Table 2.
Evolution of a zero-age main-sequence binary towards FN Sgr.
Time | M1 | M2 | Type1 | Type2 | Porb | Event |
---|---|---|---|---|---|---|
(Myr) | (M⊙) | (M⊙) | (days) | |||
0.0000 | 2.200 | 1.360 | MS | MS | 2000.000 | Zero-age MS binary |
840.5808 | 2.199 | 1.360 | SG | MS | 2001.400 | Change in primary type |
853.4929 | 2.199 | 1.360 | FGB | MS | 2001.459 | Change in primary type |
868.2086 | 2.198 | 1.360 | CHeB | MS | 2002.091 | Change in primary type |
1139.2842 | 2.196 | 1.360 | E-AGB | MS | 2004.652 | Change in primary type |
1156.3479 | 2.196 | 1.360 | TP-AGB | MS | 1997.691 | Change in primary type |
1158.3386 | 2.116 | 1.360 | TP-AGB | MS | 1785.599 | Onset of CE evolution (αCE = 0.3 and αint ≈ 0.82) |
1158.3386 | 0.606 | 1.360 | WD | MS | 630.000 | End of CE evolution |
3096.4561 | 0.606 | 1.360 | WD | SG | 630.259 | Change in secondary type |
3349.8662 | 0.606 | 1.360 | WD | SG | 630.325 | WD starts to crystallize |
3349.8662 | 0.606 | 1.360 | WD | SG | 630.325 | WD weak magnetic field is generated deep in the core |
3624.6724 | 0.606 | 1.360 | WD | FGB | 630.401 | Change in secondary type |
3949.8662 | 0.606 | 1.359 | WD | FGB | 630.713 | WD magnetic field penetrates the surface |
4041.4845 | 0.606 | 1.335 | WD | FGB | 578.405 | WD is spun up (accreted enough angular momentum) |
4041.4845 | 0.606 | 1.335 | WD | FGB | 578.405 | WD develops a super-equipartition strong magnetic field |
4041.7263 | 0.606 | 1.332 | WD | FGB | 568.701 | Onset of SySt phase (RL filling factor ≈0.90) |
4041.7403 | 0.606 | 1.331 | WD | FGB | 567.310 | Binary looks like FN Sgr |
4041.7882 | 0.611 | 1.220 | WD | FGB | 497.086 | Onset of CE evolution (αCE = 0.3 and αint = 1.0) |
4041.7882 | 0.611 | 0.452 | WD | WD | 0.954 | End of CE evolution |
Notes. For the pre-CE and post-CE evolution, we used the MESA code with the assumptions described in Sect. 3. For the CE evolution, we computed the post-CE orbital period using Eqs. (1) and (2), assuming αCE = 0.3 and αCE ≈ 0.82. The terms M1 and M2 and Type1 and Type2 are the masses and stellar types of the primary and secondary, respectively. Porb is the orbital period and the last column corresponds to the event occurring to the binary at the given time in the first column. The row in which the binary has the present-day properties of FN Sgr is highlighted in boldface. For the WD evolution, we interpolated the evolutionary sequences calculated by Bédard et al. (2020) to estimate the mass fraction of the crystallized matter. We assumed a magnetic field diffusion timescale of ∼600 Myr and that the amount of angular momentum accreted by the WD before the binary became a SySt was enough to spin up the WD towards the super-equipartition regime. 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), SySt (symbiotic star).
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