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5. Conclusion

We have presented 95 new determinations of the mean longitudinal magnetic field and of the crossover in 44 Ap stars, which complement those already published in Papers III and IV. For the mean quadratic magnetic field, only 79 measurements are reported: the attempt to diagnose this field moment yielded a result devoid of physical meaning (a negative value of the mean square magnetic field) for 16 observations. As already noted in Sect. 3, the quadratic field diagnosis proved more difficult than in Paper V, since the changes of instrumental configuration between the various observations of a given star prevented us from combining them to derive a single contribution for the combination of the non-magnetic part of the line profile and of the instrumental profile. The reduced wavelength coverage achieved with the long camera of CASPEC used with a "small'' (tex2html_wrap_inline2633 pixels) CCD, and the resulting small number of lines available in some cases to diagnose the field, also severely hampered our ability to derive a meaningful quadratic field.

As indicated in Sect. 1, one of the purposes of the observations reported here was to monitor the evolution of the performance of the Zeeman analyzer of CASPEC throughout the modifications progressively undergone by the instrument. To this effect, we reobserved several of the stars that had already been studied in detail in our previous work. The present determinations of the longitudinal field and of the crossover for these stars (e.g., HD 125248, HD 137909, HD 147010, tex2html_wrap_inline3637) are consistent with those of Papers III and IV, indicating that the polarimetric performance of CASPEC has remained mostly unaltered through the configuration changes. With the long camera of CASPEC, the uncertainty of the best measurements of tex2html_wrap_inline2667 (achieved for stars with rich, sharp-lined spectra such as HD 137909 and HD 201601) has gone down to tex2html_wrap_inline3641. This improvement with respect to the smallest errors of tex2html_wrap_inline3643 obtained in Paper III reflects well the increase of resolving power by a factor of about 2 resulting from the change from short to long camera. Similar progress is achieved in the accuracy of the crossover determinations (again, see e.g. HD 137909), where the smallest errors are in the tex2html_wrap_inline3645 range. By contrast, the accuracy of quadratic field data is often worse than, and at best similar to that achieved in Paper V, due to the already repeatedly stressed impossibility to combine observations obtained at different phases for the derivation of this field moment. As mentioned in the previous papers of this series, the formal errors that we determine from the rms of the least-squares fits performed to derive the field moments appear as good estimates of the actual measurement uncertainties. This is supported, in particular, by the fact that, for stars repeatedly observed throughout their rotation cycle, a reduced tex2html_wrap_inline3293 close to 1 is generally obtained when fitting the data by functions of the types given by Eqs. (4) or (5). This indicates that the uncertainties assigned to the measurements are consistent with their scatter about a smooth variation curve.

For several of the stars, the new measurements obtained here allowed significant improvement to be achieved in the definition of the variation curves. This happens, in particular, for HD 137509 (see Sect. 4.2.10), whose magnetic field is as a result shown to be predominantly quadrupolar, a structure which had been observed so far in only a couple of stars (Thompson & Landstreet 1985; Landstreet 1990). HD 137509 had already been pointed out in Paper V as a star of particular interest, for having the strongest quadratic field measured so far. The present finding of a strong quadrupolar component in its magnetic field still increases this interest.

Our new quadratic field data for HD 153882 bring full confirmation of the suspicion expressed in Paper V that the variation of that field moment is best represented by a sinusoid with twice the stellar rotation frequency, with no significant contribution of a term with the rotation frequency. This does not imply any peculiar structure of the magnetic field: depending on the geometry of the observation, such behaviour of tex2html_wrap_inline2781 might be seen for a centred dipole (very much like in the case of the mean field modulus, which has been discussed in some detail by MHLLM).

The knowledge of the rotation period of several of the studied stars was improved as a result of the measurements reported here. A refined value of the period of HD 119419 has been derived, thanks to the longer timebase now covered by the avaible data. New measurements of the longitudinal field of HD 24712 almost certainly solve the ambiguity between the values of the period proposed by Kurtz & Marang (1987) and in Paper II, providing strong evidence that the latter is indeed the correct one. As shown already by MHLLM, combining our tex2html_wrap_inline2667 determinations with those of other authors for HD 137949 gives clear indications that the rotation period of that star must be at least of the order of 75 years, making it one of the two Ap stars with the longest period currently known.

In the course of this study, 14 roAp stars (out of 28 such stars currently known) have been observed. For 6 of them, no attempt to detect a magnetic field had ever been made. Magnetic fields are believed to play an essential rôle in roAp stars. According to the most popular model for those stars, the oblique pulsator model (Kurtz 1982), the pulsation modes are aligned with the magnetic axis of the star. Even more fundamentally, most assumptions made about the excitation mechanism of the pulsation require the presence of a magnetic field. This stresses the interest of studies of magnetic fields in roAp stars: even the most basic question whether all those stars do have a magnetic field is crucial. The following elements of answer are brought by the present study:

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the first measurements of the longitudinal and quadratic fields of HD 166473 have been obtained. It is no surprise that these field moments are large, since the field modulus of this star, diagnosed by MHLLM, is also large (and slowly varying);
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a somewhat marginal determination of the longitudinal field of HD 19918 was achieved;
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no significant longitudinal field was found in HD 6532, but the strong quadratic field of this star appears quite definite. This is similar to HD 128898, already studied in Papers II to V, in which our new observations still fail to yield a definite longitudinal field measurement but confirm the previously diagnosed quadratic field;
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our two attempts to measure tex2html_wrap_inline2667 in HD 134214 yielded null results, but the presence of a relatively weak field in the star had been definitely established from the observation of magnetically resolved lines (MHLLM);
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no non-null value of the considered field moments could be measured in HD 193756, HD 203932, HD 217522, and HD 218495 (all stars whose magnetic field had never been studied before);
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our attempts to detect a field in HD 176232 also failed. In this star, the only evidence for the presence of a weak magnetic field rests on photographic longitudinal field measurements (Babcock 1958), whose unusually small estimated uncertainty is probably not beyond question;
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finally, new data have been obtained improving our knowledge of the fields of HD 24712, HD 83368, HD 137949, and HD 201601.

In summary, more investigations of the magnetic field of the roAp stars would be most desirable, since at present, it is not even clear whether some of them are magnetic at all. We are planning to pursue such a study.

The sample considered here also contains 21 Ap stars with resolved magnetically split spectral lines, out of the 42 such stars currently known (MHLLM). For 8 of them, we report the first determination of the longitudinal field. Our two attempts to measure the longitudinal field of HD 134214 were the first ever made; that both of them yielded null results may possibly be purely coincidental and result from an unfortunate phasing of the observations (see Sect. 4.3.14), as it definitely is for HD 165474 (see Sect. 4.2.14). A long-term programme of systematic study of the longitudinal field of the Ap stars with magnetically resolved lines is in progress, with a view to modelling the field structure from the simultaneous consideration of longitudinal field and field modulus (from MHLLM) data well distributed throughout the stellar rotation cycles.

Generally, the results presented here are intended for future use in determinations of the geometric structure of the magnetic fields of the studied stars. This will be the subject of future works.

Acknowledgements

This research has made use of the Simbad database, operated at CDS, Strasbourg, France.


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