IAO 2018, Практически тур — Задача 8. Star variability analysis

IAO 2018 — Practical round (α and β)

Practical round. Problems to solve

XXIII International Astronomy Olympiad. Colombo, Sri Lanka, 6–14 X 2018. This source combines groups α and β. The distinct task 6 of each group is identified as 6α and 6β; tasks 7 and 8 are shared and are reproduced once.

Бележки от източника

The repeated 0.25, 0.32 and 0.37 Julian-day entries in the α table 6 are retained exactly. The α data sheet bears the header Theo although the body says Practical round. Question 8.5 refers to provided graph paper, which is absent from this source pack. Matching official practical solutions were not found in the complete same-year catalogue.

Shared reference inventory

The two separately archived data photographs are labelled Theo: data_1 contains Solar-System properties, the equation of time and Colombo coordinates; data_2 contains physical constants and formulae. They were read to check reference coverage and do not contain missing practical graph paper, additional practical tasks or official solutions.

Условие

For any periodic variable star, the period is one of the most important and most informative of its observable parameters. Studying the periods of variable stars, and their changes in periods is an important part of the analysis of variable stars. If a star is perfectly periodic, then every period is exactly the same. In that case we can predict its cycles in advance.

8.1 Any perfectly periodic star with epoch time $t_0$ (the time of maximum (or minimum) for cycle number zero) and period $P$, shows its next maximum at time $t_0+P$. This maximum time is known as calculated-time of maximum (or minima) for cycle number one ($C_1$).

Using this pattern write an equation for the calculated-time of maximum ($C_n$) for any cycle number $n$ of a perfectly periodic star with a period of $P$ and epoch of $t_0$

8.2 The table 8 lists times of minima of an eclipsing binary star which has epoch: $t_0=\mathrm{JD}\ 2442502.726$ (JD: Julian Date) and period: $P=0.971534$ day. Substituting these values to the equation you wrote above, compute the calculated time of minima for each cycle of the table and fill the “JD-Calculated” column of the table.

8.3 Fill the “(O-C) (in days)” column of the table. (O-C = observed value minus calculated value)

8.4 Convert (O-C) values that you calculated in previous chapter into minutes and fill the “(O-C) (in minutes)” column of the table.

8.5 Using the data of this completed table, construct (O-C) (in minutes) graph vs the number of cycle and fit a trend line for your plotted data. (Graph papers are provided. Use maximum range of the graph paper).

8.6 According to your results mention whether this star is perfectly periodic, almost periodic or not periodic. Write English words:

“(1) perfectly periodic”, “(2) almost periodic” or “(3) not periodic”.

Table 8

Cycles	JD-Observed (Obs)	JD-Calculated (Cal)	O-C (days) (Obs - Cal)	O-C (minutes) (Obs - Cal)
300	2442794.1804
500	2442988.4867
950	2443425.6757
1000	2443474.2563
1250	2443717.1386
1350	2443814.2934
1400	2443862.8687
1700	2444154.3285
1750	2444202.9077
1850	2444300.0622
2100	2444542.9444
2400	2444834.4039
2550	2444980.1353
3200	2445611.6366
3250	2445660.2111
3500	2445903.0947

Решение

Теми и трудност

Трудност: неоценена.

Звезди · Променливи звезди · Двойни звезди

Предпоставки: Разширена олимпиадна подготовка

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Оригинал в Архива: pract.pdf · допълнителни данни: data_1.jpg · допълнителни данни: data_2.jpg