W. Ferris article in Sky and Telescope August 2003 article on ODM

How do you measure sky brightness in magnitudes per square arcsecond
(MPSA)? Is there some way to relate this measurement to the more
typical zenith limiting magnitude or limiting magnitude of the
observing field?

Bill Ferris' article in this month's Sky and Telescope on Optical
Detection Magnitude (ODM) provides a reference to Bartel's c-code
software to compute the ODM. (
http://www.efn.org/~mbartels/aa/visual.html )

One of the input parameters for this model for the visibility of
extended objects is the background brightness of the sky measured in
magnitude per square arcsecond (MPSA).

I am unable to relate this parameter to my existing knowledge of the
limiting magnitude of the observing field, so I can make estimates of
the MPSA during my observing sessions.

Some of the background internet references related to the article
suggest values like:

Mount Wilson 19.8
Palomar Mountain 21.5
Lick Obs. 20.7
Mount Lemmon 21.5 (near Tucson)
Lowell (Mars Hill) 20.5
Van Vleck 18.7 (Connecticut)
David Dunlap 18.4 (Toronto)
Haute Provence 21.8 (southern France)

Any help on how to estimate the MPSA during my local observing
sessions would be appreciated.

Thanks - Kurt

W. D. Ferris. Dark Skies Rule. Sky and Telescope. 106(2):62 (August
2003).

Brian Skiff. How dark can the sky get. Internet article.
http://www.astropix.com/HTML/L_STORY/SKYBRITE.HTM accessed July 2003
(2001)

fisherka wrote:
How do you measure sky brightness in magnitudes per square arcsecond
(MPSA)? Is there some way to relate this measurement to the more
typical zenith limiting magnitude or limiting magnitude of the
observing field?

Bill Ferris' article in this month's Sky and Telescope on Optical
Detection Magnitude (ODM) provides a reference to Bartel's c-code
software to compute the ODM. (
http://www.efn.org/~mbartels/aa/visual.html )

One of the input parameters for this model for the visibility of
extended objects is the background brightness of the sky measured in
magnitude per square arcsecond (MPSA).

I am unable to relate this parameter to my existing knowledge of the
limiting magnitude of the observing field, so I can make estimates of
the MPSA during my observing sessions.

Some of the background internet references related to the article
suggest values like:

Mount Wilson 19.8
Palomar Mountain 21.5
Lick Obs. 20.7
Mount Lemmon 21.5 (near Tucson)
Lowell (Mars Hill) 20.5
Van Vleck 18.7 (Connecticut)
David Dunlap 18.4 (Toronto)
Haute Provence 21.8 (southern France)

Any help on how to estimate the MPSA during my local observing
sessions would be appreciated.

One of the challenges I've been mulling over is finding a way to convert a
naked eye limiting magnitude estimate to a sky surface brightness value. It's a
challenge because, even among a group of experienced observers, naked eye
limiting magnitude estimates can vary significantly. See Bradley Schaefer's
1990 PASP paper for an illustration of this:

http://adsbit.harvard.edu/cgi-bin/np...=1990PASP..102
...212S&db_key=AST&page_ind=0&plate_select=NO&data _type=GIF&type=SCREEN_GIF

At best, I suspect such a conversion would get an observer in the ballpark,
perhaps to within 0.5 magnitude. Here's a table I'll throw out for commentary.
I'd be interested in hearing how well this reflects the real life experiences
of other observers:

NELM.(+/- 0.5)..===..Sky Brightness (mag./sq. arc sec.)
........8.0............22.0
........7.0............21.0
........6.0............20.0
........5.0............19.0
........4.0............18.0

The scale assumes a naked eye limiting magnitude of 8.0 (+/- 0.5) under a dark
country sky and a logarithmic relationship between sky brightness and NELM: for
every full magnitude change in sky brightness, there is a full magnitude change
in NELM.

The faint limit is actually well-established. The darkest the sky gets anywhere
on the planet is 22.0 mag. per sq. arc second. Observers with acute vision have
been known to go as faint as about 8.0 mag. (+/- 0.5 mag., depending on the
observer) under such conditions. Hence, the choice of an NELM of 8.0 with a +/-
0.5 magnitude range for a truly pristine sky.

The sky surface brightness over Mars Hill on the west side of Flagstaff,
Arizona, has been measured by Brian Skiff at 20.3 magnitude per square arc
second on a moonless, clear night. His NELM from this site is about 6.4
magnitude. It's only one data point but it falls within the NELM range for a
sky brightness of 20.0 mag. per sq. arc second.

A sky brightness of 18.0 mag. per sq. arc second corresponds to conditions at
Mars Hill during full Moon. From my home in north-central Flagstaff, about 3
miles east of Mars Hill, I can still see most of the stars in the Little Dipper
asterism under a full Moon. Also from home, I've seen M44 (3.1 mag, 95'
diameter) with the full Moon just 25-degrees away in Leo. A naked eye limit 4.0
magnitude (+/- 0.5) seems a reasonable choice for a bright sky with an 18.0
mag. per sq. arc second surface brightness.

You can also use Bartels' ODM program to explore this. Go back through your
observing records and find the most difficult visual detections of galaxies.
You can go to the NASA/IPAC Extragalactic Database (NED:
http://nedwww.ipac.caltech.edu/ ) to find magnitude and size data for the
galaxy. Enter those numbers and the aperture of your telescope in ODM. Then,
experiment with a range of sky surface brightness numbers to see where the
cutoff is for detection.

Keep in mind that an object at the very threshhold of detection may be visible
only 30% of the time or so with averted vision. In other words, if the objects
you're using to test ODM were visible with direct vision pretty much all the
time, then the LCD (Log Contrast Difference) will probably be 0.25 or greater.

Here's a recent example from my observations. MCG +7-34-50 is a 14.8 magnitude
galaxy near NGC 6166. I observed this object about three weeks ago from a true
dark sky site with my 10-inch Newtonian. Its small size, about 0.4'x0.4',
yields a quite reasonable surface brightness of 21.6 MPSA. At high
magnification, this little stinker was visible with averted vision about 40% of
the time.

Using the above numbers and a sky brightness of 22.0 MPSA, ODM predicts an
object of this type would be visible with an LCD of 0.09. Increasing the sky
brightness to 21.5 MPSA, the LCD drops to 0.02, indicating an object at the
very threshhold of visibility. The site I use is probably not perfect but,
taking into consideration photometry for the Lowell research site several miles
to the north, should fall somewhere around 21.8 MPSA.

I'd cite this as an observation which tends to confirm ODM's efficacy as a tool
for testing your observing site.

Regards,

Bill Ferris
"Cosmic Voyage: The Online Resource for Amateur Astronomers"
URL: http://www.cosmic-voyage.net
=============
Email: Remove "ic" from .comic above to respond

c (Bill Ferris) wrote in message ...
At best, I suspect such a conversion would get an observer in the ballpark,
perhaps to within 0.5 magnitude. Here's a table I'll throw out for
commentary. I'd be interested in hearing how well this reflects the real
life experiences of other observers:

NELM.(+/- 0.5)..===..Sky Brightness (mag./sq. arc sec.)
.......8.0............22.0
.......7.0............21.0
.......6.0............20.0
.......5.0............19.0
.......4.0............18.0

Bill, thank you for the post. I'll add an empirical test of the
relationship using Bartel's ODM program and your proposed table for
magnitude per square arcsecond (MPAS) to my observing list of
things-to-do for the summer season.

Regards - Kurt

P.S. references -

Bartel's version of Clark's ODM program:
http://www.efn.org/~mbartels/aa/visual.html
http://zebu.uoregon.edu/~mbartels/dnld/odm.zip

P.P.S. -

Your proposed table is the simplest to use. Perhaps a direct
relationship equation for MPAS to NELM can be teased out of equations
17 and 18 in Schaefer's 1990 paper (PASP 102:212 at 215), using
simplifying assumptions of observer visual acuity (F_s) = 1.0 and the
extinction coefficient to its mid-point of 0.25 in a range of 0.2 to
0.3? But the math is beyond me.

c (Bill Ferris) wrote in message ...
At best, I suspect such a conversion would get an observer in the ballpark,
perhaps to within 0.5 magnitude. Here's a table I'll throw out for commentary.
I'd be interested in hearing how well this reflects the real life experiences
of other observers:

NELM.(+/- 0.5)..===..Sky Brightness (mag./sq. arc sec.)
.......8.0............22.0
.......7.0............21.0
.......6.0............20.0
.......5.0............19.0
.......4.0............18.0

I believe that I have read somewhere that NELM scales roughly
as the 2/3 power of sky brightness, not directly proportional.
In other words, every extra 3 mag of sky brightness decreases
the NELM roughly 2 mag. Sorry I cannot cite the source.
Certainly, playing around with the program the Schaefer
published in S+T some while back indicates that NELM varies
much more slowly than sky brightness.

That accords with my own intuition, which is that light pollution
hurts the visibility of diffuse sources much more than it hurts
the visibility of stars. Also, I can see mag 4.0 stars fairly
easily in Manhattan, and the sky there sure *seems* more than
16 times as bright as a dark sky where I can see mag 7.0 stars.
But that is pure hunch, of course.

I would also expect NELM to vary more slowly than sky brightness
on theoretical grounds, for two reasons. First, stars to the
naked eye are effectively point sources, with (theoretically)
infinite contrast against the background. In practice, of
course, defects in your eye blur that theoretical point source.

Second, even for diffuse sources, the surface brightness of an
object at the edge of visibility must vary more slowly than
the sky brightness. That is because invisibility has two
components, one due to lack of contrast against the background
and one due to sheer faintness. As you can easily determine
by experiment inside a house at night with shades drawn, there
is some threshold surface brightness below which a light
source becomes completely invisible even against a perfectly
dark background -- a situation in which the contrast is,
again, theoretically infinite. Put another way, there are
some astronomical objects that the human eye simply can't see,
not even if you were in outer space, not even if there were no
zodiacal light.

- Tony Flanders

Tony Flanders wrote:

Certainly, playing around with the program the Schaefer
published in S+T some while back indicates that NELM varies
much more slowly than sky brightness.


Yes.

Nils-Olof Carlin has written a web page about Schaefer´s paper at
http://w1.411.telia.com/~u41105032/visual/Schaefer.htm
If you scroll down a little, you will find a table giving the
limiting magnitude for different sky backgrounds, both according to
Knoll/Schaefer and Blackwell/Clark. Behold.

Cheers -- Harald

Harald Lang wrote in message ...

To summarize -

Naked-eye-limiting-magnitude to background brightness
conversion table

=================================
Backgrd
brightns Limiting magnitude
Ba Knoll/Schaefer Blackwell/Clark

18.4 4.30
19 4.77 5.80
20 5.49 5.81
21 6.12 6.56
22 6.62 7.17
23 7.02 7.59
24 7.31 7.83
25 7.52 7.95

.. . .

Given the visual limit, the apparent background brightness Ba can be
had from the inverse of the formula above:

Ba = 21.58 - 5 log(10^(1.586-lim_mag/5) - 1)

==================================

Excerpt from Nils Olof Carlin internet page Schaefer's paper at:

http://w1.411.telia.com/~u41105032/visual/Schaefer.htm

(PrisNo6) wrote in message . com...

To summarize -
Backgrd
brightns Limiting magnitude
Ba Knoll/Schaefer Blackwell/Clark

18.4 4.30
19 4.77 5.80
20 5.49 5.81
21 6.12 6.56
22 6.62 7.17

...

Charming, isn't it, how wildly the experts vary? Let's say that
the dream sky, which can be approached but never equalled on Earth,
is mag 22 per square arcsecond. Knoll/Schaefer places the NELM
for that sky at 6.6, Blackwell/Clark at 7.2, and Ferris at 8.0.
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.

And estimates of NELM under heavy light pollution vary even more,
if possible, although I suspect for somewhat different reasons.

Oh how I long for a cheap, widely available device to give an
objective measure of sky brightness! As things stand, we are
like the people building the tower of Babel, all talking at
cross-purposes to each other.

- Tony Flannders