Gravitational waves from binary supermassive black holes missing in pulsar observations

TL;DR

It is concluded that binary evolution is either stalled or dramatically accelerated by galactic-center environments and that higher-cadence and shorter-wavelength observations would be more sensitive to gravitational waves.

Abstract

Gravitational waves are expected to be radiated by supermassive black hole binaries formed during galaxy mergers. A stochastic superposition of gravitational waves from all such binary systems will modulate the arrival times of pulses from radio pulsars. Using observations of millisecond pulsars obtained with the Parkes radio telescope, we constrain the characteristic amplitude of this background, $A_{\rm c,yr}$, to be < $1.0\times10^{-15}$ with 95% confidence. This limit excludes predicted ranges for $A_{\rm c,yr}$ from current models with 91-99.7% probability. We conclude that binary evolution is either stalled or dramatically accelerated by galactic-center environments, and that higher-cadence and shorter-wavelength observations would result in an increased sensitivity to gravitational waves.

Figures (5)

• Figure 1: Residual pulse times of arrival,$\boldsymbol{\Delta} \boldsymbol{t}$, for the four pulsars used in our analysis. These are PSR J1909-3744 (panel $A$ ), PSR J0437-4715 (panel B), PSR J1713+0747 (panel $C$ ), and PSR J1744-1134 (panel $D$ ).
• Figure 2: Predictions and limits on the GWB strain spectrum. The black asterisks (labeled P15) shows the$95 \%$ confidence limit we obtain, assuming $h_{\mathrm{c}}(f)=A_{\mathrm{c}, \mathrm{yr}}\left[f /\left(1 \mathrm{yr}^{-1}\right)\right]^{-2 / 3}$. The other symbols show previously published limits from the European Pulsar Timing Array (triangle, labeled E15, Ref. 20), the North American Nanohertz Observatory for Gravitational Waves (circle, labeled N13, Ref. 29) collaborations, and our previous limit (square, labeled P13, Ref. 8). Each panel shows a different prediction for the GWB as a shaded region that represents the $1-\sigma$ uncertainty, including four models for SMBH evolution, labeled S13 (9), M14 (10), K15 (12), and R15 (11), which predict a power-law form for $h_{\mathrm{c}}(f)$. Models Exp (See supplementary section S2.2, Ref. 13) and R14 (22) include the effects of environmentally driven binary evolution and therefore predict more complex strain spectra. The black curves show the nominal single-frequency sensitivities of our observations (see supplementary section $\mathrm{S} 2.2,13$ ), and is above our limit because of the statistical penalties applied when searching individual frequencies. In Panel $D$, the blue pentagon (labeled $\mathrm{A}_{95, \mathrm{SKA}}$ ) shows the projected upper limit on $A_{\mathrm{c}, \mathrm{yr}}$ obtained with a single-pulsar timing campaign with a next generation radio telescope (the SKA; see supplementary section S2.2, Ref. 13), and excludes all models considered with greater than $98 \%$ probability.
• Figure 3: Illustrative evolutionary paths for a pair of$\mathbf{1 0}^{\mathbf{9}}$ solar-mass SMBHs in a galaxy merger. The figure shows the pair separation and the GW emission frequency $f_{\mathrm{GW}}$, assuming the binary is in a circular orbit. The blue curve shows the evolution of the separation of the SMBHs using fiducial assumptions, which results in a GWB that is inconsistent with our data. The cyan curve labeled Fiducial, $G W$ is the portion of the evolution when GW-emission dominates orbital decay. We also show scenarios that could explain our GWB limit. First, the galaxy merger rate could be lower, as represented by the slow merger curve (green curve). Alternatively, after the SMBHs form a binary (red circle), the orbital evolution may stall prior before emitting GWs (red curve). The gray curve shows a scenario in which a dense binary SMBH environment drives orbital decay through the GW frequency band at which we are sensitive. In this case, GW emission dominates only for $f_{\mathrm{GW}}>0.5 \mathrm{yr}^{-1}$ (pink curve, labeled $E n v, G W$ ). Finally, it is possible that the post-coalescence SMBH could undergo gravitational recoil and escape its host galaxy (purple dashed curve), negating the possibility of it again forming a binary SMBH.
• Figure 4: Fig. S1: Histogram of $95 \%$ (red thick histogram) and $50 \%$ confidence limits (blue thin histogram) for 100 simulated data sets with identical cadence and white noise to our PSR J19093744 observations, but with an injected GWB with $A_{\mathrm{c}, \mathrm{inj}}=1.1 \times 10^{-15}$ (dashed black vertical line).
• Figure 5: Fig. S2: Left panel: Sensitivity of power spectral density estimates of PSR J1909-3744 (black curve). The blue line shows the power spectral density of a GWB, showing that the data set is most sensitive to a GWB at frequencies of $0.2 \mathrm{yr}^{-1}$. The peak at $1 \mathrm{yr}^{-1}$ is associated with fitting for pulsar position and proper motion. Right panel: Limit on the GWB for power-law strain spectra $h_{\mathrm{c}}(f)=A_{\mathrm{c}}\left(f / 1 \mathrm{yr}^{-1}\right)^{\alpha}$ set at different $\alpha$ (open boxes), and the best-fitting curve (black curve).