Issue 
A&A
Volume 552, April 2013



Article Number  C1  
Number of page(s)  1  
Section  Planets and planetary systems  
DOI  https://doi.org/10.1051/00046361/201015329e  
Published online  01 April 2013 
The extrasolar planet Gliese 581 d: a potentially habitable planet? (Corrigendum)
^{1}
Institut für Planetenforschung, Deutsches Zentrum für Luft und Raumfahrt,,
Rutherfordstr. 2,
12489
Berlin,
Germany
email:
philip.vonparis@dlr.de
^{2}
Zentrum für Astronomie und Astrophysik, Technische Universität
Berlin, Hardenbergstr.
36, 10623
Berlin,
Germany
We report here that the equation for H_{2}O Rayleigh scattering was incorrectly stated in the original paper. Instead of a quadratic dependence on refractivity r, we accidentally quoted an r^{4} dependence. Since the correct form of the equation was implemented into the model, scientific results are not affected.
Key words: astrobiology / planets and satellites: atmospheres / planetary systems / stars: individual: GL 581 / errata, addenda / planets and satellites: individual: GL 581 d
© 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 H_{2}O Rayleigh scattering coefficient σ_{ray,H2O}. Equation (3) in von Paris et al. (2010) shows a r(λ)^{4} dependence of σ_{ray,H2O}, where r(λ) is the wavelengthdependent refractivity of H_{2}O. Instead, as stated in Allen (1973), it should be a r(λ)^{2} dependence. Therefore, the correct equation (σ_{ray,H2O} in cm^{2}) 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) = 0.85r_{dryair}(λ) (Edlén 1966). The refractivity of dry air (r_{dryair}(λ) = n_{dryair}(λ) − 1) is obtained from an approximate formula for the refractive index n_{dryair}(λ) given by Bucholtz (1995). With this equation, we calculate 2.6 × 10^{27} cm^{2} for the H_{2}O Rayleigh scattering crosssection at 0.6 μm, close to the value of 2.32 × 10^{27} cm^{2} from Selsis et al. (2007) or 2.5 × 10^{27} cm^{2} 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 crosssection is (2)where σ_{ray} is in cm^{2} 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 wavelengthindependent factor in Eq. (2). Since N has units of cm^{3} and the cross section is in cm^{2}, 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 H_{2}O 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 H_{2}O 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 arxiv.org version (arXiv:1301.6674v2) to correct their equation and the corresponding text, however we point out that the printed journal version remains unchanged.
References
 Allen, C. 1973, Astrophys. Quant. (The Athlone Press, University of London) [Google Scholar]
 Bucholtz, A. 1995, Appl. Opt., 34, 2765 [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
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 Kopparapu, R., Ramirez, R., Kasting, J., et al. 2013, ApJ, 765, 131 [NASA ADS] [CrossRef] [Google Scholar]
 Marshall, B. R., & Smith, R. C. 1990, Appl. Opt., 29, 71 [NASA ADS] [CrossRef] [PubMed] [Google Scholar]
 Selsis, F., Chazelas, B., Bordé, P., et al. 2007, Icarus, 191, 453 [NASA ADS] [CrossRef] [Google Scholar]
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