We present new limits on an isotropic stochastic gravitational-wave background ( GWB ) using a six pulsar dataset spanning 18 yr of observations from the 2015 European Pulsar Timing Array data release .
Performing a Bayesian analysis , we fit simultaneously for the intrinsic noise parameters for each pulsar , along with common correlated signals including clock , and Solar System ephemeris errors , obtaining a robust 95 \% upper limit on the dimensionless strain amplitude A of the background of A < 3.0 \times 10 ^ { -15 } at a reference frequency of 1 \mathrm { yr ^ { -1 } } and a spectral index of 13 / 3 , corresponding to a background from inspiralling super-massive black hole binaries , constraining the GW energy density to \Omega _ { \mathrm { gw } } ( f ) h ^ { 2 } < 1.1 \times 10 ^ { -9 } at 2.8 nHz .
We also present limits on the correlated power spectrum at a series of discrete frequencies , and show that our sensitivity to a fiducial isotropic GWB is highest at a frequency of \sim 5 \times 10 ^ { -9 } Hz .
Finally we discuss the implications of our analysis for the astrophysics of supermassive black hole binaries , and present 95 \% upper limits on the string tension , G \mu / c ^ { 2 } , characterising a background produced by a cosmic string network for a set of possible scenarios , and for a stochastic relic GWB .
For a Nambu-Goto field theory cosmic string network , we set a limit G \mu / c ^ { 2 } < 1.3 \times 10 ^ { -7 } , identical to that set by the Planck Collaboration , when combining Planck and high- \ell Cosmic Microwave Background data from other experiments .
For a stochastic relic background we set a limit of \Omega ^ { \mathrm { relic } } _ { \mathrm { gw } } ( f ) h ^ { 2 } < 1.2 \times 10 ^ { -9 } , a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array .