Sources with orbit period modulation I: total number: at any instant of time, the number of decoupled SMBH binaries vs. average jet flux, limiting to orbit periods within P _min = 1 minute and P _max = 1 year (blue and dotted blue) or 1 month (green and dotted green) over the entire sky, with flux above F/ for = _{radio Edd} the composite efficiency of the jet, using the SE (small seed, efficient accretion; dashed lines) and LE (large seed, efficient accretion; solid lines) model of Sesana et al. (2011a). For example, for an efficiency = 10 ⁻³ and target flux sensitivity 1 mJy, one to several hundred binaries are bright enough to see and have periods less than 1 year; of order one has a period less than 1 month. In the limit of infinite sensitivity, all rates must be less than the all-sky rate ( 30 yr ⁻¹) times the longest time allowed (1 Myr, corresponding to the time since separation from a circumbinary disk). In the limit of poor sensitivity, the number vs. flux scales as F ^−3/2, as usual for the nearby universe. For comparison, the solid black line is 10 ⁴( F/  Jy) ^−3/2. The top axis shows ticks at z _max, the redshift at which L _edd/4π d ² _L = F/ for M = 10 ⁷ M _☉; as we assume < 1, no source can be detected at higher redshift.