A Cross-Band (X-ray × Optical) Periodicity Search for Supermassive Black Hole Binaries: A Null Result and the First Completeness-Corrected Constraint

@misc{akbari2026crossband,
  title = {{A Cross-Band (X-ray $\times$ Optical) Periodicity Search for Supermassive Black Hole Binaries: A Null Result and the First Completeness-Corrected Constraint}},
  author = {Karan Akbari},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.16787},
  eprint = {2608.16787},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.16787},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - A Cross-Band (X-ray × Optical) Periodicity Search for Supermassive Black Hole Binaries: A Null Result and the First Completeness-Corrected Constraint
AU  - Karan Akbari
PY  - 2026
DA  - 2026/08/18
PB  - arXiv
DO  - 10.48550/arxiv.2608.16787
UR  - https://arxiv.org/abs/2608.16787
AB  - We present the first sample-level search for supermassive black hole binaries (SMBHBs) requiring coherent quasi-periodicity at a common period in the X-ray and optical bands, over 1194 Swift-BAT hard X-ray AGN (Stage 1) and 175 4XMM-DR14 AGN (Stage 2). No source is a co-periodic candidate. Each light curve is modelled as a damped random walk (DRW) and searched with a Lomb-Scargle periodogram and a look-elsewhere-corrected Monte-Carlo significance. Because DRW red noise is largely independent between corona and disc, we require both bands individually significant with periods coincident within 5%, and gate the survivors with the model-independent null-signal-template test of Robnik et al. (2024). Over P=100-$900$ d the completeness-corrected 95% upper limit on the co-periodic fraction is amplitude-dependent: ≲ 3% for hard-X-ray fractional modulation ≳ 0.3, ≈ 15% (precision-limited) at 0.2, and uninformative below ∼ 0.15 (the ε=1 floor is 0.25%). The sensitivity is set by the hard X-ray monitoring, not the optical photometry or the statistics, the opposite of the usual assumption. Daily MAXI and RXTE/ASM monitoring of the brightest AGN raises the X-ray completeness 5-8-fold, and the search remains null. Integrated over the BAT black-hole mass function, the expected all-amplitude co-periodic fraction is ∼ 3×10^−2 f_bin δ_mod (modulo a factor g<1), with f_bin the sub-pc binary fraction, δ_mod the modulating duty cycle, and g the fraction reaching recoverable hard-X-ray amplitude, so a null is expected. We deliver a validated cross-band framework and the first completeness-corrected constraint on the co-periodic fraction, ready for the denser X-ray monitoring of Einstein Probe and eROSITA.
ER  -