Details of the SMC-OB-Vd3 models

The main parameters for OB-star atmospheres are the stellar temperature T and the surface gravity ggrav. These two parameters span the plane of the model grid in steps of 1 kK in temperature and 0.2 dex in surface gravity.

Furthermore, there are parameters of secondary importance (e.g. the luminosity of the star), which influence the appearance of the emergent spectra. In order to specify the stellar luminosity and mass at given T and log ggrav, we apply the non-rotating stellar evolution models (MESA Isochrones and Stellar Tracks; MIST) from Choi et al. 2016. Consequently, our model grid is restricted to parameters that are reached by these tracks for single-star evolution. In Figure 1 we display these tracks in the HRD, over-plotted by the final positions of the individual grid models.

Figure 1: HRD showing the MIST evolutionary tracks at SMC metallicity (lines), over-plotted by the positions of the grid models (squares). We show all MIST tracks in the initial mass-range of M = 4-60 M. For clarity, we highlight the tracks with initial masses of 5 M, 10 M, 15 M, 20 M 30 M, 40 M and 55 M as black solid lines, while the remaining tracks are represented by gray dotted lines.

Further parameters with potential influence on the spectra are the mass-loss rates M and the terminal wind velocity v. For specifying the mass-loss rate we adopt the recipe by Vink et al. (2001) - their Eqs. 24 and 25 for the hot and cool side of the bi-stability jump. The terminal wind velocity v is adopted to be proportional to the escape velocity vesc. As recommended by Vink et al. (2001), the proportionality factor is set to v = 2.6 vesc and v = 1.3 vesc for the hot and cool side of the bi-stability jump, respectively.

Recent empicial studies (e.g. Ramachandran et al. 2019, Rickard et al. 2022) have shown that OB-star winds in the SMC are in fact much weaker than the original recipe predicts. Therefore, we divide the predicted M by a factor 3, yielding a better agreement across the various luminosity classes (see Fig. 2).

Figure 2: Vink et al. (2001) mass-loss rates for different sets of surface gravities (lines), compared to empicial measurements of O-type stars ind the SMC (symbols) adopted from Ramachandran et al. 2019.

The model calculations account for inhomogeneities in the stellar wind (micro-clumping). Clumping is assumed to set in at the sonic point and to reach the full clumping factor of D = 10 at a radial distance of 10 R.

The abundances of C, N, O, Mg, Si, and Fe are obtained from Trundle et al. (2007). The abundances of the other trace elements are adopted as 1/7 Z, referring to the solar abundances from Asplund et al. (2009) (c.f. TMAP abundance list). The ionization stages that are taken into account are optimized according to the model's effective temperature, as documented in the tables below.

Summary of the employed model atoms:

T < 21.5 kK
IonNo. of levels
H I 22
H II 1
He I 35
He II 26
He III 1
N I 10
N II 38
N III 56
N IV 6
N V 0
N VI 0
C I 15
C II 32
C III 40
C IV 25
C V 1
C VI 0
O I 13
O II 37
O III 33
O IV 2
O V 0
O VI 0
S II 32
S III 23
S IV 25
S V 1
S VI 0
S VII 0
Mg II 32
Mg III 43
Mg IV 0
Mg V 0
Si II 20
Si III 24
Si IV 23
Si V 1
Si VI 0
Si VII 0
P III 47
P IV 12
P V 3
P VI 0
G I 1
G II 3
G III 13
G IV 18
G V 1
G VI 0
G VII 0
G VIII 0
G IX 0
21.5 kK < T < 28.5kK
IonNo. of levels
H I 22
H II 1
He I 35
He II 26
He III 1
N I 10
N II 38
N III 56
N IV 38
N V 2
N VI 0
C I 15
C II 32
C III 40
C IV 25
C V 1
C VI 0
O I 13
O II 37
O III 33
O IV 29
O V 2
O VI 0
S II 32
S III 23
S IV 25
S V 20
S VI 1
S VII 0
Mg II 32
Mg III 43
Mg IV 0
Mg V 0
Si II 20
Si III 24
Si IV 23
Si V 52
Si VI 0
Si VII 0
P III 47
P IV 12
P V 11
P VI 1
G I 0
G II 1
G III 13
G IV 18
G V 22
G VI 1
G VII 0
G VIII 0
G IX 0
28.5 kK < T < 33.5 kK
IonNo. of levels
H I 22
H II 1
He I 35
He II 26
He III 1
N I 10
N II 38
N III 56
N IV 38
N V 2
N VI 0
C I 15
C II 32
C III 40
C IV 25
C V 1
C VI 0
O I 13
O II 37
O III 33
O IV 29
O V 2
O VI 0
S II 32
S III 23
S IV 25
S V 20
S VI 22
S VII 1
Mg II 32
Mg III 43
Mg IV 1
Mg V 0
Si II 20
Si III 24
Si IV 23
Si V 52
Si VI 1
Si VII 0
P III 47
P IV 12
P V 11
P VI 1
G I 0
G II 1
G III 13
G IV 18
G V 22
G VI 29
G VII 1
G VIII 0
G IX 0
33.5 kK < T < 38.5 kK
IonNo. of levels
H I 22
H II 1
He I 35
He II 26
He III 1
N I 0
N II 38
N III 56
N IV 38
N V 20
N VI 1
C I 0
C II 32
C III 40
C IV 25
C V 29
C VI 0
O I 0
O II 37
O III 33
O IV 29
O V 54
O VI 2
S II 0
S III 23
S IV 25
S V 20
S VI 22
S VII 1
Mg II 32
Mg III 43
Mg IV 1
Mg V 0
Si II 20
Si III 24
Si IV 23
Si V 52
Si VI 1
Si VII 0
P III 0
P IV 12
P V 11
P VI 1
G I 0
G II 1
G III 13
G IV 18
G V 22
G VI 29
G VII 19
G VIII 1
G IX 0
38.5 kK < T
IonNo. of levels
H I 22
H II 1
He I 35
He II 26
He III 1
N I 0
N II 0
N III 56
N IV 38
N V 20
N VI 14
C I 0
C II 0
C III 40
C IV 25
C V 29
C VI 1
O I 0
O II 37
O III 33
O IV 29
O V 54
O VI 35
S II 0
S III 0
S IV 25
S V 20
S VI 22
S VII 15
Mg II 32
Mg III 43
Mg IV 17
Mg V 1
Si II 0
Si III 24
Si IV 23
Si V 52
Si VI 10
Si VII 1
P III 0
P IV 12
P V 11
P VI 1
G I 0
G II 0
G III 1
G IV 18
G V 22
G VI 29
G VII 19
G VIII 14
G IX 1

Notes: Element "G" stands for the generic iron-group element, which combines the elements from Sc to Ni in solar relative mixture. In case of the "G" element, the number of levels given in the above table actually refers to superlevels.

Contour plots

For a couple of lines, contour plots of the equivalent width have been prepared. The contours are labeled with Wλ in Angstroem:

logQHI ps pdf png
logQHeI ps pdf png
logQHeII ps pdf png
Hα ps pdf png
Hβ ps pdf png
He I5876 ps pdf png
He II4686 ps pdf png
He II5412 ps pdf png
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