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Register a new userThe absolute magnitude of K0V stars from HIPPARCOS parallaxes
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We investigate the properties of K0V stars with Hipparcos parallaxes and spectral types taken from the Michigan Spectral Survey. The sample of 200 objects allows the empirical investigation of the magnitude selection (Malmquist) bias, which appears clearly present. By selecting those objects that are not affected by bias, we find a mean absolute magnitude of Mv~5.7, a downward revision from 5.9 mag. listed in Schmidt-Kaler (1982). Some objects have absolute magnitudes far brighter than Mv~5.7, and it is suggested that these objects (~20% of the total sample) are K0IV stars which may have been mis-classified as a K0V star. The presence of the Malmquist bias in even this high quality sample suggests that no sample can be expected to be bias-free.
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The present determination of the absolute magnitude $M_V(RR)$ of RR Lyrae stars is twofold, relying upon Hipparcos proper motions and trigonometric parallaxes separately. First, applying the statistical parallax method to the proper motions, we find $<M_V(RR)>=0.69pm0.10$ for 99 halo RR Lyraes with $<$[Fe/H]$>$ =--1.58. Second, applying the Lutz-Kelker correction to the RR Lyrae HIP95497 with the most accurately measured parallax, we obtain $M_V(RR)$=(0.58--0.68)$^{+0.28}_{-0.31}$ at [Fe/H]=--1.6. Furthermore, allowing full use of low accuracy and negative parallaxes as well for 125 RR Lyraes with -- 2.49$leq$[Fe/H]$leq$0.07, the maximum likelihood estimation yields the relation, $M_V(RR)$=(0.59$pm$0.37)+(0.20$pm$0.63)([Fe/H]+1.60), which formally agrees with the recent preferred relation. The same estimation yields again $<M_V(RR)>$ = $0.65pm0.33$ for the 99 halo RR Lyraes. Although the formal errors in the latter three parallax estimates are rather large, all of the four results suggest the fainter absolute magnitude, $M_V(RR)$$approx$0.6--0.7 at [Fe/H]=--1.6. The present results still provide the lower limit on the age of the universe which is inconsistent with a flat, matter-dominated universe and current estimates of the Hubble constant.
We compare the absolute visual magnitude of the majority of bright O stars in the sky as predicted from their spectral type with the absolute magnitude calculated from their apparent magnitude and the Hipparcos parallax. We find that many stars appear to be much fainter than expected, up to five magnitudes. We find no evidence for a correlation between magnitude differences and the stellar rotational velocity as suggested for OB stars by Lamers et al. (1997), whose small sample of stars is partly included in ours. Instead, by means of a simulation we show how these differences arise naturally from the large distances at which O stars are located, and the level of precision of the parallax measurements achieved by Hipparcos. Straightforwardly deriving a distance from the Hipparcos parallax yields reliable results for one or two O stars only. We discuss several types of bias reported in the literature in connection with parallax samples (Lutz-Kelker, Malmquist) and investigate how they affect the O star sample. In addition, we test three absolute magnitude calibrations from the literature (Schmidt-Kaler et al. 1982; Howarth & Prinja 1989; Vacca et al. 1996) and find that they are consistent with the Hipparcos measurements. Although O stars conform nicely to the simulation, we notice that some B stars in the sample of Lamers et al. (1997) have a magnitude difference larger than expected.
Hipparcos trigonometrical parallaxes of Mira-type variables have been combined with ground-based angular diameter measurements to derive linear diameters. Of eight stars with ground-based data, six have diameters indicating overtone pulsation whilst two, both with periods over 400 day, are pulsating in the fundamental. Hipparcos parallaxes of 11 Miras have been combined with extensive infrared photometry to determine the zero-point of the Mira period-luminosity relation. Adopting the relation at K (2.2 micron), since this is less likely to be subject to abundance effects than that at Mbol, leads to a distance modulus for the LMC of 18.6 mag with a uncertainty of slightly less than 0.2 mag. A brief discussion is given of the preliminary analysis of the parallaxes of a much larger sample of Miras. Some consideration is given to possible problems in interpreting the Hipparcos data which arise because of the physical characteristics of the Mira variables. Finally the apparent low-luminosity of the carbon Mira, R Lep, implied by the Hipparcos results leads to an interesting problem in AGB evolution.
Hipparcos parallaxes fix distances to individual stars in the Hyades cluster with an accuracy of 6%. We use the Hipparcos (and Tycho-2) proper motions, which have a larger relative precision than the trigonometric parallaxes, to derive ~3 times more precise distance estimates, by assuming that all members share the same space motion. The improved parallaxes as a set are statistically consistent with the Hipparcos parallaxes. The new parallaxes confirm that the Hipparcos measurements are correlated on small angular scales, consistent with the limits specified in the Hipparcos Catalogue, though with significantly smaller `amplitudes than claimed by Narayanan & Gould. The colour-absolute magnitude diagram of the cluster based on the new paral- laxes shows a well-defined main sequence with two gaps/turn-offs. These features provide the first direct observational support of Boehm-Vitenses prediction that (the onset of) surface convection in stars affects their B-V colours. We present and discuss the theoretical HRD for an objectively defined set of 88 high-fidelity members of the cluster as well as the delta Scuti star theta^2 Tau, the giants delta^1, theta^1, epsilon, and gamma Tau, and the white dwarfs V471 Tau and HD 27483 (all of which are also members). The precision with which the new parallaxes place individual Hyades members in the Hertz- sprung-Russell diagram is limited by (systematic) uncertainties related to the transformations from observed colours and absolute magnitudes to effective temperatures and luminosities. The new parallaxes provide stringent constraints on the calibration of such transformations when combined with theoretical stellar evolutionary modelling, tailored to the chemical composition and age of the Hyades, over the large stellar mass range probed by Hipparcos.
We first review the current knowledge of Hipparcos systematic and random errors, in particular small-scale correlations. Then, assuming Gaussian parallax errors and using examples from the recent Hipparcos literature, we show how random errors may be misinterpreted as systematic errors, or transformed into systematic errors. Finally we summarise how to get unbiased estimates of absolute magnitudes and distances, using either Bayesian or non-parametrical methods. These methods may be applied to get either mean quantities or individual estimates. In particular, we underline the notion of astrometry-based luminosity, which avoids the truncation biases and allows a full use of Hipparcos samples.
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