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Astron. Astrophys. 355, 308-314 (2000)

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3. Effective temperatures and surface gravities

For surface temperature and surface gravity determinations, 17 mCP stars, with fluxes consistent with the Hayes & Latham (1975) calibration of Vega mainly from the catalogs of Breger (1976) and Adelman et al. (1989) were studied. The fluxes longward of H[FORMULA] were given lower weights than other values due to the senior author's previous difficulties in obtaining simultaneous fits to them and other spectrophotometric values. For this investigation the spectrophotometry for each star was selected to be the mean fluxes to represent the average star.

H[FORMULA] profiles came from 20 Å mm-1 spectrograms obtained with either Reticon or CCD detectors at the Dominion Astrophysical Observatory (DAO). The stellar exposures were flat fielded with the exposures of an incandescent lamp placed in the Coudé mirror train as viewed through a filter to eliminate first order light. A central stop removed light from the beam in the same manner as the secondary mirror of the telescope. The spectra were rectified using the interactive computer graphics program REDUCE (Hill et al. 1982) after which a 3.5% scattered light correction (Gulliver et al. 1996) was applied. As Balmer line profile variability has not been demonstrated to be significant in most mCP stars, we assumed that the observed H[FORMULA] profile is typical of each star.

Kurucz's ATLAS9 (1993) code calculates fully line blanketed NLTE plane parallel model atmospheres. From converged model atmospheres, one can calculate the fluxes using ATLAS9 and the H[FORMULA] region using the synthetic spectrum code SYNTHE (Kurucz & Avrett 1981). For comparison with observations the synthesized spectra were convolved with the measured stellar rotational velocity of the star and the instrumental profile of the short camera of the coudé spectrograph of the DAO 1.22-m telescope. Trends in recent elemental abundance studies indicate for normal main sequence band stars with [FORMULA] 10500 K that their microturbulence is 0 km s-1, for those with [FORMULA] between 10500 and 9500 K 1 km s-1, and for those with [FORMULA] 9500 K 2 km s-1 (Adelman 1998 and references therein).

For initial temperature and surface gravity estimates, the homogeneous uvby[FORMULA] values of Hauck & Mermilliod (1980) were used whenever possible with the program of Napiwotzki et al. (1993) based on the work of Moon & Dworetsky (1985). Using solar composition models, we compared fluxes and H[FORMULA] observations with predictions. Some of the best fits were fine while others were abysmal. Then we used models with greater than solar metallicity to fit the continuum especially the [FORMULA]5200 feature and adjusted the microturbulence as necessary. In matching the observed and predicted H[FORMULA] regions we tried to also have similar levels of metal line blanketing which was not always possible.

Table 1 shows effective temperatures and surface gravities. The photometric values are not rounded. The stars are listed in approximately decreasing effective temperature order. When the line blanketing for H[FORMULA] became large and locating the continuum became difficult, then relatively metal line free regions in the line profile were used as fitting guides. Fig. 2 shows the H[FORMULA] profile of 10 Aql, which is an example of a cooler mCP stars. In hotter stars the metal lines become weaker and the H[FORMULA] profile becomes stronger and dominates. For good matches, the synthetic spectra of both the H[FORMULA] and metal lines lie essentially on top of such profiles and cannot be distinguished at the usual figure resolution. No corrections were made for reddening as these stars should be sufficiently nearby for such corrections to be minimal. In Paper 1 HR 8216 was found to have [FORMULA] = 8400 K, log g = 3.20, log Z = +0.5, [FORMULA] = 2 km s-1, values close to those of this paper while for [FORMULA] Equ [FORMULA] = 7700 K, log g = 4.20, log Z = +0.5, [FORMULA] = 2 km s-1. Its temperature is 300 K cooler than adopted here. The later comparison indicates the difficulties in fitting H[FORMULA] profiles in heavily line blanketed stars.

[FIGURE] Fig. 2. The observed H[FORMULA] profile of 10 Aql, which is an example of the heavily metal line blanketed profiles seen in the cooler mCP stars. Near [FORMULA]4311, [FORMULA]4322, [FORMULA]4329, and [FORMULA]4379 are less line blanketed regions of the profile which act as fitting guides in matching observed and synthetic spectra. The H[FORMULA] profile was extracted from DAO spectrogram W48955557.


[TABLE]

Table 1. Effective temperature and surface gravities of magnetic CP stars
Footnotes:
* = Poor Fit, + Fair Fit, = synthetic H[FORMULA] profile metal lines too strong, ` H[FORMULA] profile lines fine, but the [FORMULA]5200 feature not fit,
@ convection calculated via mixing length theory, ! convection calculated according to Canuto \& Mazzitelli (1991, 1992)


In Fig. 3 we illustrate some of the fits for the spectrophotometry. That for 56 Ari is similar to that for CU Vir. HR 5597 is reasonably well fit. But for HR 6958 as for 17 Com A, the fit is for the Lyman continuum and the Balmer continuum from about H[FORMULA] through most of the [FORMULA]5200 feature. Beyond the longward part of the [FORMULA]5200 feature, the star is systematically brighter than the model. The [FORMULA]4000-4300 region in the star is presumably more heavily line blanketed than the model. For [FORMULA] Ser fits for enhanced metallicity models are given for both matching the [FORMULA]5200 feature and the H[FORMULA] profile line strengths. To fit satisfy both criterion will require the use of non-solar scaled odfs. The resulting temperatures and surface gravities will likely lie between the solar cases and the enhanced metallicity values. For the hottest mCP stars, the photometric effective temperature estimates are greater than those from spectrophotometry. But near 9500 K the agreement is much better and this trend continues for stars as cool as 8500 K.

[FIGURE] Fig. 3. Observed energy distributions of four magnetic CP stars compared with the predictions of ATLAS9 model atmospheres. For 56 Ari the fluxes of a [FORMULA] = 12850 K, log g = 4.00, log Z = +0.5, [FORMULA] = 2 km s-1 model are shown, for HR 5597 of a [FORMULA] = 11000 K, log g = 3.90, log Z = +1.0, [FORMULA] = 8 km s-1 model, for HR 6958 of a [FORMULA] = 10750 K, log g = 3.50, log Z = +1.5, [FORMULA] = 8 km s-1 model, and for [FORMULA] Equ of a [FORMULA] = 8000 K, log g = 4.50, log Z = +0.5, [FORMULA] = 4 km s-1 model.

Cooler than this value the efficiency of the convection may come into play. Smalley & Kupka (1997) argued that the turbulent convection theory of Canuto & Mazzitelli (1991, 1992) should be more realistic than mixing-length theory (Castelli et al. 1997). Adelman et al. (2000) found the coolest effective temperatures for which solar composition models utilizing both theories predict the same flux distribution and H[FORMULA] profile. The values are 7725 K for log g =3.00, 7850 K for log g = 3.25, 8000 K for log g = 3.50, 8150 K for log g = 3.75, 8300 K for log g = 4.00, and 8475 K for log g = 4.25. As [FORMULA] CrB has values close to this line of demarcation and both [FORMULA] Equ and 10 Aql are cooler, we found effective temperatures and surface gravities for these three stars using both mixing length and Canuto & Mazzitelli theory.

As convection should not occur in the presence of sufficiently strong magnetic fields, in some cooler mCP stars the efficiency of the convection acting in their photospheres might be less than that for normal stars with similar effective temperatures and surface gravities. If this occurs, then mixing length theory, which corresponds to less efficient convection than that of Canuto & Mazzitelli, may be a better representation of convection in these stars. For the 3 coolest mCP stars studied, the differences between the results for both convection theories is not too large. The temperatures found via mainly the H[FORMULA] profiles tend to be slightly larger than those found from uvby[FORMULA] photometry. The surface gravity determinations which come from the fluxes increase with metallicity. Fig. 4 shows the difference in effective temperature [FORMULA] between the photometric (T(uvby[FORMULA])) and spectrophotometric (T(sp))temperatures for the mCP stars as a function of T(uvby[FORMULA]). The least squares fit is

[EQUATION]

Alternatively

[EQUATION]

In addition there is on the average a 0.09 dex decrease in log g from the photometric values for the spectrophotometric-H[FORMULA] determination.

[FIGURE] Fig. 4. For the mCP stars the difference between the effective temperature determined from photometry and that from spectrophotometry and the H[FORMULA] profile is plotted as a function of the former temperature. The tendency for the difference to increase with temperature is seen although it is probably more complex than the simple regression we adopted.

If we compare the temperatures (T[c1]) fitted by Napitowski et al. (1993) for the hotter mCP stars based on [c1] (see Table 1), then better agreement results. For these stars on average

[EQUATION]

compared with

[EQUATION]

and

[EQUATION]

This indicates that in the T([c1]) values some of the effects due to the greater line blanketing and the broad, continuum features are included.

If the strength of the [FORMULA]5200 feature is in part related to that of the integrated magnetic field as we have suggested, then a photometric measure of its strength such as that of [FORMULA]a (Maitzen 1976) would possibly be useful in defining a photometrically determined temperature. Around the mean systematic offset in temperature between the photometric and the spectrophotometric and H[FORMULA] profile values there is some scatter which plausibly is due to a range in magnetic field strengths and configurations. A likely origin of the mean trend is the increasing tendency of the photospheric composition to become more metal-rich and non-solar with increasing effective temperature. If this suggestion is valid, then a similar effect might be seen in the Mercury-Manganese stars.

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Online publication: March 17, 2000
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