Search for Gravitational Wave Memory in PPTA and EPTA Data: A Complete Signal Model

TL;DR

This work advances gravitational-wave memory searches with Pulsar Timing Arrays by introducing a complete SMBHB merger waveform that includes null memory, alongside a memory-burst model, both analyzed within a Bayesian framework. A novel factorized-posterior approach using kernel density estimation and normalizing flows enables efficient, high-fidelity approximation of per-pulsar posteriors, facilitating scalable inference across large PTA datasets. Applying these methods to PPTA DR3 and EPTA DR2 data, the study finds no evidence for memory signals but sets competitive upper limits on memory amplitudes and SMBHB merger parameters, demonstrating the method’s capability to probe previously inaccessible regions of the SMBHB parameter space and guiding future PTA improvements. The results underscore the importance of physically motivated waveforms, careful stochastic-background modeling, and robust posterior approximations for memory searches in nanohertz gravitational-wave data, with implications for tests of nonlinear GR and spacetime symmetries.

Abstract

We perform searches for gravitational wave memory in the data of two major Pulsar Timing Array (PTA) experiments located in Europe and Australia. Supermassive black hole binaries (SMBHBs) are the primary sources of gravitational waves in PTA experiments. We develop and carry out the first search for late inspirals and mergers of these sources based on full numerical relativity waveforms with null (nonlinear) gravitational wave memory. Additionally, we search for generic bursts of null gravitational wave memory, exploring possibilities of reducing the computational cost of these searches through kernel density and normalizing flow approximation of the posteriors. We rule out the mergers of SMBHBs with a chirp mass of 10^10 Solar Mass up to 700 Mpc over 18 years of observation at 95% credibility. We rule out the observation of generic displacement memory bursts with strain amplitudes > 10^-14 in brief periods of the observation time but across the sky, or over the whole observation time but for certain preferred sky positions, at 95%$credibility.

Figures (11)

• Figure 1: PTA timing residuals from a merger of a non-spinning supermassive black hole binary (SMBHB) with parameters $\mathcal{M} = 10^{10} M_{\odot}$, $q=1$, and $D_\text{L} = 100$ Mpc. observed by a pulsar at $(\text{ra},\text{dec}) = (258.4564^{\circ},7.7937^{\circ})$. The merger occurs at $\mathrm{MJD}=58000$. Green : SMBHB merger model with only memory, Blue : SMBHB merger model (complete signal including IMR+memory), Orange : Memory burst model. All curves are normalized to the same final memory offset.
• Figure 2: Upper limits on strain amplitude $h_0$ of generic displacement memory bursts as a function of burst time at 95% credibility. Other burst parameters are marginalized over.
• Figure 3: Upper limits on the strain amplitude $h_0$ of generic displacement-memory bursts, shown in colour, as a function of sky position $(\theta,\phi)$ at 95% credibility (other burst parameters marginalised over). The three panels correspond to the EPTA 10‐year, EPTA 25‐year, and PPTA DR3 data sets, respectively (left → right). White stars mark the pulsar positions for each PTA.
• Figure 4: Lower limits on the luminosity distance $D_\text{L}$ as a function of source-frame chirp mass $\mathcal{M}$. This comparison is valid for equal mass binaries.
• Figure 5: Upper limits on the strain amplitude $h_{0}$ of generic memory bursts (orange) compared to the SMBHB merger model (blue) as a function of burst epoch. The merger model includes the gradual memory buildup during the inspiral, so the post-fit residuals are smaller than those of the burst model. As a result, the merger waveform yields slightly weaker upper limits compared to the generic burst model, but provides a more accurate representation of the expected memory signal. Unlike the burst model, the merger model limits do not degrade as sharply near the observation edges due to the contribution of the inspiral component.