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Evolution in the Black Hole - Galaxy Scaling Relations and the Duty Cycle of Nuclear Activity in Star-Forming Galaxies

We measure the location and evolutionary vectors of 69 Herschel-detected broad-line active galactic nuclei (BLAGNs) in the M_BH-M_* plane. BLAGNs are selected from the COSMOS and CDF-S fields, and span the redshift range 0.2< z<2.1. Black-hole masses are calculated using archival spectroscopy and single-epoch virial mass estimators, and galaxy total stellar masses are calculated by fitting the spectral energy distribution (subtracting the BLAGN component). The mass-growth rates of both the black hole and galaxy are calculated using Chandra/XMM-Newton X-ray and Herschel far-infrared data, reliable measures of the BLAGN accretion and galaxy star formation rates, respectively. We use Monte Carlo simulations to account for biases in our sample, due to both selection limits and the steep slope of the massive end of the galaxy stellar-mass distribution. We find our sample is consistent with no evolution in the M_BH-M_* relation from z~2 to z~0. BLAGNs and their host galaxies which lie off the black hole mass galaxy total stellar mass relation tend to have evolutionary vectors anti-correlated with their mass ratios: that is, galaxies with over-massive (under-massive) black holes tend to have a low (high) ratio of the specific accretion rate to the specific star formation rate. We also use the measured growth rates to estimate the preferred AGN duty cycle for our galaxies to evolve most consistently onto the local M_BH-M_Bul relation. Under reasonable assumptions of exponentially declining star formation histories, the data suggest a non-evolving (no more than a factor of a few) BLAGN duty cycle among star-forming galaxies of 10% (1sigma range of 1-42% at z<1 and 2-34% at z>1).