Timing as a probe of non-Einsteinian polarizations of gravitational waves

Einstein's theory of gravity predicts waves of the distortion of spacetime with two degrees of polarization; alternative theories predict more polarizations, up to a maximum of six. Although laser interferometric gravity wave detectors can be used to search for at least some of the non-Einsteinian polarizations, their configuration is not optimal for the task. By contrast, the angular distribution of pulsars in the sky makes pulsar timing a flexible tool for detecting all polarizations. We give here an analysis of the sensitivity of pulsar timing to an isotropic stochastic gravitational wave background of waves with non-Einsteinian polarizations and conclude that their detection may be feasible in the near future. In particular, we compute the number of pulsars necessary to detect a stochastic background made up of one type of polarization and to distinguish non-Einsteinian from standard polarizations. We conclude that for biweekly observations made for five years with rms timing accuracy of 100 ns, detecting non-Einsteinian modes will require: 60 pulsars in the case of the longitudinal mode; 60 for the two spin-1 shear'' modes; and 40 for the spin-0 breathing'' mode. These are targets that should be easily achievable with the proposed Square Kilometer Array project. To discriminate non-Einsteinian modes from Einsteinian modes, we need 40 pulsars for the breathing mode, 100 pulsars for the longitudinal mode, and 500 pulsars for the shear mode. We confirm the previous estimate that 40 pulsars are needed to detect the spin-2 transverse'' (Einsteinian) polarizations. Better focused statistical tests may allow improvements in sensitivity for some of these polarizations.