Calibrating Instrumental Magnitudes

The purpose of calibrating instrumental magnitudes is to convert them into magnitudes in the target standard photometric system. To fix ideas, think of the target system as being the Johnson-Morgan UBV system. You can think of the calibrated magnitudes as the magnitudes which would be recorded by a detector which perfectly matched the standard UBV system and was operating above the terrestrial atmosphere. The magnitudes and colours recorded by such a detector still do not correspond to the intrinsic colours of the object observed because of the effects of interstellar material in-between the object and the detector. Interstellar material reddens and dims light which passes through it. However, correcting the effects of interstellar reddening and extinction is normally considered to be part of the astrophysical interpretation and analysis of the observations rather than routine data reduction. Interstellar extinction and reddening are briefly described in Appendix , but not otherwise considered in this cookbook.

Thus, calibrating instrumental magnitudes consists of correcting two effects:

• discrepancies between the instrumental and target standard systems,

• atmospheric extinction.

Any given instrumental magnitude is, of course, simultaneously affected by both these effects. Two distinct cases can be considered for performing the calibration:

1. the instrumental system is well-matched to the target standard photometric system,

2. the instrumental system is less well or poorly matched to the standard system.

In the first case the detectors and filters used have been chosen carefully to match the responses of the target standard system as closely as possible. Thus, for example, the transmission profiles of an instrumental UBVRI system would be similar to those for the standard system shown in Figure . Often the instrumental system will closely match the corresponding standard one (and considerable effort and attention will have been expended at the observatory providing the instrumentation to ensure that this is the case). Staff at the observatory should be able to advise on how well matched the systems are. Other useful sources of information are handbooks, World Wide Web pages, newsletters and instrument manuals issued by the observatory. SG/10: Preparing to Observe[63] includes a list of URLs for the Web pages of the observatories usually used by British astronomers.

The two cases of whether the instrumental and target standard system are well or less well matched really correspond to whether it is necessary to make a colour correction when calibrating the instrumental magnitudes. The judgement of whether or not the target and instrumental systems are well matched is not absolute, but rather will depend on the precision which you wish to achieve in your photometry, which in turn will depend on the astronomical aims of your programme. Sets of observations made with the same instrumentation for different programmes may well be reduced with or without colour corrections, depending on the accuracy required and the aims of the programmes. In particular, if observations are only made in a single band then clearly colour corrections cannot be made. The following section discusses the simpler case of calibration without a colour correction and the subsequent one calibration with colour corrections.

Finally, there are types of programmes where it is not necessary to calibrate instrumental magnitudes into standard magnitudes. For example, if you are only interested in determining the periods of a variable star then these periodicities can be extracted from a time series of instrumental magnitudes as easily as from one of calibrated, standard magnitudes. (However, in this particular case it is still, of course, necessary to correct for atmospheric extinction).