The Herschel Comprehensive (U)lirg Emission Survey (Hercules): Co Ladders, Fine Structure Lines, and Neutral Gas Cooling

(Ultra) luminous infrared galaxies ((U)LIRGs) are objects characterized by their extreme infrared (8-1000 mu m) luminosities (L-LIRG > 10(11) L-circle dot and L-ULIRG > 10(12) L-circle dot). The Herschel Comprehensive ULIRG Emission Survey (PI: van derWerf) presents a representative flux-limited sample of 29 (U)LIRGs that spans the full luminosity range of these objects (10(11)L(circle dot) <= L-IR <= 10(13)L(circle dot)). With the Herschel Space Observatory, we observe [CII] 157 mu m, [O I] 63 mu m, and [O I] 145 mu m line emission with Photodetector Array Camera and Spectrometer, CO J = 4-3 through J = 13-12, [C I] 370 mu m, and [C I] 609 mu m with SPIRE, and low-J CO transitions with ground-based telescopes. The CO ladders of the sample are separated into three classes based on their excitation level. In 13 of the galaxies, the [O I] 63 mu m emission line is self absorbed. Comparing the CO excitation to the InfraRed Astronomical Satellite 60/100 mu m ratio and to far infrared luminosity, we find that the CO excitation is more correlated to the far infrared colors. We present cooling budgets for the galaxies and find fine-structure line flux deficits in the [C II], [Si II], [O I], and [C I] lines in the objects with the highest far IR fluxes, but do not observe this for CO 4 <= J(upp) <= 13. In order to study the heating of the molecular gas, we present a combination of three diagnostic quantities to help determine the dominant heating source. Using the CO excitation, the CO J = 1-0 linewidth, and the active galactic nucleus (AGN) contribution, we conclude that galaxies with large CO linewidths always have high-excitation CO ladders, and often low AGN contributions, suggesting that mechanical heating is important.