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Table 4:

Comparison of different $\chi ^2$ residuals for TrES-1 (upper values) and TrES-2 (lower values).

Fit
$\chi ^2$ $\kappa_0$ $\kappa_1$ $\kappa_2$ $\kappa_3$ $\nu$ False Alarm Probability vs.
    s s 10-4 s 10-6 s   original ephemeris offset linear polynomial
TrES-1                  
original ephemeris 50.6 0.0 0.0 - - 15 - - -
offset 39.3 -13.4 0.0 - - 14 0.065 - -
linear 28.0 9.5 -0.1 - - 13 0.021 0.039 -
quadratic 23.7 6.3 0.1 - $3.6 \pm 3.4$ - 12 0.024 0.048 0.17
cubic 23.5 9.3 0.0 1.7 -0.7 11 0.058 0.12 0.38
simulated best-fit O-C 8.7 - - - - 11 - - 0.05
simulated 1:2 MMR 18.0 - - - - 11 - - 0.32
simulated 2:3 MMR 20.0 - - - - 11 - - 0.39
simulated 3:2 MMR 46.0 - - - - 11 - - 0.85
simulated 5:3 MMR 19.9 - - - - 11 - - 0.39
simulated 2:1 MMR 158.4 - - - - 11 - - 0.999
best-fit sinusoidal fit 21.5 - - - - 12 - - 0.38
TrES-2                  
linear 13.1 28.9 -0.9 - - 5 - - -
quadratic 12.6 24.8 -1.0 $2.9 \pm 21.7$ - 4 - - 0.72
simulated best-fit O-C 0.3 - - - - 3 - - 0.011
simulated 1:2 MMR 5.3 - - - - 3 - - 0.39
simulated 2:3 MMR 1.7 - - - - 3 - - 0.11
simulated 5:3 MMR 4.0 - - - - 3 - - 0.30
simulated 2:1 MMR 7.1 - - - - 3 - - 0.49
simulated 3:1 MMR 3.9 - - - - 3 - - 0.30
best-fit sinusoidal fit 0.7 - - - - 4 - - 0.011.


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