Note on pulsar timing array correlation functions induced by peculiar velocities

Abstract

Several papers have recently calculated the contribution to pulsar timing array overlap reduction functions (ORFs) induced by our peculiar velocity with respect to the rest frame of the stochastic gravitational-wave background. Here we show that a harmonic-space calculation confirms the most recent result. We note that, with the harmonic-space calculation, the ORFs for spin-1 GWs and the correlations with astrometry measurements are also easily obtained.

Figures (2)

• Figure 1: Results for the monopole, dipole, and quadrupole ORFs from Ref. Blumke:2025nrq for $\hat{\boldsymbol{x}}_a \parallel \hat{\bm v}$, and $\theta = \text{arccos}(\hat{\bm n}_a \cdot \hat{\bm n}_b)$. The dashed curves are the results from the harmonic-space calculation.
• Figure 2: As in Fig. \ref{['fig:compare']}, but for $\hat{\bm v} \parallel \hat{\boldsymbol{x}}_a \times \hat{\boldsymbol{x}}_b$. We show only $\Gamma^{(2)}_{ab}(\hat{\bm v} \parallel \hat{\bm x}_a \times \hat{\bm x}_b)$ because $\Gamma^{(0)}_{ab}(\hat{\bm v } \parallel \hat{\bm x}_a) = \Gamma^{(0)}_{ab}(\hat{\bm v } \parallel \hat{\bm x}_a \times \hat{\bm x}_b)$ in terms of the $\theta$ dependence and $\Gamma^{(1)}_{ab}(\hat{\bm v } \parallel \hat{\bm x}_a \times \hat{\bm x}_b) = 0$.