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Super-Rayleigh Slopes in Transmission Spectra of Exoplanets Generated by Photochemical Haze

Spectral slopes in optical transmission spectra of exoplanetary atmospheres encapsulate information on the properties of exotic clouds. The slope is usually attributed to the Rayleigh scattering caused by tiny aerosol particles, whereas recent retrieval studies have suggested that the slopes are often steeper than the canonical Rayleigh slopes. Here, we propose that photochemical haze formed in vigorously mixing atmospheres can explain such super-Rayleigh slopes. We first analytically show that the spectral slope can be steepened by the vertical opacity gradient in which atmospheric opacity increases with altitude. Using a microphysical model, we demonstrate that such opacity gradient can be naturally generated by photochemical haze, especially when the eddy mixing is substantially 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 the transmission spectrum can have the spectral slope 2--4 times steeper than the Rayleigh slope if the eddy diffusion coefficient is sufficiently high and the haze mass flux falls into a moderate value. Based on the eddy diffusion coefficient suggested by a recent study of atmospheric circulations, we suggest that photochemical haze preferentially generates super-Rayleigh slopes at planets with equilibrium temperature of 1000--1500 K, which might be consistent with results of recent retrieval studies. Our results would help to interpret the observations of spectral slopes from the perspective of haze formation.