The XENON collaboration has published stringent limits on specific dark matter – nucleon recoil spectra from dark matter recoiling on the liquid xenon detector target. In this paper, we present an approximate likelihood for the XENON1T 1 t-year nuclear recoil search applicable to any nuclear recoil spectrum. Alongside this paper, we publish data and code to compute upper limits using the method we present. The approximate likelihood is constructed in bins of reconstructed energy, profiled along the signal expectation in each bin. This approach can be used to compute an approximate likelihood and therefore most statistical results for any nuclear recoil spectrum. Computing approximate results with this method is approximately three orders of magnitude faster than the likelihood used in the original publications of XENON1T, where limits were set for specific families of recoil spectra. Using this same method, we include toy Monte Carlo simulation-derived binwise likelihoods for the upcoming XENONnT experiment that can similarly be used to assess the sensitivity to arbitrary nuclear recoil signatures in its eventual 20 t-year exposure.
