Super-Rayleigh slopes of exoplanetary transmission spectra generated by photochemical haze

Spectral slopes in optical transmission spectra of exoplanetary atmospheres encapsulate information on the properties of exoplanetary aerosols. The slope is usually attributed to the Rayleigh scattering caused by tiny aerosol particles; however, recent retrieval studies have suggested that the slopes are often steeper than those caused by the Rayleigh scattering. Here, we propose that photochemical haze can explain such super-Rayleigh slopes. The spectral slope is steepened by the vertical opacity gradient in which atmospheric opacity increases with altitude. Using a microphysical model, we demonstrate that photochemical haze naturally generates such opacity gradient, especially when the eddy mixing is efficient. The transmission spectra of hazy atmospheres can be demarcated into four typical regimes in terms of the haze mass flux and eddy diffusion coefficient. We find that photochemical haze can produce a spectral slope several times steeper than the Rayleigh slope in one of those regimes, in which the eddy diffusion coefficient is sufficiently high and the haze mass flux is moderate. We also suggest that photochemical haze preferentially generates super-Rayleigh slopes at planets with equilibrium temperatures of 1000–1500 K, which is consistent with results of recent retrieval studies.