= Solution
In <transit spectroscopy>, starlight passes tangentially through the <planet>'s terminator atmosphere during primary transit. Wavelength-dependent <opacity> changes the effective occulting <radius>. For a thin atmosphere with an absorption feature spanning $N_H$ <atmospheric scale heights>,
$$
H=\frac{k_BT}{\mu m_Hg},\qquad\boxed{\Delta\delta_{\rm tr}\sim\frac{2R_pN_HH}{R_\star^2}.}
$$
Here $\mu$ is the mean particle <mass> in units of $m_H$, not a chemical potential. Large planets with warm low-<gravity>, low-molecular-weight atmospheres against small stars have larger signals. A spherical isothermal atmosphere has tangential column enhancement of order $\sqrt{2\pi R_p/H}$ over a vertical column, explaining sensitivity to tenuous high-altitude <gas>. Molecular bands, atomic lines, scattering slopes and clouds constrain the terminator, but cloud <opacity>, reference <pressure> and abundance-<temperature> degeneracies limit unique retrievals.<Theoretical Transmission Spectra During Extrasolar Giant Planet Transits by Sara Seager and Dimitar Sasselov>[Atmospheric absorption superimposed on transmitted stellar light and the small annular area]{ref}
<Occultation spectroscopy> instead subtracts the <star>-only spectrum during secondary eclipse from the <star>-plus-<planet> spectrum immediately outside eclipse. It measures the dayside <planet>/<star> flux ratio. In the blackbody approximation the <thermal eclipse depth> is
$$
\boxed{\delta_{\rm th}(\lambda)\simeq\left(\frac{R_p}{R_\star}\right)^2\frac{B_\lambda(T_p)}{B_\lambda(T_\star)}.}
$$
Longer infrared wavelengths generally improve contrast for a cooler <planet>; molecular absorption or emission depends on the vertical <temperature> gradient. At optical wavelengths reflected light can dominate, with full-phase contrast $A_g(\lambda)(R_p/a)^2$, where $A_g$ is <geometric albedo>. Eclipse spectra therefore probe dayside emission or reflection, rather than the transit's slant absorption. Clouds and <temperature> inversions affect interpretation.<Exoplanet emission spectrum>{ref}
For either measurement, the photon-limited <signal-to-noise ratio> scales as the spectral feature amplitude times $\sqrt{N_\gamma}$, with a penalty for subtracting finite in- and out-of-event samples. Finer spectral bins reduce photons per bin; bright hosts, repeated events and stable instruments improve sensitivity. Detector systematics, telluric absorption for ground observations, and variable starspots can limit the practical gain. Space observations remove telluric contamination, not stellar variability or instrumental drift. Neither technique directly measures a unique bulk composition or samples all longitudes of the <planet>.
\Image[/past-exam-of-the-exoplanets-and-planetary-systems-course-of-the-university-of-cambridge/2015/paper-1-atmospheric-spectroscopy.png]
{title=Transmission isolates a thin atmospheric annulus, while occultation isolates the planet's dayside flux}
{source=paper-1-atmospheric-spectroscopy.py}
Back to article page
