(Tony Flanders) wrote in message ...
Oh how I long for a cheap, widely available device to give an
objective measure of sky brightness!
I'll second that request for a simple device that would measure
naked-eye and through the scope sky brightness. Until then, a good
rule-of-thumb is useful.
Bill Ferris, whose record as an observer in the extraordinary skies of
Flagstaff is without comparision (see
http://members.aol.com/billferris/h400.html ), proposed a simplified
linear rule-of-thumb for relating naked-eye-limiting magnitude to sky
brightness in magnitudes per arcseconds. Boiled down, his rule is sky
brightness (Ba) = naked-eye-limiting-magnitude + 14. Ferris requested
comments on the reasonableness of his proposed rule-of-thumb. Harold
Lang commented that Schaefer's exponential model of sky brightness was
not linear and therefore Ferris's proposed rule may not work.
The following is a comparision of the Schaefer brightness model to
Ferris's proposed simplified rule:
Ferris
Schaefer simplified
Olof-Carlin rule-of-
rule thumb Diff.
NELM Ba
4.0 18.0 18.0 +0.0
4.5 18.7 18.5 +0.2
5.0 19.3 19.0 +0.3
5.5 20.0 19.5 +0.5
6.0 20.8 20.0 +0.8
6.5 21.7 20.5 +1.2
7.0 22.9 21.0 +1.9
7.5 24.9 21.5 +3.4
Schaefer revised by Olof-Carlin
Ba = 21.58 - 5 log(10^(1.586-lim_mag/5)-1)
Ferris proposed simplified rule of thumb
Ba = lim_mag + 14
Ba = sky brightness measured in
magnitude per square arcsecond (MPSA)
NELM = naked-eye limiting magnitude in field of
observation
A graphical representation of the above table is available on my
personal web page at:
http://members.csolutions.net/fisher...le_compare.gif
From the table and graph, is appears that Harold is right, after
leaving a light-polluted sky for extraordinary skies, the Ferris's
proposed simplified rule breaks down. (Although overall the
coeffiecient of correlation for the Schaefer to Ferris rules is .98.)
Conversely, most beginning amateurs, like myself, cannot measure
naked-eye limiting magnitude or zenith limiting magnitude to an
accuracy of under .5 mags. We also live in semi-light-polluted areas
under mag 6.5. So, for most people of moderate skill using the
simplified rule, they probably can use Ferris's simplified rule.
(This would not apply to advanced amateurs like yourself and Ferris.)
The purpose of all of this talk about ODM is to improve your
observing. Olof-Carlin summarizes Clark's optimum detection
magnification concept with following easily remembered rule-of-thumb:
"To detect a faint object, you can increase magnification till the sky
is so dark that you have difficulty seeing the field stop, or till the
object has an apparent size of 1 degree, whichever comes first."
and
"The thresholds here (using the ODM algorithm-program) are for
catching barely visible faint objects. If an object is brighter than
that, it may be possible to see detail by increasing the magnification
even further."
See
http://zebu.uoregon.edu/~mbartels/vi.../blackwel.html
(accessed August 2003).
Charming, isn't it, how wildly the experts vary? . . . .
And estimates of NELM under heavy light pollution vary even more,
if possible, although I suspect for somewhat different reasons.
Olof-Carlin's web page discussion pointed out that the Blackwell/Clark
estimate of sky-brightness contained some implementation errors.
Therefore, Carlin concluded that the Schaefer formulae probably better
modeled what is observered in the sky. This was based on Olof-Carlin
detecting an err in the Clark's ODM algorithm, to which Harold has
referred a couple of times. See -
http://zebu.uoregon.edu/~mbartels/vi.../blackwel.html
(Olof-Carlin states that "[t]o my surprise, my results did not quite
match Clark's' and goes on to described Clark's 'double-fault' in
implementing his algorithm.)
Bartel's ODM program, discussed in the Ferris' article in the August
Sky & Telescope, corrects Clark's error in implementation, (but does
not change Clark's important underlying insight).
Let's say that the dream sky, which can be approached but
never equalled on Earth, is mag 22 per square arcsecond.
. . . FWIW, under my customary decent rural skies --
surely no better than mag 21 per square arcsecond, if that
-- I have seen stars to mag 6.8 or 6.9, but I have done no
better at all under far darker and clearer skies out West.
For most of us living in semi-light-polluted skies, Ferris's
simplified rule would be useful. (Ba = NELM + 14 up to mag. 6.5) For
personal purposes, I'll probably use the Schaefer brightness rule
table I restated in this post, when using Bartel's ODM program
(discussed in the August 2003 Sky & Telescope). (But if I happen to
leave the table at home, "NELM + 14" is easy to remember. -
.)
For the rare luckly few of us, like Bill Ferris, an expanded rule for
extraordinary skies might still be useful. Extraordinary skies (above
mag 6.9) occur in Ferris's Flagstaff, Arizona observing location near
the Lowell Observatory, and according to some reports of varying
dispute, on rare occasions exceeds an MPAS of 22. Ferris is a
beneficiary of Flagstaff's Lighting Code, first begun in 1958, to
protect dark skies around the Lowell Observatory.
As you suggest, having a simple device that amateurs could use to
objectively quantify sky brightness would aid in training the amateur
observing eye and in improving their observing technique.
A simple, cheap device that amateurs could use to objectively quantify
sky brightness would also be a positive step in collecting local site
specific data to lobby local government to adopt ordinances similar to
Flagstaff's Lighting Code. If local government is to adopt
regulations, usually it should be based on some objective measurement
of the evil to be remedied, to assure fairness to all. In this case,
the measurement is objective data about the light pollution of a
common public resource - dark skies - that is not dependent on
subjective interpretations of light by interested persons - amateur
astronomers. If you cannot measure it; you cannot regulate it.
Regards - Kurt
References:
W. D. Ferris. Dark Skies Rule. Sky and Telescope. 106(2):62 (August
2003).
Schaefer, Bradley E. 1990. Telescopic limiting Magnitudes
Pub. ASP 102:212-229.
Clark, Roger N. 1991. Visual Astronomy of the Deep Sky. Cambridge
Univ. Press.
Olof Carlin, Nils. About Bradley E. Schaefer: Telescopic limiting
Magnitudes . . . . Web page discussion of brightness in Schaefer
(1990) and Clark (1994) at:
http://w1.411.telia.com/~u41105032/visual/Schaefer.htm (accessed
7/2003)
Olof Carlin, Nils. 1997. Another interpretation of the data from
Blackwell . . . Web page at
http://zebu.uoregon.edu/~mbartels/vi.../blackwel.html (accessed
8/2003)
Flagstaff Lighting Code.
http://c3po.cochise.cc.az.us/astro/pollution06p.htm (accessed 8/2003)