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We present the first study to synthesize results from five differentexoplanet surveys using three independent detection methods: microlensing,radial velocity, and direct imaging. The constraints derived herein representthe most comprehensive picture of the demographics of large-separation (>~ 2AU) planets orbiting the most common stars in our Galaxy that has beenconstructed to date. We assume a simple, joint power-law planet distributionfunction of the form d^2N_{pl}/[dlog(m_p)dlog(a)] =A(m_p/M_{Sat})^{alpha}(a/2.5 AU)^{beta} with an outer cutoff radius of theseparation distribution function of a_{out}. Generating populations of planetsfrom these models and mapping them into the relevant observables for eachsurvey, we use actual or estimated detection sensitivities to determine theexpected observations for each survey. Comparing with the reported results, wederive constraints on the parameters {alpha, beta, A, a_{out}} that describe asingle population of planets that is simultaneously consistent with the resultsof microlensing, RV, and direct imaging surveys. We find median and 68%confindence intervals of alpha = -0.86^{+0.21}_{-0.19} (-0.85^{+0.21}_{-0.19}),beta = 1.1^{+1.9}_{-1.4} (1.1^{+1.9}_{-1.3}), A = 0.21^{+0.20}_{-0.15} dex^{-2}(0.21^{+0.20}_{-0.15} dex^{-2}), and a_{out} = 10^{+26}_{-4.7} AU(12^{+50}_{-6.2} AU) assuming "hot-start" ("cold-start") planet evolutionarymodels. These values are consistent with all current knowledge of planets onorbits beyond ~2 AU around M dwarfs.

astrophysical journal/the astrophysical journal

Synthesizing Exoplanet Demographics: A Single Population of Long-Period  Planetary Companions to M Dwarfs Consistent with Microlensing, Radial  Velocity, and Direct Imaging Surveys