Cold Jupiters and improved masses in 38 Kepler and K2 small-planet systems from 3661 high-precision HARPS-N radial velocities. No excess of cold Jupiters in small-planet systems

The exoplanet population with orbital periods $P<100$ d around solar-type stars is dominated by super-Earths and sub-Neptunes. These planets are, however, missing in our Solar System, and the reason for that is unknown. Two theoretical scenarios invoke the role of Jupiter as the possible culprit: Jupiter may have acted as a dynamical barrier to the inward migration of sub-Neptunes from beyond the water iceline or, alternatively, may have reduced considerably the inward flux of material (pebbles) required to form super-Earths inside that iceline. Both scenarios predict an anti-correlation between the presence of small planets (SPs) and that of cold Jupiters (CJs) in exoplanetary systems. To test that prediction, we homogeneously analyzed the radial-velocity (RV) measurements of 38 Kepler and K2 transiting SP systems gathered over almost 10 years with the HARPS-N spectrograph, as well as publicly available RVs collected with other facilities. We detected five CJs in three systems, two in Kepler-68, two in Kepler-454, and a very eccentric one in K2-312. We derived an occurrence rate of $9.3^{+7.7}_{-2.9}\%$ for CJs with $0.3-13~M_{Jup}$ and 1-10 au, which is lower but still compatible at $1.3\sigma$ with that measured from RV surveys for solar-type stars, regardless of SP presence. This does not allow us to draw a firm conclusion about the predicted anti-correlation between SPs and CJs, which would require a considerably larger sample. Nevertheless, we found no evidence of previous claims of an excess of CJs in SP systems. As an important by-product of our analyses, we homogeneously determined the masses of 64 Kepler and K2 small planets, reaching a precision better than 5, 7.5 and 10$\sigma$ for 25, 13 and 8 planets, respectively. Finally, we release to the scientific community the 3661 HARPS-N radial velocities used in this work. [Abridged]