  Spitzer-IRS maps of H_2 pure rotational lines from S(0) to S(7) in 3 outflows
from Class 0 sources - L1448, BHR71, and NGC2071 - are presented. These lines
are used, in conjunction with available rovibrational, near-IR H_2 lines, to
probe the physical conditions of the warm gas between hundreds and thousands of
Kelvin. We have constructed maps of the molecular hydrogen column density,
ortho-to-para ratio and volume density, together with the index beta of the
power law describing the distribution of gas temperature. In all three
outflows, the present ortho-to-para ratio significantly deviates from the high
temperature equilibrium of 3, being on average between 2.0 and 2.3. These low
values, that reflect the young age of these flows, are found also in regions of
relatively high temperature (~ 1000 K), likely indicating that shocks are
occurring in a time shorter than that needed for a complete para to ortho
conversion. Density maps indicate upper limits close to LTE conditions, i.e.
between 10^6-10^7 cm^-3; moreover we demonstrate, based on the detections of HD
emission spots (R(3) and R(4) lines), that a density stratification does exist,
with the low density components (10^4-10^5 cm^-3) associated with the coldest
gas. The beta index is found in all flows to be above 3.8: this value is
consistent with predictions of multiple C-type bow shocks with a range of
velocities, some of which insufficient to achieve the temperature at which H_2
partially dissociates. The contribution of H_2 to the total cooling is
quantitatively similar to that of other abundant molecules emitting in the
far-infrared, such as water and CO; moreover, the luminosity radiated away is
comparable with the estimated kinetic energy of the swept-out outflow: this
supports the scenario in which the shock from which H_2 is emitted is also
capable of accelerating the molecular outflow driven at the shock working
surface.
