Since we are calculating absolute calibrated B and V magnitudes (on the ‘lucky night’ 2455945) for the DS and the BS we can convert these to surface brightnesses, for comparison with e.g. Pallé et al published work.
The formula for surface brightness is
mu = mag + 2.5*alog10(w*w*N)
where mag is the magnitude determined from a patch containing N pixels, with each pixel covering wxw arc seconds. In our case
w=6.67 arseconds/pixel and
N is 101 and 113 for the 6×6 selenographic degree patches we use (+/-3 deg). With the magnitudes for B and V, BS and DS from the paper – but using N=1, since we report average magnitudes per pixel, we get:
DS:
mu_B = 14.29 m/asec²; SD=0.06
mu_V = 13.54 m/asec²; SD=0.06
BS:
mu_B = 6.21 m/asec²; SD=0.05
mu_V = 5.31 m/asec²; SD=0.06 (all SDs are internal error estimates based on pixel bootstrapping with replacement).
BS is about 8.23 magnitudes brighter than the DS – there are published numbers for these quantities (e.g. Franklin). His Table 1 has differences of about 10 mags between DS and BS. He may be talking about magnitudes per area – not magnitudes per pixel, like we are.
Pallé et al in this paper
http://adsabs.harvard.edu/abs/2007AJ….134.1145M
give plots showing mags/asec² and for the phase we have (about -140 on their plots) they have a BS-DS difference of 8.4ish mags – so we are within 0.2 mags which seems possible, given the scatter they show in Fig 1.
Not sure I like or understand why Franklin is 1.5-2 mags different in the DIFFERENCE – would that come about when you differ by mags/pixel and mags/area?
