K2-146 is a mid-M dwarf ( M _ { \star } = 0.331 \pm 0.009 M _ { \odot } ; R _ { \star } = 0.330 \pm 0.010 R _ { \odot } ) , observed in Campaigns 5 , 16 , and 18 of the K2 mission .
In Campaign 5 data , a \added single planet was discovered with an orbital period of 2.6 days and large transit timing variations due to an unknown perturber .
Here we analyze data from Campaigns 16 and 18 , detecting the transits of a \replaced planet csecond planet , c , with an orbital period of 4.0 days , librating in a 3:2 resonance with planet b .
Large , anti-correlated timing variations of both planets exist due to their resonant perturbations .
The planets have a mutual inclination of 2.40 ^ { \circ } \pm 0.25 ^ { \circ } , which torqued planet c more closely into our line-of-sight .
Planet c was grazing in Campaign 5 and thus missed in previous searches ; in Campaigns 16 and 18 it is fully transiting , and its transit depth is three times larger .
We improve the stellar properties using data from Gaia DR2 , and \replaced use ourusing dynamical fits \deleted to find that both planets are sub-Neptunes : their masses are 5.77 \pm 0.18 and 7.50 \pm 0.23 M _ { \oplus } and their radii are 2.04 \pm 0.06 and 2.19 \pm 0.07 R _ { \oplus } , respectively .
These mass constraints set the precision record for small exoplanets ( a few gas giants have comparable relative precision ) .
These planets lie in the photoevaporation valley when viewed in Radius-Period space , but due to the low-luminosity M-dwarf host star , they lie among the atmosphere-bearing planets when viewed in Radius-Irradiation space .
This , along with their densities being 60 % -80 % that of Earth , suggests that they may both have retained a substantial gaseous envelope .