  Observations indicate that some of the largest Kuiper Belt Objects (KBOs)
have retained volatiles in the gas phase, which implies the presence of an
atmosphere that can affect their reflectance spectra and thermal balance.
Volatile escape rates driven by solar heating of the surface were estimated by
Schaller and Brown (2007) (SB) and Levi and Podolak (2009)(LP) using Jeans
escape from the surface and a hydrodynamic model respectively. Based on recent
molecular kinetic simulations these rates can be hugely in error (e.g., a
factor of $\sim 10^{16}$ for the SB estimate for Pluto). In this paper we
estimate the loss of primordial N$_2$ for several large KBOs guided by recent
molecular kinetic simulations of escape due to solar heating of the surface and
due to UV/EUV heating of the upper atmosphere. For the latter we extrapolate
simulations of escape from Pluto (Erwin et al. 2013) using the energy limited
escape model recently validated for the KBOs of interest by molecular kinetic
simulations (Johnson et al. 2013). Unless the N$_2$ atmosphere is thin
($\lesssim 10^{18}$ N$_2$/cm$^2$) and/or the radius small ($\lesssim 200-300$
km), we find that escape is primarily driven by the UV/EUV radiation absorbed
in the upper atmosphere rather than the solar heating of the surface. This
affects the previous interpretations of the relationship between atmospheric
loss and the observed surface properties. The long-term goal is to connect
detailed atmospheric loss simulations with a model for volatile transport
(e.g., Young, 2014) for individual KBOs.
