Probing the 3.6 Micron CIRB with Spitzer in 3 DIRBE Dark Spots

We observed three regions of the sky with Spitzer in which the Cosmic InfraRed Background (CIRB) has been determined at 3.5 microns using the method of subtracting 2MASS stellar fluxes from zodiacal light subtracted DIRBE maps. For each of these regions we have obtained 270 seconds of integration time per pixel with IRAC on Spitzer over the central square degree. We present galaxy counts in each of these approximately 1 square degree IRAC surveys. Along with deep galaxy counts in the Extended Groth Strip and GOODS North, we are able to compare the galactic contribution to the CIRB with the "DIRBE minus 2MASS'' determined L-band CIRB. Using the profile-fit photometry package GIM2D, we find a substantially larger flux contribution to the CIRB than that determined using aperture photometry. We have also made the first rigorous analysis of the uncertainties in determining the CIRB via galaxy counts in Spitzer images using a Monte Carlo Markov Chain simulation of our data analysis. Using a simple broken power law model for galaxy counts as a function of magnitude we find a most probable contribution to the CIRB from galaxies at 3.6 microns of 10.8^{+2.1}_{-1.1} kJy/sr. Even with this restricted model, however, we find that galaxy counting does not strongly constrain the CIRB from above. We are able to find solutions in which the CIRB runs away to large intensities without the need for an additional diffuse source.