Steps Toward the Hubble Constant. Calibration of the Linear Sizes of Extra-Galactic H II Regions

Measurements of the angular sizes of the core and halo parts of H ii regions are given for 11 galaxies in the Local and M81-NGC 2403 groups whose distances are known from Cepheid variables. Corrections for dependences on the experimental conditions are made by precepts developed in the Appendix. The apparent angular sizes are only weakly dependent on exposure time of the plates, showing that the measured sizes are defined essentially by conditions in the nebulae rather than by the observational techniques. The linear dimensions of H ii regions in the calibrating galaxies and in six galaxies of the M101 group [with (m - M)o = 29.3 from Paper III of this series] increase steeply with the luminosity of the parent galaxies at a rate A log D/AMpg = -0.14. This is close enough to the disfance-independent value of -0.2 that straightforward use of H ii diameters as distance indicators is impossible. Because of this D = f(Mpg) dependence, nearby dwarf galaxies have nearly the same angular size for their H ii regions as distant giant Sc galaxies of the same apparent magnitude. To circumvent the difficulty, we have calibrated the linear diameters versus the luminosity class of the parent galaxy. The final correlation is tight, giving a 1-sigma spread of a(AD/D) = 0.06 (6 percent) for the first-ranked halo diameters in Sc I galaxies, increasing to a(AD/D) = 0.24 for luminosity class V Ir systems. The mean size of the largest H ii region (core plus halo diameters) is 550 pc for Sc I galaxies, decreasing to 110 pc for luminosity class V galaxies. This is the first of a series of papers on successive steps for measurement of the Hubble expansion rate. This calibration of H ii regions forms the basis for distances to general field galaxies (Paper IV), which itself is an intermediate step for distances to Sc I galaxies that are distant enough (cz > 4000 km 5-1) to permit reliable determination of the Hubble constant (Papers V and VI). Subject headings: galaxies - nebulae - redshifts