SGWB Weakens PTA Dark Matter Substructure Sensitivity to Subdominant Levels

The paper develops a unified likelihood analysis for Doppler and Shapiro timing delays induced by primordial black holes and axion miniclusters across rare static encounters to stochastic flyby regimes. Monte Carlo signal injection is paired with surrogate likelihoods to handle the transition from individual events to the many-substructure limit, enabling direct comparison against the SGWB power-law spectrum inferred from 15-year PTA datasets. This approach reveals that the SGWB floor dominates timing residuals at nanohertz frequencies, suppressing sensitivity curves by factors of 10^2 to 10^4 relative to earlier idealized projections.

Contextually, the result aligns with NANOGrav 15-year and EPTA DR2 findings that a common-spectrum process with amplitude ~2e-15 is consistent with supermassive black hole binaries yet overlaps the frequency band where DM substructure signals peak. Prior PTA DM limits assumed noise floors set only by pulsar white noise and spin irregularities; incorporating the SGWB as an additional correlated red-noise component exposes an irreducible confusion limit. Only Earth-term Shapiro delays, which produce distinct geometric signatures, retain marginal reach for DM fractions below 10 percent under optimistic 30-year baselines with 100 pulsars.

Future IPTA data releases will test these projections once the SGWB spectral index is better constrained. Cross-correlation with LISA stochastic background measurements could break degeneracies between binary populations and DM, while targeted searches for non-Gaussian timing signatures may recover sensitivity lost to the Gaussian SGWB assumption. The analysis underscores that PTA DM science now requires joint modeling of all nanohertz sources rather than sequential subtraction.