Figure 15: Best fit and $1\sigma$ error region that we obtain by fitting the
CAK-type mass-loss prescription as described in Bestenlehner (2020, red solid
line and shaded area) to our observed mass-loss rates (blue circles, dark and
light error bars denote $1\sigma$ and $2\sigma$ uncertainties). The best fit
values we derive are shown in the bottom right corner. For comparison we show
the CAK-type prescription also for the case of $\alpha_{\rm eff}=0.50$, as
obtained by fitting the slope of the modified wind momentum (dark red dashed
line). Eight sources that lie close or above $\Gamma_{\rm e,trans}$ are
labelled with their abbreviated identifications (e.g., a1 is R136a1).

We can obtain $\alpha_{\rm eff}$ from our data in a different manner by
inspecting the dependence of mass-loss rate on the Eddington parameter for
electron scattering. Bestenlehner (2020) extended the CAK mass-loss
prescription (Castor et al. 1975) from the regime of optically thin to that of
optically thick winds, by expressing the stellar mass in terms of the electron
scattering Eddington parameter $\Gamma_{\rm e}$. The mass-loss rate can then
be expressed as a function of $\Gamma_{\rm e}$, the transition mass-loss rate
$\dot{M}_{\rm e,trans}$ and the force multiplier $\alpha_{\rm eff}$:

$\begin{split}\log\dot{M}=&\log\dot{M}_{\rm e,trans}\hskip 2.84544pt+\\\
&\underbrace{\left(\frac{1}{\alpha_{\rm eff}}+0.5\right)\ \log(\Gamma_{\rm
e})}_{\textrm{I. Dominates when }\Gamma_{\rm e}\ll
1}-\underbrace{\left(\frac{1-\alpha_{\rm eff}}{\alpha_{\rm eff}}+2\right)\
\log(1-\Gamma_{\rm e})}_{\textrm{II. Dominates when }\Gamma_{\rm e}\rightarrow
1}.\end{split}$ (13)

Our $\alpha_{\rm eff}$ is equal to what Bestenlehner (2020) calls $\alpha$,
and what Pauldrach et al. (1994) and Puls et al. (1996, 2008) call
$\alpha^{\prime}$. The transition mass-loss rate corresponds to the transition
Eddington parameter $\Gamma_{\rm e,trans}$. At $\Gamma_{\rm e}=\Gamma_{\rm
e,trans}$ the first (I) and the second (II) terms in Eq. 13 are equal. At this
point the mass-loss dependency changes from being dominated by the first term
to being dominated by the second term.

Figure 16: Wind structure parameters plotted against mass-loss rate of stars
in R136 (blue diamonds, dark and light shaded error bars denote $1\sigma$ and
$2\sigma$ uncertainties) and 8 Galactic stars of the sample of Hawcroft et al.
(2021, orange/yellow cirlces, $2\sigma$ uncertainties). The limits of the
$y$-axis of each plot coincide with the range of values that was allowed
during the fit. The panels $a-d$ show, from left to right, the clumping
factor, the interclump density contrast, the vorosity and the wind turbulence.
At the top of each panel the average value of the parameter ($\pm 1\sigma$
uncertainty) is quoted for two $\dot{M}$ regimes: low ($\log\dot{M}<-6$, light
grey shaded) and high ($\log\dot{M}>-6$, dark grey shaded). In the leftmost
panel, the diamonds with a white interior denote sources that are not present
in the other three panels, as the $f_{\rm ic}$, $f_{\rm vel}$ and $\varv_{\rm
windturb}$ values were not fitted in their optical + UV runs. No values of
Hawcroft et al. (2021) are shown in the rightmost panel, as they do not fit
$\varv_{\rm windturb}$.

We compute $\Gamma_{\rm e}$ for all our sources191919$\Gamma_{\rm
e}=L\kappa_{\rm e}/4\pi{\rm cG}M$ with $L$ the luminosity, $M$ the stellar
mass, $\kappa_{\rm e}$ the electron scattering opacity, $c$ the speed of light
and $G$ the gravitational constant. using the Bonnsai evolutionary masses and
fit Eq. 13 to our observations, in order to derive a mean value for
$\alpha_{\rm eff}$ for the sample, as well as the transition mass-loss rate.
We find $\alpha_{\rm eff}=0.46\pm 0.04$ ($\alpha\approx 0.56$) and $\log\
\dot{M}_{\rm e,trans}=-5.19\pm 0.10$ (see Fig. 15, red solid line). Our value
for $\dot{M}_{\rm e,trans}$ matches well with the the mass-loss rate of
$\log\dot{M}=-5.2\pm 0.2$ that Vink & Gräfener (2012) find for transition
objects in the Arches cluster. This agreement was not strictly expected as the
definitions for the transition mass-loss rates of Bestenlehner (2020) and Vink
& Gräfener (2012) differ, with the transition of Bestenlehner (2020) relating
to different terms in Eq. 13, and Vink & Gräfener (2012) deriving their rate
based on the inference that stars with a spectral type O4-6If+ correspond to
the transition from optically thin to optically thick winds. The $\alpha_{\rm
eff}$ we find from the fit with the Bestenlehner (2020) prescription is lower
than we found before using the wind momentum relation, however, taking into
account errors on both $\alpha_{\rm eff}$ and $\dot{M}_{\rm e,trans}$ we see
that $\alpha_{\rm eff}=0.50$ found from the wind momentum is just within the
$1\sigma$ uncertainty range (Fig. 15, shaded area and dashed line). In the
high mass-loss regime the relations using the different values for
$\alpha_{\rm eff}$ barely differ, for the low mass-loss regime one sees that
the rates match better the low value of $\alpha_{\rm eff}=0.46$.

Filling in the best fit values for Eq. 13, we obtain the following empirical
mass-loss rate dependence on the Eddington parameter for electron
scattering202020For this we use the non-rounded value from our fit:
$\alpha_{\rm eff}=0.456$.:

$\log\ \dot{M}=-5.19+2.69\log(\Gamma_{\rm e})-3.19\log(1-\Gamma_{\rm e}).$
(14)

This equation could be used as a mass-loss rate prescription for stellar
evolutionary computations for massive stars in the LMC. While our relation is
derived based on stars of $M\geq 15\leavevmode\nobreak\ {\rm M}_{\odot}$, the
scatter up to $M=40\leavevmode\nobreak\ {\rm M}_{\odot}$ ($\Gamma_{\rm
e,trans}=0.2$) is large and the best results will be obtained for stars with
$M\geq 40\leavevmode\nobreak\ {\rm M}_{\odot}$.

###  5.2 Wind structure

Figure 17: Positions of the WNh stars and evolutionary tracks in the
Hertzsprung-Russell diagram. _Left:_ Temperature and luminosity of the WNh
stars as found from this analysis (dark blue diamonds), as derived by Crowther
et al. (2010, red circles) and as derived by Bestenlehner et al. (2020, orange
squares). The cross indicates an alternative (but unlikely, see text) position
for R136a3. Shown in the background is a subset of the evolutionary tracks of
Köhler et al. (2015, thin grey dashed lines), on which the evolutionary masses
and ages derived in this paper are based. Also shown is the corresponding Zero
Age Main Sequence (ZAMS, thick grey dashed line) and the 0.75 Myr and 1.5 Myr
isochrones (grey dotted) of the Köhler et al. (2015) models. _Right:_
Comparison of the stellar evolution models of Crowther et al. (2010, solid
lines), Yusof et al. (2013, dotted lines), Köhler et al. (2015, dashed lines)
and Gräfener (2021, dashed-dotted lines). For each grid we show tracks of
models with an initial mass of 150, 200, 300 and 500 M⊙ in light green, dark
green, light blue and dark blue, respectively. Black thick lines denote the
ZAMS positions of each grid. The notable difference in ZAMS positions of the
tracks of Crowther et al. (2010), Yusof et al. (2013) on the one hand, and
Köhler et al. (2015) and Gräfener (2021) on the other hand is related to their
treatment of convection in the inflated envelopes of the most massive stars.
For reference, the observed positions as in the left panel are also shown in
the right panel (grey and without error bars). All tracks have an initial
rotation $\varv_{\rm eq,ini}$ of $0.4\leavevmode\nobreak\ \varv_{\rm
eq,crit}$, with $\varv_{\rm eq,crit}$ the critical velocity, except for those
of Köhler et al. (2015), for which we show the models with $\varv_{\rm
eq,ini}=350$ km s-1 for 150-300 M⊙ models and $300$ km s-1 for the 500 M⊙
model, corresponding to $\varv_{\rm eq,ini}/\varv_{\rm eq,crit}=0.38\pm 0.01$.

Upon investigating possible trends in wind structure parameters, we plot the
obtained values against mass-loss rate. The results are shown in Fig. 16. For
computing the averages $\mathcal{M}$ and the errors on the averages
$\mathcal{U}$ quoted in this section we weigh the best fit value for each
individual star, $x_{i}$, with the inverse of its $2\sigma$ uncertainty
($w_{i}$):

$\mathcal{M}=\frac{\sum^{N_{x}}_{i=0}w_{i}x_{i}}{\sum^{N_{x}}_{i=0}w_{i}}\hskip
19.91684pt\mathrm{and}\hskip
19.91684pt\mathcal{U}=\frac{\sum^{N_{x}}_{i=0}w_{i}(x_{i}-\mathcal{M})^{2}}{\sum^{N_{x}}_{i=0}w_{i}},$
(15)

where $N_{x}$ is the number of measurements of the quantity under
consideration.

The left panel ($a$) of Fig. 16 shows the derived clumping factors. We find
that all but five stars have a best fitting clumping factor of $f_{\rm
cl}>10$, with an average for all stars of $\langle f_{\rm cl}\rangle=29\pm
15$. When dividing the sample in two groups based on their mass-loss rates
being lower or higher than $\log\dot{M}=-6$, we find typically lower values
for $f_{\rm cl}$ for the stars in the higher mass-loss rate group, although
this difference is barely significant; average values and uncertainties are
displayed at the top of Fig. 16. Hawcroft et al. (2021), who analyse a sample
of 8 Galactic O-supergiants with mass-loss rates $\log\ \dot{M}>-6$ in a
similar fashion, find $\langle f_{\rm cl}\rangle=25\pm\leavevmode\nobreak\ 4$
for their sample. This is consistent with our findings.

The middle panels ($b$ and $c$) show our values for $f_{\rm ic}$ and $f_{\rm
vel}$. We find averages of $\langle f_{\rm fic}\rangle=0.13\pm^{0.15}_{0.13}$
and $\langle f_{\rm vel}\rangle=0.46\pm 0.39$. As before, we also divide the
points in two groups based on $\log\ $$\dot{M}$ and compute the averages of
each group (displayed at the top of Fig. 16). For the interclump density
contrast we find a significant difference between the two groups. The stars
with a lower mass-loss rate typically have a lower $f_{\rm ic}$ than stars
with a higher mass-loss rate (values and errors at the top of Fig. 16). In
other words for stars with lower mass-loss rate we find a stronger density
contrast between the clumps and the interclump medium, or, equivalently, a
relatively lower interclump medium density. We also find a trend in the
velocity filling factor, where for the groups with a lower and higher mass-
loss rate we find lower and higher values of $f_{\rm vel}$ respectively. We
compare our values of $f_{\rm ic}$ and $f_{\rm vel}$ to those of Hawcroft et
al. (2021) and find that these are generally in agreement with our findings.
However, given the small range of mass-loss rates of the stars of the sample
that Hawcroft et al. (2021) consider, this comparison cannot give any
confirmation of the differences we find between the low- and high mass-loss
rate groups.

The last parameter that is related to the wind structure is the wind
turbulence $\varv_{\rm windturb}$, shown in the rightmost panel ($d$). Also
here, we observe a weak trend where the turbulence seems to be less strong in
the stars with higher mass-loss rates. Hawcroft et al. (2021) do not measure
this parameter.

For all wind structure parameters, the observations show tentative trends as a
function of mass-loss. Overall, it appears that the stars with higher mass-
loss rates typically have smoother winds than the stars with lower mass-loss
rates. All wind structure diagnostics indicate this: the stars with higher-
mass loss rates have on average lower clumping factors, a lower contrast
between the density in the interclump and clump medium, less wind turbulence,
and higher velocity filling factors. The latter may sound like evidence for
stronger clumping effects, however a high velocity filling factor too can
indicate smooth wind. Namely, as $f_{\rm vel}$ $\rightarrow 1$, this ‘erases’
the density contrast, so that the wind is fully consisting of absorbing
material and there are no gaps in velocity space through which the light can
escape. In other words, the velocity-porosity effects are no longer present,
as it would in either a smooth wind or a wind with only optically thin clumps.
This follows explicitly from the equations for the effective opacity
(Sundqvist & Puls 2018), summarised in our Section 3.1.1: if $f_{\rm vel}$
$\rightarrow 1$, then $f_{\rm vor}\rightarrow\infty$ (Eq. 4), leading to
$\tau_{\rm cl}\rightarrow 0$ (Eq. 8), which then means that $\chi_{\rm
eff}\rightarrow\langle\chi\rangle$ (Eq. 6), such that the limit for either
optically thin clumping (if $f_{\rm cl}$ $>1$) or a smooth wind (if $f_{\rm
cl}$ $=1$) is recovered. We do stress that, although the wind structure
parameters of the higher mass-loss rate stars imply that their winds are on
average smoother than those of the low mass-loss rate stars, their clumping
factors are still significant ($\geq 4$ with an average of $21\pm 15$). The
high measured velocity filling factors are thus pointing to optically thin
clumps, rather than a smooth wind.

We note that while we discuss these trends only as a function of mass-loss
rate, we obtain very similar results when we plot the wind structure
parameters against other stellar or wind properties, such as luminosity. This
is due to strong correlations between mass-loss rate and stellar properties.
The interested reader can find the wind structure parameters plotted against
luminosity, temperature, Eddington parameter for electron scattering or wind
acceleration in Fig. G.16 to G.19.

###  5.3 Evolution

Since the stellar parameters we derive are generally consistent with those of
Bestenlehner et al. (2020), we do expect similar results for the age and
initial mass distributions of the cluster. Indeed this is what we find when
analysing the HRD positions of our sources (see Fig. 10 and Section 4.2): we
derive a cluster age of $1-2.5$ Myr (median: 1.46 Myr) and an initial mass
function with a power law slope of $\gamma=1.99\pm 0.11$ in the range
$30-200\leavevmode\nobreak\ {\rm M}_{\odot}$. Detailed comparisons between
this work and Bestenlehner et al. (2020) can be found in Appendices C and D.
The rest of this section will focus on mass determination of the WNh stars and
the evolution of the stars in the context of surface abundances.

####  5.3.1 Mass and age of the WNh stars

Figure 17 shows the HRD positions of these stars as we find from our analysis,
and compares these to the positions derived by Crowther et al. (2010,
UV/optical/near-IR spectroscopy) and Bestenlehner et al. (2020, optical
spectrocopy). The position of R136a3 as found from our analysis is indicated
twice as its effective temperature is hard to constrain; the diamond marks the
higher temperature HRD-position that we adopt in this discussion, the cross
the less likely alternative (see Section 4.1 and Section E.3 for details).

Table 7: Ages and masses of the WNh stars with 1$\sigma$ errors. | R136a1 | R136a2 | R136a3
---|---|---|---
${M}_{\rm spec}$ (M⊙) | $303\pm^{123}_{79}$ | $159\pm^{93}_{5}$ | $\geq 179$
${M}_{\rm evol}$ (M⊙) | $222\pm^{28}_{29}$ | $186\pm^{17}_{15}$ | $179\pm^{16}_{11}$
${M}_{\rm ini}$ (M⊙) | $273\pm^{25}_{36}$ | $221\pm^{16}_{12}$ | $213\pm^{12}_{11}$
Age (Myr) | $1.14\pm^{0.17}_{1.34}$ | $1.34\pm^{0.13}_{0.18}$ | $1.28\pm^{0.17}_{0.21}$

Looking at the left hand side of Fig. 17 we see that there is a considerable
spread in observed temperatures and luminosities for the WNhs stars. However,
while the temperature we derive for R136a1 is 7000 K lower than that of
Crowther et al. (2010), the initial masses from our and their analyses agree
rather well: 273$\pm^{25}_{36}$ M⊙ and $320\pm^{100}_{40}$ M⊙, respectively.
This is can be explained by differences in the evolutionary tracks used to
derive these masses. The right hand side of Fig. 17 shows how different
assumptions for the evolutionary computations can lead to divergent
theoretical predictions. Nonetheless, it is clear that regardless uncertainty
in both observations and theory, the previously accepted initial mass-limit
(Figer 2005) challenged by Crowther et al. (2010) is indeed well exceeded by
a1 and a2, and likely by a3 too; all different tracks in the left of Fig. 17
point to an initial mass of $\geq 250$ M⊙ for R136a1, the most massive star in
our sample, and, conservatively, $\geq 150$ M⊙ for R136a2 and R136a3. Of
course, these results might not hold if the sources turn out to be in
multiples, something that is currently being investigated with radial velocity
measurements using HST-observations (Shenar et al. 2019). Furthermore, we note
that our masses not only rely on the adequate determination of effective
temperatures, and the used evolutionary tracks, but also on the flux
calibration and reddening of the anchor magnitude used for our analysis. In
this context, we note that Rubio-Díez et al. (2017) focus in particular on the
infrared (K-band) flux calibration of R136a1, R136a2 and R136a3, and find
considerably lower initial masses for these stars compared to our analysis and
that of Crowther et al. (2010), their highest derived initial mass being an
upper limit of 194 M⊙ for R136a1. For their analysis, Rubio-Díez et al. (2017)
use VLT/SINFONI K-band spectrophotometry, effective temperatures of Crowther
et al. (2010) and evolutionary tracks of Köhler et al. (2015).

We measure the current masses of the WNh stars in a second manner. By
measuring the surface gravity, we can obtain the spectroscopic mass $M_{\rm
spec}$ ($=g_{e}R_{\star}^{2}/G$, with $g_{e}=g+(v_{\rm eq}\sin i)^{2}/R_{*}$
surface gravity corrected for centrifugal accelerations, and $G$ the
gravitational constant). Contrary to the analysis of Bestenlehner et al.
(2020), in our fits $\log g$ is a free parameter also for the WNh stars. The
winds of the WNh stars are so dense that we do not expect to see a very strong
signature of the surface gravity in the spectrum. Still, from our Kiwi-GA fits
we do constrain $\log g$ of both R136a1 and R136a2, for which we find a
$2\sigma$ range of $\log\ g=3.35-3.9$ and $\log\ g=3.55-3.75$, respectively.
For R136a3 we only find a lower limit, $\log\ g>3.4$. Figure 18 shows that the
fitness distribution of the gravity of R136a1 clearly favors a value lower
than 4.0. When using the measured $\log g$ values in combination with the
derived radii to derive spectroscopic masses, these compare well with the
evolutionary masses (see Table 7), further supporting very high masses for
these stars.

Figure 18: Measurements of the surface gravity $\log g$ of the WNh star
R136a1. Plotted is the fitness (1/$\chi^{2}_{\rm red}$) as a function of $\log
g$, where each dot is a model in the Kiwi-GA run. The colour corresponds to
the (spectroscopic) stellar mass matching each model. The yellow shaded
regions correspond to $1\sigma$ and $2\sigma$ uncertainties, and the orange
dashed line the position of the best fit.

####  5.3.2 CNO abundances

Figure 19: Comparison of our observed CNO-abundances to the theory of CNO
processing. Only for three sources all abundances were measured (red
triangles), for the rest the oxygen abundance is fixed to the LMC baseline
value of $n_{\rm O}$ $=8.35$ (see text). The yellow shaded region marks the
regime between the analytical limiting solutions (CNO- and CN-equilibrium) of
Maeder et al. (2014), their Eq. (14) and (17), respectively. Dotted, dashed
and solid blue lines show evolutionary tracks of 30, 60 and 150 M⊙,
respectively (Brott et al. 2011a; Köhler et al. 2015), where light and dark
blues indicate models with low ($\sim 100$ km s-1) and high ($\sim 500$ km
s-1) initial rotation velocities.  Figure 20: Hunter diagrams, showing stellar
age (red to blue colour bar) as a function of rotation and nitrogen surface
abundance. Evolutionary tracks are taken from Köhler et al. (2015) and depict
the evolution of stars with an initial mass of 230 M⊙ (top), 100 M⊙ (center),
and 60 M⊙ (bottom) with a range of initial rotation rates. Note that the
theoretical rotation rates are scaled by $\pi/4$ to correct for the average
projection angle, and that the tracks are cut off at $T_{\rm eff}$ $<29000$ K.
The diamond markers indicate the observed positions of sources in the
respective mass-regimes, where their colour maps to age via the same coding as
the tracks. For a discussion on the error bars on the observed rotation rates
of the WNh stars, see text.

As CNO surface abundances are expected to change over the course of stellar
evolution (e.g., Köhler et al. 2015; Eggenberger et al. 2021), they could be
used to set apart the more evolved stars from the rest. Before we assess this
for our sample, we check whether the derived abundances are consistent with
the theory of CNO-processing. This is an especially important check because
without exception the C and N abundances are derived from lines that are
(mostly) formed in the stellar wind, and thus their strength and shape not
only depends on abundance and temperature, but also on a handful of wind
properties. Since all those properties can vary independently from each other,
consistency with CNO-processing theory is not guaranteed intrinsically and
needs to be checked. The diagram in Fig. 19 allows for such a consistency
check, by comparing the ratios $n_{\rm N}/n_{\rm C}$ to $n_{\rm N}/n_{\rm O}$.
Maeder et al. (2014) derive analytically the limits of these ratios given CNO
and CN equilibrium: we expect all observations to fall somewhere between the
region bordered by those. Furthermore, evolutionary tracks of different masses
and initial rotation (Brott et al. 2011a; Köhler et al. 2015) predict quite a
narrow range in which we expect points to lie. This method has also been
applied by Martins et al. (2015) and Carneiro et al. (2019).

The WNh stars – the only sources for which we measure oxygen abundance – lie
in the area predicted by Maeder et al. (2014), and moreover match well the
evolutionary predictions depicted in Fig. 19. For the other sources, we do not
measure oxygen abundance and we therefore assumed for all stars the LMC
baseline value, $\log\ n_{\rm O}/n_{\rm H}+12=8.35$ (Kurt & Dufour 1998, as in
Brott et al. 2011a; Köhler et al. 2015), so no enrichment or depletion. With
this assumption and considering the uncertainties on the measurements, our
observations are generally consistent with CNO-processing, except for R136a7.
For this source evolutionary models predict oxygen depletion to $n_{\rm O}$
$=7.20$, assuming an initial mass of 100 M⊙ and an initial rotation of 300 km
s-1. This would move this source into the region consistent with CNO-
processing. If we also assume oxygen depletion for other sources, as was done
in the optical+UV fitting212121For each star we estimate the amount by
combining the mass, projected rotation and age of the stars according to
Bestenlehner et al. (2020), as described in Section 3.5.2., the shift along
the $\log n_{\rm N}/n_{\rm O}$ axis is small ($0.1-0.2$ dex to the right). We
note that there is an uncertainty in the observed LMC baseline abundances of
CNO (see, e.g., Dopita et al. 2019) that could affect Fig. 19. However, we
find that changes in the diagram that could result from this are smaller than
the typical error bars on our observations. Overall, we conclude that no
violation of CNO-processing is observed and that abundances and wind
parameters can be disentangled from a set of 9-11 (metal) wind lines, albeit
with large uncertainties.

Six sources stand out in Fig. 19. These are the WNh stars, R136a5, R136b, and
H30. Bestenlehner et al. (2020) show, based on the helium abundance, that the
enrichment of these stars is mainly driven by mass-loss (see also Bestenlehner
et al. 2014). Here, we further investigate the nitrogen enrichment by placing
our sources in a Hunter diagram. This diagram, introduced by Hunter et al.
2008, shows the nitrogen surface abundance of stars versus their projected
rotational velocity. By comparing these quantities, one can gain insight into
mixing processes that occur within the star; rotational mixing being one of
the mechanisms that can bring processed elements to the surface. In the Hunter
diagrams in Fig. 20 we compare our observed values with evolutionary tracks of
different rotation rates (Köhler et al. 2015). In order to account for the
different masses of the sources, we compare three subgroups of sources with
tracks of three different masses.

All WNh stars ($M_{\rm ini}=213-273$ M⊙, top panel of Fig. 20) show strong
nitrogen enrichment; we find a similar nitrogen surface abundance and age for
all three. Given the large uncertainty on the rotation rate, the nitrogen
abundance and age of R136a1 match the tracks quite well. For R136a2 and R136a3
the obtained nitrogen abundances are, given the obtained ages, slightly too
high for any of the tracks. However, the difference is not large and within
uncertainties the single star models and observations match. We emphasise
that, while the best fit values for the $\varv_{\rm eq}\sin i$ are prominently
marked (based on the best fitting model of the optical only run for each
star), one should not overlook the large error bars. In the most extreme case
of R136a3 these span all displayed $\varv_{\rm eq}\sin i$ values, implying
that we cannot put any constraints on the current $\varv_{\rm eq}\sin i$ of
this source. Adding to the uncertainty (not captured in the statistical error
bars shown here) is the fact that we derive all rotation rates by convolution
of the line profiles, hereby implicitly assuming that the emergent radiation
is emitted from one single rotating layer. This assumption likely breaks down
for all available spectral lines in the WNh spectra, casting further doubt on
the validity of the WNh rotation rates that we derive. A more sophisticated
approach would be to include the effects of rotation on the velocity field of
the wind into the formal integral (Shenar et al. 2014), however this is not
within the current capabilities of Fastwind. Regardless of the observed
$\varv_{\rm eq}\sin i$ values, a high initial rotation is suggested for all
WNh stars if one compares the tracks to the observed ages and nitrogen
abundances. This was also found from the Bonnsai runs for these sources based
on a comparison of the observed luminosity, temperature, surface gravity and
helium surface abundance to the Köhler et al. (2015) tracks.

The middle panel of Fig. 20 shows stars in the mass range $M_{\rm ini}=92-127$
M⊙. The age and position of the sources generally show good agreement with the
evolutionary tracks. The three points that lie close together (R136a4, R136a6
and H36), all seem to have started out with a moderate initial rotation rate.
R136b is highly nitrogen enriched, which suggests that the star must have had
an initial rotation in the range of $300-450$ km s-1 and is older than the
other stars. Indeed, the age of the star, derived from the observed
luminosity, temperature, surface gravity and helium abundance, is 2 Myr.
Looking at the physical position of this star in the cluster (Fig. 1) we see
that it is located a bit on the outskirts of the cluster, further away from
the centre than most other very massive stars (Fig. 1). Possibly this could be
related to its somewhat higher age, however, we do not have any evidence for
this; Bestenlehner et al. (2020) considers the ages and positions of all
sources and does not find a correlation of age and position (we confirm this
finding, see Appendix D). The outlier in this panel is R136a5, that, within
its $1\sigma$ errors, does not seem to fall on any of those tracks. We note
that this star has a slightly higher initial mass than that of the tracks
shown here ($116$ M⊙). Tracks with higher mass would have more enrichment (see
top panel), and thus would bring the tracks and the observations of R136a5
closer together. R136a7 could also be considered an outlier as it is the only
source in this mass-range not showing significant enrichment. Yet, it is
consistent with the tracks, as, with an age of 0.5$\pm^{0.37}_{0.46}$ Myr,
R136a7 is one of the youngest, if not the youngest, star in the
sample222222See Table H.2. For several other stars we find from Bonnsai a
formal age of almost zero, however in all these cases the errors bars are
extremely large (1-2.5 Myr), so we consider the age of these sources
unconstrained..

The bottom panel of Fig. 20 shows stars in the mass range $M_{\rm ini}=52-68$
M⊙. Most of them are not yet nitrogen enriched. For a few we do observe a
slight enrichment, though with very large uncertainties. Within errors, the
observations are consistent with the $60$ M⊙ tracks of Köhler et al. (2015).

It is interesting that while for the WNh stars we require high initial surface
rotation rates ($\varv_{\rm eq,ini}>300$ km s-1) in order to match the tracks,
this is not the case for most O-stars. The O-stars in Fig. 20, except R136a7
and R136b, suggest initial surface rotation rates $\varv_{\rm eq,ini}<300$ km
s-1. The inferred initial rotation rates are, for all stars, consistent with
the values inferred using Bonnsai based on different observables (luminosity,
temperature, surface gravity and helium abundance); with this we find 100 km
s-1 for all with the exception of the WNh stars, R136a7 and R136b, for which
we find $\varv_{\rm eq,ini}>300$ km s-1. The difference between the WNh stars
and R136b and R136a7 on the one hand, and the other O-stars on the other hand
might indicate that the two groups of stars are formed through a different
channel. We note that only for sources for which we observed helium enrichment
($x_{\rm He}\geq 0.14$), a high initial rotation rate was derived using
Bonnsai.

In summary, the collection of Hunter diagrams shows the enrichment of young
(very) massive stars. At an age of $\sim 1.5$ Myr the $\sim 60$ M⊙ stars are
barely nitrogen enriched, while the $\sim 100$ M⊙ and $\sim 200$ M⊙ stars show
enrichment of about one and two orders of magnitude, respectively. This is
roughly consistent with the single star models of Köhler et al. (2015). We
note that Hunter et al. (2008); Brott et al. (2011b); Grin et al. (2017)
report a population of slowly spinning nitrogen enriched stars, which we do
not identify in our study. This may potentially point to binary interaction as
a source of such stars; given the young age of our population it could be
expected that such interactions have not yet occurred frequently.

Figure 21: Comparison of terminal velocities $\varv_{\infty}$ determined by
spectral fitting (this work) to those determined by locating $\varv_{\rm
black}$ (Crowther et al. 2016). Circles indicate sources for which Crowther et
al. (2016) estimated $\varv_{\infty}$ based on $\varv_{\rm black}$, solid
triangles indicate sources for which they used $0.8\varv_{\rm edge}$. Grey
symbols indicate sources for which we could not obtained a good fit to the C
iv $\lambda\lambda$1548-1551 profile. The thick red dashed line shows where
the two methods agree, while the blue solid line shows a linear fit through
the data. See also Fig. 22.  Figure 22: Line profiles of C iv
$\lambda\lambda$1548-1551 and the best fit models ($2\sigma$) compared to the
values of $v_{\infty}$ determined by spectral fitting (this work, red dotted
line) and those of Crowther et al. (2016, yellow dashed line). The shaded
regions indicate the $2\sigma$ errors on the derived $v_{\infty}$. We used the
blue transition of the doublet ($\lambda=1548.19$Å) for indicating velocities.
We show profiles with different C iv $\lambda\lambda$1548-1551 appearances:
strong and saturated (top), strong but not saturated (middle) and weak
(bottom). In all cases $v_{\infty}$ from spectral modelling lies bluewards of
that of Crowther et al. (2016). See also Fig. 21.

###  5.4 Terminal velocity measurements

With spectral fitting we are able to break the degeneracy between
$\varv_{\infty}$ and $\varv_{\rm windturb}$. While based on the edge velocity
alone one cannot disentangle $\varv_{\infty}$ and $\varv_{\rm windturb}$, the
shape of the absorption component of C iv $\lambda\lambda$1548-1551 is
affected differently by the two parameters, and we are able to distinguish
between the two. We note that narrow absorption components, unresolved in our
spectra, may have contributed to absorption near the terminal velocity of non-
saturated line profiles (Prinja et al. 1990). As the equivalent width of these
absorption components is small, we do not expect a significant effect on our
measurements.

The terminal velocities we find from spectral fitting are systematically
larger than those of Crowther et al. (2016), who used the exact same dataset
but obtained $\varv_{\infty}$ by inspecting the blue wing of the C iv
$\lambda\lambda$1548-1551 P-Cygni line (Fig. 21). For 29 sources they identify
the maximum blueward extent of (near) saturated absorption profiles,
$\varv_{\rm black}$, and assume $\varv_{\infty}=\varv_{\rm black}$ (following
Prinja et al. 1990). For these 29 sources they also identify the velocity at
which the violet absorption meets the continuum, $\varv_{\rm edge}$, and with
this derive $\varv_{\infty}=0.8\varv_{\rm edge}$. With the latter relation
they estimate $\varv_{\infty}$ by identifying $\varv_{\rm edge}$ for the
remaining 15 sources, that have less strong wind lines.

Figure 21 shows the $\varv_{\infty}$ values derived from spectral fitting
versus those found from $\varv_{\rm black}$ or $\varv_{\rm edge}$, which we
call $\varv_{\infty\rm,blue}$. We find an average difference of 283$\pm 30$ km
s-1 between the two methods, taking into account uncertainties on the
measurements, and excluding three sources for which we could not obtain a good
fit to the C iv $\lambda\lambda$1548-1551 profile (see Section 4.3). Moreover,
a trend is visible in the difference: on average the difference between
$\varv_{\infty}$ derived with the two methods increases for lower terminal
velocities. Figure 22 shows C iv $\lambda\lambda$1548-1551 profiles for three
sources with different mass-loss rates and terminal velocities. The location
of $\varv_{\infty}$ according to this work and that of Crowther et al. (2016)
is indicated. According to the spectral models, the terminal velocity does not
coincide with the point of strongest absorption, but lies more towards the
blue. Some desaturation thus occurs close to the terminal velocity already in
H48, the star with the strongest P-Cygni profile of these three. If the
approach of Crowther et al. (2016) is followed for obtaining $\varv_{\infty}$,
the obtained values $\varv_{\infty\rm,blue}$ could be corrected for this
effect by using the relation shown as the blue solid line in Fig. 21:

$\varv_{\infty}=\varv_{\infty\rm,blue}+0.27\cdot(3700-\varv_{\infty\rm,blue}),$
(16)

(velocities in km s-1) for $1000{\ \rm km}\leavevmode\nobreak\ {\rm
s}^{-1}>\varv_{\infty\rm,blue}>3500{\ \rm km}\leavevmode\nobreak\ {\rm
s}^{-1}$. One could use this equation for getting a more accurate first order
estimate of $\varv_{\infty}$ from reading off $\varv_{\rm blue}$ from spectra
with relatively poor resolution.

Upon comparing the edge velocities of Crowther et al. (2016), obtained by
reading off the velocity at the wavelength where the blue edge of C iv
$\lambda\lambda$1548-1551 meets the continuum, to the edge velocities we
obtain by spectral modelling and assuming $\varv_{\rm
edge}=\varv_{\infty}+\varv_{\rm windturb}$, we find that they are generally in
good agreement. For our sample we find the following average:

$\displaystyle\varv_{\rm windturb}$ $\displaystyle=0.14\pm 0.06\
\varv_{\infty}\hskip 28.45274pt\mathrm{or,equivalently:}$
$\displaystyle\varv_{\infty}$ $\displaystyle=0.88\pm 0.04\ \varv_{\rm edge}$
(17)

Had Crowther et al. (2016) assumed this value instead of
$\varv_{\infty}=0.8\varv_{\rm edge}$, our respective values for
$\varv_{\infty}$ would lie closer together for the weaker wind sources
(triangles in Fig. 21), although part of the discrepancy would still remain.
We stress that Eq. 17 is based on fits of the sources for which we carried out
12-free parameter fits, that is, the sources with stronger winds. Data of
higher S/N and resolution is required to disentangle $\varv_{\infty}$ and
$\varv_{\rm windturb}$ for the sources with weaker winds.

##  6 Summary & Outlook

We have simultaneously analysed optical and UV spectroscopy of a population of
56 stars in the core of the R136 star cluster, nine members of which have
masses $M\gtrsim 100$ M⊙. For the first time we investigate the wind structure
parameters of a large range of spectral types while fitting the interclump
density, the wind turbulence and the effects of optically thick clumps such as
velocity-porosity. By taking into account these effects we improve the
accuracy of mass-loss determinations of the most massive stars. Moreover, the
derived mass-loss rates are no longer affected by the well known mass-
loss/clumping dichotomy, but are actual values. Our main findings are the
following:

  * •

The HRD-positions of the sources suggest a cluster age of 1-2.5 Myr, in line
with the findings of Bestenlehner et al. (2020). The ages of the highly
nitrogen enriched WNh stars are in line with the age of the rest of the
population.

  * •

Our conservative estimate for the initial mass of R136a1, the most massive
star in our sample, is 250 M⊙. The initial masses of R136a2 and R136a3 well
exceed 150 M⊙. The spectroscopic masses of these sources, which we measure
here for the first time, further support this conclusion.

  * •

We compare the theoretical predictions of Vink et al. (2001), Krtička & Kubát
(2018), Björklund et al. (2021) and Vink & Sander (2021) to the observed mass-
loss rates and terminal velocities and find that none of the predictions
satisfactorily reproduces both quantities. The largest discrepancies for the
terminal velocities are found for stars with $\log L/{\rm L}_{\odot}\lesssim
5.3$ for the Björklund et al. (2021) predictions, and stars with $\log L/{\rm
L}_{\odot}\gtrsim 5.3$ for the Krtička & Kubát (2018) predictions.

  * •

Overall, the mass-loss recipe of Krtička & Kubát (2018) best matches the
observed mass-loss rates of the stars in our sample. The predictions of
Björklund et al. (2021) match almost as good, performing better in the low-
luminosity regime ($\log L/{\rm L}_{\odot}\lesssim 5.3$), but worse for the
higher luminosities. The prescriptions of Vink et al. (2001) and Vink & Sander
(2021) overpredict the mass-loss rates for all luminosity regimes.

  * •

The stellar winds of the stars in our sample are highly clumped, with an
average clumping factor of $f_{\rm cl}$ $=29\pm 15$.

  * •

We find tentative trends in the wind structure parameters as a function of
mass-loss, where the stars with the highest mass-loss rates seem to have
smoother, albeit still clumpy, winds (but see below).

  * •

We provide a prescription for the mass-loss rates of the most massive stars as
a function of the electron scattering Eddington parameter, following the work
of Bestenlehner (2020). For this, we have used our best fit values of the CAK
force multiplier parameter $\alpha_{\rm eff}=\alpha-\delta=0.46\pm 0.04$ and
transition mass-loss rate $\log\dot{M}_{\rm e,trans}=-5.19\pm 0.10$.

  * •

The point with the strongest absorption in a P-Cygni profile does typically
not correspond with the terminal velocity, which lies more bluewards. We
provide an equation that quantifies this effect.

This is the first investigation of trends in wind structure parameters of
massive stars. While the measurements of Hawcroft et al. (2021) are not in
contradiction with our results, neither can they confirm the trends we
observe, given the limited span of mass-loss rates in their sample. Further
investigation of these trends is thus necessary. Hawcroft (in prep.) are
undertaking such a study, analysing optical and UV spectroscopy of a sample of
about 30 LMC and SMC stars covering most O-type subclasses (O3-O9).
Furthermore, our study can be considered a pilot for a larger investigation
making use of the high-quality HST UV spectra of the ULLYSES
project232323Hubble UV Legacy Library of Young Stars as Essential Standards, a
Director’s Discretionary program in progress (
https://ullyses.stsci.edu/index.html) (Roman-Duval et al. 2020). The ULLYSES
sample, when complete, will consist of $\sim$250 massive stars (mostly in the
Magellanic clouds), including $\sim$150 O-stars, covering all O-star subtypes
and luminosity classes. Complemented by the optical XshootU
program242424https://massivestars.org/xshootu/, ULLYSES will provide an
excellent opportunity for further study of the structure of massive star
winds.

###### Acknowledgements.

We like to thank the anonymous referee, whose constructive criticism has
helped us to improve the presentation of this work. This publication is part
of the project ‘Massive stars in low-metallicity environments: the progenitors
of massive black holes’ with project number OND1362707 of the research TOP-
programme, which is (partly) financed by the Dutch Research Council (NWO).
Observations were taken with the NASA/ESA HST, obtained from the data archive
at the Space Telescope Institute. Computations were carried out on the Dutch
national e-infrastructure with the support of SURF Cooperative. SAB would like
to thank the late Lykle Voort for his help and patience. FAD and JOS
acknowledge support from the Odysseus program of the Belgian Research
Foundation Flanders (FWO) under grant G0H9218N. TS acknowledges support from
the European Union’s Horizon 2020 under the Marie Skłodowska-Curie grant
agreement No 101024605. This work has received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and
innovation programme (Grant agreement No. 945806). This work is supported by
the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under
Germany’s Excellence Strategy EXC 2181/1-390900948 (the Heidelberg STRUCTURES
Excellence Cluster). GG acknowledges support from Deutsche Luft- und Raumfahrt
(DLR) grant No. 50 OR 2009.

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##  Appendix A Data quality

###  A.1 S/N

Distributions of S/N for all sources in our sample are shown in Fig. A.1. We
see that generally the UV spectra have the highest S/N, but note that
typically C iv $\lambda$1165-Ciii $\lambda$1170, which is very close to the
blue grating edge and is also slightly affected by Ly-$\alpha$ absorption, has
a lower S/N than the values shown in the figure. Also, in the most red part of
the UV grating, He ii $\lambda$1640 and N iv $\lambda$1718 (if used at all)
are typically a bit more noisy than the other lines.

Figure A.1: S/N distribution for each wavelength range: UV (left), blue-
optical (middle) and H$\alpha$ (right). Mean $\mu$, median $M$ and standard
devition $\sigma$ are given for each range.

###  A.2 Wavelength correction

The radial velocity shifts inferred for all stars, for each grating, are shown
in Fig. A.2. If our radial velocity measurements were accurate, we would
expect that they have a mean velocity of $267.7\pm 25$ km s-1, as measured by
Hénault-Brunet et al. (2012), who analysed high-quality spectra of stars
around the R136 core. Due to the calibration related wavelength offset
however, the dispersion we find is expected to be higher. Indeed, the standard
deviation on the radial velocities is on the order of $\pm 2$ pixels for most
gratings. The exception is H$\alpha$, where the typical offset is 3 to 4
pixels.

Figure A.2: Distribution of measured wavelength corrections $\varv_{\rm
shift}$ in km s-1, for each grating (dark blue). We indicate the mean R136
velocity of 267.7 km s-1 as measured by Hénault-Brunet et al. (2012, black
dashed lines), together with the non-binary-corrected velocity dispersion of
$\sigma=\pm$25 km s-1 (orange-red shaded), as well as a velocity range
corresponding $\pm$2 pixels around the R136 mean (yellow shaded). The numbers
in the upper right corner of each plot denote the amount of stars that fall
out of the plotted velocity range. Below that, we show the inferred mean
$\mu$, median $M$ and standard deviation $\sigma$ of each grating (all in km
s-1). Figure A.3: Distribution (top panels) and cumulative distribution
(bottom panels) of mutation sizes of different schemes. The panels in the
first three columns on the left show the behaviour of different types of
mutation that result from modifying strings that represent the parameters in
three different ways: by replacing one string digit by a random other digit
(mutation by replacement), by increasing or decreasing the value of one string
digit with 1 (creep mutation), and by changing one or more digits of a string
by slicing it during the recombination process (cross-over mutation). The
green vertical line indicates the original value of the parameter (in the
third panels from the left this are two lines: one for each parent), in
orange, red and blue the distribution of parameter values after the mutation
has taken place. The different colours refer to the amount of digits that
decode one parameter. The rightmost panels show the behaviour when the
mutation size is described by a Gaussian distribution, as is the case in Kiwi-
GA. Figure A.4: Comparison of the fitness distributions of $T_{\rm eff}$ and
log $\dot{M}$ of two genetic algorithm runs. The dark blue points show the
models of a Kiwi-GA run, the yellow points the models of a pyGA run. Setup of
the runs was identical: both runs had the same data (Fastwind model with
simulated S/N of 30), parameter space, number of individuals, and number of
generations. The left two plots show the run states after 30 generations, the
right two plots after 60 generations. The “true values”, that is, the value of
the model used for simulating the data, is indicated with a red line. Dark
blue and yellow dotted lines indicate the best fit models.

##  Appendix B Technical details of Kiwi-GA

We will now discuss how Kiwi-GA differs from the algorithm of Mokiem et al.
(2005) and Abdul-Masih et al. (2021), who follow the approach of the former.
First of all, Kiwi-GA applies operations of recombination (mixing of
parameters of two models) and mutation (addition of random variations to a
subset of the parameters) directly on the model parameters. Mokiem et al.
(2005) store the parameter values in the form of one string per model, where
each character of the string can have a value from 0…9 and different parts of
the string indirectly represent the values of all parameters. On these strings
the mutation and recombination operations are applied. The fact that this
concept is abandoned in Kiwi-GA has consequences for the way that mutation and
recombination are implemented. With this in mind, we list here the most
significant changes of our algorithm compared to that of Mokiem et al. (2005):

  * •

Recombination is carried out per parameter. Given two sets of parameters
(parents), the new parameters (offspring) are chosen by, for each parameter,
picking the value of one of the parents. The genome can thus be split in more
locations than only one or two, but not in the middle of a parameter. This
implies that mutation due to recombination can never occur.

  * •

No parents are cloned, that is, recombination always occurs252525Though not
recommended, the user can choose to include cloned models by adjusting the
clone fraction to $0\leq f_{\rm clone}\leq 1$.. All new models are thus the
product of both recombination and mutation, and none of mutation alone. This
increases the diversity of the population.

  * •

Two types of mutation are introduced, each having a different rate of
occurrence. In each case the size of the mutation, or the amount with which
the parameter value changes, follows a Gaussian distribution. Small mutations,
where the value of the mutated parameter lies close to the original value,
occur frequently: after recombination, each parameter has a large chance to
undergo a small mutation. Larger mutations occur with a lower frequency. The
exact frequencies can be set by the user, in this work we assumed a rate of
0.5 for the small mutations, and a maximum rate of 1/$n_{\rm free}$ for the
larger mutations. The latter means that on average one parameter per model
undergoes a large mutation. This manner of mutating parameters is very
different from the scheme used in Mokiem et al. (2005, see Section B.1 for
details).

  * •

Reinsertion of new individuals into the parent population is done according to
an elitist-fitness scheme, where the parent population can be larger than the
amount of individuals in one generation. This means that after each
generation, the fitness of both parent and offspring models is assessed and
the top models of each sub-population will form the new parent population. An
elitist-fitness scheme leads to a fitter parent population, while diversity is
ensured by always including a certain fraction of offspring models262626The
exact value can be set by the user, we chose a fraction 0.75..

Together, these adaptions result in a faster parameter space exploration, that
is, less generations need to be computed. Especially the exploration around
the best fit, done in order to assess the uncertainty regions, benefits from
the algorithm adaptions.

Apart from these major points there are other additions, such as the fact that
H-i, He-i and He-ii ionising fluxes and uncertainties thereof can be given as
an output, the possibility to make the first generation larger compared to the
rest of the generations272727This aids the initial exploration of the
parameter space, with only a small increase of computation time., the option
to treat X-ray parameters as free parameters, and the option to estimate an
appropriate volume filling fraction $f_{\rm X}$ for each model such that
$L_{X}/{\rm L_{bol}}\approx 10^{-7}$ (see Section F.2). Furthermore, Kiwi-GA
can be used in combination with Fastwind version 11, which can treat radiative
transfer of the full spectrum in the co-moving frame (Puls et al. 2020).

###  B.1 Mutation in Kiwi-GA

Figure A.3 shows several mutation schemes implemented in the algorithms of
Mokiem et al. (2005) and Abdul-Masih et al. (2021), next to the mutation
scheme used in Kiwi-GA. The scheme used in Kiwi-GA results in a mutation
distribution that covers the parameter space more regularly. In practice, this
gives the user more control over the ratio of small to large mutations. On the
one hand, parameters close to fit models (created by small mutations) are
expected to be more successful (because the original model was already fit),
but on the other hand parameters very different from the fit models can cause
larger improvement in fitness. This is the reason that we chose for small
mutations with a high probability, and large mutations with a low probability.

Optimising hyper parameters of a genetic algorithm, such as mutation rate, is
not trivial. An extensive study costs a lot of resources, so we limited
ourselves to educated guesses and a few test runs. Nonetheless, the choices we
have made seem to work well in practice, when the parameter space is well
behaved. In the end, the goal is to map for each parameter the envelope of the
fitness distribution (i.e., as a function of each free parameter, find the
lowest $\chi^{2}$), but without computing every model in the parameter space.
In the grid-fitting approach each model in the parameter space is computed,
and one can be certain that the envelope of the fitness distribution is
completely mapped. With a genetic algorithm, the mapping is only approximate;
one might miss certain models in the parameter space. In Fig. A.4 we compare
fitness distributions of Kiwi-GA to those of pyGA, using runs with identical
setup. The Kiwi-GA distributions are smoother (have less gaps), meaning that
that set of models provide a closer representation of the true fitness
envelope. We see that both algorithms find very similar best fit solutions,
that are in both cases close to the “true values”, that is, the ones that the
original model have (mind that deviations from this could be caused by the
simulated data: a S/N of 30 was imposed on the synthetic spectra). In
practice, this thus means that the algorithms work the same and give similar
outputs, but that with Kiwi-GA one needs to compute less models, that is,
needs a lower amount of computation time to trace the envelope of the fitness
distribution. We suspect that the reason for this lies mostly in the mutation
scheme, but also other changes in the algorithm could have contributed to the
improved performance. We note that Kiwi-GA has the option to use the mutation
operators used in the algorithms of Charbonneau (1995, demonstrated in Fig.
A.3); Mokiem et al. (2005, demonstrated in Fig. A.3). We note furthermore
that, regardless of the genetic algorithm or mutation operators used, the
amount of generations must be increased with higher quality data.

##  Appendix C Comparison of methods

In this section we compare the results of different methods. We stress that
the error bars have to be taken into account when comparing the different
methods; with a few exceptions, the agreement is good. To illustrate typical
differences in the best fit models of the different methods, we show in Figure
C.5 a selection of optical lines for two stars: one star where there is some
discrepancy between parameters, another star for which the agreement between
parameters is good; the latter being representative for the sample.

We derive the parameters $T_{\rm eff}$, $\log g$, $\dot{M}$, $\log L/{\rm
L}_{\odot}$, and in some cases also $\beta$ and nitrogen abundance, in two
different manners: the optical-only and optical + UV runs. Additionally, we
obtain a third measure for $T_{\rm eff}$ by fitting cmfgen models to the iron
pseudo-continuum in the UV. Lastly, Bestenlehner et al. (2020) have already
carried out an optical-only analysis of the same spectra, but using a
different method. For the O-stars, Bestenlehner et al. (2020) use the IACOB-
GBAT tool Simón-Díaz et al. (2011) instead of Fastwind and Kiwi-GA, while for
the WNh stars, they use cmfgen. For a few stars, values where obtained both
with Fastwind and cmfgen, in which case we adopt, in this section, the result
of their Fastwind analysis. Furthermore, in our analysis nitrogen abundance
was a free parameter that could range from 6.9 to 10.0, while Bestenlehner et
al. (2020) use only three grid values, namely 7.1, 8.2 and 8.5. In this
section we compare the outcomes of the different analyses.

###  C.1 Temperatures

Figure C.5: Comparison of optical lines of fits obtained with different
methods. The top row shows lines of H31, for which the the parameters of
Bestenlehner et al. (2020) and this work agree well: this level of agreement
is representative for most stars in the sample. The bottom row shows lines of
R136a7, where there is some discrepancy between the parameters of Bestenlehner
et al. (2020) and our results. The difference is especially clear in He ii
$\lambda$4686, and seems related to differences in $T_{\rm eff}$ and
$\dot{M}$.  Figure C.6: Comparison of different temperature analyses in units
of 1000 K. Top: the optical-only analysis of Bestenlehner et al. (2020)
against our optical-only (left) and our optical + UV analysis (right). Bottom:
our optical-only (left) and our iron pseudo-continuum analysis (right) against
our optical + UV analysis. The shaded are in the bottom right plot indicates
the region that is not covered by the cmfgen grid that we used (Bestenlehner
et al. 2014).  Figure C.7: Comparison of the mass-loss rates derived from the
optical + UV data, versus those of the optical-only data (fitted assuming a
smooth wind) corrected for clumping using the individual $f_{\rm cl}$ values
obtained from our optical + UV fits. The difference between the two seems to
be related to different values of $\beta$ (see text).  Figure C.8: Comparison
of different analyses. Left column: optical-only analysis with Kiwi-GA (this
work) against the optical-only analysis with IACOB-GBAT (Bestenlehner et al.
2020), right column: optical-only analysis with Kiwi-GA vs. optical + UV
analysis with Kiwi-GA (both this work).

Figure C.6 shows a comparison of the three $T_{\rm eff}$ measurements from
this paper to each other and to those of the optical-only analysis of
Bestenlehner et al. (2020). For the hotter stars ($T_{\rm eff}$ $\gtrsim
45000$ K) we find systematically higher temperatures from our optical-only
analysis than does Bestenlehner et al. (2020, top left panel), though within
errors also there the agreement between the methods is good. Inspecting the
top right and lower left panels, we see that these higher temperatures we find
from our optical-only analysis are not found from the optical + UV fit.
Assuming that the optical + UV analysis is the most reliable method because it
takes into account the most spectral information, the temperatures of
Bestenlehner et al. (2020) seem to be more reliable than our optical-only
values, although the difference is small. It may be the case that the nitrogen
lines do not affect strongly the goodness of fit that Kiwi-GA uses for
fitting, while this should be the case. Namely, for measuring the temperature
for stars hotter than $\sim 45000$ K one relies mostly on (weak) nitrogen
lines, as He-i/He-ii ratio can no longer be used since all He-i is gone at
those temperatures. Upon inspecting our fits and especially the fits to the
nitrogen lines, we do not see cases where the nitrogen lines have an
especially bad fit. The reason for the slight, albeit significant
overestimation of our optical-only temperatures is thus not understood.

The bottom right panel of Fig. C.6 contains a comparison of our optical + UV
temperatures and the temperatures we get from fitting the iron lines with the
cmfgen grid. Clearly, the iron (Fe) lines show a strong temperature dependence
that is consistent with the temperatures of the H-He-C-N-O lines. At the lower
end the Fe lines indicate a systematically higher temperature. This can be
explained by the fact that the lowest temperature of the cmfgen grid is 35481
K. At the higher temperature end the points are scattered. This could be due
to the fact that in the wavelength range from $1600-1700$ Å, where most of the
Fe iv lines lie, the S/N of our spectra is poor. Lastly, we note that both Fe
lines as well as H-He-C-N-O lines are sensitive to micro-turbulence, but that
a fixed value for micro-turbulence was assumed in both the cmfgen grid and in
the optical + UV runs (10 km s-1 in both cases).

###  C.2 Mass-loss rates & $\beta$

We see a systematic offset offset between the mass-loss rates obtained by our
optical-only analysis, and that of Bestenlehner et al. (2020). This can be
explained by the different assumptions and or fit-values for the wind
acceleration parameter $\beta$. For most sources, in the optical-only analysis
we assume $\beta=0.9$, while Bestenlehner et al. (2020) leaves this parameter
free, and finds for most sources a value of 1.0 (16 sources) or 1.2 (28
sources)282828Values obtained through personal communication with the author..
When basing the mass-loss only on optical lines without strong emission
features, the parameter $\beta$ is degenerate with mass-loss rate, where a
lower mass-loss rate or a lower $\beta$ are having the same effect on the wind
line. This explains the observed discrepancy in measured mass-loss rates: we
find or assume lower values for $\beta$, resulting in higher values for mass-
loss rate, compared to Bestenlehner et al. (2020). For deducing additional
uncertainties on $\dot{M}$ related to lack of knowledge of the value of
$\beta$, one should vary $\beta$ and assess for each value the corresponding
$\dot{M}$. Markova et al. (2004) and Repolust et al. (2004) carry out such an
analysis and find typical uncertainties of $0.1-0.3$ dex.

The discrepancy between the optical-only and optical + UV measurements of the
mass-loss rate is related predominantly to clumping. We investigate whether
the observed differences is in line with expectations by using the individual
$f_{\rm cl}$ values obtained from our optical + UV fits to do a clumping
correction for the mass-loss rates from our optical-only fits, where we
assumed a smooth wind, that is, $f_{\rm cl}$ $=1$. In other words, we check
whether

$\dot{M}_{\rm opt+UV}=\dot{M}_{\rm opt}/\sqrt{f_{\rm cl,opt+UV}}$ (18)

is satisfied292929From this analysis we exclude the three WNh stars, for which
we assumed $f_{\rm cl}=10$ in the optical-only runs.. In theory, the density
of the $\rho^{2}$-sensitive optical recombination lines from which the
optical-only mass-loss rates are derived should scale with $\sqrt{f_{\rm cl}}$
and the above should hold, assuming the adopted clumping factor is spatially
constant. Upon applying the clumping correction to $\dot{M}_{\rm opt}$ we find
that on average the shifted values are too low compared to $\dot{M}_{\rm
opt+UV}$. Closer inspection reveals that this discrepancy is related to
different values of $\beta$ that are assumed or derived for the optical-only
and the optical + UV runs. Again, the degeneracy of $\beta$ and $\dot{M}$
plays a role: For sources where $\beta_{\rm opt}<\beta_{\rm opt+UV}$ the
correction with $\sqrt{f_{\rm cl,opt+UV}}$ is too large, while for sources
where $\beta_{\rm opt}\geq\beta_{\rm opt+UV}$ Eq. 18 is satisfied (see Fig.
C.7). The latter group includes the sources where H$\alpha$ is in emission and
$\beta$ could be measured from the optical-only run. Lastly, we note that
after taking into account the different values of $\beta$ there remains a
group where the correction with $\sqrt{f_{\rm cl,opt+UV}}$ is not large
enough. An explanation for this could be that the mass-loss rates found from
the optical-only analysis are higher than the true mass-loss rates. For these
sources we probably derive an upper limit rather than the actual mass-loss
rate from the optical-only data.

###  C.3 Other parameters

Figure C.8 shows a comparison of the optical-only analysis of this paper to
the optical-UV analysis, and the analysis of Bestenlehner et al. (2020). The
most striking differences can be seen in the nitrogen abundance. The match of
the Bestenlehner et al. (2020) analysis with our optical-only analysis is not
particularly good, but note that Bestenlehner et al. (2020) stress that the
nitrogen abundance value that they provide is an indication rather than a
precise measurement303030Note that they measure only the nitrogen abundance
for stars with $T\gtrsim 45000$ K, so we include only these points in the
comparison plot. and that the error bars on our optical-only analysis are very
large. Furthermore, upon closer inspection of individual sources we see that
agreement is good for all six sources that have significant overabundance
(R136a1, R136a2, R136a3, R136a4, R136a5, R136b, H36, H48). This is also the
case for these sources if one compares the optical-only versus optical + UV
analysis, though there is a slight systematic towards higher abundances from
the optical-only analysis.

For $\log g$, $\log L/{\rm L}_{\odot}$, $\varv_{\rm eq}\sin i$, $x_{\rm He}$
there is generally good agreement between the different runs. The exception
are a few $\varv_{\rm eq}\sin i$ values of our analysis that seem to be very
high, however this concerns a few very low S/N stars for which $\varv_{\rm
eq}\sin i$ is essentially unconstrained. Another point that shows a clear
mismatch is the one with the highest He abundance in the bottom plot: this is
a3, where we from the optical only analysis found a temperature of 42750 K
where with the UV data we assessed that 50000 K is likely closer to the true
value, given the Nv and Ov lines in the UV. With a higher temperature, we find
a lower He abundance.

The above shows that, even if the same code is used for the analysis, the
outcome (at least the best fit parameters) can strongly depend on the analysis
method, at least when the data quality is not superb.

##  Appendix D Stellar masses and ages

Figure D.9: For more massive stars spectroscopic masses are systematically
larger than evolutionary masses. Figure D.10: Age distribution of stars in the
core of R136, as found using Bonnsai. The dark blue solid line and the shaded
area around it are the observed distribution and bootstrapped $2\sigma$
uncertainties.  Figure D.11: Distribution of initial masses of stars in the
core of R136, as found using Bonnsai. The dark blue solid line and the shaded
area around it are the observed distribution and bootstrapped $2\sigma$
uncertainties. Red solid line is the best power law fit over the region
30-200${\rm M}_{\odot}$ (light blue background), black dashed and dotted line
represent $2\sigma$ uncertainty on the slope. Figure D.12: As Fig. 1, but
colour coding after stellar age instead of mass.

The power law slope of the initial mass function that we derive,
$\gamma=1.99\pm 0.11$ in the range $30-200\leavevmode\nobreak\ {\rm
M}_{\odot}$, is consistent with the value of 1.90$\pm^{0.37}_{0.26}$ derived
for massive stars in the wider 30 Doradus region (Schneider et al. 2018b). The
sample of Schneider et al. (2018b) excludes the core of R136 and the most
massive star in their sample is 203$\pm^{40}_{44}$ M⊙. The highest initial
mass that we derive, 273$\pm^{25}_{36}$ ${\rm M}_{\odot}$ for R136a1, is
consistent with the stochastic sampling analysis of Schneider et al. (2018b),
that excludes maximum initial masses of over 500 M⊙ in 30 Doradus with 90%
certainty. We note that for our Bonnsai runs we used the Salpeter (1955)
initial mass-function, that, with a slope of 2.35, prefers lower masses. This
can impact the slope that we derive, albeit in a conservative way, that is,
without this prior we would have found an even shallower slope. Regarding the
ages; while we derive a cluster age of $1-2.5$ Myr, there is a tail of older
stars, suggesting that the stars in R136 are not coeval; this could be either
the result of a projected view onto this dense central region in 30 Doradus,
or is related to the formation of R136 (see also Crowther et al. 2016;
Schneider et al. 2018a; Bestenlehner 2020).

A comparison of the evolutionary and spectroscopic masses (see also table
Table H.2) can be found in Fig. D.9. The masses agree well within errors, but
for $M\gtrsim 70{\rm M}_{\odot}$ the spectroscopic masses are, with a few
exceptions, systematically higher than the evolutionary masses. Bestenlehner
et al. (2020) find the same (their Figure 3), although in some cases (e.g.,
R136a5, R136b) the current analysis gives larger values. Furthermore, note
that in addition we derive spectroscopic masses for the WNh stars R136a1-a3.
For an in depth discussion of the mass discrepancy, see Bestenlehner et al.
(2020).

The age distribution we derive for R136 based on the Bonnsai values is shown
in Fig. D.10. We find a strong peak at 1.1-1.3 Myr, consistent with the
results of Bestenlehner et al. (2020). A second peak peak may be suggestive of
a second burst of star formation around 2.0 Myr, though given the
uncertainties the evidence for this is not strong.

Figure D.11 shows the initial mass distribution we derive from the Bonnsai
values. We fit a power law in the form $\xi(M)\propto M^{-\gamma}$ to the
initial mass distribution in the mass range 30-200${\rm M}_{\odot}$ and find a
slope of $\gamma=1.99\pm 0.11$. This is consistent with the results of
Bestenlehner et al. (2020) of the R136 core ($\gamma=2.0\pm 0.3$), and the
findings of Schneider et al. (2018b, $\gamma=1.90\pm^{0.37}_{0.26}$) for the
rest of the Tarantula Nebula, but steeper than the standard Salpeter initial
mass function.

Lastly, we compare the age of our sources with the spatial distribution (Fig.
D.12). While many young sources are found close to the centre, several of them
are also found in the outskirts. Moreover, the old sources are scattered
throughout the cluster. The fact that we do not observe them in the very
centre might be an observational bias: the very bright WNh stars could
dominate the older, lower mass stars in that region. We thus conclude that we
do not see a strong correlation between the spatial position of the stars and
their age. This is in line with what Bestenlehner et al. (2020) conclude
(their Figure 11).

##  Appendix E Notes on individual sources

###  E.1 R136a1

Possibly contaminated by H17, which lies north of R136a1 with an angular
separation of 75 mas and a flux ratio of 0.112 in the K-band (Khorrami et al.
2017). Due to the low flux ratio and the fact that H17 lies mostly outside the
slit we assume the spectral analysis of R136a1 is not affected by H17.

For this star O v $\lambda$1371 is poorly reproduced – something that is seen
also for the other WNh stars of the sample (R136a2, R136a3). In particular,
the line is not broad enough compared to the data, implying that there is not
enough O v in the outer wind. We explored whether this could be related to our
(canonical) X-ray assumptions by probing the X-ray parameter space, and ruled
this out as a cause. Another possibility is that something might go wrong with
the Fastwind treatment particularly for very dense winds, either due to
indirect line overlap effects in the outer wind, or something else. Lastly, it
could be that the wind structure that is assumed (i.e., the clumping
stratification) is not representative for what actually happens in the wind,
and it could be that this discrepancy especially shows, or, is largest for,
the WNh stars. The exact cause of the issue is currently unidentified. We note
that O v $\lambda$1371 is sensitive to clumping, however we do not believe the
poor fit of O v $\lambda$1371 results in spurious clumping factors for the WNh
stars. Namely, for this particular line a higher clumping factor leads to a
weaker profile which is the opposite behaviour of some other of the clumping
factor sensitive lines (e.g. C iv $\lambda\lambda$1548-1551). In the WNh stars
we find rather high clumping factors, where a better fit of O v $\lambda$1371
(deeper profile) would be obtained with a lower clumping factor. It thus seems
that other clumping sensitive lines dominate the value that we obtain.

###  E.2 R136a2

O v $\lambda$1371 was poorly reproduced; see explanation in Section E.1.

###  E.3 R136a3

Figure E.13: Two Kiwi-GA runs for R136a3. In blue the original run, having a
setup identical to that of all other stars (resulting in $T_{\rm eff}$ $=42$
kK). In red the run where we fixed $T_{\rm eff}$ to 50 kK, all other aspects
of the setup held the same. For some lines the higher temperature results in a
better fit than the original run (light red background), while for other lines
the original run resulted in better fits (light blue background).  Figure
E.14: Fitness distribution of the iron pseudo-continuum fit of R136a3. The
best fitting temperature (47315 K) is indicated. A temperature of 50000 K
results in about the same fitness. The fitness is comparable to the inverse of
a $\chi^{2}$: it is the inverse of the sum of the square of the residuals. The
residuals are the difference between the normalised observed flux $F_{i}$ and
model flux $F_{{\rm mod},i}$, for all flux points of the iron pseudo-
continuum.

The best fit of the optical + UV run of R136a3 results in a $T_{\rm eff}$ of
42 kK, as opposed to 50 kK found by Bestenlehner et al. (2020) and 53 kK found
by Crowther et al. (2010). Upon inspecting the fit we see that while in
general the fit is matching the data well, this does not hold for the higher
ionisation lines C iv $\lambda$1165, O v $\lambda$1371, and N v
$\lambda\lambda$4604-4620, suggesting the derived $T_{\rm eff}$ of 42 kK is
too low. We carry out another fit where we fix $T_{\rm eff}$ to 50 kK and note
that the fits to O v $\lambda$1371 and N v $\lambda\lambda$4604-4620 improve
considerably, but the fit to many other lines gets worse (Fig. E.13). The
mass-loss rate and helium abundance we find from the two runs differ
significantly, we find $\log\ \dot{M}=-4.2\pm^{0.07}_{0.04}$ and $\log\
\dot{M}=-4.5\pm^{0.04}_{0.07}$, and $x_{\rm He}=0.49\pm^{0.01}_{0.11}$ and
$x_{\rm He}=0.37\pm^{0.10}_{0.10}$ for the low and high temperature,
respectively. Because there is no way to reproduce the strong O v
$\lambda$1371 and N v $\lambda\lambda$4604-4620 lines with a lower
temperature, and the fact that when assuming a low effective temperature
R136a3 lies far away from the other two WNh stars in the HRD, we deem the
higher temperature more likely. Further support for that comes from the fit to
the iron lines in the UV presented in Fig. E.14, resulting in a temperature of
around $47000-50000$ K. For these reasons, we adopt a temperature of $T_{\rm
eff}$ $=50$kK for R136a3. The other stellar parameters we obtain from the
optical + UV run with $T_{\rm eff}$ fixed to that value (blue model in Fig.
E.13). For the $\varv_{\rm eq}\sin i$ we stick to the value of the optical-
only run (best fit: $T_{\rm eff}=42750$ K) as we do for the other stars.

We note that Khorrami et al. (2017) resolve R136a3 into two sources, however
the flux ratio is 0.124 in the J-band (0.044 in the K-band), so in practice
one source will dominate our optical and UV spectroscopy. We do not see
evidence for unresolved binarity of R136a3 where the source would consist of a
hot and a cooler component, at least not directly: no He i lines are visible.

Furthermore, we note that, while we adapt the higher $T_{\rm eff}$ for R136a3
the rest of our analysis for reasons explained in this section, we have to
keep in mind that the low values we obtain from our original fit may point to
the limits of the applicability of this Fastwind version, that was not
designed for situations where, e.g., H$\gamma$ is in strong emission.

Lastly, we note that, also in the higher $T_{\rm eff}$ fit, O v $\lambda$1371
was poorly reproduced; see explanation in Section E.1.

###  E.4 R136a6

Consists of two stars with an approximately equal flux contribution (see also
Section 2.1). We carry out the spectral analysis but exclude it from the
analyses of the sample as a whole regarding mass-loss and clumping properties.

###  E.5 R136a8

No optical spectra available and thus not included in the analysis of
Bestenlehner et al. (2020). The optical + UV run of this source was thus in
fact carried out on UV data only. The setup was the same as for the other
sources, but instead of fixing the $\varv_{\rm eq}\sin i$ and helium abundance
on values derived of the optical, we fixed them at 150 km s-1 and $x_{\rm
He}=0.10$, respectively; these are typical values given the optical-only fits
of the other sample stars.

###  E.6 H36

From the optical-only run we find $T_{\rm eff}$ $=42000$ K for this star. This
value is low compared to what we find from the optical + UV run, 49500 K, and
inconsistent with the spectral type of the star (O2 If*). The optical-only fit
is good (i.e., profiles of models covering the uncertainty ranges coincide
with the scatter of the data points), with the exception of N v
$\lambda\lambda$4604-4620, which is too weak in our models. Upon comparison of
the optical lines of the the optical-only and optical + UV fits we see that
the the higher temperature of the optical + UV run does not improve the fit of
most optical lines, not even for N v $\lambda\lambda$4604-4620, which has a
similar best fit profile in both our runs. Most notable is the worsening of
the Balmer line fits, which generally are too deep for the optical + UV fit,
but match the data well for the optical-only fit. In this temperature regime
and with this data quality, the He i and He ii are of not much help for
constraining the temperature, between our optical-only and optical + UV runs
these lines are, within the noise level, unchanged. Bestenlehner et al. (2020)
find, based on optical data only, a high temperature for this star (52000 K).
Their N v $\lambda\lambda$4604-4620 seems to have a better fit than we get,
this seems to be at the cost of the fitness of He ii $\lambda$4686, and, as
for our optical + UV run, of the Balmer lines, which for their best model are
too deep compared to what is observed. However, the higher ionisation ions,
both the N iv lines in the optical and UV as well as the strong O v
$\lambda$1371, do strongly support a high temperature, which we therefore deem
more likely for this source.

###  E.7 H129

The position of H129 in the HRD is on the left of main sequence. We do not use
the parameters derived for this star for the further analysis, but exclude it
from the analyses of the sample as a whole regarding mass-loss and clumping
properties (see also Section 4.1). For the optical-only run we estimated
$\varv_{\infty}$ based on $\log L/{\rm L}_{\odot}$ from Bestenlehner et al.
(2020), but the extrapolated velocity was only 100 km s-1 we assumed a
velocity of 500 km s-1 instead.

##  Appendix F X-ray

###  F.1 X-rays implementation in Fastwind

Wind-embedded shocks and associated X-ray emission are implemented into
Fastwind by assuming a very small fraction of the stellar wind to be very hot
and emit X-rays313131This is the standard approach, that is employed in
several model atmosphere codes for hot stars (for references, see Carneiro et
al. 2016). In later versions of Fastwind, an alternative implementation,
accounting for the different effective emissivities from radiative and
adiabatic shock cooling zones, is also implemented (see Puls et al. 2020).
(Carneiro et al. 2016). The shocks are then described by five parameters: the
volume filling fraction of the X-ray emission $f_{\rm X}$, the maximum jump
velocity of the shocks $u_{\infty}$ and the exponent $\gamma_{X}$ that relates
the outflow velocity to the jump velocity ($u_{\infty}$ and $\gamma_{X}$
together describing the shock temperature, typically being of the order
$10^{6}$ K), and two parameters related to the onset radius of the X-ray
emission323232See Eq. (8) of Carneiro et al. (2016).: $R_{\rm min}^{\rm
input}$ and a factor $m_{\rm X}$. The total X-ray luminosity is thus not a
free parameter, but follows as output from the model. For further details on
the implementation of wind-embedded shocks in Fastwind see Carneiro et al.
(2016).

###  F.2 Assumptions regarding X-rays

For both optical-only and optical + UV fits, we include wind-embedded shocks
and resulting X-rays. The corresponding parameters are not fitted, but instead
fixed at certain values for each star. For all stars, we assume
$\gamma_{X}=0.75$, $m_{\rm X}=30$, and $R_{\rm min}^{\rm input}=1.45$. The
value of $\gamma_{X}$ sets the gradient of the shock strength relative to the
wind velocity (Pauldrach et al. 1994); a value of $\gamma_{X}<1$ means that
the relative increase in shock jump velocity as a function of radius is higher
than that of the wind velocity. Our assumed value $\gamma_{X}=0.75$ lies in
between the higher value assumed by Krtička & Kubát (2009); Carneiro et al.
(2016) and the lower values adopted in models of Pauldrach et al. (1994). For
$m_{\rm X}$ we use the best fit value from Pauldrach et al. (2001), and in our
choice of $R_{\rm min}^{\rm input}$ we follow, for example, Pauldrach et al.
(1994).

The X-ray parameters having the most profound influence on the ionisation
fractions are the maximum jump velocity of the shocks $u_{\infty}$ and the
volume filling fraction of the X-ray emission $f_{\rm X}$ (Carneiro et al.
2016), because they directly relate to the temperature distribution and total
X-ray flux. We tailor these parameters per star; for the first, we assume
$u_{\infty}=0.3\varv_{\infty}$ (after Carneiro et al. 2016, who follow Krtička
& Kubát 2009). Here we take $\varv_{\infty}$ values from Crowther et al.
(2016), or use the estimated values as discussed in Section 3.5.1. For two
stars with $\varv_{\infty}$ $\approx 3500$ (H36 and H46) we assume
$u_{\infty}=0.2\varv_{\infty}$, based on LDI simulations of winds of luminous
stars with high terminal velocities (F. Driessen, priv. comm.). The typical
maximum jump velocities we assume translate to maximum shock temperatures
ranging from $0.6-28.0\cdot 10^{6}$ K.

Then, given these assumptions, we choose $f_{\rm X}$ such that the total X-ray
luminosity in the ROSAT band (0.1-2.5 keV) equals $L_{\rm X}/L=10^{-7}$, the
canonical ratio for O-stars (e.g., Chlebowski et al. 1989; Berghoefer et al.
1997; Sana et al. 2006; Nazé et al. 2011; Rauw et al. 2015, for Galactic
O-stars; Crowther in prep. confirm that this is a reasonable assumption for
our sample stars, finding an average of $\log L_{\rm X}/L=-6.6\pm 0.3$ for
nine X-ray sources associated with R136a.). However, $L_{\rm X}$ is not a
direct input parameter of Fastwind. Instead, we estimate $f_{\rm X}$ as to
give $L_{\rm X}$ close to $L_{\rm X}/L=10^{-7}$. This is done for each model
individually during the Kiwi-GA run. Based on $\dot{M}$ and $\varv_{\infty}$
of the model, $f_{\rm X}$ is computed to satisfy:

$\log(f_{\rm X})=-5.45-1.05\log(\dot{M}_{6}/v_{\infty}),$ (19)

where $\dot{M}_{6}=\dot{M}/10^{-6}$, with $\dot{M}$ in ${\rm M}_{\odot}$ yr-1.
This equation is derived from the observational values of Kudritzki et al.
(1996, their Figure 6). Note that we extrapolate the relation that they find
to weaker winds (lower $\dot{M}_{6}/v_{\infty}$). The input and output X-ray
parameters for each source can be found in Table F.1.

###  F.3 Validity of the X-ray assumptions

We check the validity of the assumptions for our X-ray setup by comparing the
output $\log L_{\rm X}/{L}$ of each optical + UV run to the canonical value,
$\log L_{\rm X}/{L}=-7$. Figure F.15 shows that indeed, generally the output
values are close to canonical. In the six cases where it is not, we
underestimated the assumed X-ray flux. Exact values of X-ray input and output
can be found in Table F.1.

Figure F.15: _Left:_ $L_{\rm X}/{L}$ against ${L}$ of the our best fitting models (dark blue diamonds with $2\sigma$ error bars). _Right:_ Distribution of the $L_{\rm X}/{L}$ values from our best fitting models. We indicate the typical observed value of $L_{\rm X}/{L}$ (orange dashed line) and the typical scatter around this value (yellow band). We stress that the X-ray luminosity $L_{\rm X}/{L}$ is not a free parameter in our fitting and the $L_{\rm X}/{L}$ values shown here do _not_ represent the actual X-ray flux of the given stars: this plot serves solely as a check on our assumptions (see text).  Table F.1: X-ray input ($u_{\infty}$) and output ($\log f_{\rm X}$ and $\log L_{\rm X}/{L}$) values for the optical + UV runs. Error bars are $1\sigma$.  Source |  $u_{\infty}$ (km/s) | $\log f_{X}$ | $\log L_{X}/{L}$
---|---|---|---
R136a1 | 780 | -3.34$\pm$ | ${}^{0.02}_{0.15}$ | -8.41$\pm$ | ${}^{0.17}_{0.09}$
R136a2 | 728 | -3.53$\pm$ | ${}^{0.05}_{0.12}$ | -8.50$\pm$ | ${}^{0.07}_{0.14}$
R136a3 | 720 | -3.42$\pm$ | ${}^{0.04}_{0.11}$ | -8.59$\pm$ | ${}^{0.13}_{0.15}$
R136a4 | 743 | -1.91$\pm$ | ${}^{0.07}_{0.03}$ | -7.24$\pm$ | ${}^{0.03}_{0.01}$
R136a5 | 846 | -2.71$\pm$ | ${}^{0.07}_{0.07}$ | -7.47$\pm$ | ${}^{0.05}_{0.08}$
R136a6 | 795 | -2.16$\pm$ | ${}^{0.06}_{0.07}$ | -7.08$\pm$ | ${}^{0.08}_{0.01}$
R136a7 | 813 | -2.29$\pm$ | ${}^{0.07}_{0.16}$ | -7.10$\pm$ | ${}^{0.12}_{0.02}$
R136a8 | 743 | -1.96$\pm$ | ${}^{0.05}_{0.07}$ | -7.09$\pm$ | ${}^{0.02}_{0.02}$
R136b | 846 | -2.91$\pm$ | ${}^{0.05}_{0.00}$ | -8.03$\pm$ | ${}^{0.03}_{0.02}$
H30 | 747 | -1.72$\pm$ | ${}^{0.27}_{0.03}$ | -7.17$\pm$ | ${}^{0.06}_{0.09}$
H31 | 844 | -1.61$\pm$ | ${}^{0.01}_{0.00}$ | -6.95$\pm$ | ${}^{0.00}_{0.01}$
H35 | 831 | -1.79$\pm$ | ${}^{0.19}_{0.02}$ | -6.65$\pm$ | ${}^{0.01}_{0.12}$
H36 | 700 | -2.41$\pm$ | ${}^{0.08}_{0.02}$ | -7.52$\pm$ | ${}^{0.06}_{0.03}$
H40 | 825 | -1.61$\pm$ | ${}^{0.15}_{0.11}$ | -6.88$\pm$ | ${}^{0.04}_{0.10}$
H45 | 786 | -1.47$\pm$ | ${}^{0.31}_{0.00}$ | -7.11$\pm$ | ${}^{0.18}_{0.12}$
H46 | 688 | -2.58$\pm$ | ${}^{0.03}_{0.14}$ | -6.99$\pm$ | ${}^{0.08}_{0.11}$
H47 | 914 | -2.50$\pm$ | ${}^{0.08}_{0.07}$ | -6.89$\pm$ | ${}^{0.04}_{0.04}$
H48 | 914 | -2.16$\pm$ | ${}^{0.09}_{0.03}$ | -6.72$\pm$ | ${}^{0.00}_{0.14}$
H49 | 894 | -1.49$\pm$ | ${}^{0.31}_{0.10}$ | -6.75$\pm$ | ${}^{0.05}_{0.18}$
H50 | 786 | -1.66$\pm$ | ${}^{0.23}_{0.00}$ | -6.77$\pm$ | ${}^{0.00}_{0.14}$
H52 | 846 | -1.55$\pm$ | ${}^{0.17}_{0.00}$ | -6.69$\pm$ | ${}^{0.02}_{0.18}$
H55 | 864 | -1.46$\pm$ | ${}^{0.18}_{0.06}$ | -6.74$\pm$ | ${}^{0.01}_{0.12}$
H58 | 894 | -1.22$\pm$ | ${}^{0.20}_{0.11}$ | -6.95$\pm$ | ${}^{0.05}_{0.14}$
H62 | 831 | -1.74$\pm$ | ${}^{0.12}_{0.09}$ | -6.64$\pm$ | ${}^{0.16}_{0.04}$
H64 | 531 | -1.20$\pm$ | ${}^{0.23}_{0.22}$ | -7.30$\pm$ | ${}^{0.14}_{0.14}$
H65 | 762 | -1.74$\pm$ | ${}^{0.17}_{0.10}$ | -6.95$\pm$ | ${}^{0.17}_{0.10}$
H66 | 777 | -1.58$\pm$ | ${}^{0.02}_{0.07}$ | -6.62$\pm$ | ${}^{0.02}_{0.00}$
H68 | 573 | -1.17$\pm$ | ${}^{0.28}_{0.10}$ | -7.11$\pm$ | ${}^{0.04}_{0.35}$
H69 | 774 | -0.90$\pm$ | ${}^{0.10}_{0.37}$ | -6.97$\pm$ | ${}^{0.27}_{0.03}$
H70 | 801 | -1.50$\pm$ | ${}^{0.15}_{0.10}$ | -6.74$\pm$ | ${}^{0.09}_{0.11}$
H71 | 743 | -1.23$\pm$ | ${}^{0.47}_{0.01}$ | -6.59$\pm$ | ${}^{0.05}_{0.29}$
H75 | 765 | -1.32$\pm$ | ${}^{0.33}_{0.04}$ | -6.52$\pm$ | ${}^{0.00}_{0.22}$
H78 | 713 | -1.11$\pm$ | ${}^{0.16}_{0.29}$ | -6.72$\pm$ | ${}^{0.17}_{0.07}$
H80 | 497 | 0.51$\pm$ | ${}^{0.35}_{0.12}$ | -7.81$\pm$ | ${}^{0.12}_{0.32}$
H86 | 743 | -1.44$\pm$ | ${}^{0.18}_{0.00}$ | -6.38$\pm$ | ${}^{0.00}_{0.11}$
H90 | 743 | -1.15$\pm$ | ${}^{0.34}_{0.16}$ | -6.55$\pm$ | ${}^{0.08}_{0.21}$
H92 | 624 | -0.06$\pm$ | ${}^{0.25}_{0.29}$ | -7.27$\pm$ | ${}^{0.21}_{0.20}$
H94 | 747 | -0.61$\pm$ | ${}^{0.21}_{0.21}$ | -6.88$\pm$ | ${}^{0.13}_{0.17}$
H143 | 444 | -0.11$\pm$ | ${}^{0.22}_{0.38}$ | -7.35$\pm$ | ${}^{0.20}_{0.19}$
H73 | 603 | 0.96$\pm$ | ${}^{0.99}_{0.09}$ | -8.18$\pm$ | ${}^{0.11}_{0.93}$
H108 | 312 | 0.04$\pm$ | ${}^{0.35}_{0.43}$ | -7.46$\pm$ | ${}^{0.35}_{0.30}$
H112 | 565 | 0.34$\pm$ | ${}^{0.38}_{0.37}$ | -7.78$\pm$ | ${}^{0.31}_{0.29}$
H114 | 531 | -0.39$\pm$ | ${}^{0.40}_{0.27}$ | -7.02$\pm$ | ${}^{0.19}_{0.25}$
H116 | 288 | 0.83$\pm$ | ${}^{0.74}_{0.50}$ | -8.27$\pm$ | ${}^{0.39}_{0.70}$
H120 | 313 | 0.01$\pm$ | ${}^{0.49}_{0.29}$ | -7.38$\pm$ | ${}^{0.33}_{0.40}$
H121 | 344 | 0.94$\pm$ | ${}^{0.88}_{0.31}$ | -8.03$\pm$ | ${}^{0.15}_{0.91}$
H123 | 485 | -0.20$\pm$ | ${}^{0.25}_{0.16}$ | -6.97$\pm$ | ${}^{0.16}_{0.15}$
H129 | 150 | 0.02$\pm$ | ${}^{0.88}_{0.28}$ | -8.43$\pm$ | ${}^{0.21}_{0.92}$
H132 | 464 | 0.29$\pm$ | ${}^{0.70}_{0.35}$ | -7.59$\pm$ | ${}^{0.29}_{0.54}$
H134 | 351 | 0.22$\pm$ | ${}^{0.25}_{0.34}$ | -7.55$\pm$ | ${}^{0.37}_{0.10}$
H135 | 363 | -0.30$\pm$ | ${}^{0.58}_{0.11}$ | -7.64$\pm$ | ${}^{0.20}_{0.22}$
H139 | 369 | 0.13$\pm$ | ${}^{0.40}_{0.14}$ | -7.43$\pm$ | ${}^{0.11}_{0.31}$
H141 | 300 | 0.05$\pm$ | ${}^{0.51}_{0.74}$ | -7.82$\pm$ | ${}^{0.30}_{0.24}$
H159 | 388 | 0.18$\pm$ | ${}^{0.33}_{0.29}$ | -7.66$\pm$ | ${}^{0.20}_{0.19}$
H162 | 350 | -0.72$\pm$ | ${}^{2.72}_{0.73}$ | -7.56$\pm$ | ${}^{0.56}_{1.47}$
H173 | 212 | 0.61$\pm$ | ${}^{0.75}_{0.88}$ | -8.41$\pm$ | ${}^{0.33}_{0.56}$

##  Appendix G Trends in wind structure

Figure G.16 to G.19 show the trends in the wind structure parameters as a
function of effective temperature, luminosity, $beta$, and the Eddington
parameter for electron scattering. As these parameters are strongly correlated
with each other, in all these plots similar trends are visible (see Section
5.2).

Figure G.16: As Fig. 16 but as a function of $T_{\rm eff}$. The cutoff value
for the ‘low’ and ‘high’ regime is at $T_{\rm eff}=45000$ K. Figure G.17: As
Fig. 16 but as a function of $\log L/{\rm L}_{\odot}$. The cutoff value for
the ‘low’ and ‘high’ regime is at $\log\ L/{\rm L}_{\odot}=6$. Figure G.18: As
Fig. 16 but as a function of $\beta$. The cutoff value for the ‘low’ and
‘high’ regime is at $\beta=0.9$. Figure G.19: As Fig. 16 but as a function of
$\log\Gamma_{\rm Edd,e}$. The cutoff value for the ‘low’ and ‘high’ regime is
at $\log\Gamma_{\rm Edd,e}=-0.40$ corresponding to $\Gamma_{\rm Edd,e}=0.40$.
Note that $\Gamma_{\rm Edd,e}$ is proportional to $T_{\rm eff}^{4}/g$.

##  Appendix H Additional tables

Table H.3 contains the values of the optical-only runs. Table H.2 contains
stellar masses, ages and ionising fluxes based on the parameters derived from
optical + UV runs. Furthermore, it contains the temperatures derived based on
the iron continuum. Note that the uncertainties we quote for $M_{\rm evol}$,
$M_{\rm ini}$ and age are only statistical uncertainties that result from the
Bonnsai tool. Systematic uncertainties, that is, those resulting from the
chosen input-physics of the evolutionary model, for example, the assumed
mixing scheme, or mass-loss rate prescription, are not included. We discuss
the systematic uncertainties on evolutionary masses for the WNh stars in
Section 5.3.1. Table H.4 lists for each star the diagnostic lines that were
used in the analysis.

Table H.2: Additional parameters and $1\sigma$ uncertainties: spectral types, initial, evolutionary, spectroscopic and spectroscopic masses, ages, H-i, He-i and He-ii ionising radiation $Q_{0}$, $Q_{1}$, $Q_{2}$, the H-i ionising luminosity, the Eddington factors for electron scattering $\Gamma_{\rm Edd,e}$, and the effective temperature derived from the iron continuum and used for the normalisation of the UV spectra $T_{\rm iron}$. This table is complimentary to Tables 4 and 5 and is based on the optical + UV runs.  Source |  Spectral Typea) |  Mini |  Mevol |  Mspec | Age |  log $Q_{0}$ |  log $Q_{1}$ |  log $Q_{2}$ |  $L_{\rm 13.6}$ b) | $\Gamma_{\rm Edd,e}$ |  Tiron
---|---|---|---|---|---|---|---|---|---|---|---
| [-] |  [M⊙] |  [M⊙] |  [M⊙] | [Myr] |  [s-1] |  [s-1] |  [s-1] | [-] | [-] | [kK]
R136a1 | WN5h |  273$\pm$ | ${}^{25}_{36}$ |  222$\pm$ | ${}^{29}_{28}$ |  303$\pm$ | ${}^{123}_{79}$ |  1.14$\pm$ | ${}^{0.17}_{0.14}$ | 50.71 | 50.13 | 45.24 | 6.66 |  0.77$\pm$ | ${}^{0.10}_{0.10}$ | 50
R136a2 | WN5h |  221$\pm$ | ${}^{16}_{12}$ |  186$\pm$ | ${}^{17}_{15}$ |  159$\pm$ | ${}^{93}_{5}$ |  1.34$\pm$ | ${}^{0.13}_{0.18}$ | 50.59 | 50.05 | 45.19 | 6.55 |  0.60$\pm$ | ${}^{0.05}_{0.05}$ | 50
R136a3c) | WN5h |  213$\pm$ | ${}^{12}_{11}$ |  179$\pm$ | ${}^{16}_{11}$ |  387$\pm$ | ${}^{2949}_{208}$ |  1.28$\pm$ | ${}^{0.17}_{0.21}$ | 50.56 | 50.04 | 44.97 | 6.52 |  0.61$\pm$ | ${}^{0.06}_{0.04}$ | 47
R136a4e) | O3V ((f*))(n) |  113$\pm$ | ${}^{7}_{7}$ |  108$\pm$ | ${}^{6}_{7}$ |  178$\pm$ | ${}^{73}_{32}$ |  0.84$\pm$ | ${}^{0.19}_{0.08}$ | 50.10 | 49.55 | 45.65 | 6.05 |  0.46$\pm$ | ${}^{0.03}_{0.03}$ |  47d)
R136a5e) | O2 I(n)f* |  123$\pm$ | ${}^{6}_{6}$ |  116$\pm$ | ${}^{6}_{5}$ |  364$\pm$ | ${}^{1}_{181}$ |  0.98$\pm$ | ${}^{0.11}_{0.09}$ | 50.13 | 49.56 | 43.71 | 6.08 |  0.44$\pm$ | ${}^{0.02}_{0.02}$ | 44
R136a6f) | O2 I(n)f*p |  109$\pm$ | ${}^{8}_{10}$ |  105$\pm$ | ${}^{8}_{10}$ |  100$\pm$ | ${}^{12}_{25}$ |  0.76$\pm$ | ${}^{0.28}_{0.28}$ | 50.10 | 49.59 | 45.98 | 6.06 |  0.44$\pm$ | ${}^{0.03}_{0.04}$ | 44
R136a7e) | O3 III(f*) |  131$\pm$ | ${}^{14}_{14}$ |  127$\pm$ | ${}^{15}_{16}$ |  230$\pm$ | ${}^{58}_{121}$ |  0.50$\pm$ | ${}^{0.37}_{0.46}$ | 50.21 | 49.73 | 46.16 | 6.18 |  0.46$\pm$ | ${}^{0.05}_{0.06}$ | 42
R136a8 | - |  100$\pm$ | ${}^{6}_{5}$ |  96$\pm$ | ${}^{6}_{6}$ |  179$\pm$ | ${}^{140}_{66}$ |  0.90$\pm$ | ${}^{0.21}_{0.24}$ | 49.98 | 49.43 | 45.26 | 5.93 |  0.40$\pm$ | ${}^{0.02}_{0.02}$ | 53
R136b | O4 If |  107$\pm$ | ${}^{6}_{5}$ |  92$\pm$ | ${}^{5}_{5}$ |  209$\pm$ | ${}^{121}_{1}$ |  2.02$\pm$ | ${}^{0.10}_{0.14}$ | 50.00 | 49.04 | 40.86 | 5.88 |  0.62$\pm$ | ${}^{0.04}_{0.03}$ | 35
H30 | O6.5 Vz |  52$\pm$ | ${}^{3}_{2}$ |  50$\pm$ | ${}^{3}_{2}$ |  147$\pm$ | ${}^{141}_{2}$ |  2.22$\pm$ | ${}^{0.21}_{0.24}$ | 49.38 | 48.57 | 42.14 | 5.28 |  0.31$\pm$ | ${}^{0.02}_{0.01}$ | 39
H31 | O2 V((f*)) |  76$\pm$ | ${}^{3}_{3}$ |  73$\pm$ | ${}^{3}_{3}$ |  79$\pm$ | ${}^{1}_{16}$ |  1.26$\pm$ | ${}^{0.13}_{0.19}$ | 49.79 | 49.20 | 45.27 | 5.74 |  0.35$\pm$ | ${}^{0.02}_{0.01}$ | 44
H35 | O3 V |  63$\pm$ | ${}^{4}_{3}$ |  62$\pm$ | ${}^{4}_{3}$ |  65$\pm$ | ${}^{46}_{1}$ |  1.10$\pm$ | ${}^{0.26}_{0.48}$ | 49.62 | 49.03 | 45.19 | 5.56 |  0.28$\pm$ | ${}^{0.02}_{0.01}$ | 44
H36 | O2 If* |  115$\pm$ | ${}^{5}_{5}$ |  110$\pm$ | ${}^{5}_{5}$ |  162$\pm$ | ${}^{2}_{47}$ |  0.90$\pm$ | ${}^{0.12}_{0.11}$ | 50.10 | 49.55 | 43.94 | 6.06 |  0.44$\pm$ | ${}^{0.02}_{0.02}$ | 53
H40 | O3 V |  67$\pm$ | ${}^{7}_{7}$ |  65$\pm$ | ${}^{6}_{7}$ |  56$\pm$ | ${}^{7}_{11}$ |  1.44$\pm$ | ${}^{0.44}_{0.51}$ | 49.76 | 49.15 | 45.00 | 5.70 |  0.35$\pm$ | ${}^{0.04}_{0.04}$ | 50
H45g) | O4: Vz |  57$\pm$ | ${}^{5}_{3}$ |  54$\pm$ | ${}^{5}_{3}$ |  127$\pm$ | ${}^{15}_{55}$ |  2.06$\pm$ | ${}^{0.26}_{0.41}$ | 49.48 | 48.75 | 43.31 | 5.39 |  0.31$\pm$ | ${}^{0.03}_{0.02}$ | 42
H46e) | O2-3 III(f*) |  84$\pm$ | ${}^{5}_{6}$ |  80$\pm$ | ${}^{5}_{6}$ |  84$\pm$ | ${}^{122}_{17}$ |  1.30$\pm$ | ${}^{0.25}_{0.14}$ | 49.94 | 49.36 | 45.51 | 5.88 |  0.41$\pm$ | ${}^{0.03}_{0.03}$ |  47d)
H47 | O2 V((f*)) |  72$\pm$ | ${}^{5}_{4}$ |  68$\pm$ | ${}^{4}_{4}$ |  308$\pm$ | ${}^{79}_{198}$ |  1.74$\pm$ | ${}^{0.17}_{0.24}$ | 49.70 | 49.05 | 43.15 | 5.63 |  0.37$\pm$ | ${}^{0.02}_{0.02}$ | 42
H48 | O2-3 III(f*) |  71$\pm$ | ${}^{4}_{4}$ |  68$\pm$ | ${}^{4}_{4}$ |  65$\pm$ | ${}^{37}_{4}$ |  1.46$\pm$ | ${}^{0.22}_{0.21}$ | 49.77 | 49.16 | 44.05 | 5.71 |  0.35$\pm$ | ${}^{0.02}_{0.02}$ |  50d)
H49 | O3 |  57$\pm$ | ${}^{6}_{4}$ |  55$\pm$ | ${}^{6}_{5}$ |  48$\pm$ | ${}^{51}_{20}$ |  1.84$\pm$ | ${}^{0.33}_{0.84}$ | 49.53 | 48.86 | 44.68 | 5.46 |  0.28$\pm$ | ${}^{0.03}_{0.02}$ | 42
H50e) | O3-4 V((f*)) |  66$\pm$ | ${}^{5}_{4}$ |  64$\pm$ | ${}^{5}_{4}$ |  86$\pm$ | ${}^{10}_{20}$ |  1.14$\pm$ | ${}^{0.32}_{0.52}$ | 49.64 | 49.04 | 44.62 | 5.58 |  0.30$\pm$ | ${}^{0.02}_{0.02}$ | 42
H52 | O3-4 Vz |  53$\pm$ | ${}^{3}_{3}$ |  52$\pm$ | ${}^{3}_{3}$ |  55$\pm$ | ${}^{26}_{11}$ |  1.46$\pm$ | ${}^{0.37}_{0.50}$ | 49.48 | 48.84 | 43.58 | 5.41 |  0.26$\pm$ | ${}^{0.02}_{0.01}$ | 42
H55 | O2 V((f*))z |  61$\pm$ | ${}^{6}_{4}$ |  60$\pm$ | ${}^{6}_{5}$ |  44$\pm$ | ${}^{18}_{5}$ |  1.16$\pm$ | ${}^{0.37}_{0.69}$ | 49.59 | 48.99 | 45.06 | 5.53 |  0.27$\pm$ | ${}^{0.03}_{0.02}$ | 44
H58e) | O2-3 V: |  66$\pm$ | ${}^{7}_{6}$ |  65$\pm$ | ${}^{7}_{6}$ |  150$\pm$ | ${}^{52}_{74}$ |  0.96$\pm$ | ${}^{0.47}_{0.65}$ | 49.64 | 49.06 | 44.79 | 5.58 |  0.30$\pm$ | ${}^{0.03}_{0.03}$ | 42
H62g) | O2-3 V |  49$\pm$ | ${}^{5}_{4}$ |  48$\pm$ | ${}^{5}_{4}$ |  50$\pm$ | ${}^{24}_{14}$ |  1.50$\pm$ | ${}^{0.52}_{0.88}$ | 49.40 | 48.76 | 42.95 | 5.33 |  0.23$\pm$ | ${}^{0.03}_{0.02}$ |  50d)
H64 | O4-5 V: |  61$\pm$ | ${}^{5}_{5}$ |  59$\pm$ | ${}^{6}_{5}$ |  130$\pm$ | ${}^{30}_{69}$ |  1.44$\pm$ | ${}^{0.47}_{0.57}$ | 49.60 | 48.99 | 44.55 | 5.54 |  0.32$\pm$ | ${}^{0.03}_{0.03}$ | 42
H65 | O4 VC16 |  51$\pm$ | ${}^{4}_{3}$ |  49$\pm$ | ${}^{3}_{3}$ |  52$\pm$ | ${}^{50}_{11}$ |  2.18$\pm$ | ${}^{0.28}_{0.37}$ | 49.46 | 48.74 | 42.54 | 5.38 |  0.29$\pm$ | ${}^{0.02}_{0.02}$ | 39
H66 | O2 V-III(f*) |  54$\pm$ | ${}^{3}_{3}$ |  53$\pm$ | ${}^{3}_{3}$ |  47$\pm$ | ${}^{19}_{0}$ |  0.78$\pm$ | ${}^{0.44}_{0.51}$ | 49.46 | 48.87 | 45.02 | 5.41 |  0.23$\pm$ | ${}^{0.01}_{0.01}$ | 42
H68 | O4-5 Vz |  48$\pm$ | ${}^{4}_{4}$ |  46$\pm$ | ${}^{4}_{4}$ |  60$\pm$ | ${}^{45}_{11}$ |  2.16$\pm$ | ${}^{0.42}_{0.50}$ | 49.40 | 48.67 | 43.37 | 5.31 |  0.28$\pm$ | ${}^{0.02}_{0.02}$ | 39
H69 | O4-5 Vz |  39$\pm$ | ${}^{3}_{2}$ |  38$\pm$ | ${}^{3}_{2}$ |  62$\pm$ | ${}^{16}_{27}$ |  2.36$\pm$ | ${}^{0.45}_{0.71}$ | 49.13 | 48.38 | 41.96 | 5.04 |  0.21$\pm$ | ${}^{0.02}_{0.01}$ | 42
H70g) | O5 Vz |  54$\pm$ | ${}^{4}_{4}$ |  53$\pm$ | ${}^{4}_{4}$ |  72$\pm$ | ${}^{121}_{8}$ |  1.32$\pm$ | ${}^{0.46}_{0.66}$ | 49.48 | 48.85 | 44.29 | 5.41 |  0.26$\pm$ | ${}^{0.02}_{0.02}$ |  47d)
H71 | O2-3 V((f*)) |  41$\pm$ | ${}^{4}_{4}$ |  40$\pm$ | ${}^{4}_{4}$ |  24$\pm$ | ${}^{9}_{7}$ |  1.68$\pm$ | ${}^{0.70}_{0.94}$ | 49.26 | 48.60 | 43.85 | 5.19 |  0.19$\pm$ | ${}^{0.02}_{0.02}$ | 44
H75g) | O6 V |  43$\pm$ | ${}^{3}_{3}$ |  43$\pm$ | ${}^{3}_{3}$ |  77$\pm$ | ${}^{45}_{29}$ |  0.06$\pm$ | ${}^{1.04}_{0.07}$ | 49.21 | 48.62 | 44.12 | 5.15 |  0.18$\pm$ | ${}^{0.01}_{0.01}$ |  39d)
H78 | O4: V |  41$\pm$ | ${}^{4}_{4}$ |  40$\pm$ | ${}^{4}_{4}$ |  31$\pm$ | ${}^{14}_{8}$ |  1.52$\pm$ | ${}^{0.80}_{1.00}$ | 49.30 | 48.68 | 44.26 | 5.24 |  0.22$\pm$ | ${}^{0.02}_{0.02}$ | 42
H80 | O8 V |  25$\pm$ | ${}^{1}_{1}$ |  24$\pm$ | ${}^{1}_{1}$ |  28$\pm$ | ${}^{15}_{10}$ |  4.18$\pm$ | ${}^{0.66}_{0.51}$ | 48.56 | 47.33 | 41.51 | 4.42 |  0.14$\pm$ | ${}^{0.01}_{0.01}$ | 37
H86e) | O5: V |  41$\pm$ | ${}^{3}_{2}$ |  41$\pm$ | ${}^{3}_{2}$ |  18$\pm$ | ${}^{2}_{5}$ |  0.60$\pm$ | ${}^{0.53}_{0.59}$ | 49.19 | 48.55 | 43.95 | 5.12 |  0.16$\pm$ | ${}^{0.01}_{0.01}$ | 42
H90 | O4: V: |  36$\pm$ | ${}^{4}_{3}$ |  36$\pm$ | ${}^{4}_{3}$ |  27$\pm$ | ${}^{33}_{3}$ |  1.94$\pm$ | ${}^{0.63}_{1.21}$ | 49.06 | 48.34 | 42.92 | 4.98 |  0.17$\pm$ | ${}^{0.02}_{0.01}$ | 42
H92 | O6 Vz |  32$\pm$ | ${}^{2}_{1}$ |  31$\pm$ | ${}^{2}_{1}$ |  40$\pm$ | ${}^{10}_{17}$ |  2.36$\pm$ | ${}^{0.44}_{0.72}$ | 48.87 | 48.05 | 42.42 | 4.77 |  0.15$\pm$ | ${}^{0.01}_{0.01}$ | 42
H94 | O4-5 Vz |  39$\pm$ | ${}^{3}_{3}$ |  39$\pm$ | ${}^{3}_{3}$ |  24$\pm$ | ${}^{13}_{7}$ |  1.16$\pm$ | ${}^{0.69}_{0.90}$ | 49.15 | 48.48 | 43.89 | 5.08 |  0.16$\pm$ | ${}^{0.01}_{0.01}$ | 47
H143 | O8-9 V-III |  28$\pm$ | ${}^{3}_{3}$ |  28$\pm$ | ${}^{3}_{3}$ |  16$\pm$ | ${}^{16}_{4}$ |  2.60$\pm$ | ${}^{1.22}_{1.49}$ | 48.85 | 48.05 | 42.74 | 4.76 |  0.14$\pm$ | ${}^{0.01}_{0.01}$ | 37
H73 | O9.7-B0 V |  24$\pm$ | ${}^{3}_{2}$ |  24$\pm$ | ${}^{3}_{2}$ |  74$\pm$ | ${}^{65}_{15}$ |  4.46$\pm$ | ${}^{0.98}_{1.02}$ | 48.25 | 46.16 | 41.05 | 4.10 |  0.17$\pm$ | ${}^{0.02}_{0.02}$ | 37
H108 | O Vn |  22$\pm$ | ${}^{3}_{3}$ |  22$\pm$ | ${}^{3}_{3}$ |  16$\pm$ | ${}^{11}_{6}$ |  1.46$\pm$ | ${}^{2.22}_{1.47}$ | 48.53 | 47.73 | 42.37 | 4.43 |  0.10$\pm$ | ${}^{0.01}_{0.01}$ | 35
H112 | O7-9 Vz |  25$\pm$ | ${}^{3}_{3}$ |  25$\pm$ | ${}^{3}_{3}$ |  45$\pm$ | ${}^{63}_{16}$ |  3.78$\pm$ | ${}^{1.30}_{1.84}$ | 48.50 | 47.21 | 41.47 | 4.36 |  0.14$\pm$ | ${}^{0.02}_{0.02}$ | 35
H114 | O5-6 V |  32$\pm$ | ${}^{3}_{3}$ |  31$\pm$ | ${}^{4}_{3}$ |  28$\pm$ | ${}^{23}_{13}$ |  0.00$\pm$ | ${}^{2.06}_{0.01}$ | 48.96 | 48.31 | 43.62 | 4.89 |  0.14$\pm$ | ${}^{0.02}_{0.01}$ | 39
H116 | O7 V |  21$\pm$ | ${}^{3}_{2}$ |  21$\pm$ | ${}^{3}_{2}$ |  21$\pm$ | ${}^{24}_{9}$ |  3.20$\pm$ | ${}^{1.56}_{2.29}$ | 48.30 | 47.06 | 41.05 | 4.16 |  0.09$\pm$ | ${}^{0.01}_{0.01}$ | 37
H120 | - |  19$\pm$ | ${}^{3}_{3}$ |  18$\pm$ | ${}^{3}_{3}$ |  34$\pm$ | ${}^{2}_{22}$ |  0.00$\pm$ | ${}^{4.92}_{0.01}$ | 48.43 | 47.60 | 42.19 | 4.33 |  0.10$\pm$ | ${}^{0.02}_{0.02}$ | 37
H121 | O9.5 V |  19$\pm$ | ${}^{2}_{2}$ |  19$\pm$ | ${}^{2}_{2}$ |  23$\pm$ | ${}^{11}_{11}$ |  4.56$\pm$ | ${}^{2.01}_{2.61}$ | 47.98 | 46.08 | 40.98 | 3.82 |  0.09$\pm$ | ${}^{0.01}_{0.01}$ | 35
H123 | O6 V |  26$\pm$ | ${}^{2}_{1}$ |  26$\pm$ | ${}^{2}_{1}$ |  14$\pm$ | ${}^{11}_{5}$ |  0.36$\pm$ | ${}^{1.30}_{0.37}$ | 48.57 | 47.77 | 42.39 | 4.48 |  0.09$\pm$ | ${}^{0.01}_{0.00}$ | 37
H129 | - |  18$\pm$ | ${}^{2}_{2}$ |  18$\pm$ | ${}^{2}_{2}$ |  7$\pm$ | ${}^{15}_{4}$ |  0.00$\pm$ | ${}^{2.20}_{0.01}$ | 48.16 | 47.44 | 42.38 | 4.07 |  0.04$\pm$ | ${}^{0.00}_{0.00}$ | 39
H132 | O7: V |  27$\pm$ | ${}^{3}_{2}$ |  27$\pm$ | ${}^{3}_{3}$ |  28$\pm$ | ${}^{34}_{12}$ |  1.40$\pm$ | ${}^{1.02}_{1.41}$ | 48.65 | 47.82 | 42.36 | 4.55 |  0.10$\pm$ | ${}^{0.01}_{0.01}$ | 37
H134 | O7 Vz |  20$\pm$ | ${}^{3}_{2}$ |  20$\pm$ | ${}^{3}_{2}$ |  16$\pm$ | ${}^{12}_{8}$ |  2.64$\pm$ | ${}^{1.62}_{2.16}$ | 48.18 | 46.99 | 40.88 | 4.05 |  0.07$\pm$ | ${}^{0.01}_{0.01}$ | 37
H135 | B |  16$\pm$ | ${}^{2}_{2}$ |  16$\pm$ | ${}^{2}_{2}$ |  25$\pm$ | ${}^{17}_{11}$ |  7.18$\pm$ | ${}^{2.70}_{2.96}$ | 47.22 | 44.43 | 40.37 | 3.05 |  0.08$\pm$ | ${}^{0.01}_{0.01}$ | 39
H139 | - |  24$\pm$ | ${}^{2}_{2}$ |  24$\pm$ | ${}^{2}_{2}$ |  19$\pm$ | ${}^{23}_{7}$ |  0.06$\pm$ | ${}^{2.52}_{0.07}$ | 48.53 | 47.73 | 42.38 | 4.43 |  0.09$\pm$ | ${}^{0.01}_{0.01}$ | 39
H141 | O5-6 V |  17$\pm$ | ${}^{3}_{2}$ |  17$\pm$ | ${}^{3}_{2}$ |  21$\pm$ | ${}^{50}_{9}$ |  6.54$\pm$ | ${}^{2.14}_{3.73}$ | 47.44 | 44.88 | 40.38 | 3.28 |  0.08$\pm$ | ${}^{0.01}_{0.01}$ | 35
H159 | - |  17$\pm$ | ${}^{1}_{1}$ |  17$\pm$ | ${}^{1}_{1}$ |  22$\pm$ | ${}^{20}_{8}$ |  6.46$\pm$ | ${}^{1.74}_{1.96}$ | 47.58 | 45.13 | 40.56 | 3.41 |  0.08$\pm$ | ${}^{0.01}_{0.01}$ | 35
H162 | - |  18$\pm$ | ${}^{4}_{3}$ |  18$\pm$ | ${}^{4}_{3}$ |  34$\pm$ | ${}^{110}_{22}$ |  2.28$\pm$ | ${}^{3.04}_{2.29}$ | 48.19 | 46.86 | 40.50 | 4.05 |  0.10$\pm$ | ${}^{0.02}_{0.02}$ | 35
H173 | O9 + V |  12$\pm$ | ${}^{2}_{2}$ |  12$\pm$ | ${}^{2}_{2}$ |  20$\pm$ | ${}^{16}_{9}$ |  9.52$\pm$ | ${}^{4.59}_{5.34}$ | 46.44 | 43.35 | 40.05 | 2.25 |  0.06$\pm$ | ${}^{0.01}_{0.01}$ | 37
a) Spectral types from Crowther et al. (2016, WN5h stars) and Caballero-Nieves
(in prep., all other stars). b) This quantity is expressed as $L_{\rm
13.6}=\log\ L_{E>13.6{\rm eV}}/{\rm L}_{\odot}$. c) Formal uncertainties
assuming a $T_{\rm eff}$ of 50 kK. In reality uncertainties on all parameters
are larger due to the uncertain $T_{\rm eff}$. d) No good fit obtained to iron
pseudo-continuum; assumed value closest to Bestenlehner et al. (2020) for UV
normalisation. e) Cross-contamination of the spectrum as a result of crowding
(as in Bestenlehner et al. 2020, with the addition of R136a8). f) Severe
cross-contamination of the spectrum as a result of crowding: R136a6 consists
of H19 and H26, see Section 2.1. g) Potential spectroscopic binary (as in
Bestenlehner et al. 2020).
Table H.3: Best fit parameters and $1\sigma$ error bars for the optical-only fits for all stars except R136a8, for which optical data is not available. A smooth wind ($f_{\rm cl}=1$) was assumed during the fit for all stars except the WNh stars R136a1, R136a2, R136a3, where we assumed $f_{\rm cl}=10$.  Source | $\log L/{\rm L}_{\odot}$ |  $T_{\rm eff}$(K) | $\log g$ | $R_{\star}/{\rm R}_{\odot}$ | $\log\dot{M}$ | $\beta$ | $\varv_{\rm eq}\sin i$ | $n_{\rm He}/n_{\rm H}$
---|---|---|---|---|---|---|---|---
R136a1 |  6.76$\pm$ | ${}^{0.08}_{0.03}$ |  42500$\pm$ | ${}^{2500}_{500}$ |  3.80$\pm$ | ${}^{0.85}_{0.20}$ |  44.9$\pm$ | ${}^{0.8}_{1.6}$ |  -4.24$\pm$ | ${}^{0.04}_{0.04}$ |  0.93$\pm$ | ${}^{0.07}_{0.12}$ |  160$\pm$ | ${}^{160}_{90}$ |  0.29$\pm$ | ${}^{0.14}_{0.03}$
R136a2 |  6.75$\pm$ | ${}^{0.06}_{0.07}$ |  46250$\pm$ | ${}^{2000}_{2500}$ |  4.00$\pm$ | ${}^{1.05}_{0.45}$ |  37.1$\pm$ | ${}^{1.3}_{1.1}$ |  -4.31$\pm$ | ${}^{0.06}_{0.11}$ |  0.93$\pm$ | ${}^{0.23}_{0.12}$ |  140$\pm$ | ${}^{370}_{90}$ |  0.28$\pm$ | ${}^{0.17}_{0.06}$
R136a3 |  6.51$\pm$ | ${}^{0.06}_{0.05}$ |  42750$\pm$ | ${}^{2000}_{1500}$ |  3.50$\pm$ | ${}^{0.70}_{0.20}$ |  32.9$\pm$ | ${}^{0.9}_{1.1}$ |  -4.24$\pm$ | ${}^{0.07}_{0.12}$ |  0.95$\pm$ | ${}^{0.28}_{0.10}$ |  300$\pm$ | ${}^{210}_{300}$ |  0.45$\pm$ | ${}^{0.06}_{0.14}$
R136a4 |  6.35$\pm$ | ${}^{0.06}_{0.10}$ |  53000$\pm$ | ${}^{2750}_{4000}$ |  4.22$\pm$ | ${}^{0.17}_{0.15}$ |  18.0$\pm$ | ${}^{0.8}_{0.5}$ |  -5.34$\pm$ | ${}^{0.10}_{0.08}$ | - |  145$\pm$ | ${}^{35}_{40}$ |  0.10$\pm$ | ${}^{0.06}_{0.01}$
R136a5 |  6.13$\pm$ | ${}^{0.05}_{0.04}$ |  42000$\pm$ | ${}^{2000}_{1250}$ |  4.17$\pm$ | ${}^{0.30}_{0.45}$ |  22.1$\pm$ | ${}^{0.5}_{0.6}$ |  -4.46$\pm$ | ${}^{0.05}_{0.03}$ |  0.89$\pm$ | ${}^{0.03}_{0.06}$ |  95$\pm$ | ${}^{58}_{40}$ |  0.18$\pm$ | ${}^{0.04}_{0.04}$
R136a6 |  6.25$\pm$ | ${}^{0.07}_{0.11}$ |  52500$\pm$ | ${}^{3000}_{4500}$ |  4.08$\pm$ | ${}^{0.12}_{0.10}$ |  16.3$\pm$ | ${}^{0.7}_{0.5}$ |  -4.95$\pm$ | ${}^{0.05}_{0.05}$ |  0.70$\pm$ | ${}^{0.04}_{0.01}$ |  165$\pm$ | ${}^{28}_{35}$ |  0.10$\pm$ | ${}^{0.03}_{0.02}$
R136a7 |  6.47$\pm$ | ${}^{0.04}_{0.08}$ |  58500$\pm$ | ${}^{2000}_{3500}$ |  4.15$\pm$ | ${}^{0.28}_{0.15}$ |  17.0$\pm$ | ${}^{0.6}_{0.4}$ |  -5.12$\pm$ | ${}^{0.13}_{0.09}$ |  0.88$\pm$ | ${}^{0.12}_{0.17}$ |  260$\pm$ | ${}^{95}_{42}$ |  0.14$\pm$ | ${}^{0.14}_{0.04}$
R136a8 | - | - | - | - | - | - | - | -
R136b |  6.24$\pm$ | ${}^{0.03}_{0.02}$ |  32500$\pm$ | ${}^{750}_{250}$ |  3.52$\pm$ | ${}^{0.20}_{0.05}$ |  41.8$\pm$ | ${}^{0.8}_{0.9}$ |  -4.58$\pm$ | ${}^{0.05}_{0.08}$ |  1.15$\pm$ | ${}^{0.12}_{0.06}$ |  95$\pm$ | ${}^{12}_{20}$ |  0.14$\pm$ | ${}^{0.06}_{0.01}$
H30 |  5.69$\pm$ | ${}^{0.08}_{0.10}$ |  38000$\pm$ | ${}^{2500}_{2750}$ |  4.12$\pm$ | ${}^{0.20}_{0.28}$ |  16.3$\pm$ | ${}^{0.7}_{0.6}$ |  -5.77$\pm$ | ${}^{0.20}_{1.08}$ | - |  125$\pm$ | ${}^{50}_{45}$ |  0.09$\pm$ | ${}^{0.05}_{0.01}$
H31 |  6.00$\pm$ | ${}^{0.14}_{0.11}$ |  48000$\pm$ | ${}^{5500}_{4000}$ |  3.92$\pm$ | ${}^{0.17}_{0.15}$ |  14.6$\pm$ | ${}^{0.6}_{0.8}$ |  -5.67$\pm$ | ${}^{0.15}_{0.19}$ | - |  120$\pm$ | ${}^{30}_{40}$ |  0.09$\pm$ | ${}^{0.04}_{0.01}$
H35 |  5.99$\pm$ | ${}^{0.07}_{0.21}$ |  54250$\pm$ | ${}^{3000}_{8000}$ |  4.28$\pm$ | ${}^{0.12}_{0.30}$ |  11.3$\pm$ | ${}^{0.9}_{0.3}$ |  -5.79$\pm$ | ${}^{0.18}_{0.79}$ | - |  110$\pm$ | ${}^{45}_{55}$ |  0.10$\pm$ | ${}^{0.06}_{0.01}$
H36 |  6.04$\pm$ | ${}^{0.08}_{0.06}$ |  42000$\pm$ | ${}^{3000}_{2000}$ |  3.70$\pm$ | ${}^{0.25}_{0.11}$ |  20.0$\pm$ | ${}^{0.6}_{0.7}$ |  -4.45$\pm$ | ${}^{0.05}_{0.10}$ |  0.70$\pm$ | ${}^{0.11}_{0.03}$ |  165$\pm$ | ${}^{50}_{52}$ |  0.10$\pm$ | ${}^{0.03}_{0.01}$
H40 |  5.82$\pm$ | ${}^{0.24}_{0.12}$ |  43500$\pm$ | ${}^{9000}_{3750}$ |  3.67$\pm$ | ${}^{0.40}_{0.12}$ |  14.4$\pm$ | ${}^{0.7}_{1.3}$ |  -5.57$\pm$ | ${}^{0.13}_{0.23}$ | - |  120$\pm$ | ${}^{45}_{65}$ |  0.10$\pm$ | ${}^{0.12}_{0.01}$
H45 |  5.86$\pm$ | ${}^{0.13}_{0.13}$ |  43500$\pm$ | ${}^{5000}_{4500}$ |  4.08$\pm$ | ${}^{0.28}_{0.25}$ |  15.2$\pm$ | ${}^{0.8}_{0.8}$ |  -6.12$\pm$ | ${}^{0.35}_{1.90}$ | - |  165$\pm$ | ${}^{60}_{60}$ |  0.09$\pm$ | ${}^{0.13}_{0.01}$
H46 |  6.07$\pm$ | ${}^{0.10}_{0.07}$ |  46500$\pm$ | ${}^{3750}_{2500}$ |  3.92$\pm$ | ${}^{0.29}_{0.17}$ |  16.9$\pm$ | ${}^{0.5}_{0.7}$ |  -4.98$\pm$ | ${}^{0.15}_{0.15}$ |  0.93$\pm$ | ${}^{0.15}_{0.20}$ |  190$\pm$ | ${}^{72}_{55}$ |  0.12$\pm$ | ${}^{0.10}_{0.03}$
H47 |  6.06$\pm$ | ${}^{0.13}_{0.09}$ |  46500$\pm$ | ${}^{5000}_{3000}$ |  4.03$\pm$ | ${}^{0.38}_{0.17}$ |  16.7$\pm$ | ${}^{0.6}_{0.8}$ |  -4.93$\pm$ | ${}^{0.10}_{0.15}$ |  0.70$\pm$ | ${}^{0.14}_{0.03}$ |  120$\pm$ | ${}^{70}_{90}$ |  0.10$\pm$ | ${}^{0.11}_{0.01}$
H48 |  5.92$\pm$ | ${}^{0.16}_{0.08}$ |  45000$\pm$ | ${}^{6250}_{3000}$ |  3.92$\pm$ | ${}^{0.33}_{0.17}$ |  15.1$\pm$ | ${}^{0.5}_{0.9}$ |  -5.25$\pm$ | ${}^{0.10}_{0.11}$ | - |  130$\pm$ | ${}^{50}_{65}$ |  0.10$\pm$ | ${}^{0.09}_{0.01}$
H49 |  6.12$\pm$ | ${}^{0.02}_{0.41}$ |  58000$\pm$ | ${}^{500}_{16000}$ |  4.25$\pm$ | ${}^{0.50}_{0.51}$ |  11.5$\pm$ | ${}^{2.3}_{0.2}$ |  -5.56$\pm$ | ${}^{0.25}_{0.98}$ | - |  215$\pm$ | ${}^{150}_{160}$ |  0.09$\pm$ | ${}^{0.20}_{0.01}$
H50 |  5.82$\pm$ | ${}^{0.13}_{0.11}$ |  46000$\pm$ | ${}^{5250}_{4000}$ |  4.03$\pm$ | ${}^{0.23}_{0.20}$ |  12.9$\pm$ | ${}^{0.6}_{0.7}$ |  -5.92$\pm$ | ${}^{0.18}_{0.45}$ | - |  125$\pm$ | ${}^{50}_{52}$ |  0.09$\pm$ | ${}^{0.05}_{0.01}$
H52 |  5.74$\pm$ | ${}^{0.10}_{0.14}$ |  47250$\pm$ | ${}^{3750}_{5000}$ |  4.10$\pm$ | ${}^{0.16}_{0.30}$ |  11.2$\pm$ | ${}^{0.7}_{0.4}$ |  -5.65$\pm$ | ${}^{0.13}_{0.25}$ | - |  135$\pm$ | ${}^{58}_{50}$ |  0.09$\pm$ | ${}^{0.08}_{0.01}$
H55 |  5.92$\pm$ | ${}^{0.10}_{0.22}$ |  53000$\pm$ | ${}^{4000}_{8250}$ |  4.05$\pm$ | ${}^{0.17}_{0.35}$ |  10.9$\pm$ | ${}^{1.0}_{0.4}$ |  -5.77$\pm$ | ${}^{0.20}_{0.60}$ | - |  110$\pm$ | ${}^{60}_{55}$ |  0.09$\pm$ | ${}^{0.14}_{0.01}$
H58 |  5.98$\pm$ | ${}^{0.18}_{0.14}$ |  52500$\pm$ | ${}^{8000}_{5500}$ |  4.38$\pm$ | ${}^{0.20}_{0.25}$ |  11.9$\pm$ | ${}^{0.7}_{0.8}$ |  -7.03$\pm$ | ${}^{0.65}_{0.50}$ | - |  105$\pm$ | ${}^{55}_{80}$ |  0.11$\pm$ | ${}^{0.08}_{0.03}$
H62 |  5.87$\pm$ | ${}^{0.13}_{0.24}$ |  54000$\pm$ | ${}^{6000}_{9500}$ |  4.00$\pm$ | ${}^{0.21}_{0.33}$ |  9.9$\pm$ | ${}^{1.0}_{0.5}$ |  -5.42$\pm$ | ${}^{0.05}_{0.18}$ |  0.70$\pm$ | ${}^{0.17}_{0.03}$ |  160$\pm$ | ${}^{60}_{85}$ |  0.10$\pm$ | ${}^{0.15}_{0.02}$
H64 |  5.94$\pm$ | ${}^{0.03}_{0.20}$ |  49500$\pm$ | ${}^{1000}_{7500}$ |  4.17$\pm$ | ${}^{0.28}_{0.35}$ |  12.9$\pm$ | ${}^{1.1}_{0.2}$ |  -6.04$\pm$ | ${}^{0.23}_{0.63}$ | - |  150$\pm$ | ${}^{95}_{90}$ |  0.09$\pm$ | ${}^{0.08}_{0.01}$
H65 |  5.67$\pm$ | ${}^{0.43}_{0.08}$ |  40000$\pm$ | ${}^{16000}_{2500}$ |  3.77$\pm$ | ${}^{0.60}_{0.25}$ |  14.3$\pm$ | ${}^{0.5}_{2.2}$ |  -5.72$\pm$ | ${}^{0.18}_{0.58}$ | - |  155$\pm$ | ${}^{75}_{110}$ |  0.09$\pm$ | ${}^{0.11}_{0.01}$
H66 |  5.77$\pm$ | ${}^{0.13}_{0.14}$ |  51500$\pm$ | ${}^{5500}_{5500}$ |  4.15$\pm$ | ${}^{0.19}_{0.28}$ |  9.7$\pm$ | ${}^{0.6}_{0.5}$ |  -5.42$\pm$ | ${}^{0.08}_{0.16}$ |  0.70$\pm$ | ${}^{0.12}_{0.03}$ |  35$\pm$ | ${}^{85}_{35}$ |  0.09$\pm$ | ${}^{0.06}_{0.01}$
H68 |  5.86$\pm$ | ${}^{0.16}_{0.19}$ |  48000$\pm$ | ${}^{6500}_{7000}$ |  4.25$\pm$ | ${}^{0.35}_{0.35}$ |  12.4$\pm$ | ${}^{1.0}_{0.8}$ |  -6.42$\pm$ | ${}^{0.50}_{1.60}$ | - |  230$\pm$ | ${}^{85}_{90}$ |  0.09$\pm$ | ${}^{0.06}_{0.01}$
H69 |  5.45$\pm$ | ${}^{0.13}_{0.11}$ |  40000$\pm$ | ${}^{4375}_{3250}$ |  4.03$\pm$ | ${}^{0.25}_{0.28}$ |  11.1$\pm$ | ${}^{0.5}_{0.6}$ |  -6.82$\pm$ | ${}^{0.80}_{1.60}$ | - |  155$\pm$ | ${}^{45}_{50}$ |  0.09$\pm$ | ${}^{0.05}_{0.01}$
H70 |  5.65$\pm$ | ${}^{0.16}_{0.08}$ |  43500$\pm$ | ${}^{6000}_{2750}$ |  4.17$\pm$ | ${}^{0.30}_{0.30}$ |  11.9$\pm$ | ${}^{0.5}_{0.7}$ |  -5.75$\pm$ | ${}^{0.13}_{0.16}$ | - |  145$\pm$ | ${}^{72}_{62}$ |  0.09$\pm$ | ${}^{0.09}_{0.01}$
H71 |  5.64$\pm$ | ${}^{0.16}_{0.23}$ |  51000$\pm$ | ${}^{7000}_{8500}$ |  3.98$\pm$ | ${}^{0.20}_{0.25}$ |  8.6$\pm$ | ${}^{0.8}_{0.5}$ |  -6.17$\pm$ | ${}^{0.25}_{1.30}$ | - |  100$\pm$ | ${}^{70}_{60}$ |  0.12$\pm$ | ${}^{0.14}_{0.04}$
H75 |  5.23$\pm$ | ${}^{0.13}_{0.16}$ |  38000$\pm$ | ${}^{4250}_{4250}$ |  4.40$\pm$ | ${}^{0.23}_{0.30}$ |  9.6$\pm$ | ${}^{0.7}_{0.5}$ |  -6.34$\pm$ | ${}^{0.28}_{0.85}$ |  0.80$\pm$ | ${}^{1.15}_{0.12}$ |  105$\pm$ | ${}^{78}_{55}$ |  0.09$\pm$ | ${}^{0.10}_{0.01}$
H78 |  5.45$\pm$ | ${}^{0.32}_{0.18}$ |  43500$\pm$ | ${}^{12500}_{6000}$ |  4.03$\pm$ | ${}^{0.42}_{0.30}$ |  9.4$\pm$ | ${}^{0.7}_{1.1}$ |  -5.87$\pm$ | ${}^{0.25}_{0.80}$ | - |  100$\pm$ | ${}^{85}_{100}$ |  0.09$\pm$ | ${}^{0.15}_{0.01}$
H80 |  5.17$\pm$ | ${}^{0.07}_{0.11}$ |  36000$\pm$ | ${}^{2125}_{3000}$ |  3.92$\pm$ | ${}^{0.17}_{0.28}$ |  9.9$\pm$ | ${}^{0.5}_{0.3}$ |  -6.42$\pm$ | ${}^{0.15}_{1.03}$ | - |  125$\pm$ | ${}^{48}_{35}$ |  0.09$\pm$ | ${}^{0.05}_{0.01}$
H86 |  5.38$\pm$ | ${}^{0.14}_{0.11}$ |  45500$\pm$ | ${}^{5500}_{4000}$ |  3.88$\pm$ | ${}^{0.35}_{0.23}$ |  7.9$\pm$ | ${}^{0.4}_{0.5}$ |  -5.75$\pm$ | ${}^{0.10}_{0.15}$ | - |  210$\pm$ | ${}^{55}_{98}$ |  0.09$\pm$ | ${}^{0.07}_{0.01}$
H90 |  5.34$\pm$ | ${}^{0.19}_{0.17}$ |  41500$\pm$ | ${}^{7250}_{5000}$ |  4.12$\pm$ | ${}^{0.28}_{0.25}$ |  9.1$\pm$ | ${}^{0.7}_{0.7}$ |  -6.62$\pm$ | ${}^{0.70}_{0.90}$ | - |  75$\pm$ | ${}^{78}_{75}$ |  0.09$\pm$ | ${}^{0.07}_{0.01}$
H92 |  5.38$\pm$ | ${}^{0.13}_{0.13}$ |  43500$\pm$ | ${}^{5000}_{4500}$ |  4.20$\pm$ | ${}^{0.30}_{0.25}$ |  8.7$\pm$ | ${}^{0.5}_{0.5}$ |  -6.62$\pm$ | ${}^{0.55}_{1.40}$ | - |  85$\pm$ | ${}^{68}_{60}$ |  0.10$\pm$ | ${}^{0.11}_{0.01}$
H94 |  5.66$\pm$ | ${}^{0.10}_{0.23}$ |  54000$\pm$ | ${}^{4500}_{9000}$ |  4.22$\pm$ | ${}^{0.30}_{0.35}$ |  7.8$\pm$ | ${}^{0.7}_{0.3}$ |  -6.19$\pm$ | ${}^{0.25}_{1.00}$ | - |  180$\pm$ | ${}^{75}_{90}$ |  0.10$\pm$ | ${}^{0.15}_{0.01}$
H143 |  5.29$\pm$ | ${}^{0.19}_{0.20}$ |  43500$\pm$ | ${}^{7000}_{6500}$ |  3.95$\pm$ | ${}^{0.45}_{0.45}$ |  7.9$\pm$ | ${}^{0.7}_{0.6}$ |  -6.20$\pm$ | ${}^{0.28}_{0.95}$ | - |  250$\pm$ | ${}^{55}_{110}$ |  0.10$\pm$ | ${}^{0.21}_{0.01}$