Astron. Astrophys. 319, 535-546 (1997)

4. Doppler imaging

4.1. The line-profile inversion code

As for previous papers in this series, all maps were generated with the Doppler-imaging code of Rice et al. (1989), originally developed for use with chemical abundance inhomogeneities of Ap stars. For temperature mapping we use a more rigorous treatment of the local line profile than presented in Rice et al. (1989) and also solve for the relative continuum light in two photometric bandpasses (Rice 1994, Piskunov & Rice 1993). Local line profiles are now computed with the same opacities as in the ATLAS-9 code (Kurucz 1993).

In this paper we chose a Maximum-Entropy regularization although the program also allows a Tikhonov reconstruction. A grid of nine model atmospheres with temperatures between = 3500 and 5500 K in steps of 250 K and were taken from the ATLAS-9 CDs (Kurucz 1993). We found that fits the wings of the line profiles also very nicely but the entire profile fits seem to be overally better when using a atmosphere and we adopted this gravity for the final maps.

For each model atmosphere local line profiles were computed with the abundances determined in Sect. 3.6 but also included trial inversions with strictly solar abundances for all elements that, however, did not result in equally good fits and were rejected. The late spectral type of IN Virginis, combined with the limited wavelength coverage of our spectra, is such that we can make use of only three moderately unblended lines; Ca I 6439.075, Fe I 6430.852, and Fe I 6421.360 Å with values of , -1.85, and -2.20 and lower excitation potentials of 2.52 eV, 2.18 eV, and 2.28 eV, respectively. The upper panel in Fig. 5 indicates the amount of blending for each of the three mapping lines and we actually synthesize a total of 9, 12, and 6 blends for the 6439, 6430, and 6421-line region, respectively. We emphasize that all of these blends are included in the inversion simultaneously but that the three wavelength regions are treated separately.

Other lines with comparable profile deformations were the Fe I lines at 6393.602, 6400.000 and 6400.314, 6408.016 and 6411.647 Å. Unfortunately, all of these lines are heavily blended with up to even 20 weak lines that, more importantly, do not show up at solar temperature and have rather uncertain transition probabilities. Therefore, we chose not to use these lines for mapping.

4.2. Results

The combined map from three spectral lines and three photometric bandpasses is shown in Fig. 6. The observed and computed line profiles are plotted in Fig. 7 along with the individual Doppler maps, the observed and computed light curves are compared in Fig. 8. We emphasize that our maps are based on ten spectra taken on 13 consecutive nights in March 1994, i.e. within one and a half stellar rotations (see Table 1).

Fig. 6. Combined Doppler image of IN Virginis for the observing epoch March 1994. This map is a combination of six maps derived from three spectral lines, Ca I 6439 Å , Fe I 6430 Å , and Fe I 6421 Å ; each one with both the VR and the VI light curves as additional constraints. All individual maps were given equal weight for the average map.

Fig. 7a-f. Observed and computed line profiles for Ca I 6439.075 Å (panel a), Fe I 6430.852 Å (panel b) and Fe I 6421.360 Å (panel c). The plusses are the observations and the full lines are the fits. The right column shows the maps from the individual lines in a pseudo-mercator projection. Note that the spectral lines are arranged from top to bottom according to decreasing equivalent width of the main mapping line and thus approximate their depth of formation.

Fig. 8. Observed and computed VRI light curves. The fits are from Ca I 6439 Å (full line), Fe I 6430 Å (dotted line) and Fe I 6421 Å (dashed line). The plusses are the simultaneous and contemporaneous APT observations included in Fig. 2b. The arrows indicate the phases of the spectroscopic observations.

The "bumps" in the absorption line profiles of IN Vir are easily detectable despite the relatively small of the star. The strongest bump reaches an amplitude of about 5% of the continuum when measured in the line center and is thus comparable with the bumps seen in other, broader-lined, active stars, e.g. in the RS CVn system UZ Librae (Strassmeier 1996= paper I) or in the weak-lined T Tauri star V410 Tau (Rice & Strassmeier 1996= paper II) and others. Visual inspection of the observed line profiles reveal two bumps crossing the central stellar meridian at phases of around 0.25-0.30 and 0.60, respectively.

The map in Fig. 6 is dominated by a polar spot and an appendage (or high-latitude spot) with a temperature difference of 800-1000 K cooler than the photospheric temperature of 4600 K and centered at a longitude of around . A second appendage of smaller contrast is present at a longitude of around . Furthermore, we see some detailed structure along the stellar equator, however, not all of it is likely real. Features at the stellar equator can appear somewhat elongated in latitudinal direction when only a too coarse a grid of line profiles is available, and is an artifact. Our phase coverage is quite good though and is shown for comparison in the light curves in Fig. 8. Very small and/or very weak equatorial features that do not appear in the maps from all three lines are judged to be spurious and are automatically suppressed in the combined map although their inclusion leads to a better fit of a particular line profile.

Despite the known elongation and resolution problem for low-latitude features we may still identify three consistently cool spots at longitudes of , and and at latitudes within of the equator (Table 5). Additionally, there appear three areas with temperatures above the photospheric temperature, but the only one judged significant is at a longitude of and a latitude of with 150 K above the photospheric temperature. The line profiles at that particular phase show no evidence for systematic errors like, e.g., continuum displacement. This warm spot shows up with high enough contrast in all three maps and should be considered real. The other two areas are just between 50-100 K warmer than the photosphere and are within the estimated external uncertainties of our spectra. In two previous images of the weak T Tauri star V410 Tau (paper II and Strassmeier et al. 1994), we have found several hot spots with 500 K from the photospheric absorption spectrum and suggested that they are caused by mass accretion from left-over circumstellar material. Their spectral signature, however, were much more pronounced compared to the warm areas on IN Vir.

Table 5. Detected surface features¹

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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