Astron. Astrophys. 347, 212-224 (1999)

5. Discussion of the individual maps

5.1. Doppler image for April 1997

Fig. 3 presents the results from the April 6-16, 1997 data set. Eleven spectra were available along with 31 VI-band light curve points. The combined sum of the squared residuals from the fit to the line profiles and the photometry was 0.0152 for the final solution.

Fig. 3. Doppler image of HD 199178 for the observing epoch April 1997. The map in the top panel is shown in a pseudo mercator projection and plots temperature as a grey scale. Zero longitude corresponds to rotational phase zero and is increasing from left to right. The middle panels show the observed (plusses) and computed (line) line profiles, and the lower panels show the absolute photometry in two bandpasses (V and I) and their respective fits.

The map is dominated by a large and very cool polar spot. It appears asymmetric in shape as well as in its temperature distribution and is the main cause of the light curve minimum at phase zero. The average polar temperature is 3750100 K (rms), and thus 1700 K below the unspotted photosphere. Five appendages of the polar spot are seen in the map. We name these features with longitudes, , of ^o, 77^o, 140^o, 225^o and 300^o, respectively (Table 4). and are of lesser contrast than , , and ; having a temperature difference of 1000 K. Several low-latitude spots are also recovered but with comparably even lower contrast. It is possible that the weaker of these features are spurious and were introduced by the external uncertainties of our spectra.

Table 4. Longitudinal positions and temperatures of the individual polar appendages

Another noteworthy structure in the map in Fig. 3 is the group of spots gathered within a longitude of 225-360^o. Its four main features are clearly seen as pseudo emission bumps in the line profiles at phase 0.754 and partially also at 0.659 (Fig. 3). The four bumps with amplitudes of 2-3% of the continuum force the code to apply very steep temperature gradients that appear in the map as the adjacent bright and dark features near 270^o. Despite that the maximum bump amplitudes at this particular phase are nicely fitted with our spot model, the time resolution of our spectra cannot exclude a single, time-variable phenomenon like a local flare-like event.

5.2. Doppler image for May 1990

Fig. 4 ("map-1990") displays the map, the observed and computed line profiles as well as the observed and computed BV-light curve for May 1990. The combined sum of the squared residuals from the line profiles and the photometry was 0.00206 for the final map.

Fig. 4. Doppler images of HD 199178 for the four observing epochs 1990 (May), 1989b (May-June), 1989a (April), and 1988 (August). Otherwise as in Fig. 3. All maps were obtained from Ca I 6439 Å and Johnson B (4340 Å) and V (5500 Å) photometry.

Fig. 4. (continued).

Only five line profiles and 22 BV-data points were available, and such a poor phase coverage will introduce some spurious surface features. Especially suspicious would be those that have low contrast and do not show up in the maps from other lines and are located at very low or even negative latitudes or have a sinusoidal shape across large parts of the image. However, the calcium and iron fits (not shown) have similar and the maps agree very well. The only significant difference perhaps is that the small features in the Ca map with  K below are always slightly cooler in the Fe map where some of them appear with  K. The reason for this lies most likely with the different temperature sensitivities of the two lines and possibly also with the uncertain values, resulting in artificially stronger or weaker mapping lines and thus requiring slightly warmer or cooler spots to fit the profiles equally well.

In 1990, HD 199178 had again a large cap-like polar spot similar to that seen in 1997. We detect two large appendages ( and ) at 17^o and 320^o, and three weaker appendages () at 77^o, 140^o and 240^o (see Table 4). These are basically the same locations as for the five appendages recovered in the April-1997 map seven years later. Besides, six "equatorial" spots were reconstructed at longitudes of approximately 50^o, 105^o, 138^o, 175^o, 263^o and 330^o (called spots in Table 5). The dominating feature at ^o has a temperature difference of 1200 K, similar to the polar spot, while the others appear with  K. The combined effect of the large equatorial spot and the polar appendage at 17^o is the cause for the light-curve amplitude of 0:m 05 in V at phase 0:p20 (i.e. 70^o). The APT photometry in Fig. 4 shows the light curve minimum exactly at that phase as well as a broad maximum near 0:p550:p05, and is well matched by the fit from the Doppler image.

Table 5. Positions and temperatures of lower-latitude spots or spot groups

5.3. Doppler image for May-June 1989

Seven observations of the Ca I 6439-Å line were obtained between May 25 and June 13, 1989. The map, the line profiles, and the photometry is again shown in Fig. 4 (labeled "map-1989b"). The combined sum of the squared residuals from the line profiles and the photometry was 0.0152 for the final solution.

As in the previous maps, we find a big asymmetric polar spot. The three coolest polar-spot appendages are now , , and , and appear near 180^o, 235^o, and 330^o, respectively. The other appendages, and , are still visible at 30^o and 107^o, respectively, but appear weaker. Both maps, from 1990 and 1989b, indicate a possible connection of with the moderate-latitude spot at 65^o and 30-40^o. The average spot temperature of 1300 K below the photospheric temperature is in reasonable agreement with the 1500 K obtained by O'Neal et al. (1996) from TiO-band observations in October 1989. The May-June 1989 map also recovers several low-to-moderate latitude spots or spot groups but with comparably lesser contrast (Table 5) and thus higher uncertainty. It is possible though that these spot groups evolved into the spots recovered in 1990, despite that many of these features are uncertain due to the less-than-perfect phase coverage.

5.4. Doppler image for April 1989

Six observations of the Ca I 6439-Å region were made between April 10 and May 2, 1989. The Doppler image is shown in Fig. 4 (labeled "map-1989a"). The combined sum of the squared residuals from the line profiles and the photometry was 0.00375 for the final map. This map is particularly interesting because it is only one month apart from the previously discussed May-June 1989 map. The effects of time-variable phenomena are thus minimized and a direct comparison allows us to detect short-term evolution of particular surface structures. For example, one of the large polar-appendages () from May-June was either not yet formed one month earlier or significantly smaller, weaker, and sligthly shifted in longitude. The polar cap is still dominating the reconstructed spot distribution, but the now largest and coolest appendage might be a combined and feature with respect to the previous month. The phase coverage at this particular longitude is good and there is no obvious reason for a significant artifact in this surface region. Appendage and the high-latitude spot at ^o and ^o are merged as compared to May-June where they still appear separated. The phase gap from 0:p0-0:p2 causes the reconstruction algorithm to shift more weight to the photometry at these longitudes and thus explains some inconsistencies between the two 1989 maps. The reidentification of the equatorial spots remains ambiguous because of the large amount of surface detail.

5.5. Partial Doppler image for August 1988

Only four line profiles were available for epoch August 3-10, 1988 and are, together with BV photometry from August through September, used for a partial Doppler image (Fig. 4, labeled "map-1988"). The combined sum of the squared residuals from the line profiles and the photometry was 0.00342 for the final map.

This partial image shows again a polar spot very similar to the one discussed in the previous sections. It has four appendages at longitudes of 65^o, 240^o, 275^o, and possibly at 330^o that could be identified as and from the April-1989 map. At this point the reader should be reminded again that the interpretation of spatial information from a few line profiles is somewhat ambiguous because we can just estimate possible external errors, and other cross-identifications could be equally likely. This is especially true for the low-latitude features because their longitudes are more prone to a coarse phase coverage than the polar features. Intercomparison of maps from different years introduces yet additional uncertainty due to differences in the adopted rotation periods as well as due to intrinsic spot variations.

Nevertheless, our code reconstructed five low-to-mode- rate latitude spots or spot groups at longitudes of 17^o, 125^o, 220^o, 250^o, and 320^o. These features are severely distorted due to the poor phase coverage but are required by the line-profile data, as can be seen from the quality of the fit, but also by the photometry to explain the broad and asymmetric minimum. The apparently most significant low-latitude spot is the one at 130^o whose position, however, falls within the large spectroscopic phase gap; its contrast and latitude are thus most uncertain and should be viewed with caution. A feature at ^o and at a latitude between 30-60^o appears significant but it is not clear whether it is a polar appendage or an isolated spot at medium latitude. Table 5 lists it as an "equatorial" feature.

© European Southern Observatory (ESO) 1999

Online publication: June 18, 1999
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