3 Analysis

For our explorations of possible group properties of roAp stars, we only considered stars which have been tested for rapid light variations. The list of known roAp stars was taken from Kurtz & Martinez (1993), five additional roAp stars were added, namely: HD 9289, HD 99563, HD 122970, HD 185256, HD 213637 resulting in 31 roAp stars known at the writing of this paper. The null results (noAp) were taken from Martinez & Kurtz (1994), including results from other surveys (see Tables 1 and 2 in Martinez & Kurtz 1994) as well. No further references on null results were found in the literature. We have to emphasize that the temperature range for the noAp stars (15000 - 6000 K) is wider than that of the roAp stars (8500 - 6500 K), i.e. some objects desgined as noAp may in fact be Bp stars.

We have used the Hipparcos and Tycho catalogues (Perryman et al. 1997) to retrieve parallaxes and apparent places for all stars. For the given sample (31 roAp and 229 noAp stars) only stars with $\frac{\sigma(\pi)}{\pi} < 0.18$ ($\sigma(M_{ V}) < 0.3$mag) were considered. A Lutz-Kelker correction according to Koen (1992) was applied. Because of the chosen error limit for the parallax, the Lutz-Kelker correction is very small for all program stars. We have not applied any correction for interstellar extinction because of two reasons:

• Most of our program stars are within 100pc resulting in negligible reddening.
• Values for (B-V)₀, (b-y)₀ and (B2-V1)₀ are derived for "normal'' type stars only. It has been proven that these calibrations are, in general, not valid for magnetic chemically peculiar stars ("blueing effect'').

Taking all considerations into account we are left with 12 roAp and 54 noAp stars. Figure 4 shows the M _V(Hip) vs. $\beta$ diagram. There are several points evident from the figure:

• All roAp stars behave "normal'', in the sense that the fall in the region of other main sequence stars.
• Most of the noAp stars are above the normality line. This could mean that either the $\beta$-values are systematically too large or that the absolute magnitude is systematically too bright. Latter cannot be explained by reddening since it would even more brighten the stars.

It is worthwhile to note that the roAp stars are separated from the noAp's in Fig. 4: they are all rather cool main-sequence objects. Only a few stars, for which no rapid oscillations have been detected, are located close to the pulsators (HD 15233, HD 25354, HD 35353, HD 62140, HD 115708, HD 154708, HD 170397 and HD 188854). HD 25354 and HD 170397 are probably Bp stars (as judged from their Stromgren indices), while HD 35353 is poorly observed and there is no spectral classification available (hence it could be an Am star). The remaining three stars are well observed and from Fig. 4 there is no reason why they should not be roAp stars, except that HD 15233 and HD 188854 may be too evolved. We note that the most famous noAp star, HD 137909 ($\beta$ CrB), appears to be hotter and more evolved than all roAp stars.

  

Figure 4: $M_{ V}\ (Hip)$ vs. $\beta$ diagram for 12 roAp (filled cricles) and 54 noAp (open circles) stars, the normality line is from Crawford (1979)

There is more evidence that effective temperatures for Ap stars determined from $\beta$ are systematically too high. Alonso et al. (1996) compared $T_{\rm eff}$ values from the Infrared Flux method with $\beta$ measurements for a large range of metallicities. They found a clear trend of increasing $\beta$ with increasing metallicity for fixed $T_{\rm eff}$.

Matthews et al. (1998) compared asteroseismological parallaxes with those measured by Hipparcos. They noted that the Hipparcos parallaxes are generally larger than the asteroseismic ones, and suggested this may be due to systematically incorrect effective temperatures estimated from $\beta$.

Some more support for this idea comes from a comparison of $\beta$-temperatures and those determined by model atmosphere analysis for a number of roAp stars (Gelbmann 1998 and references therein). This is summarized in Fig. 5. We find that the best fitting model atmospheres generally point towards lower effective temperatures. The mean temperature difference is $-80\pm90$ K, which is not significant. However, this analysis can be improved when higher resolution spectra of (ro)Ap stars become available (allowing to determine more accurate temperatures) and a larger sample is investigated.

The Hipparcos parallaxes strongly suggest that the roAp stars are main-sequence objects. This is supported by the study of Gómez et al. (1998), who examined the positions of Bp-Ap stars in the HR diagram. They show that these stars are on the main sequence, and this also holds for the SrCrEu stars, i.e. the spectral subgroup containing the roAp stars. When examining the effective temperatures of roAp stars one obtains from $\beta$ by using the calibrations of Moon & Dworetsky (1985), it can be noted that three out of the 31 roAp stars (HD 122970, HD 213637, HD 217522) are clearly outside the cool border of the $\delta$ Scuti instability strip, especially since these temperatures are presumably overestimates.

For some years, it has been believed that the $\delta$ Scuti and roAp instability strips coincide, which has been taken as an argument that the driving mechanism for these two classes of pulsating star could be the same (partial He⁺ ionisation). Very recently, Gautschy et al. (1998) presented model calculations, which led them to suggest that the actual driving of roAp pulsations might be due to partial H/He ionisation. They obtained overstable high-order modes by assuming that these stars have chromospheres and therefore a temperature inversion in their atmospheres. Under these assumptions their models showed roAp pulsations outside the cool edge of the $\delta$ Scuti instability strip, and hence they can explain why the three stars mentioned above do pulsate.

In Fig. 6 we present a l vs. b diagram for all program stars. Beside the "southern hemisphere effect'' no systematic differences of the galactic distribution for roAp and noAp stars are evident.

  

Figure 5: Effective temperatures for six roAp stars from H$\beta$ photometry compared with those from model atmosphere analysis. The solid line corresponds to exact agreement. Except for one star (HD 166473), the H$\beta$ temperatures are always higher

  

Figure 6: l vs. b diagram for all program stars