## 6. Discussion## 6.1. The detection of strong magnetic fieldsThe significance of the magnetic field strengths obtained can be estimated in three different ways: -
The absolute value of the correlation coefficients and the number of underlying data points can be used to estimate the significance of the results. In this way we test the presence of a strong magnetic field. -
We can estimate the confidence level of the obtained correlation coefficients using the Fisher -transformation (e.g. Fig. 5). This method gives an estimate of the uncertainties in , and of also constrains all possible combinations of the separate values for *B*and*f*. -
Compared to the EWs calculated without the magnetic intensification, the scatter around the empirical curve of growth has to decrease if we take the magnetic intensification of the EWs into account.
From the first item, we find that the probability is that the correlation obtained is significant, being higher than 99%, for VY Ari, LkCa 15, LkCa 16, T Tau, and UX Tau A. Because of the large GW Ori is the star with the smallest number of suitable lines and thus the star with the lowest accuracy obtained. The correlation coefficient thus is small, and we conclude that the 16 lines are not sufficient to detect a magnetic field of kG, as a level of has to be reached to give a 95% probability for a detection. The areas given by the dotted lines in the contour plots refer to a
95% significance level. The fact that many lines are needed is further
highlighted by the data from VY Ari and LkCa 15. These stars are the
ones with the largest number of suitable lines, and correspondingly
both upper and lower limits of The results of the third test are given in the last column of Table 3. Taking the magnetic intensification into account, the scatter of the empirical curves of growth is reduced by a factor of more than 2 for VY Ari, LkCa 15 and T Tau, and by 30% for LkCa 16. However for UX Tau A, for which the first two tests yield a marginal detection of a magnetic field, the scatter of the curve of growth increases by a factor of three, rather than decreases. We are thus cautious about the detection of a field on UX Tau A. ## 6.2. Geometry of the magnetic fieldIn principle, our method allows us to disentangle -
The large values obtained for the constant (Table 3) for the case of the optimal regression (recall that if , then ). -
The consistency of the derived *B*and*f*was checked by removing the mean inclination of the field as a free parameter in the reduction process by assuming a radial field geometry (see below).
We thus have to conclude that in the cases where we have unambiguous evidence of a strong magnetic field, the filling factor has to be larger than 0.5. To test if the derived magnetic field strengths and filling factors
(calculated above using a homogeneous geometry with constant mean
inclination) are sensitive to the assumed field geometry we computed
EWs for different field strengths,
## 6.3. Possible influence of veiling on the resultsThe possible presence of veiling in the cTTS may complicate the
analysis of the spectra. This is especially true if the amount of
veiling depends on wavelength. By defining the veiling The wavelength dependence of the veiling has been studied by a number of authors (Hartigan et al. (1989), Hartigan et al. (1991), Bertout et al. (1988), Basri & Bertout (1988), Hartmann & Kenyon (1990, Basri & Batalha (1990)). The general result is that the amount of veiling drops rapidly between 3000 and 5000 Å , and is often almost constant between 5000 and 9000 Å. As shown by Hartigan et al. (1991) the spectrum of the veiling can be modelled by the emission from a region with and temperatures of 6000 to 10000 K. For sources with very high veiling, the emission approaches a blackbody. An optical thin veiling continuum results in a slight increase of the veiling with wavelength, and thus causes no problem for the magnetic field determination if lines in the 5000 to 9000 Å region are used. An optically thick veiling continuum will decrease with wavelength. In fact, since the veiling is typically strongest in the blue, and weakest in the red, the EW of lines from a highly veiled cTTS would appear to grow relative to a standard star as the wavelength increases. Since the Zeeman effect grows as , the question is whether the presence of veiling might mimic the results of our method. To answer this question, we artificially veiled the spectrum of our
non-magnetic K3 template star using the wavelength dependence of the
veiling calculated by Basri & Batalha (1990) to model the observed
veiling of GG Tau. The veiling declines from
## 6.4. The influence of the magnetic field on measurements of veiling and spectral typeAs was shown in Fig. 3, the EW of photospheric spectral lines can increase by a noticeable amount under the influence of a magnetic field. As explained in Sect. 4, this effect may change the spectral type of a star if it is derived from the curve of growth of Fe i lines. Table 3 lists the temperature as computed from the curve of growth of these lines both taking the enhancement due to the magnetic field into account, and not doing so. For the T Tauri stars studied, accounting for the magnetic enhancement increases the temperature of the star by 100 to 300 K compared to what would otherwise be determined. For T Tau, the star with the largest of 2.35 kG, this effect is most pronounced and would make the spectral type of T Tau appear to be later than it really is by about one to two subclasses. The other effect of the enhancement of the EW of lines sensitive to the magnetic field is that any measurement of the veiling using such lines might be influenced. For example, using magnetic field strength of one, two and three kG, we derive that the average EW of 48 Fe i lines used in this work would increase by about 10%, 28%, and 43% for a K3V star. If a template star of the correct spectral type is chosen, the enhancement of the EW would thus result in an underestimation of the veiling. For example, failing to account for a 2 kG field would change the deduced veiling from 2.00 to 1.34. Fig. 15 shows the measured against the true veiling for various magnetic field strengths.
The presence of magnetic fields on T Tauri stars thus may alter
both derived effective temperature and veiling, depending on the
particular lines used. Obviously, lines with larger magnetic
intensification are more affected
than lines with smaller magnetic intensification. © European Southern Observatory (ESO) 1999 Online publication: December 16, 1998 |