Question

6) A pair of eclipsing binaries viewed edge-on shows the following light curve. (You can estimate relevant quantities by reading off the scales.) 1.0 0.8 0.6 0.2 0.4 0.6 0.8 1.0 Time (days) (a) If the larger star is 0.5Ro in radius, estimate the radius of the smaller star. (b) If the larger star has an effective temperature of 5000 K, estimate Tef of the smaller star.

Answer 1

Given that - light curves for pair of eclipsing binaries status given that - larger star radius r_R = 0.5 R_0 As we know radius y each Star - For smaller star - r_s = v/2 Vertical-bar (t_a - t_b) Vertical-bar Where v in velocity y star and t_a amount y time between first contact and t_b minimum light. Similarly for larger star - r_l = v/2 Vertical-bar (t_a - t_c) Vertical-bar from equn (i) and (ii) r_s/r_l = Vertical-bar t_a - t_b Vertical-bar /t_a - t_c Vertical-bar = 0.1/1.1 r_s = r_l times 0.1/1.1 = 0.5 R times 0.1/1.1 = 0.045 R_0 Hence smaller star radius r_s = 0.05 R_0 if both star brightness are same then temperature y each star - B_s = k pi r^2 s middot 6 T^4_5 B_l = K pi r^2_l middot T^4_l l = B_s/B_l = r^2_s T^4_s/r^2_1 T^4_1 \r\n T^4_s = r^2_1 T^4_1/r^2_s = > (0.5/0.045)^2 times (5000)^4 T^4_s = 7.716 times 10^16 T_s = 16666.64 K