An Introduction to Modern Astrophysics · Problem 7.6

The Classification of Stellar Spectra — Carroll & Ostlie

Physics — Astrophysics · eclipsing-spectroscopic-binary-parameters

Problem

From the light and velocity curves of an eclipsing, spectroscopic binary star system, it is determined that the orbital period is 6.31 yr, and the maximum radial velocities of Stars A and B are 5.45.4 km s−1^{-1} and 22.422.4 km s−1^{-1}, respectively. Furthermore, the time period between first contact and minimum light (tb−ta)(t_b - t_a) is 0.58 d, the length of the primary minimum (tc−tb)(t_c - t_b) is 0.64 d, and the apparent bolometric magnitudes of maximum, primary minimum, and secondary minimum are 5.40 magnitudes, 9.20 magnitudes, and 5.44 magnitudes, respectively. From this information, and assuming circular orbits, find the ((a)) Ratio of stellar masses. ((b)) Sum of the masses (assume i≃90∘i \simeq 90^\circ). ((c)) Individual masses. ((d)) Individual radii (assume that the orbits are circular). ((e)) Ratio of the effective temperatures of the two stars.

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