Hunting Hidden Axion Signals in Pulsar Dispersion Measurements with Machine Learning

TL;DR

The paper tackles the challenge of detecting axion dark matter via frequency-dependent dispersion in pulsar signals, focusing on a resonant signature near $\omega = m_a/2$ that is finite under realistic observational bandwidths. It derives the axion-induced time delay using an axion-photon coupling framework and engineers a detection pipeline based on an attention-enhanced InceptionTime network trained with curriculum learning on $PsrSigSim$-generated data that include white and red noise. The method achieves about 90% classification accuracy and demonstrates robustness against false positives, mapping the axion parameter space to observable time delays and projecting substantial gains in constraints with future instruments like the Qitai Radio Telescope. Real data from PSR J1933-6211 yield no evidence of axion-induced delays, but the approach provides a viable path for high-precision pulsar timing arrays to probe $f_a^{-1}$ over a wide mass range, potentially improving constraints by up to ~4 orders of magnitude for $m_a$ between $10^{-6}$ and $10^{-4}$ eV.

Abstract

In axion models, interactions between axions and electromagnetic waves induce frequency-dependent time delays determined by the axion mass and decay constant. These small delays are difficult to detect, limiting the effectiveness of traditional methods. We compute such delays under realistic radio telescope conditions and identify a prominent dispersive feature near half the axion mass, which appears non-divergent within the limits of observational resolution. Based on this, we develop a machine learning method that achieves 90\% classification accuracy and demonstrates well performance in low signal-to-noise regimes. The method's robustness is confirmed against false positives using both simulated noisy data and real-world, known-null observations. Future improvements in optical clock precision and telescope bandwidth, particularly with instruments such as the Qitai Radio Telescope, may enhance constraints on the axion decay constant by up to four orders of magnitude in the $10^{-6} \sim 10^{-4}$ eV mass range.

Figures (7)

• Figure 1: Feynman diagrams for photon scattering on axion. The left panel represents the $s-channel$, where the four-momenta of the incoming photon and axion are $k$ and $p$, respectively. The resulting virtual photon propagates with momentum $k + p$. The outgoing momenta are $k'$ (photon) and $p'$ (axion), satisfying four-momentum conservation: $k + p = k' + p'$. The right panel represents the $u-channel$, which is similar to the $s$-channel, except that the four-momentum of the virtual photon, $k + p$ is replaced by $k - p'$.
• Figure 2: Time delay caused by axion(Left) and electron media(Right) as a function of the incident electromagnetic wave energy. In this calculation,We set $\nu_1 = 1$ GHz and take $\nu_2$ as a variable, with a maximum value of 100 GHz. To facilitate a clearer comparison, all time delay curves have been normalized. Here, we set the example axion mass with $m^{'}_{a}$ corresponding to 3 GHz. It can be seen that a prominent peak appears at $\nu_2 = \frac{1.5}{2\pi}$ GHz, which corresponds to $\frac{1}{2} m^{'}_{a}$.
• Figure 3: Waterfall dynamic spectra (1–2 GHz) used to derive time–delay curves. Top: baseline simulation including radiometer (thermal white) noise only. Bottom: same setup with intrinsic achromatic red timing noise added, modeled as a power–law Fourier–GP and applied as a common time warp. Source parameters follow PSR J1933$-$6211 ($P=3.543$ ms, ${\rm DM}=11.520~{\rm pc\,cm^{-3}}$). The band is assembled from 50 MHz tiles (32 channels each; $f_s=1$ MHz). Intensity is in arbitrary units; both panels share the same color scale.
• Figure 4: Comparison of time-delay signals under different axion parameters. In left panel, the data labeled “1” represent a time-delay signal induced by axion with parameters $\bigl(f_{a}^{-1}, m_{a}\bigr)=\bigl(10^{-10}\,\mathrm{GeV}^{-1},1.3\times10^{-6}\,\mathrm{eV}\bigr)$. As shown, the SNR for these data points is significantly greater than 1, indicating that the signal can be easily identified using simple peak-search methods. In right panel, the data labeled “1” correspond to a time-delay signal caused by axion with parameters $\bigl(f_{a}^{-1}, m_{a}\bigr)=\bigl(10^{-10}\,\mathrm{GeV}^{-1},1.7\times10^{-6}\,\mathrm{eV}\bigr)$. Here the SNR lies in the range $\sim10^{-1}$ to $\sim10^{0}$, making the signal nearly indistinguishable from white noise and challenging for traditional detection algorithms.
• Figure 5: Schematic diagram of the attention-enhanced InceptionTime network architecture. Building upon the classical multi-scale temporal structure of InceptionTime, the model integrates a temporal receptive field pyramid formed by stacked heterogeneous convolutional kernels and a temporal attention module incorporating BLSTM. These components establish a dynamic weight allocation mechanism to enhance spatiotemporal localization capability for transient peaks. Global average pooling combined with dual regularization layers (batch normalization and dropout) further improves noise robustness. Notably, during the unsupervised pre-training phase, the classification head is replaced by a reconstruction decoder, forming an autoencoder architecture. This stage is designed to learn robust feature representations from the unlabeled data by minimizing a reconstruction loss. Subsequently, these learned features are fed into a clustering algorithm to group the signals into distinct categories.