In this post we commented on the problems we have with the requested and actual exposure times. It turned out NOT to be a good idea to correct the requested exposure times – certain colour problems got worse!
What happened was that B-V for the BS plotted against time of day showed a decided reddening towards the end of the Julidan day – this corresponded to the setting Moon. Airmasses were growing towards the end of the day.
When time of day and B-V were plotted we could see slopes using UNcorrected exposure times of 0.4 magnitudes/day. If we DID correct the exposure times as explained in the above link we got almost a whole magnitude per day in slope!
This got me thinking about whether the extinction corrections we perform are correct – they depend on knowing what the airmass is and knowing what the extinction coefficient is. If either, or both, are wrong we can expect colour-terms to pop up.
The airmass we have been using assumed surface pressure and 0 degrees C and 0 % relative humidity and a wavelength of 0.56 microns. More appropriate is the pressure that occurs at the MLO (we guessed it is 0.6*760 mm Hg), and a temperature of at least a few degrees C (we never observed in frost), and a relative humidity of 20%. Some of these quantities could actually be replaced by the available MLO meteorological data available – more on that later. We should also use an appropriate wavelength for B and V of 0.445 and .551 microns, for B and V respectively. However, using these better values will at most give an offset in B-V and cannot explain an airmass-dependent colour term. [or can it? gotta think about that one …]
Next we must consider the formula used for the airmass. Looking in the IDL code ‘airmass.pro’ provided by Marc W. Buie, we see it is the “cosine based formula derived by David Tholen” with an update 2003. The formula appears to be:
cz = cos(zenith[z])
am[z] = sqrt(235225.0*cz*cz + 970.0 + 1.0) – 485*cz
When we have a reference for this I shall return to the question of whether the approximate formula is good enough.
Finally there are the extinction coefficients. Since we see an increase in B-V with airmass it is either the V magnitude that is being over-corrected or the B magnitude that is being under-corrected. Experimenting, I find that kV=0.08 and kB=0.17, instead of the 0.1 and 0.15 that Chris found from standard-star observations, givea a colour-free B-V progression with time of day (at Moon-set – Moon-rise is too underrepresented to be useful here). Is it within the error margins that kV and kB should have these values? Old man Chris says he estimated the values 0.1 and 0.15 ‘by eye’ here but I think he also listed some regression results elsewhere, with errors – but I can’t find ’em!
Anyway, using the values 0.08 and 0.17 gives a mean BS B-V of 0.898 +/- 0.054 (error of mean +/- 0.004). This value is relevant when keeping the discussion about the “van den Berg value for B-V=0.92” in mind, link here. Our own average of vdB62 data gives 0.88 +/- 0.02 – within the errors we have, easily.
In short — YES! the differences of ~0.02 mag in the extinctions you derive and what I got are perfectly plausible given both the data and the method I used — in which case yours are certainly to be preferred! I did remove the very highest airmass data from the fitting, since the scatter out there was pretty high, and the number of observations rather small anyway. Did you fit right out to the highest airmasses in the data? I’ll have to look into this though and get back to you.