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Re: (meteorobs) Request for data

To answer Terry's question, here is a repost of the material which prompted
my question about the affect of zenith angle on meteor magnitudes:

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Below is an excerpt from D.W.R. McKinley's "Meteor Science and Engineering"
(1961) 

>>>>>>>>>>

[figures omitted, some scanning errors]

     The absolute visual magnitude M. of a meteor is defined as the magni-
tude it would have if it were placed in the zenith at a standard height of
100 km. It is convenient here to adopt 100 km as the unit of length;
similarly, we shall have occasion to use 101 kM2 as the unit of area. Two
corrections to the apparent visual magnitude of a meteor are necessary to
convert it to absolute magnitude. The first is the usual inverse square
law of attenuation of luminosity with the distance R to the meteor. The
second correction is due to atmospheric absorption of the light. Since
this absorption occurs almost entirely in the lower troposphere, it is inde-
pendent of the meteor's height and is a function only of the meteor's
zenith distance Z, which is the angle between the observers vertical and
his line of sight to the meteor. In Fig. 2-1 the distance correction is
found by using R and curve A, solid line, and the absorption correction
from sec Z and curve B, dashed line. The equation of curve A is simply
m = 5 log,,, R, which follows from Eq. (2-1) and the inverse square law.
The absorption correction has been taken from the Handbuch der
Astrophy-sik. The use of the same abscissa scale for both R and see Z
is merely a convenience. In general, the abscissa values will not coincide
exactly for a given meteor unless one assumes a flat earth and a meteor
height H       100 km, whence R (in 100-km units)               sec Z. To a
first
approximation, though, the ordinates of the two curves may be added to
yield the total correction, if either R or Z alone is known.  For example,
a meteor which appears to be third magnitude when observed at a dis-
tance of 400 km would be about four magnitudes brighter if it were in the
zenith; hence its absolute magnitude is - 1. One word of caution: the
atmospheric correction should be applied if, for example, a meteor far
from the zenith is compared either directly with a star of known mag-
nitude near the zenith or indirectly by comparison with a nearby star
whose apparent brilliance is in turn referred to a known star overhead.
The atmospheric correction should not be made if the meteor is compared
only with a nearby star of known magnitude at the same zenith distance,
as the absorption will affect both equally. In either case, of course, the
distance correction should be applied. In practice, experienced observers
seem to develop an absolute sense of magnitude; that is, they tend to
express all meteor magnitudes in terms of known zenithal magnitudes.
Hence both corrections are usually applicable.

>>>>>>>>>>

To clarify the above a little, the standard equation used to correct an
apparent magnitude to an absolute magnitude (correcting for both absorption
and distance) is:

Ma = Mo + (5 * log10 (sin(H)))

where Mo is the initial magnitude, H is the altitude angle above the
horizon for the meteor, and Ma is the absolute magnitude.

Thus, a 3rd magnitude meteor at 45 deg of altitude would have an absolute
magnitude of 2 (rounded), while the same 3rd magnitude meteor at 15 deg of
altitude would have an absolute magnitude of 0 at the zenith.  Such
differences in apparent vs absolute magnitudes can directly affect the
determination of such study population properties as magnitude distribution
/ population index.  

In doing research, when and how these corrections are applied depends upon
how the visual observer collected the data.  There are two methods which
might be used to obtain absolute magnitudes, each with their own
disadvantages;

(1)  The observer determines his limiting magnitude from stars at the
zenith, and judges all meteor magnitudes by comparison to this area.  In
order to obtain absolute magnitudes, the observer must also record the
angular height of each meteor observed, and the correction equation must be
applied to each meteor before determining a population's magnitude
distribution.  Both distance and absorption must be corrected for.

(2)  The observer determines his/her limiting magnitude from stars directly
within the field of view which will be monitored, and judges all meteor
magnitudes from stars within this field.  Done correctly, only the distance
correction factor would need to be applied to the collected magnitudes.

Method (1) was used more frequenctly in the past, while method (2) is the
most commonly used today, although I have still heard a few observers on
this list reporting their limiting magnitude from zenith stars.

However, (and here I am playing Devil's advocate) I tend to agree with Dr.
McKinley in that most experienced visual observers probably tend to use
their own mentally intrinsic magnitude scale when judging meteor
magnitudes.  Thus, a meteor of X luminosity would gbe judged as 3rd
magnitude no matter where it appeared in the sky.  That is, with meteors of
the exact same brightness, I think that most observers would have a
difficult time calling it 3rd magnitude at the zenith, but 0 magnitude near
the horizon.

Hence, it would seem that method (1) would yield more accurate magnitude
distributions, and allow observers to utilized their seasoned "sense" for
meteor magnitudes.  

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My request for data was to gain an idea of the affect of atmospheric
absorption on stellar magnitudes, and investigate the pros and cons of
methods (1) and (2).  McKinley presents this in graphical formbut does not
provide an independent equation fort atmospheric absorption.  if you have
the equations used today to correct for this effect, Terry, i would
appreciate you sending them to me.  

Thanks,

Jim


James Richardson
Graceville, Florida
richardson@digitalexp.com

Operations Manager / Radiometeor Project Coordinator
American Meteor Society (AMS)
http://www.serve.com/meteors/
References: