Table 1.
Evolution of a zero-age MS binary toward KOI 3278.
| Time | M1 | M2 | R2 | Teff, 2 | log g2 | Type1 | Type2 | Porb | Event |
|---|---|---|---|---|---|---|---|---|---|
| (Myr) | (M⊙) | (M⊙) | (R⊙) | (K) | (cm s−2) | (d) | |||
| 0.0000 | 1.500 | 0.900 | 0.790 | 5218 | 4.597 | MS | MS | 920.0000 | Zero-age MS binary |
| 2170.1105 | 1.497 | 0.900 | 0.817 | 5257 | 4.568 | SG | MS | 922.2610 | Change in primary type |
| 2524.7782 | 1.496 | 0.900 | 0.821 | 5267 | 4.564 | FGB | MS | 923.0199 | Change in primary type |
| 2893.2300 | 1.358 | 0.909 | 0.841 | 5326 | 4.547 | CHeB | MS | 953.7384 | Change in primary type |
| 3017.6612 | 1.333 | 0.910 | 0.835 | 5319 | 4.554 | E-AGB | MS | 978.3332 | Change in primary type |
| 3029.7819 | 1.333 | 0.910 | 0.835 | 5319 | 4.554 | TP-AGB | MS | 989.6612 | Change in primary type |
| 3029.8615 | 1.184 | 0.910 | 0.835 | 5319 | 4.553 | TP-AGB | MS | 978.1196 | Begin RLOF |
| 3029.8615 | 1.184 | 0.910 | 0.835 | 5319 | 4.553 | TP-AGB | MS | 978.1196 | Onset of CE evolution |
| 3029.8615 | 0.531 | 0.910 | 0.835 | 5319 | 4.553 | WD | MS | 88.1540 | End RLOF |
| 5219.1031 | 0.531 | 0.910 | 0.861 | 5385 | 4.527 | WD | MS | 88.1805 | Binary looks like KOI 3278 |
Notes. For the pre-CE evolution, we used the MESA code with the assumptions described in Sect. 2. For the CE evolution, we computed the post-CE orbital period using Eqs. (1) and (2), assuming αCE ≈ 0.97. The terms M1 and Type1 are the mass and stellar type of the WD progenitor, respectively, while M2, R2, Teff, 2, log g2, and Type2 are the mass, radius, effective temperature, log-scaled gravity, and stellar type of its companion, respectively. Porb is the orbital period and the last column corresponds to the event occurring in the binary at the given time in the first column. The row in which the binary has the present-day properties of KOI 3278 is highlighted in boldface. Abbreviations: MS (main sequence star), SG (subgiant star), FGB (first giant branch star), CHeB (core helium burning), E-AGB (early asymptotic giant branch star), TP-AGB (thermally pulsing asymptotic giant branch star), WD (white dwarf), RLOF (Roche lobe overflow), CE (common envelope).
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