Stochastic gravitational wave background:: Upper limits in the 10-6 to 10-3 Hz band

We have used precision Doppler tracking of the Cassini spacecraft during its 2001-2002 solar opposition to derive improved observational limits to an isotropic background of low-frequency gravitational waves. Using the Cassini multilink radio system and an advanced tropospheric calibration system, the effects of heretofore leading noises-plasma and tropospheric scintillation-were, respectively, removed and calibrated to levels lower than other noises. The resulting data were used to construct upper limits to the strength of an isotropic background in the 10(-6) to 10(-3) Hz band. Our results are summarized as limits on the strain spectrum S-h(f), the characteristic strain (h(c) = the square root of the product of the frequency and the one-sided spectrum of strain at that frequency), and the energy density (Omega = energy density in bandwidth equal to center frequency assuming a locally white energy density spectrum, divided by the critical density). Our best limits are S-h(f) < 6 x 10(-27) Hz(-1) at several frequencies in the millihertz band, h(c) < 2 x 10(-15) at about 0.3 mHz, and Omega < 0.025 x h(75)(-2), where h(75) is the Hubble constant in units of 75 km s(-1) Mpc(-1), at 1.2 x 10(-6) Hz. These are the best observational limits in the low-frequency band, the bound on Omega, for example, being about 3 orders of magnitude better than previous constraints from Doppler tracking.