In the following we compare those multiwavelength PL relations with the Hipparcos sample of Galactic Cepheids, individually corrected for foreground reddening and scaled to their geometric parallax distances. These form rather disjoint subsets. We have analyzed these four groups of stars independently, but self-consistently, in the following way. The resulting PL relations are shown in the six panels of Figure 27.
Error bars are one-sigma uncertainties from the quoted parallaxes.
Note the highly correlated nature of the individual data points about the fiducial lines. A full treatment of this issue is beyond the scope of this paper, but we note that selection biases at least are minimized for stars having the smallest reported errors. Multiwavelength Period-Luminosity relations for Cepheids with Hipparcos parallaxes, plotting all stars that have data available at the particular wavelength, as noted in the upper left corner of each panel. The total lack of correlation in the latter instance is unexpected except in the limit where the residuals are dominated by distance errors in the derived parallaxes. The variance in each mean offset was then calculated from the average of the squares of these same residuals again inversely weighted by the variance in the individually quoted parallaxes.