3 Data reduction

Since the aim of this study is a quantitative light curve analysis, care must be taken to subtract the contribution of the planetary nebulae from underneath the stellar image before measuring its magnitude because any such contribution would dilute the light curve, faking smaller amplitudes. Therefore, standard photometry techniques on CCD images cannot be used.

In order to solve this problem, first a high S/N image of the nebula was constructed: The individual CCD frames of 1997 Aug. 26 (a night with photometric observing conditions) were cross-correlated in x and ydirections to one particular frame which served as template. Gaussian fits to the peak of the cross-correlation function yielded the positional drift between individual frames. After correction for this shift, the frames were co-added. An attempt to subtract (after sky subtraction) scaled versions of the profile of the brightest star in the field of view, located approximately $4^{\prime}_{\raisebox{.6ex}{\hspace{.12em}.}}3$ west and 3' north of MT Ser (henceforth called C₁), always left spurious spikes or dips in the difference image, presumable because of slight dependences of the PSF on the location in the image. Another, less rigorous method met more success: Spline interpolations were calculated for the pixels of each image line and column containing a contribution of the planetary nebula. Those regions which are (according to a visual inspection) noticeably influenced by the PSF of the central star, got zero weight. Thus, the spline was interpolated beneath the stellar profile. The difference between the spline and the original image then contains only the contribution of the central star. It was subtracted from the original, yielding the intrinsic profile of the nebula. Clearly, this procedure is not ideal. The outer (visually not obvious) parts of the stellar PSF may still contribute to the nebular, and in particular the method assumes that the nebula is not strongly structured beneath the stellar profile. However, the star being much brighter than the integrated nebular light beneath the stellar image we are confident that such systematic errors remain small enough to be neglected in view of the other sources of uncertainty in the final results.

Summing up all the counts of the nebula (taking care to avoid some faint stars projected on its outer parts) and comparing them to the counts observed from star C₁, yields a magnitude difference $m_{\rm neb} - m_{C_1} = 3^{\raisebox{.3ex}{\scriptsize m}}_{\raisebox{.6ex}{\hspace{.17em}.}}06$. The systematic errors certainly dominate over the random ones. Therefore, we do not quote statistical errors.

In order finally to perform the photometry of MT Ser, the IRAF script LCURVE was applied which makes use of DAOPHOT/APPHOT routines. In the normal mode this routine defines annuli for the star and the sky around the centre of the stellar image which scale with the width of the PSF in order to account for seeing variations. In this way, instrumental magnitudes for C₁ and several other comparison stars in the field were determined. However, this method cannot be applied to MT Ser because it would inevitably lead to a wrong background subtraction. Therefore, in the next reduction step the extraction aperture was held fixed at a diameter of 4 pixels. The sky radius was defined large enough to ensure that no nebular contribution would be seen and was also fixed. With these parameters, magnitudes were determined for MT Ser and again for the comparison stars. At a FWHM of the stellar profile of 2.0 pixels some light of the star is lost when a 4 pixel aperture is used. This holds for MT Ser as well as for the comparison stars. The difference between the instrumental magnitudes of the latter, determined with the standard procedure and the small aperture, respectively, measures thus the loss of light which occurred when the small aperture was used. It was applied as a correction to the magnitude determined for MT Ser, after the contribution of the nebula to the light in the small aperture - determined from the nebular image constructed above - had been subtracted.

The mean magnitude difference between MT Ser and C₁ is found to be $3^{\raisebox{.3ex}{\scriptsize m}}_{\raisebox{.6ex}{\hspace{.17em}.}}21 \pm 0^{\raisebox{.3ex}{\scriptsize m}}_{\raisebox{.6ex}{\hspace{.17em}.}}11$, where the uncertainty is dominated by the orbital variations of MT Ser. Together with the above derived magnitude difference between C₁ and the nebula, this leads to a flux ratio $F_{\rm MT}/F_{\rm neb}=0.87$ in the B band. This value agrees quite well with the ratio of 0.814 determined by Shaw & Kaler (1989).