N-jettiness subtractions for gg → H at subleading power

N-jettiness subtractions provide a general approach for performing fully-differential next-to-next-toleading order (NNLO) calculations. Since they are based on the physical resolution variable N-jettiness, T-N, subleading power corrections in iota = T-N/Q, with Q a hard interaction scale, can also be systematically computed. We study the structure of power corrections for 0-jettiness, T-0, for the gg -> H process. Using the soft-collinear effective theory we analytically compute the leading power corrections a(s)tau ln tau and alpha(2)(s) iota ln(3) iota (finding partial agreement with a previous result in the literature), and perform a detailed numerical study of the power corrections in the gg, gq, and q (q) over bar channels. This includes a numerical extraction of the alpha(s)iota and alpha(2)(s)iota ln(2) tau corrections, and a study of the dependence on the T-0 definition. Including such power suppressed logarithms significantly reduces the size of missing power corrections, and hence improves the numerical efficiency of the subtraction method. Having a more detailed understanding of the power corrections for both q (q) over bar and gg initiated processes also provides insight into their universality, and hence their behavior in more complicated processes where they have not yet been analytically calculated.