Close binary black hole in a radio-quiet quasar: a candidate of Nano-Hertz gravitational wave emitter


 Close supermassive binary black holes (SMBBHs) with separations less than about 0.1 parsec are expected to be Nano-Hertz gravitational wave sources. SMBBH systems should exhibit periodic variability. However, periodic variability in radio-loud quasars may be interpreted with the jet model. Here we report the detection of a robust periodic signal in the optical variability of the radio-quiet quasar PG 0923+201 with an observed period of 726.8±4.7 days, obtained from the sinusoid-like light curve of a temporal baseline of about 9 years. This periodicity is probably from a close SMBBH with a total mass of 109.3 solar masses and a separation of about 0.01 parsec, implying relativistic orbital speeds. Such a system has passed through the well-known “final parsec problem” of SMBBH systems, and the Nano-Hertz gravitational wave radiation becomes significant. The ratio of the separation between these two black holes to the broad-line region size is about 0.1. A close SMBBH is also suggested by this small ratio and the spectral properties of Balmer broad lines in this quasar. This radio-quiet quasar is a candidate emitter of Nano-Hertz gravitational waves at a frequency of about 30 Nano-Hertz.

galaxy M87 5 and the first direct detection of gravitational waves of a binary black hole merger (with masses of about thirty to forty M ) 6 . Searching for close supermassive binary black holes (SMBBHs) and observational identification are big challenges. The hydrodynamic and magnetohydrodynamic simulations show that streams of gas are efficiently peeled by an SMBBH off the inner edge of a circumbinary disk, and rapidly traverse the central cavity in the circumbinary disk, forming individual mini disks surrounding each SMBH [7][8][9][10][11][12] .
The SMBBH accretion from circumbinary disk can produce a more bursty and sawtooth pattern of the optical-ultraviolet light curves of active galactic nuclei and quasars 9,10,12,13 . The relativistic Doppler boosting due to the orbit motion of the secondary SMBH in a circular orbit can produce the sinusoidal light curves 2,14,15 . The first order approximation in β = v/c of the relativistic Doppler boosting is equivalent to a sinusoid model that is favored by the sinusoid-like variability of the light curve of PG1302-102, and is strongly preferred over other models, such as the Doppler boosting model of SMBBH with non-zero eccentricity orbits, the accretion model of SMBBH, and the pure noise model 14 . Figure 1 shows the optical light curve of the Sloan Digital Sky Survey (SDSS) 16 radio-quiet quasar PG 0923+201 (=SDSS J092554.72+195405.1) at a redshift of z = 0.192. The light curve is compiled from photometry data of the All-sky Automated Survey for Supernovae (ASAS-SN) 17,18 V, ASAS-SN g, Zwicky Transient Facility (ZTF) 19 g, and ZTF r. The photometry data are calibrated to the ASAS-SN V band. After de-trending of the light curve, a sinusoid-like light curve emerges. The generalised Lomb-Scargle periodogram (GLS) 20 of the sinusoid-like light curve shows a strong and smooth periodic signal, corresponding to an observed period of P obs = 726.8 ± 4.7 days. The total mass M and the orbital period of SMBBH in a circular orbit P orb give an SMBBH separation of d = 7.89M 1/3 9 (P orb /1.6yr) 2/3 lt-days (M 9 = M/10 9 M ). From M 9 = 2.0 (see Methods) and P orb = 1.67 years, we obtain d = 10.2 lt-days = 0.009 parsec(pc) for PG 0923+201. As d 200 r g (r g = GM/c 2 is the gravitational radius, G and c are the gravitational constant and the speed of light, respectively), the shrinking binary/circumbinary disk system eventually reaches a state in which the disk has decoupled from the rapidly shrinking binary 21,22 . For PG 0923+201, 200 r g = 22.7 lt-days and then d < 200 r g . Thus, the close SMBBH in PG 0923+201 is in the gravitational wave driven regime, where the SMBBH orbital shrink is driven by its gravitational wave emission. The rest-frame gravitational wave frequency f of a close SMBBH on circular orbits equals two times the orbital frequency, and f ≈ 2.7 × 10 −8 Hertz for PG 0923+201.
Thus, PG 0923+201 is a candidate of Nano-Hertz gravitational wave source, which is expected to be detected by pulsar timing arrays.
The optical spectrum of PG 0923+201 in the SDSS shows the redward asymmetric profiles of the broad emission lines Hβ and Hα (Figures 2 and 3). A large number of active galactic nuclei The central cavity radius (the inner radius of the circumbinary disk) is about two times separation of SMBBH 9,26 . The cavity radius is about 20 lt-days for PG 0923+201, and the cavity is well within the circumbinary BLR.
The sinusoid fitting gives a variability amplitude of 0.301 ± 0.006 mJy. The average flux of the sinusoid-like variability is 2.6 mJy, because the long-term 3rd-order polynomial is ∼ 2.6 mJy at the beginning and this value is a sum of these two component contributions. We have ∆F ν ≈ 0.3 mJy and F ν 2.6 mJy for the sinusoid-like variability. Thus, ∆F ν /F ν is 0.12. ∆F ν /F ν = ±(3 -α ν ) β cos ϕ sin i, where i and ϕ are the inclination and phase of the orbit, respectively 14

Methods
Photometric and spectroscopic data. The All-sky Automated Survey for Supernovae (ASAS-SN) data are downloaded from http://www.astronomy.ohio-state.edu/asassn while the Zwicky Transient Facility (ZTF) data are downloaded from https://www.ztf.caltech.edu. We first remove some  shows the false alarm probability of 10 −5 corresponds to the power p = 0.13, i.e., p = 0.13 is at the confidence level of 99.999%. In order to remove artifacts due to seasonal gaps and cadences aliasing, P obs < 400 days is excluded from our periodicity detection. To minimize false periodicity from stochastic quasar variability 35 , we remove any periodicity with 3P obs > the total time baseline, i.e., P obs > 1100 days. The reliability of the strongest peak is tested by the Monte Carlo simulation of 1000 realizations of the light curves generated with the model-independent random subset selection method, i.e., a randomly chosen subset of the detrended data points 36 (Figure 4).
About 63% (∼ 1 -1/e) of the data of the detrended light curve is randomly sampled in each realization.. Thus, the periodicity between 400 and 1100 days is not the false one resulting from the uneven sampling of the light curve. All the authors contributed to the interpretation of the results of the manuscript.
Competing Interests The authors declare that they have no competing financial interests.
Data Availability The data that support the plots within this paper and other finding of this study are available from the corresponding authors upon reasonable request.