The Luminosity Function of Nebulae. II. The Luminosity Function as Indicated by Residuals in Velocity-Magnitude Relations

Velocity-magnitude relations (log v =o.2m+c) are derived from apparent magni- tudes of (a) brightest stars in resolved field nebulae, (b) field nebulae of all types, and (c) fifth brightest nebulae in clusters. Since the absolute magnitude of brightest stars, IT8, is known, M~ and Mc5 are indicated by the values of c in the three relations. Re- siduals in the relation for field nebulae of all types indicate the form of the luminosity function as distorted by peculiar motions. The effects of the distortion are reduced in velocity-distance relations (v = kd) derived from (a) brightest stars and (b) field nebulae. The coefficient k is about 526 km/sec per million parsecs, and the dispersion of peculiar motions is about 200 km/sec. The luminosity function derived from the residuals agrees closely with that de- termined in Part I (Mt. Wilson Conir., No. 548; Ap. J. 84, 158) from brightest stars in resolved nebulae alone. The various types of nebulae are comparable, with the ex- ception of the irregulars, which average about half as bright as the others. The distance of the Virgo cluster is found to be of the order of 2.3 X io6 parsecs (m-M= 26.8)