Solution (source code)

= Solution

One approach uses <exoplanet transmission spectra>. Three aerosol signatures are:

* Muted molecular-band amplitudes in the near-infrared, for example weak <water> structure around $1.4\,\mu\mathrm m$: an <optically thick> <exoplanet cloud deck> raises the continuum and hides part of the gas column.
* A nearly grey transit-radius continuum across optical/near-infrared wavelengths, roughly $0.5$--$2\,\mu\mathrm m$, when particles are large relative to the wavelengths. Suppressed optical atomic-line wings provide a related indication that deep high-<pressure> layers are hidden.
* A radius increasing toward blue/ultraviolet wavelengths, roughly $0.3$--$1\,\mu\mathrm m$, for small-particle <scattering of light>. In a simple <Rayleigh scattering> limit, $\sigma\propto\lambda^{-4}$, and the <scattering slope of a transmission spectrum> is $dR_p/d\log\lambda=-4H$.

A second approach uses the dayside spectrum and brightness obtained with <exoplanet secondary eclipses>, optionally supported by orbital phase variations. Its three useful aerosol signatures are:

* Enhanced reflected-light <geometric albedo> or characteristic colour in the visible, roughly $0.4$--$0.9\,\mu\mathrm m$, for a scattering <exoplanet cloud>. Absorbing <atmospheric haze> can instead lower the reflected flux, so high albedo is not a universal aerosol rule.
* Weak near-/mid-infrared gas features and a cloud-set continuum <brightness temperature>, roughly $1$--$10\,\mu\mathrm m$, when an opaque cloud moves the thermal photosphere to a different <pressure>. Changes in the <exoplanet thermal phase curve> can support a spatially patchy cloud interpretation, though circulation also affects it.
* Broad condensate-dependent infrared spectral structure, for example a silicate resonance around $10\,\mu\mathrm m$, if particles are sufficiently small and the optical-depth/temperature geometry permits the feature. Its presence and sign depend on particle composition, size and vertical thermal structure.

\b[Transmission measures aerosol extinction along the limb; eclipse/reflection measurements test dayside scattering and emission.] No single flattened feature proves clouds: small <atmospheric scale height>, low molecular abundances, stellar heterogeneity and thermal-gradient degeneracies must be considered. Joint wavelength coverage and geometries make the inference stronger.