Table A.1
Values of the adiabatic ζad and thermal ζeq response of the radius to mass loss for different types of stars.
k | Evolutionary state | ζ ad | ζ eq |
|
|||
0, 1 | Main-sequence: | ||
Mo < 0.4 | −1/3 | 0 | |
0.4 < Mo < 1.5 | 2 | 0.9 | |
Mo > 1.5 | 4 | 0.55 | |
|
|||
2 | Hertzsprung gap: | ||
Mo < 0.4 | 4 | 0 | |
Mo > 0.4 | 4 | –2 | |
|
|||
3 | First giant branch: | ||
· shallow convective layer | 4 | 0 | |
· deep convective layer | HW87 | 0 | |
|
|||
4 | Horizontal branch: | ||
Mo < MHef | 4 | 4 | |
MHef < Mo < MFGB: | |||
· decent along GB | as k = 3 | 0 | |
· blue phase | 4 | 4 | |
Mo > MFGB: | |||
· blue phase | 4 | –2 | |
· ascent to AGB | HW87 | 0 | |
|
|||
5, 6 | Asymptotic giant branch | HW87 | 0 |
|
|||
7 | Helium main-sequence: | ||
M < 0.2 | 15 | –0.19 | |
M > 0.2 | 15 | 1 | |
|
|||
8, 9 | Helium giant: | ||
Mc < 0.4 | HW87 | −1/3 | |
Mc > 0.4 | HW87 | –2 | |
|
|||
10, 11, 12 | White dwarf | −1/3 | −1/3 |
Notes. The types of stars correspond to the definition by Hurley et al. (2000) expressed by their integer k. The stellar tracks are distinguished by the mass Mo, which is equivalent to the ZAMS mass the star would have had without interaction. MHef and MFGB are defined by Eqs. (2) and (3) from Hurley et al. (2000). MHef represents the maximum initial mass for which helium ignites degenerately in a helium flash, which is ~2 M⊙ for solar metallicities. MFGB is the maximum initial mass for which helium ignites on the first giant branch, which is ~13 M⊙ for solar metallicities. M is the total mass of the star and Mc the mass of the core. HW87 represents Hjellming & Webbink (1987), who calculated ζad for condensed polytropes, consisting of a compact core surrounded by an envelope with polytropic index n = 3/2. For stars on the first giant branch there are two prescriptions of ζad. If the convective zone in the upper layers of the envelope is shallow (fits from Yungelson, priv. comm.), we assumed the envelope responds to mass loss in a similar manner as radiative envelopes.
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