Upper limits on microhertz gravitational waves from supermassive black-hole binaries using PSR J1909-3744 data from the second IPTA data release

TL;DR

This work demonstrates a Bayesian, high-cadence CW search for individual SMBHBs in the microhertz band using PSR J1909-3744 data from the IPTA-DR2 subset. By modeling white, red, and DM noise and incorporating both Earth and Pulsar terms, the authors place 95% upper limits on CW strain across 61 frequency bins and 768 sky pixels, achieving a sky-averaged limit of $2.3\times10^{-13}$ at $f_{GW}=1\times10^{-6}$ Hz and a best-case sky limit of $8.9\times10^{-14}$ at the same frequency, with even tighter limits at 71 nHz. The complete data set yields a notably stronger limit near 10 nHz ($4.9\times10^{-15}$), underscoring the value of high-cadence IPTA data in extending GW sensitivity into the µHz regime. The results illustrate the potential of staggered sampling to push PTA sensitivity beyond conventional Nyquist constraints and highlight how microhertz CW searches complement nanohertz PTA studies in constraining the population of nearby, massive SMBHBs and guiding future multi-PTA analyses toward bridging to LISA.

Abstract

We present the results of a search for gravitational waves (GWs) from individual sources using high-cadence observations of PSR J1909\(-\)3744 obtained during an intensive observing campaign with the International Pulsar Timing Array second data release (IPTA-DR2) between July 2010 and November 2012. The observations, conducted at three different radio frequencies with the Nançay Radio Telescope (NRT) and Parkes Telescope (PKS) and five frequencies with the Green Bank Telescope (GBT), enabled precise corrections for dispersion measure effects and scattering variations. After these corrections, the timing residuals showed an unmodeled periodic noise component with an amplitude of 340 ns. Our analysis yields upper limits on the GW strain from individual sources, constraining it to be below \(1.9 \times 10^{-14}\) at 71 nHz and \(2.3 \times 10^{-13}\) at 1 \textmu Hz for average sky locations, while for optimal source locations the limits improve to \(6.2 \times 10^{-15}\) and \(8.9 \times 10^{-14}\) at the same frequencies, respectively. Our new limits are about a factor of 1.52 more stringent than those of Perera et al. based on an earlier EPTA data.

Figures (5)

• Figure 1: The timing residuals of PSR J1909$-$3744. The weighted rms of the residuals is 1.20$\ \mathrm{\mu}$s. For clarity of the plot, the residuals of the different telescope are shown in separate panels. Data from the GBT, PKS, and NRT are shown in green, blue, and red, respectively. The top panel displays the residuals from the complete dataset, while the bottom panel shows the subset.
• Figure 2: 2D marginalized posterior distribution for a subset of the noise parameters: DM stochastic noise component (logarithmic amplitude ($\mathrm{log_{10}A}$) and spectral index(${\gamma}$)), and red noise component.
• Figure 3: The 95 $\%$ upper limits on the GW strain amplitude produced by SMBHBs based on the timing observations of PSR J1909$-$3744. The blue, and green lines represent GW sky-averaged sensitivity. The blue curve and red curve are derived from a partial data set, whereas the green curve reflects the complete data set. The red line shows sensitivity for the most sensitive sky location.
• Figure 4: Sky map of 95% upper limits on the GW strain amplitude produced by SMBHBs based on the timing observations of PSR J1909$-$3744 at $f_\mathrm{GW} = 71 \mathrm{nHz}$ GW freqency. Pulsar location is shown as yellow stars. yellow diamonds indicate the positions of three known SMBHB candidates that could contain an SMBHB. The most sensitive pixel is marked with a red dot, and is located at an RA of $\mathrm{17^h 14^m 58^s}$ and a DEC of $-27^{\circ} 19^{'} 35^{"}$. While our single-pulsar analysis achieves optimal sensitivity near the pulsar position, it shows negligible response to the antipodal sky location (anti-pulsar direction).
• Figure 5: Sky map of 95% upper limits on the GW strain amplitude produced by SMBHBs based on the timing observations of PSR J1909$-$3744 at $f_\mathrm{GW} = 1 \mu\mathrm{Hz}$ GW freqency. The most sensitive pixel is marked with a red dot, and is located at an RA of $\mathrm{19^h 17^m 8^s}$ and a DEC of $-32^{\circ} 19^{'} 00^{"}$.