In contrast to radial velocity surveys , results from microlensing surveys indicate that giant planets with masses greater than the critical mass for core accretion ( \sim 0.1 ~ { } M _ { Jup } ) are relatively common around low-mass stars .
Using the methodology developed in the first paper , we predict the sensitivity of M-dwarf radial velocity ( RV ) surveys to analogs of the population of planets inferred by microlensing .
We find that RV surveys should detect a handful of super-Jovian ( > M _ { Jup } ) planets at the longest periods being probed .
These planets are indeed found by RV surveys , implying that the demographic constraints inferred from these two methods are consistent .
We show that if total RV measurement uncertainties can be reduced by a factor of a few , it is possible to detect the large reservoir of giant planets ( 0.1 - 1 ~ { } M _ { Jup } ) comprising the bulk of the population inferred by microlensing .
We predict that these planets will likely be found around stars that are less metal-rich than the stars which host super-Jovian planets .
Finally , we combine the results from both methods to estimate planet frequencies spanning wide regions of parameter space .
We find that the frequency of Jupiters and super-Jupiters ( 1 \lesssim m _ { p } \sin { i } / M _ { Jup } \lesssim 13 ) with periods 1 \leq P / { days } \leq 10 ^ { 4 } is f _ { J } = 0.029 ^ { +0.013 } _ { -0.015 } , a median factor of 4.3 ( 1.5 - 14 at 95 % confidence ) smaller than the inferred frequency of such planets around FGK stars of 0.11 \pm 0.02 .
However , we find the frequency of all giant planets with 30 \lesssim m _ { p } \sin { i } / M _ { \oplus } \lesssim 10 ^ { 4 } and 1 \leq P / { days } \leq 10 ^ { 4 } to be f _ { G } = 0.15 ^ { +0.06 } _ { -0.07 } , only a median factor of 2.2 ( 0.73 - 5.9 at 95 % confidence ) smaller than the inferred frequency of such planets orbiting FGK stars of 0.31 \pm 0.07 .
For a more conservative definition of giant planets ( 50 \lesssim m _ { p } \sin { i } / M _ { \oplus } \lesssim 10 ^ { 4 } ) , we find f _ { G ^ { \prime } } = 0.11 \pm 0.05 , a median factor of 2.2 ( 0.73 - 6.7 at 95 % confidence ) smaller than that inferred for FGK stars of 0.25 \pm 0.05 .
Finally , we find the frequency of all planets with 1 \leq m _ { p } \sin { i } / M _ { \oplus } \leq 10 ^ { 4 } and 1 \leq P / { days } \leq 10 ^ { 4 } to be f _ { p } = 1.9 \pm 0.5 .