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Astron. Astrophys. 333, 231-250 (1998)

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3. Discussion

3.1. Empirical temperature calibrations

Fundamental temperatures are not known for many stars. Radii were measured for some O-F stars by the stellar-intensity interferometer and an empirical temperature scale for early type stars was derived by Code et al. (1976).

For cooler giant stars, radii have been derived by lunar occultation and Michelson interferometry. The very influential paper by Ridgway et al. (1980) used lunar occultation data to determine a [FORMULA]   versus (V-K) relation for KM giants. More recently, Michelson interferometry has been producing much more precise radii for the KM stars and longer baseline interferometers nearing completion will produce very precise radii for hotter stars and for variable stars such as cepheids. Fig. 1 shows the best Ridgway et al. (1980) occultation data and the Di Benedetto & Rabbia (1987), Dyck et al. (1996), and Perrin et al. (1997) interferometer data. There is good agreement between these data although the Michelson derived data has much higher accuracy. The shorter line is the 1980 Ridgway et al. temperature scale. The longer line is a polynomial fit to the interferometer data alone and suggests that a small adjustment only is required to the Ridgway et al. temperature scale between 3700 and 3300K.

[FIGURE] Fig. 1. The empirical [FORMULA]   versus V-K diagram for giants for the best occultation data of Ridgway et al. (1980) (open circles) and the Michelson interferometer data of Di Benedetto & Rabbia (1987), Dyck et al. (1996) and Perrin et al. (1997) (closed squares). Error bars in the measured temperatures are shown

For M dwarfs, the empirical data is very scarce there being only two radii measurements, both from eclipsing binary stars. These will be discussed later.

More recently the infrared flux method (IRFM) has been used to derive accurate temperatures for A-M stars. Megessier (1994, 1995) discusses the reliability and accuracy of this technique. Tsuji was amongst the first to promote the IRFM for deriving the temperatures of carbon (Tsuji 1981a) and M giants (Tsuji 1981b) and M dwarfs (Tsuji et al. 1995, 1996a), while Blackwell and co-workers have done much of the pioneering work on hotter stars. BLG94 have derived an effective temperature scale for Pop I A-K giants and dwarfs using the IRFM and the Kurucz (1992) model atmospheres. AAM96 have more recently derived IRFM temperatures and bolometric corrections for F0-K5 dwarfs with a range of metal abundances.

Many authors give their data in terms of V-K which is well suited for K and M giants but is less useful for A and F stars where the lower precision of much V-K photometry (from independent measurements of V and K magnitudes) produces larger uncertainties in the [FORMULA]  -color relations. The color V-I is the more useful temperature sensitive color for A-K stars but unfortunately is not available for all the calibrating stars. However, precise b-y values are available for many stars, particularly the brighter ones and b-y can be converted into V-I very accurately for Pop I A-G stars. We have therefore obtained b-y from Hauck & Mermilliod (1990) for almost all the BLG94, AAM96 and Code et al. (1976) stars and transformed the b-y values using the relation V-I = -0.00395 + 2.071846 (b-y) -1.09643 (b-y)2 + 0.631039 (b-y)3 obtained from 122 E-region secondary standards of Cousins (1976, 1987). Some of the stars also have measured V-I values (Cousins 1980a,b; Bessell 1990a) and these were used in preference to the transformed ones.

Caldwell et al. (1993) have also derived polynomial relations to transform between UBVRIJHK and uvby. Such representations are very useful, but over the 10 mag range of V-K and 5 mag range of V-I such fitted polynomials are unable to recover the nuances of the original mean relation across the full color range. In such cases it is better to break up the whole range into several overlapping sections and fit each section separately. Although mean color-color relations can be used successively to transform colors for a homogeneous group of stars it is not good practise for stars with a range of stellar parameters and it is important to measure accurate BVRI colors for all the AAM96 stars, in particular the extreme subdwarfs.

When using or interpreting the colors of stars one should always be aware that the observed colors of stars are likely to be affected by interstellar reddening. Estimates of the reddening can be made in several ways. The most accurate way is to use a reddening independent colour or index such as the Q index for OB stars (see Appendix F) or the [FORMULA] index for F stars.

Another technique is to use maps of the galactic distribution of dust, such as those of Fitzgerald (1986) and Burnstein & Heiles (1982) combined with estimate of the distance of the star from a trigonometric parallax or spectral/luminosity class. However, it is generally believed that within 100 pc of the Sun the interstellar reddening is insignificant and many of the stars used to calibrate color-color and color-temperature relations are nearby. In fact, none of the stars that we used from the AAM96 list were reddened and only 7 of the stars used in BLG94 had (V-K) reddenings larger than 0.02 mag. A comparison of the Yale and Hipparcos parallaxes for the 15 stars with reddening between 0.02 and 0.04 mags showed that Hipparcos moved six of the stars closer and five further away. Looking at the residuals to the fit between [FORMULA]   and color and correlating with the new distances showed that some of the reddenings did appear to be overestimated. However, as the reddenings were already quite low, the calibration scarcely changed. BLG94 show in their Table 13 the effect of interstellar extinction on angular diameters for a range of temperatures.

The Hipparcos parallax database when combined with photometric catalogs and the Burstein & Hailes maps should enable the production of much better maps of reddening versus distance than previously available, thus permitting better reddening corrections for more distant stars.

Fig. 2 shows the [FORMULA]   versus V-I diagram using IRFM temperatures from BLG94 and AAM96 (for -0.2 [FORMULA] [Fe/H] [FORMULA] 0.2) together with the intensity interferometer measurements of Code et al. (1976) for A-F stars. The IRFM data yield higher precision for the A-F stars than did the intensity interferometer measures but the results show good agreement except for the hottest stars in the IRFM data and HR7557 of Code et al.

[FIGURE] Fig. 2. Empirical [FORMULA]   versus V-I relation for dwarfs. Solid symbols are data from BLG94; crosses indicate AAM96 (for -0.2 [FORMULA] [Fe/H] [FORMULA] 0.2); open circles with error bars indicate Code et al. (1976)

[FIGURE] Fig. 3. a Theoretical evolutionary tracks near the main sequence for 1 (filled circles), 1.5 (triangles), 2.5 (open circles), 5 (crosses)  [FORMULA] models with Z = 0.02 from Schaller et al (1992). b Theoretical giant branch tracks for 1 (filled circles), 1.5 (open triangles), 2.5 (open circles), 5 (crosses), 9 (filled diamonds) and 15 (pluses) [FORMULA] models with Z = 0.02 from Schaller et al (1992) together with extensions to higher luminosities and cooler temperatures from Bessell et al. (1991).

By good fortune, the mean empirical temperature scale for A-M stars has not changed appreciably from that summarised by Bessell (1979) although the precision of empirical temperature derivations has greatly improved over the past 16 years. The most significant improvements have occurred in the model atmospheres, in the computation of more realistic line blanketed spectra which permit better broad-band colors to be synthesised and in the precision and accuracy of observed colors of stars from the UV to the IR.

In Table 7 are listed the coefficients for polynomial fits for giant stars between [FORMULA]   and V-K. The interferometer data were fitted alone then combined with the IRFM data. Table 8 lists the mean empirical [FORMULA]   versus V-I relation for A-K dwarfs.


Table 7. Polynomial fits to empirical [FORMULA] versus V-K relations for giants. [FORMULA] = M0 + M1*(V-K) + M2*(V-K)2 +...


Table 8. Polynomial fit to empirical [FORMULA] versus V-I relations for A-K dwarfs [FORMULA] = M0 + M1*(V-I) + M2*(V-I)2 +...

In Table 9 for completeness we list the empirical temperature scale for the O and B stars adopted by Sung (1997) based on Crowther (1997) and Böhm-Vitense (1982).


Table 9. Empirical [FORMULA]   versus Spectral Type and U-B relation for OB dwarfs from Sung (1997), Crowther (1997), and Böhm-Vitense (1982)

3.2. Comparison between model atmosphere and empirical [FORMULA]   versus color relations

We compared empirical relations [FORMULA] -(U-B), [FORMULA] -(V-K), [FORMULA] -(V-I), [FORMULA] -(I-K) for dwarfs and [FORMULA] -(V-K) for giants with the corresponding theoretical relations. We discuss the ranges 50000 - 10000K for (U-B), 4500-9500K for dwarfs and 2600-5000K for giants for (V-K), 9500-2000K for (V-I), and 4500-1500K for (I-K).

We derive the relevant test gravities for our models in the following way. Most of the A-G stars used by BLG94 and AAM96 for their IRFM calibration are in the Yale parallax catalog so one can estimate their luminosities and gravities. (Most of the stars will eventually have higher precision parallaxes from the Hipparcos database). This shows that few of the A-F stars observed are ZAMS stars and on the average they lie about 1 magnitude brighter than the ZAMS. An average gravity therefore should be between 3.5 and 4.

The relevant gravities and temperatures can also be well deduced for giants and dwarfs from theoretical isochrones (eg. Bertelli et al. 1994) and evolutionary tracks (eg. Schaller et al. 1992; Schaerer et al. 1993a,b; Charbonnel et al. 1993). Figs. 3a and 3b show the near main sequence and giant branch evolutionary tracks for 1, 1.5, 2.5, 5, 9, [FORMULA] solar abundance (Z = 0.02) models from Schaller et al. (1992) supplemented by extensions to cooler temperatures by Bessell et al. (1991). Similar plots can be made for other abundances. The gravities of stars on the solar abundance giant branch range from log g = 3.0 [FORMULA] 0.5 near 5000K to log g = -0.2 [FORMULA] 0.5 at 3000K. ZAMS stars with spectral-types between O and late-F will have gravities between log g= 4.1- 4.2 .

In Fig. 4 we show the U-B versus [FORMULA]   relation from the OB dwarf models and from the empirical temperature scale of Crowther (1997). The agreement is excellent for temperatures below 30000K. However, for the hottest stars, ground-based UBVRI photometry is not recommended for accurate temperature determination and fluxes measured further into the UV such as with the WPFC2 filters F160BW are better to use. In a future paper we will present colors for the F160BW passband.

[FIGURE] Fig. 4. The [FORMULA] versus U-B diagram from the model atmospheres (full line) compared with the empirical relation from Crowther (1997) (crosses)

Figs. 5a and 5b compare the observed and theoretical V-K and V-I color-temperature relations for A-G dwarfs. Empirical (V-K)- [FORMULA]   data are from BLG94 and AAM96 while the (V-I)- [FORMULA]   relation shown (Table 8) was the line fitted to the data in Fig. 2. The model atmosphere colors are for the no-overshoot ATLAS9 models for three values of log g= 3.5, 4.0, 4.5. Although these no-overshoot model colors being a little bit bluer fit the observations better than the overshoot models do, the V-K and perhaps the V-I still appear a little too red also for log g included between 3.5 and 4.0, which roughly corresponds to that of the calibrating stars.

Such a small difference could result from the adopted model and colors for Vega and Sirius used to fix the zero points, from remaining problems with the models or from passband mismatches. Nevertheless, with a small adjustment the theoretical colors are in excellent agreement with the observations.

[FIGURE] Fig. 5. a [FORMULA]   versus V-K relation from the model atmospheres compared with the empirical relation from the IRFM method for A-G dwarfs taken from BLG94 and AAM96. Symbols for observations are as in Fig. 2. b [FORMULA]   versus V-I relation from model atmospheres compared with the polynomial fit to the empirical [FORMULA] versus V-I relation for A-K dwarfs given Table 8. In both figures a and b open circles are the colors from ATLAS9 no-overshoot models (Table 2). They are plotted for log g = 4.5, 4.0, 3.5; higher gravity gives redder color

Fig. 6 compares empirical and computed V-I versus [FORMULA]   relations for the G - M dwarfs. IRFM temperatures are available for some G-K dwarfs (BLG94, AAM96, Tsuji et al. 1995, 1996), but only two eclipsing binary M dwarfs, YY Gem (Leung and Schneider 1978; Habets & Heintze 1981) and CM Dra (Lacy 1977) have measured radii. YY Gem is an old disk star with near-solar abundances but CM Dra is a high velocity star although its spectrum does not indicate an obviously large metal deficiency. Chabrier & Baraffe (1995) have recently discussed both systems. The Plez (1997) NMARCS model colors (Table 6) appear a good match to the eclipsing binaries temperature scale and seem to indicate convergence with the ATLAS9 models at 4250K. For the log g = 4.5 solar abundance grid the Brett (1995a, b) colors computed with the older opacities set (Table 6) show a V-I smaller by about 0.07 at 3800K, increasing to 0.4 at 3000K and to 1.0 at 2400K.

[FIGURE] Fig. 6. Comparison between model and empirical [FORMULA]   versus V-I colors for G-M dwarfs. The dwarfs with IRFM temperatures are plotted as filled circles BLG94 and plus signs (AAM96). The dwarfs with directly measured radii (large crosses with error bars) are the Sun and the eclipsing binaries YY Gem and CM Dra. The ATLAS9 no-overshoot models for log g =4.5 and 4.0 are indicated by open squares; the open circles are the NMARCS models for log g = 4.5

The ATLAS9 no-overshoot model colors are a good representation of the colors of the hotter dwarfs. However, one should note that an earlier paper by Leung & Schneider (1978) derived an effective temperature of 3770K for YY Gem about 300K cooler than that used here and in addition, Chabrier & Baraffe (1995) suggest that CM Dra could be 3300K (150K hotter).

Empirical and theoretical (I-K)- [FORMULA]   relations for M dwarfs are compared in Fig. 7. The ATLAS9 dwarf models are indicated by the upper line and the Plez (1997) dwarf relation by the lower line. Here in addition to YY Gem and CM Dra (open circles) are shown the IRFM temperatures for some M dwarfs from Tsuji et al. (1996a) (crosses) and fits to far-red spectra by Brett (1995a) (filled circles). As seen for V-I, the model [FORMULA]   versus I-K relations are in quite good agreement with the observations. The advantage of using the I-K color for cool M dwarfs is that it continues to increase monotonically with decreasing temperature unlike the observed V-I color which becomes bluer in the latest M dwarfs. They are in good agreement with Tsuji's IRFM temperatures around 2000K.

[FIGURE] Fig. 7. The comparison between model and empirical [FORMULA]   versus I-K color for M dwarfs. The open circles with error bars are YY Gem and CM Dra; the crosses are IRFM data from Tsuji et al. (1995, 1996); the filled circles are Brett (1995a) fits to far-red spectra. The upper line represents the no-overshoot ATLAS9 models of Table 2, the lower line represents the Plez (1997) NMARCS models of Table 6.

In Fig. 8 we compare the observed and the model [FORMULA]  -(V-K) color relations for the GKM giants. The plotted observational data are from BLG94, Di Benetto & Rabbia (1987), Dyck et al. (1996) and Perrin et al. (1997). The continuous line is the mean empirical relation discussed in Sect. 3.1. The model colors are in extremely good agreement with the observations even given the complication of a range in model color depending on gravity and extension. For temperatures between 4000K and 3400K the effect of mass (or sphericity) is comparable or greater than the effect of gravity on the V-K color but below 3200K the effect of gravity is very great. However, the expected log g for M giants (old disk) at around 3200K is about 0.25. Lower gravities are more typical of supergiants.

[FIGURE] Fig. 8. Comparison between model [FORMULA]   versus V-K colors and the IRFM and interferometer temperatures for GKM giants . The closed circles are IRFM data; the small open circles are Michelson interferometer data. The open squares are ATLAS9 no-overshoot model colors from Table 2 for log g = 0.0, 0.5, 1.0, 1.5; the large open circles are NMARCS models for the same gravities from Table 4 and Table 5. Table 5 also gives colors for a range of extensions appropriate for 1 to 5 [FORMULA] giants.

In Fig. 9 we show the difference between the empirical V-K versus [FORMULA]   relation and the theoretical NMARCS and ATLAS9 [FORMULA]   versus V-K color relation appropriate (solar abundance, [FORMULA]   and log g for a 1.5 [FORMULA] track) for old disk giant branch stars. The error bars indicate the Michelson interferometer data. The remaining points are from BLG94. The open circles indicate the residual to the spline fit to the ATLAS9 and NMARCS data. It is clear that the agreement is excellent, although there seems to be small systematic difference of about 50K near 5000K.

[FIGURE] Fig. 9. The difference between the empirical and theoretical [FORMULA]   versus V-K for old disk giants. The data with error bars are the interferometer measurements. The other points are IRFM estimates. The open circles indicate the residuals to the spline fit to the NMARCS and ATLAS9 models.

3.3. Comparison between model atmospheres and empirical color-color relations

Empirical relations are compared with theoretical relations for (J-K,V-K), (V-I,V-K), and (B-V,V-I) indices for both dwarfs and giants. [FORMULA]   ranges from 5000 to 2500K for (J-K, V-K); from 9500K to 2500K for dwarfs and from 5000K to 2800K for giants for (V-I,V-K); from 9500K to 2500K for dwarfs and from 4000K to 2500K for giants for (B-V,V-I).

Fig. 10 compares the observed and theoretical J-K versus V-K diagram for [FORMULA] [FORMULA] 5000 K . The upper line represents the locus of the nearby giant stars, the lower line the dwarfs. The NMARCS and ATLAS9 giant model colors are in a good agreement with each other and with the observed locus for temperatures hotter than 4250K (V-K [FORMULA] 3.0). Below 4000K (V-K [FORMULA] 3.5) the NMARCS models better fit the observations. The ATLAS9 dwarf models (plotted as solid squares) lacking H2 O opacity do not fit the J-K color at all for temperatures below 4250K and the NMARCS models whilst showing the correct trend with temperature, obviously compute too strong H2 O bands. Brett (1995a,b) used as an H2 O line list derived from a statistical treatment of empirical mean opacity and line separation data for these preliminary models. The Plez (1997) models incorporate a better ab initio line list from Jorgensen (1996), which still does not provide a better fit to the observations in J-K. In the NMARCS grid currently being computed, H2 O opacity will also be incorporated on the basis of the very extensive line list from Partridge & Schwenke (1997) and we anticipate better although not perfect agreement. We suspect water vapour is not the only factor responsible for the bad fit in J-K. In addition, modelling of the atmospheres of the coolest M dwarfs may require the inclusion of grain opacities and an understanding of how grains form and segregate (see Tsuji et al. 1996b).

[FIGURE] Fig. 10. Comparison between the observed and theoretical J-K versus V-K diagram. The small filled circles joined by a line represent the mean colors of nearby stars with spectral types from K0 to M7 for giants (upper line) and K2 to M7.5 (M10: Boeshaar 1976 for dwarfs (lower line) taken from Bessell & Brett (1988) and Bessell (1991). The ATLAS9 no-overshoot model colors (Table 2) are indicated by open squares (log g = 3.0 - 1.0) and filled squares (log g = 4.0, 4.5). The open circles are NMARCS giants from Tables 4 and 5. The filled circles are Plez (1997) NMARCS dwarfs from Table 6.

Fig. 11 shows the good agreement between the observed and computed V-I versus V-K colors for dwarfs, although this may be coincidence given the uncertainties that we know still exist in the line opacities. The observed turnover in the V-I colors are not shown by the coolest models. Fig. 12 shows that the agreement is excellent for M giant stars with temperatures below 4000K. The disagreement was large with the original colors from both NMARCS grids. With the old opacities the V-I color was too blue by a full magnitude around V-K = 7.

[FIGURE] Fig. 11. Comparison of V-I versus V-K relations for dwarfs. The filled circles joined by a line represents the observed locus for solar-neighbourhood dwarfs from Bessell & Brett (1988) and Bessell (1991). The squares are ATLAS9 model colors from Table 2; the open circles the Plez (1997) NMARCS model colors of Table 6.

[FIGURE] Fig. 12. Comparison of V-I versus V-K relations for giants. The filled circles are the observed locus for solar-neighbourhood giants from Bessell & Brett (1988) the line is the locus from Caldwell et al. (1993). The squares are ATLAS9 model colors from Table 2; the open circles the NMARCS model colors of Table 4 and 5.

B-V is a color which does not agree well between observation and theory especially for cool stars. Fig. 13 and Fig. 14 show the B-V versus V-I relation for dwarfs and giants respectively. For the A-G dwarfs the agreement is reasonable although the synthetic B-V is slightly too red for the A-F stars. But for the M dwarfs the agreement is poor, the synthetic colors being 0.2 to 0.8 mags bluer than observed. For the giants (Fig. 14) the computed colors, in particular the NMARCS models, are also seen to be too blue by a few hundredths at 4750K and increasing to almost 0.2 mag at 3600K. Part of this may be due to the range in metallicity in the field stars; however, it mainly reflects the opacity incompleteness in the blue and UV. The NMARCS model V band flux has greatly improved (i.e. decreased) with the inclusion of new opacities and the revision of older ones. All the opacities at shorter wavelengths have not yet been carefully checked. The final NMARCS model grid will incorporate atomic line data from the VALD (Piskunov et al. 1995) database supplemented by the latest Kurucz data for lines not appearing in VALD. The current NMARCS models used line data from an older Kurucz (1989) tape. It is worth noting also that many molecules have electronic transitions in the blue-UV region.

[FIGURE] Fig. 13. Comparison of B-V versus V-I relations for dwarfs. The line is the observed locus from Caldwell et al (1993). The squares are ATLAS9 models colors (Table 2); the closed circles are the Brett (1995) NMARCS model colors (Table 6) for three metallicities, [M/H] = -2, -1 and 0; the open circles are the Plez (1997) NMARCS models for solar metallicity (Table 6).

[FIGURE] Fig. 14. Comparison of B-V versus V-I relations for giants. The line connecting the small dark points is the observed locus for G0-M2 stars from Bessell & Brett (1988). The squares are ATLAS9 models colors (Table 2) for ([FORMULA]  , log g) = 3500, 0.5; 3750, 1.0; 4000, 1.5; 4250, 2.0; 4500, 2.5; 4750, 3.0; 5000, 3.5; 5750, 3.5; 5500, 4.0. The circles are the NMARCS model colors (Table 4 and 5) for ([FORMULA]  , log g) = 3600, 0.5; 3800, 1.0; 4000, 1.5; 4250, 2.0; 4500, 2.5; 4750, 3.0.

3.4. Abundance effects on color indices for KM giants

In the following Figs. 15 - 18, we show the effect of abundance on the B-V, V-I, V-K and J-K colors of KM giants. The abundances illustrated cover the range found in the centre of the Galaxy, the old and young disk and the Magellanic Clouds. We chose a set of temperature and gravity pairs appropriate for solar abundance old disk giants and used the same set of parameters for the different abundances. The plots therefore do not represent the giant branch loci for different abundances.

For B-V, V-I and V-K decreasing metallicity means bluer colors (except in B-V for [FORMULA]   [FORMULA] 3900K). However, J-K gets redder with decreasing metallicity. V-K is the least sensitive to metallicity and for temperatures greater than 4000K can be considered essentially independent of abundance.

[FIGURE] Fig. 15. The theoretical [FORMULA]   versus B-V relations for KM giants for parameters ([FORMULA]  , log g) = 3600, 0.5; 3800, 1.0; 4000, 1.5; 4250, 2.0; 4500, 2.5; 4750, 3.0 and 5 metallicities, [M/H] = -0.6, -0.3, 0, 0.3, 0.6. NMARCS models (Table 5).

[FIGURE] Fig. 16. The theoretical [FORMULA]   versus V-I relations for KM giants. Details and symbols as in Fig 15.

[FIGURE] Fig. 17. The theoretical [FORMULA]   versus V-K relations for KM giants. Details and symbols as in Fig 15.

[FIGURE] Fig. 18. The theoretical [FORMULA]   versus J-K relations for KM giants. Details and symbols as in Fig 15.

3.5. Comparison between model atmospheres and (V-I)- [FORMULA] and (I-K) - [FORMULA] empirical relations

Figs. 19a,b show the comparison between observed and computed bolometric corrections in I and K for dwarfs. The observed and model [FORMULA] are in good agreement except for the coolest models whose V-I colors are too red. The [FORMULA] are in excellent agreement. There is a small systematic difference between the Tinney et al. (1993) corrections and the model corrections. This is probably due partly to a slightly different adopted flux for Vega and Sirius and partly to the remaining model problems mentioned above. Finally, Fig. 20 also shows excellent agreement between the model and observed [FORMULA] for giants. The small difference for the coolest stars is certainly within the observational uncertainties and the model uncertainties. The NMARCS models of Table 5 shown in Figs. 15-18 have virtually identical [FORMULA] for different metallicities.

[FIGURE] Fig. 19. a Comparison between the observed and theoretical I mag bolometric correction versus V-I for A-M dwarfs. The straight line is the relation given by Reid and Gilmore (1984) (adjusted for a different solar [FORMULA]); the curved line is from Tinney et al. (1993). The squares are ATLAS9 model data for log g=4.5 (Table 2) and the open circles are Plez (1997) NMARCS model data (Table 6). b Comparison between the observed and theoretical K mag bolometric correction versus I-K for A-M dwarfs. The line is from Tinney et al. (1993). The squares are ATLAS9 model data for log g=4.5 (Table 2) and the open circles are Plez (1997) NMARCS model data for log g = 4.5 (Table 6).

[FIGURE] Fig. 20. Comparison between the observed and theoretical K mag bolometric correction versus V-K for KM giants. The line is from Bessell & Wood (1984); the filled circles are from Frogel et al. (1981). The squares are ATLAS9 giant model data (Table 2) and the open circles are NMARCS model data from Tables 4 and 5.

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Online publication: April 15, 1998