Beta UMi "variability"
Posted: Mon Aug 30, 2004 2:57 pm
Bob, extinction close to the horizon does not behave as astronomy textbooks tell you it should do. In general, one uses the "regular" extinction correction: m(lambda)=m0(lambda)+k(lambda)*AM, where m(lambda) is the object magnitude, m0(lambda) is its magnitude outside the atmosphere, k(lambda) is the extinction coefficient at the wavelength of observation, and AM is the airmass of observation.
Textbook astronomy teaches that AM is sec(z), where z is the zenith angular distance, however when the altitude of the object is small the airmass needs to be corrected for the Earth curvature, for the change in atmospheric density with altitude, etc.
One of the useful corrections is by Hardie (1962, in Astronomical Techniques, ch. 8) and is an expansion:
AM=sec(z)-0.0018167*[sec(z)-1]-0.002875*[sec(z)-1]^2-0.0008083*[sec(z)]^3
Another useful formula is by Young & Irvine (1967, AJ 72, pp. 945-950):
AM=sec(z)*{1-0.0012*[sec(z)^2-1]}
You may also want to look at the paper dealing with low altitude observations of comets: http://cfa-www.harvard.edu/icq/ICQExtinct.html.
Finally, I wonder whether the differential refraction could play a role in your findings. Because of refraction, point objects that are not at the zenith present essentially short spectra that are perpendicular to the horizon. Obviously, the lower an object is, the 'longer' is the spectrum. The CONCAM magnitudes use a fixed aperture; this may miss part ofth light from a star when it is close tothe horizon.
Noah Brosch
Textbook astronomy teaches that AM is sec(z), where z is the zenith angular distance, however when the altitude of the object is small the airmass needs to be corrected for the Earth curvature, for the change in atmospheric density with altitude, etc.
One of the useful corrections is by Hardie (1962, in Astronomical Techniques, ch. 8) and is an expansion:
AM=sec(z)-0.0018167*[sec(z)-1]-0.002875*[sec(z)-1]^2-0.0008083*[sec(z)]^3
Another useful formula is by Young & Irvine (1967, AJ 72, pp. 945-950):
AM=sec(z)*{1-0.0012*[sec(z)^2-1]}
You may also want to look at the paper dealing with low altitude observations of comets: http://cfa-www.harvard.edu/icq/ICQExtinct.html.
Finally, I wonder whether the differential refraction could play a role in your findings. Because of refraction, point objects that are not at the zenith present essentially short spectra that are perpendicular to the horizon. Obviously, the lower an object is, the 'longer' is the spectrum. The CONCAM magnitudes use a fixed aperture; this may miss part ofth light from a star when it is close tothe horizon.
Noah Brosch