How To Discover New Forces? (Physics / Astronomy)

Jeff Dror and colleagues in their recent paper, considered the possibility that black holes in binaries are charged under a new long-range force and found that these forces can be detected with the help of pulsar-timing arrays. In particular, they showed that, in the presence of a new force, the spectral index of the stochastic gravitational wave background (SGWB) spectrum is modified, thus making the measurement of the spectral shape a powerful test of fundamental physics. Their study recently appeared in Arxiv.

Supermassive black hole binary mergers produced a stochastic gravitational wave background (SGWB) which can be detectable by pulsar timing arrays. PTAs use the extremely stable timing of successive light pulses from pulsars to detect gravitational waves (GWs) in the form of correlated timing distortions. In the presence of GWs, the observed time between pulses deviates from the stable rhythm in the frame of the source. The correlation of these deviations between pulsars exhibits a characteristic dependence on their angular separation, known as the Hellings and Downs curve, and this is considered the hallmark of a GW detection.

Recently, Zaven Arzoumanian and colleagues search for an isotropic stochastic gravitational-wave background (GWB) in the 12.5-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. This maybe the first signal of the SGWB from SMBH mergers. While the signal does not yet conclusively exhibit the Hellings and Downs angular dependence, upcoming datasets from NANOGrav and other collaborations will be able to confirm their discovery.

Now, Jeff Dror and colleagues point out that, the study of the SGWB from SMBH mergers will open an entirely new observable for particle physics: the spectral shape of the SGWB. They showed that, in the presence of a new force, the standard power-law prediction for the SGWB spectrum is modified, presenting the spectral index as a robust prediction.

Supermassive black holes and their environments can acquire charge due to high-energy particle production or dark sector interactions, making the measurement of the spectral shape a powerful test of fundamental physics.

— told Jeff Dror, postdoc at UC Santa Cruz and first author of the study

They also mentioned that pulsar timing arrays are rapidly improving in sensitivity. For identical pulsars, the signal-to-background ratio of a pulsar timing array analysis scales,

where, T is the observation time and Np is the number of pulsars.

The large scaling with observation time suggested that NANOGrav will be able to significantly improve the estimate of the spectral index and amplitude as it continues observing the current pulsar set.

In addition, they suggested that, combining the 12.5-year NANOGrav data with the European Pulsar Timing Array (EPTA) and Parkes Pulsar Timing Array (PPTA) datasets may be enough to detect the Hellings and Downs correlation function between pulsars, which, if observed, would confirm the first detection of a stochastic GW background. Once a discovery is made, the measurement of the spectral index will be critical to measure the charges of the SMBHs and search for additional forces.

FIG. 1. A comparison of the spectral index as measured in the NANOGrav 12.5-year data set to the value predicted by merging supermassive charged black hole binaries. The shaded and bounded regions correspond to the 1σ and 2σ posteriors derived by the NANOGrav Collaboration. The black lines correspond to charged binaries under a new long-range vector force with different values of the dipole-strength parameter γ, assuming the potential-strength parameter is negligible (α = 0). Since this spectrum is not strictly a power law, they evaluated the spectrum at roughly the peak sensitivity of NANOGrav, f = (5 yr)-¹. © Jeff Dror et al.

Moreover it has been suggested that, pulsar timing arrays are particularly well suited to measure stochastic GW spectra at frequencies of order nHz–100 µHz. If we shall be able to confirm consistent spectral index and amplitude across this wide range of frequencies, it would be a remarkable confirmation of gravity-only mergers.

On the other hand, if a new force is present with a mediator mass above the pulsar timing range and below that of higher frequency detectors, it would show up as an observable break in the spectrum. This displays the critical complementarity between the different GW searches.

Other GW experiments may also detect stochastic binary merger backgrounds. In particular, LISA is expected to see a stochastic background of white dwarf, neutron star, and lighter black hole binary mergers.”

— told Jeff Dror, postdoc at UC Santa Cruz and first author of the study

Finally, they note that since the GW spectrum from SMBH binaries is yet to be discovered, it is possible that SMBHs have charges so large that new force is strong relative to gravity. In this case, we may uncover additional signals in the SGWB.

Firstly, for sufficiently large dark charges, a repulsive force will stall the merger on cosmological timescales. This could reduce the SGWB amplitude below lower bounds estimated for gravity-only mergers.

Secondly, while gravitational radiation tends to rapidly circularize binaries, dipole radiation can have the opposite effect as the binary passes through the mediator mass threshold and can have a dramatic effect on the spectrum.

All these effects they will gonna study in the future work.

Reference: Jeff A. Dror, Benjamin V. Lehmann, Hiren H. Patel, Stefano Profumo, “Discovering new forces with gravitational waves from supermassive black holes”, Arxiv, pp. 1-10, 2021.

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