Measuring kinematic anisotropies with pulsar timing arrays

TL;DR

This work develops a formalism for detecting kinematic Doppler anisotropies in a cosmological SGWB with Pulsar Timing Arrays, showing that the leading dipolar signal scales as $\beta\sim10^{-3}$ and depends on the SGWB spectral shape and pulsar sky distribution. Using current NG15 data, the authors set a 95% C.L. upper limit $\beta<0.297$ under the cosmological-origin assumption, indicating sensitivity is far from per-mil levels. Fisher forecasts indicate that detecting the dipole at per-mil precision requires thousands of pulsars and strategic sky coverage, with improvements when pulsars align with the dipole direction; spectral features in the SGWB can further enhance detectability. The results have potential implications for resolving the CMB-LSS dipole tension and for testing gravity theories with GW anisotropies in future SKA-like PTAs.

Abstract

Recent Pulsar Timing Array (PTA) collaborations show strong evidence for a stochastic gravitational wave background (SGWB) with the characteristic Hellings-Downs inter-pulsar correlations. The signal may stem from supermassive black hole binary mergers, or early universe phenomena. The former is expected to be strongly anisotropic while primordial backgrounds are likely to be predominantly isotropic with small fluctuations. In case the observed SGWB is of cosmological origin, our relative motion with respect to the SGWB rest frame is a guaranteed source of anisotropy, leading to $\textit{O}(10^{-3})$ energy density fluctuations of the SGWB. For such cosmological SGWB, kinematic anisotropies are likely to be larger than the intrinsic anisotropies, akin to the cosmic microwave background (CMB) dipole anisotropy. We assess the sensitivity of current PTA data to the kinematic dipole anisotropy, and we also forecast at what extent the magnitude and direction of the kinematic dipole can be measured in the future with an SKA-like experiment. We also discuss how the spectral shape of the SGWB and the location of the pulsars to monitor affect the prospects of detecting the kinematic dipole with PTA. In the future, a detection of this anisotropy may even help resolve the discrepancy in the magnitude of the kinematic dipole as measured by CMB and large-scale structure observations.

Figures (6)

• Figure 1: Left: the magnitude of the PTA response function $\Gamma^{(1)}_{ab}$ to kinematic dipole anisotropies, as defined in eq \ref{['defF11']}. We fix the velocity vector $\hat{v}$ along the the direction measured by the CMB ($\hat{v}$ and $-\hat{v}$ are denoted by red and yellow stars respectively). We plot the response as a function of the positions of a pair of pulsars, for simplicity oriented in the same direction. Right: the dipole response as a function of the angle between the pulsars, without including the $(\hat{v}\cdot \hat{x}_a+\hat{v}\cdot \hat{x}_b)$ factor in eq \ref{['defF11']}.
• Figure 2: Parameter distributions and $95\%$ C.L limits for the SGWB amplitude $A$\ref{['I0equivalenceA']}, spectral index $\gamma$\ref{['gammadef']} and dipole magnitude $\beta$. (See main text and Appendix \ref{['app_conv']} for the definition of these quantities.) The recovered amplitude and tilt are consistent with the NG15 results (grey markers). We also obtain $\beta < 0.297$ at $95\%$ C.L.
• Figure 3: Representation of the sky position of the monitored NANOGrav pulsars (yellow), and the directions (positive and negative) of the velocity vector $\hat{v}$ among frames (red and dark blue stars), in galactic coordinates. Light blue stars indicate the position of pulsars in random positions orthogonal to the velocity vector.
• Figure 4: Results of our analysis when adding 67 additional pulsars to the NG15 data set, in directions orthogonal ( left panel) and parallel ( right panel) to the velocity vector $\hat{v}$, as explained in the main text.
• Figure 5: Fisher forecast for $\beta$ and the dipole direction parameters, as discussed in the main text around eq \ref{['resila1']}.