Signature of polarized ultralight vector dark matter in pulsar timing arrays

TL;DR

This work addresses detecting ultralight vector dark matter in pulsar timing arrays by allowing general polarization states. It derives the metric perturbations and monochromatic timing residuals at frequency $f = m/\pi$, and computes the angular correlation function $\Gamma_{VDM}(\xi;\beta)$ that encodes the polarization dependence and enhances the quadrupole for circular polarization. The paper further shows how vector DM deforms the Hellings–Downs curve when combined with a stochastic gravitational-wave background, via the effective angular function $\Gamma_{eff}(\xi)$ and effective power $\Phi_{eff}$, offering a concrete observational template to separate DM from GW signals. These results provide polarization-aware, testable predictions for PTAs and offer a pathway to distinguish vector DM from scalar DM and GW backgrounds, with implications for upcoming facilities like the SKA.

Abstract

We investigate observational signatures of ultralight vector dark matter with masses $m \sim 10^{-24}$-$10^{-22}$ eV in pulsar timing arrays, taking into account general polarization states of the vector field. We find that vector dark matter induces pulsar timing residuals with nontrivial directional dependence, reflecting the anisotropic property and polarization structure specific to vector dark matter, unlike scalar dark matter. We also derive angular correlation curves of the timing residuals. Intriguingly, circular polarization of the vector dark matter enhances the quadrupole nature of the correlation curve, resulting in a more notable bending of the Hellings-Downs curve. The derived correlation curves offer a useful means to distinguish gravitational wave and dark matter contributions and to probe the nature of dark matter.

Figures (6)

• Figure 1: The ellipse traced by the vector $\mathbf{A}(t,\mathbf{x})$ in Eq. \ref{['pol2']}. The $+$ and $-$ axes are aligned with the principal axes of the ellipse.
• Figure 2: The dependence of the pattern functions $F^{++}(\mathbf{n}; \mathbf{x})$ (left), $F^{--}(\mathbf{n}; \mathbf{x})$ (center), and $F^{+-}(\mathbf{n}; \mathbf{x})$ (right) on the direction $\mathbf{n}$ is illustrated. The yellow and blue regions indicate where the function takes positive and negative values, respectively.
• Figure 3: The red curves represent the angular correlation function induced by vector DM, $\Gamma_{\text{VDM}}(\xi; \beta)$, for $\beta = 0$ (solid curve), $\beta = \pi/8$ (dashed curve), and $\beta = \pi/4$ (dotted curve). The cases $\beta = 0$ and $\beta = \pi/4$ correspond to vector DM states with perfect linear and circular polarization, respectively. The dotted gray line represents the angular correlation function induced by scalar DM, $\Gamma_{\text{SDM}}(\xi)$.
• Figure 4: The blue curves show the Hellings--Downs curve $\Gamma_{\text{HD}}(\xi)$. The red curves represent the effective angular correlation curve $\Gamma_{\text{eff}}(\xi)$ modified by ultralight vector DM with $\beta = 0$ (solid curves), $\beta = \pi/8$ (dashed curves), and $\beta = \pi/4$ (dotted curves). The gray dotted curves show the modification due to ultralight scalar DM. The DM mass is set to $m = 1 \times 10^{-24}\,\text{eV}$ in the left panel and $m = 3 \times 10^{-24}\,\text{eV}$ in the right panel, corresponding to the frequency $f = 4.8 \times 10^{-10}\,\text{Hz}$ and $f = 1.5 \times 10^{-9}\,\text{Hz}$, respectively. We use $\rho_{A}(\text{or}\,\rho_\phi) = 0.3 \,\text{GeV/cm}^3$ and $\Phi_{\text{GW}}$ given by Eq. \ref{['PhiGW2']} with $T_{\text{obs}} = 15\,\text{yr}$.
• Figure 5: Angular correlations induced by linearly polarized vector DM for simulated sets of 200 pulsars distributed isotropically over the sky (left) and anisotropically within the region of the sky where the declination lies within $\pm 45^\circ$ (right). The blue, yellow, and green points correspond to vector DM orientations $\theta_{\text{VDM}} = \pi/2$, $\pi/4$, and $0$, respectively, where $\theta_{\text{VDM}}$ is measured from the north pole. In both panels, the gray curve represents the analytical correlation assuming an isotropic pulsar distribution.