IOAA 2015, data-analysis — Задача 2. Problem 2

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

Условие

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.

Table 5 BVRIJHKLMN photometry of two stars in Cassiopeia

Star	MK class	$\dfrac{B}{\mathrm{mag}}$	$\dfrac{V}{\mathrm{mag}}$	$\dfrac{R}{\mathrm{mag}}$	$\dfrac{I}{\mathrm{mag}}$	$\dfrac{J}{\mathrm{mag}}$	$\dfrac{H}{\mathrm{mag}}$	$\dfrac{K}{\mathrm{mag}}$	$\dfrac{L}{\mathrm{mag}}$	$\dfrac{M}{\mathrm{mag}}$	$\dfrac{N}{\mathrm{mag}}$
HD 4817	K3Iab	8.08	6.18	4.73	3.64	2.76	1.86	1.54	1.32	1.59	-
HD 11092	K4II	8.66	6.57	-	-	3.10	2.14	1.63	1.41	1.65	1.44

Table 6 $(B-V)_0$ intrinsic colours for selected sp. types and luminosity classes

	$\dfrac{(B-V)_0}{\mathrm{mag}}$
	II	Iab / Ia
F0	-	0.15
G0	0.73	0.82
K0	1.06	1.18
K3	1.40	1.42
K4	1.42	1.50

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

	$\dfrac{(V-R)_0}{\mathrm{mag}}$	$\dfrac{(V-I)_0}{\mathrm{mag}}$	$\dfrac{(V-J)_0}{\mathrm{mag}}$	$\dfrac{(V-H)_0}{\mathrm{mag}}$	$\dfrac{(V-K)_0}{\mathrm{mag}}$	$\dfrac{(V-L)_0}{\mathrm{mag}}$	$\dfrac{(V-M)_0}{\mathrm{mag}}$	$\dfrac{(V-N)_0}{\mathrm{mag}}$
F0	0.20	0.31	0.36	0.51	0.60	0.64	0.65	0.82
G0	0.55	0.90	1.14	1.52	1.71	1.72	1.72	1.98
K0	0.95	1.59	2.01	2.64	2.80	2.87	2.79	3.14
K3	1.13	1.96	2.41	3.14	3.25	3.39	3.25	3.63
K4	1.20	2.13	2.59	3.37	3.44	3.62	3.46	3.84

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

	$\dfrac{(V-R)_0}{\mathrm{mag}}$	$\dfrac{(V-I)_0}{\mathrm{mag}}$	$\dfrac{(V-J)_0}{\mathrm{mag}}$	$\dfrac{(V-H)_0}{\mathrm{mag}}$	$\dfrac{(V-K)_0}{\mathrm{mag}}$	$\dfrac{(V-L)_0}{\mathrm{mag}}$	$\dfrac{(V-M)_0}{\mathrm{mag}}$	$\dfrac{(V-N)_0}{\mathrm{mag}}$
K0	0.60	1.03	1.23	1.72	1.94	1.97	1.90	1.92
K3	0.86	1.39	1.84	2.40	2.69	2.82	2.70	2.73
K4	0.96	1.61	2.16	2.77	3.05	3.22	3.08	3.02

Table 9 Effective wavelengths of selected photometric filters

Filter	B	V	R	I	J	H	K	L	M	N
$\lambda_P$/nm	450	555	670	870	1200	1620	2200	3500	5000	9000

a) Using the data given in Tables 5 to 9, plot $E_{\mathrm{X-V}}/E_{\mathrm{B-V}}$ as a function of $1/\lambda_{\mathrm{X}}$ for filters B, V, R, I, J, H, K, L, M, N for both stars. Fit approximate curves by eye (in particular, note that $E_{\mathrm{X-V}}/E_{\mathrm{B-V}} \sim const.$ as $1/\lambda_{\mathrm{X}} \rightarrow 0$). X is each band in the photometric system.

b) Using the graphs obtained in a), estimate $R_{\mathrm{V}}$ for each star. $R_{\mathrm{V}} = \frac{A_{\mathrm{V}}}{E_{\mathrm{B-V}}}$ ($A_{\mathrm{V}}$ is the absorption in V, and $E_{\mathrm{B-V}}$ is the color excess)

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: $\langle M_{\mathrm{R}} \rangle = -2.91\left(\log\left(\frac{P}{\mathrm{day}}\right) - 1\right) - 4.04 \quad \mathrm{and} \quad \langle M_{\mathrm{I}} \rangle = -3.00\left(\log\left(\frac{P}{\mathrm{day}}\right) - 1\right) - 4.06$ where $\langle M_{\mathrm{R}} \rangle$ and $\langle M_{\mathrm{I}} \rangle$ are the mean absolute magnitudes in filters R and I, find $A_{\mathrm{R}}$ for objects in IC 342. Find the distance to IC 342.

Решение

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