European Pulsar Timing Array Limits on Continuous Gravitational Waves
  from Individual Supermassive Black Hole Binaries
  We have searched for continuous gravitational wave (CGW) signals produced by
individually resolvable, circular supermassive black hole binaries (SMBHBs) in
the latest EPTA dataset, which consists of ultra-precise timing data on 41
millisecond pulsars. We develop frequentist and Bayesian detection algorithms
to search both for monochromatic and frequency-evolving systems. None of the
adopted algorithms show evidence for the presence of such a CGW signal,
indicating that the data are best described by pulsar and radiometer noise
only. Depending on the adopted detection algorithm, the 95\% upper limit on the
sky-averaged strain amplitude lies in the range $6\times
10^{-15}<A<1.5\times10^{-14}$ at $5{\rm nHz}<f<7{\rm nHz}$. This limit varies
by a factor of five, depending on the assumed source position, and the most
constraining limit is achieved towards the positions of the most sensitive
pulsars in the timing array. The most robust upper limit -- obtained via a full
Bayesian analysis searching simultaneously over the signal and pulsar noise on
the subset of ours six best pulsars -- is $A\approx10^{-14}$. These limits, the
most stringent to date at $f<10{\rm nHz}$, exclude the presence of
sub-centiparsec binaries with chirp mass $\cal{M}_c>10^9$M$_\odot$ out to a
distance of about 25Mpc, and with $\cal{M}_c>10^{10}$M$_\odot$ out to a
distance of about 1Gpc ($z\approx0.2$). We show that state-of-the-art SMBHB
population models predict $<1\%$ probability of detecting a CGW with the
current EPTA dataset, consistent with the reported non-detection. We stress,
however, that PTA limits on individual CGW have improved by almost an order of
magnitude in the last five years. The continuing advances in pulsar timing data
acquisition and analysis techniques will allow for strong astrophysical
constraints on the population of nearby SMBHBs in the coming years.
