IOAA 2015 Data Analysis Problems Ver 20150730_1851

Data Analysis Problem Problem 1 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⨀ = 3.96 × 1026 𝐽 𝑠 −1 and its bolometric magnitude 𝑀⨀𝑏𝑜𝑙 = 4.72. Please do not use period-luminosity relation from the second question for this question. a. b. c. d. e.

Plot the light curve based on Table 1, between phases 0.6 and 1. Plot the color in Table 2, between phases 0.6 and 1. Plot the Radial Velocity curve from Table 3, between phases 0.6 and 1. Calculate the average radial velocity of the star. 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.

Fig. 1 The V-R color and temperature relation. Different symbols correspond to different authors. 1/7

Table 1 Phase V mag

Table 2 Phase V–R

0.11 0.13 0.14 0.16 0.19 0.19 0.24 0.43 0.46 0.46 0.51 0.54 0.54 0.56 0.59 0.59 0.61 0.64 0.64 0.72 0.74 0.77 0.79 0.80 0.80 0.82 0.82 0.82 0.84 0.85 0.85 0.87 0.87 0.89 0.90 0.92

0.22 0.24 0.25 0.27 0.29 0.29 0.34 0.51 0.53 0.53 0.57 0.60 0.60 0.62 0.64 0.64 0.66 0.68 0.69 0.76 0.78 0.80 0.82 0.82 0.82 0.84 0.84 0.84 0.86 0.86 0.87 0.88 0.89 0.90 0.91 0.93

12.81 12.84 12.87 12.88 12.90 12.94 12.99 13.32 13.31 13.32 13.36 13.41 13.45 13.46 13.53 13.52 13.55 13.60 13.62 13.68 13.61 13.45 13.18 13.12 13.07 12.80 12.78 12.73 12.57 12.54 12.53 12.48 12.47 12.49 12.51 12.51

0.71 0.73 0.74 0.75 0.75 0.75 0.77 0.87 0.85 0.87 0.85 0.87 0.88 0.87 0.90 0.90 0.88 0.91 0.90 0.88 0.82 0.79 0.70 0.70 0.68 0.60 0.59 0.58 0.53 0.51 0.52 0.51 0.51 0.55 0.53 0.56

Phase 0.03 0.05 0.08 0.08 0.13 0.13 0.18 0.20 0.23 0.28 0.33 0.35 0.36 0.38 0.40 0.44 0.46 0.46 0.49 0.51 0.54 0.54 0.56 0.59 0.61 0.62 0.64 0.67 0.67 0.69 0.71 0.72 0.74 0.77 0.77 0.79 0.80 0.82 0.85 0.87 0.90 0.92 0.92 0.95 0.96

Table 3 RadVel (km/s) 232 234 234 237 242 246 243 249 250 254 259 261 260 266 265 266 272 265 270 270 272 273 274 274 273 274 274 276 274 274 274 276 278 271 264 253 259 242 230 228 224 224 225 228 228

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Table 4. Bolometric correction

Teff, K 9600 9400 9150 8900 8400 8000 7300 7100 6500 6150 5950 5800 5500 5250 5050 4950 4850 4700 4600 4400 3900 3750 3550 3400

BC, mag -0.25 -0.16 -0.10 -0.03 0.05 0.09 0.13 0.11 0.08 0.03 0.00 -0.05 -0.13 -0.22 -0.29 -0.35 -0.42 -0.57 -0.75 -1.17 -1.25 -1.40 -1.60 -2.00

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Problem 2 BVRIJHKLMN photometry of 2 stars from the constellation Cassiopeia is given in Table 5. For both stars it is believed that their light is affected by extinction by diffuse Interstellar Medium (ISM) only. Assuming that the observation is done from outside the atmosphere. a) Using the data given in Tables 5 to 9, plot 𝐸X−V /𝐸B−V as a function of 1/𝜆X for filters B, V, R, I, J, H, K, L, M, N for both stars. Fit approximate curves by eye (in particular, note that 𝐸X−V / 𝐸B−V ~ 𝑐𝑜𝑛𝑠𝑡. as 1/𝜆X → 0). X is each band in the photometric system.

𝐸B−V is the colour excess. b) Using the graphs obtained in a), estimate 𝑅V and 𝑅R for each star. 𝐴V

𝑅V = 𝐸

B−V

𝐴R

and 𝑅R = 𝐸

R−I

(𝐴V is the absorption in V). Now apply these results in order to derive a distance estimate for IC 342, a spiral galaxy in Cassiopeia obscured by Milky Way. You should assume that the properties of the ISM in IC 342 are similar to those of the ISM in our Galaxy. c) Using the period-magnitude diagrams for 20 Cepheids from IC 342 (Figures 2 and 3) and assuming the period-luminosity relations:

〈𝑀R 〉 = −2.91 (log (

𝑃

𝑃

) − 1) − 4.04 and 〈𝑀I 〉 = −3.00 (log (day) − 1) − 4.06

day

where 〈𝑀R 〉 and 〈𝑀I 〉 are the mean absolute magnitudes in filters R and I, find 𝐴R for objects in IC 342. Find the distance to IC 342.

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Table 5 BVRIJHKLMN photometry of two stars in Cassiopeia MK class

Star

HD 4817 HD 11092

K3Iab K4II

𝐵 mag

𝑉 mag

𝑅 mag

𝐼 mag

𝐽 mag

𝐻 mag

𝐾 mag

𝐿 mag

𝑀 mag

𝑁 mag

8.08 8.66

6.18 6.57

4.73 -

3.64 -

2.76 3.10

1.86 2.14

1.54 1.63

1.32 1.41

1.59 1.65

1.44

Table 6 (𝐵 − 𝑉)0 intrinsic colours for selected sp. types and luminosity classes (𝐵 − 𝑉)0 mag

II 0.73 1.06 1.40 1.42

F0 G0 K0 K3 K4

Iab / Ia 0.15 0.82 1.18 1.42 1.50

Table 7 Infrared intrinsic colours for selected sp. types of supergiant stars

F0 G0 K0 K3 K4

(𝑉 − 𝑅)0 mag

(𝑉 − 𝐼)0 mag

(𝑉 − 𝐽)0 mag

(𝑉 − 𝐻)0 mag

(𝑉 − 𝐾)0 mag

(𝑉 − 𝐿)0 mag

(𝑉 − 𝑀)0 mag

(𝑉 − 𝑁)0 mag

0.20 0.55 0.95 1.13 1.20

0.31 0.90 1.59 1.96 2.13

0.36 1.14 2.01 2.41 2.59

0.51 1.52 2.64 3.14 3.37

0.60 1.71 2.80 3.25 3.44

0.64 1.72 2.87 3.39 3.62

0.65 1.72 2.79 3.25 3.46

0.82 1.98 3.14 3.63 3.84

Table 8 Infrared intrinsic colours for selected sp. types of giant stars

K0 K3 K4

(𝑉 − 𝑅)0 mag

(𝑉 − 𝐼)0 mag

(𝑉 − 𝐽)0 mag

(𝑉 − 𝐻)0 mag

(𝑉 − 𝐾)0 mag

(𝑉 − 𝐿)0 mag

(𝑉 − 𝑀)0 mag

(𝑉 − 𝑁)0 mag

0.60 0.86 0.96

1.03 1.39 1.61

1.23 1.84 2.16

1.72 2.40 2.77

1.94 2.69 3.05

1.97 2.82 3.22

1.90 2.70 3.08

1.92 2.73 3.02

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〈𝑅〉

Fig. 2 〈𝑅〉 is the mean apparent magnitude in filter R Table 9 Effective wavelengths of selected photometric filters Filter 𝜆F /nm

B 450

V 555

R 670

I 870

J 1200

H 1620

K 2200

L 3500

M 5000

N 9000

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〈𝐼〉

Fig. 3 〈𝐼〉 is the mean apparent magnitude in filter I

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