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Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects

F. A. Jenet, G. B. Hobbs, W. van Straten, R. N. Manchester, M. Bailes, J. P. W. Verbiest, R. T. Edwards, A. W. Hotan, J. M. Sarkissian, S. M. Ord

TL;DR

This work develops a frequentist, Monte Carlo–calibrated method to place upper bounds on an isotropic stochastic GW background in the pulsar timing band, treating backgrounds as a power-law $h_c(f)=A\left(\frac{f}{\mathrm{yr}^{-1}}\right)^{\alpha}$ and relating it to $\Omega_{gw}(f)$. Using seven white-timing-residual pulsars and a red-spectrum statistic $\Upsilon$, the authors derive current upper bounds: $\Omega_{gw}(1/8\text{yr})h^2 \le 1.9\times10^{-8}$ for SMBH binaries, $2.0\times10^{-8}$ for relic GWs, and $1.9\times10^{-8}$ for cosmic strings (0.1% FAP, 95% detection). They show that PPTA data can constrain merger rates and SMBH–halo relations, and, in the relic and cosmic-string sectors, place meaningful limits on early-universe expansion and string tension, with full PPTA potentially detecting signals or ruling out most current models. The methodology and quantified bounds provide a practical framework for interpreting future PTA data in terms of fundamental cosmology and astrophysics.

Abstract

Using a statistically rigorous analysis method, we place limits on the existence of an isotropic stochastic gravitational wave background using pulsar timing observations. We consider backgrounds whose characteristic strain spectra may be described as a power-law dependence with frequency. Such backgrounds include an astrophysical background produced by coalescing supermassive black-hole binary systems and cosmological backgrounds due to relic gravitational waves and cosmic strings. Using the best available data, we obtain an upper limit on the energy density per unit logarithmic frequency interval of Ω^{\rm SMBH}_g(1/8yr) h^2 <= 1.9 x 10^{-8} for an astrophysical background which is five times more stringent than the earlier Kaspi et al. (1994) limit of 1.1 x 10^{-7}. We also provide limits on a background due to relic gravitational waves and cosmic strings of Ω^{\rm relic}_g(1/8yr) h^2 <= 2.0 x 10^{-8} and Ω^{\rm cs}_g(1/8yr) h^2 <= 1.9 x 10^{-8} respectively. All of the quoted upper limits correspond to a 0.1% false alarm rate together with a 95% detection rate. We discuss the physical implications of these results and highlight the future possibilities of the Parkes Pulsar Timing Array project. We find that our current results can 1) constrain the merger rate of supermassive binary black hole systems at high red shift, 2) rule out some relationships between the black hole mass and the galactic halo mass, 3) constrain the rate of expansion in the inflationary era and 4) provide an upper bound on the dimensionless tension of a cosmic string background.

Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects

TL;DR

This work develops a frequentist, Monte Carlo–calibrated method to place upper bounds on an isotropic stochastic GW background in the pulsar timing band, treating backgrounds as a power-law and relating it to . Using seven white-timing-residual pulsars and a red-spectrum statistic , the authors derive current upper bounds: for SMBH binaries, for relic GWs, and for cosmic strings (0.1% FAP, 95% detection). They show that PPTA data can constrain merger rates and SMBH–halo relations, and, in the relic and cosmic-string sectors, place meaningful limits on early-universe expansion and string tension, with full PPTA potentially detecting signals or ruling out most current models. The methodology and quantified bounds provide a practical framework for interpreting future PTA data in terms of fundamental cosmology and astrophysics.

Abstract

Using a statistically rigorous analysis method, we place limits on the existence of an isotropic stochastic gravitational wave background using pulsar timing observations. We consider backgrounds whose characteristic strain spectra may be described as a power-law dependence with frequency. Such backgrounds include an astrophysical background produced by coalescing supermassive black-hole binary systems and cosmological backgrounds due to relic gravitational waves and cosmic strings. Using the best available data, we obtain an upper limit on the energy density per unit logarithmic frequency interval of Ω^{\rm SMBH}_g(1/8yr) h^2 <= 1.9 x 10^{-8} for an astrophysical background which is five times more stringent than the earlier Kaspi et al. (1994) limit of 1.1 x 10^{-7}. We also provide limits on a background due to relic gravitational waves and cosmic strings of Ω^{\rm relic}_g(1/8yr) h^2 <= 2.0 x 10^{-8} and Ω^{\rm cs}_g(1/8yr) h^2 <= 1.9 x 10^{-8} respectively. All of the quoted upper limits correspond to a 0.1% false alarm rate together with a 95% detection rate. We discuss the physical implications of these results and highlight the future possibilities of the Parkes Pulsar Timing Array project. We find that our current results can 1) constrain the merger rate of supermassive binary black hole systems at high red shift, 2) rule out some relationships between the black hole mass and the galactic halo mass, 3) constrain the rate of expansion in the inflationary era and 4) provide an upper bound on the dimensionless tension of a cosmic string background.

Paper Structure

This paper contains 8 sections, 15 equations, 2 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Observations
  3. New upper bounds on the stochastic backgrounds
  4. Results
  5. Implications and Discussion
  6. Supermassive black holes
  7. Relic gravitational waves
  8. Cosmic strings

Figures (2)

  • Figure 1: Pulsar timing residuals. The length of the vertical line on the left hand edge represents 10$\mu s$.
  • Figure 2: Minimum detectable A (or $\Omega_{gw}(1 {\rm yr}^{-1})h^2$ - right axis) versus $\alpha$ for our current limits (solid line) and potential future limits from the PPTA (dashed line). The star symbol indicates the limit obtainable using the Kaspi et al. (1994) observations of PSR B1855+09. From left to right the near-vertical dotted lines indicate the expected range of amplitudes for the cosmic strings, relic GW and supermassive black hole background respectively.