A Cross-Band (X-ray × Optical) Periodicity Search for Supermassive Black Hole Binaries: A Null Result and the First Completeness-Corrected Constraint · arXivDesk
2608.16787Aug 17, 2026Accepted for publication in ApJ. 16 pages, 11 figures, 1 table. Code and result tables: doi:10.5281/zenodo.21386388
A Cross-Band (X-ray × Optical) Periodicity Search for Supermassive Black Hole Binaries: A Null Result and the First Completeness-Corrected Constraint
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
Nearby in the stack
,
≈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
∼3×10−2fbinδmod
(modulo a factor
g<1
), with
fbin
the sub-pc binary fraction,
δmod
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.