PHOTOELECTRIC PHOTOMETRY OF NGC 6210.
A series of photoelectric measurements of the planetary nebula NGC 6210 were carried out in May, 1999 using a 0.51m Newtonian telescope along with an SSP-3 solid state photometer and filters that have been transformed to the Johnson B, V, R and I system. The respective B, V, R and I magnitudes for NGC 6210 are: 9.70[+ or -]0.02, 9.08[+ or -]0.02, 9.66[+ or -]0.02 and 10.35[+ or -]0.04. If a distance of 1.57 kiloparsecs is used for NGC 6210 then the absolute magnitudes of this object are: -1.28, -1.90, -1.32 and -0.63 for the B, V, R and I filters respectively.
Planetary nebulae are believed to be stars in their final life cycle stage and thus the study of these nebulae may give further clues about the life cycles of stars. By knowing the distance and apparent magnitudes at different wavelengths, one can compute absolute magnitudes and the total light output of these objects. In this report, we present photoelectric magnitude measurements of the planetary nebula NGC 6210.
NGC 6210 is at a distance of 1.57[+ or -]0.40 kiloparsecs  and has an angular diameter of 16 arc-seconds . NGC 6210 has a diameter of 0.12 parsecs or 0.40 light years. Through a large telescope, this nebula appears as a bluish smudge [3, 4]. The total photographic magnitude of NGC 6210 is reported to be 9.3  while the central star is reported to have a photoelectric V magnitude of 12.90 . Bently  reports that NGC 6210 may have a cool companion star. The temperature of the central star is 60,000 K .
METHODS AND MATERIALS
An SSP-3 solid state photometer along with a 0.51 meter f/4.5 Newtonian telescope was used in measuring the brightness and color of NGC 6210 in May 1999. Filters that have been transformed to the Johnson B, V, R and I system, were also used in this study.
Transformation coefficients were evaluated using the two star method as described by Hall and Genet . The two stars used in measuring the transformation coefficients were chi-Pegasus and gamma-Pegasus; both stars are listed as U, B, V, R and I standard stars in the Astronomical Almanac and the magnitudes used for these two stars were taken directly from the Astronomical Almanac . The transformation coefficients are: [[epsilon].sub.B] = 0.091[+ or -]0.020; [[epsilon].sub.V] = -0.019[+ or -]0.010, [[epsilon].sub.R] = -0.072[+ or -]0.010 and; [[epsilon].sub.I] = -0.107[+ or -]0.010. Transformation corrections for each filter were computed from:
[delta]B = [delta]b + [[epsilon].sub.B]([delta]B-V) (1)
[delta]V = [delta]V + [[epsilon].sub.V]([delta]B-V) (2)
[delta]R = [delta]r + [[epsilon].sub.R]([delta]B-V) (3)
[delta]I = [delta]i + [[epsilon].sub.I]([delta]B-V) (4)
The comparison star used for all measurements was zeta-Hercules and the magnitudes used for this star were B = +3.47, V = +2.81, R = +2.27 and I = + 1.96 .
On several occasions dark current readings were made and this enabled us to measure the brightness of the dark sky at our location. The mean sky brightness per square arc-second based on these measurements are: B = 20.77[+ or -]0.03, V = 19.85[+ or -]0.04 R = 19.51[+ or -]0.04 and I = 18.40[+ or -]0.05. All sky brightness measurements were made within 10 arc-minutes of NGC 6210. The moon was either not in the sky or was at a very thin phase during the measurements.
A total of three 10-second integrations were always made of the comparison star and of the sky near the comparison stars. Since NGC 6210 is rather faint, six 10-second integrations were always made of this object. Three 10-second sky readings were taken before and after the NGC 6210 readings.
The measured magnitudes for NGC 6210 are listed in Table I. All magnitudes have been corrected for both atmospheric extinction and transformation. Extinction corrections were made in the same way as is described in Hall and Genet ; [k.sub.b]" was assumed to equal -0.03 while [k.sub.v]", [k.sub.r]" and [k.sub.i]" were all assumed to equal 0.00. All k' values were measured on the same night as the photoelectric measurements; typical values (magnitudes/air magnitudes) were: [k.sub.b]' 0.553; [k.sub.v]' = 0.355, [k.sub.r]' = 0.272 and [k.sub.i]' = 0.218. The dates in Table I correspond to the V-filter measurement of NGC 6210; other filter measurements in the same row were made within 10 minutes of the V-filter measurements.
The selected magnitudes for NGC 6210 are: B = 9.70[+ or -]0.02, V = 9.08[+ or -]0.02 R = 9.66 [+ or -] 0.02 and I = 10.35[+ or -]0.04. Uncertainties (U) were calculated from:
U = [[[(S/[square root]N).sup.2] + [(0.001).sup.2] + [(0.005).sup.2]].sup.1/2] (5)
where [sigma] is the standard deviation, N is the number of measurements (14 in this paper) and the 0.01 term is the uncertainty in the star magnitude and the 0.005 term is the uncertainty in transformation and k" corrections.
NGC 6210 is at a right ascension of [16.sup.h] [44.5.sup.m] and is at a declination of +23[degrees] [49.sup.m] which corresponds to approximate galactic coordinates of 410 longitude and 380 latitude . Since this nebula is 38[degrees] from the galactic equator, we do not anticipate that interstellar extinction and reddening will change the magnitudes significantly.
A range of magnitudes have been reported for NGC 6210; a few of these are: 9.7 , 9.3 , 9.5 , 9.3 , 8.8 , 8.8-visual  and 9.3-photographic . The photoelectric V-filter value selected in this study is 9.08[+ or -]0.02. One possible reason for the range of previously reported magnitudes may be that the nebula has a variable magnitude and this is one reason for carrying out precise magnitude measurements so that in the future, measurements can be compared with the results in this paper. A few planetary nebulae have been reported to have a variable brightness .
There seems to be some uncertainty in the size of NGC 6210. Angular diameters (in arc-seconds) of: 16x20 , 17 , 14 , 16  and 15  are listed for NGC 6210. The average of all five values yields an area of 202[+ or -]17 square arc-seconds which is the value selected here. If it is assumed that interstellar extinction is negligible then the surface brightness and absolute magnitude of NGC 6210 can be determined. The selected surface brightness (magnitude per square arc-second) for NGC 6210 are: B = 15.5[+ or -]0.1, V = 14.8[+ or -]0.1, R = 15.4[+ or -]0.1 and I = 16.1[+ or -]0.1 where the uncertainty is almost entirely due to the uncertainty in the angular size of NGC 6210. These values can be compared to a surface brightness of V = 9.4 for Neptune (8) and V = 14.4 for NGC 7027 . The surface brightness of NGC 6210 was at least 4 magnitudes brighter than the sky brightness except for the I-filter where the difference was only 2.3 magnitudes. This smaller difference for the I filter is prob ably why there was more scatter in values of the I magnitude.
The distance to NGC 6210 is reported to be 1.57[+ or -]0.40 kiloparsecs  and so the absolute magnitudes for this object are selected as B = -1.28[+ or -]0.57, V = - 1.90[+ or -]0.57, R = -1.32[+ or -]0.57 and I = -0.63[+ or -]0.57. Persi et al.  report J, H, K and L photometric magnitudes for NGC 6210 of 10.15, 10.60, 9.91 and 6.69 which yield respective absolute magnitudes of -0.83 (J), -0.38 (H), -1.07 (K) and -4.29 (L). All of the normalized magnitudes are of course based on the assumption that there is no interstellar extinction.
The authors would like to thank the Atlanta Astronomy Club for maintaining the facilities at the Walter Barber Observatory.
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Photoelectric magnitude measurements of NGC 6210 made in May, 1999. Date - 1999 Magnitude (Universal Time) B V R May 11.202 9.64 9.10 9.67 May 11.232 9.70 9.10 9.66 May 11.256 9.67 9.10 9.65 May 11.280 9.69 9.11 9.67 May 16.296 9.68 9.05 9.66 May 16.328 9.68 9.12 9.67 May 16.356 9.81 9.02 9.58 May 16.395 9.77 9.11 9.68 May 17.300 9.71 9.08 9.62 May 17.338 9.68 9.09 9.67 May 17.364 9.69 9.07 9.66 May 20.300 9.70 9.07 9.65 May 20.329 9.75 9.08 9.69 May 20.369 9.67 9.04 9.68 Average 9.70[+ or -]0.02 9.08[+ or -]0.01 9.66[+ or -]0.01 Date - 1999 (Universal Time) I May 11.202 10.34 May 11.232 10.23 May 11.256 10.43 May 11.280 10.22 May 16.296 10.25 May 16.328 10.73 May 16.356 10.31 May 16.395 10.44 May 17.300 10.47 May 17.338 10.28 May 17.364 10.38 May 20.300 10.07 May 20.329 10.42 May 20.369 10.30 Average 10.35[+ or -]0.04
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|Author:||Schmude, Jr., Richard W.; Mehta, Prital|
|Publication:||Georgia Journal of Science|
|Date:||Sep 22, 2000|
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