2011-05-17 16:02:45
The transit of exoplanet HD 209458b calls into question models of stellar atmospheres
The exoplanet HD 209458b is, since its discovery by D. Charbonneau and collaborators (2000), a special extrasolar planet. It was the first in a series of exoplanets discovered by the transit technique. This technique is based on the fact that the planet, when making transits over the disk of its mother star, subtracts light (very little, of course) from it and this loss can be detected by current instruments. A curiosity that may be interesting for Astrophysics fans is that the mother star of HD 209458b can be seen with binoculars in the Pegasus constellation since this is a magnitude 7 star (it is about 150 light-years away). our solar system).
The mass of HD 209458b is 0.7 times the mass of Jupiter or about 220 times the mass of Earth and its year is about 3.5 days. Its radius is 1.3 times the radius of Jupiter. Due to its proximity to the mother star, its temperature is high (1100 K) and signs of evaporation of its atmosphere have been detected, due to the irradiation effect of the star.
But the curiosities of our exoplanet do not end here: its atmosphere was the first to be characterized and traces of Oxygen and Carbon have been found. More recently, Barman (2007) announced that he had detected water vapor in the exoplanet’s atmosphere. It is a very difficult measurement to carry out and depends, among other factors, on the models adopted. Such a result must be taken with caution since the study of the transit of HD 209458 reveals to us, as we will see later, that some models used in its analysis present some problems. The investigation of the transit of an exoplanet follows, roughly speaking, the same techniques. used in the study of eclipsing binary stars. In a certain sense, transits are easier to analyze since the mass of the planet is much lower and it is much colder than the parent star and its light does not contribute to the total luminosity of the whole. Furthermore, we only have to study the irradiation of the mother star on the planet and not the mutual irradiation, as occurs in eclipsing binaries. The shape of the transit depends on how the star’s light is distributed in its disk. Such an effect is called limb-darkening, or edge-darkening. If we could look closer at a star, we would see that its center is brighter than its edges. It is an effect due to the depth at which we look at the star: we see deeper (and hotter) layers when we look towards its center and shallower (and colder) layers towards the edges.
Well, this effect has a lot to say when an exoplanet transits in front of the disk of its mother star. We do not know how light is distributed in a star, so we have to use theoretical models of stellar atmospheres, which can give us this information. Using these models, we can calculate the theoretical light curve and infer some properties of exoplanets. If the light curve is of very good quality, we can even empirically derive the edge obscuration coefficients. About a year ago, we detected that these models presented certain problems when we compared the empirical coefficients of some eclipsing binaries with the theoretical values (Claret 2008). However, the data for these stars were scarce and scattered and did not allow us to draw a definitive conclusion about the validity or otherwise of the stellar atmosphere models. It was a hint, but only a hint.
A few months ago, one of our collaborators, J. Southworth (2008), analyzed the transit of HD 209458b. The light curve was obtained using the Hubble space telescope (Figure 1) and is one of the best so far obtained for exoplanets. Such quality made it possible to infer the darkening coefficients towards the edge empirically. From his analysis comes the same clue found by us using the eclipsing binaries although this was not the main objective of his work. We decided to attack the problem with more sophisticated theoretical tools, such as monochromatic calculations (on a single wavelength, instead of filters) and more geometrically and physically sophisticated models of atmospheres (Claret 2009).
Now we had more elements to analyze the real situation of the stellar atmosphere models: instead of the usual observations with 4 filters, we had 10 observations covering a wide spectral sector: from 320 to 980 nanometers. There are several possible causes to explain a disagreement between the theoretical and empirical edge darkening coefficients: 1) the type of function used for modeling. 2) observational errors related to the mother star. 3) intrinsic problems in atmosphere models. The linear and quadratic approximations are used to describe how the intensity is distributed over the stellar disk. The linear approximation can be discarded when we have observations of very good quality, as is the present case. We also analyze the influence of the errors on the gravity and effective temperature of the parent star and these error bars are not large enough to explain the disagreement.
The remaining explanation is related to the ability of stellar atmosphere models to describe the distribution of intensities. We used more sophisticated models with spherical geometry and the discrepancies persisted (Figure 3). So, eliminating the other possible causes, we can conclude that the current models of stellar atmosphere models are not capable of predicting with the necessary precision how the intensities are distributed throughout the stellar disk, at least for the range of the effective temperature of the mother-star (Claret 2009).
Such a result indicates that there are systematic errors in the masses and mainly in the radii of the exoplanets studied. For example, the error bars on the radius ratio may be 3-5 times what is published. The problems detected in atmosphere models can also have consequences in other key fields of Astrophysics that depend on their use (which are many and varied). It would be interesting to check the validity of atmosphere models in the various areas of Astrophysics and confirm (or not) the discrepancies described here.
References:
Barman, T. 2007, Astrophysical Journal, 661, 191
Claret, A. 2009, Astronomy & Astrophysics, in press
Claret, A. 2008, Astronomy & Astrophysics, 482, 259
Claret, A., Hauschildt, P. H. 2003, Astronomy & Astrophysics, 412, 91
Southworth, J. 2008, Monthly Notices of the Royal Astronomical Society, 386, 1644
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