Kepler KOI-730 (KIC10227020) 4-(or more?)-Planet System
TTVs are derived from Q1-Q17 Kepler data. x-axes: “Observed Tc” (Mid-Transit Time): EXOFAST’s best-fits from Normalized PDCSAP_FLUX Kepler light flux vs. time (BJD_tdb - 2454900) data. y-axes: “(O – C)”: difference between Observed Tc and the Calculated Tc from the graphically obtained linear ephemeris.
Numerous literature and major Tc#, Tc, and TTV tabulation references can be found on my “TTV Summary" webpage following the table.
3 Oct 2015
Discussion: A sinusoidal curve-fit of the [(O-C) vs. Time] data for KOI-730.01, the 3rd planet in this system, showed (Figure 1. below) a periodicity (P_ttv) of 1290.23 ± 97.48 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 1670.36 days.
Similarly, a sinusoidal curve-fit of the [(O-C) vs. Time] data for KOI-730.03. the 4th planet in this system, showed (Figure 2. below) a periodicity (P_ttv) of 1579.57 ± 391.16 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 1462.11 days.
Despite (a) substantial errors due to weak planetary transits and a noisy star and (b) there being only about one TTV cycle, the two sinusoidal arrays are reasonably well anti-correlated (compare the plots), a good indication of the strength of the two planets’ mutual gravitational interactions. Their period ratio also suggests they are in a mean motion resonance relationship very close to 4 to 3 (or, precisely, 4.0000 to 2.9989).