[Paper Review] Probing ultralight scalar, vector and tensor dark matter with pulsar timing arrays

Caner Ünal, F. Urban+1 more|arXiv (Cornell University)|Sep 6, 2022

Dark Matter and Cosmic Phenomena49 references4 citations

TL;DR

This paper demonstrates that pulsar timing arrays (PTAs) can probe ultralight scalar, vector (dark photon), and tensor (spin-2) dark matter across the mass range $10^{-26}-10^{-23}$ eV with high sensitivity. By leveraging the scaling of signal amplitude and PTA sensitivity at low frequencies, current 15-year IPTA data can constrain the dark matter fraction to $O(1-10\%)$, improving to $0.1-1\%$ with 30 years of data and $0.01-0.1\%$ with SKA, closing a key gap in the ultralight dark matter parameter space.

ABSTRACT

Pulsar timing arrays (PTAs) are sensitive to oscillations in the gravitational potential along the line-of-sight due to ultralight particle pressure. We calculate the probing power of PTAs for ultralight bosons across all frequencies, from those larger than the inverse observation time to those smaller than the inverse distance to the pulsar. We show that since the signal amplitude grows comparably to the degradation in PTA sensitivity at frequencies smaller than inverse observation time, the discovery potential can be extended towards lower masses by over three decades, maintaining high precision. We demonstrate that, in the mass range $10^{-26} -10^{-23}$ eV, existing 15-year PTA data can robustly detect or rule out an ultralight component down to $O(1 - 10)\%$ of the total dark matter. Non-detection, together with other bounds in different mass ranges, will imply that ultralight scalar/axion can comprise at most $1-10\%$ of dark matter in the $10^{-30}\!-\!10^{-17}$ eV range. With 30 years of observation, current PTAs can extend the reach down to $0.1-1 \%$, while next-generation PTAs such as SKA can attain the $0.01-0.1\%$ precision. We generalize the analysis and derive predictions for ultralight spin-1 vector (i.e. dark photon) and spin-2 tensor dark components.

Motivation & Objective

• To extend the discovery potential of pulsar timing arrays (PTAs) for ultralight dark matter candidates across scalar, vector, and tensor fields.
• To address the unexplored mass range $10^{-26}-10^{-23}$ eV, where existing cosmological probes have reduced sensitivity.
• To quantify the probing power of current and future PTAs for the energy density fraction $\mathcal{F}_{\rm ULDM}$ of ultralight bosons.
• To generalize signal modeling for spin-0 (scalar/axion), spin-1 (vector/dark photon), and spin-2 (tensor) dark matter components in PTAs.
• To demonstrate that signal-to-noise ratio (SNR) scaling with observation time and pulsar distance enables extended sensitivity to lower masses.

Proposed method

• Model the gravitational potential oscillations induced by ultralight scalar, vector, and tensor dark matter fields via their energy-momentum tensor perturbations.
• Derive the metric perturbation $\delta g_{00} = -2\Phi$ and $\delta g_{ij} = 2\psi\delta_{ij}$ from linearized Einstein equations, with $\psi_c \propto \rho/m^2$ for scalar and vector modes.
• Calculate the time residual in pulsar timing as $\delta\Delta t \propto \int \frac{\nu' - \bar{\nu}}{\bar{\nu}} dt$, linking it to the oscillating gravitational potential.
• Compute the signal-to-noise ratio (SNR) for each spin type, accounting for $h_{\rm signal} \propto f^{-1}, f^{-2}, f^{-1}$ for scalar/vector/tensor, and $h_{\rm noise} \propto f^{-1}$.
• Analyze three frequency regimes: $f > 1/T_{\rm obs}$, $1/D_{\rm pulsar} < f < 1/T_{\rm obs}$, and $f < 1/D_{\rm pulsar}$, to determine scaling of detectable $\mathcal{F}_{\rm ULDM}$ with $f$, $T_{\rm obs}$, and $D_{\rm pulsar}$.
• Use SNR scaling to derive constraints: $\mathcal{F}_{\rm ULDM} \propto (f \cdot T_{\rm obs})^{-1/4}$ for scalar/vector, and $\mathcal{F}_{\rm ULDM} \propto (f \cdot T_{\rm obs})^{-5/2}$ for tensor.

Experimental results

Research questions

• RQ1 Can pulsar timing arrays detect or constrain ultralight scalar, vector, and tensor dark matter components in the $10^{-26}-10^{-23}$ eV mass range?
• RQ2 How does the signal-to-noise ratio (SNR) of PTAs scale with observation time and pulsar distance for different spin modes of ultralight dark matter?
• RQ3 What is the minimum fraction of dark matter that current and future PTAs can probe for these ultralight bosons?
• RQ4 Why is the $10^{-26}-10^{-23}$ eV range particularly accessible to PTAs despite being poorly constrained by CMB and large-scale structure?
• RQ5 How do the distinct signal amplitudes of scalar, vector, and tensor dark matter affect their detectability in pulsar timing?

Key findings

• Current 15-year PTA data can constrain the energy density fraction of ultralight scalar/axion dark matter to $O(1-10\%)$ of the total dark matter in the $10^{-26}-10^{-23}$ eV mass range.
• With 30 years of observation, the sensitivity improves by one order of magnitude, enabling constraints at the $1\%$ level.
• Next-generation PTAs such as SKA can achieve $0.1\%$ precision, extending the reach to $0.01-0.1\%$ for the same mass range.
• For scalar and vector dark matter, the signal amplitude scales as $f^{-1}$, matching the noise scaling, enabling detection down to $f \sim 1/D_{\rm pulsar}$, corresponding to $m \sim 10^{-26}$ eV.
• For tensor dark matter, the signal scales as $f^{-1}$, but the SNR scales as $(f \cdot T_{\rm obs})^{-5/2}$, making it most sensitive near $f \sim 1/T_{\rm obs}$.
• Combined with existing constraints from CMB, Lyman-α, and SMBH superradiance, PTAs can now probe ultralight scalar dark matter continuously from $10^{-30}$ to $10^{-17}$ eV with $\mathcal{O}(1\%)$ precision.