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Appendix A: Automatic line characterization procedure and resolution effects

In brief; one of the most difficult steps in automating the measurement of line properties is the determination of the continuum on top of (or below) which the line lies. Even when this task is performed manually, different astronomers might select different points to represent the continuum when, for example, analyzing a noisy spectrum or a line embedded in a molecular band. The code that we have developed tries to solve this problem by proceeding in an iterative and consistent way.

First of all, it locates where the actual peak of the line is. In this step, the wavelength calibration accuracy is taken into account providing limits to the wavelength coverage where the search for the peak of the line is carried out. Once this task is accomplished, two regions are defined (to the right and to the left of the estimated central wavelength) and the width of the regions is fixed to 100 points to be statistically significant: the width in wavelength units therefore depends on the resolution of the spectra. A linear fit using those regions is performed (red dotted line in Fig. A.1). With this attempt to define a continuum (the linear fit), the code calculates a first guess of the FWHM (red cross in Fig. A.1).

For the second iteration, the code considers that the line is a Gaussian, and, therefore that . Assuming that at a distance of  ± 10σ, one should be outside the line, two new regions in the spectra are selected, starting at  ± 10σ from the wavelength of the peak and ending at the same limits as before. These two regions are close to the edges of the line unless the line has a very wide double-peaked structure.

At this point, the code will perform two linear fits in a sequential way; a second continuum is derived with a linear fit to these new regions of the spectra close to the edges of the line, and the third one with another linear fit, but this time considering only those data points that differ from the second continuum by less than one dispersion of the difference between the actual spectra and this second continuum (the blue dots in Fig. A.1 represent the data points considered to define a third continuum and the blue dashed line is the resulting continuum fit).

Once the third guess of the locus of the continuum is estimated, the code calculates a second iteration of the FWHM (blue cross in Fig. A.1). Assuming one more time that the line can be described with a Gaussian (and calculating the associated σ), it considers three pairs of wavelengths in the spectra to make the final measurements (pairs located at  ± 3σ,  ± 4σ and  ± 5σ from the wavelength of the peak). As a final refinement, for each selected pair of wavelengths, for example λ₁ and λ₂ corresponding to λ_peak ± 3σ, the code checks whether the linear continuum defined by (λ₁, F(λ₁)), (λ₂, F(λ₂)) intersects the wings of the line; when this is the case (for example the upper-left panel of Fig. A.1), the code uses the third continuum to perform the measurements.

Prior to providing these measurements, the code subtracts the instrumental profile from the values estimated for the FWHM and FW_10% considering that the FWHM of the convolution (G_measured) of two Gaussians (G_instr, G_line) is given by: (A.1)and that FWHM and FW_10% are related by: FW_10% =   ×  FWHM.

The final product is the mean of the three measurements for each parameter (FWHM, FW_10%, and EW) and their corresponding standard deviation σ.

Fig. A.1 Example of the output of the code designed to measure EW, FWHM, and FW10% of the different lines detected on the spectra in an automatic manner. In this case, we show four of the measured lines in the average MIKE spectra obtained for LOri031: Hα at 6562.80 Å, He I at 6678.15 Å, Li I at 6707.8 Å, and S II at 6717.0 Å. For each case, the canonical wavelength for the measured line and the actual wavelength where the line has been found in our spectra are displayed as the title of the plot (all of them within the errors in the wavelength calibration). The iterative process in the continuum determination is displayed using different colors: red for the first iteration (including the first guess for the half maximum flux value, red cross), blue for the second one (filled blue dots on the data-points used to refine the first continuum, blue cross showing the second half maximum estimation), and the three green lines (filled, dotted and dashed) representing the final determined continuum.

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Once we had an automatic procedure to characterize the lines present in our spectra, we had to address the effect that the wide dispersion in resolution might introduce to our measurements. We proceeded in the following manner: we degraded one of our FLAMES spectra (from LOri038, a M3, accreting, Class II, confirmed member) to different resolutions (including those listed in Table 1). We then used (on those degraded spectra) our code to measure the FWHM, EW, and FW_10% of the Hα (emission) and Li λ6708 Å  lines (absorption). In Fig. A.2, we provide these values (EW and FW_10% for Hα and EW for Li I λ6708 Å) as a function of the resolution of the spectra. The length of the y-axes has been intentionally fixed for each plot: in the first panel (from left to right), it represents the variation in the instrumental response (the FWHM measured on the respective arc adapted for each value of the resolution) among the resolutions considered. In the cases of the middle and right-side panels, the length of these axes provides an idea of the variation within members of Collinder 69 for the corresponding equivalent width. We note that in the case of Hα there is clearly no significant dependence on the measurements made at different resolutions (the variations lie within the error bars). For the case of lithium, owing to the intrinsic weakness of the line, the accuracy of the measurement (meaning the error bars) lowers with the spectral resolution, but it still seems perfectly reasonable to compare measurements at R ~ 2000 and R ~ 8000. In the same figure, we have highlighted the range of resolutions where Li is no longer detectable. A detailed view of the “degeneration” of the lines for this example is provided in Fig. A.3

	Fig. A.2 Relationship between different measurements of the Hα and Li I line profiles and the resolution of the spectra where the measurement has been performed.
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Fig. A.3 Sequence providing a detailed view of the evolution of the profiles of the Hα (emission) and Li I (absorption) lines with the variation in the spectral resolution. The first panel (from left to right) corresponds to the original resolution of our FLAMES spectrum of LOri038, a M3 member of C69 (R ~ 8000). In the last panel, we have degraded the FLAMES spectra to a resolution similar to that of our low-resolution campaign (R ~ 800 obtained with the B&C spectrograph). As can be seen in this figure and in Fig. A.2 the lithium equivalent width can be measured down to resolutions of the order of 1250 (for a high S/N as in the case of our spectrum of LOri038). The linestyles and color code are those explained in the text.

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© ESO, 2011