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Astron. Astrophys. 361, 265-272 (2000)

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2. The technique

The CORALIE spectra, with a bandpass from about 3900 Å to 6800 Å, include the two CaII H and K resonant lines centered at 3968.49 Å and 3933.68 Å, respectively. In Fig. 1 we can see two high S/N CORALIE spectra of the CaII H line central region. The upper spectrum corresponds to the chromospherically active star HD 22049 (K2V), and the lower one to the rather low activity star HD 115617 (G8V).

[FIGURE] Fig. 1. Two CORALIE spectra of the central region of the CaII H line. The upper spectrum corresponds to an active star, while the lower spectrum to a low activity star. The dashed lines represent the emission region of the spectra used to compute the activity index.

The technique described in this paper to compute our chromospheric activity index mimics the procedure used at Mount-Wilson (MW) for more than three decades (Vaughan et al. 1978). At MW, the flux in two [FORMULA]1 Å wide spectral windows centered on the CaII H and K lines is divided by the flux in two 20 Å wide comparison windows placed on each side of the H and K lines. In our case, to compute the chromospheric activity index [FORMULA], we simply sum and divide the flux in a 1 Å wide window centered on the CaII H line by the flux in a 15 Å comparison window centered at 3996.5 Å. We only make use of the H line, since the K component is in a spectral order with very low typical fluxes, introducing undesirable noise.

The index is computed as follows. CORALIE spectra are extracted online following a standard echelle spectra reduction procedure. The details can be found in Baranne et al. (1996). The spectra are then corrected for the Doppler shift using the previously computed radial velocities, and they are rebinned with steps of 0.01 Å (about twice as small as the original binning), using an algorithm that conserves the flux. This way, we have about 100 bins in the CaII H line central band.

The technique employed with the CORALIE spectrograph to determine high-precision radial velocities implies the use of a Thorium-Argon (hereafter ThAr) calibration lamp, whose spectra are simultaneously recorded in the "sky" orders (see Baranne et al. 1996 for a description of a similar instrument). The resulting inter-order space is very small, and the task of subtracting the background light becomes difficult. In addition, the ThAr lamp produces scattered light all over the CCD, that will add to the usual background light.

In order to account for this "pollution" we have to follow a different approach. We first "eliminate" the lines in the ThAr spectra using an appropriate routine which "cuts" all the fluxes higher than the "local" mean. This proved to be essential to the next step, where we adjust a cubic smoothing spline to the remaining ThAr spectrum (which is at this moment the sum of the background light and the "continuum" spectrum of the ThAr lamp). For this we used the E02BBF and E02BEF NAG fortran routines 2. Finally, we subtract from each stellar spectral order of interest the spline adjusted to the corresponding ThAr order. In this procedure we suppose that the continuum spectrum of the ThAr lamp is very low and so we can ignore it. As we will see below, the results prove this is a good approximation.

After this subtraction, we compute our "S" index from the remaining spectrum by adding the counts in each of the spectral windows of interest (as described above).

Given the large amount of data available (in average, more than 30 stellar spectra are obtained every night), it was essential to have a completely automatic procedure. This implied the development of some automatic mechanisms to control eventual hazards in the spectra. In our routines we have thus some flags that give us information whenever cosmic rays are found in the continuum comparison window. Cosmis rays on the central H line region are also automatically detected whenever there are unusually high flux values (exceeding 5 [FORMULA]), and a corresponding flag is raised. In such cases the spectra can be analysed and if confirmed, the [FORMULA] value is not used.

Unfortunately, the CORALIE spectra are not always as good as those shown in Fig. 1. The blue orders where these lines are located have usually low fluxes. On the other hand, the technique used to obtain high-precision radial velocities does not require very high S/N ratios in the blue. We thus took the conservative decision of only using [FORMULA] values for those measurements having more than about 4000 counts in the central region of the CaII H line (this would correspond to 1800 counts for a non-rebinned spectrum). This limits our "survey", but is necessary since lower fluxes give high uncertainties in [FORMULA].

Finally, the use of the CaII H line alone instead of both H and K is not expected to cause any serious systematic errors. Cuntz et al. (1999) showed that for a set of K dwarfs the ratio of the fluxes for this two lines is almost constant. This ratio depends on the rotational period of the star, but the dependence is small, and we expect errors to be significantly lower than 10%. Moreover, the Cuntz et al. relation is only valid for K dwarfs. We thus do not make any corrections.

2.1. Calibration to the Mount-Wilson system

In order to convert our [FORMULA] values to the Mount-Wilson scale, we use observations of some stars for which we have values of [FORMULA]. In Table 1 we present the list of calibration stars. In Columns 2 and 3 we list the values of [FORMULA] and their dispersions, [FORMULA]([FORMULA]). The values were computed from Duncan et al. (1991), and correspond to the mean and rms of the [FORMULA] values over all the seasons listed in his Table 1. In Columns 4 and 5 we present our [FORMULA] values and corresponding dispersions. In the case of HD 155885 we only have 1 measurement (Column 6), and so we adopt a conservative error of 10%. The best least-square fit to the data holds (Fig. 2):


[FIGURE] Fig. 2. Mean [FORMULA] values compared with [FORMULA] values for a set of 18 calibration stars. The solid line represents the best least-square linear fit. Horizontal error-bars represent the dispersion of [FORMULA] values around the mean seasonal value (Duncan et al. 1991). Vertical error-bars represent the dispersion in our [FORMULA] values over one year. The values are taken from Table 1.


Table 1. Stars used to calibrate the [FORMULA] values into the Mount-Wilson "S" scale.
[FORMULA]) From Duncan et al. (1991).

This relation is valid for [FORMULA] between 0.10 and 0.79 ([FORMULA] between 0.14 and 0.69). The fit is quite remarkable ([FORMULA] = 0.030) reflecting the precision of our [FORMULA] values. Since both our [FORMULA] and the [FORMULA] values correspond to the mean over a long period of time (a few seasons for the case of the [FORMULA] and about one year for our [FORMULA] values), [FORMULA] reflects not only the uncertainties in our procedure but also intrinsic stellar variation.

From this calibration we can then compute values of the CaII H and K flux corrected for the photospheric flux, [FORMULA] (Noyes et al. 1984), for our programme stars.

2.2. Our precision: two examples

To better illustrate the stability and precision of the [FORMULA] index, we plot in Fig. 3 (upper panel) the values of [FORMULA] as a function of time for the star HD 20794, a chromospherically-quiet G8 dwarf. The quality of these values is representative of our usual measurements.

[FIGURE] Fig. 3. Upper panel : values of [FORMULA] obtained on the same night for HD 20794. Each point corresponds to one individual measurement; lower panel : the same [FORMULA] values plotted against the flux in the center of the CaII H line. The dotted line represents the best least-square linear fit.

The spectra were taken over one night with exposure times going from 2 to 3 minutes. As we can see from the figure, the rms around the mean [FORMULA] value is quite low, amounting to about 0.005. If we take all the 61 measurements of this star over one year we find a mean value of [FORMULA]=0.155[FORMULA]0.016 (where the error corresponds to the rms around the mean), corresponding in the MW system to [FORMULA]=0.175. Henry et al. (1996) found [FORMULA] = 0.167 with 6 measurements. The difference might be related to errors in the [FORMULA] vs. [FORMULA] calibrations, both in this work and in the work of Henry et al., as well as to eventual activity level variations: the observations presented here were not carried out during the same season as the survey of Henry et al.

Since we have to use a rather "tricky" technique to subtract the background light over the CCD, one might eventually expect some systematic errors. In Fig. 3 (lower panel) we plot the [FORMULA] values against the flux in the central region of the CaII H line. As we can see from the plot, there is no systematic error in [FORMULA] connected with the number of counts in the central H line region, at least in the range of observed fluxes. The fit shows a small, but not significant trend (dotted line); the Spearman correlation coefficient is 0.18, and a F-test shows that the probability against a trend is [FORMULA]50% (the error in the slope is higher than the slope itself).

In Fig. 4 we can see our results for the star Procyon (HD 61421) over one night (upper panel) and for a series of 10 almost consecutive nights (lower panel). Given the brightness of the star, the fluxes are much higher than for the case of HD 20794, and our precision is also much better. In this case we have a mean [FORMULA] value of 0.170 with a rms of only 0.001 over all the 10 nights. This corresponds to [FORMULA] = 0.188. A value of [FORMULA] = 0.185 was found over two seasons by Duncan et al. (1991). Although this star is particularly bright and the obtained fluxes are particularly high, this example shows that the [FORMULA] index is very stable, not only during one night but also from night to night.

[FIGURE] Fig. 4. Upper panel : values of [FORMULA] obtained on the same night for Procyon. Each point corresponds to one individual measurement; lower panel : the mean of the [FORMULA] values for 10 nights for this same star. Each point corresponds to the mean of all the measurements over one night, and is centered on the mean of the JD of that night. Error bars are smaller than the size of the points.

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Online publication: September 5, 2000