Investigating ultra-long gravitational waves with measurements of pulsar rotational parameters

A method is suggested with which to explore the gravitational wave background (GWB) in the frequency range 10^?12–10^?8 Hz. This method is based on the precise measurements of pulsar rotational parameters: the influence of gravitational waves (GWs) in this frequency range will affect these parameters and therefore some conclusions about the energy density of the GWB can be made using analysis of the derivatives of pulsar rotational frequency. The calculated values of the second derivative from a number of pulsars limit the density of the GWB, Ω_gw, as follows:  Ω_gw < 2 × 10^?6  . Also, the time series of the frequency ν of different pulsars in a pulsar array can be cross-correlated pairwise in the same manner as in anomalous residuals analysis, thus providing the possibility of GWB detection in the ultra-low-frequency range.