IOAA 2015, data-analysis — Задача 1. Problem 1

International Olympiad on Astronomy and Astrophysics — Data Analysis Problem (Central Java - Indonesia, 2015)

Условие

Photometry and radial velocity data for the Cepheid type star HV2257 are given in Table 1-3, based on observations by Gieren (MNRAS vol 265, 1993) . The pulsation period of the star is $P = 39.294$ days. A reference graph for the temperature – color relation and the bolometric correction tables are given in Figure 1 (Houdashelt $et\ al.$, 2000) and Table 4 (http://xoomer.virgilio.it/hrtrace/Straizys.htm). Given that the solar luminosity is $L_{\odot} = 3.96\times10^{26} J\ s^{-1}$ and its bolometric magnitude $M_{\odot bol} = 4.72$. Please do not use period-luminosity relation from the second question for this question.

Table 1

Phase	V mag
0.11	12.81
0.13	12.84
0.14	12.87
0.16	12.88
0.19	12.90
0.19	12.94
0.24	12.99
0.43	13.32
0.46	13.31
0.46	13.32
0.51	13.36
0.54	13.41
0.54	13.45
0.56	13.46
0.59	13.53
0.59	13.52
0.61	13.55
0.64	13.60
0.64	13.62
0.72	13.68
0.74	13.61
0.77	13.45
0.79	13.18
0.80	13.12
0.80	13.07
0.82	12.80
0.82	12.78
0.82	12.73
0.84	12.57
0.85	12.54
0.85	12.53
0.87	12.48
0.87	12.47
0.89	12.49
0.90	12.51
0.92	12.51

Table 2

Phase	V – R
0.22	0.71
0.24	0.73
0.25	0.74
0.27	0.75
0.29	0.75
0.29	0.75
0.34	0.77
0.51	0.87
0.53	0.85
0.53	0.87
0.57	0.85
0.60	0.87
0.60	0.88
0.62	0.87
0.64	0.90
0.64	0.90
0.66	0.88
0.68	0.91
0.69	0.90
0.76	0.88
0.78	0.82
0.80	0.79
0.82	0.70
0.82	0.70
0.82	0.68
0.84	0.60
0.84	0.59
0.84	0.58
0.86	0.53
0.86	0.51
0.87	0.52
0.88	0.51
0.89	0.51
0.90	0.55
0.91	0.53
0.93	0.56

Table 3

Phase	RadVel (km/s)
0.03	232
0.05	234
0.08	234
0.08	237
0.13	242
0.13	246
0.18	243
0.20	249
0.23	250
0.28	254
0.33	259
0.35	261
0.36	260
0.38	266
0.40	265
0.44	266
0.46	272
0.46	265
0.49	270
0.51	270
0.54	272
0.54	273
0.56	274
0.59	274
0.61	273
0.62	274
0.64	274
0.67	276
0.67	274
0.69	274
0.71	274
0.72	276
0.74	278
0.77	271
0.77	264
0.79	253
0.80	259
0.82	242
0.85	230
0.87	228
0.90	224
0.92	224
0.92	225
0.95	228
0.96	228

Table 4. Bolometric correction

$T_{\mathrm{eff}}$, K	BC, mag
9600	-0.25
9400	-0.16
9150	-0.10
8900	-0.03
8400	0.05
8000	0.09
7300	0.13
7100	0.11
6500	0.08
6150	0.03
5950	0.00
5800	-0.05
5500	-0.13
5250	-0.22
5050	-0.29
4950	-0.35
4850	-0.42
4700	-0.57
4600	-0.75
4400	-1.17
3900	-1.25
3750	-1.40
3550	-1.60
3400	-2.00

a. Plot the light curve based on Table 1, between phases 0.6 and 1.

b. Plot the color in Table 2, between phases 0.6 and 1.

c. Plot the Radial Velocity curve from Table 3, between phases 0.6 and 1.

d. Calculate the average radial velocity of the star.

e. Calculate the distance to this pulsating star using the observed data and supplementary data given in Table 4 and Figure 1. Assume that there is no extinction in this direction.

Решение

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Оригинал в Архива: IOAA 2015 Data Analysis Problems ver 20150730_1717.pdf · официални решения: DataAnalysis_sol.pdf