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A phase curve is the brightness of an astronomical body as a function of its phase, in the sense of the Moon's phases (full, half, quarter, new, etc.), but considering the body to have a continuous set of phases, one for each possible angle (phase angle) at the body between the direction of view and the star illuminating it. Information can be gleaned from a body's phase curve.
The phase curve of extra-solar planets is studied by studying the light (e.g., at a particular wavelength) as the planet orbits its star, which is easiest to establish if the planet is a transiting planet, and is easiest to interpret if it is tidally locked, so its rotation is also determined. A spectroscopic phase curve is information gathered by a spectrograph through the planet's orbit, i.e., offering information at a number of specific wavelengths simultaneously. This offers information about albedo, surface hot spots, and atmosphere. After determining and subtracting the effects of reflection, the rest is termed the thermal phase curve, that due to the temperature of the planet. Though a planet's transit makes it very clear that you are recording such a phase curve, some non-transiting planets also exhibit observable and analyzable phase curves.