Measuring Supermassive Black Hole Spin in the Chandra COSMOS-Legacy
  Survey
  Spin measurements of supermassive black holes (SMBHs) provide crucial
constraints on the accretion processes that power active galactic nuclei (AGN),
fuel outflows, and trigger black hole growth. However, spin measurements are
mainly limited to a few dozen nearby sources for which high quality, high S/N
spectra (e.g., from Chandra, XMM-Newton, Suzaku, NuSTAR) are available. Here we
measure the average SMBH spin of $\sim$1900 AGN in the Chandra COSMOS-Legacy
survey using spectral stacking analysis. We find broad Fe K$\alpha$ line
emission in the average COSMOS spectrum (Gaussian width $\sigma=0.27\pm0.05$
keV), and by fitting this emission line profile with relativistic line models,
we measure the average black hole spin parameter $a=0.62~\substack{+0.07 \\
-0.17}$. The sample size, availability of multiwavelength data, and spatial
resolution of the COSMOS Legacy field also provide a unique environment to
investigate the average SMBH spin as a function of other observables (e.g.,
redshift, luminosity) up to $z\sim5.3$. We find that optically classified Type
1 sources have broader Fe K$\alpha$ line emission than Type 2 sources. X-ray
unobscured and obscured sources, as defined by their column densities, have
widths that are consistent with the optically defined unobscured and obscured
sources, respectively. There is some evidence for evolution of the Fe K$\alpha$
width and black hole spin parameter with luminosity, but not conclusively with
redshift. The results of this work provide insights into the average spins of
SMBHs in AGN, shedding light on their growth mechanisms and observed
co-evolution with their host galaxies.
