Detecting Exoplanets

A planet and star orbit their common centre of mass. Although the star moves only a little, periodic Doppler shifts of its absorption lines reveal the component of that motion along our line of sight. Plotting radial velocity against time gives a repeating curve whose period is the orbital period.

Large planets close to their stars generally produce larger stellar velocity amplitudes and shorter observing cycles, making them easier to detect. A nearly face-on orbit has little radial motion, so a planet can be present without a strong signal. The signal constrains a mass that depends on inclination; do not infer an exact mass from amplitude alone without the orbital model.

If the orbit is aligned so the planet passes across the stellar disc, observed intensity drops temporarily. A repeating transit gives the period. The depth estimates the area of stellar surface blocked, and hence the ratio of planet radius to star radius in a simple model of a uniform bright disc.

The light curve has a normal baseline, ingress, reduced brightness and egress. Real stars have limb darkening, and grazing transits alter the shape. Star spots, eclipsing binary stars and instrumental effects can imitate a dip, so repeated observations and other measurements are needed.

Direct imaging is difficult because starlight overwhelms reflected or emitted planet light and angular separation is tiny. Transit photometry gives a radius ratio; radial velocity constrains orbital motion and mass. Together with a stellar model they can constrain planetary density.

The two methods select different systems. Transits require a particular orientation, and long-period planets require long observing campaigns. A non-detection therefore describes the sensitivity and observing window of a survey rather than proving that no planets exist.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.