We present an analysis of the extended mid-infrared (MIR) emission of the Great Observatories All-Sky LIRG Survey (GOALS) sample based on 5-15um low resolution spectra obtained with the IRS on Spitzer. We calculate the fraction of extended emission as a function of wavelength for the galaxies in the sample, FEE_lambda. We can identify 3 general types of FEE_lambda: one where it is constant, one where features due to emission lines and PAHs appear more extended than the continuum, and a third which is characteristic of sources with deep silicate absorption at 9.7um. More than 30% of the galaxies have a median FEE_lambda larger than 0.5 implying that at least half of their MIR emission is extended. Luminous Infrared Galaxies (LIRGs) display a wide range of FEE in their warm dust continuum (0<=FEE_13.2um<=0.85). The large values of FEE_13.2um that we find in many LIRGs suggest that their extended MIR continuum emission originates in scales up to 10kpc. The mean size of the LIRG cores at 13.2um is 2.6kpc. However, once the LIR of the systems reaches the threshold of ~10^11.8Lsun, all sources become clearly more compact, with FEE_13.2um<=0.2, and their cores are unresolved. Our estimated upper limit for the core size of ULIRGs is less than 1.5kpc. The analysis indicates that the compactness of systems with LIR>~10^11.25Lsun strongly increases in those classified as mergers in their final stage of interaction. The FEE_13.2um is also related to the contribution of an active galactic nucleus (AGN) to the MIR. Galaxies which are more AGN-dominated are less extended, independently of their LIR. We finally find that the extent of the MIR continuum emission is correlated with the far-IR IRAS log(f_60um/f_100um) color. This enables us to place a lower limit to the area in a galaxy from where the cold dust emission may originate, a prediction which can be tested soon with the Herschel Space Telescope.
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