AdvancedIOAA 2015 | Central Java, Indonesia | Data Analysis Problem 2

2015 P2 | The extinction law and the distance to IC 342

BVRIJHKLMN photometry of two stars in Cassiopeia is given in Table 1. For both stars the light is believed to be affected only by extinction in the diffuse interstellar medium (ISM). Assume the observations are made from outside the atmosphere.

(a) Using Tables 1 to 5, plot $E_{X-V}/E_{B-V}$ as a function of $1/\lambda_X$ for the filters B, V, R, I, J, H, K, L, M, N for both stars. Fit approximate curves by eye (note in particular that $E_{X-V}/E_{B-V}$ tends to a constant as $1/\lambda_X\to0$ ). X is each band of the photometric system.

(b) Using these graphs, estimate $R_V = A_V/E_{B-V}$ for each star.

Now apply these results to derive a distance to IC 342, a spiral galaxy in Cassiopeia obscured by the Milky Way. Assume the ISM along this line of sight has the same properties as in (a) and (b).

(c) The paper gives period–magnitude diagrams for 20 Cepheids in IC 342 in R and I. Read at $\log(P/{\rm day}) = 1.6$ , the fitted lines give $\langle R\rangle \approx 23.2$ and $\langle I\rangle \approx 22.7$ . Assuming the period–luminosity relations

\langle M_R\rangle = -2.91\left(\log\frac{P}{\rm day} - 1\right) - 4.04, \qquad \langle M_I\rangle = -3.00\left(\log\frac{P}{\rm day} - 1\right) - 4.06,

find $A_R$ for objects in IC 342 and the distance to IC 342.

Table 1 | Photometry of two stars in Cassiopeia (mag)

Star	MK class	B	V	R	I	J	H	K	L	M	N
HD 4817	K3 Iab	8.08	6.18	4.73	3.64	2.76	1.86	1.54	1.32	1.59	–
HD 11092	K4 II	8.66	6.57	–	–	3.10	2.14	1.63	1.41	1.65	1.44

Table 2 | Intrinsic

(B-V)_0

(mag)

Type	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 3 | Intrinsic colours of supergiants (mag)

Type	$(V-R)_0$	$(V-I)_0$	$(V-J)_0$	$(V-H)_0$	$(V-K)_0$	$(V-L)_0$	$(V-M)_0$	$(V-N)_0$
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 4 | Intrinsic colours of giants (mag)

Type	$(V-R)_0$	$(V-I)_0$	$(V-J)_0$	$(V-H)_0$	$(V-K)_0$	$(V-L)_0$	$(V-M)_0$	$(V-N)_0$
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 5 | Effective wavelengths

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

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