The Targeted Standard Siren Cosmology with Pulsar Timing Arrays

Abstract

The sky localisation of about $10$ to $100~\text{deg}^2$, which is expected to be achieved in all-sky blind searches for gravitational waves from supermassive black hole binaries (SMBHBs) with Pulsar Timing Array (PTA) experiments, has long been posed as a prohibitive factor in utilising these sources as standard sirens for precision cosmology. We propose a solution to this problem, which makes use of targeted searches rather than all-sky blind searches for SMBHBs. Using our simulated data informed by current PTA observations, we show that the Chinese Pulsar Timing Array (CPTA) alone could infer the Hubble constant with a precision of 2~km/s/Mpc. Such precision in an independent cosmological probe could provide decisive support in the resolution of the Hubble tension. We demonstrate the application of our method to several simultaneously observed SMBHBs, as well as the method's robustness against confusion between the host galaxies of SMBHB sources in realistic observing scenarios.

Figures (9)

• Figure 1: Marginalised posterior distributions for Hubble constant $H_0$. The result of our analysis with 40 best pulsars of the simulated 30-yr CPTA data (solid pink) is compared with the $H_0$ measurements from GW170817 (dashed grey), Planck 2018 (shaded olive), and SH0ES (shaded viridian). The vertical black line indicates the simulated value $H_0 = 67.4 \text{ km s}^{-1} \text{ Mpc}^{-1}$.
• Figure 2: Marginalised posteriors on $H_0$ for the simulated observation of SMBHB targets P1, P2, and P3. The horizontal axis corresponds to the addition of these sources to the simulation one by one. Central points and vertical error bars denote the median and $1\sigma$ credible intervals, respectively. Horizontal shaded regions indicate $1\sigma$ constraints from other cosmological probes: Planck 2018 (grey), SH0ES (pink), and the GW170817 standard siren measurement (purple).
• Figure 3: The average number of brightest CGW sources in the universe, $N_\text{brightest}$, shown as a function of assumed parameter estimation uncertainties ($\Delta$) with the PTA all-sky search for CGWs. Values $N_\text{brightest}<1$ correspond to a low likelihood of confusion between the targeted SMBHB and any other plausible SMBHB, solely based on the match of their $\log_{10}f$ and $\log_{10}\mathcal{M}$. The colour corresponds to a source P1. The solid white line corresponds to a threshold for P1 where $N_\text{brightest}=0.5$. The dashed, the dash-dotted, and the dotted lines correspond to the same threshold for P2, P3, and 3C 66B, respectively. The top star and the bottom star correspond to reference parameter estimation uncertainties from CharisiTaylor2024 and PetrovSchult2025, respectively. The smallest value along the axes corresponds to $3\sigma$ credible levels in our simulated all-sky search for B1 with the $40$-year CPTA data.
• Figure 4: The left panel shows the posterior for the Hubble constant $H_0$ as a function of observation time in the simulated targeted search for the SMBHB candidate B1 with 20 best pulsars of the CPTA. Central points and vertical error bars denote the median and $1\sigma$ credible intervals, respectively. The right panel shows the marginalised posterior for $H_0$ for an increasing subset of pulsars used in the analysis. Horizontal shaded regions indicate $1\sigma$ constraints from other cosmological probes: Planck 2018 (orange), SH0ES (purple), and the GW170817 standard siren measurement (pink).
• Figure 5: A demonstration of the impact of pulsar distance uncertainties on our parameter estimation for $H_0$ and the cosine of the inclination angle $\iota$ with the $40$-year observation of the 10 best CPTA pulsars. The posterior in red corresponds to our standard model, where pulsar distances are fitted. The posterior in blue corresponds to the case where pulsar distances are fixed.