In Figure 26 we compare differentially four calibrations (heavy dotted lines) of the V-band Cepheid PL relation with the FC97 Hipparcos-based relation (solid horizontal lines). The first two comparisons (in the upper two panels) are with the relations given by Madore & Freedman (1991; hereafter MF91), derived from self-consistent sets of LMC Cepheid data whose stars either had complete BVRI observations (MF91.1 containing 32 Cepheids) or complete BVRIJHK observations (MF91.2 containing 25 stars).* These first two solutions indicate the sensitivity of slopes and zero points to sample selection, which are considerable, but within the quoted statistical uncertainties: ± 0.11 and ± 0.20, respectively for the slopes, and ± 0.05 and ± 0.09 mag, for the zero points. So as to make the subsequent comparisons consistent, the original Sandage & Tammann (1968) calibration (ST68.1 in the lower left panel) has been placed on the modern Hyades/Pleiades Galactic cluster distance scale by applying a single offset of +0.13 mag derived from the average difference between the absolute magnitudes of the Cepheids used in the 1968 calibration updated to Feast and Walker (1987), their Table 2. This distance scale corresponds to a Hyades modulus of 3.27 (see Pel 1985) and uses the Pleiades main sequence, at a modulus of 5.57 (van Leeuwen 1983) to effectively correct for the over-metallicity of the Hyades with respect to the older Galactic clusters in which the Cepheid calibrators are found.** Finally, the FW87 calibration itself is plotted in the lower left panel. In all panels the dashed horizontal lines represent the fiducial Hipparcos calibration flanked by thin parallel lines at ± 0.10 mag.
Figure 26. Differential comparison of
recently published V-band
PL relations (heavy lines) relative to the Hipparcos calibration (thin
lines). Plotted is the difference [V - V(Hipparcos)]
versus log P, in the sense that if Hipparcos is brighter the difference
shown is positive.
The error bars of all of the plotted previously published relations overlap with errors quoted for the Hipparcos solution (a formal uncertainty was not given by ST68, so we have arbitrarily assigned them an error of ± 0.05 mag). However, the offsets are not randomly distributed, with each of the solutions appearing to be systematically fainter in V with respect to the Hipparcos calibration by about 0.1 mag. We discuss the significance and possible implications of this difference in the following sections.
* Tanvir (1997) has suggested that there may be small corrections (ranging from 0.02 to 0.09 mag) to the published I-band magnitudes of these LMC Cepheids arising from the originally sparse sampling and consequent averaging of their light and color curves. For the past five years we have been obtaining new VI CCD observations of the LMC calibrators at Las Campanas and now also at Siding Springs Observatories. These new data are designed to address those concerns.
** At the February 14, 1997 meeting of the Royal Astronomical Society in London on February 14, 1997 F. van Leeuwen and C.S. Hansen Ruiz reported a true distance modulus of 5.29 ± 0.06 mag for the Pleiades cluster, based on Hipparcos trigonometric parallaxes. Following the Venice Meeting in June 1997 the value had changed only slightly to 5.33 ± 0.06 mag (C. Turon, private communication). If adopted, this Pleiades modulus would make the Galactic-cluster-based calibrations approximately 0.3 mag fainter than the FC97 solution plotted in Figure 27. At this point in time, the Galactic cluster zero point appears to be in a state of flux, and we will not comment on it further, except to note that the Hipparcos calibration will undoubtedly converge on a more accurate zero point than we have access to at this precise moment.