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Stars are complicated dynamical systems, which have a variety of kinds of “surface” motions. The poorly-characterized noise features in stellar radial velocity data sets are usually referred to as “stellar jitter”, and encompass a wide range of physics including asteroseismology, magnetic activity such as starspots and plages, granulation, and other effects. Stellar jitter is currently the most serious impediment to detecting low-mass planets in radial velocity datasets. Here we describe some forms of stellar jitter, their timescales, and their relative amplitudes. For a good exposition of these forms of stellar noise, see Dumusque et al. (2011c) and Dumusque et al. (2011a).

(a) (b)

Figure 1.10: (Left) An image of the Sun’s surface, showing spots and convective granulation, with the Earth to scale.4(Right) An example of a radial velocity signal induced by a starspot. In this figure, the left part of the star is rotating towards the reader. As the spot rotates into view, following the stellar rotation period, a redshift is recorded. After the star crosses the center, a blueshift is recorded. For more complicated starspot paths, the signal would change in complex ways. This figure is taken from Dumusque et al. (2011a)

Magnetic activity jitter is a common form of noise, which occurs on the timescales of the stellar

rotation period, typically tens of days, as well as very long term cycles on the order of years. In the short term, as a star rotates, the radial velocity measured from the stellar photosphere is composed of blueshifted light from the part of the star rotating towards the observer, and redshifted light from the part rotating away. In a smooth, featureless photosphere, these motions would cancel out, resulting in a zero radial velocity signal. However, any differential brightness between the approaching and receding parts of the stars will create a net radial velocity signal. As an example, a starspot comprising a small fraction of the stellar surface will cause a radial velocity signal of a few m/s (see Figure 1.10). This starspot may last for months or longer, move around the star, and eventually disappear. Multiple, high cadence observations over significant periods of time would be required to disentangle this sort of signal from true underlying planetary signals. Long-term activity cycles, like the 11 year solar starspot cycle, can cause the mean level of noise to change significantly, but are not understood well enough to characterize their net effect on precision.

Magnetic activity can be countered in a few ways. First, target selection is important. Old, quiet, solar-type stars with less active dynamos have generally been the targets of choice for radial velocity surveys. Young stars, which are extremely active, make radial velocity investigation of low-mass planets essentially impossible. An empirical measurement of the activity-induced jitter by Hillenbrand et al. (2015) found that for stars younger than a few hundred million years, the jitter noise is tens to hundreds of meters per second, corresponding to masses of a third to a tenth of Jupiter’s. Observations of particular spectral emission lines, such as Ca II, known to correlate with activity, can flag data that is problematic. Another popular method is “bisector” analysis, were the exact shape of the spectral line is analyzed for tell-tale signs of starspots and plages (bright regions), which tend to skew the lines to one direction or the other, while planets shift the lines uniformly (Huerta et al., 2008). Finally, starspots and plages are less extreme at infrared wavelengths, so observations over independent bands (for example, H and V) can be used to distinguish activity from true planet signals, as the measured velocity at each band should be consistent with a planet, and different for a starspot.

Another surface effect is granulation, arising from the convective upwelling and downwelling of material in the photosphere (see Figure 1.10). The typical velocities of these effects are many km/s per granule, but the millions of granules on the surface of the star tend to average out the radial velocities to a much lower level over 15 minute timescales. These kinds of effects also have much larger scales, called “meso-” and “super-” granulation, with longer timescales of hours to a day, and scales of up to 30,000 km in the Sun. The presence of these phenomena require detailed, high cadence observing over at least a few days to successfully characterize and average over.

The final major form of jitter is stellar oscillations, which are caused by fast moving pressure waves in stars. These oscillations typically have bulk amplitudes of tens of cm/s, and periods of a few minutes. The stellar p-modes are such an example, with 30 cm/s amplitudes at 5-minute

periods. These may be averaged away by observing the star over multiple periods, up to several days, though the contributions of oscillation modes at very long periods is not perfectly understood. The lack of control of stellar jitter at intermediate and long periods has seemed to impose a current velocity noise floor of slightly less than 1 m/s on the radial velocity method. No program has ever managed to exceed this level of precision over periods of time longer than a year, even with thousands of observations over many years. As an example of the difficulty of extracting small planetary signals at the instrumental precision, in the presence of many noise sources, a spectacular discovery of an Earth-mass planet orbiting alpha Centauri B at 0.5m/s amplitude (Dumusque et al., 2012), with an instrumental precision of about 0.7m/s, was recently disproven as an artifact of the data preprocessing (Rajpaul et al., 2016). It remains to be seen how the next generation of instruments, with precisions of about 10 cm/s, will be able to improve the planet yield in the presence of these noise sources.