Geodesic Noise and Gravitational Wave Observations by Pulsar Timing
  Arrays
  Signals from millisecond pulsars travel to us on geodesics along the
line-of-sight that are affected by the space--time metric. The exact
path-geometry and redshifting along the geodesics determine the observed
Time-of-Arrival (ToA) of the pulses. The metric is determined by the
distribution of dark matter, gas, and stars in the galaxy and, in the final
stages of travel, by the distribution of solar system bodies. The inhomogeneous
distribution of stellar masses can have a small but significant statistical
effect on the ToAs through the perturbation of geodesics. This will result in
additional noise in ToA observations that may affect Pulsar Timing Array (PTA)
constraints on gravitational waves at very low frequencies. We employ a simple
model for the stellar distribution in our galaxy to estimate the scale of both
static and dynamic sources of what we term generically "geodesic noise". We
find that geodesic noise has a standard deviation of ${\cal O}(10)$ ns for
typical lines-of-sight. This suggests geodesic noise is relevant for estimates
of PTA sensitivity and may limit future efforts for detection of gravitational
waves by PTAs.
