= Exoplanet transit photometry
<Exoplanet transit photometry> measures the decrease in a <star>'s <observed radiative flux> during an <exoplanet transit>. Define $F_0$ as the unobscured <star>'s <observed radiative flux> and $F(t)$ as the value at time $t$. For a dark, opaque <exoplanet> crossing a uniformly bright circular stellar disc, a fully superimposed planetary disc blocks exactly the fraction
$$
\delta=\frac{F_0-F_{\rm full}}{F_0}=\frac{\pi R_p^2}{\pi R_\star^2}=\left(\frac{R_p}{R_\star}\right)^2.
$$
Here $R_p$ and $R_\star$ are the <planet> and <star> <radii>. This <exoplanet transit depth> determines a <radius> ratio, $R_p/R_\star=\sqrt\delta$; an absolute <planet> <radius> requires an independently estimated stellar <radius>. For $R_p/R_\star=0.10$, $\delta=0.010$: a one-percent dip, with $F_{\rm full}/F_0=0.990$. Halving the <radius> ratio to $0.05$ reduces the <exoplanet transit depth> to $0.0025$, a quarter as much.
For the central <exoplanet transit> illustrated below, the <transit impact parameter> is $b=0$. Write $k=R_p/R_\star<1$ and let $z$ be the projected centre-to-centre separation in units of $R_\star$. The <light curve> is $F/F_0=1-A(z)/\pi$, where $A(z)$ is the overlap <area> of <circles> of <radii> $1$ and $k$. There is no overlap when $z\ge1+k$; the planetary disc is fully inside when $z\le1-k$, giving $A=\pi k^2$. Between those limits, the overlap <area> grows or shrinks continuously. Thus even a uniform <star> has curved ingress and egress, with a flat bottom only during full overlap. The illustration uses approximately constant transverse <velocity> over the short crossing, so $z=|u t|/R_\star$ with mid-transit at $t=0$. Analytic models also handle <limb darkening>. https://arxiv.org/abs/astro-ph/0210099[Mandel and Agol (2002)]{ref}.
\Image[/exoplanet-transit-light-curve.png]
{title=Central transit: a radius ratio of 0.10 blocks one percent of a uniform star}
The simple <exoplanet transit depth> formula assumes constant stellar brightness, no <limb darkening> or <starspots>, negligible light from the <exoplanet>, and no <transit dilution> by other light. It describes full overlap in a non-grazing <exoplanet transit>, requiring $b<1-k$ for a full-overlap interval. A grazing <exoplanet transit> never hides the whole planetary disc against the <star>, and <limb darkening> weights different blocked <areas> differently. Repeating dips are valuable evidence, but eclipsing <binary stars> and <starspots> can imitate parts of the signal, so confirmation and joint modelling matter.
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