Abstract
Abstract
We quantify pulsar timing array (PTA) sensitivity to anisotropy in the gravitational-wave (GW) background using the cross-correlation-based Fisher information matrix in the pixel and spherical harmonic bases. We use a set of simulations to empirically determine scaling relations of a PTA’s sensitivity to anisotropy with the number of pulsars
N
psr
in the array, the error
δt
on the times of arrival, the frequency
f
GW
of the GWs, and the angular scale ΔΩ of the anisotropy. The sensitivity scales approximately as
N
psr
0.8
,
δt
−0.08
, and ΔΩ
1.6
− ΔΩ
2.1
(depending on the ranges of
ℓ
and
m
under consideration). In addition, we use realistic simulations to project the NANOGrav PTA sensitivity to a 30 yr baseline and quantify the growth in sensitivity at several time slices. Except at the lowest frequencies, we find negligible effect on sensitivity through increasing the observation duration only. Finally, we introduce a multi-resolution pixel basis motivated by the large dependence of the sensitivity on sky location, and demonstrate the operation of the basis through a set of injections and recoveries.