Flux calibrating spectra

[David Boyd]

Following advice posted in the Forum by, among others, Martin Dubs, Robin Leadbeater, Francois Teyssier and Christian Buil, I have put together the following short summary of the method I am now using to flux calibrate my spectra. Comments welcome.

David

A method of flux calibrating spectra

This method of flux calibrating spectra is based on the contributions of several individuals to the ARAS Forum. It relies on knowing the V magnitude of the target at the time the spectrum was recorded together with the transmission profile of the V filter used to measure this magnitude. In most cases the filter profile can be found from the filter manufacturer. Failing that, a standard V filter profile can be used. Ideally the V magnitude should have been transformed to the photometric standard magnitude system but failing that the method will still give an acceptable result. The method is straightforward to implement using commands in the ISIS software (1).

First you need to find the spectroscopic zero point of your magnitude measurements. One way to do this is to use flux calibrated spectra from the CALSPEC library (2). These spectra are available in the ISIS database (3) which can be downloaded from the ISIS website. Select a star from the library and load its spectral profile into ISIS. Multiply this profile by the transmission profile of your V filter using the Arithmetic tab in ISIS and the command Multiplied by a profile. Close this tab and open the FWHM tab. Double-click first to the left of the filtered profile and then to the right of the profile. The Sum field in the FWHM tab then gives the integrated total flux, F, transmitted by the filter. If V is the magnitude of this star, which you can find on the CALSPEC website, the zero point, ZP, for this star is given by the formula
ZP = -V -2.5*log10(F)

Repeat this for about a dozen stars from the CALSPEC library and calculate the mean value of the zero point. In my case it was 13.630 with a standard deviation of 0.014. This value is used for all subsequent flux calibrations.

Calculate the absolute flux from your target which is transmitted by the V filter using the formula
Absolute flux = 10^[-0.4*(V magnitude + ZP)]

You are now ready to convert your spectrum into absolute flux units. The starting point is a spectrum of the target in relative flux units corrected for instrument response and atmospheric extinction in the normal way. This is multiplied by the transmission profile of the V filter using the Arithmetic tab in ISIS as described above. The total relative flux transmitted by the filter is then obtained using the FWHM tab by double-clicking on either side of the filtered profile. The Sum field within the FWHM window gives this total flux. Take a copy of this value. Reload the original spectrum of the target to replace the filtered version. Using the Arithmetic tab again, paste the total flux value into the field labelled Divide by a constant. Also paste the absolute flux from your target transmitted by the V filter calculated above into the field labelled Multiply by a constant. Then click the Compute button to the right of each of these fields in turn. The spectrum is now flux calibrated. As you run the cursor across the spectrum you will see that the intensity now has a large negative power of ten indicating that it is in units of erg/cm2/sec/Å.

Finally, as a check that everything is working properly, record the spectrum of a spectrophotometric standard star, for example one from the CALSPEC database, in the normal way and flux calibrate it as described above. You can then compare your calibrated spectrum with the standard spectrum supplied with ISIS and you should find that the two align well.

References

(1) ISIS software: http://www.astrosurf.com/buil/isis/isis_en.htm
(2) CALSPEC library: http://www.stsci.edu/hst/observatory/crds/calspec.html
(3) ISIS database: http://www.astrosurf.com/buil/isis/down ... ase_v7.zip