Central flashes during stellar occultations. Effects of diffraction, interferences, and stellar diameter

Central flashes may occur during stellar occultations by objects in the Solar System. 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. 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. 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_ ̊m CF /λ_ ̊m F )^2 ϕ_⊥(0), where R_̊m CF is the central flash layer radius, λ_̊m 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 2π^2 (R_ ̊m CF H)/λ_ ̊m F ^2. Fringes surrounding the central flash are separated by λ_ ̊m P = λ_ ̊m F ^2/R_ ̊m CF , which is related to the separation between the primary and secondary stellar images. For a projected stellar diameter D_* ≫ λ_ ̊m 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 8H/D_*. For Earth-based occultations by Pluto and Triton observed in the visible with point-like stars, diffraction causes flashes with very large heights of ∼104-10^5$, 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.