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-935.01, P = 20.86 days [Plot avg. error bars = ± 4.20 min.]
TTV_minimum: 253.52 ± 18.21 days, Amp_ttv_minimum: -16.86 ± 1.53 min.
TTV_maximum: 729.34 ± 22.28 days, Amp_ttv_maximum: 25.61 ± 1.53 min.
TTV_minimum: 1205.17 ± 28.65 days, Amp_ttv_minimum: -16.86 ± 1.53 min.
P_ttv: 951.65 ± 17.86 days.
Amp_ttv: 42.47 ± 2.17 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 944.31 days; Power: 23.91; FAP: 2.647 x 10^-8.
Linear ephemeris (this work): Tc = [20.86023033](Tc#) + [113.01893988]


Figure: KOI-935.02, P = 42.63 days [Plot avg. error bars = ± xxx min.]
TTV_maximum: 236.26 ± 57.58 days, Amp_ttv_maximum: 17.59 ± 3.34 min.
TTV_minimum: 789.40 ± 74.26 days, Amp_ttv_minimum: -24.53 ± 3.34 min.
TTV_maximum: 1342.55 ± 100.42 days, Amp_ttv_maximum: 17.59 ± 3.34 min.
P_ttv: 1106.30 ± 68.87 days.
Amp_ttv: 42.11 ± 4.73 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1126.55 days; Power: 9.45; FAP: 6.057 x 10^-6.
Linear ephemeris (this work): Tc = [42.63422630](Tc#) + [74.17238515]


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

26 May 2015

Exoplanet-Science.com

        Kepler KOI-935 (Kepler-31; KIC-9347899) 4-(or more?)-Planet System

Discussion:
KOI-935.01 (Kepler-31b): A sinusoidal curve-fit of the [(O-C) vs. Time] data showed (Figure 1.) a periodicity (P_ttv) of 951.65 ± 17.86 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 944.31 days.
KOI-935.02 (Kepler-31c): A sinusoidal curve-fit of the [(O-C) vs. Time] data showed (Figure 2.) a periodicity (P_ttv) of 1106.30 ± 68.87 days; a Lomb-Scargle Periodogram (LSP) of the same data gave a high-credibility periodicity of 1126.55 days.
The TTVs for the above two planets are fairly well anti-correlated suggesting they are the primary cause of each others TTVs; their periods are also in the near MMR ratio of 2.044.  Further, since their Amp_ttv’s (see below) and their NEA-reported radii (935.01: Rp/R_Earth = 5.28; 935.02: Rp/R_Earth = 4.99) are very similar, their densities must also be very similar.  That they are not  precisely anti-correlated and that more scatter was found for 935.02 suggests that the latter may also be undergoing a significant interaction with 935.03; the period ratio for 932.03 vs. 935.02 is also a near MMR value: 2.056.
KOI-935.03 (Kepler-31d) & KOI-935.04:  No (or a very low) TTVs were observed.

Scroll Down  to

KOI's (Blue)  or
K2 Objects (Green)