  The Orion Bar is one of the nearest and best-studied photodissociation or
photon-dominated regions (PDRs). Observations reveal the presence of H2 lines
from vibrationally or rotationally excited upper levels that suggest warm gas
temperatures (400 to 700 K). However, standard models of PDRs are unable to
reproduce such warm rotational temperatures. In this paper we attempt to
explain these observations with new comprehensive models which extend from the
H+ region through the Bar and include the magnetic field in the equation of
state. We adopt the model parameters from our previous paper which successfully
reproduced a wide variety of spectral observations across the Bar. In this
model the local cosmic-ray density is enhanced above the galactic background,
as is the magnetic field, and which increases the cosmic-ray heating elevating
the temperature in the molecular region. The pressure is further enhanced above
the gas pressure in the H+ region by the momentum transferred from the absorbed
starlight. Here we investigate whether the observed H2 lines can be reproduced
with standard assumptions concerning the grain photoelectric emission. We also
explore the effects due to the inclusion of recently computed H2 + H2, H2 + H
and H2 + He collisional rate coefficients.
