 27 54 9 -0.0424 -1.5529 -2.2297 -2.4214 -2.5343 -2.5501 - 2.5552 NGC 157 11 .1 2.8x2 .1 21. 7 1.0 171 84 51 41 41 81 10 0.0498 -1.4655 -2.1659 -2.3763 -2.5047 -2.5269 - 2.5333 11 0.1596 -1.3581 -2.0810 -2.3036 -2.4499 -2.4823 - NGC 175 12 .8 1. 5x1 . 3 22 .2 0.8 2.4937 243 148 104 68 60 81 12 0.2934 -1.2256 -1.9674 -2.1965 -2.363 1 -2.4092 - 2.4318 NGC 185 11 . 8 3.5x2 .8 22 .9 0.5 103 44 30 28 41 13 0.4557 -1.0673 -1.8186 -2.0531 -2.2445 -2.3083 NGC 205 10 .8 8.0x3 .0 22 .9 0.5 89 38 28 27 41 -2.3491 14 0.6500 -0.8841 -1.6292 -1.8741 -2.0989 -2.1848 - 2.2505 NGC 224 4.0 150x5 0 15 0.8808 -0.6687 -1.3967 -1.6611 -1.9284 22 .3 -2.0411 0.8 7 14 20 27 -2.1375 16 1.1558 -0.3952 -1.1264 -1.4176 -1.7300 -1.8727 - 2.0034 NGC 221 17 1.4822 -0.0419 -0.8243 -1. 1475 -1.5021 -1.6768 -1.8420 NGC 225 8. 14x14 22 .4 0.8 7 14 20 27 41 1.8559 0.3458 -0.4924 -0.8561 -1.2661 -1.4721 -1.6624 NGC 246 8.5 4.0x2 .5 19 .6 1.8 133 36 32 19 2.2669 0.6960 -0.1315 -0.5510 -1.0562 -1.2892 18 20 2.6760 1.0880 0.2060 -0.3210 -0.8800 -1. 1370 21 2.7766 1.2065 0.3467 -0. 1 377 -0.7361 -0.9964 -1.4827 -1.3620 - 1 .2439 NGC 188 10 . 15x15 24 .5 -0.1 7 14 20 27 41 54 81 9.5 54 54 54 41 54 3.6x3 .1 20 .7 1.4 82 35 26 27 41 54 81 NGC 247 10 .7 18 .0x5 .0 24 .2 0.0 29 16 20 27 41 57 41 81 81 81 54 81 54 81 NGC 253 7.0 22x6 20 .9 1.3 19 14 20 27 41 54 81 22 2.9304 1.3821 0.5353 0.0328 -0.5605 -0.8606 -1.1187 NGC 255 12 .8 1. 5x1 . 5 22 .3 0.8 177 108 76 81 NGC 278 55 23 3.1634 1.6107 0.7708 0.2531 -0.3895 -0.7030 11 .6 -0.9681 1. 2x1 . 2 20 .6 1.5 300 290 124 67 81 NGC 292 1.5 210x2 10 21. 7 3.4643 1.9034 1.0338 0.4943 -0.2033 -0.5259 -0.8288 1.0 7 14 20 24 27 41 81 NGC 288 7.2 10xl0 20 .8 1.4 8 14 1.3265 0.7605 0.0172 -0.2992 20 -0.6394 27 41 81 25 3.8211 2.2564 NGC 281 8.0 23x27 23 .6 0.3 7 14 20 27 41 81 54 26 4.2210 2.6320 1.6990 1.1320 0.2860 -0.0510 -0.4080 27 4.6100 3.0660 2.1320 1.5850 0.6520 0.2410 -0.1210 NGC 300 11 .3 21x14 26 .1 -0.7 u7 u14 u20 27 41 NGC 309 12 .5 2.4x2 .1 22 .9 0.5 84 51 41 41 Scl - Sys 8.8 60x60 26 .3 -0.8 u7 14 20 27 41 54 81 NGC 337 12 .8 3.0xO .5 21. 9 1.0 720 720 720 531 227 you still might find it. Of all the objects for be seen at any power in any of the telescopes. NGC 362 10xl0 19 .6 1.8 8 14 20 27 41 81 which magnitude data could be found, all can Again, the ODM is a guide for when you're be detected in at least one of the telescope having difficulty detecting an object; it's not 1.1613 12 .0 11x9 25 .6 -0.5 u9 u14 20 27 41 81 sizes listed. an absolute rule. NGC 404 11 .9 1. 3x1 . 3 21 .1 1.3 277 243 148 104 68 60 81 In some cases, the listed optimum de tec- Finally, a computer program in FOR- NGC 428 11 .7 3.9x3 .5 23 .2 0.4 63 27 22 27 41 81 NGC 457 tion magnification is extremely high because TRAN that computes the ODM for any ob- 10xl0 20 .6 1.4 8 14 20 27 NGC 488 11 .2 3.5x3 .0 22 .4 the object is very small. A good example is ject, and indicates whether or not the con- 89 38 28 27 41 54 81 the tiny planetary nebula NGe 3918. How- trast is high enough to see it in a dark country NGC 520 12 .4 3.0xO .7 21 . 8 1.0 514 514 412 251 177 122 ever, its contrast is so high (Cl = 4.6, for a sky, is given in Table F.5. NGC 581 8. 8x8 21 .1 1.2 11 14 20 27 54 81 contrast of nearly 40 OOO!) that it can easily NGC 598 6. 7. 5.3 NGC 604 lxl 0.7 177 76 41 41 54 54 54 54 54 54 373 54 54 54 81 81 81 54 81 60x60 22 .8 0.6 7 14 20 27 41 54 81 NGC 613 11 .1 3.0x2 .0 21 . 7 1.0 180 93 57 44 41 54 81 322 323
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OF THE ROGER N. CLARK
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Published by Sky Publishing Corpora
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CONTENTS M78 (NGC 2068) NGC 207 1,
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PREFACE During research for this bo
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VISUAL ASTRONOMY OF THE DEEP SKY AB
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VISUAL ASTRONOMY OF THE DEEP SKY TH
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.. .. .. .. VISUAL ASTRONOMY OF THE
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e viewed with enough magnification
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lens and a piano-convex eye lens. A
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controlled depends on how many laye
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The Lumicon H-Beta Filter (Figure 3
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every 1 ° in declination and 4 min
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error of only one quarter the field
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Table 4.1. Ideal limiting magnitude
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5 Making drawings and keeping recor
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more detail in the future. They add
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.. .. .. ... Contrast (C) C Log(C)
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VISUAL ASTRONOMY OF THE DEEP SKY A
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--- VISUAL ASTRONOMY OF THE DEEP SK
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--- M76 (NGC 650-651), PLANETARY NE
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-- -- M45, THE PLEIADES OPEN CLUSTE
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-- Brightest stars of the Pleiades
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M42 (NGC 1976), M43 (NGC 1982), THE
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--- --- --- VISUAL ASTRONOMY OF THE
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-- --- NGC 2023 NGC 2024, IC 434 (T
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--- --- M78 (NGC 2068), NGC 2071, D
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VISUAL ASTRONOMY OF THE DEEP SKY --
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--- M67 (NGC 2682), OPEN CLUSTER IN
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-- VISUAL ASTRONOMY OF THE DEEP SKY
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--- -- M82 (NGC 3034), PECULIAR GAL
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-- --- --- MI05 (NGe 3379) NGe 3384
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MI09 (NGe 3992), GALAXY IN URSA MAJ
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-- --- M99 (NGC 4254), GALAXY IN CO
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== -- VISUAL ASTRONOMY OF THE DEEP
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--- --- -- NGC 4449, GALAXY IN CANE
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-- -- --- VISUAL ASTRONOMY OF THE D
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--- -- M90 (NGC 4569), GALAXY IN VI
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--- -- M94 (NGC 4736), GALAXY IN CA
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-- VISUAL ASTRON0MY OF THE DEEP SKY
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-- --- -- VISUAL ASTRONOMY OF THE D
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-- -- VISUAL ASTRONOMY OF THE DEEP
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--- -- M83 (NGC 5236), GALAXY IN HY
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--- VISUAL ASTRONOMY OF THE DEEP SK
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--- -- VISUAL ASTRONOMY OF THE DEEP
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---------------- 5 / --------______
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--- -- VISUAL ASTRONOMY OF THE DEEP
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VISUAL ASTRONOMY OF THE DEEP SKY --
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Page 119 and 120: -- -- VISUAL ASTRONOMY OF THE DEEP
Page 121 and 122: VISUAL ASTRONOMY OF THE DEEP SKY A
Page 123 and 124: -- MI5 (NGC 7078), GLOBULAR CLUSTER
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Page 131 and 132: -- VISUAL ASTRONOMY OF THE DEEP SKY
Page 133 and 134: -- ·rl E I u L ro 5 +J Q) (f) 0 Y
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Page 137 and 138: VISUAL ASTRONOMY OF THE DEEP SKY NG
Page 139 and 140: '2 5 -rl E I U L CO '---' -t-J ill
Page 141 and 142: VISUAL ASTRONOMY OF THE DEEP SKY AP
Page 145 and 146: VISUAL ASTRONOMY OF THE DEEP SKY Ta
Page 149 and 150: -- Appendix E A catalog of deep-sky
Page 151 and 152: --- -- VISUAL ASTRONOMY OF THE DEEP
Page 153 and 154: -- -- --- VISUAL ASTRONOMY OF THE D
Page 155 and 156: --- --- VISUAL ASTRONOMY OF THE DEE
Page 165 and 166: -- -- VISUAL ASTRONOMY OF THE DEEP
Page 167: -- APPENDIX F: OPTIMUM DETECTION MA
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Page 173 and 174: VISUAL ASTRONOMY OF THE DEEP SKY -
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Page 183 and 184: G VISUAL ASTRONOMY OF THE DEEP SKY
Page 185 and 186: INDEX INDEX M70 (NGC 6681), 312, 31
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OF THE ROGER N. CLARK

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