Probing Ultralight Axion-like Dark Matter: A Pulsar Timing Arrays-Pulsar Polarization Arrays Synergy

Abstract

Ultralight axionlike dark matter (ALDM) is a leading candidate in the dark matter realm, characterized by its prominent wave properties on astronomical scales. Pulsar timing arrays (PTAs) and Pulsar polarization arrays (PPAs) aim to detect this dark matter through timing and polarization measurements, respectively, of pulsars. The PTA relies on gravitational effects, while the PPA detects nongravitational effects. These two methods complement each other, synergistically enhancing the pulsar array's capability to identify the ALDM signals in the data. In this article, we provide a foundational development of this synergy. We begin by revisiting previously derived two-point correlation functions for both PTA and PPA, and extend the analysis to include the leading-order correlation between timing and polarization signals, encoded as a three-point function. We then explore the constructions of likelihood functions for PTA and combined PTA-PPA analyses within a Bayesian framework, aimed at detecting the characteristic correlations of ALDM signals. We emphasize the non-Gaussianity of the ALDM timing signals, which arises from their nonlinear dependence on the field, in contrast to the Gaussian nature of its polarization signals. To address the complexities introduced, we approach this investigation in two ways: one involves a Gaussian approximation with proper justifications, while the other derives the formalism from the generic Gaussian characteristics of the ALDM field. Particularly, for the combined PTA-PPA case, a clear connection between the three-point correlation function and the likelihood is established. We anticipate that these efforts will lead to further developments in PTA and PTA-PPA analysis methods, better accounting for the influence of non-Gaussianity.

37 pages, 2 figures, 1 table; matches version published in Phys. Rev. D

References in corpus (17)

• Ultralight scalars as cosmological dark matter
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• Wave Dark Matter
• On measuring the gravitational-wave background using Pulsar Timing Arrays
• The second data release from the European Pulsar Timing Array: VI. Challenging the ultralight dark matter paradigm
• Narrowing the mass range of Fuzzy Dark Matter with Ultra-faint Dwarfs
• A Gamma-ray Pulsar Timing Array Constrains the Nanohertz Gravitational Wave Background
• Dark Matter Interferometry
• The NANOGrav 15-year Gravitational-Wave Background Methods
• Dwarf galaxies imply dark matter is heavier than $2.2\times 10^{-21}\mathbf{eV}$
• Bayesian estimation of non-Gaussianity in pulsar timing analysis
• A Quantum Description of Wave Dark Matter
• Constraining ultralight dark matter using the Fermi-LAT pulsar timing array
• Constraints on conformal ultralight dark matter couplings from the European Pulsar Timing Array
• Stochastic Wave Dark Matter with Fermi-LAT $\gamma$-ray Pulsar Timing Array
• Ultralight Dark Matter Statistics for Pulsar Timing Detection
• Pulsar Polarization Array Limits on Ultralight Axion-like Dark Matter