  Previous secondary eclipse observations of the hot Jupiter Qatar-1b in the Ks
band suggest that it may have an unusually high day side temperature,
indicative of minimal heat redistribution. There have also been indications
that the orbit may be slightly eccentric, possibly forced by another planet in
the system. We investigate the day side temperature and orbital eccentricity
using secondary eclipse observations with Spitzer. We observed the secondary
eclipse with Spitzer/IRAC in subarray mode, in both 3.6 and 4.5 micron
wavelengths. We used pixel-level decorrelation to correct for Spitzer's
intra-pixel sensitivity variations and thereby obtain accurate eclipse depths
and central phases. Our 3.6 micron eclipse depth is 0.149 +/- 0.051% and the
4.5 micron depth is 0.273 +/- 0.049%. Fitting a blackbody planet to our data
and two recent Ks band eclipse depths indicates a brightness temperature of
1506 +/- 71K. Comparison to model atmospheres for the planet indicates that its
degree of longitudinal heat redistribution is intermediate between fully
uniform and day side only. The day side temperature of the planet is unlikely
to be as high (1885K) as indicated by the ground-based eclipses in the Ks band,
unless the planet's emergent spectrum deviates strongly from model atmosphere
predictions. The average central phase for our Spitzer eclipses is 0.4984 +/-
0.0017, yielding e cos(omega) = -0.0028 +/- 0.0027. Our results are consistent
with a circular orbit, and we constrain e cos(omega) much more strongly than
has been possible with previous observations.
