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The Advanced Camera for Surveys is an imaging instrument on the Hubble Space Telescope, designed with separate wide-field, high-resolution and ultraviolet channels. Filters select spectral bands; dispersing elements also provide low-resolution spectroscopy. The different channels have different detectors and optical paths, so the instrument name alone does not specify the relevant wavelength coverage.^[ref]

For an exoplanet transit, a sequence of dispersed images can be divided into spectral channels, each yielding its own light curve. Comparing fitted exoplanet transit depths constructs an exoplanet transmission spectrum. Detector response and pointing variations must be calibrated along with the planetary signal. Historical observations should be interpreted using the channel and observing mode actually employed.

Take a planet with opaque radius $R_p$ and an atmosphere of thickness $z\ll R_p$, projected against a uniform stellar disc of radius $R_{\star }$. If the atmospheric annulus has one representative slant optical depth ${\tau }_{\lambda }$, its additional transit depth isThe general exoplanet transmission spectrum instead uses an integral over impact parameter $b$,The annulus model replaces this varying slant opacity by an effective constant. The atmospheric signal scales with optical depth when optically thin and saturates at the annular area when opaque.

An atmospheric retrieval fits a parametrized radiative transfer model to an exoplanet transmission spectrum or exoplanet emission spectrum. Temperature, abundances, clouds and reference radius/pressure can trade off against one another. Posterior precision within one model is not proof that its structural assumptions are unique.

An exoplanet transmission spectrum measures a wavelength-dependent transit depth. In a simple opaque-disk geometry with uniform stellar brightness, an effective planetary radius $R_p$ gives $D=(R_p/R_{\ast }{)}^2$, where $R_{\ast }$ is the stellar radius. If stronger atmospheric absorption increases that radius by $\Delta R=N_{H}H$, define $H$ as the atmospheric scale height and $N_H$ as the number of scale heights separating the two spectral levels. The additional occulted annulus givesThe last approximation requires $N_{H}H\ll R_p$. For instance, $R_p/R_{\ast }=0.1$ and $N_{H}H/R_p=0.05$ give exact $\Delta D=0.001025$ and leading estimate $0.001$; these are stipulated geometric ratios.

Since $H=k_{B}T/(\mu m_{H}g)$ in the thin isothermal atmosphere model, larger temperature, smaller mean molecular weight or weaker gravity can increase the signal. The factor $N_H$ is set by the atmospheric opacity, composition and cloud structure; it is not a universal constant. Limb darkening, stellar heterogeneity and instrumental effects also affect the observed transit depth.^[ref]

With constant gravity and mean molecular weight, hydrostatic equilibrium gives $P_c=P_s\exp (-H_c/h)$, where $h$ is the atmospheric scale height. A flat exoplanet transmission spectrum alone does not determine $H_c$ or a unique cloud-top pressure.

An exoplanet cloud is suspended condensed material in an exoplanet atmosphere. Condensation makes particles when local composition and temperature permit; mixing can keep them aloft while atmospheric condensate rainout removes them by settling. The resulting distribution depends on transport as well as on local chemical equilibrium.

Particles absorb and scatter radiation, changing the reflected brightness, thermal spectrum and exoplanet transmission spectrum. An opaque exoplanet cloud deck hides deeper molecular absorption, while a thinner cloud can leave wavelength-dependent structure. Particle size, composition and coverage therefore matter as much as the statement that a cloud is present. A weak gas band can indicate obscuration rather than low molecular abundance, making clouds a central uncertainty in atmospheric retrieval.

An exoplanet transmission spectrum is the measured exoplanet transit depth as a function of wavelength. Light from the star passing through the limb of an exoplanet atmosphere is absorbed or scattered differently in different spectral bands. At a strongly absorbing wavelength, a ray becomes opaque farther from the centre, making the effective planetary radius larger.

The annulus model for transmission spectroscopy estimates the extra blocked area, while the slant optical depth of an isothermal atmosphere explains why this method can detect tenuous gas. Molecular-band amplitudes depend on the atmospheric scale height, abundances, and exoplanet cloud deck. Stellar contamination of a transmission spectrum and reference-pressure degeneracy in transmission spectroscopy limit how directly this observable can be translated into a unique composition.

Atmospheric haze consists of small suspended particles that scatter or absorb radiation, often formed through atmospheric photochemistry rather than direct condensation of a locally abundant vapour. In an exoplanet atmosphere, transport, growth and settling determine the particles' altitude and size distribution.

A haze can add a wavelength-dependent continuum to an exoplanet transmission spectrum and conceal molecular bands. The scattering slope of a transmission spectrum connects an idealized extinction law with the atmospheric scale height, but a measured slope alone does not establish a particular haze composition. Stellar contamination of a transmission spectrum can also alter the slope. Distinguishing these explanations requires spectral coverage and a joint model of the star and planet.

Let $R_p$ be a reference radius at pressure $P_0$ in an isothermal atmosphere. It can be a reference isobar on a gas giant, rather than a solid surface. Assume constant temperature $T$, constant mean molecular weight $\mu$ in units of hydrogen mass $m_H$, and approximately constant gravitational acceleration $g$. The ideal gas law and hydrostatic equilibrium giveIntegrating from the reference isobar yieldsReducing the pressure by a factor $e$ therefore increases the pressure-level radius by one atmospheric scale height. Constant gravity is a thin-atmosphere approximation over the height range being modeled.

A pressure-level radius is not automatically the observed transit radius. Transmission depends on the line-of-sight optical depth, which also requires composition and opacity. Different reference pressures or cloud assumptions can therefore assign different pressure levels to the same observed exoplanet transmission spectrum.^[ref]

The inferred dayside water mixing ratio is about $500$ times below the solar-equilibrium reference. Several explanations are possible. A high atmospheric carbon-to-oxygen ratio, especially near or above unity in hot carbon monoxide-dominated gas, locks much of the oxygen in CO and leaves little water. A genuinely oxygen-poor or low-metallicity envelope also reduces water, although bulk elemental abundances must apply to both hemispheres. Atmospheric photochemistry can destroy water at low pressures. In portions of the dayside that are substantially hotter than the stated minimum, thermal dissociation can also reduce water, especially at low pressure; $1800\mathrm{K}$ alone does not establish strong dissociation throughout the emitting region. Temperature/opacity degeneracies or incomplete treatment of exoplanet clouds and horizontal structure in an atmospheric retrieval can bias the inferred abundance.

At the cooler terminator, $10^{-4}$ is only a factor of five below the reference. Moderately reduced oxygen abundance, an enhanced C/O ratio, and exoplanet cloud/atmospheric haze dilution of spectral features are plausible explanations. Water is comparatively stable at $1000\mathrm{K}$, so strong thermal dissociation is not the natural explanation there. A exoplanet transmission spectrum samples a slant path through the limb, and the degeneracy among exoplanet cloud height, reference pressure and gas abundance can mimic a lower mixing ratio.

The two measurements need not describe the same pressure range or longitude. Local dissociation/photochemistry on the hotter dayside and reformation on the cooler limb can produce a real spatial difference. Even at one elemental C/O ratio, hot carbon monoxide-rich chemistry can leave less oxygen for water than cooler methane-rich chemistry, an example of carbon partition and atmospheric water abundance. Transport can modify or homogenize those tendencies, depending on the reaction and advection timescales. Alternatively, inconsistent assumptions in the emission and transmission retrievals can create an apparent discrepancy. A reconciliation should use one bulk elemental inventory, separate dayside/limb temperature profiles and contribution pressures, and consistent exoplanet cloud and transport physics; it should not assign independent planetary metallicities to the two hemispheres.

Transmission spectroscopy, eclipse/emission spectroscopy and direct-imaging spectroscopy probe atmospheres in complementary geometries.

A exoplanet transmission spectrum uses the wavelength dependence of primary-transit depth to measure slant-path absorption at the limb. Its long path length gives sensitivity to trace absorbers, but only transiting systems qualify; exoplanet clouds, stellar heterogeneity and the reference-radius/abundance degeneracy complicate interpretation, and the result samples the terminator rather than the dayside.

An exoplanet secondary eclipse isolates the dayside thermal/reflected spectrum by removing the planet behind the star. It constrains brightness temperatures, molecules and thermal inversions, but the planet/star contrast is small, a suitable orbital geometry is needed, and temperature-abundance degeneracies remain. A exoplanet thermal phase curve extends this method to longitudinal information.

Exoplanet direct imaging spatially separates a planet from its star and permits repeated spectroscopy without requiring a transit. It is effective for young, luminous, widely separated giant planets, but demands high contrast and angular separation; old small planets close to their stars are difficult. Inferred gravities, radii and masses can depend strongly on atmosphere and evolutionary models.

Three observable signatures are a blue optical transmission slope, muted molecular transmission features, and enhanced reflected optical light.

Small-particle atmospheric haze can increase the apparent transit radius toward short wavelengths, roughly $0.3$--$1\mu \mathrm{m}$. For Rayleigh scattering-like extinction, $\sigma \propto {\lambda }^{-4}$ and an isothermal atmospheric scale height model gives $d{R}_p/d\ln \lambda \simeq -4H$. Larger particles instead produce a flatter, approximately grey continuum.

An optically thick exoplanet cloud deck can truncate the slant path through gas and flatten molecular bands in a exoplanet transmission spectrum, for example over $0.4$--$2.5\mu \mathrm{m}$ and the water band around $1.4\mu \mathrm{m}$. The observed quantity is reduced band-to-continuum radius contrast, not necessarily a low molecular abundance.

exoplanet cloud scattering can produce a high geometric albedo and distinctive optical secondary eclipses/phase curves around $0.4$--$0.9\mu \mathrm{m}$. Longitudinal exoplanet cloud variation can shift a reflected-light phase maximum. A spectral slope or flat spectrum alone is not a unique exoplanet cloud identification: particle size, gas scattering, metallicity and stellar contamination must be considered together.

Take $R_p$ to be the radius of an opaque planetary disc and $H$ the geometric thickness of the model atmosphere, not necessarily one atmospheric scale height. Assume a uniform stellar specific intensity, a fully projected non-grazing transit, negligible planetary emission in the measured band, and no scattering or refraction returning light to the beam. The cylindrical approximation assigns the same slant optical depth ${\tau }_{\lambda }$ to every ray through the annulus.

The opaque disc blocks area $\pi R_p^2$. The annulus has projected area $\pi [(R_p+H{)}^2-R_p^2]$, and the radiative transfer equation transmits fraction $e^{-{\tau }_{\lambda }}$ through it. Its blocked fraction is therefore $1-e^{-{\tau }_{\lambda }}$. Dividing the missing light by the unobscured stellar-disc light gives the exoplanet transmission spectrumFor $H\ll R_p$, the annulus model for transmission spectroscopy becomesThe optically thin excess is $2R_{p}H{\tau }_{\lambda }/R_s^2$; the optically thick limit is the area ratio $(R_p+H{)}^2/R_s^2$ before the thin-annulus approximation. For a realistic atmosphere, the slant optical depth varies with the ray's impact parameter $b$, giving insteadLimb darkening replaces the simple area weighting by the local stellar specific intensity. The constant-depth model is therefore an explicit geometric approximation, not the slant-depth law of a spherical hydrostatic atmosphere.

The two measurements sample different atmospheric regions and different radiative transfer geometries. An exoplanet emission spectrum probes the dayside; an exoplanet transmission spectrum probes the morning and evening limbs of the day-night terminator. Several alternatives to an exoplanet cloud deck can therefore suppress the transmission feature.

Temperature, mean molecular weight, limb chemistry, continuum opacity and the dayside temperature gradient are alternatives or degeneracies to test. In particular, the three-scale-height amplitude alone cannot establish different CO abundances between the hemispheres.

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 an isothermal atmosphere in hydrostatic equilibrium, with constant gravity $g$, mean molecular weight $\mu$, and an ideal gas equation of state. Use $h$ for the atmospheric scale height, to distinguish it from the total observable height $H$. Thenso the cloud-top pressure in an isothermal atmosphere isAn opaque, approximately grey exoplanet cloud deck can flatten the exoplanet transmission spectrum if the remaining gas above it has little wavelength-dependent extinction. If its top nearly reaches the observable atmospheric extent, $H_c\simeq H$, this gives $P_c\simeq P_s{e}^{-H/h}$. More generally, a top at $N$ atmospheric scale heights has $P_c/P_s=e^{-N}$; illustrative values $N=5$ and $10$ give $6.7\times 10^{-3}$ and $4.5\times 10^{-5}$.

A flat exoplanet transmission spectrum and $P_s$ alone do not determine a unique cloud-top pressure. The temperature, gravity, mean molecular weight and cloud altitude, or equivalent opacity information, are also needed. A large mean molecular weight can itself suppress spectral features, so the exoplanet cloud deck interpretation is conditional.

Four possible molecular signatures of disequilibrium chemistry in an exoplanet atmosphere, measured through an exoplanet transmission spectrum or exoplanet emission spectrum, are:

The first two signatures can be consequences of the same process and are not independent evidence for two mechanisms. Changes in atmospheric carbon-to-oxygen ratio, atmospheric metallicity of a giant planet, exoplanet cloud coverage, and the atmospheric pressure-temperature profile can mimic abundance changes. A convincing inference compares several molecular bands with a chemically consistent equilibrium model rather than identifying one unusual band alone.

Three major research directions, appropriate to the scientific questions posed in 2018, are:

These are research goals rather than claims that the relevant mechanisms or habitable atmospheres have already been established.

Assume a uniform stellar disc of radius $R_{\star }$, an opaque planetary radius $R_p$, and a thin atmospheric annulus of thickness $z\ll R_p$. Neglect planetary light during transit and scattering back into the beam. The attenuation part of the radiative transfer equation gives $I_{\lambda }=I_{\lambda ,0}{e}^{-{\tau }_{\lambda }}$, where ${\tau }_{\lambda }$ is the slant optical depth along a stellar ray through the atmosphere. The fraction of light removed from that annulus is therefore $1-e^{-{\tau }_{\lambda }}$.

If the annulus is represented by one effective optical depth, its area divided by the stellar area isThe annulus model for transmission spectroscopy consequently gives the extra transit depthHere ${\delta }_{\lambda }$ is normalized to the unobscured stellar flux and excludes the opaque-disc depth $(R_p/R_{\star }{)}^2$. For a spectral feature measured relative to a continuum with slant optical depth ${\tau }_c$, the corresponding contrast is $A(e^{-{\tau }_c}-e^{-{\tau }_{\lambda }})$; the displayed formula takes the annular continuum to be transparent.

A real exoplanet transmission spectrum has an impact-parameter-dependent optical depth. Its more accurate expression isStellar limb darkening and horizontally varying clouds further modify the weighting. The single-annulus approximation is useful for estimating an atmospheric spectral-feature amplitude, rather than predicting every spectral line.

In the annulus model for transmission spectroscopy, an added aerosol optical depth changes the signal to $A[1-e^{-({\tau }_{\mathrm{gas}}+{\tau }_{\mathrm{aerosol}})}]$. Large particles can supply nearly wavelength-independent extinction. An opaque high exoplanet cloud deck then masks deeper gas, flattens the optical exoplanet transmission spectrum, and weakens atomic or molecular features.

Small particles can instead produce a rising transit radius toward short wavelengths. In an isothermal atmosphere, the slant optical depth of an isothermal atmosphere isTaking the effective radius near ${\tau }_{\lambda }\sim 1$ gives $z(\lambda )=H\log {\sigma }_{\lambda }+\mathrm{constant}$. For Rayleigh scattering, ${\sigma }_{\lambda }\propto {\lambda }^{-4}$, so the scattering slope of a transmission spectrum isA steeper-than-expected optical slope or suppressed gas features can therefore indicate atmospheric haze or exoplanet clouds. These signatures are not unique: high mean molecular mass reduces $H$, gas itself can produce Rayleigh scattering, and stellar surface heterogeneity can mimic slopes. Consistent optical and infrared features help distinguish these explanations.