Dusty tails of evaporating exoplanets - II. Physical modelling of the KIC 12557548b light curve

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Table 5

Parameters of the dust species considered in this study.

Dust species

Density

Complex refractive index^a

Sublimation parameters^h

ρ _d

log ₁₀(k₁)

Refs.

ℬ′

log ₁₀(J_{1700 K})

Refs.

[g cm^-3]

[10⁴ K]

[cgs]

Iron (Fe)

7.87

3.5^b

0.50 ± 0.50 ^c

O88

4.84 ± 0.12

31.3 ± 0.7

− 4.8 ± 0.4

F04

Silicon monoxide (SiO)

2.13

1.9

see note (d)

P85, W13

4.95 ± 0.14

31.2 ± 1.0

− 5.1 ± 0.6

G13

Cryst. fayalite (Fe₂SiO₄)

4.39

1.8

− 2.25 ± 0.25

Z11, F01

6.04 ± 0.11

38.1 ± 0.7ⁱ

− 4.8 ± 0.4

N94

Cryst. enstatite (MgSiO₃)

3.20

1.6^e

− 4.25 ± 0.25 ^e

D95, J98

6.89 ± 0.88

37.8 ± 5.0ⁱ

− 7.1 ± 3.1

M88, K91

Cryst. forsterite (Mg₂SiO₄)

3.27

1.6

− 3.75 ± 0.25

Z11, F01

6.53 ± 0.40

34.3 ± 2.5

− 7.8 ± 1.5

G10, N94

Quartz (SiO₂)

2.60

1.6^f

− 3.25 ± 0.25 ^f

Z13

6.94 ± 0.34

35.1 ± 1.8

− 8.5 ± 1.2

H90

Corundum (Al₂O₃)

4.00

1.6^g

− 1.75 ± 0.25 ^c^g

K95

7.74 ± 0.39^j

39.3 ± 2.0^j

− 8.7 ± 1.3

S04, L08

Silicon carbide (SiC)

3.22

2.5

− 3.50 ± 0.25

La93

7.85 ± 0.39^j

37.4 ± 1.9ⁱ^j

− 9.8 ± 1.3

Li93

Graphite (C)

2.16

3.2^b

− 0.25 ± 0.50

D84

9.36 ± 0.05

36.2 ± 1.8ⁱ^j

− 14.2 ± 0.8

Z73

Notes. The list only includes crystalline species because amorphous dust is expected to anneal rapidly (see Sect. 4.2.3 of Kimura et al. 2002).

^(a)

See text and Appendix B on how the values for n and k₁ were derived from the wavelength-dependent complex-refractive-index data.

^(b)

For iron and graphite, n(λ) steadily rises in the wavelength regime considered (see Fig. B.1).

^(c)

For iron and corundum, the best-matching k₁ values give temperatures that are slightly too low (see Appendix B).

^(d)

Our two-parameter complex-refractive-index recipe cannot reproduce the T_d(s) profile of SiO (see Appendix B).

^(e)

The optical properties at wavelengths below 8 μm use amorphous enstatite.

^(f)

The n(λ) and k(λ) data we use for quartz only cover wavelengths of 3 μm and higher. To compute n and k₁, these were extrapolated down.

^(g)

The data of Koike et al. (1995) were obtained using a material consisting mostly of γ-Al₂O₃, while corundum is α-Al₂O₃.

^(h)

Additional notes and details on the sublimation parameters can be found in Table 3 of Paper I.

⁽ⁱ⁾

For these materials, no measurements of the evaporation coefficient α are available. In the computation of ℬ′, we arbitrarily adopt α = 0.1.

^(j)

For sublimation parameters without a reported uncertainty, we set the standard deviation on and/or ℬ to 5%, which is comparable to the level of uncertainty of sublimation parameters that do include an error bar.

Reference. D84: Draine & Lee (1984); D95: Dorschner et al. (1995); F01: Fabian et al. (2001); F04: Ferguson et al. (2004); G10: Gail (2010); G13: Gail et al. (2013); H90: Hashimoto (1990); J98: Jaeger et al. (1998); K91: Kushiro & Mysen (1991); K95: Koike et al. (1995); La93: Laor & Draine (1993); Li93: Lilov (1993); L08: Lihrmann (2008); M88: Mysen & Kushiro (1988); N94: Nagahara et al. (1994); O88: Ordal et al. (1988); P85: Palik (1985); S04: Schaefer & Fegley (2004); W13: Wetzel et al. (2013); Z73: Zavitsanos & Carlson (1973); Z11: Zeidler et al. (2011); Z13: Zeidler et al. (2013).

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