Variations in the Brightness and Color of a Star During Eclipsing by a Protoplanet

Changes in the brightness and color of stars obscured by gas-dust protoplanets are studied using Equation (1). In a quite general case, assuming only that τ(x, y)∈[0, τ^max ] , it is shown that the ratio ${{{\left( {\Delta m_2^{\min }-\Delta m_1^{\min }} \right)}} \left/ {{\Delta m_1^{\min }}} \right.}$ decreases with increasing $\Delta m_1^{\min }$ at the brightness minima. The region where points from the set {E₁; E₂} can lie on an E₂ vs E₁ diagram is localized within a rather narrow parallelogram with a long diagonal given by Eq. (10). If $\uptau \left( {x,y} \right)={\uptau^{\max }}\sqrt{{1-{{{\left( {{x^2}+{y^2}} \right)}} \left/ {{{R^2}}} \right.}}}$, then the unknown E₂ as a function of E₁ is essentially given by Eq. (10). Calculated “brightness-color” curves are fundamentally different from the interstellar absorption law. If it is held that the color indices increase linearly in Ae/Be Herbig stars with falling brightness, i.e., ${{{\left( {\Delta {m_2}-\Delta {m_1}} \right)}} \left/ {{\Delta {m_1}=\mathrm{const}}} \right.}$, and that this ratio is independent of the depth of eclipsing, then it appears that the Algol-like variation in the brightness of Ae/Be Herbig stars cannot be explained in terms of a model of occultation by a protoplanet.