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Astron. Astrophys. 321, 497-512 (1997)

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5. The emission lines

The large spectral range of the low resolution spectra allows us to study a large variety of emission lines. From all accessible lines, we selected just the Ca II H line (0.00 eV) line, the Ca II [FORMULA] 8662 (1.69 eV) line, H [FORMULA] (10.2 eV), H [FORMULA] (10.2 eV), and He I [FORMULA] 5876 (20.87 eV), because these lines sample all the different temperature regimes available. The Ca II lines sample the regions of the lowest temperatures (less than 6000 K), the He I line must be formed in a region of about 30 000 K, and the the Balmer lines are formed in regions with temperatures between these two extremes. The temperature regimes are so different that the lines should be formed in spatially different regions.

5.1. Equivalent width versus flux variations

The weak correlation between the EW of H [FORMULA] and the veiling continuum is not unexpected: as the veiling continuum rises, the strength of the line should decrease, making the EW less negative. We saw in Sect. 4.1 that the variations of [FORMULA] around H [FORMULA] and of the I-band continuum are 20-30%. If the line fluxes were constant, this would produce a 10-20% variation in the EW of H [FORMULA], in agreement with the 12% observed (Table 2). Similarly, the factor of 2 range in the veiling continuum in DR Tau (Fig. 5) should produce roughly the 30% variation in H [FORMULA] seen. However, it is not clear if the correlation is strictly true at all timescales or merely represents some average behavior. Fortunately, we can test these simple hypotheses with our time-resolved (relative) spectrophotometric data.

Since simultaneous photometry is only available for DG Tau and DI Cep or a few nights, it is only possible to derive the fluxes of the lines for some of the spectra. This is unfortunate, since the equivalent widths may vary either because of a variable continuum, or because of variations in the line fluxes. For example:

  • if the equivalent width variations during a single night were solely due to variations in the strength of the veiling continuum (i.e. without corresponding line emission), the line fluxes would be constant and the equivalent widths would vary as [FORMULA], i.e. the extrapolated equivalent width for zero line flux [FORMULA] ; alternatively
  • if the veiling continuum were constant during a single night, the line fluxes would vary directly with the equivalent widths, i.e. [FORMULA].

For some intermediate case (simultaneous line and continuum variations), one might expect a roughly linear relationship between line flux and EW but with a non-zero [FORMULA].

We therefore investigated whether the variations of the equivalent widths in DG Tau and DI Cep are mainly due to variations of the continuum, or due to variations in the line fluxes in that subset for which I-band relative photometry was available. For this purpose, the equivalent widths of 14 spectral lines in the I-band were measured: He I [FORMULA] 7065, 10630; Paschen 7, 8, 9, 10, 11, 12, 14, 17, and 19; and Ca II [FORMULA] 8662, 8542, 8498. The relative flux calibration was derived using the photometric data.

DG Tau

In Fig. 7, we have plotted the relative line fluxes against the equivalent widths for 4 representative lines and for each of the five nights during which simultaneous photometry was available. The solid lines are fits to the data assuming that the equivalent widths vary directly with the line fluxes (i.e. [FORMULA]). Clearly, this model is a very good representation of the data on timescales of hours, showing that - during each night and for each line - there are no significant underlying veiling continuum variations. The fact that the slopes of the lines vary from night-to-night is easily interpreted as longer term changes in the veiling strength.

[FIGURE] Fig. 7. A plot showing the nightly correlations between the equivalent widths and emission line fluxes of four lines in the I-band for DG Tau. The fluxes were obtained by calibrating the spectroscopic data with the relative CCD photometry. The straight lines are excellent fits to the data assuming that the EW vary directly with the line fluxes ([FORMULA]), i.e. that the underlying continuum is constant during the night. Changes in the slopes from night-to-night are easily interpreted as longer-term changes in the veiling continuum. See the text for a detailed discussion.

DI Cep

When the data for DI Cep are plotted in a similar manner, the behavior of the emission line fluxes is the same - despite the fact that DI Cep has much less veiling continuum.

We conclude that, for a very wide range in emission line excitation conditions and veiling strengths, the variations in the equivalent widths during a night must be mostly due to line flux variations, and not due to variations in the veiling continuum; and that the timescale for line flux variations is thus about an order-of-magnitude shorter than that of the veiling continuum variations.

5.2. Equivalent width variations

Fig. 4 show the variations of the relative equivalent widths ([FORMULA]) for the different lines of DG Tau, DR Tau and DI Cep. In the case of DG Tau, two prominent peaks can be seen bs occur more or less simultaneously in all lines. The data of DR Tau shows at least one well-defined peak. The amplitudes of the variations are listed in Table 3. The correlations between the lines are very high for all lines except Ca II [FORMULA] 8662 (Table 4). The data for DI Cep does not show the peak structure seen in the other stars. However, the correlations between the variations of H [FORMULA] and all other lines except for the Ca II lines are still quite high (Table 4).


Table 3. Variations of the emission line equivalent widths1


Table 4. E.W.-Correlations between H [FORMULA] and the other lines1

5.3. Quasi-periodic modulations

The light curves of DG Tau and DR Tau give the impression of being periodic. However, even if the variations are due to truly periodic modulations and not to the chance superposition of random emission line "flares", a formal periodogram analysis is complicated by the fact that the "flickering noise" is not Gaussian, and that many consecutive (correlated) measurements fall within the same phase bin. Thus, the effective number of data points is quite small. Nevertheless, we calculated the "Analysis of Variance" (AoV) periodograms (see Schwarzenberg-Czerny 1989) for our data in order to quantify the effect - particularly in order to compare the quasi-periods with published rotation rates. AoV is a "Phase Dispersion Minimization" method with well-defined statistical properties (unlike the classical PDM method) and is ideally suited for generally non-sinusoidal signals.

The lines appear to show the same behavior and no obvious phase-shifts between different lines greater than about half a day (about [FORMULA] in phase) are visible, so we used the mean of the relative EW variations for the strongest lines: Ca II H, He I [FORMULA] 5876, H [FORMULA], H [FORMULA], and Ca II [FORMULA] 8662. The AoV statistic [FORMULA] was calculated for a range of test periods between 3 and 8 days using [FORMULA] phase bins. Due to the nightly spacing of the 93 DG Tau and 117 DR Tau data points, all measurements within a given phase bin and within 8 hours of each other were averaged and considered a single data point. Thus, the effective number of data points n and hence the expectation value for the "noise-level" [FORMULA] varies slightly across the periodogram. The mean range of n for both stars was 22, so that a peak is significant at the 5% (1%) level for values of [FORMULA] greater than 2.96 (4.67) (F-test with [FORMULA] and [FORMULA] degrees of freedom).

DG Tau

The mean equivalent widths show no clear variations in this range at the 95% significance level (Fig. 8). There is a hint of a signal at about 4.6-5.0 days (88% significance level), but - strangely - no sign of a signal at or around the photometric period of 6.3 days (Bouvier et al. 1993).

[FIGURE] Fig. 8. Results of the search for quasi- periodic variability DG Tau using the mean of the normalized EW for Ca II H, He I [FORMULA] 5876, H [FORMULA], H [FORMULA], and Ca II [FORMULA] 8662 from DG Tau. Left: the AoV periodogram (with the 95% significance and noise levels indicated) and plots showing the effective number of data points and number of bins (see text). Right: the data phased at the best guess quasi-period (bottom) and the original data with arrows indicating the relative phase times (top).

DR Tau

Our data show a nominally significant narrow peak at 4.48 days and a broader peak between 4.5-5.0 days (also at about the 88% significance level: Fig. 9)). By analyzing sub-sets of the data, we found that the narrow peak is due to the Balmer lines only (98% level). The broad peak is mainly due to the Ca II lines, unlike the case in DG Tau (and is thus not simply an artifact due to the data spacing, etc.). Johns and Basri (1995) found quasi-periods for the H [FORMULA] line in DR Tau of [FORMULA] days at [FORMULA] km/s and [FORMULA] days at [FORMULA] km/s. Richter et al. (1992) found a quasi-period of 9 days and Bouvier et al. (1993) of 2.8 and 7.3 days from their photometric observations. Thus, a quasi-period of 4.5-5.0 days - if real - is within the range of variation timescales found for this unusually active star.

[FIGURE] Fig. 9. Like Fig. 8 but for the DR Tau data.

DI Cep

The equivalent-width light curves for DI Cep do not show the peak structure seen in the other two stars. However, the correlations between the variations of H [FORMULA] and all other lines using all individual spectra is still quite high (see Table 4), indicating that the correlations are not simply produced by rotational modulation effects.

5.4. Line profile variations

Although the low and the high resolution spectra where not taken simultaneously, the larger dispersion of the high resolution data can be used find out which parts of the line profiles are actually variable. However, since high resolution spectra are available from only 3 nights in the case of DR Tau, and only six in the case of DI Cep - compared to the 117 spectra per star on which the correlation analysis is based - these results do not carry as much weight. As a measure of the variability in line profile, we followed Johns & Basri (1995) and computed the normalized variance for each point of the line profile of H [FORMULA], H [FORMULA] and He I in DI Cep and DR Tau. The results are shown in Fig. 10.

[FIGURE] Fig. 10a-f. Line profiles (full line) and their normalized variances [FORMULA] (shaded) for selected lines in DR Tau (left; 3 spectra) and DI Cep (right; 10 spectra): H [FORMULA] (top), He I [FORMULA] 5876 (middle), and H [FORMULA] (bottom). The velocities are relative to the photospheric absorption lines.

DR Tau

Despite the small number of spectra (3), H [FORMULA] shows clear profile variability, predominantly in the the blue wing: there are three peaks of the variance at about [FORMULA], [FORMULA] and [FORMULA]. There is one prominent peak in the variance of H [FORMULA] which is again in the blue wing at [FORMULA] and a weaker component at [FORMULA]. The latter may have an equivalent component in H [FORMULA] at [FORMULA]. Though Johns & Basri (1995) report seeing similar components, the quasi-periodic variations are from the line center.

The differences between the observed He I line profiles are very small - the peak of the variance is only 0.15 compared to 0.4-0.5 for H [FORMULA] and H [FORMULA], and this peak is seen in the absorption component of the He I line. Although this appears to be consistent with the lower correlation between He I and H [FORMULA] of 0.56 compared to the correlation between H [FORMULA] and H [FORMULA] of 0.85 in DR Tau, we do see variability of the He I line in the low resolution data. Since the correlation between H [FORMULA] and He I is not zero, some part of the emission component of the He I profile has to correlate with H [FORMULA], but from the present data, we are unable to tell which part it is.

DI Cep

The H [FORMULA] and H [FORMULA] profiles of DI Cep are P-Cygni profiles, and it is in the absorption feature of the P-Cygni profiles where the relative variance peaks. The velocity of the P-Cygni components is about -200 to [FORMULA] in both lines. However, these weak components cannot be the source of the very high emission line correlation. There is, however, a second peak of the relative variance in the emission lines at [FORMULA] in H [FORMULA], [FORMULA] in H [FORMULA], and [FORMULA] in He I - surprisingly, the line with the lowest excitation energy shows the highest velocity. These components in the Balmer lines may be the same as the weaker peak variance components in DR Tau (H [FORMULA] at [FORMULA] and H [FORMULA] at [FORMULA]). Since all three lines are highly correlated (0.75 for H [FORMULA] and H [FORMULA] and 0.73 for H [FORMULA] and He I)) it seems very likely that these variance peaks are the source of the correlations in the end.

5.5. Line-flux ratios

The flux ratios of the emission lines and the height of the Balmer-jump (the spectra do not show any Paschen jump) are important diagnostic tools. For example, the emission process can be investigated from the line flux ratios of H [FORMULA] /H [FORMULA], H [FORMULA] /H [FORMULA], and H [FORMULA] /H [FORMULA]. Since the emission lines H9 and P9 (and similarly H10 and P10, H11 and P11, H12 and P12, H14 and P14) arise from the same upper levels, their line ratios can be used to derive the amount of extinction. The optical depth and temperature of an emitting region can be derived from the height of the Balmer-jump and the slope of the Paschen-continuum. We thus present in Table 6 the measured flux-ratios (for the spectra with the minimum and the maximum veiling, see below) and the measured height of the Balmer-jump, but will leave their interpretation to a follow-up paper in which we construct detailed models for the emission regions (Guenther & Hessman 1996).


Table 5. Emission line and continuum flux ratios1

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998