JSTOR

1. INTRODUCTION

Olin Wilson (1961) showed that for G8–M1 dwarfs of a given spectral type the range in P−V colors is about 0.30 mag whereas for earlier types the color range is only about 0.12 mag. He reasoned that the larger amount could not be attributed to observational errors. Figure 1 is a copy of his diagram that shows the spread in P−V colors as a function of spectral type. Wilson was mystified by this effect and attempted to explain the larger color range by noting that it occurs in the temperature domain where the metals supply the electrons, rather than hydrogen. He proposed that the large range is due to varying hydrogen‐to‐metal ratios (up to a factor of 100) among the G8–M1. He supported that explanation by showing with high‐dispersion spectra that the hydrogen lines are stronger among those stars that have the bluer colors. However, most of these stars are low‐velocity stars, such as are found in open clusters; studies of open clusters do not confirm such large variations in hydrogen‐to‐metal ratios.

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Fig. 1.— Reproduction of Fig. 1 in Wilson (1961), showing the increased color range for samples of dG8–dM1 stars. The filled circles represent stars classified in the MK system and the open circles those classified in the Mount Wilson system. © 1961 by The American Astronomical Society, reproduced with permission.

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There is another explanation that does not involve abnormal abundances and that can be tested with other data. It involves an assessment of the accuracy of the observational parameters, which could not have been done when Wilson did his work.

2. OBSERVATIONAL PARAMETERS

Wilson’s data were taken from the compilation of Eggen (1955) of his V magnitudes and P−V colors of 833 northern and southern stars. Eggen listed his measured photometry, and he quoted spectral types from various sources, which he specified for each star. Let us consider those parameters.

Eggen’s P−V colors can be compared with B−V colors obtained outside the atmosphere by the Hipparcos satellite. The relation is shown in Figure 2 for 12 stars called dG5 by Eggen and 21 stars called dK5, although two of them (HD 154610 and HD 173954) are now known to be giants. The smooth curve in Figure 2 is best represented by the quadratic expression Using this expression, we find that the mean value of P−V is ±0.021 mag, even including the star (HD 51866) that shows the large deviation of 0.120 mag. This mean error in color of ±0.021 mag is a reasonable error for all‐sky photoelectric photometry, but it will not explain the range of 0.30 mag in color at a given spectral type.

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Fig. 2.— Comparison of the P−V colors of Eggen (1955) with Hipparcos B−V colors for 31 G and K dwarfs and two giants. The mean deviation is ±0.019 mag in P−V, even including the one discrepant point.

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I next wondered whether the large color range could be due to evolutionary deviations from the zero‐age main sequence (ZAMS). I collected stellar parallaxes from Hipparcos for the seven pairs of extreme examples for which Wilson obtained high‐dispersion spectra. In all seven pairs the bluer stars had slightly higher luminosities; the average difference was (s.e. in the mean) mag, which is one‐quarter of the luminosity difference between classes V and IV. Also consistent with Wilson’s spectra, the bluer (more luminous) stars have stronger hydrogen lines. However, stars of higher luminosities should be redder, not bluer, than the ones near the ZAMS. Therefore, the Wilson effect cannot be explained by a luminosity difference.

Wilson also noted that the redder star in each pair had stronger Ca ii H and K emission. We can ask whether the presence of the emission affects the colors. The H and K lines occur at wavelengths where the transmission of the Johnson B filter is 80% of the peak value (Johnson & Morgan 1951). However, the overall widths of the H and K lines in dwarfs are about 0.6 Å compared with a half‐width of the B transmission filet of about 1000 Å. Because the emission peaks seldom exceed the continuum level (Wilson & Bappu 1957, Fig. 9) except in short‐period binaries such as λ And, the contribution of the emission lines is less than about 0.003 mag. Furthermore, the effect is in the wrong sense: emission in the B filter would make the color bluer, not redder as observed.

On the other hand, the emission signifies chromospheric activity, so we wonder whether the occurrence of such activity will cause stars to be redder through its contribution of the chromospheres to the colors. Baliunas et al. (1995) have measured chromospheric activity averaged over 30 yr by measures of the strength of the H and K emission lines for stars with various B−V colors and MK types. At each type, the late‐type dwarfs from G8 V to K3 V show no significant correlation between the strength of the emission and the colors. Therefore, we cannot attribute the increased range in colors for dwarfs later than G8 to the increased chromospheric activity found among such stars.

Finally, I raised the question of whether the spectral classification errors are enough to explain the large color range for G8–M1 stars. Eggen stated the source for each spectral classification that he used. For almost all of the G8–M1 dwarfs, the types came from the radial velocity catalog of R. E. Wilson (1953). Ralph Wilson had persuaded Alfred Joy to classify many of the stars for which radial velocity measurements had been made. However, most of the photographic spectra used to measure the radial velocities of the fainter stars were unwidened. In unwidened spectra it is difficult to see the weaker lines, such as the Balmer lines in K dwarfs, although the Balmer lines are strong in G dwarfs. The strengths of the Balmer lines are a major criterion for classification (Keenan & McNeil 1976). Therefore, we can expect a tendency to classify K dwarfs less accurately than G dwarfs.

Let us consider first the stars labeled dG5 by Eggen. Four of them had spectral types derived by Morgan or his students. For those the B−V color range was from 0.681 to 0.714, for a range of 0.033 mag. The other five stars had Mount Wilson types; their colors ranged from 0.666 to 0.812, or a range of 0.146 mag. These two very different ranges suggest that the Mount Wilson types are less reliable than the MK types.

Let us consider larger samples of stellar colors for various spectral types. Here I will use the Hipparcos B−V colors to be independent of Eggen’s photometry while exploring the accuracy of the spectral classifications. I listed all of Eggen’s stars for which he gave MK types. The B−V colors for the 48 G0 V–M1 V stars are shown as a function of MK type in Figure 3. The mean dispersion in color per star for the types having two or more stars is ±0.025 (s.e. per star) mag. That dispersion in color corresponds to about 0.6 subtypes. A typical error in classification (Abt & Morrell 1995) is about 1 subtype. Therefore, the MK classifications are good. The mean color range, which should be more than twice the dispersion, is 0.053 mag. This is considerably less than the amounts (0.13 mag for G0–G7 and 0.30 mag for G8–M1) that Wilson reported for late‐type dwarfs.

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Fig. 3.— Hipparcos B−V colors for 48 stars classified in the MK system. The types are counted in subtypes from F0, so 10 represents G0, 20 is K0, and 30 is M0. The weighted mean dispersion for groups of two or more stars is ±0.025 mag.

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Next, consider the stars classified in the Mount Wilson system as quoted by R. E. Wilson. I considered an equal number of stars as above. The Hipparcos B−V colors as a function of Mount Wilson types are shown in Figure 4. The weighted mean dispersion in color is ±0.044 mag, which corresponds to a classification error of 1 subtype. It is nearly independent of type, being ±0.037 mag for dG0–dG7 and ±0.049 mag for dG8–dM1. Again, these dispersions correspond to reasonable errors in classification but give larger values than for the MK types. In this case the mean range in colors is 0.085 mag.

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Fig. 4.— Hipparcos B−V colors for 48 stars classified in the Mount Wilson system. The horizontal scale is counted in subtypes from F0, so 10 represents G0, 20 represents K0, and 30 represents M0. The weighted mean dispersion for groups of two or more stars is ±0.044 mag (s.e. per star). The wildly discrepant star (HDE 241596) at dK3 was not included.

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However, notice in Figure 1 that Wilson drew boundaries representing nearly the largest color ranges, not the mean color ranges. The largest range in B−V color in Figure 4 was 0.179 mag at dK5. Furthermore, I did not include all of the Eggen stars in Figure 4 but only a sample to match in size that in Figure 3. Statistically, if a sample is increased in size, the range will continue to increase without limit but the dispersion will remain constant. For instance, if we included all of Eggen’s dK5 stars, the range in B−V colors increased to 0.256 mag but the dispersion was ±0.084 mag. That dispersion is nearly the same as the dispersion (±0.079 mag) for the stars represented in Figure 4, but the range has increased by nearly 50%.

The dG stars are much more likely to have been classified on the MK system than the dK stars because, for example, the median magnitude for Eggen’s dG5 stars is 5.0 mag while for his dK5 stars it is 7.8 mag. Therefore, we would expect larger color ranges for the K dwarfs because they have poorer classifications.

We conclude that the reasons for Wilson’s effect shown in Figure 1 are as follows:

Therefore, we can explain Wilson’s diagram in terms of observational parameters without resorting to abundance anomalies. Eggen’s photometry is good and is not a cause of the effect. Neither are differing amounts of chromospheric activity.