Detectability of Trojan and Co-orbital Exoplanets

Details Detectability of Trojan and Co-orbital Exoplanets Detectability of Trojan and Co-orbital Exoplanets

Oct 2010

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2010dps....42.2716d&link_type=abstract

American Astronomical Society, DPS meeting #42, #27.16; Bulletin of the American Astronomical Society, Vol. 42, p.1062

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By now there have been many papers on the possibility of Trojan companions to planets of other stars. The purpose is of this work is to point out that radial velocity measurements can seriously misjudge the masses of planets in such systems.
In a Trojan system, where two exoplanets of similar mass share the same orbit, but are separated by 60 degrees of longitude, the radial velocity method gives a sinusoidal signal 1.73 times as great as that of each individual planet, but only 0.83 times as great as that of a single planet with the combined mass of both.
In principle, any number of planets can share the same orbit. Salo and Yoder (A & A 205, 309-327, 1988) have shown that more than 8 planets of equal mass sharing a circular orbit must be equally spaced for dynamical stability.
In contrast, less than 7 equal-mass planets are stable only in a configuration where all of the planets remain on the same side of their parent star. In the intermediate cases of 7 or 8 equal-mass planets, both the equally- and unequally-spaced configurations are stable. If they indeed exist, the lopsided "Salo systems" will produce a greater radial velocity signal than a single such planet would, but a smaller signal than if all of the planets were combined into one.
In fact, such systems with 7 or 8 planets induce Doppler shifts almost 4 times as great as an individual planet, but only about half as great as their combined mass would. By symmetry, it is clear that equally-spaced Salo systems will produce no reflex motion or radial velocity signal at all in their parent stars. This could lead to their being overlooked entirely, unless they happen to be detected by the transit method.

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