Spot the binary

What you're seeing

Every quasar in the game is simulated. The random flicker is a damped random walk, which is the usual model for how quasars vary (Kelly et al. 2009; MacLeod et al. 2010): the brightness wanders and slowly forgets where it was, over about 500 days here. Vaughan et al. (2016) argue that most periods claimed from single light curves are this kind of noise. A real binary adds a sine wave with a period somewhere between 150 and 750 days, 0.10 to 0.20 mag high, which is about the size of the flicker itself. You never see the answer until you press Check.

The 3D quasar is drawn from the same numbers as the plots. The disc's glow follows the optical light curve and the blue-violet hot spot above the black hole follows the X-ray one, so when the disc brightens, the moving dot in the light curve goes up. After Check, a real binary shows its second black hole going round at the injected period. The optical dots are spaced like ASAS-SN, about 390 points from 2012 to 2023 with a gap every year when the Sun is in the way. The X-ray dots are spaced like Swift-BAT, 157 monthly points from late 2004 to 2017.

The periodogram (Lomb 1976; Scargle 1982) fits a sine wave at every period from 100 days up to a third of the light curve and shows how much of the wiggle each one explains. The dashed line is a false-alarm line, set so only 1 in 100 noise-only curves goes above it anywhere. The textbook line assumes white noise, where every point is independent of the last. Quasar flicker wanders slowly instead, and slow wandering piles up power at long periods, which is where a binary would show up too. The red-noise line in round 3 is set by simulating that wandering, 1,000 curves per band. The grey stripes near 180 and 365 days are skipped, because the yearly gaps in the data make fake peaks there.

The real version ran on 1,369 active galaxies: 1,194 hard X-ray AGN from Swift-BAT and 175 from 4XMM-DR14, against optical light curves from ZTF and ASAS-SN. Both bands had to pass a red-noise line at 1 in 1,000 and agree on the period within 5%. None did. Noise alone predicted about 0.015 fake candidates across the BAT sample, and I got 0. Putting fake signals into the real light curves and running everything again says at most about 3% of the BAT galaxies can have a shared period between 100 and 900 days with a hard X-ray modulation of 30% or more (95% confidence). Below about 15% the limit says nothing, because monthly X-ray points can't pull out a signal that small.