The plot shows the apparent magnitude of the moon in V and B as a function of lunar phase (phase=0 is new moon).
We measured the flux in images in which the filter was reliably V or B and used the transformations determined from NGC6633 (i.e. http://earthshine.thejll.com/#post229) to get the apparent magnitude.
These data have been obtained for a large range of airmass (z) — from z = 1 to 10, with most of the data in the range z = 1 to 3. We derived extinctions of 0.10 mag/airmass for V and 0.17 mag/airmass for B, by comparing to the apparent V magnitude from the JPL ephemeris for the Moon (http://ssd.jpl.nasa.gov/horizons.cgi) (more about this below). The solid black line shows the V apparent magnitude as a function of
phase after extinction correction, and adjusting the zeropoint by 0.2
mag in V to fit.
Note that B is ~ 1.0 mag fainter (i.e. B-V ~ 1.0, as we’d expect).
The airmass fits are shown above : the plot is the difference between the apparent magnitude from the JPF ephermeris and our transformed instrumental V band (or B band) magnitudes, shown as a function of airmass. The two lines show 0.10 mag/airmass (V band) and 0.17 mag/airmass (B band) — they are not fits. There are some bad outliers, especially in the V band, which are probably due to the incorrect filter being in the beam.
Peter e-mailed JPL and we got back that the source of the JPL magnitudes for the moon is Eqn 8 of http://adsabs.harvard.edu/abs/1991PASP..103.1033K
I checked their web based documentation already but they don’t seem to cover this for the moon specificially – but you may find sonething I missed. I will produce a more accurate comparison with JPL than the plotted one there could still be considerable structure in there.
Argh! JPL knows more than us then! I will check what the absolute mag formula is based on.
Yes – the black line is from JPL – apparent Lunar magnitude directly from their ephemeris. It has only been shifted by 0.2 mag to fit, no other adjustments. I don’t know if it is empirical or theoretical (ie for some assumed reflectance model) but we are certainly close to it!
Where is the smooth black line from? JPL? In that case you seem to have found a function for V with better built in reflectance than we have access to – or is it an empirical function?Anyway – looks great!