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This article is an erratum for:

Volume 552, April 2013
Article Number C1
Number of page(s) 1
Section Planets and planetary systems
Published online 01 April 2013

© ESO, 2013

It was recently brought to our attention (Kopparapu et al. 2013) that in our original paper (von Paris et al. 2010), we stated an incorrect equation for the calculation of the H2O Rayleigh scattering coefficient σray,H2O. Equation (3) in von Paris et al. (2010) shows a r(λ)4 dependence of σray,H2O, where r(λ) is the wavelength-dependent refractivity of H2O. Instead, as stated in Allen (1973), it should be a r(λ)2 dependence. Therefore, the correct equation (σray,H2O in cm2) reads (1)where D is the depolarization ratio and λ the wavelength in μm. Our work assumes D = 0.17 from Marshall & Smith (1990). The refractivity is calculated as r(λ) = 0.85rdryair(λ) (Edlén 1966). The refractivity of dry air (rdryair(λ) = ndryair(λ) − 1) is obtained from an approximate formula for the refractive index ndryair(λ) given by Bucholtz (1995). With this equation, we calculate 2.6 × 10-27  cm2 for the H2O Rayleigh scattering cross-section at 0.6 μm, close to the value of 2.32 × 10-27 cm2 from Selsis et al. (2007) or 2.5 × 10-27 cm2 from Kopparapu et al. (2013).

The numerical factor 4.577 × 10-21 in Eq. (1) is derived from Allen (1973) in the following way: Allen (1973) states that the Rayleigh cross-section is (2)where σray is in cm2 and λ is in μm. N is the number of particles per unit volume, and we took, as stated in Allen (1973),

standard temperature and pressure conditions (T = 273.1 K, p = 1.013 bar). This yielded 4.577 × 10-37 for the wavelength-independent factor in Eq. (2). Since N has units of cm-3 and the cross section is in cm2, one must then transform λ from μm to cm, i.e. multiply by 10-4. To the 4th power, this is 10-16, which then results in the factor 4.577 × 10-21, as stated in Eq. (1).

The correct equation (Eq. (1)) was implemented in the model code, hence the calculations of the H2O Rayleigh scattering were treated correctly in the model used by von Paris et al. (2010). Therefore the results reported in von Paris et al. (2010) are not affected.

The equation for H2O Rayleigh scattering reported in Kopparapu et al. (2013, their Eq. (1)) is incorrect. Hence, their statement that “the coefficient in the Rayleigh scattering cross section given in von Paris et al. (2010) should be seven orders of magnitude smaller” (Kopparapu et al. 2013) is also incorrect. We have contacted the authors of Kopparapu et al. (2013) about this, and they subsequently changed the online version (arXiv:1301.6674v2) to correct their equation and the corresponding text, however we point out that the printed journal version remains unchanged.


  1. Allen, C. 1973, Astrophys. Quant. (The Athlone Press, University of London) [Google Scholar]
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