We have completed a high-contrast direct imaging survey for giant planets around 57 debris disk stars as part of the Gemini NICI Planet-Finding Campaign .
We achieved median H -band contrasts of 12.4 mag at 0.5 ^ { \prime \prime } and 14.1 mag at 1 " separation .
Follow-up observations of the 66 candidates with projected separation < 500Â AU show that all of them are background objects . To establish statistical constraints on the underlying giant planet population based on our imaging data , we have developed a new Bayesian formalism that incorporates ( 1 ) non-detections , ( 2 ) single-epoch candidates , ( 3 ) astrometric and ( 4 ) photometric information , and ( 5 ) the possibility of multiple planets per star to constrain the planet population .
Our formalism allows us to include in our analysis the previously known \beta  Pictoris and the HR 8799 planets .
Our results show at 95 % confidence that < 13 % of debris disk stars have a \geq 5 M _ { Jup } Â planet beyond 80Â AU , and < 21 % of debris disk stars have a \geq 3 M _ { Jup } Â planet outside of 40Â AU , based on hot-start evolutionary models .
We model the population of directly-imaged planets as d ^ { 2 } N / dMda \propto m ^ { \alpha } a ^ { \beta } , where m is planet mass and a is orbital semi-major axis ( with a maximum value of a _ { max } ) .
We find that \beta < -0.8 and/or \alpha > 1.7 .
Likewise , we find that \beta < -0.8 and/or a _ { max } < 200 Â AU .
For the case where the planet frequency rises sharply with mass ( \alpha > 1.7 ) , this occurs because all the planets detected to date have masses above 5 M _ { Jup } , but planets of lower mass could easily have been detected by our search .
If we ignore the \beta  Pic and HR 8799 planets ( should they belong to a rare and distinct group ) , we find that < 20 % of debris disk stars have a \geq 3 M _ { Jup }  planet beyond 10 AU , and \beta < -0.8 and/or \alpha < -1.5 .
Likewise , \beta < -0.8 and/or a _ { max } < 125 Â AU .
Our Bayesian constraints are not strong enough to reveal any dependence of the planet frequency on stellar host mass . Studies of transition disks have suggested that about 20 % of stars are undergoing planet formation ; our non-detections at large separations show that planets with orbital separation > 40 Â AU and planet masses > 3 Â M _ { Jup } Â do not carve the central holes in these disks .