A weak longitudinal component in a gravitational-wave background can imitate the angular response of a propagation mass, and a new analysis quantifies how far that ambiguity reaches. Building a compressed Gaussian experiment from the NANOGrav 15-year pulsar timing data set, the authors measure how much rejection power is lost when the background is allowed to have a longitudinal component. At a false-alarm probability of 10⁻³, allowing that freedom in a massless background costs at least 16.29 percentage points of optimal rejection power for a specified source in a 20-pulsar subarray.
The work addresses an open problem in detecting gravitational-wave backgrounds through pulsar timing: how to distinguish an effective propagation mass in the signal — a sign of physics beyond standard gravity — from a background with properties other than those assumed. The advance is concrete: expanding the array from 20 to 40 pulsars at the same background level recovers at least 7.62 percentage points of the lost power, showing that array size partially mitigates the degeneracy.
In a separate low-background experiment, the authors allow the same continuous range of longitudinal amplitudes at zero and positive mass. Across that range and three injected background levels, one test rejects zero mass with at least 97.38% power at either of two masses separated by 1.08%. However, with false assignment limited to 10⁻³ at the other mass, the power to identify which of the two masses is present is at most 1.584%.
The conclusion is that a cutoff can be identifiable before its position within a frequency cell can be resolved: the test detects the presence of a propagation mass but cannot determine its value with fine precision. This matters for interpreting NANOGrav results and future data sets, where attributing a signal to a propagation mass rather than a background with a longitudinal component requires care. Increasing the number of pulsars and improving sensitivity below the current background level will be key to breaking the degeneracy.