Angular correlation and deformed Hellings-Downs curve from spin-2 ultralight dark matter

TL;DR

The paper analyzes how a spin-2 ultralight dark matter field, coupled to matter with strength $\alpha$, can modify pulsar timing array signals by deforming the Hellings-Downs angular correlation curve in a narrow band around $f_m=\frac{m}{2\pi}$. The authors derive the homogeneous spin-2 ULDM background, show that the induced pulsar timing residuals exhibit a purely quadrupolar angular pattern, and obtain a cross-correlation $C^{\rm DM}_{ab}(\tau) \propto \Gamma_{\rm DM}(\zeta)\cos(m\tau)$ with $\Gamma_{\rm DM}(\zeta)=\frac{1}{2}P_2(\cos\zeta)$. In the combined SGWB+ULDM scenario, the HD curve is effectively deformed to a weighted sum $\Gamma_{\rm eff}(\zeta)$, with deformation appreciable for $\alpha$ around $10^{-5}$ and ULDM mass in the $10^{-24}$–$10^{-22}$ eV range, potentially detectable in current or future PTA datasets. This work provides a concrete, frequency-local signature to constrain spin-2 ULDM with pulsar timing observations and distinguishes it from other beyond-GR scenarios by its quadrupolar, monochromatic imprint.

Abstract

The pulsar timings are sensitive to both the nanohertz gravitational-wave background and the oscillation of ultralight dark matter. The Hellings-Downs angular correlation curve provides a criterion to search for stochastic gravitational-wave backgrounds at nanohertz via pulsar timing arrays. We study the angular correlation of the timing residuals induced by the spin-2 ultralight dark matter, which is different from the usual Hellings-Downs correlation. At a typical frequency, we show that the spin-2 ultralight dark matter can give rise to the deformation of the Hellings-Downs correlation curve induced by the stochastic gravitational wave background.

Figures (4)

• Figure 1: The blue and orange curves represent the angular correlation of the timing residuals induced by stochastic GW background (Hellings-Downs curve) and spin-2 ULDM, respectively. Both curves are normalized at $\zeta=0$ such that $\Gamma(0)=1/2$.
• Figure 2: Effective cross-correlation curves with $\alpha=10^{-6}$ and mass ranging from $10^{-24}$eV to $10^{-22}$eV. It can be seen that in this range and at the typical frequencies $f_{m}=m/2\pi$, the deformation of spin-2 ULDM on the Hellings-Downs curve is relatively small.
• Figure 3: Effective cross-correlation curves with $\alpha=10^{-5.5}$ and mass ranging from $10^{-24}$eV to $10^{-22}$eV. The deformation is very strong in this parameter range, suggesting that if the coupling constant $\alpha$ is above this magnitude, existing ultralight spin-2 ULDM would have considerable effects on the deformation of the Hellings-Downs curve at the typical frequencies $f_{m}=m/2\pi$.
• Figure 4: Effective cross-correlation curves with $\alpha=10^{-5}$ and mass ranging from $10^{-24}$eV to $10^{-22}$eV. In this range of $\alpha$, the curves are dominated by the spin-2 ULDM at the typical frequencies $f_{m}=m/2\pi$.