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Testing scalar dark matter clumps with Pulsar Timing Arrays

Philippe Brax, Patrick Valageas

TL;DR

This study expands the search for ultralight scalar dark matter by leveraging cross-pulsar timing correlations in Pulsar Timing Arrays to access higher scalar masses than standard single-pulsar analyses. It shows that coherent oscillations of DM in solitons around pulsars induce a slow, beat-type timing signal through a Sachs-Wolfe–like effect, which can be filtered to extract a low-frequency DM imprint. The authors derive the mean and variance of the cross-pulsar observable, accounting for white noise, red noise, and the stochastic GW background, and they map the detectable density–mass parameter space, finding a reach up to m ∼ 10^−19 eV for certain cadences, with synchronized observations enabling exploration of even higher masses given sufficiently dense clumps. Self-consistency checks indicate the required densities are extreme but not excluded, and the work highlights synergy with future GW observatories (LISA/DECIGO) and potential astrophysical channels (binary black holes, black hole–pulsar systems) for probing late-universe DM structures.

Abstract

Scalar dark matter is a viable alternative to particle dark matter models such as Weakly Interacting Massive Particles (WIMPS). This is particularly the case for scalars with a low mass $m \gtrsim 10^{-21} {\rm eV}$ as required to make quantum effects macroscopic on galactic scales. We point out that by synchronising the measurements of arrival times of pairs of pulsars, Pulsar Timing Arrays (PTA) could probe ultralight dark matter (ULDM) scenarios with a mass $10^{-23} {\rm eV}\lesssim m \lesssim 10^{-19} {\rm eV}$ that is greater than the one reached in standard analysis. The upper limit on the mass $m$ is set by the time lag $Δt$ between the observations of the two pulsars and could be pushed above $10^{-19} {\rm eV}$ for $Δt$ smaller than one hour. However, for these high scalar masses only very high density dark matter clouds could be detected and the capture rate of neutron stars is too low to provide sufficient statistics. Significant detection probabilities would thus require direct dark-matter-baryon interactions that favor the formation of neutron stars within such dark matter clouds, or the discovery of black hole/pulsar binary systems, taking advantage of the dark matter spike generated by the black hole.

Testing scalar dark matter clumps with Pulsar Timing Arrays

TL;DR

This study expands the search for ultralight scalar dark matter by leveraging cross-pulsar timing correlations in Pulsar Timing Arrays to access higher scalar masses than standard single-pulsar analyses. It shows that coherent oscillations of DM in solitons around pulsars induce a slow, beat-type timing signal through a Sachs-Wolfe–like effect, which can be filtered to extract a low-frequency DM imprint. The authors derive the mean and variance of the cross-pulsar observable, accounting for white noise, red noise, and the stochastic GW background, and they map the detectable density–mass parameter space, finding a reach up to m ∼ 10^−19 eV for certain cadences, with synchronized observations enabling exploration of even higher masses given sufficiently dense clumps. Self-consistency checks indicate the required densities are extreme but not excluded, and the work highlights synergy with future GW observatories (LISA/DECIGO) and potential astrophysical channels (binary black holes, black hole–pulsar systems) for probing late-universe DM structures.

Abstract

Scalar dark matter is a viable alternative to particle dark matter models such as Weakly Interacting Massive Particles (WIMPS). This is particularly the case for scalars with a low mass as required to make quantum effects macroscopic on galactic scales. We point out that by synchronising the measurements of arrival times of pairs of pulsars, Pulsar Timing Arrays (PTA) could probe ultralight dark matter (ULDM) scenarios with a mass that is greater than the one reached in standard analysis. The upper limit on the mass is set by the time lag between the observations of the two pulsars and could be pushed above for smaller than one hour. However, for these high scalar masses only very high density dark matter clouds could be detected and the capture rate of neutron stars is too low to provide sufficient statistics. Significant detection probabilities would thus require direct dark-matter-baryon interactions that favor the formation of neutron stars within such dark matter clouds, or the discovery of black hole/pulsar binary systems, taking advantage of the dark matter spike generated by the black hole.

Paper Structure

This paper contains 26 sections, 83 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Ultralight dark matter
  3. Oscillating scalar field
  4. Oscillating gravitational potentials
  5. Sachs-Wolfe effect and time delays
  6. Moving the observational window to higher scalar mass
  7. Correlation of a pair of pulsars
  8. Dark matter mass window
  9. Noise contributions
  10. Noise contributions to the timing residuals
  11. Statistics of measurement times
  12. Mean signal
  13. Variance of the signal
  14. White noise
  15. Red noise
  16. ...and 11 more sections

Figures (1)

  • Figure 1: The shaded regions are the exclusion domains obtained from standard pulsar time delays analysis NANOGrav:2023hvmEuropeanPulsarTimingArray:2023egv. The blue solid line is our estimate (\ref{['eq:rho-SNR']}). The horizontal dot-dashed line is the detection limit of a dark matter cloud, which would contain a white-dwarf binary system, for the observation of the waveform by the future satellite DECIGO.