OlympiadIOAA 2015 | Central Java, Indonesia | Data Analysis Problem 1

2015 P1 | Distance to the Cepheid HV 2257

Skills:Graphs Time series Photometry Velocities Distances

Photometry and radial velocity data for the Cepheid HV 2257 are given in Tables 1 to 3, based on observations by Gieren (MNRAS 265, 1993). The pulsation period of the star is $P = 39.294$ days. A temperature–colour relation and a bolometric correction table are given in Tables 4 and 5. The solar luminosity is $L_\odot = 3.96\times10^{26}$ W and its absolute bolometric magnitude is $M_{\odot,\rm bol} = 4.72$ . Do not use a period–luminosity relation in this problem.

(a) Plot the light curve from Table 1 between phases 0.6 and 1.

(b) Plot the colour from 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 the supplementary data in Tables 4 and 5. Assume there is no extinction in this direction.

Table 1 | V light curve

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 | V − R colour curve

Phase	V − R (mag)
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 | Radial velocity curve

Phase	RV (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 | Temperature–colour relation (read from the official Fig. 1)

$(V-R)$ (mag)	$T_{\rm eff}$ (K)
0.50	5000
0.54	4750
0.60	4500
0.68	4250
0.80	4000

The paper gives this relation as a graph (Houdashelt et al. 2000). These points are read from its filled squares and are good to roughly ±100 K. Interpolate linearly between them.

Table 5 | Bolometric correction

$T_{\rm eff}$ (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

Saved in this browser only, no account needed.

Reading resources

Material that covers the physics behind this problem.