TTV-determined Masses for Warm Jupiters and their Close Planetary Companions

Although the formation and the properties of hot Jupiters (with orbital periods $P<10\,$d) have attracted a great deal of attention, the origins of warm Jupiters ($10<P<100\,$d) are less well-studied. Using a transit timing analysis, we present the orbital parameters of five planetary systems containing warm Jupiters, Kepler 30, Kepler 117, Kepler 302, Kepler 487 and Kepler 418. Three of them, Kepler-30 c($M_p=549.4{\pm{5.6}}M_{\oplus}$), Kepler-117 c($M_p=702{\pm{63}}M_{\oplus}$) and Kepler 302 c($M_p=933\pm 527M_{\oplus}$), are confirmed to be real warm Jupiters based on their mass. Insights drawn from the radius-temperature relationship lead to the inference that hot Jupiters and warm Jupiters can be roughly separated by ${T_{\rm eff,c}} =1123.7\pm3.3$ K. Also, ${T_{\rm eff,c}}$ provides a good separation for Jupiters with companion fraction consistent with zero($T_{\rm eff}>T_{\rm eff,c}$) and those with companion fraction significantly different from zero ($T_{\rm eff}<T_{\rm eff,c}$).