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TTVs are derived from Q0-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.

KOI-232.02, LC Q1-17, P = 5.77 days [Plot avg. error bars = ± 6.08 min.]
Lomb-Scargle periodogram, no credible periodicities.
Linear ephemeris (this work): Tc = 5.76614885(Tc#) + 67.01824962

KOI-232.01, LC Q1-17, P = 12.47 days [Plot avg. error bars = ± 2.03 min.]
Lomb-Scargle periodogram, no credible periodicities.
Linear ephemeris (this work): Tc = 12.46600349(Tc#) + 67.00408987

KOI-232.03, LC Q1-17, P = 21.59 days [Plot avg. error bars = ± 8.34 min.]
Lomb-Scargle periodogram, no credible periodicities.
Linear ephemeris (this work): Tc = 21.58715708(Tc#) + 75.97964590

KOI-232.03, LC Q1-5 + SC Q6-17, P = 21.59 days [Plot avg. error bars = ± 7.11 min.]
Lomb-Scargle periodogram, no credible periodicities.
Linear ephemeris (this work): Tc = 21.58725315(Tc#) + 75.97703982

KOI-232.04, LC Q1-17, P = 37.99 days [Plot avg. error bars = ± 7.83 min.]
TTV_maximum: 542.34 ± 109.67 days, Amp_ttv_maximum: 44.41 ± 13.08 min.
TTV_minimum: 1059.31 ± 144.66 days, Amp_ttv_minimum: -38.67 ± 13.08 min.
P_ttv: 1033.92 ± 107.18 days.
Amp_ttv: 83.09 ± 18.49 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 1034.95 days; Power: 5.23; FAP: 0.0389.
Linear ephemeris (this work): Tc = 37.99440579(Tc#) + 96.00812229

KOI-232.04, LC Q1-5 + SC Q6-17, P = 37.99 days [Plot avg. error bars = ± 6.60 min.]
TTV_maximum: 454.82 ± 88.05 days, Amp_ttv_maximum: 41.14 ± 10.76 min.
TTV_minimum: 997.65 ± 117.45 days, Amp_ttv_minimum: -42.03 ± 10.76 min.
P_ttv: 1085.66 ± 95.05 days.
Amp_ttv: 83.17 ± 15.21 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 1086.92 days; Power: 6.53; FAP: 0.00436.
Linear ephemeris (this work): Tc = 37.99453569(Tc#) + 96.00227281

KOI-232.05, LC Q1-5 + SC Q6-17, P = 56.26 days [Plot avg. error bars = ± 8.43 min.]
TTV_maximum: 157.16 ± 62.20 days, Amp_ttv_maximum: 27.59 ± 10.61 min.
TTV_minimum: 392.61 ± 66.00 days, Amp_ttv_minimum: -22.50 ± 10.61 min.
TTV_maximum: 628.05 ± 72.54 days, Amp_ttv_maximum: 27.59 ± 10.61 min.
TTV_minimum: 863.50 ± 81.14 days, Amp_ttv_minimum: -22.50 ± 10.61 min.
TTV_maximum: 1098.95 ± 91.24 days, Amp_ttv_maximum: 27.59 ± 10.61 min.
TTV_minimum: 1334.39 ± 102.39 days, Amp_ttv_minimum: -22.50 ± 10.61 min.
P_ttv: 470.89 ± 28.90 days.
Amp_ttv: 50.09 ± 15.00 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 467.77 days; Power: 3.17; FAP: 0.368 (low credibility).
Linear ephemeris (this work): Tc = 56.26024352(Tc#) + 97.20407009

Literature: Tc#, Tc, and TTV Major Tabulations and Other References: see my "Summary" webpage.

21 July 2014
KOI-232 (Kepler-122, KIC-4833421) 6-(or more?)-Planet System

TTV Evidence:
The presence of both a credible (i.e.: False Alarm Probability (FAP) < 0.1) periodicity in the Lomb-Scargle Periodogram (LSP) of [(O-C) vs. Time] ("TTVxy") data points, along with a sinusoidal distribution of the same points displaying a corresponding periodicity ("P_ttv") (see Figure(s) below), is strongly suggestive of the presence of an unseen (non-transiting), gravitationally perturbing planetary object(s) in the system.

No clear TTVs were observed for three closest-in planets in the KOI-232 system.  The 4th and 5th planets do show TTVs but their P_ttv's do not appear to be near an anti-correlated match and, in fact, the credibility of the 5th-planet TTV is relatively poor.  (The latter might improve through additional quarters of observations…possibly during the recently-announced Kepler K2 project.)  The clear TTV of the 4th planet implies the presence of a non-transiting 6th planet having a possible stellar distance intermediate between those of the 4th and 5th ones.  Detailed results are listed below the figures.

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KOI's (Blue)  or
K2 Objects (Green)