Jupiter mass
In a simulation, HD 37605 b's orbit "sweeps clean" most test particles within 0.5 AU; leaving only asteroids "in low-eccentricity orbits near the known planet’s apastron distance, near the 1:2 mean-motion resonance" with oscillating eccentricity up to 0.06, and also at 1:3 with oscillating eccentricity up to 0.4. Also, observation has ruled out planets heavier than 0.7 Jupiter mass with a period of one year or less; which still allows for planets at 0.8 AU or more.