Central flashes during stellar occultations

Context . Central flashes may occur during stellar occultations by objects in the Solar System. Aims . Catalog diffraction effects on the flash with point-like stars, monochromatic waves, and different cases of spherical transparent atmosphere; describe the corrections due to stellar diameters. Methods . To describe diffraction, we used the Huygens principle, the Sommerfeld lemma, and the stationary phase method, and we treated the effects of finite stellar diameter using Clausius’ theorem. Results . For point-like stars, the central flash shape is that of the classical Poisson spot, but with a greater height. For tenuous atmospheres that cannot focus the stellar rays at the shadow center, the flash is amplified by the factor ( R 0 / r 0 ) 2 compared to the Poisson spot, where R 0 and r 0 are the object and the shadow radii, respectively. For denser atmospheres that can focus the rays at the shadow center, the flash peaks at 2π 2 ( R CF /λ F ) 2 ϕ ⊥ (0), where R CF is the central flash layer radius, λ F is the Fresnel scale, and φ ⊥ (0) is the flux that would be observed at the shadow center without focusing. For isothermal atmospheres with scale height H , the height is 2 π 2 ( R CF H )/ λ F 2 . Fringes surrounding the central flash are separated by λ P = λ F 2 / R CF , which is related to the separation between the primary and secondary stellar images. For a projected stellar diameter D * ≫ λ P , the flash is described by complete elliptic integrals, and has a full width at half maximum of 1.14 D * and a peak value of 8 H / D * . Conclusions . For Earth-based occultations by Pluto and Triton observed in the visible with point-like stars, diffraction causes flashes with very large heights of ∼10 4 −10 5 , spread over a very small meter-sized region in the shadow plane. In practice, the flash is usually smoothed by the stellar diameter, but still reaches high values of ∼50 and ∼200 during Pluto and Triton occultations, respectively. Diffraction dominates when using millimeter wavelengths or longer. We discuss the effects of departure from sphericity, atmospheric waves, and stellar limb darkening.