  One of the proposed explanations for the broad, double-peaked Balmer emission
lines observed in the spectra of some active galactic nuclei (AGNs) is that
they are associated with sub-parsec supermassive black hole (SMBH) binaries.
Here, we test the binary broad-line region hypothesis through several decades
of monitoring of the velocity structure of double-peaked H-alpha emission lines
in 13 low-redshift, mostly radio-loud AGNs. This is a much larger set of
objects compared to an earlier test by Eracleous et al. (1997) and we use much
longer time series for the three objects studied in that paper. Although
systematic changes in radial velocity can be traced in many of their lines,
they are demonstrably not like those of a spectroscopic binary in a circular
orbit. Any spectroscopic binary period must therefore be much longer than the
span of the monitoring (assuming a circular orbit), which in turn would require
black hole masses that exceed by 1-2 orders of magnitude the values obtained
for these objects using techniques such as reverberation mapping and stellar
velocity dispersion. Moreover, the response of the double-peaked Balmer line
profiles to fluctuations of the ionizing continuum and the shape of the
Ly-alpha profiles are incompatible with a SMBH binary. The binary broad-line
region hypothesis is therefore disfavored. Other processes evidently shape
these line profiles and cause the long-term velocity variations of the double
peaks.
