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The Orion's Arm Facebook group shared Andrew LePage's post at his blog Drew Ex Machina for the search for planets at Proxima Centauri, the small red dwarf that is not only the closest star to our solar system but which is likely the third component in the Alpha Centauri trinary. LePage goes over the various searches and notes that none have been found, but then, none would be likely to be found given the propensity of red dwarfs not to have massive planets.

The best planet survey results to date have failed to detect any planets or brown dwarfs orbiting Proxima Centauri. These results effectively eliminate the possibility of any Jupiter-size or larger planets with orbital periods ranging from a short as two days to in excess of 12 years to a confidence level of 90% to 95% or better. The results also effectively eliminate the possible presence any Saturn-size planets with orbital periods less than about 2000 days or Neptune-size planets with orbital periods less than about 40 days to a 95% confidence level or better. No planets with masses greater than 6 to 10 ME are likely to be present in the habitable zone of Proxima Centauri leaving the possibility that rocky, potentially habitable sub-Earth-size to super-Earth-size planets can exist in this zone and still escape detection by published searches to date with a high probability.

While there have been some who have been alarmed by the lack of any planet detections to date, it is not unexpected given what we have learned about the planetary systems of other M-dwarf stars. A recent statistical analysis of the Kepler database for M-dwarf stars performed by Courtney Dressing and David Charbonneau (Harvard-Smithsonian Center for Astrophysics) has shown that planets with radii greater than about 2.5 times that of the Earth (corresponding to 0.64 times the radius of Neptune) and orbital periods less than 200 days are rare. Planets larger than Neptune are exceptionally rare in M-dwarf systems. And since the “typical” M-dwarf in the analysis by Dressing and Charbonneau is over four times more massive than the diminutive Proxima Centauri (with the corresponding planets also tending to be larger), the lack of any planetary detections to date is even less surprising.
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