Correlations between the stellar, planetary, and debris components of exoplanet systems observed by <em>Herschel</em>

Context. Stars form surrounded by gas-and dust-rich protoplanetary discs. Generally, these discs dissipate over a few (3-10) Myr, leaving a faint tenuous debris disc composed of second-generation dust produced by the attrition of larger bodies formed in the protoplanetary disc. Giant planets detected in radial velocity and transit surveys of main-sequence stars also form within the protoplanetary disc, whilst super-Earths now detectable may form once the gas has dissipated. Our own solar system, with its eight planets and two debris belts, is a prime example of an end state of this process. Aims. The Herschel DEBRIS, DUNES, and GT programmes observed 37 exoplanet host stars within 25 pc at 70, 100, and 160 μm with the sensitivity to detect far-infrared excess emission at flux density levels only an order of magnitude greater than that of the solar system's Edgeworth-Kuiper belt. Here we present an analysis of that sample, using it to more accurately determine the (possible) level of dust emission from these exoplanet host stars and thereafter determine the links between the various components of these exoplanetary systems through statistical analysis. Methods. We have fitted the flux densities measured from recent Herschel observations with a simple two parameter (Td, LIR /L) black-body model (or to the 3σ upper limits at 100 μm). From this uniform approach we calculated the fractional luminosity, radial extent and dust temperature. We then plotted the calculated dust luminosity or upper limits against the stellar properties, e.g. effective temperature, metallicity, and age, and identified correlations between these parameters. Results. A total of eleven debris discs are identified around the 37 stars in the sample. An incidence of ten cool debris discs around the Sun-like exoplanet host stars (29 ± 9%) is consistent with the detection rate found by DUNES (20.2 ± 2.0%). For the debris disc systems, the dust temperatures range from 20 to 80 K, and fractional luminosities (LIR /L) between 2.4 ×10-6 and 4.1 ×10-4 . In the case of non-detections, we calculated typical 3σ upper limits to the dust fractional luminosities of a few ×10-6 . Conclusions. We recover the previously identified correlation between stellar metallicity and hot-Jupiter planets in our data set. We find a correlation between the increased presence of dust, lower planet masses, and lower stellar metallicities. This confirms the recently identified correlation between cold debris discs and low-mass planets in the context of planet formation by core accretion.