Surface Brightnesses in the U, B, V System with Applications of Formula and Dimensions of Stars

The surface brightnesses are expressed in the V system in terms of V₀ and $$d^{\prime\prime}$$ (the angular diameter) with the formula $$s_{V} = V_{0} + 5 \,\text{log} d. sv$$ is derived for 18 stars from observation and the relation between sv and $$(B-V_{B})_{0}$$ is obtained. The central problem is the determination of Mv from R (the linear radius) or vice versa; the formula $$M_{v} - sv + 5 \,\text{log} R = + 15.15$$ is basic for the solution thereof. The use of sv is compared with a method based on BC and T _e currently employed in the same problem. The two methods are equivalent provided a certain condition is satisfied. Lines of equal radius have been drawn in a HR diagram having ( B–V ) ₀ and M _v coordinates and the radii of stars along the zero age main sequence are given. The mean absolute magnitude of δ Cephei has been derived in good accord with other modern determinations $$(M_{v} = -3.56).$$ The absolute magnitudes M _v for the components of some eclipsing variables are derived and a mass-luminosity relation is drawn with small scatter. The dimensions of some supersupergiants belonging to the Magellanic Clouds are calculated; HDE 268757 is one of the largest known stars with a radius of 10.3 a.u. A check is made on a published list of BC and T _e , using the results of this paper.