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 1.: KOI-841.03, Period: 6.55 days [Plot avg. error bars = ± 9.41 min.]
Linear ephemeris (this work): Tc = 6.54625731(Tc#) + 66.85993401

Figure 2.: KOI-841.01, Period: 15.34 days [Plot avg. error bars = ± 4.29 min.]
TTV_maximum: 265.54 ± 25.76 days, Amp_ttv_maximum: 12.83 ± 1.66 min.
TTV_minimum: 624.18 ± 30.13 days, Amp_ttv_minimum: -12.28 ± 1.66 min.
TTV_maximum: 982.81 ± 36.72 days, Amp_ttv_maximum: 12.83 ± 1.66 min.
TTV_minimum: 1341.45 ± 44.55 days, Amp_ttv_minimum: -12.28 ± 1.66 min.
P_ttv: 717.27 ± 19.83 days.
Amp_ttv: 25.10 ± 2.35 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 708.75 days; Power: 20.98; FAP: 6.254 x 10^-7.
Linear ephemeris (this work): Tc = 15.33527340(Tc#) + 107.00433731

Figure 3.: KOI-841.02, P = 31.33 days [Plot avg. error bars = ± 3.08 min.]
TTV_minimum: 295.71 ± 37.29 days, Amp_ttv_minimum: -15.45 ± 2.80 min.
TTV_maximum: 642.52 ± 44.09 days, Amp_ttv_maximum: 14.14 ± 2.80 min.
TTV_minimum: 989.33 ± 53.91 days, Amp_ttv_minimum: -15.45 ± 2.80 min.
TTV_maximum: 1336.14 ± 65.41 days, Amp_ttv_maximum: 14.14 ± 2.80 min.
P_ttv: 693.62 ± 28.61 days.
Amp_ttv: 29.60 ± 3.95 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 692.84 days; Power: 10.11; FAP: 1.377 x 10^-5.
Linear ephemeris (this work): Tc = 31.33050898(Tc#) + 86.43099732

Figure 4.: Residuals of Figure 3. [Plot avg. error bars = ± 4.16 min.]
TTV_maximum: 152.10 ± 15.67 days, Amp_ttv_maximum: 8.37 ± 2.05 min.
TTV_minimum: 262.55 ± 16.12 days, Amp_ttv_minimum: -8.87 ± 2.05 min.
TTV_maximum: 373.00 ± 16.78 days, Amp_ttv_maximum: 8.37 ± 2.05 min.
TTV_minimum: 483.45 ± 17.64 days, Amp_ttv_minimum: -8.87 ± 2.05 min.
TTV_maximum: 593.90 ± 18.66 days, Amp_ttv_maximum: 8.37 ± 2.05 min.
TTV_minimum: 704.35 ± 19.82 days, Amp_ttv_minimum: -8.87 ± 2.05 min.
TTV_maximum: 814.80 ± 21.10 days, Amp_ttv_maximum: 8.37 ± 2.05 min.
TTV_minimum: 925.25 ± 22.48 days, Amp_ttv_minimum: -8.87 ± 2.05 min.
TTV_maximum: 1035.70 ± 23.94 days, Amp_ttv_maximum: 8.37 ± 2.05 min.
TTV_minimum: 1146.15 ± 25.46 days, Amp_ttv_minimum: -8.87 ± 2.05 min.
TTV_maximum: 1256.60 ± 27.04 days, Amp_ttv_maximum: 8.37 ± 2.05 min.
TTV_minimum: 1367.05 ± 28.66 days, Amp_ttv_minimum: -8.87 ± 2.05 min.
P_ttv: 220.90 ± 3.90 days.
Amp_ttv: 17.24 ± 2.89 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 220.45 days; Power: 8.11; FAP: 7.602 x 10^-4.

Figure 5.: Residuals of Figure 4. (Residuals-of-the-Residuals of Figure 3.) [Plot avg. error bars = ± 4.64 min.]
TTV_maximum: 432.86 ± 151.37 days, Amp_ttv_maximum: 5.82 ± 1.48 min.
TTV_minimum: 1279.17 ± 257.95 days, Amp_ttv_minimum: -6.84 ± 1.48 min.
P_ttv: 1692.62 ± 293.71 days.
Amp_ttv: 12.66 ± 2.09 minutes.
Lomb-Scargle periodogram, candidate P_ttv: 1617.09 days; Power: 8.87; FAP: 3.004 x 10^-4.

Figure 6.: Added combination of Figures 3., 4., and 5. [Plot error bars = ± 6.95 min.]

Figure 7.: KOI-841.04, P = 269.29 days [Plot avg. error bars = ± 18.61 min.]
Linear ephemeris (4 points, this work): Tc = 269.29696994(Tc#) + 218.62507060

* "Lineweaver-Bovaird Rule" is a recent improvement on the Titius-Bode Rule; reference: Bovaird & Lineweaver, 2013, arXiv:1304.3341.

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

27 Sep 2014
KOI-841 (Kepler-27, KIC-5792202) 5-(or more?)-Planets

Summary of the following Figures:
Figure 1.: KOI-841.03, Period: 6.55 days, no TTV observed.

Figure 2.: KOI-841.01, Period: 15.34 days; TTV present: P_ttv: 717.27 ± 19.83 days, well anti-correlated with the strongest P_ttv of KOI-841.02.

Figure 3.: KOI-841.02, Period: 31.33 days, strong TTV with P_ttv: 693.62 ± 28.61 days, well anti-correlated with that of 841.01.
Figure 4.: Sinusoidal array of 1st-order Residuals from Figure 3, implying the presence of a second TTV superimposed upon the first one (of Figure 3.), potentially due to an unseen, non-transiting planet ("841.06") in the "Lineweaver-Bovaird Rule"* orbital space (potentially near ~ 0.43 AU with a Period of ~ 103 days) between 841.02 and 841.04.
Figure 5.: Sinusoidal array of Residuals from Figure 4., i.e.: 2nd-order Residuals from Figure 3., potentially due to the TTV resulting from the mutual interaction of 841.02 and 841.04.
Figure 6.: Summed sinusoidal arrays of Figures 3., 4., and 5. showing the close agreement with the original data points of Figure 3.

Figure 7.: KOI-841.04, Period: 269.29 days, too few data points to clearly define a TTV.  However, such is suggested by the relatively large amplitude (probably of the order of 50 minutes) of the few available (O-C)'s points.

[KOI-841.05 is currently listed in the NASA Exoplanet Archive as a False Positive.]

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