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Astron. Astrophys. 323, 881-885 (1997)

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3. Variation curves

The photometric, magnetic, and spectroscopic variations of HD 137509 with the period derived in the previous section are illustrated in Fig. 2.

[FIGURE] Fig. 2. Phase diagrams of the variations of HD 137509 in the Geneva photometric bands [FORMULA], [FORMULA], and [FORMULA], of its mean longitudinal magnetic field [FORMULA] and of its crossover [FORMULA], and of the equivalent width of the lines Fe   [FORMULA] @ [FORMULA], Si   [FORMULA] @ [FORMULA], and Cr   [FORMULA] @ [FORMULA]. Filled dots represent photometric data with weights greater than or equal to 2 in both magnitude and colour; the remaining photometric measurements appear as open circles. The longitudinal field and crossover data are from Mathys (1994, 1995a; filled squares), Mathys & Hubrig (1996; open squares and filled triangles depending on the instrumental configuration used - see the cited reference for details), and Bohlender et al. (1993; crosses). The symbols used in the equivalent width plots distinguish different series of observations in the same way as for the magnetic field. The solid curves are least-squares fits of the photometric and magnetic data by a cosine wave and its first harmonic (see resp. Table 2 and Mathys & Hubrig 1996)

In the panels of the bottom row of this figure, the measurements of the mean longitudinal magnetic field [FORMULA] and of the crossover [FORMULA] are plotted against phase. The curves are least-squares fits to the data by a cosine wave and its first harmonic. The corresponding fit coefficients have been given in Tables 4 and 5 of Mathys & Hubrig (1996). Note that the longitudinal field measurements of Bohlender et al. (1993), although they are shown in the figure, were not taken into account to compute the best fit. The remarkable double-wave character of the variations of both [FORMULA] and [FORMULA] has already been stressed by Mathys & Hubrig (1996). It indicates that the magnetic field of HD 137509 includes an unusually large quadrupolar component. Such a strong quadrupolar character of the magnetic field structure was known so far only in two other stars, HD 37776 (Thompson & Landstreet 1985) and HD 133880 (Landstreet 1990). This unusual feature strengthens even more the interest of studying HD 137509.

The quadrupolar character of the field of HD 137509 is reflected in its photometric and spectroscopic variations. Examples of the photometric variations are shown in the upper three panels of the left column of Fig. 2, where the [FORMULA], [FORMULA], and [FORMULA] measurements are plotted against rotation phase. All the data of Table 1 appear in the figure, where open symbols are used to distinguish the points that were not used in the period search on the account of weight lower than 2 in either magnitude or colour (or both). These points were not taken into account either to compute the least-squares fits to the data that appear as solid curves in the figure. The fitting function used is of the form:


The fit parameters [FORMULA], [FORMULA], [FORMULA], [FORMULA], and [FORMULA], and their respective standard errors, are given in Table 2 for the 7 colours of the Geneva system. One sees in Fig. 2 and in Table 2 that the variation curves are similar in all the photometric bands, with a marked double-wave character reminiscent of that of the magnetic variations. The primary brightness maximum roughly coincides in phase with the stronger positive extremum of the longitudinal field, while the secondary brightness maximum occurs close to the phase of the secondary maximum of [FORMULA].


Table 2. Coefficients of the fits of photometric data by a cosine wave and its first harmonic

Mathys (1991) had pointed out that HD 137509 also undergoes quite conspicuous spectroscopic variations, which are illustrated here in the upper three panels of the right column of Fig. 2. The panels show phase diagrams of the variations of the lines Fe   [FORMULA] @ [FORMULA], Si   [FORMULA] @ [FORMULA], and Cr   [FORMULA] @ [FORMULA]. All spectral lines of HD 137509 are strongly distorted by the combination of Zeeman and rotational Doppler effect, and are accordingly difficult to measure. Only lines that are sufficiently strong can be measured, yet with a limited accuracy. Unrecognized weaker blends may furthermore affect the derived equivalent widths. These circumstances explain the rather large scatter seen in Fig. 2 in the equivalent width plots. For the same reasons, we did not attempt to fit a mathematical function to the equivalent width data. Nonetheless, definite variability is found for Fe   [FORMULA] and Cr   [FORMULA] @ Again the variations mirror to a large extent those of the longitudinal field, with two minima per cycle close to the phases of the negative extrema of the latter. The case of Si   [FORMULA] is less clearcut. The evidence for the occurrence of a minimum of the equivalent width near phase 0.45, where [FORMULA] also reaches a negative extremum, mostly rests on a single measurement, but the difference between this and other measurements is large enough to support its significance. The figure also gives some marginal hint of a secondary minimum of the Si   [FORMULA] line equivalent width close to the phase of the other extremum of [FORMULA].

In summary, we have refined the determination of the rotation period of HD 137509, using new photometric and magnetic data. The star proves very interesting, with a magnetic field which is one of the strongest known in any Ap or Bp star and whose structure includes a large quadrupolar contribution, such as observed so far in only two other stars. HD 137509 is definitely an object deserving a more detailed study. The latter should in particular aim at modelling both the magnetic field and the surface distribution of the chemical elements.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998