This week we have a look at our basic photometry calibration and try to answer the question “Why does my calibration look weird?” – Which sometimes comes up when someone’s calibration graph looks a bit like the one shown in the above plot.
The basic idea behind the calibration is simple. We assume, that on average the brightness of all stars in a given area does not change. We know that some stars are variable, up or down, but averaged over a large number of stars, their total flux stays unchanged. Thus, HOYS has for each target field and filter a very deep image (observed under ideal conditions) that we use as a reference. In other words we do know how to convert the fluxes (f; counts) of the stars in this image into apparent magnitudes (m). This is done using Pogsons equation, which is: m=-2.5log(f/f0), where we have determined f0 for each region and filter.
If we calibrate any new image that has been taken in the same filter, but with a different telescope and/or exposure time, then we measure the fluxes f of all stars, and compare them to the fluxes they have in our reference image. If the telescope gathers a different amount of photons, due to e.g. a different mirror size or exposure time, the fluxes of all stars will be different by the same factor. e.g. all stars will have half the flux in the new image compared to the reference image. Thus, when we plot the top panel in the calibration plot, which shows the magnitude difference of the stars in the new and reference image, then the points will will roughly scatter around a horizontal line at m=-2.5log(2)=-0.75mag. There will be some scatter, which increases towards the fainter stars, which is caused by the uncertainties in measuring the fluxes. And some of the scatter is real variability. Our procedure then simply determines the off-set and corrects for this, and that is what the bottom plot shows.
“Problems” arise, when the new images are not taken with the exact filters as the reference images. All the reference images are taken with a standard set of filters, the UBVRI system. This plot shows how much light these filters let through as a function of wavelength. Now, lets assume your filter is slightly different, and say it lets relatively more red light through than blue light, compared to our reference filter. What will happen in this case is that red stars will appear relatively more bright in your image, compared to blue stars, which will relatively be fainter. Hence, if we compare the magnitude of the stars in your image to our reference frame, there will be a general off-set, like in the above example. But also red stars will appear brighter than the off-set and blue stars will appear fainter than the off-set. However, typically in any picture, the faint stars tend to be more red on average than the blue stars. Thus, what one typically seems is a magnitude dependent off-set, as shown in the above plot. We simply fit a function to this off-set and correct it to calibrate the magnitudes as a function of brightness, to create the final plot at the bottom. In principle, the steeper the slope (positive or negative) of the points in the top plot, the stronger does your filter differ from our reference filter. This slope is what we usually call ‘colour-term’.
Of course, the colours of stars can also differ when they have the same magnitude. Thus, typically there will be more scatter in the bottom plots around y=0, when the colour terms are large. We are aware of this, and before using the data for science, we do correct this effect. In other words, we determine the colour of a star and also correct a colour-dependent off-set from the magnitudes. We are not able to perform this correction directly when you are submitting your images. Because we need to determine the colours of the stars. We can only do this if we have images in two different filters. Thus, if you take a new image e.g. in V, and submit that, we do not know the e.g. the V-I colour. Only when we have someone, or yourself, submit an I image, do we know the colour and can correct the effect. Thus, this has to be one after we have collected all the data.
There are of course other reasons for colour terms, than just using slightly different filters – though this has usually the strongest effect. Some cameras are more sensitive to red or blue light, and thus change the relative brightness of stars of different colours. If you are observing through thin (or even thick) cirrus clouds, then this also changes the brightness of different coloured stars. Cirrus clouds typically scatter blue light stronger than red light. Thus, red stars remain brighter compared to blue stars when observed through cirrus. However, our procedure does correct all these effects simultaneously. Thus, it does not really matter what filter, detector and observing conditions you are using. As long as there are enough stars in your image, we are able to accurately calibrate the brightness of the stars in all your images.