Phase curve (astronomy)

In astronomy a phase curve describes the brightness of a reflecting body as a function of its phase angle. The brightness usually refers the object's absolute magnitude, which, in turn, is its apparent magnitude at a distance of one astronomical unit from the Earth and Sun. The phase angle equals the arc subtended by the observer and the sun as measured at the body.

The phase curve is useful for characterizing an object's regolith (soil) and atmosphere. It is also the basis for computing the geometrical albedo and the Bond albedo of the body. In ephemeris generation, the phase curve is used in conjunction with the distances from the object to the Sun and the Earth to calculate the apparent magnitude.

The phase curve of Mercury is very steep, which is characteristic of a body on which bare regolith (soil) is exposed to view. At phase angles exceeding 90° (crescent phase) the brightness falls off especially sharply. The shape of the phase curve indicates a mean slope on the surface of Mercury of about 16°, which is slightly smoother than that of the Moon. Approaching phase angle 0° (fully illuminated phase) the curve rises to a sharp peak. This surge in brightness is called the opposition effect because for most bodies (though not Mercury) it occurs at astronomical opposition when the body is opposite from the Sun in the sky. The width of the opposition surge for Mercury indicates that both the compaction state of the regolith and the distribution of particle sizes on the planet are similar to those on the Moon.

Early visual observations contributing to the phase curve of Mercury were obtained by G. Muller in the 1800s and by André-Louis Danjon in the mid-twentieth century. W. Irvine and colleagues used photoelectric photometry in the 1960s. Some of these early data were analyzed by G. de Vaucouleurs, summarized by D. Harris and used for predicting apparent magnitudes in the Astronomical Almanac for several decades. Highly accurate new observations covering the widest range of phase angles to date (2 to 170°) were carried out by A. Mallama, D. Wang and R. Howard using the Large Angle and Spectrometric Coronograph (LASCO) on the Solar and Heliospheric Observatory (SOHO) satellite. They also obtained new CCD observations from the ground. These data are now the major source of the phase curve used in the Astronomical Almanac for predicting apparent magnitudes.

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