The surface gravity of the components

Green et al. ([1984]) estimated the surface gravity of MT Ser comparing the mean of their two spectra with synthetic spectra for hot high-gravity stars of Wesemael et al. ([1984]). They get log g = 6 +- 1.³With the component radii as given in Table 6 and the assumed masses surface gravities can be calculated for the various models. They are also quoted in Table 6. In the case of Model 1 the secondary can be disregarded in this context because its contribution to the total light is very small; therefore the observed surface gravity is only due to the primary.

The calculated values for log g are only marginally consistent with the observations, and more so for Model 1 than for Model 2. Several factors may contribute to this discrepancy:

(1) Green et al. ([1984]) based their estimate of log g on LTE model atmosphere calculations. They point out that such models overestimate gravities by factors of 2-4 as compared to more realistic NLTE models.

(2) The surface gravity is a sensitive function of the absorption line width. Larger widths lead to higher gravities. In a close binary system such as MT Ser a bound rotation of the components can be expected. Considering the orbital inclination, the period, and the stellar radii, projected rotational velocities of 97 - 187 km s^-1 (Model 1) and 105 - 205 km s^-1 (Model 2) are calculated for the different model assumptions.

(3) The surface gravity quoted by Green et al. ([1984]) is based on the sum of two spectra. Possible line shifts due to orbital motion which may mimick a broader line are not considered. In the different cases of Model 1 the orbital inclination, the component separation, the period and the mass ratio yield a projected radial velocity amplitude of the primary star (the contribution of the secondary to the optical light is negligible) in the range 109 - 210 km s^-1. Within Model 2 both components have comparable luminosities [L₁/L₂= (R₁²/R₂²)=0.69 in the most favourable case]. Therefore, the observed spectrum will be a superposition of the spectra of both components. Hence even in a single spectrum the lines are broadened by orbital motion. Here, the expected radial velocity difference of the components is up to 237 - 452 km s^-1 in the different model cases.

(4) At least within Model 1 a significant reflection effect is present which will tend to reduce the depth of the absorption lines.

In order to investigate if the effects of rotation and orbital motion are able to broaden the observed spectral lines sufficiently to mimick the high surface gravity observed by Green et al. ([1984]) we calculated line profiles for Hbeta, assuming LTE and hydrostatic equilibrium (and neglecting radiation pressure) for a temperature of 40000 K (note that in this case the line depth is somewhat deeper than for higher temperatures but the shape of the lines is not much affected). Three profiles were calculated assuming log g=6; V sin i=0 (profile h), log g=5; V sin i=0 (profile l1) and log g=5; V sin i=200km s^-1 (profile l2).

As expected, profile h is significantly broader than profiles l1 and l2. The difference between the latter is basically confined to the line centres. The rotation decreases the line depth, but the flancs are hardly affected. Thus, a rotation of the star up to the maximum velocity expected in the case of MT Ser does not significantly broaden the line. Therefore, this effect is not likely to explain the discrepancy between observed and predicted surface gravities.

This is different when orbital motion is considered. We shifted profile l2 by +-2.5 A (166 km s^-) and added the results in order to simulate the combined profile due to two stars in orbital revolution. The results (as well as profile h) were convolved with a Gaussian in order to mimick the resolution of the MT Ser spectrum of Green et al. ([1984]). The final line shapes of the simulated binary line and the high gravity line differ in detail, but - disregarding the shallow outer parts of the line flancs and the depth relative to the continuum - are not so different as to be easily distinguished in a spectrum with a S/N ratio as low as observed by Green et al. ([1984]). This, together with the fact that the value of log g quoted by Green et al. ([1984]) may in reality be an upper limit, lets us conclude that the apparent disparity between the observed and the calculated surface gravity of MT Ser is not a matter of concern.

Although best fit values of the only model parameters which are directly a function of the surface gravity, namely the limb darkening coefficients, are well consistent with high gravity hot stars (Wade & Rucinski [1985]), their confidence ranges are large enough so that no contradictions arise even if considerably lower gravities are assumed. This holds true also if the component temperatures are as low as those proposed by Tylenda et al. ([1991]).