The following material comes from Chapter 13 of the HOA Manual which discusses variables stars and O-C Diagrams.
O-C for Eclipsing Binary Stars
You have studied pulsating variables, both short-period Cepheids such as delta Cep and long-period Miras such as V Cas. Now we will use O-C to study the behavior of an eclipsing binary star. Remember that for eclipsing binaries, it is the time of minimum brightness, rather than maximum, that is of most interest. This is because minimum corresponds to the middle of the eclipse, and the eclipse is what we are really interested in timing. In fact, a large number of variable star observers specialize in eclipsing binary stars, and design their observing programs to get accurate timings of the minimum brightness. Table 13.9 lists AAVSO data for the eclipsing binary star X Tri. Instead of containing magnitudes, it lists times of minima.
Let's construct an O-C diagram for the minima of X Tri. To do so, we need to estimate the period and the epoch. We will use the following values:
Epoch: t0 = JD 2442502.721
Period: P = 0.975352 day
Using this period and epoch, we can calculate the computed time Cn of any minimum.
There are a lot of minima in Table 13.9 (below). Your teacher will assign each of you a small number of cycles to compute. For the cycles assigned to you, take the cycle number n and use it to calculate the computed time of minimum Cn. When all the students have completed the cycles assigned to them, collect all the class data into a large table, listing cycle number n (from Table 13.9), observed time of minimum On(also from the Table 13.9), and your computed time Cn.
Now subtract Cn from On, for each cycle, to get (O-C)n, for every cycle n listed in the table. Finally, prepare an O-C diagram, showing cycle number n on the x-axis and O-C value on the y-axis.
What can you tell about the behavior of X Tri from this O-C diagram? Are the estimated period and epoch correct? Did the period change?
Table 13.9
Minima Timings of X Tri
Cycle' JD (minimum) Cycle' JD (minimum) Cycle' JD (minimum)
230 2442726.175 3197 2445608.722 5107 2447464.348
318 2442811.668 3198 2445609.694 5108 2447465.310
322 2442815.551 3233 2445643.695 5168 2447523.601
523 2443010.832 3233 2445643.697 5169 2447524.576
524 2443011.802 3508 2445910.867 5200 2447554.687
524 2443011.806 3544 2445945.845 5202 2447556.637
524 2443011.811 3619 2446018.711 5237 2447590.644
557 2443043.863 3621 2446020.646 5238 2447591.611
560 2443046.783 3621 2446020.649 5446 2447793.689
564 2443050.666 3621 2446020.652 5447 2447794.661
567 2443053.582 3622 2446021.618 5447 2447794.667
945 2443420.818 3622 2446021.618 5448 2447795.639
948 2443423.741 3622 2446021.620 5449 2447796.604
952 2443427.615 3626 2446025.508 5477 2447823.805
984 2443458.717 3659 2446057.567 5478 2447824.776
985 2443459.687 3660 2446058.540 5481 2447827.690
985 2443459.689 3690 2446087.686 5516 2447861.695
1020 2443493.687 3725 2446121.692 5520 2447865.581
1021 2443494.658 3934 2446324.737 5555 2447899.589
1262 2443728.797 3936 2446326.679 5829 2448165.784
1338 2443802.635 3974 2446363.599 5903 2448237.677
1408 2443870.641 4003 2446391.772 5903 2448237.677
1686 2444140.727 4004 2446392.745 5942 2448275.566
1687 2444141.700 4008 2446396.633 6180 2448506.792
1688 2444142.671 4042 2446429.665 6570 2448885.692
1689 2444143.641 4044 2446431.605 6573 2448888.606
1760 2444212.623 4078 2446464.635 6608 2448922.610
1762 2444214.566 4079 2446465.612 6637 2448950.781
1795 2444246.628 4322 2446701.688 6639 2448952.724
1797 2444248.567 4354 2446732.781 6641 2448954.668
1829 2444279.660 4356 2446734.726 6642 2448955.638
2075 2444518.656 4358 2446736.671 6957 2449261.673
2077 2444520.602 4389 2446766.785 7031 2449333.558
2112 2444554.600 4391 2446768.728 7348 2449641.535
2182 2444622.609 4397 2446774.559 7728 2450010.717
2419 2444852.863 4432 2446808.560 7734 2450016.550
2452 2444884.926 4668 2447037.839 7763 2450044.721
2527 2444957.790 4740 2447107.788 7764 2450045.693
2566 2444995.678 4741 2447108.761 7769 2450050.555
2845 2445266.743 4742 2447109.735 7800 2450080.669
2878 2445298.797 4742 2447109.735
'Times of minima of X Tri are from AAVSO monographs Observed Minima Timings of Eclipsing Binaries, Nos. 1, 2,3, prepared by M. Baldwin and G. Samolyk (1993, 1995, 1996).
'Repeated cycles indicate times of minimum from different observers.
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