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Astron. Astrophys. 317, 761-768 (1997)

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6. Distance estimates

6.1. Method

Lockwood has measured apparent magnitudes in 104 filter which is a continuum region at several phases for each star. Individual mean apparent magnitudes [FORMULA] are calculated. We take as average value two-thirds of the maximum plus one-third of the minimum to be consistent with the parameters determined previously. The bolometric correction [FORMULA] as a function of temperature is obtained by estimating the flux integral and by applying the 104 filter on the photospheric synthetic spectra (M0 to M10) given by Fluks et al. The filter 104 has been calibrated with a spectrum of Vega, as the zero point of the Lockwood system is defined by m104=0.00 mag for [FORMULA] Lyr. The resulting apparent bolometric magnitudes are listed in Table 2.

The absolute bolometric magnitudes determined in Sect. 5 are based on the Feast et al. relation. They might be fainter if a metallicity correction is needed. We rely on known trigonometric parallaxes taken from the catalogues by Jenkins (1963) and Van Altena et al. (1991) to examine if such a correction must be made. Unfortunately, in our sample only R Cnc, T Cas, o Cet and R Leo have measured parallaxes (Table 3).


Table 3. Trigonometric parallaxes. The first value for each star is taken from Jenkins (1963) and the second from Van Altena et al. (1991)

If we suppose no metallicity correction of the period-luminosity relation, we find R Cnc at 250 pc, T Cas at 290 pc, o Cet at 100 pc and R Leo at 120 pc. These distances seem too large. Thus, we decide to adopt a correction in order to obtain smaller distances. We suppose that the absolute bolometric magnitudes determined in Sect. 5.1 are 0.9 mag fainter in order to derive a distance of 80 pc for R Leo. We obtain by this way "preliminary" corrected distances, in the sense that we apply the correction to all the Miras of the sample. The choice of R Leo to calibrate the period-luminosity relation has been made for the two following reasons: 1. its Jenkins parallax is well confirmed by Van Altena et al. (it is not the case for o Cet), 2. Hipparcos will certainly provide a good parallax ([FORMULA] less than 20%) for R Leo; it may not be the case for R Cnc and T Cas (Turon, 1995). So, as soon as Hipparcos results will be available, it will be easy to see if the distances we propose need a scale correction by comparing with R Leo parallax.

6.2. Comparisons with other distance estimates

Figure 7 shows the comparison between our preliminary distances and those determined using infrared photometry and the K-band period-luminosity relationship of Feast et al. (Jura & Kleinman 1992; Jura et al. 1993).

[FIGURE] Fig. 7. Comparison between our preliminary distances (see Sect. 6.1) and those based on infrared photometry and the K-band period-luminosity relationship. Dotted line is the one-to-one line

The graph representating both distances shows a small dispersion. The estimations by Jura et al. are systematically greater than ours by a factor of 1.4, approximatively. Since they used the K-band period-luminosity relation, it is not surprising to find such a small dispersion. The systematic factor is due to different metallicity correction: as proposed by Wood (1990), they assumed that the local stars are intrinsically fainter in K by 0.25 mag than the Magellanic Cloud stars. This correction in the K band corresponds to 0.44 mag in [FORMULA] while we apply a correction of 0.9 mag to determine our distances. Furthermore Jura et al. consider a mean absolute K magnitude but do not systematically use the mean apparent K magnitude because data at various phases are not always available; this may induce an overestimate of their distance moduli. Only more numerous precise parallaxes ([FORMULA]) could provide a good calibration and give reliable absolute distances.

Figure 8 shows the comparison with distances determined by Luri et al. from a maximum likelihood method applied to kinematical data and visual magnitudes (Luri et al. 1996a). These authors find that Miras belong to different galactic populations: principally to the thick disk but some are probably halo stars (Mennessier et al. 1995).

[FIGURE] Fig. 8. Comparison between our preliminary distances (see Sect. 6.1) and those of Luri et al. (1996b) using the maximum likelihood method. Dashed lines give limits of 30% error. Square symbols indicate Miras classified as extended thick disk or halo stars by Luri et al. Circles indicate the new distances without metallicity correction (see text)

The agreement is acceptable for the thick disk stars, despite the fact that both methods and sets of data are totally different. Discrepancies might be due to the uncertainty in the mean [FORMULA] determination (some stars have different minimum or maximum values for different cycles; it is the case for o Cet). Moreover, the interstellar or circumstellar extinction is not taken into account in our study while a correction for the first one is included in the procedure of Luri et al. The distances are also dependent on the metallicity correction and, as with the distances determined by Jura et al., there might be a systematic scale error. Hipparcos trigonometrical parallaxes will clear up some of these points and improve the calibration of the period-luminosity relation by furnishing several stars with known distances.

The estimations of distances are however discrepant for Miras classified as extended thick disk or halo stars by Luri et al (1996b). These stars are indicated by square symbols on Fig. 8. This expresses the fact that, if the metallicity correction of 0.9 mag seems appropriate to the disk Miras, it is not the case for the halo Miras which have a metallicity closer to the LMC ones. If we use the magnitudes without correction for the halo Miras, then their distances are in better agreement with those of Luri et al. (these new distances are indicated by circles in Fig. 8). Some halo Miras have still under-estimated distances.

All Miras classified as halo stars by Luri et al. have short periods. This is consistent with the fact that metal-poor Miras certainly belong to the group of variables with periods less than 200 days (Hron 1991). So, we made the assumption that also Miras of our sample with short period but not belonging to the sample of Luri et al. are halo stars. The absolute bolometric magnitudes and the definitive distances listed in Table 2 take into account the following:
- Miras with period greater than 200 days are supposed to be thick disk stars. There is a metallicity correction of 0.9 mag in bolometric magnitudes determined in Sect. 5.
- Miras with period less than 200 days might be halo stars. The [FORMULA] listed are those determined in Sect. 5 without correction. An 'H' (halo) in the last column of Table 2 identifies Miras belonging to the halo stars group of Luri et al. and an 'SP' (short-period) those which are not in their sample.
This value of 200 days is of course somewhat arbitrary but it enables us to point out which values must be taken with great caution.

6.3. Choice of the calibration star. MS Miras

By taking R Leo at 80 pc as calibration star, we find R Cnc at 170 pc, T Cas at 190 pc and o Cet at 60 pc. For R Cnc, this distance is compatible with the range of distance deduced from trigonometric parallaxes (Table 3); for o Cet, it agrees with the parallax given by Jenkins. These results and the agreement between our distances and those determined from kinematical data and visual magnitudes justify a posteriori the choice of R Leo as calibration star for disk stars.

For T Cas, the distance is far outside intervals defined by error bars. Jura et al. give T Cas at 250 pc, which is consistent with the value of 190 pc we found when the systematic factor discussed above is taken into account. So, the discrepancy, if the trigonometric parallax is confirmed, is not due to an error in apparent magnitude [FORMULA] but it may be due to the fact that T Cas does not follow the same period-luminosity relation as the disk Miras. Wing & Yorka (1977) classified T Cas as an MS-Mira due to the presence of ZrO bands. Moreover, Luri et al. (1996b) find that T Cas could belong to a group of kinematically peculiar Miras. So, we decide to identify all stars classified as the same type with an 'MS' in Table 2: those stars might not obey the same period-luminosity relation as the others Miras and the distances might be not reliable.

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© European Southern Observatory (ESO) 1997

Online publication: July 8, 1998