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       Kepler KOI-284 (Kepler-132; KIC-6021275) 5-(or more?)-Planet System

Discussion:
Among the four known transiting planet in this system, only one, KOI-284.04, appears to show a credible TTV of about 320 days.

It is surprising that the two with nearly the same periods, namely
284.02 and 284.03, do not exhibit credible TTVs even though they would have passed within 300,000 km of each other 9 times during Kepler's Q1-17.
[average Earth/Moon distance = 384,400 km].

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.

Figures:
KOI-284.03, Kepler-132b, P = 6.18 days [Plot avg. error bars = ± 5.13 min.]
Linear ephemeris (this work): Tc = [6.17814747 ± 0.00002056](Tc#) + [101.86599148 ± 0.00256995]

KOI-284.02, Kepler-132c, P = 6.41 days [Plot avg. error bars = ± 4.61 min.]
Linear ephemeris (this work): Tc = [6.41490070 ± 0.00001581](Tc#) + [102.64143580 ± 0.00195292]

KOI-284.01, Kepler-132d, P = 18.01 days [Plot avg. error bars = ± 4.19 min.]
Linear ephemeris (this work): Tc = [18.01011051 ± 0.00007384](Tc#) + [112.42649539 ± 0.00328856]

KOI-284.04, P = 110.29 days [Plot avg. error bars = ± 10.33 min.]

TTV_minimum: 122.04 ± 26.32 days, Amp_ttv_minimum: -34.87 ± 14.45 min.
TTV_maximum: 281.80 ± 28.77 days, Amp_ttv_maximum: 37.97 ± 14.45 min.
TTV_minimum: 441.56 ± 32.70 days, Amp_ttv_minimum: -34.87 ± 14.45 min.
TTV_maximum: 601.33 ± 37.64 days, Amp_ttv_maximum: 37.97 ± 14.45 min.
TTV_minimum: 761.09 ± 43.26 days, Amp_ttv_minimum: -34.87 ± 14.45 min.
TTV_maximum: 920.86 ± 49.32 days, Amp_ttv_maximum: 37.97 ± 14.45 min.
TTV_minimum: 1080.62 ± 55.68 days, Amp_ttv_minimum: -34.87 ± 14.45 min.
TTV_maximum: 1240.39 ± 62.25 days, Amp_ttv_maximum: 37.97 ± 14.45 min.
P_ttv: 319.53 ± 14.60 days.
Amp_ttv: 72.84 ± 20.44 minutes.
Lomb-Scargle periodogram, periodicity (P_ttv): 322.86 days; Power: 2.62; FAP: 0.091.
Linear ephemeris (this work): Tc = [110.28827915 ± 0.00217698](Tc#) + [172.24000301 ± 0.01378993]


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

11 Feb 2015