Primary transits

The primary transit by an extrasolar planet, in which the planet passes between its parent star and the Earth, is useful for several reasons. The light curves from such transits have been used to estimate gross properties of all of the presently known transiting planets and of their stars, measuring the stellar and planetary radii, the inclination of the planets' orbit, and the strength of limb darkening on the stars. Moreover, for the two nearest transiting planets, more-or-less successful attempts have been made to use the variations with wavelength in the depth of the observed transits to learn about the composition of the planets' atmospheres. I shall further discuss all of these results below. In addition to these measurements, one can use radial velocity measurements taken during the primary transit to infer the inclination of the planetary orbital axis to the rotational axis of its star (e.g., Winn et al. 2005). Although this procedure (based on the Rossiter-McLaughlin effect) is very interesting, I shall not discuss it further here.

4.1. Bulk properties

As described in the introduction, the observed transit light curves may be parameterized (conceptually, at least) in terms of four quantities: the transit duration, its depth (measured relative to the out-of-transit intensity of the star), the duration of the ingress and egress phases of the transit, and the curvature of the light curve between the end of ingress and the beginning of egress. This parameterization is useful for achieving an intuitive understanding of how light curve properties relate to those of the star/planet system, and, in fact, it is the basis for a helpful technique for distinguishing between true planetary transits and false alarms (which merely resemble planetary transits) involving grazing eclipses or multiple-star systems (Seager & Mallen-Ornelas 2003).

To obtain numerical estimates of planetary properties, however, one usually bypasses the approximations inherent in the four-element parameterization. Rather, one performs a suitable error-weighted fit to the photometric and radial velocity observations, adjusting the parameters of a detailed numerical model so as to minimize the mismatch with observed data. The most significant parameters to emerge from these fits are, of course, the planetary masses and radii. The relation between them is shown in Figure 5, for all of the transiting planets known as of this writing (1 Sept. 2005). This figure is a compilation of results from Brown et al. (2001); Udalski et al. (2002a,b); Konacki et al. (2003, 2005); Moutou et al. (2004); Alonso et al. (2004); Sozzetti et al. (2004); Pont et al. (2004), and Sato et al. (2005), with photometry and radial velocities coming from a wide variety of sources. There is a fairly clear distinction between the OGLE planets (which, because they are faint, show relatively large uncertainties in both mass and radius) and the planets of brighter stars (HD 209458b, TrES-1, and HD 149026b, for which the uncertainties are smaller). The radius uncertainties are not, however, tremendously different between the two sets of stars. The reason is that, beyond a certain level of precision, uncertainties

Figure 5. Observed mass/radius relation for transiting extrasolar planets. The observed mean densities are mostly consistent with hydrogen/helium gas giants that lack significant internal energy sources. Exceptions are HD 209458b, which is less dense than predicted for such objects, and HD 149026b, which is more dense.

Figure 5. Observed mass/radius relation for transiting extrasolar planets. The observed mean densities are mostly consistent with hydrogen/helium gas giants that lack significant internal energy sources. Exceptions are HD 209458b, which is less dense than predicted for such objects, and HD 149026b, which is more dense.

in the planetary radius are dominated by uncertainties in the radius of the parent star. With superb photometry (as is obtainable with HST, for instance) it is possible to estimate the stellar and planetary radii separately, but the stellar radius estimate remains fairly imprecise. Thus, in these cases the ratio Rp/Rt is much better known than either individual value.

Most of the planets shown in Figure 5 have radii that are in fairly close agreement with theoretical predictions—assuming that the planets have near-solar composition, migrated near to their stars early in their lives, and contain no significant internal energy sources (e.g., Bodenheimer et al. 2003; Burrows et al. 2004; Chabrier et al. 2004, but also see Gaudi 2005). Exceptions are HD 209458b (and possibly 0GLE-Tr-10b), which are larger than theory predicts, and HD 149026b, which is smaller. The latter object has roughly Saturn's mass, but considerably higher density, in spite of orbiting very close to its star. It is possible to explain this high density by assuming that the planet contains a very large core of material with high atomic weight (60-80 Earth masses, as compared to a total planetary mass of only about 100 Earth masses; Sato et al. 2005). The error bars associated with 0GLE-Tr-10b are large enough that its size might agree with theoretical predictions, and recent observations by Holman et al. (2007) indicate that this is actually the case. HD 209458b, on the other hand, is still thought to be anomalously large for its mass, and the reason remains obscure.

A favored generic method for producing large planetary radii is to invoke an internal energy source. One possible source is the dissipation of waves generated by vigorous near-surface flows, which in turn might be driven by the large dayside-to-nightside difference in stellar energy flux (Guillot & Showman 2002). Details of the generation and dissipation mechanisms are unclear, however. One must also ask why, if such a mechanism works efficiently on HD 209458b, it does not do so on any other planet. A different suggestion is that the heat-input method for close-in giant planets requires the presence of another large planet in the system, one able to pump up the eccentricity of the known planet's orbit, which can then cause internal energy dissipation via tidal dissipation. But in the

Figure 6. Theoretical transit spectra of HD 209458b from Brown (2001), showing the effect of varying the height of an opaque cloud deck. The spectrum features arise mostly from the pressure-broadened lines of alkali metals, and from molecules of H2O, CO, and (to a small extent) CH4.

case of HD 208458b, there is no radial velocity evidence for a second large planet (Mazeh et al. 2000; Naef et al. 2004), and timing measurements of the secondary eclipse (described below) show that either its orbital eccentricity is very small, or that Earth lies very near to its orbital major axis (Deming et al. 2005). The reason for HD 209458b's large radius thus remains mysterious.

As described above, atomic or molecular species that have strong absorption lines will cause a transiting planet to appear larger at absorbing wavelengths than at nearby wavelengths, where the opacity is smaller. Many of the strong molecular bands that are expected in the atmospheres of hot Jupiters arise from H2O and CH4, molecules that are also fairly abundant in the Earth's atmosphere. Thus, telluric obscuration makes these bands difficult to detect from the ground (though the possibility of detecting signals from relatively high-excitation molecular lines should not be discounted—see, e.g., Carr et al. 2004). There are, however, a few species with strong lines that are not fatally contaminated by telluric absorption; these include the alkali metals (especially Na) and the CO molecule.

Sodium is a minor constituent of the Sun, with an abundance of roughly 2 x 10~6 by number relative to hydrogen. The opacity of the Na D resonance lines is so large, however, that they are expected to be two of the most prominent lines in the atmosphere of a hot Jupiter. They are also strongly susceptible to pressure broadening, so that at pressures of a bar or so, the pressure-broadened wings of the D lines are the dominant source of opacity for a wide range of wavelengths around the lines themselves. At lower pressures the lines become much narrower. Thus, barring some process that removes neutral sodium atoms from the atmosphere, these lines are expected to be opaque to tangential rays up to heights of perhaps 5000 km (6% of the planetary radius) above the one bar level. In the absence of clouds, the equivalent width of the resulting transmission spectrum features could be quite large, as shown in the top trace in Figure 6.

Motivated by these considerations, Charbonneau et al. (2002) used the wavelength-resolved transit photometry measurements taken with HST to measure the difference in transit depth between three increasingly broad regions surrounding the Na D lines and the surrounding continuum. They succeeded in detecting increased absorption in the D lines, but with an increase of transit depth of only (2.32 ± 0.57) x 10~4 (compared to a total transit depth of 0.0165). The increase in transit depth was measured to be largest in the smallest (1.2 nm wide) wavelength band analyzed, smaller in the intermediate (3.8 nm wide) band, and undetectable in the largest (10 nm wide) band. In the narrowest band, the increase in transit depth was about 0.5 times that expected from a "fiducial" model with a cloud deck topping out at 0.03 bar, indicated by the trace labeled ".1" on Figure 6. This observation remains the only statistically significant (4a) measurement of a spectral feature in the transit spectrum of an extrasolar planet. This fact alone should motivate further work on observational transit spectroscopy, though from ground-based telescopes the difficulties involved in such measurements are formidable.

Clouds are not the only mechanism that could result in weak Na D lines. Any process that reduces the abundance of atoms in the lower state of the D line transitions would also reduce the absorption. The magnitude of the Na depletion would have to be quite large, however, by virtue of Eq. (2.2). Indeed, to reduce the equivalent width of the Na feature by the observed factor of two would require depleting the Na abundance by a factor of about 100. Nevertheless, a variety of mechanisms for generating such a depletion have been suggested, including low initial abundance of all heavy elements, and combination of Na atoms to form molecules (such as Nal) that might exist in the solid phase and ultimately rain out of the upper parts of the atmosphere. Perhaps the mechanism that has been best studied quantitatively removes atoms from the D line lower state via non-LTE effects, driven by short-wavelength radiation from the star (Barman et al. 2002). This study suggests that non-LTE corrections to the atomic level populations may be important, particularly high in the atmosphere. The radiative transfer model used is not directly applicable to the transit geometry, however, so some caution is required in interpreting the results.

Among the various molecular features that can be identified in the synthetic spectrum in Figure 6, the most prominent in the wavelength range 1.0 ¡m ^ A ^ 2.5 ¡m are caused by H2O. Because of the already-mentioned time-varying extinction from telluric water vapor, serious efforts to observe any of these molecular bands have so far been made only from space. Grism observations of three transits of HD 209458b searching for H2O absorption near A = 1.5 ¡m using NICMOS on HST have recently been executed. Analysis of these data is underway, but no results are yet reported.

The next most promising molecular signature in the NIR part of the spectrum is the CO bandhead near 2.2 ¡m. Although the concentration of CO in the Earth's atmosphere is low enough that it does not cause significant extinction, observations of the CO band are nevertheless severely hampered by overlying lines of CH4 and H2O. Two attempts to detect the CO band in the transit spectrum of HD 209458b have been carried out using the NIRSPEC spectrometer on the Keck II telescope. The first of these was hampered by poor weather, and gave an upper limit on the CO band strength that was larger even than that predicted by cloud-free models (Brown et al. 2002). Although astrophys-ically uninteresting, these observations suggested that with improved techniques and better weather, a meaningful measurement might be obtained. This goal was achieved by Deming et al. (2005a), who used the same equipment (but with an improved observing strategy) to set an upper limit on the band strength that is smaller by a factor of about six than that predicted by models with clouds up to 0.03 bar. To account for the observed upper limit on band absorption, it is again necessary either to increase the cloud-top height to 3.3 mb or higher, or to invoke some mechanism to drastically reduce the mixing ratio of CO in the planet's upper atmosphere.

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