Appendix A
The Stellar Calibration

The standard star system, selected calibrating stars, and mean stellar color relationships have been presented and discussed in Papers I and II and in Persson, Aaronson, and Frogel (1977). The observations in these papers were made with two independent InSb detector systems in use at the Harvard College Observatory (the HCO system) and at the California Institute of Technology (the CIT system). For K magnitudes, and CO and H₂O indices, intercomparison of measurements on the two systems have revealed no systematic differences greater than 0.01 mag for either dwarf stars, giant stars, or galaxies. However, the following transformations were found for the J - H and H - K colors:

(A1)

and

(A2)

Equation (Al) is well explained by a difference in effective wavelength between the J_HCO and J_CIT filters. The reason for the transformation indicated by equation (A2) is less clear, as the H_HCO and H_CIT filters are identical. ⁸

In Table A1 the J - H colors are given for standard stars from Paper I independently set up on the HCO system. All stars have been observed between one and three times on at least 5 different nights, and the internal accuracy of the system is 0.02 mag. The colors of additional standards set up for this study are listed in Table A2, and are of comparable internal precision as the standards of Table Al and in Papers I and II. The V magnitudes in Table A2 are adopted from the Catalogue of Bright Stars (Hoffleit 1964).

In Table A3 the colors are listed for some additional calibrating stars not included in Papers I or II. (As discussed in Paper II, the CO and H₂O indices for most carbon stars are in the opposite sense expected due to the single sideband nature of the absorption measurements.) Using the extra data in Table A3, we have rederived the mean stellar relation for the H₂O index in M giants. As shown in Table A4, the revised calibration does not differ significantly from the calibration used in Paper II. The errors given for types M6 and M7 in Table A4 reflect the large dispersion of the H₂O absorption strength found in giant stars of very late spectral type.

The adopted mean CO and H₂O indices of M supergiants are listed for synthesis purposes in Table A5. The spectral type, V - K relationship is taken from Lee (1970). At a given spectral type, the CO index is 0.10 mag stronger in supergiants than in giants, while the H₂O index varies from being only marginally stronger at type M0, to 0.12 mag stronger at type M4 - results roughly consistent with the earlier work of Baldwin et al. (1973).

J and K magnitudes for many stars observed in this study were also measured by Johnson et al. (1966). Allowing for the value of J ( Lyr) = K ( Lyr) = 0.02 mag given by Johnson et al., a comparison of these measurements yields

and

where the quoted errors are dispersions of the mean. Thus, except for a zero-point shift, the J and K values in this paper are on the same infrared photometric system described by Johnson (1966a).

⁸ Note that equation (A2) was derived by an intercomparison of dwarf stars and galaxies only, because an insufficient number of late-type giant stars were observed in common at H on the two systems. The mean H - K color relation for giant stars adopted in this paper is taken directly from Table A3 in Paper I, without applying a transformation. Furthermore, to transform the mean H - K color relation for dwarf stars listed in the aforementioned Table A3 to the HCO system, equation (A2) should be applied to all the values of H - K. Back.