Upper limits on the isotropic gravitational radiation background from pulsar timing analysis

A pulsar and the Earth may be thought of as end masses of a free-mass gravitational wave antenna in which the relative motion of the masses is monitored by observing the Doppler shift of the pulse arrival times. Using timing residuals from PSR 1133+16, 1237+25, 1604-00, and 2045-16, an upper limit to the spectrum of the isotropic gravitational radiation background has been derived in the frequency band 4 x 10/sup -9/ to 10/sup -7/ Hz. This limit is found to be S/sub E/ = 10/sup 21/f/sup 3/ ergs cm/sup -3/ Hz/sup -1/, where S/sub E/ is the energy density spectrum and f is the frequency in Hz. This would limit the energy density at frequencies below 10/sup -8/ Hz to be 1.4 x 10/sup -4/ times the critical density.