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The first exoplanets were detected in 1992 around a millisecond pulsar (Wolszczan & Frail, 1992). Pulsars are rapidly spinning, compact stellar remnants that emit beams of electromagnetic radiation (Pacini, 1967). The frequency of these beams as observed from Earth is very regular, even rivaling atomic clocks (Matsakis et al., 1997). The influence of planets orbiting the pulsar will introduce slight anomalies into the pulsar timing which may be used to reveal the parameters of the planetary orbit and the planetary mass.

Figure 1.12: The properties of detected exoplanets colored by detection technique. Solar system planets are plotted for context. The vast majority of Earth-size exoplanets were discovered with the transit method by the Kepler telescope. Small planets at long-period orbits remain difficult to detect.

Figure 1.13: Example of a radial velocity detection of a≥3.6 Earth-mass exoplanet orbiting just inside the habitable zone of the nearby K-type star, HD 85512. The velocity measure- ments are folded to the 58.4 day period of the planet. [Image from Pepe et al. (2011)] 0.1 Earth masses, as well as planets at long period orbits. Pulsars with orbiting planets are rare, however, and only four pulsar planetary systems have been detected to date. In recent years, variations in the timing of stellar pulsations of hot subdwarf and main-sequence stars have been used to detect several planetary candidates (Silvotti et al., 2007; Murphy et al., 2016).

Radial Velocity

The gravitational influence of an orbiting planet will induce velocity variations in the host star, typically on the order of a few meters per second. The light from the star is Doppler shifted due to these velocity variations. High-resolution spectroscopy is able to measure the line-of-sight stellar velocity using the slight shift of emission and absorption lines in the stellar spectra. With velocity measurements from observations over multiple epochs, the influence of an unseen planet on the host star can be revealed, as shown in Figure 1.13.

Radial velocity is able to place limits on a planet’s minimum mass. The true planetary mass is dependent on the planet’s orbital inclination. The orbital period of a planet can also be measured from the RV curve. Radial velocity is sensitive to planets at a wide-range

of orbital inclinations. Because the star-planet interaction is mediated by gravity, smaller planets result in lower stellar velocity amplitudes and are thus difficult to detect. In addition, the measurements required to detect and study a single planet are time-intensive and require a large-aperture telescope and stable, high-resolution spectrographs.

In 1995, the first exoplanet was discovered around a main-sequence star, 51 Pegasi b, using the radial velocity technique (Mayor & Queloz, 1995). This method dominated the exoplanet discovery field for over a decade and revealed many surprises, such as the existence of “hot Jupiters.” Since 2011, the number of detected exoplanets with radial velocity has declined, as telescope time has been dedicated to follow-up planets from transit surveys. New instruments in the coming years, such as NEID (Halverson et al., 2016), will be sensitive to velocity amplitudes as low as 10 cm−1_{, consistent with an Earth-size planet orbiting at 1} AU.

Direct Imaging

The majority of exoplanets have been discovered by indirect measurements, observing their effect on more visible objects. Imaging a spatially resolved planet is an enormous challenge, as the host star emits far more light than the planet. For illustration, if a twin of our solar system were placed at 10 parsecs, Jupiter, the brightest planet, would emit only around 10−9 _{the flux of the parent star at an angular separation of 0.5”.}

Directly imaging massive, self-luminous planets is possible with boutique instruments, combining extreme adaptive optics to correct wavefront aberrations, a coronograph to reduce the intensity of light from the host star, and an integral field spectrograph to reduce speckle noise with chromatic differential imaging (Crepp et al., 2011). In addition, a large number of observing methods are used to suppress speckles, such as angular differential imaging (Sparks

Figure 1.14: Directly imaged planets orbiting HR8799, observed in the near-infrared with Keck adaptive optics. The four planets range from 3 to 7 Jupiter masses. The light from the central star has been reduced in intensity with a coronograph. [Image from Marois et al. (2010)]

planets 10−5 _{fainter than the host star at separations of 1”. An example of directly imaged} planets is shown in Figure 1.14.

The first image of an exoplanet, the five Jupiter-mass 2M1207b which orbits a brown dwarf, came in 2004 (Chauvin et al., 2004). A total of 18 more planetary systems have been imaged in the intervening years, far fewer than was initially expected2_{. This suggests} a significant discrepancy exists between the planet mass function extrapolated from radial velocity surveys and the true giant exoplanet mass function (Bowler, 2016).

Future instruments on extremely large telescopes and the proposed coronagraphic capa- bility for the 2.4m space-based WFIRST mission (Spergel et al., 2013) will allow imaging

2_{Macintosh et al. (2006) suggested that nearly 100 planets could be discovered with GPI. In the first 2.5}

Figure 1.15: A Neptune-sized planet detected with the microlensing method. The brightness of the background star is observed. Gravity from the planet, orbiting the foreground star, contributes to the magnification of the background star. [Image from Sumi et al. (2010)] of planets at close orbits and be sensitive to reflected starlight. At their theoretical per- formance limit, these instruments could even detect rocky planets in the habitable zone of nearby M-dwarfs (Guyon et al., 2012).

Microlensing

Gravitational microlensing occurs when two stars at different distances pass within ∼1 mas of each other on the plane of the sky (Gaudi, 2012), and the gravitational field of the foreground star acts as a lens (Chwolson, 1924; Einstein, 1936). The light from the background star is then magnified, with the brightness of the star increasing over the span of a few days or weeks. If the foreground star has a planet, the gravitational field of the planet will also lens the background star, adding a detectable contribution to the lensing light curve. An example of a planet detected with microlensing is shown in Figure 1.15.

and Microlensing Observations in Astrophysics (MOA, Bond et al., 2004) surveys.

Microlensing is able to detect planets at wide-orbits, low-mass planets (down to Mars- size with WFIRST), and planets around distant stars. The planetary mass can be loosely constrained from microlensing, as well as the planet’s separation from the host star at the time of the lensing event. A microlensing event only happens a single time, however, and the host star is often too distant for follow-up observations, severely limiting characterization of any detected planetary system.

Astrometry

The astrometric method for detecting planets uses precise measurements of a star’s position in the sky. Both components in a planet-star system orbit their mutual center of mass or barycenter. The astrometric method seeks to observe the small shift in stellar position as a star orbits the system barycenter. The variation in position is so small that ground-based telescopes, contending with the effects of atmospheric turbulence, have not yet been able to detect any planets with this method. The Hubble Space Telescope did use astrometry to determine the mass of a previously known planet, Gliese 876b (Benedict et al., 2002).

The Gaia space telescope will provide microarcsecond astrometric precision for the brightest stars, and is expected to discover approximately 20,000 long-period planets with masses between 1-15 Jupiter masses within 500 pc (Perryman et al., 2014). If extended for a 10-yr mission, the number of planet detections will more than triple.