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Context. Searches for magnetic fields in white dwarfs have clarified both the frequency of occurrence and the global structure of the fields found down to field strengths of the order of 500 kG. Below this level, the situation is still very unclear. Aims. We are engaged in a project to find and study the weakest magnetic fields that are detectable in white dwarfs, in order to empirically determine how the frequency of occurrence and the structure of fields present changes with field strength. In this paper we report the successful testing of a very sensitive method of longitudinal field detection in DA white dwarfs. We use this method to carry out an extremely sensitive search for magnetism in the bright white dwarf 40 Eri B. Methods. The method of field measurement we use is to measure, at high spectral resolution, the polarisation signal V/I of the narrow non-LTE line core in Hα in DA stars. This small feature provides a much higher amplitude polarisation signal than the broad Balmer line wings. We test the usefulness of this technique by searching for a weak magnetic field in 40 Eri B. Results. One hour of observation of I and V Stokes components of the white dwarf 40 Eri B using ESPaDOnS at the CFHT is found to provide a standard error of measurement of the mean longitudinal magnetic field B z of about 85 G. This is the smallest standard error of field measurement ever obtained for a white dwarf. The non-detections obtained are generally consistent with slightly less accurate measurements of 40 Eri B obtained with ISIS at the WHT and the Main Stellar Spectrograph at SAO, in order to provide comparison standards for the new method. These further measurements allow us to make a quantitative comparison of the relative efficiencies of low-resolution spectropolarimetery (using most or all of the Balmer lines) with the new method (using only the core of Hα). Conclusions. The new method of field detection reaches the level of sensitivity that was expected. It appears that for suitable DA stars, about the same field uncertainties can be reached with ESPaDOnS on the CFHT, in a given integration time, as with FORS on an 8-m telescope, and uncertainties are a factor of two better than with low-resolution spectropolarimetry with other 4-6-m class telescopes. However, even with this extraordinary sensitivity, there is no clear indication of the presence of any magnetic field in 40 Eri B above the level of about 250 G.

The hot γ Doradus stars have multiple low frequencies characteristic of γ Dor or SPB variables, but are located between the red edge of the SPB and the blue edge of the γ Dor instability strips where all low-frequency modes are stable in current models of these stars. Though δ Sct stars also have low frequencies, there is no sign of high frequencies in hot γ Dor stars. We obtained spectra to refine the locations of some of these stars in the H-R diagram and conclude that these are, indeed, anomalous pulsating stars. The Maia variables have multiple high frequencies characteristic of β Cep and δ Sct stars, but lie between the red edge of the β Cep and the blue edge of the δ Sct instability strips. We compile a list of all Maia candidates and obtain spectra of two of these stars. Again, it seems likely that these are anomalous pulsating stars which are currently not understood.

We report a discovery of the Zeeman resolved spectral lines, corresponding to the extremely large magnetic field modulus B s = 17.5 kG, in the cool Ap star HD 178892. The mean longitudinal field of this star reaches 7.5 kG, and its rotational modulation implies the strength of the dipolar magnetic component B p ≥ 23 kG. We have revised rotation period of the star using the All Sky Automated Survey photometry and determined P = 8.2478 d. Rotation phases of the magnetic and photometric maxima of the star coincide with each other. We obtained Geneva photometric observation of HD 178892 and estimated T eff = 7700 ± 250 K using photometry and the hydrogen Balmer lines. Preliminary abundance analysis reveals abundance pattern typical of rapidly oscillating Ap stars.

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