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On Pulsar Timing Detection of Ultralight Vector Dark Matter

Jeff A. Dror, Qiushi Wei

TL;DR

This work develops a statistical-field framework for ultralight vector dark matter in pulsar timing arrays by modeling the field as a stochastic background with three polarization states in equipartition. It derives explicit two-point timing residual correlators for the fast mode ($\omega \simeq 2m$) and the slow mode ($\omega \lesssim m v_0^2$), revealing a distinctive angular dependence for the fast mode and a scalar-like slow mode with reduced amplitude. The analysis connects metric perturbations to observable timing residuals via the redshift integral and accounts for coherence scales $\tau$ and $\ell$, enabling PTA searches to target specific mass ranges. It estimates sensitivities: the fast mode probes the local DM density for $m \sim 10^{-24}-10^{-22}$ eV, while the slow mode can access much larger effective densities for $m \sim 10^{-18}-10^{-16}$ eV, offering a concrete path to detect or constrain ultralight vector DM.

Abstract

Ultralight vector dark matter induces metric fluctuations that generate timing residuals in the arrival times of pulsar emissions through two distinct modes: a fast mode, sourced by coherent field oscillations, and a slow mode, arising from interference patterns. These modes enable the detection of vector dark matter with masses $m \sim 10^{-24} - 10^{-22}\ \mathrm{eV}$ and $m \sim 10^{-18} - 10^{-16}\ \mathrm{eV}$, respectively, using pulsar timing arrays. While previous studies have explored the fast mode, they neglect the full statistical treatment of the vector field and a precise treatment of its polarization structure. In this work, we investigate the timing residuals from both modes, fully accounting for the statistical properties of ultralight vector dark matter, assuming equipartition among its three polarization states. The two-point correlation functions of timing residuals that we derive serve as direct tools for identifying vector dark matter signatures as a stochastic background in pulsar timing data.

On Pulsar Timing Detection of Ultralight Vector Dark Matter

TL;DR

This work develops a statistical-field framework for ultralight vector dark matter in pulsar timing arrays by modeling the field as a stochastic background with three polarization states in equipartition. It derives explicit two-point timing residual correlators for the fast mode () and the slow mode (), revealing a distinctive angular dependence for the fast mode and a scalar-like slow mode with reduced amplitude. The analysis connects metric perturbations to observable timing residuals via the redshift integral and accounts for coherence scales and , enabling PTA searches to target specific mass ranges. It estimates sensitivities: the fast mode probes the local DM density for eV, while the slow mode can access much larger effective densities for eV, offering a concrete path to detect or constrain ultralight vector DM.

Abstract

Ultralight vector dark matter induces metric fluctuations that generate timing residuals in the arrival times of pulsar emissions through two distinct modes: a fast mode, sourced by coherent field oscillations, and a slow mode, arising from interference patterns. These modes enable the detection of vector dark matter with masses and , respectively, using pulsar timing arrays. While previous studies have explored the fast mode, they neglect the full statistical treatment of the vector field and a precise treatment of its polarization structure. In this work, we investigate the timing residuals from both modes, fully accounting for the statistical properties of ultralight vector dark matter, assuming equipartition among its three polarization states. The two-point correlation functions of timing residuals that we derive serve as direct tools for identifying vector dark matter signatures as a stochastic background in pulsar timing data.

Paper Structure

This paper contains 14 sections, 89 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. The Local Ultralight Vector Dark Matter Field
  3. The Quantum Statistical Formalism and Classical Nature
  4. Behavior and Coherence Scales
  5. Framework of Pulsar Timing Signals
  6. Structure of Metric Perturbations
  7. Structure of Timing Residuals and Observability
  8. Fast mode timing residual two-point correlation function
  9. The slow mode pulsar timing signal
  10. Conclusion
  11. Solutions to Einstein's Equations in Different Gauges
  12. Impact of Metric Perturbations on Pulsar Timings
  13. Influence of Relative Motion Between Pulsar and Observer
  14. Eigenvalue Problem of the Fast Mode Timing Residual Covariance Matrix

Figures (1)

  • Figure 1: Dependence on $\theta_{ab}$ of $\mathcal{A}_{ab}$ for scalar dark matter, $C_{\mathrm{S}}(\theta_{ab})$, and vector dark matter, $C_{\mathrm{V}}(\theta_{ab})$, and the Hellings-Downs curve for a stochastic gravitational wave background, $C_{\mathrm{H\text{-}D}}(\theta_{ab})$. $C_{\mathrm{S}}(\theta_{ab})$ and $C_{\mathrm{V}}(\theta_{ab})$ are normalized as the factor apart from the $\pi^2 G^2 \bar{\rho}^2/m^6$ in $\mathcal{A}_{ab}$ such that $C_{\mathrm{S}}(\theta_{ab}) = 1/4$ and $C_{\mathrm{V}}(\theta_{ab}) = - (5 - 16\cos^2\theta_{ab})/36$.