Here we present an analysis of high-precision pulsar timing data taken as part of the North American Nanohertz Observatory for Gravitational waves ( NANOGrav ) project .
We have observed 17 pulsars for a span of roughly five years using the Green Bank and Arecibo radio telescopes .
We analyze these data using standard pulsar timing models , with the addition of time-variable dispersion measure and frequency-variable pulse shape terms .
Sub-microsecond timing residuals are obtained in nearly all cases , and the best root-mean-square timing residuals in this set are \sim 30–50 ns .
We present methods for analyzing post-fit timing residuals for the presence of a gravitational wave signal with a specified spectral shape .
These properly and optimally take into account the timing fluctuation power removed by the model fit , and can be applied to either data from a single pulsar , or to a set of pulsars to detect a correlated signal .
We apply these methods to our dataset to set an upper limit on the strength of the nHz-frequency stochastic supermassive black hole gravitational wave background of h _ { c } ( 1 ~ { } \mathrm { yr } ^ { -1 } ) < 7 \times 10 ^ { -15 } ( 95 % ) .
This result is dominated by the timing of the two best pulsars in the set , PSRs J1713 + 0747 and J1909 - 3744 .