2. New data and period analysis
In this paper, we report about the derivation of a refined value of the rotation period of HD 137509, achieved thanks to the acquisition of new photometric and magnetic data.
20 new photometric measurements have been performed in the Geneva system. Like the data discussed by Mathys & Lanz (1991), they were obtained using the P7 photometer attached to the 0.7 m Swiss telescope located on La Silla (Chile) and reduced within the general reduction framework at the Geneva Observatory. Both the old and the new photometric measurements (56 observations in total) are presented in Table 1, which is available only in electronic form. The magnitude and colour weights (Rufener 1988) are also given in that table.
The mean longitudinal magnetic field and crossover measurements analysed by Mathys (1991) were revised to deal more adequately with the errors in the procedure of determination of those field moments (Mathys 1994; 1995a). Mathys (1995b) also diagnosed the mean quadratic magnetic field , which revealed that HD 137509 has one of the strongest magnetic fields of any Ap or Bp star. Five additional determinations of the longitudinal field, of the crossover, and of the quadratic field, were recently reported by Mathys & Hubrig (1996). All these magnetic data were derived from observations performed with the ESO 3.6 m telescope, the spectrograph CASPEC and its Zeeman analyzer. A full description of those observations is given in the cited references.
All the datasets mentioned above were taken into account in the period determination described here. For the latter, we used the same method of minimization of the residuals of the observations with respect to a least-squares fit of the variations as Manfroid & Mathys (1985). More specifically, we fitted the data by a cosine wave and its first harmonic, for a series of rotation frequencies. Periodograms were then built by plotting the reduced of the fit against the frequency.
This approach was applied to the photometric data in each of the seven Geneva bands separately, and to the , , and measurements. Only those photometric data having weights larger than or equal to 2 in both magnitude and colour were used for the period search: 36 of the 56 measurements of Table 1 met this condition. For the magnetic data, the least-squares fit were weighted by the measurement uncertainties, as explained e.g. in Mathys (1994). In the case of the longitudinal field, the 2 measurements of Bohlender et al. (1993) were also used for the period derivation.
In this way, 10 independent periodograms were obtained. Comparing them and requiring the same period to represent the variations of all the considered quantities, we could resolve the remaining aliasing ambiguities and rule out spurious period values appearing in some of the periodograms. In a first run, the periodograms were computed over the frequency range 0.1-1.0 d-1, at equidistant frequencies separated by d-1. This allowed us to check the absence of any plausible value of the frequency outside the interval 0.2-0.25 d-1. Our next periodograms sampled this interval at frequency steps of d-1. The result is shown in Fig. 1 for the 3 wide colour bands , , and , and for the longitudinal field and the crossover. The aliasing ambiguity and the presence of spurious peaks in the periodograms (especially for the magnetic data, due to the relatively small number of data available and to their limited accuracy) are quite apparent in the figure. However, a careful intercomparison of the periodograms (including those for the other 4 colour bands and for the quadratic field) reveals that there is only one value of the frequency which is consistent with all the observations. This value is identified in Fig. 1 by a dashed vertical line in each panel. To determine its value accurately, we repeated the period search around it, using a smaller frequency step, d-1. Again, all the periodograms so obtained were confronted with each other to derive the final value of the rotation frequency and to estimate its uncertainty.
As a result, we found that the rotation frequency of HD 137509 is
corresponding to a period
This value of the period is quite consistent with the one that we had previously derived (Lanz & Mathys 1991), within the uncertainty of the latter. The accuracy of the new determination is about 5 times better than the old one.
© European Southern Observatory (ESO) 1997
Online publication: May 26, 1998