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.

1st Figure: KOI-1884.02, P = 4.78 days [Plot avg. error bars = ± 12.63 min.]
Linear ephemeris (this work): Tc = [4.77502128 ± 0.00003223](Tc#) + [288.45931634 ± 0.00477159]

2nd Figure: KOI-1884.01, P = 23.12 days [Plot avg. error bars = ± 8.13 min. (smaller than symbols)]
TTV_maximum: 877.20 ± 129.07 days, Amp_ttv_maximum: 323.09 ± 173.66 min.
P_ttv: 2250.15 ± 234.09 days.
Amp_ttv: 1477.09 ± 245.59 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1341.15 days; Power: 18.40; FAP: 0.
Linear ephemeris (this work): Tc = [23.09327869 ± 0.00198077](Tc#) + [83.05504740 ± 0.07548207]

Numerous literature and major Tc#, Tc, and TTV tabulation references can be found on my "Summary" webpage following the table.

29 May 2015
                 Kepler KOI-1884 (KIC-4851530) 3-(or more?)-Planet System

The close-in transiting planet in this system, KOI-1884.02, shows no TTV at all.

For KOI-1884.01, the presence of both a highly credible periodicity in the Lomb-Scargle Periodogram (LSP) of [(O-C) vs. Time] ("TTVxy") data points [1341.15 days, FAP: 0] along with a sinusoidal distribution of the same points that also displays a marked periodicity, 2250.15 ± 234.09 days (see Figure below), is strongly suggestive of the presence of a third, non-transiting, gravitationally perturbing planetary object(s) in this system.  As in this and many other cases, when periodicity values from both methods are large and visually obvious, the periodicities may not correspond very closely to one another if considerably less than one cycle of periodicity has been observed.  This condition would significantly affect both the choice of "best-fit" sinusoidal curve and the precision of the LSP periodicity.   This is clearly the case for KOI-1884.01.

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