The ‘width’ of the halo we see is due to scattering in the atmosphere and the telescope. With data of the Moon rising it may be possible to extract information on how much of the halo is due to atmosphere and how much is due to the telescope. We first inspect data from night 2456003.
We do two things:
1) We run the FFM method on all aligned and coadded images thus getting values for alfa and airmass, and terrestrial albedo.
2) We calculate the fractional area in each image where the intensities fall in a specific fractile. We choose the fractiles between 0.1 and 0.3 % which turns out to be mainly in the BS halo. Doing this for all images gives us fractile area, or ‘halo size’, as well as airmass.
First we look at the contour plots from each image, in the B band. We have subtracted not only a bias frame but also a fitted linear surface – fitted to the corners of the bias reduced image.
We see 9 images of the Moon (each from the aligned and coadded images available at 9 different times in the B band on the given night).
We have extracted the area (counted in number of pixels) of the fractile between 0.1% and 0.3% (heavy dashed and next contour outwards) cumulated intensity. [Quite complex statistic that: 0.1% refers to the 99.9% brightest pixels of the image. 0.3% refers to ‘99.7% brightest pixels’.] We plot this, against other information extracted:
Upper Left: fractile area vs. time (Moon was rising). We see a smaller area as the Moon rises – less light is being scattered into that intensity fractile.
Upper right: Airmass and fractile area almost proportional.
Middle Left: FFM alfa vs time – the width of the PSF depends on where the Moon is.
Middle right: albedo vs airmass – the FFM-fitted albedo depends on the airmass: Not so good!
Lower left: albedo and alfa are dependent: Not so good
Lower right: fractile area and alfa are dependent: Not so good.
The last three results are not independent, of course.
We can learn a few things from this:
a) the FFM is not (yet) able to determine albedo etc independent of image quality – this is probably due to a degeneracy in the factors of the model we use – it seems that pedestal, alfa and albedo are coupled.
b) the nice relationship between fractile area and airmass, and alfa and fractile area promises an equally nice relationship between alfa and airmass. By linear regression we find:
alfa = 1.76 – 0.0036*airmass
which suggests that alfa (in the B band) is 1.76 at zero airmass – i.e. the contribution of the telescope in the B band to the PSF is a power law with power 1.76.
For all bands we get:
B 1.757 0.0010
V 1.763 0.0014
VE1 1.757 0.0006
VE2 1.745 0.0002 (one outlier discarded)
IRC 1.758 0.0004
Within +/- 0.001 it is possible to see no real color-dependence in the alfa_0 parameter. A consistent value for almost all bands is alfa_0=1.76. The VE2 PSF may be slightly broader with alfa_0 at 1.75. VE1 and IRCUT (which are almost identical filters) have very similar alfa_0 and errors.
We have on some nights by other means found alfa near 1.8.
The problem that albedo depends on the PSF power has to do with our model definition and fitting techniques and is open to improvement by adjusting fitting weights and so on. While it is too bad we are not ‘there’ yet with the FFM we see a tool for detecting when we succeed – namely, when the albedo no longer depends on alfa, and this information will be put to use.