A&A 392, 1031-1037 (2002)
DOI: 10.1051/0004-6361:20020889

On the effective temperatures and surface gravities of superficially normal main sequence band B and A stars

Saul J. Adelman1,2 - O. I. Pintado3,4 - F. Nieva3 - K. E. Rayle1 - S. E. Sanders, Jr.1


1 - Department of Physics, The Citadel, 171 Moultrie Street, Charleston, SC 29409, USA
2 - Guest Investigator, Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council of Canada, 5071 W. Saanich Road, Victoria V9E 2E7 Canada
3 - Departamento de Fisica, Facultad de Ciencias Exactas y Tecnologia, Universidad Nacional de Tucumán,
Av. Independencia 1800, 4000 San Miguel de Tucumán, Argentina
4 - Member of the Carrera del Investigador Científico, CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina

Received 26 February 2002 / Accepted 12 June 2002

Abstract
Effective temperatures and surface gravities for 48 main sequence band B and A stars were found by matching optical region spectrophotometry and H$\gamma $ profiles with the predictions of ATLAS9 solar composition model atmospheres. When these values were compared with those found using Strömgren uvby$\beta $ photometry based on ATLAS6 model atmospheres, we found a difference (photometry-spectrophotometry) of $25\pm 118$ K for 29 stars with 8000 K $\le$ $T_{\rm eff}$ $\le$ 10 050 K compared to 76 $\pm$ 105 K for 14 stars with 10 050 K $\le$ $T_{\rm eff}$ $\le$ 17 000 K. The surface gravity scales are in agreement. These stars are sufficiently hot that their effective temperatures and surface gravity determinations are unaffected by discrepancies due to the choice of Mixing-Length or Canuto-Mazzitelli convection theories.

Key words: stars: fundamental parameters - stars: early-type


1 Introduction

Astronomers can determine the effective temperatures and surface gravities of single main sequence band B and A stars by matching their optical region flux distributions as measured spectrophotometrically and their observed H$\gamma $ profiles with the predictions of the best model atmospheres. When these observations are not available, investigators have used photometric indices calibrated by this method, e.g. for Strömgren uvby$\beta $ photometry the work of Moon & Dworetsky (1985), which has been updated by Napiwotzki et al. (1993). The errors are of order $\pm$200 K and $\pm$0.2 dex in the middle B to early F star regime (Lemke 1989) (see Ribas et al. 1997 concerning which values are better). Our current ability to calculate physically realistic model atmospheres is the greatest in this region of the HR Diagram. These calibrations are based mainly on model atmospheres used prior to 1992. In the optical region, there can be small differences in the predicted fluxes between ATLAS9 (Kurucz 1993) and the older ATLAS6 (Kurucz 1979) models due in part to an improved treatment of line blanketing and to the use of opacity distribution functions with different microturbulences. This paper to a large extent investigates the effects of these differences.

In determining stellar effective temperatures and surface gravities, two basic concerns are the agreement of the predictions of the models with the observations as this is what many abundance workers use to select appropriate models and whether these results show systematic errors when one uses flux observations covering a much wider range of wavelengths. In this paper we are concerned mainly with the former. One can obtain infrared and perhaps ultraviolet fluxes and use the results of this study as a basis for determining effective temperatures via the infrared flux method. But for single and binary stars with sufficiently faint companions if there are no systematic errors in the model fluxes, our approach should yield as good results without the complications of additional sources of error.

The ATLAS9 code produces fully line blanketed LTE plane parallel model atmospheres. From converged model atmospheres, one can calculate the fluxes using ATLAS9 and the H$\gamma $ 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 and the instrumental profile of the short camera of the coudé spectrograph of the Dominion Astrophysical Observatory (DAO) 1.22-m telescope. Trends in recent elemental abundance studies indicate for main sequence band stars with temperatures greater than 10 250 K their microturbulence is 0 km s-1, for those with temperatures between 10 250 and 9500 K 1 km s-1, and for those with temperatures less than 9500 K 2 km s-1 (Adelman 1999). In this investigation, grids of ATLAS9 models with effective temperature and surface gravity spacings of 500 K and 0.25 dex, respectively, were employed. Additional models were calculated to confirm the interpolated values. In general the greater the number of spectrophotometric flux values, the better the resultant temperature determination.

2 Observational data

To assess the discrepancies of the effective temperatures and surface gravities found with the algorithm of Napiwotzki et al. (1993) and those found by comparison of fluxes and H$\gamma $ profiles with ATLAS9 model predictions, 48 stars with fluxes based on the Hayes-Latham (1975) calibration of Vega mainly from the catalogs of Breger (1976) and Adelman et al. (1989) were studied. The homogeneous uvby$\beta $ values of Hauck & Mermilliod (1980) were employed. The H$\gamma $ profiles were extracted from 20 Å mm-1 spectrograms obtained with either Reticon or CCD detectors at the Dominion Astrophysical Observatory (DAO) and had a resolution of 0.6 Å  (2 pixels). The exposures were flat fielded with those 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 with the interactive computer graphics program REDUCE (Hill et al. 1982). A 3.5% correction (Gulliver et al. 1996) was applied for scattered light along the dispersion direction.

The normalization of the H$\gamma $ observations is not without problems. The continuum can be difficult to locate for late A and cooler stars and while the sensitivity of the spectrograph at the DAO changes over the 200 Å interval centered on this Balmer line due to the high reflective coatings used in the Coudé mirror train. In retrospect one might be able to improve somewhat the normalization by the use of all of the observations from a single night, especially if observations were made of a range of spectral types, rather than processing each spectrum independently. This would necessitate some changes in reduction software. Alternatively if such data becomes available one might be able to use spectrophotometry having continuous wavelength coverage and a resolution of a few Å to help the normalization process.

 
Table 1: Effective temperature and surface gravity determinations.
Star HD uvby$\beta $   spectro. + H$\gamma $   spectro. reddening
Name number $T_{\rm eff}$ log g $T_{\rm eff}$ log g [m/H] source E(b-y)
$\tau$ Vir 122 408 8085 3.84 8150 3.75 0.0 APW 0.00
95 Leo 103 578 8331 4.14 8300 3.65 0.0 APW 0.01
$\delta$ Her 154 494 8361 3.95 8500 4.00 0.0 DP 0.01
HR 6410 156 164 8615 3.70 8500 4.00 0.0 APW 0.00
$\delta$ UMa 106 591 8664 3.87 8650 4.10 0.0 AP 0.00
$\lambda$ Boo 125 162 8925 4.11 8750 4.00 0.0 OKE 0.02
        8700 4.15 -1.5    
$\delta$ Aqr 216 677 8657 3.56 8750 3.50 0.0 MOR 0.00
68 Tau 27 962 9025 3.95 9000 4.00 0.0 LL 0.00
        8900 4.00 0.2    
$\lambda$ UMa 89 021 8790 3.75 9000 3.75 0.0 SPO 0.00
        9000 3.75 0.2    
$\theta$ And 1280 8968 3.87 9000 4.00 0.0 APW 0.00
$\gamma $ Oph 161 868 9388 4.09 9100 4.00 0.0 APW 0.02
$\gamma $ Gem 47 105 9277 3.51 9150 3.60 0.0 TAY 0.00
$\epsilon$ Aqr 198 001 9229 3.56 9200 3.50 0.0 SPO 0.00
$\nu $ Tau 25 490 9226 3.93 9250 4.00 0.0 MOR 0.00
$\theta$ Leo 97 633 9289 3.62 9250 3.60 0.0 APW 0.00
27 Lyn 67 006 9320 3.77 9250 3.75 0.0 A 0.01
60 Leo 95 608 9053 4.22 9250 4.25 0.0 BVJ 0.00
        9250 4.25 0.5    
$\gamma $ UMa 103 287 9361 3.79 9350 3.75 0.0 APW 0.00
$\theta$ Vir 114 330 9407* 3.87* 9350 3.50 0.0 SPO 0.00
21 Lyn 58 142 9601 3.74 9425 3.75 0.0 AP 0.00
HR 6127 148 330 9670 4.00 9500 3.80 0.0 AP93 0.01
$\zeta$ Aql 177 724 9542 3.84 9500 3.90 0.0 SPO 0.01
o Peg 214 994 9591 3.64 9525 3.70 0.0 A 0.00
$\gamma $ Lyr 176 437 9674 2.67 9550 2.75 0.0 SPO 0.01
$\beta $ UMa 95 418 9601 3.85 9600 3.80 0.0 AP 0.00
        9600 3.80 0.2    
HR 7086 174 262 9507 4.12 9600 4.20 0.0 APW 0.00
HR 5169 119 763 9639 4.12 9700 4.15 0.0 APW 0.00
$\alpha$ Sex 87 887 9862 3.54 9875 3.55 0.0 MOR 0.01
$\alpha$ Dra 123 299 9975 3.63 10 000 3.50 0.0 A 0.00
$\sigma $ Aqr 213 320 10 188 3.94 10 100 3.85 0.0 A 0.00
29 Vul 196 724 10 397 4.14 10 200 4.00 0.0 WKH 0.00
$\kappa$ Cep 192 907 10 341 3.64 10 250 3.75 0.0 APW 0.00
$\nu $ Cap 193 432 10 311 3.86 10 250 4.00 0.0 A 0.00
21 Peg 209 459 10 375 3.47 10 350 3.55 0.0 AP 0.01
14 Cyg 185 872 10 953 4.11 10 750 3.55 0.0 APW 0.00
134 Tau 38 899 10 928 4.01 10 750 4.10 0.0 A 0.00
5 Aqr 198 667 11 288 3.37 11 125 3.55 0.0 A 0.01
$\beta $ Lib 135 742 12 036 3.26 12 125 3.50 0.0 KUB 0.01
21 Aql 179 761 13 029 3.44 13 000 3.60 0.0 A 0.05
$\pi$ Cet 17 081 13 174 3.70 13 100 3.85 0.0 A 0.01
HR 2154 41 692 14 330 3.21 14 500 3.50 0.0 A 0.02
$\tau$ Her 147 394 15 022 3.93 15 000 4.10 0.0 A 0.02
$\epsilon$ Cas 11 415 15 290 3.85 15 125 3.55 0.0 SPO 0.02
$\eta$ Aur 32 630 16 887 4.08 16 375 4.10 0.0 SPO 0.00
$\eta$ UMa 120 315 17 319 4.31 16 900 4.30 0.0 AP 0.00
$\gamma $ Peg 886 21 482 3.92 21 250 4.00 0.0 A 0.00
1 Cas 218 376 27 334 4.10 29 000 4.00 0.0 A 0.17
10 Lac 214 680 32 845 4.61 33 000 4.40 0.0 KUB 0.06

Notes: Breger (1976) converted data from DP, KUB, MOR, OKE, SPO, and WKH to the Hayes & Latham (1975) calibration of Vega. The spectrophotometric sources are: A = Adelman (1978), AP = Adelman & Pyper (1983), AP93 = Adelman & Pyper (1993), APW = Adelman et al. (1980), BVJ = Böhm-Vitense & Johnson (1978), DP = Dickens & Penny (1971), KUB = Kubiak (1973), LL = Lane & Lester (1980), MOR = Gutierrez-Moreno et al. (1968), OKE = Oke (1964), SPO = Schild et al. (1971), TAY = Taylor (1984), and WKH = Wolff et al. (1968). * = estimated with predicted $\beta $ value.


  \begin{figure} \par\includegraphics[width=13cm,clip]{ms1198f1.eps}\end{figure} Figure 1: The spectrophotometric fluxes for $\nu $ Cap (open squares) compared with the predictions of a solar composition $T_{\rm eff} = 10~250$ K, $\log~ g = 4.00$ ATLAS9 model atmosphere with a microturbulence of 0 km s-1 (thin line connecting solid triangles). The axes are inverse microns and the magnitude of the flux in frequency units in ergs cm-2 s-1 Hz-1. The constant was chosen to make the flux at 5000 Å be 0.0 for the observations. The theoretical fluxes were shifted for the best match over as much of the observed wavelength range as possible.
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  \begin{figure} \par\includegraphics[width=16cm,clip]{ms1198f2.eps}\end{figure} Figure 2: The synthesized spectrum of $\gamma $ Peg (thicker line) centered at H$\gamma $ calculated with a solar composition $T_{\rm eff} = 21~250$ K, $\log~ g = 4.00$ ATLAS9 model atmosphere with a microturbulence of 0 km s-1 (thinner line).
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3 B and A star temperatures and surface gravities

As most spectrophotometers capable of determining high quality stellar fluxes in the optical region were retired from service about twenty years ago, the candidate stars for H$\gamma $ observation were those whose values were cataloged and could be observed from the DAO in Victoria. Additional selection criteria were that the spectrophotometric wavelength range must span the Balmer jump and that Strömgren indices derived from the spectrophotometry were in good accord with those values directly observed. The reddening, if any, was deduced using the computer program of Napiwotzki et al. (1993) and is uncertain to $\sim$0.005 mag. If positive and would result in an observable change in the flux distribution, the spectrophotometric values were dereddened using those of Schild (1977). The information content of the spectrophotometric values is greater than that of the photometric values.

  \begin{figure} \par\includegraphics[width=16cm,clip]{ms1198f3.eps}\end{figure} Figure 3: The synthesized spectrum of $\sigma $ Aqr (thicker line) centered at H$\gamma $ calculated with a solar composition $T_{\rm eff} = 10~100$ K, $\log~ g = 3.85$ ATLAS9 model atmosphere with a microturbulence of 1 km s-1 (thinner line).
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In this study we also wanted to avoid studying stars for which uncertainties in convection theory have observable effects on the fluxes and H$\gamma $profiles. 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). Kupka (private communication) supplied the necessary subroutine for Canuto-Mazzitelli convection in ATLAS9. Smalley & Kupka (1997) indicate the discrepancies in effective temperatures and surface gravities between these theories.

As it would be useful to know where these two theories predict observable discrepancies, we found the last stellar models which exhibit minimal differences (less than 1%) in the optical region fluxes and H$\gamma $ profiles as one proceeds towards cooler temperatures. These models had the fine solar abundance opacity distribution function, a microturbulence of 2 km s-1, and 64 depths converged usually to better than 1% in flux and in flux derivative. The convergence properties of the models with Canuto & Mazzitelli convection are often nicer than those for Mixing-Length theory. The synthetic spectra whose resolution is 500 000 were broadened by the instrumental profile of the DAO long camera (Gulliver & Hill 1990). Our comparisons were made by making plots of the H$\gamma $ profiles and flux distributions that utilized most of the dimensions of letter sized pages. Initially we used a grid of models with a 500 K spacing in effective temperature. As the comparisons proceeded we reduced the spacing to find the onset of differences to $\pm$25 K. Thus the coolest models with no significant differences occur at 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 $\log~ g = 4.25$. These boundary values are likely to depend on microturbulence and metallicity, variables not investigated at this time. The stars studied in this paper are on the hot side of this boundary.

Table 1 contains the determinations of the temperatures and surface gravities along with the HD number and another identification, the metallicities (with $[m/\rm H] = 0$ being solar), the sources of the spectrophotometry, and the reddenings for 48 stars whose effective temperatures are $\ge$8000 K. The values longward of H$\alpha$ were given lower weights than other values owing to the authors' previous difficulties in obtaining simultaneous fits to them and other spectrophotometric values (see, e.g., Adelman et al. 1999). Figure 1 shows as an example the best fit for $\nu $ Cap. For most stars the discrepancies are less between the observations and the best theoretical fits. But in the Paschen continuum the spectrophotometric values of $\beta $ Lib, $\tau$ Her, and $\epsilon$  Cas produced only a fair fit to the predicted fluxes of the models. As the photometric values of $T_{\rm eff}$ and $\log~ g$ for $\theta$ Vir were determined without the use of a measured $\beta $ value, they are not used for comparison with the spectrophotometrically derived values. For 22 Dra which has spectrophotometry by Schild et al. (1971), we found $T_{\rm eff} = 12~500$ K and $\log~ g = 3.55$, but this star lacks published uvby$\beta $ values. For most stars the synthesized H$\gamma $ regions match the observations quite well, especially the Balmer line, but not perfectly. Three representative examples are shown in Figs. 2-4 with the thicker lines being the synthesized spectra and the thinner lines the observations. For $\gamma $ Peg, the He I line $\lambda$4388 is not satisfactorially synthesized and for $\gamma $ Gem the metal lines in the synthesized spectrum are slightly too deep. For 10 Lac, the worst case in fitting, the Balmer line profile fit was to the H$\gamma $ line wings with the observed core being deeper, especially in the central 5 Å, by about 5%, which may represent non-LTE effects while for 60 Leo models with a 4 km s-1 microturbulence were used consistent with the analysis by Adelman et al. (1999).


  \begin{figure} \par\includegraphics[width=16cm,clip]{ms1198f4.eps}\end{figure} Figure 4: The synthesized spectrum of $\gamma $ Gem (thicker line) centered at H$\gamma $ calculated with a solar composition $T_{\rm eff} = 9150$ K, $\log~ g = 3.60$ ATLAS9 model atmosphere with a microturbulence of 2 km s-1 (thinner line).
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For 48 stars the average difference in $T_{\rm eff}$ (photometric minus spectrophotometric-H$\gamma $ value) is 29 $\pm$ 293 K. For those stars with 8000 K $\le$ $T_{\rm eff}\le 10~050$¹ K, we find a difference of 25 $\pm$ 118 K and for stars with 10 050 K $\le$ $T_{\rm eff}$ $\le$ 17 000 K, 76 $\pm$ 105 K. This suggests a slight decrease of the derived temperature scale which is not unexpected as it reflects an increase in the metal line opacity for ATLAS9 relative to ATLAS6 models. Figure 5 shows the difference ( $\Delta T_{\rm eff}$ (K)) between the effective temperatures as derived using photometry and spectrophotometry as a function of the photometric temperature ( $T_{\rm eff}$ ($uvby\beta$) (K)).

The mean difference in $\log~ g$ (photometric minus spectrophotometric-H$\gamma $ value) for 47 stars is $-0.007 \pm 0.169$ dex. The scatter is similar to the uncertainty found by Lemke (1989) 0.20 dex. But two stars, 95 Leo and 14 Cyg, have $\log~ g$ values with rather large discrepancies, 0.49 dex and 0.56 dex, respectively. Together they have a 0.02 dex effect on the average. Figure 6 shows the difference ( $\Delta \log~g$ (dex)) between the surface gravity as derived using photometry and from spectrophotometry and the H$\gamma $ profile as function of the photometric temperature $T_{\rm eff}$ (uvby$\beta $) (K). It is best described as a scatter diagram. Since the discrepancies in the temperatures are small relative to the derived temperatures, the basic agreement of the surface gravity scales is not unexpected.

In Table 2 we compare the calibration or "known'' temperatures that Napiwotzki et al. (1993) used from Code et al. (1976), Beeckmans (1977), and Malagini et al. (1986) with those from their uvby$\beta $ calibation and our values. Smalley & Dworestsky (1995) re-evaluated the fundamental values of Code et al. (1976) using more recent flux measurements and found no significant changes. In general our results agreed better with the photometric values than the calibrator values and exhibit agreement with the calibrator similar to that of the photometric values. However this comparison can be done only for a few calibrators. How the nonunformity of the spectrophotometric data affects these results is unclear and is a possible source of some differences as the data quality is not uniform among the spectrophotometric sources.


 
Table 2: Comparison of effective temperature and surface gravity determinations.
    $T_{\rm eff}$  
Star "known'' uvby$\beta $ spectro.+H$\gamma $
$\gamma $ Gem 9240 9277 9150
$\beta $ UMa 9170 9601 9600
$\nu $ Cap 9950 10 311 10 250
134 Tau 10 790 10 928 10 750
$\pi$ Cet 12 820 13 174 13 100
$\eta$ Aur 17 580 16 887 16 375



  \begin{figure} \par\includegraphics[width=8.8cm,clip]{ms1198f5.eps}\end{figure} Figure 5: The differences ( $\Delta T_{\rm eff}$ (K)) (photometric minus spectrophotometric-H$\gamma $ values) of the effective temperatures as a function of the photometric temperature $T_{\rm eff}$ ( uvby$\beta $) (K).
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  \begin{figure} \par\includegraphics[width=8.8cm,clip]{ms1198f6.eps}\end{figure} Figure 6: The differences ( $\Delta \log~g$ (dex)) (photometric minus spectrophotometric-H$\gamma $ values) of the surface gravities as a function of the photometric temperature $T_{\rm eff}$ ( uvby$\beta $) (K).
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4 Conclusions

To substantially decrease the errors from this type of study we need a set of uniform high quality optical flux measurements with near continuous coverage for many more stars. Small systematic differences in effective temperature, but not in surface gravity have been found between matching optical spectrophotometery and H$\gamma $ profiles with the predictions of ATLAS9 solar composition model atmospheres and those derived from Strömgren uvby$\beta $ photometry based on ATLAS6 model atmospheres. These discrepancies have been attributed to small differences in the line opacities. In performing elemental abundance analyses, their effects will be small. But as one must do many steps as well as possible, the total effect of many such differences might be substantial.

Acknowledgements
SJA's contribution to this paper was support in part by grants from The Citadel Foundation as was that of KER. Some H$\gamma $ observations at the DAO were made by Frank Younger and Charles Perry. We thank F. Kupka for his implementation of Canuto-Mazzitelli convection in ATLAS9.

References

 

Copyright ESO 2002