Search for ultra-long gravitational waves in pulsars’ rotational parameters

A method is suggested to explore the gravitational wave background (GWB) in the frequency range from 10−12 to 10−8 Hz. That method is based on the precise measurements of pulsars’ rotational parameters: the influence of the gravitational waves (GW) in the range will affect them and therefore some conclusions about energy density of the GWB can be made using analysis of the derivatives of pulsars’ rotational frequency. The calculated values of the second derivative from a number of pulsars limit the density of GWB Ωgw as follows: Ωgw h2 < 10−6 . Also, the time series of the frequency ν of different pulsars in pulsar array can be cross-correlated pairwise in the same manner as in anomalous residuals analysis thus providing the possibility of GWB detection in ultra-low frequency range.