Department of Physics AstroLab

Setting the magnitude zero-point for instrumental magnitudes

Consider the case where you have instrumental magnitudes for a variable star of unknown magnitude and two calibration stars with known magnitudes. Now, instrumental magnitudes are defined as as

        m(vstar)' = C' - 2.5 log10(flux(vstar)) 
        m(c1)'    = C' - 2.5 log10(flux(c1))    
        m(c2)'    = C' - 2.5 log10(flux(c2))    
where m(vstar, c1, c2)' are instrumental magnitudes and flux(vstar, c1, c2) are the observed fluxes for the variable star (vstar) and the two calibration stars (c1, c2). So far, you have probably been using a somewhat arbitary constant of instrumental magnitude scale (C'). However the known magnitudes of the calibration stars can be used to place the instrumental magnitude of the variable star onto the standard system with the raw2dif routine.

Let C be the real constant of the instrumental magnitude scale, i.e. the magnitudes m(vstar, c1, c2) on the standard system are defined by

        m(vstar) = C - 2.5 log10(flux(vstar))
        m(c1)    = C - 2.5 log10(flux(c1))   
        m(c2)    = C - 2.5 log10(flux(c2))   

The unknown magnitude of the variable star, m(vstar), can now be determine as follows:

        m(vstar) = m(vstar)' + (C - C') 
                 = m(vstar)' + 0.5*(C - C') + 0.5*(C - C')
                 = m(vstar)' + 0.5*[m(c1)-m(c1)']    +  0.5*[m(c2)-m(c2)']

                 = m(vstar)' - 0.5*[m(c1)'+ m(c2)']  +  0.5*[m(c1)+m(c2)]
                   --------------------------------     ---------------------
                   the instrumental magnitudes          the average catalogue
                   output by qmag                       magnitude of the two
                   (variable star minus the average     calibration stars
                   of the two calibration stars)
The raw2dif routine applies this equation prompting for the third term of the RHS as
 ZEROPOINT - constant to add to magnitude difference /xx/ >

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