Background information
m1 measures the comet as whole; m2 measures the nucleus.
The methods described below are designed to visually measure the m1 magnitude of a comet. The m1 magnitude is the integrated brightness of coma and nucleus of the comet. m2 is the integrated brightness of the nucleus. Generally, this is accomplished by comparing the average visual surface brightness of the defocused comet with the visual surface brightness of a comparison star, defocused to the same diameter as the comet.Magnification applied.
Low magnification (typically 30x-40x) is applied to make the measurement unless unpractical due to a small comet size. Low magnification is used because as higher levels of magnification are applied, the outer portions of the comet's coma fade below the surface brightness of the night sky. Higher magnification makes the comet appear smaller in diameter and with a lower total integrated magnitude than is seen with low magnification.Estimating in-focus and out-of-focus comet size.
In-focus and out-of-focus comet diameters can be crudely measured using the drift method and a stopwatch. Even if you have not calibrated the drift rate of your low magnification eyepieces or do not have a low magnification eyepiece with a graduated reticule, the relative diameter of a defocused comparison star and the defocused comet can be estimated by measuring their drift rate in seconds, assuming the comparison objects are at nearly the same declination. See Section 2.2, below.Adjusting estimated magnitude for atmospheric extinction.
Magnitudes can be described as either apparent - that is unadjusted for the effect of atmospheric extinction - or zenithal - that is adjusted for the effect of atmospheric extinction. Because there is less air mass at the zenith, magnitudes measured when an object is close to the zenith are higher than those measured when the object is near the horizon. Typically, the magnitude of the defocused comet is compared to the magnitude of a defocused comparison star. The magnitude of the comparison star is looked-up in a reputable catalogue - like the Tycho 2 catalogue - and its "V" band magnitude is used to describe the integrated magnitude of the comet. If the comparison star and the comet are in same part of the sky and are dimmed by the same level of atmospheric extinction, then the catalogue "V" band magnitude is the true zenithal magnitude of the comparison star and comet. If the comparison star is significantly higher or lower than the comet, then the catalogue "V" band magnitude of the comparison star needs to be adjusted for atmospheric extinction to yield the true zenithal magnitude of the comet and comparison star and/or the apparent magnitude of the comet.Number of measurements.
Although for pleasure observing, one measurement often is taken, the usual practice is to make several measurements using various sets of comparison stars and then the results are averaged.Confirming doubtful magnitudes.
If in doubt, the V magnitude of a star can be verified using the Centre de Donn,es astronomiques de Strasbourg (CDS) Simbad database query form at << http://simbad.u-strasbg.fr/sim-fid.pl >>.
The diameter of the comet should also be measured. The integrated surface brightness of an object is more useful when you also measure the area over which that brightness is spread. Most beginning amateurs have used similar information when observing small faint galaxies. Both the integrated magnitude and diameter of the galaxy are reported in astronomical catalogues. Typically, the diameter is measured by the drift method. (The drift method is not covered in depth by this note.)
The atmospheric extinction adjustment is described below in Section 3.0, below.
Magnitude measuring methods
Out-Out Method (comet defocused out; comparison star defocused out; a.k.a. the VBM - Van Biesbroeck-Bobrovnikoff-Meisel method)
Best used for.
The Out-Out method is best used when (1) there is a higher contrast between the comet and the background night sky and (2) comparison stars are available within the same field of view or within an adjacent eyepiece field of view.Procedure.
- Apply the lowest usable magnification.
- Defocus (either inside or outside focus) until -
- the coma and nucleus of the comet are a uniform circular brightness, and,
- the diameter of the defocused stars in the field of view and the defocused comet are similar.
- Find a defocused star in the field of view slightly brighter than the defocused comet. Find a defocused star in the field of view slightly dimmer than the defocused comet.
- Lookup the comparison stars' "V"-band magnitude in a reputable catalogue, like the Tycho 2 catalogue.
- If needed, adjust for atmospheric extinction as described below.
- The comet's zenithal estimated magnitude is the midpoint between the adjusted magnitudes of the two comparison stars. Report your magnitudes as either apparent or zenithal adjusted.
Modified Out-Out Method (comet defocused out; comparison star defocused out; a.k.a. the Morris-O'Meara method)
Best used for.
Same as the Out-Out method. The modified Out-Out method is almost identical to the Out-Out method, but it attempts to compensate for the fact that appropriate comparison stars are often not available in the same field of view as the comet.Procedure
- the angular size and brightness of the defocused comet is memorized.
- The telescope or binoculars then is slewed to a new field-of-view containing the comparison star.
- The comparison star is defocused to the memorized diameter of the defocused comet.
Extra-focal extinction method (comet and comparison star defocused until they disappear against the brightness of the background night sky; a.k.a. the Beyer method)
Best used for.
Best used for comets that have a low contrast between the comet and the background night sky. This occurs with fainter comets and in suburban/rural and rural/dark transition skies with low light pollution.Procedure
- The comet is defocused until it just disappears against the background night sky, as seen in the eyepiece. Then back-in the focus until the disk of the defocused comet is faintly visible.
- Estimate or measure (using the drift method) the angular size of the disk.
- A comparison star is located that disappears against the background night sky at nearly the same angular size when defocused. Alternatively, two defocused stars, one slightly brighter and one slightly dimmer than the defocused comet are located.
- Lookup the comparison stars' "V"-band magnitude in a reputable catalogue, like the Tycho 2 catalogue.
- If needed, adjust for atmospheric extinction as described below.
- The comet's zenithal estimated magnitude is the midpoint between the adjusted magnitudes of the two comparison stars.
The In-Out Method (comet in-focus, star out-of-focus; a.k.a. the VSS method - Vekhsvyatskij-Steavenson-Sidgwick method)
Best used for.
Best used for higher contrast comets.Procedure
- Guess or estimate the m1 surface brightness of the comet.
- Measure or memorize the diameter of the comet.
- Locate nearby comparison stars in a catalogue, usually 1 or 2 magnitudes brighter than your estimate.
- Defocus the comparison star to the same diameter as the in-focus comet.
- Lookup the comparison stars' "V"-band magnitude in a reputable catalogue, like the Tycho 2 catalogue.
- If needed, adjust for atmospheric extinction as described below.
- The comet's zenithal estimated magnitude is the midpoint between the adjusted magnitudes of the two comparison stars.
The procedure for the modified Out-Out method is the same as for the Out-Out method, but -
This procedure involves a subjective measurement of the diameter of the defocused comet and the comparison star.
One modification that might improve the measurement of the diameter of the defocused objects is to measure their diameter using the drift method. Place with one side of the object against the field stop, turnoff any drive motors on your telescope's mount, and measure the numbers seconds it takes for the object to drift out of the field of view, using a stopwatch. When the comet and comparison star are defocused so they have nearly the same drift rate (assuming they are at nearly the same altitude), then they have the same diameter.
Table 1.0 gives the size in arcminutes for various seconds of drift at 9d30' of declination:Table 1.0 - Object size from drift rates at 9d30' declination Sec Rate " Size " Size ' 12 14.79 177 3.0 14 14.79 207 3.5 16 14.79 237 4.0 18 14.79 266 4.4 20 14.79 296 4.9 22 14.79 325 5.4 24 14.79 355 5.9 26 14.79 385 6.4 28 14.79 414 6.9 30 14.79 444 7.4 32 14.79 473 7.9 34 14.79 503 8.4 36 14.79 532 8.9 38 14.79 562 9.4 40 14.79 592 9.9 42 14.79 621 10.4
Defocused comparison stars on the celestial equator will have a size of 15 arcseconds for second of drift or as listed in the following table of declinations 0 to 9 degrees:
Table 2.0 - Drift rates per second for declinations 0 deg to -8 degs Dec Drift rate arcsec per sec +0 15.00 -1 15.00 -2 14.99 -3 14.98 -4 14.96 -5 14.94 -6 14.92 -7 14.89 -8 14.85 -9 14.82
Atmospheric extinction adjustment
International Comet Quarterly table (Green 1992) provides rough correcting values for atmospheric extinction based on the kilometers of the observing point above sea level:
Table 3.0 "Average" Atmospheric Extinction in Magnitudes for Various Elevations Above Sea Level (h, in km) (Excerpts from Green 1992) z h = 0 h = 0.5 h = 1 h = 2 h = 3 01 0.28 0.24 0.21 0.16 0.13 10 0.29 0.24 0.21 0.16 0.13 20 0.30 0.25 0.22 0.17 0.14 30 0.32 0.28 0.24 0.19 0.15 40 0.37 0.31 0.27 0.21 0.17 45 0.40 0.34 0.29 0.23 0.19 50 0.44 0.37 0.32 0.25 0.21 55 0.49 0.42 0.36 0.28 0.23 60 0.56 0.48 0.41 0.32 0.26 62 0.60 0.51 0.44 0.34 0.28 64 0.64 0.54 0.47 0.37 0.30 66 0.69 0.59 0.51 0.39 0.32 68 0.75 0.64 0.55 0.43 0.35 70 0.82 0.70 0.60 0.47 0.39 72 0.91 0.77 0.66 0.52 0.43 74 1.02 0.86 0.74 0.58 0.48 76 1.15 0.98 0.84 0.66 0.54 78 1.34 1.13 0.98 0.76 0.63 80 1.59 1.34 1.16 0.91 0.74
The "z" value is the degrees from zenith to the celestial object. So z=80 is 20 degrees altitude above the local horizon.
For example, if the "V" band catalogue magnitude of your comparison star is 7.5, the star is located 30 degrees above the horizon (or 60 degrees from the zenith), the observer is at sea level, and the comet and the comparison star are nearly at the same altitude above the horizon, then the true zenithal brightness of the comet is v7.5 and its apparent brightness is v6.9 (7.5-0.56).
If the comet (at 40 degrees altitude) is higher than the comparison star (at 30 degrees altitude), the comet's true zenithal brightness is 7.4 (7.5+0.44-0.56). The 0.1 magnitude represents the additional extinction between 30 and 40 degrees altitude.
Conversely, if the comet (at 30 degrees altitude) is lower than the comparison star (at 40 degrees altitude), the comet's true zenithal brightness is 7.6 (7.5-0.44+0.56). The 0.1 magnitude adjusts for the additional extinction between 40 and 30 degrees altitude.
Describing the density profile of the comet
List 1.0
Degree of concentration number Description
- DC=0 Coma completely uniform in brightness. Flat brightness profile across the coma.
- DC=1 Central coma possibly very slightly brighter than outer coma.
- DC=2 Central zone slightly brighter. Some brightness in balance across the coma.
- DC=3 Central coma definitely brighter than the outer coma. Coma still very diffuse.
- DC=4 Central zone outstandingly brighter; frequently two distinct levels of brightness within the coma. Moderately condensed.
- DC=5 Still more condensed; the central condensation strongly influences m1, hampering the use of the In-out method.
- DC=6 Central zone very prominent. Steep brightness profile; most of the light is in the central condensation.
- DC=7 Sharp peeked brightness profile. The outer coma influences very little the total brightness.
- DC=8 The coma is quasi-starlike, just slightly diffuse; the rest of the coma brightness is irrelevant to the total brightness.
- DC=9 Stellar coma, or small disk. No diffuse coma.
An easy method for beginners to apply the DC scale is to make only rough estimates using levels 0 (no coma), 3 (central coma brighter than outer coma), 6 (prominent central zone), and 9 (comet looks like a star).
Nearest Landolt star fields and CCD calibration stars (Count=5 stars)
Univ. of Hawaii. 2005. Landolt Photometry Reference Fields << Link >>
CFHT Table of Landolt Standard Stars on the Celestial Equator << Link >>
Sonoma College Landolt Standard Star Field Charts << Link >>
Landolt, A. Jul. 1992. CDS Catalogue II/183A for Landolt UBVRI photometric standard stars << Link >>
Landolt, A. 1973. UBV photoelectric sequences in the celestial equator selected areas 92-115. 1973AJ.....78..959L; CDS Cat. VI/19 1996yCat.6019....0L << Link >>
Landolt, A. Jul. 1992. UBVRI photometric standard stars in the magnitude range 11.5-16.0 around the celestial equator. 1992AJ....104..340L; CDS Cat. II/183A/ << Link >>
References:
Green, Daniel. July 1992. Correcting for Atmospheric Extinction. International Comet Quarterly. 14:55 << http://cfa-www.harvard.edu/cfa/ps/icq/ICQExtinct.html >>
Green, Daniel. Oct. 1996. International Comet Quarterly. 104:18
Kraus, Herbert. Nov. 27, 2004. Drift Testing to Determine Your Eyepiece's True Field of View << http://www.astromart.com/articles/article.asp?article_id=188 >>
Levy, David. 2003. David Levy's Guide to Observing and Discovering Comets. Cambridge Univ. Press. At pp. 132-134
Pereira, A and Vitorino, C. ____. The visual photometry of comets. << http://cometforum.planetaclix.pt/meth.html accessed June 2005 >>
