Compelling Evidence for a Harmonic in the Light Curve of the Supermassive Black Hole Binary Candidate PKS J1309+1154

TL;DR

The paper presents convincing evidence that PKS J1309+1154's radio light curve contains a real fundamental periodicity of approximately $P \approx 6550$ days ($\approx$17.9 years) and a first harmonic at $P/2 \approx 3275$ days ($\approx$9 years), derived from 46 years of UMRAO+OVRO monitoring at 14.5/15 GHz. Using sine-trend fits, regional quadratic tests, folded light-curve analyses, and WWZ spectra, the authors demonstrate the harmonic's coherence and its in-phase relation to the fundamental, with a global p-value of $4.9\times10^{-4}$ indicating a robust detection. They interpret these periodicities within a modified SMBHB jet framework, proposing two jets with different powers modulated by orbital motion and wind-driven jet focusing, which reproduces the observed light curves and predicts testable phenomenology such as a future flattening around 2026–2034. The discovery of a compelling harmonic strengthens the SMBHB interpretation, suggests that a sizeable fraction of SMBHB candidates may display harmonics, and motivates coordinated gravitational-wave searches across pulsar timing arrays and next-generation observatories, as well as optical/IR follow-up to measure orbital masses.

Abstract

We recently discovered a supermassive black hole binary (SMBHB) candidate, PKS J1309+1154, in the combined 46-yr University of Michigan Radio Astronomy Observatory (UMRAO) plus Owens Valley Radio Observatory (OVRO) blazar monitoring programs at 14.5/15 GHz. The light curve of PKS 1309+1154 exhibits a 17.9 year periodicity. We also reported a hint of a first harmonic with a 9 year periodicity in this object. Further analysis of the PKS J1309+1154 light curve provides compelling evidence that both the fundamental and the harmonic are real, confirming the existence of real periodicities in blazar light curves. This is the first case, to our knowledge, of watertight evidence for a fundamental and a harmonic periodicity in a blazar light curve. It makes PKS J1309+1154 a \textit{strong\/} supermassive black hole binary (SMBHB) candidate, and thus the third such candidate to be revealed through long-term radio monitoring, the other two being PKS J0805--0111 and PKS 2131--021, both discovered through the OVRO 40 m Telescope monitoring program. It is argued that hundreds of SMBHB candidates will be discovered by the Vera Rubin and Simons Observatories. Coherent searches for gravitational waves from a network of SMBHB candidates, starting immediately, are strongly motivated.

Figures (5)

• Figure 1: The PKS J1309+1154 fundamental and harmonic periodicities. Orange and blue symbols denote the UMRAO and OVRO data, respectively. (a) shows the observed light curve, (b) shows the residual light curve after subtraction of the black curve in (a), which is the least squares sine wave plus trend fit to the observed light curve. The solid green curve in (b) shows the fitted least squares sine wave to the residual light curve, which has a period of the first harmonic of the fundamental (see text). The green dashed line in (a) shows the combined fundamental+trend+harmonic.
• Figure 2: The PKS J1309+1154 light curve analyzed in the eleven distinct regions where the harmonic crosses zero, demarcated by the vertical dashed lines. In each region a quadratic polynomial has been fitted to the light curve in that region anchored at the crossing points. In many cases the quadratic fit lies so close to it that it is indistinguishable from the fundamental+harmonic fit. In all eleven regions the quadratic fit lies on the same side of the fundamental fit alone as the fundamental+harmonic fit. We therefore reject the hypothesis that the data is randomly distributed relative to the fundamental, and, consequently, that the harmonic is not real, at the level p-value $=4.9\times 10^{-4}$ --- i.e., 3.3$\sigma$.
• Figure 3: The detrended, folded light curve of PKS J1309+1154, assuming a period of 6550 days for the fundamental periodicity. (a) The folded light curve showing the different cycles (see Table \ref{['tab:cycles']}). Here we have folded cycles 0, 2, and 3 on to cycle 1. (b) Here the folded data have been divided into the four sections listed in Table \ref{['tab:cycles']}. Least squares fits of quadratic polynomials have been performed on each section separately, with the polynomials anchored at the zero points of the harmonic, shown here by the crossover points of the fundamental vs. the fundamental+harmonic fits. Rather surprisingly these quadratic fits now lie almost identically on the fit of the fundamental + harmonic, showing clearly that the data are far more consistent with the fit including the harmonic rather than that excluding the harmonic. Comparison of the quadratic polynomial fits in Fig. \ref{['plt:J1309regions']} compared to those shown in (b) above, shows that some of these fits are significantly better in the folded light curve, indicating the coherence of the underlying fundamental+harmonic signal over the 2.5-cycle duration of the observations.
• Figure 4: WWZ spectra of PKS J1309+1154 showing the fundamental periodicity and the first harmonic, which are both coherent over the whole light curve (see text). (a) This is the spectrum of the full UMRAO+OVRO 46-yr light curve on the conventional linear power scale. (b)-(d) Show WWZ spectra using the square root of the power (see text). (b) Here we show the spectrum of the full (1979-2012.5) UMRAO light curve alone. (c) The spectrum of the full UMRAO light curve from 1979--2012.5 plus the OVRO light curve from 2012.5--2015. (d) The spectrum of the full UMRAO light curve from 1979--2012.5 plus the OVRO light curve from 2012.5--2019.
• Figure 5: The proposed model for the de-trended PKS J1309+1154 OVRO light curve using a modified version of the SMBHB jet model of Paper 4. Both black holes in the SMBHB have jets, but these are of unequal strength. The model jet parameters are listed in the text.