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CRIRES is a high-resolution infrared spectrograph. Its upgraded form supports molecular spectroscopy of exoplanet atmospheres and measurements based on the Doppler effect. See ESO's instrument overview.

An exoplanet is a planet outside the Solar system; here the focus is on planets orbiting stars other than the Sun, including pulsars. Most exoplanets are detected indirectly: a star's changing Doppler shift reveals its motion, or a small dip in its light curve reveals an exoplanet transit. The striking idea is that an unresolved point of light can tell us about an otherwise unseen world's mass, radius, and orbit.

The measurements answer different questions. Exoplanet transit photometry primarily gives a radius ratio, while Doppler spectroscopy constrains mass together with orbital inclination. Combining them with the host star's properties gives a mean mass density, ${\bar{\rho }}_p=3M_p/(4\pi R_p^3)$, useful for exoplanet interior models. Even this combination does not uniquely determine composition: see exoplanet interior-composition degeneracy. Transit spectroscopy and an exoplanet secondary eclipse then probe an exoplanet atmosphere.

The discovery history has two distinct milestones. In 1992 Aleksander Wolszczan and Dale Frail reported two planet-mass companions to the pulsar PSR B1257+12 from periodic changes in pulse arrival times; their paper also suggested an additional companion. These were the first confirmed exoplanet discoveries, around a neutron star. ^[ref]. Wolszczan's contemporary conference account, archived by NASA, likewise distinguishes the two reported companions from a possible third. ^[ref].

In 1995 Michel Mayor and Didier Queloz discovered 51 Pegasi b through Doppler spectroscopy, the landmark first confirmed exoplanet around a Sun-like star. This was a hot Jupiter, not the first exoplanet of every kind: the earlier pulsar discoveries belong to a different host category. ^[ref]. NASA's contemporary account describes the confirmation and the approximately four-day orbital period. ^[ref].

A general circulation model evolves rotating fluid dynamics together with heating/cooling and suitable transport parameterizations. Atmospheric applications can couple radiative transfer, clouds and chemistry to resolve longitudinal and latitudinal structure. For an exoplanet atmosphere, it can predict winds and an exoplanet thermal phase curve. Unresolved turbulence and cloud microphysics still require approximate closures.

Methods of detecting exoplanets infer or resolve an exoplanet through its effects on the host star's light or through its own light. The observable determines what can be learned:

An exoplanet secondary eclipse measures the loss of the exoplanet's light when it passes behind its star, complementing exoplanet transit photometry. A detection method also selects which systems are easiest to find: deeper exoplanet transits favour larger radius ratios, and larger stellar radial-velocity semi-amplitudes favour more massive companions, shorter orbital periods, and larger $\sin i$. These preferences must be accounted for when inferring the underlying exoplanet population.

Interpret the quoted band amplitude as an absolute transit-depth increment $\Delta D=0.0003$, or $300$ parts per million. For a thin atmospheric annulus of extra height $\Delta z$, the atmospheric spectral-feature amplitude isLet the water band span $N_H$ atmospheric scale heights, so $\Delta z=N_{H}H$. For a nearly isothermal atmosphere with constant gravity and mean molecular weight $\mu$, $H=k_{B}T/(\mu m_{u}g)$. The temperature from a transmission-band amplitude is thereforeHere $T_0,H_0,{\mu }_0,g_0$ refer to the chosen Jupiter reference layer. Assuming $g=g_J\simeq 25\mathrm{m}{\mathrm{s}}^{-2}$, an H/He exoplanet atmosphere with $\mu \simeq 2.3$, and a clear strong band with $N_H\simeq 5$, gives $H\simeq 210\mathrm{km}$ and $T\simeq 1.4\times 10^3\mathrm{K}$. Equivalently, a Jovian reference with $T_0\simeq 165\mathrm{K}$ has $H_0\simeq 24\mathrm{km}$, giving $H/H_0\simeq 8.7$.

The assumptions are hydrostatic, approximately isothermal limb gas, constant gravity, negligible cloud truncation, H/He composition, and an effective opacity contrast yielding about five scale heights. In an ideal clear limb, $N_H\simeq \log ({\kappa }_{\mathrm{band}}/{\kappa }_{\mathrm{cont}})$ follows from the slant optical depth of an isothermal atmosphere. The data fix $N_{H}H$, not $H$ separately: the temperature is conditional on the band opacity contrast and composition. For $N_H=3$–$7$ with the same composition and gravity, the estimate is about $1000$–$2400\mathrm{K}$.

Three routes away from local thermochemical equilibrium are:

Vertical mixing, horizontal advection, and photochemistry supply three mechanisms and examples in both exoplanets and Solar-System atmospheres. A photochemical steady state balances production and loss; it is different from a Gibbs free energy minimum. These examples describe mechanisms and model expectations rather than asserting unique observational attribution for every planet.

For the two-zone cloudy annulus transmission model, assume a uniform stellar disc, an opaque planet below $R_p$, $0\le H_c\le H$, and constant total slant optical depth within each radial zone. Neglect scattered light entering the beam and the planet's own emission. A ray transmits the fraction $e^{-\tau }$, so each zone blocks its projected area multiplied by $1-e^{-\tau }$.

The opaque disc, cloudy annulus and clear annulus have areas $\pi R_p^2$, $\pi [(R_p+H_c{)}^2-R_p^2]$ and $\pi [(R_p+H{)}^2-(R_p+H_c{)}^2]$, respectively. Thus the exoplanet transmission spectrum, expressed as total transit depth, isHere ${\tau }_{\lambda ,c}$ means the total optical depth on rays assigned to the cloudy zone. If it denotes cloud extinction alone, its exponent must instead contain the sum of cloud and gas optical depths. For a geometrically thin exoplanet atmosphere, the two atmospheric prefactors become $2R_p{H}_c/R_s^2$ and $2R_p(H-H_c)/R_s^2$.

An opaque exoplanet cloud deck gives the simpler expressionThe exoplanet cloud deck raises the wavelength-independent occulting radius and suppresses the clear atmospheric contribution. If $H_c=H$, the spectrum is flat at $(R_p+H{)}^2/R_s^2$; if $H_c=0$, the ordinary annulus model for transmission spectroscopy is recovered. Stellar limb darkening and varying tangent-ray optical depth would require an intensity-weighted radial integral rather than this constant-depth model.

Assume that the optical continuum is dominated by Rayleigh scattering by particles much smaller than the wavelength, and that their column abundance is fixed. Their cross-section, hence the slant optical depth, scales as ${\tau }_{\lambda }\propto {\lambda }^{-4}$. Differentiating the annulus model for transmission spectroscopy exactly gives the logarithmic slope of total transit depthFor $A\ge 0$ and $B>0$, the slope lies between $-4$ and zero, but generally depends on wavelength. In the optically thin limit, ${\delta }_{\lambda }\simeq A+B{\tau }_{\lambda }$, so its slope is $-4B{\tau }_{\lambda }/(A+B{\tau }_{\lambda })$. It vanishes as the atmospheric signal becomes negligible compared with the opaque disc; it also approaches zero in the saturated optically thick limit.

The familiar value $m\simeq -4$ applies to the optically thin atmospheric excess,or formally to a model in which $A$ is negligible. For an ordinary thin exoplanet atmosphere, however, $B/A\simeq 2H/R_p\ll 1$, so neglecting the opaque planetary baseline in the total transit depth is not usually justified. A universal $m=-4$ for the logarithm of the total transit depth does not follow from the stated model.

In a stratified isothermal atmosphere, the related scattering slope of a transmission spectrum is instead $d{R}_{\mathrm{tr}}/d\ln \lambda =-4h$, obtained by moving the effective tangent level to keep its slant optical depth of order unity. Consequently $d\ln \delta /d\ln \lambda =-8h/R_{\mathrm{tr}}$ there. The radius slope, atmospheric-excess slope and total-depth slope are different observables.

The thermal optical depth increases inward, so an atmospheric thermal inversion requires $dT/d\tau <0$. Differentiating the semi-grey irradiated atmosphere profile givesTherefore the inversion criterion with intrinsic planetary flux isAn inverted layer exists at the top precisely whenFor $T_{\mathrm{int}}>0$, it extends overprovided the logarithm is positive. Otherwise the profile has no inverted interval. For a strongly irradiated hot Jupiter, $T_{\mathrm{int}}\ll T_{\mathrm{irr}}$ and the threshold is approximately $\gamma >1$; the intrinsic flux eventually restores an inward-increasing temperature at greater depth.

Large visible absorption opacity deposits stellar heat high in the exoplanet atmosphere. Gas-phase titanium monoxide and vanadium monoxide are candidate absorbers in sufficiently hot layers. An atmospheric cold trap or other condensate loss can remove them, while sufficiently high temperature and vigorous mixing can help keep them in the gas. The condition concerns absorbing opacity: highly reflective scattering alone does not deposit the required heat.

Thermal dissociation is temperature-driven breaking of a molecule into simpler fragments. The chemical equilibrium abundance depends on pressure as well as temperature: reactions increasing particle number are generally favored at low pressure. In an exoplanet atmosphere, reduced water on a very hot dayside does not by itself establish a low planetary oxygen abundance.

Transit spectroscopy infers the properties of an exoplanet atmosphere from the wavelength dependence of an exoplanet transit. Its measured product is an exoplanet transmission spectrum, while an annulus model for transmission spectroscopy connects the spectrum to atmospheric optical depth. The observing technique is described by NASA.