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.

Figure: KOI-5651.01, P = 83.50 days [Plot avg. error bars = ± 17.73 min.]
TTV_minimum: 871.90 ± 1774.47 days, Amp_ttv_minimum: -110.98 ± 580.91 min.
P_ttv: 1807.50 ± 2609.20 days.
Amp_ttv: 395.78 ± 821.53 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1247.79 days; Power: 2.91; FAP: 0.240.
Linear ephemeris (this work): Tc = [83.50924427 ± 0.00640200](Tc#) + [96.46050593 ± 0.06361858]


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

13 April 2015
                Kepler KOI-5651 (KIC-9282853) 2-(or more?)-Planet System

Discussion:
In the example of KOI-5651.01, a sinusoidal (less than one cycle) curve-fit of the (O-C) vs. Time data showed an approximate periodicity (P_ttv) of ~ 1807.50 days; 1247.79 days was observed in the Lomb-Scargle Periodogram (LSP) of the same data.  When less than one cycle of periodicity has been observed by Kepler, the P_ttv values derived from a best-fit sinusoidal curve and the corresponding Lomb-Scargle periodogram can be quite different and show large errors.  This is the case for KOI-5651.01 (see plot and data below).  Clearly, this can only be remedied by longer-term observations…which may or may not be in the offing via the Kepler K2 project.

Exoplanet-Science.com

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