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We propose a stringent observational test on the formation of warm Jupiters(gas-giant planets with 10 d <~ P <~ 100 d) by high-eccentricity (high-e)migration mechanisms. Unlike hot Jupiters, the majority of observed warmJupiters have pericenter distances too large to allow efficient tidaldissipation to induce migration. To access the close pericenter required formigration during a Kozai-Lidov cycle, they must be accompanied by a strongenough perturber to overcome the precession caused by General Relativity (GR),placing a strong upper limit on the perturber's separation. For a warm Jupiterat a ~ 0.2 AU, a Jupiter-mass (solar-mass) perturber is required to be <~ 3 AU(<~ 30 AU) and can be identified observationally. Among warm Jupiters detectedby Radial Velocities (RV), >~ 50% (5 out of 9) with large eccentricities (e >~0.4) have known Jovian companions satisfying this necessary condition forhigh-e migration. In contrast, <~ 20 % (3 out of 17) of the low-e (e <~ 0.2)warm Jupiters have detected additional Jovian companions, suggesting thathigh-e migration with planetary perturbers may not be the dominant formationchannel. Complete, long-term RV follow-ups of the warm-Jupiter population willallow a firm upper limit to be put on the fraction of these planets formed byhigh-e migration. Transiting warm Jupiters showing spin-orbit misalignmentswill be interesting to apply our test. If the misalignments are solely due tohigh-e migration as commonly suggested, we expect that the majority of warmJupiters with low-e (e <~0.2) are not misaligned, in contrast with low-e hotJupiters.

Warm Jupiters Need Close "Friends" for High-Eccentricity Migration -- A Stringent Upper Limit on the Perturber's Separation