The distance to MT Ser

In order to obtain a photometric parallax for MT Ser, the ratio of the total energy emitted per surface unit of black bodies with temperatures such as those of the MT Ser components to the energy emitted per wavelength unit at the central wavelength of the B band (4400 A) was first calculated. The luminosities of the individual components were divided by this ratio and then the resulting values of the two stars were summed, yielding the energy emitted by the system per wavelength unit at 4400 Å. Together with the calibration constant of Bessel ([1979]) for the B band this yields the absolute B magnitudes as listed in Table 6 for the two cases T₁=50000 K and T₂=35000 K.

This energy corresponds to the mean apparent B magnitude of MT Ser which can be estimated from Figs. 1 and 2 of GB83. However, the light level is different at the two observations, B =15.63 on 1982, May 28, and B =15.77 during 1982, April. GB83 attribute this difference to different filter sets and diaphragm sizes used at the two occasions, and in consequence to different contributions from the surrounding planetary nebula. At a diameter of 18.4" (Acker et al. [1992]) the latter has a size typical for apertures used in photoelectric photometry. Therefore we assume that those observations yielding the brighter mean magnitude for MT Ser contains most of the planetary nebula. The flux ratio between the nebula and the central star derived in Sect. 3 translates into a magnitude difference of 0.83 mag Thus, the B magnitude of the central star alone is 16.46 mag. This is in good agreement with Shaw & Kaler ([1989]) who found B =16.45+-0.11.

The last ingredient needed to determine a photometric parallax is the interstellar extinction. Shaw & Kaler ([1989]) derived the reddening constant c (the logarithmic extinction at Hbeta) from the Halpha-to-Hbeta ratio of the planetary nebula as c=0.85. Interpolating between their values of the conversion factor between c and E(B-V), which is itself a function of c (see also Kaler & Lutz [1985]), we get E(B-V)=0.56. Assuming the ratio between total to selective absorption to be R=3.1 and using the interstellar extinction curve of Cardelli et al. ([1989]) this yields an absorption in the B band of A_B=2.28 mag A value of c discrepant from that of Shaw & Kaler ([1989]) has been derived by Tylenda et al. ([1991]). They give three values (two based on the Halpha-to-Hbeta ratio and the other one on the radio-to-Hbeta ratio) with a mean of c=0.38 which translates into A_B=1.09. An independent estimate of the extinction by Green et al. ([1984]) is based on the comparison of the expected colours of a pure Rayleigh-Jeans spectrum and the observed colours of MT Ser. They find A_V=1.5, corresponding to A_B=2.0, close to the higher of the two values derived from nebular physics.

The resulting distances for the high and low temperature cases and the two absorption values are listed in Table 6. In the literature statistical distances for the planetary nebula are cited as 4.3 kpc (Abell [1966]), 4.51 kpc (Cahn & Kaler [1971]), 5.4 kpc (Maciel [1984]), <3.76 kpc (Shaw & Kaler [1989]), and 4.60 kpc (Cahn et al. [1992]). This is consistent with the range of photometric parallaxes predicted from Model 1 in the high absorption case. In constrast, the parallaxes derived from Model 2 are only marginally consistent with the literature values in the low mass, low temperature, high aborption case.

These results are certainly a strong argument in favour of Model 1. However, it would be premature to rule out Model 2 based on the only marginal consistency of the predicted distance with measurements for the planetary nebula. It is well known that such measurements are notoriously difficult and unreliable as discussed e.g. by Cahn et al. ([1992]), resulting in significant systematic errors.