Table 1
Characteristics of the dynamic model atmospheres for pulsating and mass-losing C-rich AGB stars used for the photometric modelling.
Model: | T | R | S | C1 | C2 | ||
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(i) | L⋆ | [L⊙] | 5200 | 7000 | 10 000 | 10 000 | 10 000 |
M⋆ | [M⊙] | 1 | 1 | 1 | 1.5 | 1.5 | |
T⋆ | [K] | 3000 | 2800 | 2600 | 2400 | 2400 | |
[Fe/H] | [dex] | 0 | 0 | 0 | 0 | 0 | |
C/O | by number | 1.1 | 1.4 | 1.4 | 1.69 | 2.38 | |
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(ii) | R ⋆ | [R⊙] | 268 | 355 | 493 | 580 | 580 |
[AU] | 1.24 | 1.65 | 2.29 | 2.70 | 2.70 | ||
log (g⋆ [cm s-2]) | – 0.42 | – 0.66 | – 0.94 | – 0.91 | – 0.91 | ||
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(iii) | P | [d] | 295 | 390 | 490 | 640 | 640 |
Δup | [km s-1] | 4 | 5 | 4 | 6 | 6 | |
f L | 1 | 1 | 2 | 2 | 2 | ||
Δmbol | [mag] | 0.41 | 0.53 | 0.86 | 1.49 | 1.49 | |
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(iv) | ⟨ Ṁ ⟩ | [M⊙ yr-1] | – | 3.5 × 10-6 | 4.3 × 10-6 | 9.1 × 10-6 | 1.4 × 10-5 |
⟨ u ⟩ | [km s-1] | – | 15 | 15 | 17 | 28.6 | |
⟨ fc⟩ | – | 0.33 | 0.28 | 0.43 | 0.58 | ||
⟨ ρd/ρg ⟩ | [10-3] | – | 0.75 | 0.63 | 1.22 | 3.23 | |
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(v) | τdust (0.55 μm) | – | 3.26 | 4.00 | 11.06 | 19.45 | |
τdust (1.6 μm) | – | 1.01 | 1.24 | 3.42 | 6.02 | ||
τdust (3.8 μm) | – | 0.37 | 0.45 | 1.25 | 2.20 |
Notes.Listed are (i) parameters of the hydrostatic initial models; (ii) quantities derivable from these parameters; (iii) attributes of the inner boundary conditions (piston) used to simulate the pulsating stellar interiors as well as the resulting bolometric amplitudes Δmbol; (iv) properties of the resulting wind; and (v) dust optical depths of the formed circumstellar envelope. The notation follows previous papers (Höfner et al. 2003; Nowotny et al. 2010, 2011a): R⋆ – stellar radius of the hydrostatic initial model calculated from the luminosity L⋆ and temperature T⋆ via the relation L⋆ = 4; P, Δup – period and velocity amplitude of the piston at the inner boundary; fL – free parameter to adjust the luminosity amplitude at the inner boundary; ⟨ Ṁ ⟩, ⟨ u ⟩ – mean mass-loss rate and outflow velocity at the outer boundary; ⟨ fc ⟩ – mean degree of condensation of the element carbon into amC dust grains at the outer boundary; ⟨ ρd/ρg ⟩ – mean dust-to-gas ratio at the outer boundary (cf. Eq. (2) of Höfner & Dorfi 1997); τdust – optical depth of the dust envelope at the specified wavelength (V-, H-, L′-band) based on radial structures at φbol ≈ 0.25 (see Sect. 4.2). The radial coordinates in this work are plotted in units of the corresponding stellar radii R⋆ of the hydrostatic initial models, calculated from their luminosities L⋆ and temperatures T⋆ (as given in the table) via the relation L⋆ = 4
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