A research team led by astronomers from the Shanghai Astronomical Observatory (SHAO) of the Chinese Academy of Sciences (CAS) has placed stringent new constraints on ultralight dark matter (ULDM) with pulsar timing arrays (PTAs).

Published in Physical Review D, the work incorporates pulsar distance information for more accurate density modeling, further demonstrating the potential of PTAs as a multi-purpose probe for dark matter physics.

Dark matter accounts for approximately 27% of the energy density content of the Universe, yet its fundamental nature remains elusive. While the standard cold dark matter paradigm has proven remarkably successful on cosmological scales, it continues to face persistent small-scale challenges, notably "core–cusp problem", "missing satellite problem", and "too-big-to-fail problem".

ULDM, also known as fuzzy dark matter, represents a particle-physics proposal designed to alleviate these tensions. In this scenario, the dark matter particle has a typical mass around 10^-22 eV, for which the corresponding de Broglie wavelength becomes comparable to galactic scales, thereby naturally inducing wave-like phenomena on those scales.

PTA experiments monitor tens of highly stable millisecond pulsars to obtain high-precision measurements of their pulse times of arrival, effectively forming a Galactic-scale detector primarily designed to detect the nanohertz gravitational waves. PTA also offers a promising avenue to search for ULDM signals, as the wave nature of ULDM may leave an imprint in the timing residuals.

Such signals generally arise through two channels: gravitational effects and interactions. For example, ultralight scalar dark matter induces oscillations of the spacetime metric via gravitational effects, producing an additional gravitational time delay in the pulse signals; dark photon dark matter, by contrast, couples to ordinary matter, generating an effective "fifth force" that perturbs the pulse arrival times through the Doppler effect.

Using the third data release of the Parkes Pulsar Timing Array (PPTA DR3) and the second data release of the European Pulsar Timing Array (EPTA DR2), the team searched for the gravitational signal of ultralight scalar dark matter and the "fifth force" signal of dark photon dark matter.

In the analysis, the difference in dark matter density between Earth and the pulsars was taken into account, and pulsar distance information was incorporated. The results revealed no significant signal for either dark matter candidate. The team accordingly placed stringent constraints on the parameter space of these dark matter models.

The results show that the PTA constraints on ultralight scalar dark matter are already approaching the local dark matter density, posing a serious challenge to such models. For dark photon dark matter, the limits on the coupling strength have also reached the level of its own gravitational signal, for example, the time delay induced by oscillations of the gravitational potential.

As a result, the coupling signal tends to become degenerate with the gravitational signal, making the two difficult to distinguish. To further search for dark matter signals in the future, it will be necessary to exploit the correlation between dark matter density fluctuations at the Earth and at the pulsars in order to disentangle the gravitational signal.

According to the researchers, this work not only expands the scientific frontiers of PTAs, but also establishes new benchmark constraints for the theoretical and experimental exploration of ULDM.

With the continued advancement of nanohertz gravitational-wave detection capabilities, the parameter space of dark matter models will be progressively narrowed, laying a solid observational foundation for uncovering the nature of dark matter.

The research is led by Dr. LIU Kuo and Dr. CHEN Siyuan from SHAO, together with Prof. ZHU Xingjiang from Beijing Normal University. The first author of this study is HU Xiaosong, a Ph.D. student jointly supervised by Beijing Normal University and SHAO.

This work was supported by the National Key Research and Development Program of China, the Fundamental Research Funds for the Central Universities, and the Matching Funds for Major Research Projects at Beijing Normal University (Zhuhai).

Artistic rendering of pulsar timing array probing ultralight dark matter. (Image by SHAO)