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Any unambiguous detection of a stochastic gravitational wave background by apulsar timing array will rest on the measurement of a characteristic angularcorrelation between pulsars. The ability to measure this correlation willdepend on the geometry of the array. However, spatially correlated sources ofnoise, such as errors in the planetary ephemeris or clock errors, can producefalse-positive correlations. The severity of this contamination will alsodepend on the geometry of the array. This paper quantifies these geometriceffects with a spherical harmonic analysis of the pulsar timing residuals. Atleast 9 well-spaced pulsars are needed to simultaneously measure agravitational wave background and separate it from ephemeris and clock errors.Uniform distributions of pulsars can eliminate the contamination for arrayswith large numbers of pulsars, but pulsars following the galactic distributionof known millisecond pulsars will always be affected. We quantitativelydemonstrate the need for arrays to include many pulsars and for the pulsars tobe distributed as uniformly as possible. Finally, we suggest a technique tocleanly separate the effect of ephemeris and clock errors from thegravitational wave signal.

Ephemeris Errors and the Gravitational Wave Signal: Harmonic Mode Coupling in Pulsar Timing Array Searches