Central flashes during stellar occultations. Effects of diffraction, interferences, and stellar diameter
Central flashes occur during stellar occultations by solar system objects. We catalog diffraction effects on the flash with point-like stars, monochromatic waves and spherical transparent atmosphere. Diffraction involves the Huygens principle, the Sommerfeld lemma and the stationary phase method, while finite stellar diameter cases involve Clausius' theorem. For point-like stars, the central flash shape is that of the classical Poisson spot, but with larger height. For tenuous atmospheres that cannot focus the stellar rays at shadow center, the flash is amplified by the factor (R_0/r_0)^2 compared to the Poisson spot, where R0 and r0 are the object and the shadow radii, respectively. For denser atmospheres that can focus the rays at shadow center, the flash peaks at 2[(pi*R/lambda_F})^2]*phi0, where R is the central flash layer radius, lambda_F is the Fresnel scale and phi0 is the flux that would be observed at shadow center without focusing. For isothermal atmospheres with scale height H, the height is 2(R*H)(pi/lambda_F)^2. Fringes surrounding the central flash are separated by lambda_P=lambda_F^2/R, related to the separation between the primary and secondary stellar images. For a projected stellar diameter D*>lambda_P, the flash is described by complete elliptic integrals, and has full width at half maximum of 1.14D* and peak value 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 ~10e4-10e5, 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. Effects of departure from sphericity, atmospheric waves and stellar limb darkening are discussed.