Title: Impact of numerical-relativity waveform calibration on parametrized post-Einsteinian tests
Authors: Simone Mezzasoma, Carl-Johan Haster, Nicolás Yunes
First Author’s Institution: The Grainger College of Engineering, Illinois Center for Advanced Studies of the Universe & Department of Physics, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA
Status: Available on arXiv [open access]
Gravitational waveforms
When Albert Einstein found that his theory of general relativity predicted tiny deformations in space and time that we call gravitational waves, he thought they’d be too weak to ever detect. Now, over a century later, hundreds of gravitational wave observations from binary black hole and neutron star mergers have allowed us to put one of the most successful theories in physics through a variety of rigorous tests. So far, Einstein’s equations have passed every one.
But what predictions are we verifying? The main observable in gravitational-wave astronomy is the waveform: the shape of the gravitational wave over time as the binary components spiral into each other and eventually merge.
The problem is that waveforms are not simple functions. We generally need supercomputers to solve Einstein’s equations numerically, and even then, each simulation models only one specific binary system at a time. To cover the full range of masses and spins a binary can have, we rely on waveform models that combine approximation techniques with fits to numerical simulations.
If you’ve ever fit a model to data, you know the fit is never perfect; there’s always some uncertainty. Waveform models are no different. The uncertainty in fits to numerical simulations depends on the quality and quantity of available simulations. Despite that, most models fix the fit coefficients and neglect their uncertainties. Rather than reflecting the range of waveforms consistent with the numerical simulations, they return a single waveform for a given set of binary system parameters.
The authors of today’s paper know that uncertainty is the only certainty we have. They implement an uncertainty-aware waveform model that, instead of generating a single waveform, can generate many waveforms, all consistent with the underlying numerical simulations used in the fits. The distribution of different waveforms this model generates reflects the uncertainties in the fit coefficients. They find that throwing away uncertainty could lead us to detect false deviations from general relativity, and that using uncertainty-aware waveform models can prevent this.
Avoiding false deviations from general relativity
The parameterized post-Einsteinian (ppE) test is one of many tools for checking whether gravity behaves as Einstein predicted. It essentially works by adding an extra term to the waveform, controlled by a parameter β, which should be exactly zero if general relativity is correct.
The authors created some fake data by injecting the expected waveforms of two binary black hole systems, with total masses of 20 and 60 solar masses respectively, into noise. Both signals are perfectly consistent with general relativity, but lie at the edge of the model’s credible band. When the standard waveform model is used to analyze the data, β comes out to be nonzero, highlighting the limitations of models that neglect uncertainty.
This deceiving bias grows with how loud the signal appears in our data. For faint signals from distant or low-mass systems, detector noise dominates and hides the bias. But for moderately loud signals that may be observed in future gravitational-wave detectors that are more sensitive, systematic differences between waveform models can disguise themselves as a violation of general relativity. They can even affect the binary masses and spins that we infer from the data.
Switching to an uncertainty-aware model can fix the problem. As shown in Figure 1, when a signal is injected using the uncertainty-aware (blue) model itself, the probability distribution for β peaks at zero in this case, right where it should. This demonstrates that the blue model correctly recognizes a GR-consistent signal despite the waveform variability introduced by numerical-relativity uncertainty.
The importance of uncertainty
Before claiming a deviation from general relativity, scientists would need to be absolutely sure the deviation isn’t an artifact of systematic errors. This work exposes a vulnerability lurking in current gravitational-wave analyses: fit uncertainty, which is quietly disregarded by many waveform models, can fabricate the appearance of deviations from general relativity where none exist.
The good news is that efforts to incorporate uncertainty into waveform models are well underway. As detectors get more sensitive and the signals we observe get louder, the margin for this kind of error will get smaller, making it all the more urgent to make sure models reflect what we actually know.
Einstein’s theory has survived over a century of scrutiny. Extraordinary claims require extraordinary evidence, and that evidence must stand firm even after every source of uncertainty has been accounted for.
Astrobite edited by Nicki Bond
Featured image credit: Viviana Cáceres
