  A large number of studies have responded to the growing body of confirmed
terrestrial habitable zone exoplanets by presenting models of various possible
climates. However, the impact of the partial pressure of background gases such
as N$_2$ has not yet been well-explored, despite the abundance of N$_2$ in
Earth's atmosphere and the lack of constraints on its typical abundance in
terrestrial planet atmospheres. We use PlaSim, a fast 3D climate model, to
simulate many hundreds of climates around Sun-like stars with varying N$_2$
partial pressures, instellations, and surface characteristics to identify the
impact of the background gas partial pressure on the climate. We find that the
climate's response is nonlinear and highly sensitive to the background gas
partial pressure. We identify pressure broadening of greenhouse gas (such as
CO$_2$ and H$_2$O) absorption lines, amplification of warming or cooling by the
water vapor greenhouse positive feedback, heat transport efficiency, and
cooling through Rayleigh scattering as the dominant competing mechanisms that
determine the equilibrium climate for a given N$_2$ partial pressure. Finally,
we show that different amounts of N$_2$ should have a significant effect on
broadband reflected light observations of terrestrial exoplanets around
Sun-like stars.
