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Measuring Star Formation and Black Hole Accretion Rates in Tandem using Mid-Infrared Spectra of Local Infrared-Luminous Galaxies

We present the results of a stacking analysis performed on Spitzer/Infrared Spectrograph high-resolution mid-infrared spectra of luminous infrared galaxies (LIRGs) in the Great Observatories All-Sky LIRG Survey (GOALS). By binning on mid-infrared active galactic nucleus (AGN) fraction and stacking spectra, we detect bright emission lines [Ne II] and [Ne III], which trace star formation, and fainter emission lines [Ne V] and [O IV], which trace AGN activity, throughout the sample. We find the [Ne II] luminosity is fairly constant across all AGN fraction bins, while the [O IV] and [Ne V] luminosities increase by over an order of magnitude. Our measured average line ratios, [Ne V]/[Ne II] and [O IV]/[Ne II], at low AGN fraction are similar to H II galaxies while the line ratios at high AGN fraction are similar to LINERs and Seyferts. We decompose the [O IV] luminosity into star-formation and AGN components by fitting the [O IV] luminosity as a function of the [Ne II] luminosity and the mid-infrared AGN fraction. The [O IV] luminosity in LIRGs is dominated by star formation for mid-infrared AGN fractions $\lesssim0.3$. With the corrected [O IV] luminosity, we calculate black hole accretion rates ranging from $10^{-5}$ M$_{\odot}$/yr at low AGN fractions to 0.2 M$_{\odot}$/yr at the highest AGN fractions. We find that using the [O IV] luminosity, without correcting for star formation, can lead to an overestimate of the BHAR by up to a factor of 30 in starburst dominated LIRGs. Finally, we show the BHAR/SFR ratio increases by more than three orders of magnitude as a function of mid-infrared AGN fraction in LIRGs.