A candidate of binary black hole system in AGN with broad Balmer emission lines having quite different line widths

Abstract: In the manuscript, a candidate of sub-pc binary black hole (BBH) system is reported in SDSS J1257+2023 through different properties of broad Balmer emission lines. After subtractions of host galaxy contributions, Gaussian functions are applied to measure emission lines in SDSS J1257+2023, leading line width (second moment) 760${\rm km/s}$ of broad H$\beta$ to be 0.69 times of line width 1100${\rm km/s}$ of broad H$\alpha$, quite different from normal line width ratio 1.1 of broad H$\beta$ to broad H$\alpha$ in quasars. The quite broader component in broad H$\alpha$ in SDSS J1257+2023 can be confirmed with confidence level higher than $5\sigma$ through F-test technique, through different model functions applied to measure emission lines. The broad Balmer emission lines having different line widths can be naturally explained by a BBH system with different obscurations on central two independent BLRs. Meanwhile, through ZTF light curves and corresponding phase folded light curves well described by sinusoidal function, BBH system expected optical QPOs can be detected with periodicity about 1000days, confirmed with confidence level higher than $3\sigma$ by Generalized Lomb-Scargle periodogram. And through CAR process simulated light curves, confidence level higher than $2\sigma$ can be determined to support the optical QPOs in SDSS J1257+2023 not from intrinsic AGN activities, although the ZTF light curves have short time durations. Moreover, through oversimplified BBH system simulated results, studying different broad Balmer lines as signs of BBH systems in normal quasars with flux ratios around 4 of broad H$\alpha$ to broad H$\beta$ could be done in near future.