The multi-frequency radio light curve of the sub-pc SMBH binary candidate PG 1302-102
Supermassive black hole binary (SMBHB) candidates with sub-parsec (sub-pc) orbital separations are rare, high-value systems, thought to be the dominant sources of the recently detected nanoHertz (nHz) gravitational wave (GW) background. Alongside pulsar-timing-array searches for localized nHz GW sources from SMBHBs, an increasing number of candidates have been identified from synoptic surveys of large quasar optical light curves over increasingly long baselines. The optical light curve of the quasar PG~1302-102 at a redshift of $z=0.278$ exhibits a pronounced, smoothly varying periodic signal of ~5.2 years over approximately 20 years. Although the cause of this periodicity remains debated, a plausible explanation is a binary system of two SMBHs with a sub-pc separation. At this close distance, the $10^{8.3-9.4} M_{\odot}$ nuclear black holes in PG 1302-102 are expected to merge within $\sim$$10^{5}$ yr solely due to GW emission. We present a multi-frequency radio light curve analysis of PG~1302-102 spanning a $\sim$19-year baseline, with observations between 2005 and 2024 drawn from the Australian Telescope Compact Array (ATCA). The ATCA radio light curve is highly variable at 5.5~GHz but shows no significant evidence of the periodicity seen at optical wavelengths. However, we report fractionally stronger evidence of periodicity in the in-band spectral index time-series at 5.5~GHz, with a period consistent with the optical periodicity. Furthermore, the recently reported change in optical periodicity is also present in the radio in-band spectral index light curve. These two results suggest that radio and optical periodicity may be physically coupled despite very different emission mechanisms. We argue that this radio-optical coupling reinforces the SMBHB interpretation, despite the optical periodicity change, and provides an intriguing case study ahead of the LSST-SKAO era.