Pulsar Polarization Array Limits on Ultralight Axion-like Dark Matter

TL;DR

This work introduces the first Pulsar Polarization Array (PPA) analysis to search for ultralight axion-like dark matter via cosmic birefringence, leveraging cross-pulsar correlations in polarization data from 22 MSPs in PPTA DR3. A Bayesian framework is developed to model PA residuals with ALDM-induced correlations, instrumental and astrophysical noises, and deterministic trends, enabling robust upper limits on the ALDM Chern-Simons coupling $g_{a\gamma\gamma}$ across $m_a\sim 10^{-22}-10^{-21}$ eV. The Parkes PPA yields the strongest global limits in this fuzzy DM mass range, $g_{a\gamma\gamma} \lesssim 10^{-13.5}-10^{-12.2}$ GeV$^{-1}$ for $\rho_0=0.4$ GeV cm$^{-3}$, with cross-pulsar correlations proving essential to interpreting the results and avoiding spurious signals. The methodology lays the groundwork for future, more sensitive polarization-array analyses that can combine multiple PTAs and extend to higher frequencies, potentially advancing independent probes of ultralight ALDM.

Abstract

We conduct the first-ever Pulsar Polarization Array (PPA) analysis to detect the ultralight Axion-Like Dark Matter (ALDM) using the polarization data of 22 millisecond pulsars from the third data release of Parkes Pulsar Timing Array. As one of the major dark matter candidates, the ultralight ALDM exhibits a pronounced wave nature on astronomical scales and offers a promising solution to small-scale structure issues within local galaxies. While the linearly polarized pulsar light travels through the ALDM galactic halo, its position angle (PA) can be subject to an oscillation induced by the ALDM Chern-Simons coupling with electromagnetic field. The PPA is thus especially suited for detecting the ultralight ALDM by correlating polarization data across the arrayed pulsars. To accomplish this task, we develop an advanced Bayesian analysis framework that allows us to construct pulsar PA residual time series, model noise contributions properly and search for pulsar cross-correlations. We find that for an ALDM density of $ρ_0=0.4\,\textrm{GeV}/\textrm{cm}^3$, the Parkes PPA offers the best global limits on the ALDM Chern-Simons coupling, namely $\lesssim 10^{-13.5}-10^{-12.2}~{\rm GeV}^{-1}$, for the mass range of $10^{-22} - 10^{-21}~{\rm eV}$. The crucial role of pulsar cross-correlation in recognizing the nature of the derived limits is also highlighted.

Figures (14)

• Figure 1: 95% upper limits on the ALDM characteristic signal strength $S_a$ as a function of its mass $m_a$, for six representative PPPA MSPs. In each panel, the black solid line represents the single-pulsar limits with full noise modeling in Eq. (\ref{['eq:PAmodel']}), while the colored lines show the limits excluding individual noise components: additional white noise (blue), red noise (orange), linear and quadratic deterministic noise (purple), and ionospheric effects (green). The difference between the black and colored lines reflects the contribution of each noise component to the analysis. As a reference, we present $T_{\rm obs}$ of each pulsar, and timescales of solar cycle (11 years), one year and one day, as colored and gray vertical dotted lines, respectively. The timescale and $m_a$ are related by $m_a = 2\pi/T$.
• Figure 2: 95% upper limits of the PPPA on the ALDM Chern-Simons coupling $g_{a\gamma\gamma}$ as a function of its mass $m_a$, with $\rho_0=0.4\,\textrm{GeV}/\textrm{cm}^3$. The blue and red curves represent the limits obtained with the autocorrelation-only and full-correlation signal models, respectively, with (solid) and without (dashed) the ionospheric subtraction. As a reference, the smoothened constraints from the observation of PA variation in Crab Nebula with POLARBEAR POLARBEAR:2024vel, the analysis of PPTA data of DR1 and Crab Nebula data from QUIJOTE Castillo:2022zfl, the measurement of the CMB polarization with SPT-3G SPT-3G:2022ods, and the investigation of PLANCK mission on the ALDM-induced washout effects during recombination Fedderke:2019ajk are presented as cyan, yellow, green, and purple dashed lines. The limits from the CAST experiment CAST:2017uph and the observations of SN1987A Payez:2014xsa and x-ray spectral distortion in quasar H1821+643 Reynes:2021bpe are also presented as black dashed lines. The shaded regions above these lines indicate the range of $m_a$ and $g_{a\gamma\gamma}$ that they have excluded. The vertical dotted lines denote the reference timescales, including the PPPA observation period $T_{\rm obs}\approx 18~{\rm yrs}$, solar cycle, one year and one day. In the lower subpanel, the Bayes factors are displayed in two scenarios: the full-correlation signal model against the null-signal model (red) and the full-correlation signal model against the autocorrelation-only signal model (black).
• Figure 3: Standard profiles of PA (upper sub-panel) and intensity (bottom sub-panel) for the linearly polarized light of PPPA MSPs.
• Figure 4: Same as Fig. \ref{['fig:Profiles1']} for other MSPs.
• Figure 5: Same as Fig. \ref{['fig:Profiles1']} for other MSPs.