= Light curve
A <light curve> records an astronomical source's received brightness against <time>, in a specified <photometric passband>. Its measured form is a <time series> of timestamps, brightness estimates, and uncertainties; a smooth $F(t)$ is a model of that record. Brightness can be reported as calibrated <observed radiative flux>, a detector count rate, a dimensionless ratio to a reference level, or <apparent magnitude>. These quantities require different units and calibration conventions. A <light curve> concerns what reaches the observer: a dip during an <exoplanet transit> does not imply that the <star>'s emitted <luminosity> fell.
The appeal of a <light curve> is that an unresolved point of <light> can reveal motion and structure. In <exoplanet transit photometry>, repeated dips constrain the <orbital period>; under the uniform-disc, dark-<planet>, full-overlap assumptions, the <exoplanet transit depth> is the blocked <area> fraction $(R_p/R_\star)^2$. A toy one-percent dip therefore corresponds to a <radius> ratio of $0.10$. Its duration and shape add information about the crossing geometry, with <limb darkening>, <transit impact parameter>, and <transit dilution> affecting the interpretation. See <exoplanet transit photometry> for the geometry. The first figure instead follows the measurement: an instrumental trend and sky contribution can obscure a small physical dip.
\Image[/light-curve-aperture-calibration.png]
{title=Toy light curve: a one-percent transit recovered from a known sky contribution and gain drift; synthetic data, not observations}
An instructive real observation is the early Kepler record of the already known <exoplanet> HAT-P-7b. Welsh and colleagues analysed 33.5 days from 13 May to 15 June 2009, containing 15 complete <exoplanet transits> at an <orbital period> of about $2.20473$ days. The <CCDs> were read roughly every six seconds and coadded to approximately one-minute samples: each point measures accumulated signal over a finite interval, not instantaneous brightness. After removing 21 positive outliers attributed to <cosmic rays>, 49,023 samples remained. The authors estimated a scatter of about $150$ parts per million per one-minute sample. A gradual $0.13\%$ count decrease, suspected to arise from focus drift with a fixed extraction aperture, was removed with a cubic <polynomial> fitted while masking the <exoplanet transits>. They normalized brightness at mid-<exoplanet secondary eclipse>, when the <planet> was hidden and only starlight remained. https://www.ucolick.org/~jfortney/papers/Welsh10.pdf[Welsh et al. (2010), observations, section 2]{ref}.
What does the instrument actually measure? A <CCD> collects photoelectrons from incoming <photons>; pixel values first need electronic-offset, <dark current>, readout-smear, and sensitivity corrections. https://nexsci.caltech.edu/workshop/2012/keplergo/PipelineCAL.shtml[Kepler Guest Observer Program, pixel calibration; edited by Martin Still]{ref}. <Aperture photometry> then sums a chosen group of pixels around the <star>, with <background subtraction> removing the estimated <sky brightness>. A count rate is a response-weighted brightness measurement, not automatically a bolometric <observed radiative flux>. Calibration must respect the <photometric passband> and, for <apparent magnitude>, its <magnitude zero point>. Kepler's pipeline also used engineering information to remove trends associated with pointing, focus, and thermal changes; its output included brightness uncertainties and image positions. https://arxiv.org/pdf/1001.0258[Jenkins et al. (2010), pipeline overview, sections 2–5]{ref}.
Calibration and interpretation need separate checks. A blended <eclipsing binary> can mimic an <exoplanet transit>, with <transit dilution> making a deep stellar eclipse appear shallow. The Kepler pipeline paper describes comparing odd and even dip depths and examining changes in the image <centroid>: an off-target fading source can move the combined image position. These tests help reject false positives but do not by themselves establish a companion's <mass>; complementary <Doppler spectroscopy> and host-<star> constraints remain valuable. https://arxiv.org/pdf/1001.0258[Jenkins et al. (2010), data validation, section 6]{ref}.
Even a real <exoplanet>'s signal can have several contributors. Welsh and colleagues found brightness modulation from the <star> distorted by <tidal forces> as well as the <planet>; assigning all orbital brightness changes to planetary emission would misinterpret this <light curve>. https://www.ucolick.org/~jfortney/papers/Welsh10.pdf[Welsh et al. (2010), interpretation, section 4]{ref}. <Starspots>, <limb darkening>, and <transit dilution> likewise belong in the relevant physical model. A flexible trend fitted through a dip could absorb that dip; the masked fit in the real example illustrates why the fitting procedure is part of the measurement. <Exposure-averaged light curves> and <phase folding of a light curve> make two further limitations explicit.
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