  The bright M dwarf K2-18 at 34 pc is known to host a transiting
super-Earth-sized planet orbiting within the star's habitable zone; K2-18b.
Given the superlative nature of this system for studying an exoplanetary
atmosphere receiving similar levels of insolation as the Earth, we aim to
characterize the planet's mass which is required to interpret atmospheric
properties and infer the planet's bulk composition. We obtain precision radial
velocity measurements with the HARPS spectrograph and couple those measurements
with the K2 photometry to jointly model the observed radial velocity variation
with planetary signals and a radial velocity jitter model based on Gaussian
process regression. We measure the mass of K2-18b to be $8.0 \pm 1.9$
M$_{\oplus}$ with a bulk density of $3.7 \pm 0.9$ g/cm$^3$ which may correspond
to a predominantly rocky planet with a significant gaseous envelope or an ocean
planet with a water mass fraction $\gtrsim 50$%. We also find strong evidence
for a second, warm super-Earth K2-18c at $\sim 9$ days with a semi-major axis
2.4 times smaller than the transiting K2-18b. After re-analyzing the available
light curves of K2-18 we conclude that K2-18c is not detected in transit and
therefore likely has an orbit that is non-coplanar with K2-18b. A suite of
dynamical integrations with varying simulated orbital eccentricities of the two
planets are used to further constrain each planet's eccentricity posterior from
which we measure $e_b < 0.43$ and $e_c < 0.47$ at 99% confidence. The discovery
of the inner planet K2-18c further emphasizes the prevalence of multi-planet
systems around M dwarfs. The characterization of the density of K2-18b reveals
that the planet likely has a thick gaseous envelope which along with its
proximity to the Solar system makes the K2-18 planetary system an interesting
target for the atmospheric study of an exoplanet receiving Earth-like
insolation.
