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).
