THETA and SIGMA AND (Theta and Sigma Andromedae). About five degrees south-southwest of the great Andromeda Nebula, in the constellation Andromeda, lies a smallish triangle of fifth magnitude stars. The brighter two (both to the west and close to fourth magnitude) are aligned more or less vertically, with Theta Andromedae (4.61) a couple degrees north of Sigma And (4.52). You can hardly tell the difference between them. Moreoever, both are white class A2 dwarfs. So they must be very similar stars at about the same distance, right? Well, no. Sigma is 135 (give or take just 1) light years away, while Theta is 309 light years (plus or minus 28) distant, 2.9 times farther away. (The eastern star of the triangle, Rho And, 158 light years away, is rather in between and irrelevant here.) Taking a closer look at the "twin" class A stars, we first make a small correction of 0.1 magnitude for each as a result of dimming by interstellar dust. With a temperature of 8360 Kelvin, Sigma And (the nearer of the two) shines with the light of 22.9 Suns, which yields a radius of 2.94 times solar. Theta, on the other hand, has a much greater luminosity of 118 Suns (5.1 times greater than Sigma) and a radius of 4.22 times solar. How then can they look so similar? It's a matter of mass and age. Theta carries 2.5 solar masses around with it, Sigma 2.0. Luminosity is terribly sensitive to mass, on the average rising as mass to the 3.5 power. If that's all there were involved, however, Theta would be only twice as bright as Sigma. Dwarfs in this mass range brighten with age even though their internal fuel supplies go down. Sigma is about halfway through its lifetime of 1.1 billion years, while, with an age of about 900 million years and born as a B8 star, Theta's core hydrogen has run out and the star, having brightened as much as it can and still be a dwarf, is nearly a subgiant. The two together (mass and age) then fully explain the difference. By coincidence the distances are such that the stars have about the same brightness. Theta was born as a B8 star, Sigma just hotter than A0, and the two are now crossing over in temperature and class. There are other similarities. Both are fairly rapid rotators. The projected equatorial velocity of Theta is 105 kilometers per second, while Sigma's is 118 km/s, which with radius yield respective rotation periods under 2.0 and 2.9 days. The true velocities are clearly high enough so that there is no separation of elements, some falling under the force of gravity, others lofted up by radiation pressure. Neither seem to have infrared-radiating dusty debris disks that would imply planets. Theta Andromedae, however, seems to have a companion lurking a tenth of a second of arc away. At Theta's distance it would be at least 9.5 Astronomical Units from Theta proper and take more than 40,000 years to make a complete circuit. Together, the two stars, Theta and Sigma, illustrate that the class of a star is meant to be a description of its spectrum, not a statement of its evolutionary status.

Written byJim Kaler 2/10/17. Return to STARS.