[Paper Review] Asymptotic tails of massive gravitons in light of pulsar timing array observations

R. A. Konoplya, A. Zhidenko|arXiv (Cornell University)|Jul 3, 2023

Pulsars and Gravitational Waves Research48 references17 citations

TL;DR

The paper argues that asymptotic oscillatory tails of massive gravitons—from massive gravity theories or extra-dimensional scenarios—could contribute to gravitational waves with very long wavelengths detectable by pulsar timing arrays, potentially explaining part of the NANOGrav signal, with constraints placing graviton masses around 2×10^-23 to 2×10^-24 eV/c^2; the effect is expected to be small and sourced mainly by nearby Galactic black holes.

ABSTRACT

We demonstrate that the late time oscillatory tails of massive gravitons, present in both massive theories of gravity and effectively in extra-dimensional scenarios, could potentially contribute to gravitational waves with very long wavelengths. However, their impact on recent pulsar timing array observations might be relatively small, predominantly consisting of radiation emitted by black holes in our region of the Milky Way.

Motivation & Objective

• Motivate the possibility that massive gravitons with tiny masses can produce long-wavelength gravitational waves observable by pulsar timing arrays.
• Propose that late-time oscillatory tails of massive fields from black-hole ringdowns can contribute to the gravitational-wave background.
• Highlight that these tails may provide an alternative or additional source to supermassive black hole binaries for the NANOGrav signal.
• Compare estimated graviton-mass ranges with existing gravitational-wave constraints and astrophysical considerations.

Proposed method

• Discuss the universal late-time decay law for massive fields in black-hole backgrounds: |ψ ∝ t^(-5/6) sin(μ c^2 t/ħ)| and its applicability across scalar, Proca, Dirac, and massive graviton cases.
• Argue that the Compton range R ∼ ħ/(2μc) can imply cosmologically long interaction ranges for ultralight gravitons (order of light-years).
• Relate the tail signal to pulsar timing residuals with Earth and pulsar terms that can be treated as independent sources.
• Use observational context from NANOGrav and LIGO bounds to frame viable graviton-mass windows and compare with other astrophysical constraints.

Experimental results

Research questions

• RQ1 Can asymptotic oscillatory tails of massive gravitons produce a detectable ultra-long-wavelength gravitational-wave background observed by pulsar timing arrays?
• RQ2 What graviton mass ranges are compatible with NANOGrav-like signals and existing gravitational-wave constraints?
• RQ3 To what extent do nearby Galactic black-hole ringdowns contribute to a stochastic background through massive-tail dynamics?
• RQ4 How do massive-polarization scenarios alter the interpretation of pulsar timing data compared to purely massless GR predictions?

Key findings

• Long-wavelength gravitational tails from massive gravitons could contribute to the gravitational-wave background with wavelengths of order light-years.
• Pulsar timing array observations allow graviton masses in the range roughly 2×10^-24 eV/c^2 ≤ μ ≤ 2×10^-23 eV/c^2 ( Compton length ~1–10 ly ).
• The magnitude of the massive tail signal is expected to be small, predominantly arising from radiation emitted by nearby Galactic black holes.
• Massless LIGO/Virgo detections provide upper bounds on graviton mass that are of the same order as the suggested range, though different data and assumptions apply.
• If even longer-wavelength waves are observed in the future, ultra-light massive gravitons with μ ≲ 2×10^-24 eV/c^2 could be implicated.