  We examine the effect of varying background N2 surface pressure (labelled as
pN2) on the inner edge of the habitable zone for 1:1 tidally locked planets
around M dwarfs, using the three-dimensional (3D) atmospheric general
circulation model (AGCM) ExoCAM. In our experiments, the rotation period is
fixed when varying the stellar flux, in order to more clearly isolate the role
of pN2. We find that the stellar flux threshold for the runaway greenhouse is a
non-monotonous function of pN2. This is due to the competing effects of five
processes: pressure broadening, heat capacity, lapse rate, relative humidity,
and clouds. These competing processes increase the complexity in predicting the
location of the inner edge of the habitable zone. For a slow rotation orbit of
60 Earth days, the critical stellar flux for the runaway greenhouse onset is
1700--1750, 1900--1950, and 1750--1800 W m$^{-2}$ under 0.25, 1.0, and 4.0 bar
of pN2, respectively, suggesting that the magnitude of the effect of pN2 is
within ~13%. For a rapid rotation orbit, the effect of varying pN2 on the inner
edge is smaller, within a range of ~7%. Moreover, we show that Rayleigh
scattering effect as varying pN2 is unimportant for the inner edge due to the
masking effect of cloud scattering and to the strong shortwave absorption by
water vapor under hot climates. Future work using AGCMs having different cloud
and convection schemes and cloud-resolving models having explicit cloud and
convection are required to revise this problem.
