Estimating comet magnitudes - brightness (long)

Although Comet 9P/Tempel will be well-covered by professional
astronomers, the Deep Impact experiment will be visible to amateurs in
the western United States and provides a good opportunity for amateurs
to learn or practice the visual estimation of comet brightness. This
post provides a beginner-intermediate level review of amateur
techniques for visually estimating the magnitudes of comets using four
methods -

- Out-Out method,
- Modified Out-Out method,
- Extra-focal extinction method, and,
- In-Out method.

For beginners looking for Comet 9P finder charts, see Section V(A),
near the bottom of this post.

For advanced CCD astrophotographers, references to nearby Landolt
photometry calibration stars and finder images are given in Section VI,
near the bottom of this post.

Although the non-nuclear Deep Impact experiment may be difficult to
observe because it will be low in western continental U.S. sky, the
experiment is a once-in-lifetime opportunity to potentially see a U.S.
experiment involving high-explosive physics in space. 1962 was the last
time that the United States conducted an even roughly analogous
experiment - the Starfish Prime 1.4 megaton nuclear bomb detonation in
low earth orbit. <<
http://en.wikipedia.org/wiki/Operation_Dominic_I_and_II ;
http://www.atomicarchive.com/Photos/LANL/image56.shtml >>. By
comparison, the non-nuclear Deep Impact kinetic collision will release
energy equivalent to only 4.8 tons of TNT (1/300,000ths of Starfish
Prime), or about the energy consumed by the average U.S. home in one
month. << http://deepimpact.umd.edu/science/cratering.html >> (On the
other hand, it's pretty amazing you might be able to 5 tons of TNT
exploded from 7 1/2 light secs away.)

I. Background information

A. Measurements to estimate comet magnitudes. 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.

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.
See Section II.B.2.iii, below, for how to apply the drift method to
Comet 9P.)

B. 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.

C. 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. (Reports of Comet 9P/Tempel compiled by the
International Comet Quarterly around June 16 list a magnitude around
10.0 and a diameter of 4 to 6 arcmins, about the size of a small
globular cluster.) 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 II.B.2.iii, below.

D. 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.

The atmospheric extinction adjustment is described below in Section
III, below.

E. 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.

F. 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 >>.

II. Magnitude measuring methods

A. Out-Out Method (comet defocused out; comparison star defocused out;
a.k.a. the VBM - Van Biesbroeck-Bobrovnikoff-Meisel method)

1) 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. (If Comet 9P/Tempel brightens to a
potential high magnitude of 7.0, this may be the best method to
visually measure the brightness of the impact.)

2) Procedure.

i) Apply the lowest usable magnification.

ii) Defocus (either inside or outside focus) until -

A) the coma and nucleus of the comet are a uniform circular
brightness, and,

B) the diameter of the defocused stars in the field of view and the
defocused comet are similar.

iii) 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.

iv) Lookup the comparison stars' "V"-band magnitude in a reputable
catalogue, like the Tycho 2 catalogue.

v) If needed, adjust for atmospheric extinction as described below.

vi) 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.

B. Modified Out-Out Method (comet defocused out; comparison star
defocused out; a.k.a. the Morris-O'Meara method)

1) 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.

2) Procedure

The procedure for the modified Out-Out method is the same as for the
Out-Out method, but -

i) the angular size and brightness of the defocused comet is
memorized.

ii) The telescope or binoculars then is slewed to a new field-of-view
containing the comparison star.

iii) The comparison star is defocused to the memorized diameter of the
defocused comet.

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.

At the point of impact, the Comet 9P will be at approximately
J133751.52 -093400.5. At -09ø34' declination, the drift rate of
celestial objects will be 0.247 arcminutes per second or 14.79
arcseconds per second. Table 1.0 gives the size in arcminutes for
various seconds of drift at 9ø30' of declination:

Table 1.0 - Object size from drift rates at 9ø30' 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

C. 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)

1) 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. (Comet 9P/Tempel 1, before the Deep Impact
experiment fits this category. Reports of Comet 9P/Tempel compiled by
the International Comet Quarterly around June 16 list a magnitude
around 10.0.)

2) Procedure

i) 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.

ii) Estimate or measure (using the drift method) the angular size of
the disk.

iii) 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.

iv) Lookup the comparison stars' "V"-band magnitude in a reputable
catalogue, like the Tycho 2 catalogue.

v) If needed, adjust for atmospheric extinction as described below.

vi) The comet's zenithal estimated magnitude is the midpoint between
the adjusted magnitudes of the two comparison stars.

D. The In-Out Method (comet in-focus, star out-of-focus; a.k.a. the VSS
method - Vekhsvyatskij-Steavenson-Sidgwick method)

1) Best used for. Best used for higher contrast comets.

2) Procedure

i) Guess or estimate the m1 surface brightness of the comet.

ii) Measure or memorize the diameter of the comet.

iii) Locate nearby comparison stars in a catalogue, usually 1 or 2
magnitudes brighter than your estimate.

iv) Defocus the comparison star to the same diameter as the in-focus
comet.

v) Lookup the comparison stars' "V"-band magnitude in a reputable
catalogue, like the Tycho 2 catalogue.

v) If needed, adjust for atmospheric extinction as described below.

vi) The comet's zenithal estimated magnitude is the midpoint between
the adjusted magnitudes of the two comparison stars.

III. 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.

IV. Describing the density profile of the comet

The following descriptions, from <<
http://cometforum.planetaclix.pt/meth.html >> may be of use in
describing the density profile of a comet -

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).

V. Comet 9P/Tempel - Finding and stellar magnitude charts

A. Finder charts

The "official" Deep Impact site finder chart -
http://deepimpact.umd.edu/gallery/Finder_Charts.html

Detailed finders at Astrosite Groningen with stellar magnitudes -
http://www.shopplaza.nl/astro/comets/9pcharts/comets.htm
http://www.shopplaza.nl/astro/comets/9pcharts/9PCH11.png
http://www.shopplaza.nl/astro/comets/9pcharts/9PCH1C.2.png

Author's finder charts to mag 12 -

Topocentric position of Salt Lake City, Utah -

RA/Dec Chart:
http://members.csolutions.net/fisherka/astronote/finder/Comet9PFinder.gif

Alt-Az Chart (for 111 W, 41 N):
http://members.csolutions.net/fisherka/astronote/finder/Comet9PFinderAltAz.gif

B. Some practical tips on finding Comet 9P/Tempel 1

At dusk, on any basic star chart find the line between alpha Virgo
(Spica) and gamma Virgo. Currently Jupiter is just southwest of gamma
Virgo. Mid-way between gamma Virgo-Jupiter and Spica is theta Virgo
(v4.4).

Your first finder line is between Spica and theta Virgo.

Next, using binoculars or your finder scope, establish a second
reference line about 5 degrees north of your first reference line. The
second reference line is defined by 82 Virgo (v5.0), 74 Virgo (v4.7),
72 Virgo (v6.1), 66 Virgo (v5.8) and 65 Virgo (v5.8).

Comet 9P/Tempel 1 is between these two reference lines as indicated on
the above charts for any given night.

C. Recent magnitude data

Amateur observations are compiled by the International Comet Quarterly
at:

<< http://cfa-www.harvard.edu/iau/icq/CometMags.html >>

Some recent observations for Comet 9P from the ICQ website are
reproduced here:

Decimal_day; V_mag; Diameter_arcsec; (Observer, OP, scope, camera)

2005
June 16.06, 09.9, 6.0' (J. J. Gonzalez, Leon, Spain, 25x100
binoculars);
13.92, 10.1, 4.0' (A. Baransky, Bucha, Ukraine, 0.20-m
reflector);
13.00, 11.1, +1.8' (T. Scarmato, Calabria, Italy, 0.25-m
reflector + CCD);
11.92, 10.0, 4.5' (A. Baransky, Pylypovychi, Ukraine, 0.36-m
reflector);
10.95, 10.6, 4.0' (C. Gros, Besancon, France, 20x100
binoculars);
10.90, 11.2, +1.8' (T. Scarmato, Calabria, Italy, 0.25-m
reflector + CCD + R_c filter);
10.03, 09.4, 6.0' (J. J. Gonzalez, Leon, Spain, 11x80
binoculars);

VI. Nearest Landolt star fields and CCD calibration stars (Count=5
stars)

Source and more photometry information:
http://www.cfht.hawaii.edu/ObsInfo/Standards/Landolt/
1) G14 55
JPos 13 28 22 -02 21 28
V_mag 11.34
Link to SAO area chart -
http://www.cfht.hawaii.edu/ObsInfo/Standards/Landolt/G14.gif

2) 105 505
Jpos 13 35 24 -00 23 47
V_mag 10.27
Link to SAO area chart -
http://www.cfht.hawaii.edu/ObsInfo/Standards/Landolt/SA105.gif

3) 105 815
Jpos 13 40 04 -00 02 19
V_mag 11.45
Link to SAO area chart -
http://www.cfht.hawaii.edu/ObsInfo/Standards/Landolt/SA105.gif

4) +2 2711
Jpos 13 42 20 +01 29 58
V_mag 10.37
Link to SAO area chart -
http://www.cfht.hawaii.edu/ObsInfo/Standards/Landolt/PLUS2.gif

5) HD121968
Jpos 13 58 51 -02 55 38
V_mag 10.25
Link to SAO area chart -
http://www.cfht.hawaii.edu/ObsInfo/Standards/Landolt/HD121968.gif

Enjoy - Canopus56

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 >>

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