3. Veiling derivation from high resolution spectra
In this and the next section, we study from an experimental point of view the veiling derivation from the HHKHS approach in the light of the analysis of CH99. Here we examine the high spectral resolution case. For this purpose, we use a high resolution spectrum ( 40000) of the K7 CTTS BP Tau obtained with one hour integration time on November 28, 1995 (JD=2450050.32), at the 1.93m telescope of the Observatoire de Haute Provence (France) with the instrument ELODIE (Baranne et al. 1995). The selected template is the bright K7V star HD 201092 observed with the same instrument. The spectra are composed of 67 orders covering roughly the wavelength domain [4000 Å, 6800 Å]. Although HD 201092 is perhaps not the best template to be used for veiling derivation in BP Tau through the whole spectral range, this is not important here because we are just interested in probing the algorithm. We restrict the analysis to 8 spectral orders, each of a few tens of Angstroms width, corresponding to a deep spectral depression between 4950 and 5280 Å, seen at low resolution. The orders are first regularly resampled and oversampled with a 0.03 Å wavelength step. They are then smoothed by gaussian filtering to a spectral resolution of about 10000, leading to q values larger than 6 and 25 for BP Tau and the template, respectively. From Eqs. (2) and (3), we conclude that the relative veiling bias will be dominated by spectral mismatches, but not by bad noise estimates whose maximum effect is of a few % only.
Figs. 1a and 1b show a selected spectrum of BP Tau and the relevant template, each one normalized to its mean flux. We can check by eye that the system of absorption lines of BP Tau is roughly the same than that of the template and that it is about half less deep, which would correspond to a veiling around 1. To asses quantitatively this point, we apply the HHKHS algorithm, adopting the R definition for the veiling, in which the excess is referred to the mean flux of the template (see Sect. 2). The veiling is still assumed constant through the working band, but to take into account a possible slope difference between the object and the template spectra, we do not longer assume a constant scaling factor p. Instead, we approximate its variations within the band by a linear function. The quantity Q given by Eq. (1) then becomes a function of three unknowns (the veiling R plus two for the function p). Its minimum is automatically found, to a precision of one fourth of point in wavelength, by recentering one of the spectra via Fourier transform.
Figs. 1c and 1d show the best fits of BP Tau selected spectrum (solide line) by the veiled template (dotted line), , for and . The results of the fits are =1.02 and =0.90, corresponding to a relative difference of about 6% and essentially attributable to spectral mismatches between the object and the template spectra. A careful examination of the fits over the eight spectral orders shows that the template deepest absorption lines are not as well adjusted for as for . For , i.e. , the algorithm will in someway tend to interpret part of the high frequency information of the template spectrum, mostly contained in the deepest lines, as if it was spurious noise and will not try to closely adjust it (CH99). Although the solution for seems to be in general apparently better than the solution for , it cannot be considered as such. The reason just lies in spectral mismatches, which make that the object cannot be exactly represented by the veiled template. Fig 2 presents the veiling with its error bar (mean and half difference between and ) as a function of wavelength (white points). Clearly, from 4950 to 5280 Å, the veiling is fairly constant with a mean through the band of =0.89 and a standard deviation of =0.11 (excluding the two end points ).
© European Southern Observatory (ESO) 1999
Online publication: September 13, 1999