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The near-infrared radius-luminosity relationship for active galactic nuclei

Black hole masses for samples of active galactic nuclei (AGN) are currently estimated from single-epoch optical spectra. In particular, the size of the broad-line emitting region needed to compute the black hole mass is derived from the optical or ultraviolet continuum luminosity. Here we consider the relationship between the broad-line region size, R, and the near-infrared (near-IR) AGN continuum luminosity, L, as the near-IR continuum suffers less dust extinction than at shorter wavelengths and the prospects for separating the AGN continuum from host-galaxy starlight are better in the near-IR than in the optical. For a relationship of the form R propto L^alpha, we obtain for a sample of 14 reverberation-mapped AGN a best-fit slope of alpha=0.5+/-0.1, which is consistent with the slope of the relationship in the optical band and with the value of 0.5 naively expected from photoionisation theory. Black hole masses can then be estimated from the near-IR virial product, which is calculated using the strong and unblended Paschen broad emission lines (Pa alpha or Pa beta).