3. TiO and VO indices as temperature indicators
Gray and Johanson (1991) showed that the ratio of line depths for two spectral lines can be used to determine stellar temperature with a very high precision. Similarly, it is possible to use two indices linked with two depths of molecular band heads as temperature indicators.
The first one, 78-88, is proportional to the ratio between two different band heads of TiO. This index is a good indicator for temperatures above 3000 K. For lower temperatures, the TiO bands begin to saturate. 78-88 should depend not too strongly on metallicity in so far as it concerns the ratio of two bands of the same element (however saturation effects may make this untrue). The second index, 105-104, is related to a VO band and a continuum point. It depends strongly on temperature below 3000 K when the VO molecules begin to appear. This index might be sensitive to the vanadium abundance. These two molecular indices complement each other as temperature indicators.
In order to calibrate the 78-88 and 105-104 indices as a function of temperature, we have used averaged observed spectra of red giants (Fluks et al. 1994). These authors have obtained intermediate resolution long-slit spectra (3800 Å 9000 Å) with the ESO 1.52 m telescope for a sample of 97 M giant stars.
Fluks et al. averaged the spectra for subtypes of the Case and MK classification systems from M0 to M10 and they fitted the results to photospheric synthetic spectra obtained with the model atmosphere code of Plez et al. (1992) in order to derive an effective temperature for each spectral type. They found an effective temperature-spectral type relationship closed to that of Ridgway et al. (1980). Since there is no non-variable M giants of subtypes M9 and M10, these subtypes have been based on spectrum of R Leo and U Her respectively which are Mira variables close to their minimum luminosity.
To each averaged spectrum representative of the spectral subtypes of the Case and MK classification (that is to say 18 different spectra), we have applied the filters described above. Given the fact that the displayed spectral region ends around 9000 Å, we have only obtained results for the 78-88 index. The characteristics of the different filters are given by Lockwood and Wing (1971). The zero point of the photometric system is defined by I(104)=0.00 mag for Lyr. The zero points of the other bands than 104 are not mentioned explicitly but the set of colours of Vega is given. So, the filters have been calibrated on the basis of a spectrum of Lyr. Figure 1 shows 78-88 as a function of temperature.
The diamonds are the indices measured on the 18 averaged spectra and the dashed line represents the (78-88)- relationship we use subsequently. The asterisk is a point we have added for the calibration; it represents R Cas. Indeed, in Lockwood's sample of Mira stars, the index 78-88 has a maximum value (1.77) for R Cas at minimum (phase 0.57). On the other hand, the spectrum which Fluks et al. take as representative of spectral type M10 is that of U Her, a Mira star which Lockwood classified as M9 at minimum (in his classification spectral type M10 is only represented by R Cas at minimum). This expresses the unreliability of the spectral classification for these very evolved stars. However, we have decided to add the point ( K) which represents R Cas at minimum in order to cover all the data from Lockwood's sample. The effective temperature of 2300 K has been taken to keep the progression: M7 3100 K, M8 2900 K, M9 2700 K, M10 2500 K.
The two triangles represent R Leo and U Her taken from Lockwood's data at phase 0.44 and 0.61, respectively, when the 78-88 index agrees well with the one deduced from the spectrum of the two stars (the M9 and M10 spectra).
The crosses are the indices of 61 standard red giants observed by Lockwood in the same five-colour system as the Miras. He gave them a spectral type (K5 to M8), which corresponds to a temperature using the effective temperature-spectral type relation of Fluks et al. The observations agree well with the (78-88)- relationship, given the uncertainties in the spectral type.
New temperatures are obtained for these standard stars (plus R Leo, U Her and R Cas as they complete the list beyond M8) by using the (78-88)- relationship of Fig. 1. The 105-104 measurements of the stars are then plotted as a function of effective temperature (Fig. 2). A fit by a polynomial function gives the behaviour of 105-104 as temperature indicator. We are conscious that the results might be uncertain especially for low temperatures (only three points below 2800 K), but temperatures are very poorly known for very evolved stars in general, and a considerable ambiguity cannot be avoided at present.
We have thus arrived at a calibration of the sequence of stars in the 78-88/105-104 plane.
© European Southern Observatory (ESO) 1997
Online publication: July 8, 1998