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Astron. Astrophys. 322, 511-522 (1997)

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6. Doppler imaging of IN Comae

6.1. The line-profile inversion technique

All maps in this paper were generated with the Doppler-imaging code of Rice et al. (1989) called TEMPMAP. We chose a maximum-entropy regularization for the line profile inversion. A grid of model atmospheres with temperatures between [FORMULA] = 3500 and 5750 K in steps of 250 K and fixed [FORMULA] were taken from the ATLAS-9 CD (Kurucz 1993). For each model atmosphere local line profiles are computed under the assumption of solar abundances and a microturbulence of 2 km s-1. Gray (1988) gives typical radial-tangential macroturbulence velocities of 4.0 and 6.7 km s-1 for a subgiant/giant, with [FORMULA] mag. We adopted 5.0 km s-1 for the line profile inversions.

We can make use of three relatively unblended spectral regions around the main mapping lines Ca I 6439.075, Fe I 6411.647 and Fe I 6393.602 Å . Their transition probabilities ([FORMULA] values) and lower excitation potentials ([FORMULA]) are listed in Table 2 along with the values for other, much weaker, lines within an approximately [FORMULA] 2Å region from the mapping-line center. The [FORMULA] values were obtained by fitting synthetic spectra to observed spectra of the Sun, [FORMULA]  CrB, and Arcturus (see, e.g., Strassmeier 1996b).


[TABLE]

Table 2. The spectral lines for Doppler imaging


Our mapping code uses many lines simultaneously, including blends, but can handle only one spectral region at a time. Also, two continuum bandpasses (usually V and I or V and R) are used as additional constraint but with less weight, and are solved for simultaneously with the line profiles. This allows us to fit the shapes of the light and color curves but not their zeropoints. Furthermore, note that we deconvolve the observed spectrum from the instrumental profile before the profile inversion (for more details see Piskunov & Rice 1993).

6.2. Summary of fixed input parameters

Table 3 lists the adopted stellar parameters for mapping IN Comae. An extensive parameter study is presented in Sect. 7 and the values in Table 3 represent the best compromise from this study.


[TABLE]

Table 3. Stellar parameters for IN Comae


A precise value for [FORMULA] was obtained from an iterative process of minimizing symmetric bright and dark-band structure at or close to the stellar latitude of the sub-earth line. We found the most consistent value from all three spectral lines to be [FORMULA] km s-1 (but see also Sect. 7).

The adopted value of [FORMULA] was obtained by selecting, from within the range of literature values for [FORMULA], a value that maintained in the maps a reasonable maximum surface temperature, and was still consistent with the broad-band colors of the star. Bell & Gustafsson (1989) list for [FORMULA]  CrB a [FORMULA] of 3.1, Gray (1988) gives 3.0, the tables in Lang (1992) cite 2.5 (each for a G5III star), and Donati et al. (1995) found 2.5 [FORMULA] 0.2 for the G8III-IV RS CVn binary [FORMULA]  And. Generally, a higher [FORMULA] atmosphere results in a higher reconstructed average surface temperature until the misfit in the line wings starts to dominate the inversion and symmetric artifacts appear (see discussion in Sect.  7).

From the entire photometry discussed in Sect. 3 we extracted the data obtained between JD 2,449,390 and 2,449,455 ([FORMULA] days). These 57 [FORMULA] points are used in the line-profile inversion.

6.3. Doppler images for March 1994

The map in Fig. 5 represents the average map from altogether six maps from three spectral regions and two continuum bandpasses. The averaging process strengthens surface features that are seen in all maps while simultaneously suppressing features that are not repeatedly recovered. Of course, such an average map is not a true maximum-entropy map but it allows a simple evaluation of the standard deviations of the individual maps per surface pixel. The maps from all three spectral regions are shown in Fig. 6 and are proper individual maps where overfitting the data has been constrained by a maximum-entropy penalty function. Fig. 6 also shows the line profiles and their respective fits from the Doppler-imaging inversion. The fits to the photometry are almost perfect and are not shown here.

[FIGURE] Fig. 5. Average Doppler image of IN Comae with the 5.9-day period. The map is the unweighted average from three spectral lines and two photometric bandpasses.
[FIGURE] Fig. 6a-f. Doppler maps (left column) and the respective line profiles of IN Comae (right column), plusses are the observations and the lines are the fits. Shown are maps in pseudo mercator projection obtained from (top to bottom): Ca I 6439 Å , Fe I 6393 Å and Fe I 6411 Å (only the maps with VI photometry are shown). From top to bottom the maps may represent a crude height distribution in the stellar photosphere based on their equivalent widths (250 mÅ , 225 mÅ , and 190 mÅ , respectively). Notice that the map from the weakest line shows the higher latitude spots.

While the map from Fe I 6411 reveals a weak polar spot the Fe I 6393 and Ca I 6439 maps do not. The Fe I 6393 map shows a high-latitude feature at around [FORMULA] and at a longitude of [FORMULA]. This feature is probably seen as an appendage of the polar spot in the Fe I 6411 map but is absent in the map from the stronger Ca line. This is not expected because, if the cores of the strong lines were filled in by chromospheric emission, then the opposite effect should be seen, i.e. the stronger lines would produce the more pronounced polar feature. The Fe I -6411 line is the weakest of our mapping lines ([FORMULA]  mÅ) and its line core should thus be formed deeper down in the atmosphere where the temperature difference between spot and surrounding photosphere should be larger according to solar spot models (e.g. Stix 1989). We performed a series of simulations on the Fe I 6411 line with an artificial input map. All parameters were kept at the values used for IN Comae. These simulations show that, with a misplaced continuum of 0.003, one can get a temperature gradient toward the visible polar region but not a polar spot and, that in both the simulations and the actual data such a misfit in the continuum is quite noticeable. Further, the fit to the observed Fe I 6411 profiles is significantly worse when the continuum is moved from where it was originally placed. Therefore, we tentatively propose that the maps in Fig. 6 show a real height dependence in the stellar photosphere.

Notice that an unknown cause had deteriorated the Fe I 6411 profile at phase 0.150 (Fig. 6, Fe I 6411 panel). Since we did not see any obvious problem with the other lines at that phase we decided to keep the 0.150 Fe I 6411 profile for the final inversion. Test runs without the 0.150 profile did not alter the map at all.

A distinct cool feature is also seen at a longitude of [FORMULA] in all three maps. Once again, it appears significantly shifted towards a latitude of [FORMULA] in the Fe I 6411 map as compared to [FORMULA] in the other two maps. Unfortunately, our phase coverage is such that most of the surface detail at this longitude mostly relies on the one line profile at phase 0.842 and the spots' latitude is thus not well constrained. This might also be the reason for the appearance of a bright feature at around [FORMULA] in the Ca map and in the iron-6393 map. Table 4 compares the areal coverages of the cool regions in the three maps.


[TABLE]

Table 4. Areal coverages within certain temperature intervals in units of the entire stellar surface


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© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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