PHI UMA (Phi Ursae Majoris). Relatively faint, and a bit lost among the bright stars of Ursa Major, just-barely-fifth magnitude (4.59) Phi Ursae Majoris (of no proper name) still occupies a significant place at the crook of the Bear's rather odd, forward-bending front leg. At least it does according to the way some draw the figure. In any case, it and Theta Uma lead the way south to the Arab's "third leap of the gazelle" (made of Kappa and Iota UMa). Not one star, but two, Phi UMa is a very close binary in which two similar fifth magnitude (5.28 and 5.39) components are as pair known as a class A (A3) subgiant, implying that the two are starting their death throes. Only a few tenths of a second of arc apart, they are very difficult to split at the telescope, and have been studied mostly by sophisticated interferometry in which very short exposures overcome the atmospheric twinkling of the stars. A stated temperature of 11,200 Kelvin appears much too high for the class, so we adopt 9800 K for both as more appropriate. With that we can estimate the amount of ultraviolet light, and with a distance of 510 light years (give or take 37), find respective luminosities for Phi UMa A (the brighter) and Phi-B of 182 and 164 times that of the Sun, radii of 4.7 and 4.5 solar, rotation periods (from a projected speed of 29 km/s) under 8 days, and similar masses of 3.0 to 3.2 times that of the Sun. Theory also shows that the stars are indeed subgiants near the end of their hydrogen-fusing lifetimes of 220 million years. Metal abundances relative to hydrogen are light, iron coming in at 40 percent solar. The orbit gives us more information. They go around each other every 105.4 years at an average measured separation of 54 Astronomical Units, a high eccentricity taking them between 30 and 79 AU apart. Last closest passage took place in 1987.
Phi UMa The orbit of Phi UMa B, the fainter of the two class A3 subgiants, is plotted as if it is going around the brighter, Phi A (at the cross), every 105.4 years. In reality, each goes around a common center of mass that is close to midway between them. The arrow gives the direction of motion. The scales are in seconds of arc; note how close the stars are to each other. Though the orbital analysis gives an average separation of 54 Astronomical Units, it may be more like 40. Phi-A is not at the focus of the elliptical orbit because of a 25 degree tilt of the orbit to the plane of the sky. From the Sixth Catalog of Orbits of Visual Binary Stars , W. I. Hartkopf and B. D. Mason, US Naval Observatory Double Star Catalog, 2006.
Kepler's Laws, however, gives a combined mass 14.5 times that of the Sun, which is much too high for such stars. (Using the higher above temperature does not help, the combined evolutionary mass climbing just to 7.4 solar.) Mass determination, though, is very sensitive to the measure of separation, which given the closeness of the stars is quite difficult. We can get a good fit with evolutionary theory by shrinking the average separation a bit to 40 AU, the stars then moving between 22 and 59 AU apart. Further measures will no doubt refine the orbital data (as well as distance), such work of crucial importance for finding the relations between stellar luminosities and masses.
Written by Jim Kaler 4/23/10. Return to STARS.