# The NLTE Analyses of Carbon Emission Lines in the Atmospheres of O and B
type Stars

Sofya Alexeeva  Shandong Provincial Key Laboratory of Optical Astronomy and
Solar-Terrestrial Environment, Institute of Space Sciences, Shandong
University, Weihai 264209, China
<EMAIL_ADDRESS>Kozo Sadakane  Astronomical Institute, Osaka Kyoiku
University, Asahigaoka, Kashiwara-shi, Osaka 582-8582, Japan
Masayoshi Nishimura  2-6, Nishiyama-Maruo, Yawata-shi, Kyoto 614-8353, Japan
Junju Du  Shandong Provincial Key Laboratory of Optical Astronomy and Solar-
Terrestrial Environment, Institute of Space Sciences, Shandong University,
Weihai 264209, China
Shaoming Hu  Shandong Provincial Key Laboratory of Optical Astronomy and
Solar-Terrestrial Environment, Institute of Space Sciences, Shandong
University, Weihai 264209, China
<EMAIL_ADDRESS>
###### Abstract

We present a model atom for C i–C ii–C iii–C iv using the most up-to-date
atomic data and evaluated the non-local thermodynamic equilibrium (NLTE) line
formation in classical 1D atmospheric models of O-B-type stars. Our models
predict the emission lines of C ii 9903 Å and 18 535 Å to appear at effective
temperature $T_{\rm eff}$ $\geq$ 17 500 K, those of C ii 6151 Å and 6461 Å to
appear at $T_{\rm eff}$ $>$ 25 000 K, and those of C iii 5695, 6728–44,
9701–17 Å to appear at $T_{\rm eff}$ $\geq$ 35 000 K (log $g$=4.0). Emission
occurs in the lines of minority species, where the photoionization-
recombination mechanism provides a depopulation of the lower levels to a
greater extent than the upper levels. For C ii 9903 and 18 535 Å, the upper
levels are mainly populated from C iii reservoir through the Rydberg states.
For C iii 5695 and 6728–44 Å, the lower levels are depopulated due to photon
losses in UV transitions at 885, 1308, and 1426–28 Å which become optically
thin in the photosphere.

We analysed the lines of C i, C ii, C iii, and C iv for twenty-two O-B-type
stars with temperature range between 15 800 $\leq$ $T_{\rm eff}$ $\leq$ 38 000
K. Abundances from emission lines of C i, C ii and C iii are in agreement with
those from absorption ones for most of the stars. We obtained log
$\epsilon_{\rm C}$=8.36$\pm$0.08 from twenty B-type stars, that is in line
with the present-day Cosmic Abundance Standard. The obtained carbon abundances
in 15 Mon and HD 42088 from emission and absorption lines are 8.27$\pm$0.11
and 8.31$\pm$0.11, respectively.

non-LTE line formation, chemical abundance, stars

††journal: ApJ††software: DETAIL (Butler & Giddings, 1985), SynthV_NLTE
(Ryabchikova et al., 2016), BINMAG (Kochukhov, 2010, 2018)

##  1 Introduction

The spectra of the majority of main sequence B-type stars have absorption
lines of different chemical elements, which mainly form in the photosphere of
a star. Rapid development of observational techniques has resulted in dramatic
improvement of the quality of spectral observations. When spectrographs of
much higher resolution (R $>$ 30 000) became available, the phenomenon of
sharp and weak emission lines (WELs) of metals in optical spectra of B-type
stars was evident. WELs of C i, Mg ii, Al ii, Si ii, P ii, Ca ii, Cr ii, Mn
ii, Fe ii, Ni ii, Cu ii, and Hg ii were detected in the visible and near IR
spectral regions in the spectra of B-type stars (Sigut et al., 2000; Wahlgren
& Hubrig, 2000; Sadakane et al., 2001; Sigut, 2001a, b; Castelli & Hubrig,
2004; Wahlgren & Hubrig, 2004; Hubrig & González, 2007; Castelli & Hubrig,
2007; Alexeeva et al., 2016; Sadakane & Nishimura, 2017). Recently, Sadakane &
Nishimura (2019) published a detailed list of WELs observed in $\iota$ Her
(B3IV). Their list contains numerous previously unknown very weak WELs
originating from highly excited levels of Fe ii in the visual region, and an
emission line of C ii at 9903.46 Å.

The WELs originated from high-excitation states, are detected over a range of
element abundance and are found among both chemically-normal and chemically-
peculiar stars. What is the physical nature of WELs and whether they could be
used for abundance determination? Which processes do produce emission
component in these lines? These enigmatic features are still not well
understood.

In the literature, there are some examples of reproducing the observed
emission lines using standard plane-parallel non-local thermodynamic
equilibrium (NLTE) modeling. For example, Mg i 12 $\mu$m in the Sun (Carlsson
et al., 1992) and Procyon (Ryde et al., 2004), Mg i 12 and 18 $\mu$m in three
K giants (Sundqvist et al., 2008), Mg i 7 and 12 $\mu$m in the Sun and
Arcturus (Osorio et al., 2015), Mg i 7 and 12 $\mu$m in the Sun, Procyon and
three K giants (Alexeeva et al., 2018), Mn ii 6122–6132 Å in the three late-
type B stars (Sigut, 2001a), C ii 6151, 6462 Å in $\tau$ Sco (B0V) and C ii
6462 Å in HR 1861 (B1V), HR 3055 (B0III), and HR 2928 (B2II) (Nieva &
Przybilla, 2006, 2008), C i 8335, 9405, 9061–9111, and 9603–58 Å in 21 Peg
(B9.5V), $\pi$ Cet (B7IV), $\iota$ Her (B3IV) (Alexeeva et al., 2016), Ca ii
8912–27 and 9890 Å in $\iota$ Her (B3IV) (Sitnova et al., 2018).

One of the pioneer works regarding the interpretation of emission lines of C
iii in the spectra of O-type stars belongs to Sakhibullin et al. (1982). They
performed theoretical analyses of the C iii 9710 Å line by using plane-
pararell model atmospheres and NLTE approach and predicted the line to appear
in emission as a results of departures from LTE (among O-type stars). After
decades, the emission lines of C iii at 4647–50–51 and 5696 Å were predicted
theoretically in O-type stars in Martins & Hillier (2012) with using the code
cmfgen (Hillier & Miller, 1998) to compute NLTE models including winds, line-
blanketing and spherical geometry. Martins & Hillier (2012) found that a tight
coupling of the C iii 4647–50–51 and C iii 5696 Å lines to UV-transitions
regulates the population of the associated levels. Carneiro et al. (2018)
derived realistic carbon abundances by means of the NLTE atmosphere code
fastwind (Puls et al., 2005) with recently developed model atom C ii–C iii–C
iv. They investigated the spectra of a sample of six O-type dwarfs and
supergiants, and found in most cases a moderate depletion compared to the
solar value. In the literature, we can find no theoretical studies in which
emission line of the C ii 9903 Å, observed in B-type stars, and C i 8335,
9405, 9061–9111, and 9603–58 Å emission lines, observed in hotter B-type stars
(with $T_{\rm eff}$$>$17 500 K), are well reproduced.

Carbon is one of the most abundant elements in the Universe and the main
element in thermonuclear reactions. The determination of carbon abundances in
O-B-type stars is important for stellar and galactochemical evolution. There
are many NLTE studies of carbon in OB stars available in the literature from
the last decades, such as Gies & Lambert (1992); Cunha & Lambert (1994);
Andrievsky et al. (1999); Daflon et al. (1999, 2001b, 2001a, 2004a, 2004b);
Hunter et al. (2009); Nieva & Przybilla (2012); Martins et al. (2015a, b,
2017). Several model atoms of carbon were constructed and several independent
codes were used to perform the analyses.

Carbon lines in the visible spectral region can be measured over a wide range
of effective temperatures up to 55 000 K. In the low-resolution spectroscopy,
the strongest features in the metal line spectra are demanded for study. In
the case of carbon, the C ii 4267 and C iii 4647 Å lines are strong in B-type
stars, and C iii 5695 and C iv 5801, 5811 Å in O-type stars. These lines can
be used as abundance indicators even in low-resolution spectroscopy. It should
be noticed that the C iii 5695 Å line can be a good gravity indicator, since
it strongly depends on luminosity classes (and surface gravity), that was
pointed out in the spectroscopic atlas of O-B stars of Walborn (1980) and
theoretical analyses of Carneiro et al. (2018). However, these lines are
highly sensitive not only to the choice of stellar atmospheric parameters but
also to the NLTE effects. For example, Lyubimkov et al. (2013) found that for
stars with $T_{\rm eff}$ between 20 000 and 24 000 K the C ii 4267 Å line to
give lower log $\epsilon_{\rm C}$ values, and the underestimation amounts to
0.20–0.70 dex. A tendency of the 4267 Å line to yield lower values of log
$\epsilon_{\rm C}$ for B stars has been noted in earlier studies, e.g. Gies &
Lambert (1992); Kilian (1992); Sigut (1996). Nieva & Przybilla (2006) and
Nieva & Przybilla (2008) presented a solution to the long-standing discrepancy
between NLTE analyses of the C ii 4267 and 6578/82 Å multiplets in six slowly-
rotating early B-type dwarfs and giants, which cover a wide parameter range.
Their comprehensive NLTE model atom of C ii/ iii/ iv was constructed with
critically selected atomic data and calibrated with high-SN spectra.

The aims of our work are $(1)$ to treat the method of accurate abundance
determination in O-B stars from different carbon lines of four ionization
stages, C i, C ii, C iii, and C iv based on NLTE line formation; $(2)$ to
present the modeling of C i, C ii and C iii emission lines in the spectra of
O-B-type stars and an interpretation of these lines in the NLTE framework,
including C ii 9903 Å emission lines, which were not reported before; $(3)$ to
eliminate the significant discrepancy between C ii 4267 Å and other C ii lines
with future possibility applying it in both high- and low-resolution
spectroscopy; $(4)$ and check the reliability of C i, C ii and C iii emission
lines in carbon abundance determination.

We construct a comprehensive model atom for C i–C ii–C iii–C iv using the most
up-to-date atomic data available so far, and analyse lines of C i, C ii, C
iii, and C iv in high-resolution spectra of reference B- and O-type stars with
well-known stellar parameters. We focus on carbon emission lines, C i 8335,
9405, 9061–9111, and 9603–58 Å, C ii 9903 Å, and C iii 5695, 6744, 9710 Å in
the spectra of O-B-type stars, trying to reproduce them along with absorption
ones using the uniformly presented model atom for C i–C ii–C iii–C iv.

The paper is organized as follows. Section 2 describes an updated model atom
of C i–C ii–C iii–C iv, discusses departures from LTE in the model atmospheres
of O and B-type stars, and investigates mechanisms of producing the C ii–C iii
emission lines. In Section 3, we analyse the carbon absorption and emission
lines observed in a sample of twenty B-type stars and two O stars. We
determine the C abundance of the selected stars, make some discussions and
compare our results with other studies from literature. Our conclusions are
summarized in Section 4.

##  2 NLTE Line formation for C ii – C iii

###  2.1 Model atom and atomic data

Energy levels. The term structures of C i and C ii were described in detail in
Alexeeva & Mashonkina (2015) and Alexeeva et al. (2016), respectively. Here,
the model atom was updated by extending levels of C ii with $n$ = 7–10,
$l$=6–8, C iii levels belonging to singlet and triplet terms of the 1s22p $nl$
($n$ = 3–4, $l$=0–2), 1s22s $nl$ ($n$ = 3–10, $l$=0–2), 1s22s $n$f ($n$ =
4–10), 1s22s $n$g ($n$ = 5–10), 1s22s2, 1s22p2 electronic configurations, C iv
levels belonging to doublet terms of the 1s2 $nl$ ($n$ = 2–6, $l$=0–1), 1s2
$n$d ($n$ = 3–6), 1s2 $n$f ($n$ = 4–6), 1s2 5g electronic configurations. Fine
structure splitting was taken into account everywhere up to $n$ = 5 for C i
and C ii, but the fine structure was neglected for C iii and C iv levels. Most
energy levels were taken from the NIST database
111https://www.nist.gov/pml/atomic-spectra-database (Kramida et al., 2018).
The term diagrams for C ii and C iii are shown in Fig. 1 and Fig. 2,
respectively.

Radiative and collisional data.

C i: Radiative and collisional data for C i were described in detail in
Alexeeva et al. (2016).

C ii: The transition probabilities were taken from the NIST and VALD
222http://vald.astro.uu.se/~vald/php/vald.php (Kupka et al., 1999) data bases,
where available, and the Opacity Project (OP) data base TOPbase
333http://cdsweb.u-strasbg.fr/topbase/topbase.html (Luo et al., 1989; Cunto et
al., 1993; Hibbert et al., 1993) except for the transitions between levels
with $n$ = 7$-$10 and $l$ = 6$-$8, for which oscillator strengths were
calculated following Green et al. (1957). Photo-ionization cross sections for
levels with $n\leq 10$, $l\leq 3$ were taken from TOPbase, and for levels $n$g
($n$ = 5–9) relevant data were adopted from NORAD-Atomic-Data web-page
444http://norad.astronomy.ohio-state.edu/ (Nahar, 1995). For C ii levels with
$n$ = 7–10, $l$ = 5–8, we adopted the hydrogen-like cross sections. For the
transitions connecting the 30 lowest fine-structure levels in C ii, we used
the effective collision strengths from Wilson et al. (2005). The remaining
transitions in both C ii and C iii were treated using an approximation formula
of van Regemorter (1962) for the allowed transitions and assuming the
effective collision strength $\Omega_{ij}$ = 1 for the forbidden transitions.
Threshold photoionization cross sections were adopted from TOPbase and Nahar
(1995), with empirical correction of one order of magnitude higher for the 6f
2Fo and 6g 2G levels following by Nieva & Przybilla (2008).

C iii: The transition probabilities were taken from TOPbase. Photo-ionization
cross sections for levels of C iii were adopted from NORAD-Atomic-Data web-
page (Nahar & Pradhan, 1997). For electron-impact excitation of all the
transitions between the lowest 98 energy levels of C iii (up to 1s22s 7d), we
adopted recent accurate collisional data from Fernández-Menchero et al.
(2014), which are available in the archives of APAP (Atomic Processes for
Astrophysical Plasmas) Network 555http://www.apap-network.org/.

C iv: The transition probabilities were adopted from NIST. Effective collision
strengths for transitions between the lowest nine terms (up to 1s2 4f) were
adopted from Griffin et al. (2000) and downloaded from APAP Network. Photo-
ionization cross sections of ground and excited states of C iv were taken from
NORAD-Atomic-Data web-page (Nahar & Pradhan, 1997).

Ionization by electronic collisions was everywhere treated through the Seaton
(1962) classical path approximation with threshold photoionization cross
sections from OP and Nahar (1995); Nahar & Pradhan (1997).

Figure 1: Term diagram for C ii with extended levels. The dashed lines
indicate the transitions, from which the investigated spectral lines arise.
Figure 2: Term diagram for C iii. The dashed lines indicate the transitions,
from which the investigated spectral lines arise.

###  2.2 Method of calculations

To solve the radiative transfer and statistical equilibrium equations, we used
the code detail (Butler & Giddings, 1985) based on the accelerated
$\Lambda$-iteration method (Rybicki & Hummer, 1991). The detail opacity
package was updated by Przybilla et al. (2011) by including bound-free
opacities of neutral and ionized species. We then used the code synthV_NLTE
(Ryabchikova et al., 2016) to calculate the synthetic NLTE line profiles with
the obtained departure coefficients, $b_{\rm{i}}$ = $n_{\rm{NLTE}}$ /
$n_{\rm{LTE}}$. Here, $n_{\rm{NLTE}}$ and $n_{\rm{LTE}}$ are the statistical
equilibrium and thermal (Saha-Boltzmann) number densities, respectively.
Comparison with the observed spectrum and spectral line fitting were performed
with the binmag code666http://www.astro.uu.se/~oleg/binmag.html (Kochukhov,
2010, 2018). For consistency, the calculations were performed with plane-
parallel (1D), chemically homogeneous model atmospheres from the Kurucz’s
grid777http://www.oact.inaf.it/castelli/castelli/grids.html (Castelli &
Kurucz, 2003) for all stars, including two late O-type stars. We suppose that
for O-type stars, the spherical and hydrodynamic NLTE atmospheres would be
more physically justified. However, our two O-type stars are unevolved (log
$g$ = 3.84 and 4.00) with the simple photospheric physics. They must be
unaffected by strong stellar winds unlike the hotter and more luminous
supergiants. As for NLTE models, Nieva & Przybilla (2007) demonstrated that,
at least, in the range of 20 000 $\leq$ $T_{\rm eff}$ $\leq$ 35 000 K and 3.0
$\leq$ log $g$ $\leq$ 4.5, the hybrid NLTE approach (LTE model atmosphere plus
NLTE line formation) is equivalent to full hydrostatic NLTE computations.
Although, the temperatures of our O-type stars are higher by $\sim$ 3000 K
compared to investigated limit of Nieva & Przybilla (2007), we believe that it
will not affect the final results too much.

Table 1 lists lines of C i, C ii, C iii, and C iv used in line formation
analyses together with the adopted line data. Oscillator strengths were taken
from the NIST database (Kramida et al., 2018). For most lines, Stark
collisional data are adopted from the VALD data base.

Table 1: Lines of C i, C ii, C iii, and C iv used in our analysis.  $\lambda$ | Transition | $E_{\rm exc}$ | log $gf$
---|---|---|---
Å |  | eV |
C i |  |  |
9078.28 | 3s 3Po – 3p 3P | 7.48 |  $-$0.581
9088.51 | 3s 3Po – 3p 3P | 7.48 |  $-$0.43
9094.83 | 3s 3Po – 3p 3P | 7.49 |  0.151
9111.80 | 3s 3Po – 3p 3P | 7.49 |  $-$0.297
9405.73 | 3s 1Po – 3p 1D | 7.49 |  0.286
9658.43 | 3s 3Po – 3p 3S | 7.49 |  $-$0.280
C ii |  |  |
3918.96 | 3p 2Po – 4s 2S | 16.33 |  $-$0.533
3920.68 | 3p 2Po – 4s 2S | 16.33 |  $-$0.232
4267.00 | 3d 2D – 4f 2Fo | 18.05 |  0.563
4267.26 | 3d 2D – 4f 2Fo | 18.05 |  0.716
4267.26 | 3d 2D – 4f 2Fo | 18.05 |  $-$0.584
5132.95 | 2p3s 4Po – 2p3p 4P | 20.70 |  $-$0.211
5133.28 | 2p3s 4Po – 2p3p 4P | 20.70 |  $-$0.178
5137.25 | 2p3s 4Po – 2p3p 4P | 20.70 |  $-$0.911
5139.17 | 2p3s 4Po – 2p3p 4P | 20.70 |  $-$0.707
5143.49 | 2p3s 4Po – 2p3p 4P | 20.70 |  $-$0.212
5145.16 | 2p3s 4Po – 2p3p 4P | 20.71 |  0.189
5151.09 | 2p3s 4Po – 2p3p 4P | 20.71 |  $-$0.179
5648.07 | 3s 4Po – 3p 4S | 20.70 |  $-$0.424
5662.47 | 3s 4Po – 3p 4S | 20.70 |  $-$0.249
6151.26 | 4d 2D – 6f 2Fo | 20.84 |  $-$0.164
6151.53 | 4d 2D – 6f 2Fo | 20.84 |  $-$1.310
6151.53 | 4d 2D – 6f 2Fo | 20.84 |  $-$0.009
6461.94 | 4f 2Fo – 6g 2G | 20.95 |  0.161
6461.94 | 4f 2Fo – 6g 2G | 20.95 |  0.048
6461.94 | 4f 2Fo – 6g 2G | 20.95 |  $-$1.383
6578.05 | 3s 2S – 3p 2Po | 14.45 |  $-$0.021
6582.88 | 3s 2S – 3p 2Po | 14.45 |  $-$0.323
6779.94 | 3s 4Po – 3p 4D | 20.70 | 0.025
6780.59 | 3s 4Po – 3p 4D | 20.70 |  $-$0.377
6783.90 | 3s 4Po – 3p 4D | 20.70 |  0.304
6800.68 | 3s 4Po – 3p 4D | 20.70 |  $-$0.343
9903.46 | 4f 2Fo – 5g 2G | 20.95 |  $-$0.523
9903.46 | 4f 2Fo – 5g 2G | 20.95 |  0.908
9903.46 | 4f 2Fo – 5g 2G | 20.95 |  1.021
18 535.94 | 5g 2G – 6h 2Ho | 22.20 |  1.217
18 535.94 | 5g 2G – 6h 2Ho | 22.20 |  1.129
18 535.94 | 5g 2G – 6h 2Ho | 22.20 |  $-$0.515
C iii |  |  |
4056.06 | 4d 1D – 5f 1Fo | 40.19 |  0.267
4152.51 | 3p 3D – 5f 3Fo | 40.05 |  $-$0.112
4162.86 | 3p 3D – 5f 3Fo | 40.06 |  0.218
4516.00 | 4p 3Po – 5s3S | 39.40 |  $-$0.058
4647.42 | 3s 3S – 3p 3Po | 29.53 |  0.070
4650.25 | 3s 3S – 3p 3Po | 29.53 |  $-$0.151
4651.47 | 3s 3S – 3p 3Po | 29.53 |  $-$0.629
4652.05 | 3s 3Po – 3p 3P | 38.21 |  $-$0.432
4663.64 | 3s 3Po – 3p 3P | 38.21 |  $-$0.530
4665.86 | 3s 3Po – 3p 3P | 38.22 |  0.044
5695.92 | 3p 1Po – 3d 1D | 32.10 |  0.017
6731.04 | 3s 3Po – 3p 3D | 38.22 |  $-$0.293
6744.39 | 3s 3Po – 3p 3D | 38.22 |  $-$0.022
7037.25 | 3s 1Po – 4d 1D | 38.44 |  0.443
8500.32 | 3s 1S – 3p 1Po | 30.64 |  $-$0.484
9705.41 | 3p 3Po – 3d 3D | 32.20 |  $-$0.378
9706.44 | 3p 3Po – 3d 3D | 32.20 |  $-$0.855
9715.09 | 3p 3Po – 3d 3D | 32.20 |  $-$0.107
9717.75 | 3p 3Po – 3d 3D | 32.20 |  $-$0.855
C iv |  |  |
5801.31 | 3s 2S – 3p 2Po | 37.55 |  $-$0.194
5811.97 | 3s 2S – 3p 2Po | 37.55 |  $-$0.495

###  2.3 Departures from LTE for C ii – C iii in B-type star

Figure 3: Ionization fractions of C i, C ii, C iii, and C iv in the model
atmospheres of different effective temperatures.

Figure 4: Departure coefficients for the C ii and C iii levels as a function
of $\log\tau_{Ross}$ in the model atmospheres with $T_{\rm eff}$/log $g$ =
20750 / 3.8; 26100/ 4.25; 32000 / 4.3; and 38000 / 4.0. The vertical lines
indicate the formation depths of cores of individual lines.

Figure 5: Departure coefficients for the C iv levels as a function of
$\log\tau_{Ross}$ in the model atmospheres with $T_{\rm eff}$/log $g$ = 32000
/ 4.3; and 38000 / 4.0.

Figure 3 displays the ionization fraction of different carbon ions C i, C ii,
C iii, and C iv in stellar atmospheres of different effective temperatures. In
the atmospheres with $T_{\rm eff}$ $\lesssim$ 32 000 K, C iii is the dominant
ionization stage in the line-formation region, while C iv becomes the major
species in the hotter atmospheres.

Figures 4 and 5 show the departure coefficients for the selected levels in the
model atmospheres with $T_{\rm eff}$/log $g$ = 20 750 / 3.8, 26 100 / 4.25, 32
000 / 4.3, and 38 000 / 4.0. The departure coefficients are equal to unity
deep in the atmosphere, where the gas density is large and collisional
processes dominate, enforcing the LTE.

In the models 20 750 / 3.8, 26 100 / 4.25, and 32 000 / 4.3, the NLTE leads to
depleted populations of the C ii levels because of UV overionization, while in
the last two models the C iii ground state is close to the TE population,
since doubly ionized carbon dominates the element abundance outwards log
$\tau_{Ross}=0$.

In the model 20 750 / 3.8, outward of log $\tau_{Ross}=-0.2$, the C iii ground
state is overpopulated via photoionization processes C ii\+ h$\nu$
$\rightarrow$ C iii+e-, and the overpopulation is extended to the remaining C
iii levels due to their coupling to the ground state. In hotter atmospheres 26
100 / 4.25 and 32 000 / 4.3, spontaneous transitions dominate, resulting in a
depopulation of the C iii levels, while the C iii ground state keeps its LTE
populations.

In the model 38 000 / 4.0, outward of log $\tau_{Ross}=0.3$, NLTE leads to
depleted populations of the C ii and C iii levels because of UV
overionization, while the C iv ground state almost keeps its LTE populations.

Analysis of the departure coefficients of the lower (bl) and upper (bu) levels
at the line-formation depths allows to understand NLTE effects for a given
spectral line. If b${}_{l}>$ 1 and (or) the line source function is smaller
than the Planck function, that is, b${}_{l}>$ bu, a NLTE strengthening of
lines occurs. The carbon lines of four ionization stages are listed in Table
1.

C ii 4267 Å This line, arising from 3d 2D – 4f 2Fo, is strong. In the 20 750 /
3.8 model, its core forms at atmospheric depths ($\log\tau_{Ross}=-1.2$)
dominated by overionization of C ii, resulting in the weakened line and
positive abundance correction, $\Delta_{\rm NLTE}$ = log$\epsilon_{\rm NLTE}$
\- log$\epsilon_{\rm LTE}$, which equals to +0.25 dex. In the model 26 100 /
4.25, the line shifts to the outer layers, where the deviations from LTE are
strong and abundance correction amounts to +0.77 dex. While in the model 32
000 / 4.3, the line shifts to the inner layers and $\Delta_{\rm NLTE}$ = +0.33
dex.

C ii 6151, 6461 Å These lines, arising from 4d 2D – 6f 2Fo, 4f 2Fo – 6g 2G,
are weak and their cores form at atmospheric depths around
$\log\tau_{Ross}=-0.75$ in the models 20 750 / 3.8, 26 100 / 4.25, and 32 000
/ 4.3, where b${}_{l}<$ bu and b${}_{l}<$1, that leads to weakening of these
lines. The abundance corrections for C ii 6151 Å are $\Delta_{\rm NLTE}$ =
+0.28, +1.19 dex in the 20 750 / 3.8, 26 100 / 4.25 models, respectively,
while it appears as weak emission line in 32 000 / 4.3. For C ii 6461 Å,
$\Delta_{\rm NLTE}$ = +0.38 dex in the 20 750 / 3.8, while this line appears
as emission in the hotter models.

C ii 6582 Å This line, together with 6578, arising from 3s 2S – 3p 2Po, is
strong and in the model 20 750 / 3.8 its core forms around
$\log\tau_{Ross}=-2.0$, where the departure coefficient of the upper level 3p
2Po drops rapidly. This results in dropping the line source function below the
Planck function and enhancing absorption in the line core. In contrast, in the
line wings, absorption is weaker compared with the LTE case due to overall
overionization. As a result the abundance correction is slightly negative
$-$0.16 dex. In the 26 100 / 4.25 and 32 000 / 4.3 models, the overionization
of C ii leads to weakening of these lines and results in positive abundance
corrections, +0.45 and +0.22 dex, respectively. Moreover, these lines are
lying in the wing of the H$\alpha$ line at 6563Å. This makes the formation of
these lines very sensitive to modeling of the hydrogen line formation.

C ii 9903 Å This line, arising from 4f 2Fo – 5g 2G, is strong. In the line
formation region, $\log\tau_{Ross}\sim-1.25$, b${}_{l}<$ bu and b${}_{l}<$1,
that leads to weakening of the line. It appears as an emission line in the
presented models with $T_{\rm eff}$ from 17 500 to 33 400 K, and disappears
when $T_{\rm eff}$ is higher than 33 400 K.

C iii 4650 Å This line, as with 4647 Å and 4651 Å lines, arising from 3s 3S –
3p 3Po, is strong and in the models 20 750 / 3.8, 26 100 / 4.25, and 32 000 /
4.3, b${}_{l}>$ bu in the line formation region and the line source function
drops below the Planck function resulting in strengthened lines and negative
NLTE abundance corrections of $\Delta_{\rm NLTE}$ = $-$0.23 dex, $-$0.33 dex,
$-$0.61 dex respectively. In the model 38 000 / 4.0 b${}_{l}<$ bu in the line
formation region, which leads to weakening of the line and $\Delta_{\rm NLTE}$
= $+$0.64 dex.

C iii 5695 Å The line, arising from 3p 1Po – 3d 1D, is strong. Its core forms
at atmospheric depths around $\log\tau_{Ross}=-1.0$. The line has slightly
negative abundance correction, $-$0.12, in the model 26 100 / 4.25 and
slightly positive one, +0.06 dex, in 32 000 / 4.3. In the model 38 000 / 4.0,
the line formation region moves to inner layers, where b${}_{l}<$ bu, and
b${}_{l}<$1, and the line appears in emission.

C iv 5811 Å This line and 5801 Å arising from 3s 2S – 3p 2Po, appear to be
stronger in the hotter atmospheres. In the line formation region b${}_{l}>$ bu
that results in strengthened line and negative NLTE abundance correction of
$\Delta_{\rm NLTE}$ = $-$0.37 dex in the model 32 000 / 4.3. In a hotter
model, 38 000 / 4.0, line formation region moves to outer layers (Fig. 5),
where the departures from LTE are stronger. So, in the model 38 000 / 4.0 the
NLTE abundance correction is $-$1.29 dex.

###  2.4 C i emission lines

The mechanisms driving the C i emission were described in details in Alexeeva
et al. (2016). Our NLTE calculations predicted that C i emission lines to
appear at effective temperature from 9250 to 10 500 K depending on log $g$.
They are near IR C i lines at 8335 Å (3s 1Po – 3p 1S) and 9405 Å (3s 1Po – 3p
1D) singlet lines and at higher temperature, $T_{\rm eff}$$>$ 15 000 K (log
$g$ = 4), in the 9061–9111 Å (3s 3Po – 3p 3P), and 9603–9658 Å (3s 3Po – 3p
3S) triplet lines. Having appeared at specific $T_{\rm eff}$/log $g$, the
emission is strengthened towards higher temperature, reaches its maximum and
disappears at about $T_{\rm eff}$$=$ 22 000 K (in the case of log $g$ = 3).

###  2.5 C ii emission lines

Our NLTE calculations in the grid of model atmospheres with 18 000 K $\leq$
$T_{\rm eff}$ $\leq$ 35 000 K and log $g$ = 4 predict that C ii lines at 6151
Å (4d 2D – 6f 2Fo), 6461 Å (4f 2Fo – 6g 2G), 9903 Å (4f 2Fo – 5g 2G), and 18
535 Å (5g 2G – 6h 2Ho) may appear as emission lines depending on the
atmospheric parameters (Fig. 6). The NET rates, that were calculated as NET =
$n_{\rm{l}}$($R_{\rm{lu}}$ \+ $C_{\rm{lu}}$)$-$$n_{\rm{u}}$ ($R_{\rm{ul}}$ \+
$C_{\rm{ul}}$), allow to know what processes in C ii do drive the emission in
the lines. Here, $R_{\rm{lu}}$ and $C_{\rm{lu}}$ are radiative and collisional
rates, respectively, for the transition from low to upper level, and
$R_{\rm{ul}}$ and $C_{\rm{ul}}$ for the inverse transition. The upper levels
of the investigated transitions, 6f 2Fo, 5g 2G, 6g 2G, 6h 2Ho, are mainly
populated by recombination from C iii and cascade transitions from Rydberg
states, while the low-excitation levels (4d 2D and 4f 2Fo) have depleted
populations due to photon losses in the lines of C ii arising from the
transitions 3p 2Po – 4d 2D (2746 Å) and 3d 2D – 4f 2Fo (4267 Å). Extra
depopulation of the level 4f 2Fo is caused by overionization. These mechanisms
result in a depopulation of the lower levels to a greater extent than the
upper levels and are responsible for the emission phenomenon. Test
calculations with the model atom, where the Rygberg states ($l>$6) were not
included, demonstrate the decrease of the relative flux at the line center of
C ii 9903 Å from 1.30 to 1.06 in the model atmosphere 26 100 / 4.25. It
demonstrates a crucial role of these Rygberg states in emission phenomenon at
C ii 9903 Å.

###  2.6 C iii emission lines

Our NLTE calculations predict that the emission lines of C iii at 5695 Å (3p
1Po – 3d 1D) and those of 6727–6762 Å (3s 3Po – 3p 3D) and 9705–9717 Å (3p 3Po
– 3d 3D) to appear at effective temperature $T_{\rm eff}$$>$ 35 000 K (log $g$
= 4). The emission line of C iii 7037 Å (3s 1Po – 4d 1D) appears at effective
temperature $T_{\rm eff}$$>$ 37 000 K (log $g$ = 4) (Fig. 6). The analysis of
NET values and test calculations show that the photoionization-recombination
mechanisms play a crucial role in emission line formation. The lower levels of
investigated transitions, 3p 1Po, 3s 3Po, and 3p 3Po, are depopulated due to
ionization, while the upper levels, 3d 1D, 3p 3D, and 3d 3D are populated due
to recombination from C iv reservoir. Extra depopulation of the levels 3p 1Po
and 3s 3Po is caused by photon losses in UV transitions 2p2 1D – 3p 1Po (885
Å), 2p2 1S – 3p 1Po (1308 Å), 3s 3S – 3s 3Po (1426 – 1428 Å). The upper level
3d 3D is effectively populated due to transitions 3d 3D – 3d 3Fo (1577 Å) and
3d 3D – 4f 3Fo (1923 Å).

On the base of the structure of terms (Fig. 2), the C iii 9705–9717 Å triplet
lines are similar to the 5695 Å singlet line. The intensity of emission line
at 9705–9717 Å is higher than 5695 Å. There are two reasons for the
difference: its position in the near-IR region, where the continuum flux is
lower, and the line formation region of 9705–9717 Å is located closer to outer
layers (Fig. 4), where the deviations from LTE are stronger.

Figure 6: Evolutions of the C ii 6151, 6461, 9903, and 18 535 Å, and C iii
5695, 6744, 7037 and 9715 Å, line profiles with the effective temperature. In
every cases, we assume A(C)=8.43, $v$ sin $i$ = 10 km s-1, and $\xi_{t}$ = 2
km s-1. The theoretical spectra are convolved with an instrumental profile of
R = 50 000.

##  3 Carbon lines in the selected stars

###  3.1 Stellar sample, Observations, and stellar parameters

We analyse high resolution spectral data of 22 stars listed in Table 2. The
sample contains 20 B-type stars (ranging in spectral types from B3 to B0) and
two O-type stars. All of these stars show relatively sharp spectral lines
(slowly rotating). Atmospheric parameters of 20 B-type stars are taken from
Nieva & Przybilla (2012) or from Nieva & Simón-Díaz (2011). Those of 15 Mon
(HD 47839) and HD 42088 are taken from Markova et al. (2004) and from Martins
et al. (2015c), respectively.

Spectral data from the visible to near IR spectral ranges were obtained with
the Echelle Spectro Polarimetric Device for the Observation of Stars
(ESPaDOnS) (Donati et al., 2006) attached to the 3.6 m telescope of the
Canada-France-Hawaii Telescope (CFHT) observatory located on the summit of
Mauna Kea,
Hawaii888http://www.cfht.hawaii.edu/Instruments/Spectroscopy/Espadons/.
Observations with this spectrograph cover the region from 3690 to 10480 Å, and
we use data from 3855 to 9980 Å in the present study. The resolving power is
$\it R$ = 65 000. Calibrated intensity spectral data were extracted from the
ESPaDOnS archive through Canadian Astronomical Data Centre (CADC).

After averaging downloaded individual spectral data of each star, we converted
the wavelength scale of spectral data of each star into the laboratory scale
using measured wavelengths of five He i lines (4471.48, 4713.15, 4921.93,
5015.68, and 5875.62 Å). In the case of O-type stars, we add measured
wavelengths of two He ii lines (4685.68 Å and 5411.52 Å). Errors in the
wavelength measurements are around $\pm$ 3 km s-1 or smaller. Re-fittings of
the continuum level of each spectral order were carried out using polynomial
functions. The signal-to-noise ratios (SN) measured at the continuum near 5550
Å range from 380 to 1800. Five stars among the sample show very high qualities
(SN ratio higher than 1000).

Table 2: Atmospheric parameters of the selected stars, SN ratio, and sources
of the data.

Number | Star | Name | Sp. T. | $T_{\rm eff}$ | log $g$ | $\xi_{t}$ | $V_{mac}$ |  $v$ sin $i$ | SN | Ref.
---|---|---|---|---|---|---|---|---|---|---
|  |  |  | K | CGS | km s-1 | km s-1 | km s-1 |  |
1 | HD 209008 | 18 Peg | B3 III | 15 800 | 3.75 | 4 | 10 | 15 | 710 | 1
2 | HD 160762 |  $\iota$ Her | B3 IV | 17 500 | 3.80 | 1 |  | 6 | 1820 | 1
3 | HD 35912 | HR 1820 | B2-3 V | 19 000 | 4.00 | 2 | 8 | 15 | 650 | 2
4 | HD 36629 | HIP 26000 | B2 V | 20 300 | 4.15 | 2 | 5 | 10 | 630 | 2
5 | HD 35708 |  $o$ Tau | B2.5 IV | 20 700 | 4.15 | 2 | 17 | 25 | 820 | 1
6 | HD 3360 |  $\zeta$ Cas | B2 IV | 20 750 | 3.80 | 2 | 12 | 20 | 1570 | 1
7 | HD 122980 |  $\chi$ Cen | B2 V | 20 800 | 4.22 | 3 |  | 18 | 520 | 1
8 | HD 16582 |  $\delta$ Cet | B2 IV | 21 250 | 3.80 | 2 | 10 | 15 | 1050 | 1
9 | HD 29248 |  $\nu$ Eri | B2 II | 22 000 | 3.85 | 6 | 15 | 26 | 550 | 1
10 | HD 886 |  $\gamma$ Peg | B2 IV | 22 000 | 3.95 | 2 | 8 | 9 | 1110 | 1
11 | HD 74575 |  $\alpha$ Pix | B1.5 III | 22 900 | 3.60 | 5 | 20 | 11 | 800 | 1
12 | HD 35299 | HR 1781 | B2 III | 23 500 | 4.20 | 0 |  | 8 | 380 | 1
13 | HD 36959 | HR 1886 | B1 V Ic | 26 100 | 4.25 | 0 | 5 | 12 | 860 | 2
14 | HD 61068 | HR 2928 | B2 II | 26 300 | 4.15 | 3 | 20 | 14 | 560 | 1
15 | HD 36591 | HR 1861 | B2 III | 27 000 | 4.12 | 3 |  | 12 | 720 | 1
16 | HD 37042 |  $\theta^{2}$ Ori B | B0.5 V | 29 300 | 4.30 | 2 | 10 | 30 | 690 | 2
17 | HD 36822 |  $\phi^{1}$ Ori | B0.5 III | 30 000 | 4.05 | 8 | 18 | 28 | 570 | 1
18 | HD 34816 |  $\lambda$ Lep | B0.5 V | 30 400 | 4.30 | 4 | 20 | 30 | 550 | 1
19 | HD 149438 |  $\tau$ Sco | B0.2 V | 32 000 | 4.30 | 5 | 4 | 4 | 1730 | 1
20 | HD 36512 |  $\upsilon$ Ori | B0 V | 33 400 | 4.30 | 4 | 10 | 20 | 700 | 1
21 | HD 47839 | 15 Mon | O7 V | 37 500 | 3.84 | 12 | 65∗ | 62 | 560 | 3
22 | HD 42088 |  | O6 V | 38 000 | 4.00 | 12∗∗ | 37 | 41 | 820 | 4

Note. — Note. References: 1 Nieva & Przybilla (2012); 2 Nieva & Simón-Díaz
(2011); 3 Markova et al. (2004); 4 Martins et al. (2015c). ∗ Simón-Díaz et al.
(2017) ; ∗∗ Holgado et al. (2018). Spectral types are extracted from the
SIMBAD database. (10) Measured SN ratio near 5550 Å.

Figure 7: Best NLTE fits (solid curves) of C i 9405 Å in $\iota$ Her, HIP
26000, $\zeta$ Cas, and $\chi$ Cen. The observed spectra are shown by open
circles.

Figure 8: Best NLTE fits (solid curves) of C ii 4267, 6151, 6461, and 9903 Å
in the program stars (from left to right). The observed spectra are shown by
open circles.

###  3.2 Determination of carbon abundances in B-stars

In this section, we derive the carbon abundances of the selected B-stars from
emission C i, emission and absorption C ii and absorption C iii lines using
the atomic data from Table 1. In Table 3, we show the NLTE and LTE abundances
derived from absorption and emission lines by the spectrum fitting method.
Emission lines are marked by $e$ in the corresponding LTE columns. The
averaged NLTE abundances obtained from emission and absorption lines of four
ionization stages are shown in Table 5.

Emission lines of C i were detected in the observed spectra of the five stars:
$\iota$ Her, HR 1820, HIP 26000, $\zeta$ Cas, and $\chi$ Cen. In the spectra
of 18 Peg and $o$ Tau, the C i lines were not used, because they are blended
with telluric lines located in near-IR spectral region. All the C i lines
almost disappear in the spectra of stars with $T_{\rm eff}$ higher than 22 000
K, because carbon become predominantly singly- or doubly ionized (Fig. 3). For
each star, our NLTE calculations reproduce well the observed C i emission
lines, using our model atom and adopted atmospheric parameters. The best NLTE
fits of the C i 9405 Å emission lines in $\iota$ Her, HIP 26000, $\zeta$ Cas,
and $\chi$ Cen are presented in Fig. 7.

The C ii emission line at 9903 Å was detected in the observed spectra of all
B-type stars in our sample. The hotter stars, HR 1886, HR 2928, HR 1861,
$\theta^{2}$ Ori B, $\phi^{1}$ Ori, $\lambda$ Lep, $\tau$ Sco, and $\upsilon$
Ori, also have the emission lines at 6461 Å in their spectra, and the five
B-type stars show the emission lines at 6151 Å, too. The best fits of C ii
4267, 6151, 6461, and 9903 Å, are presented in Figure 8. For each star, our
NLTE calculations reproduce satisfactorily the observed C ii 6151, 6461 Å
absorption and emission lines. In four stars, $\iota$ Her, $\delta$ Cet,
$\gamma$ Peg, and HR 1861, we excluded the abundances obtained from C ii 6151
and 6461 Å lines in the mean value, because these two lines give apparently
discrepant abundances among other lines. It should be noticed that these two
lines are sensitive to the choice of threshold photoionization cross sections,
that were corrected one order of magnitude higher for the upper levels, 6f 2Fo
and 6g 2G, of investigated transitions.

The C iii 8500 Å line should be considered with caution, because it is lying
almost in the core of the broad Paschen P16 line at 8502.5 Å, which also was
included in spectral synthesis. We analysed this line in seven stars and the
derived abundances were found to be consistent with other C iii lines.

For each star, NLTE provides smaller line-to-line scatter that is illustrated
in Fig. 9 (left panel). The ionization equilibrium C i/C ii/C iii was achieved
for the four stars, and C ii/C iii for eleven stars of our sample. For two
stars, $\tau$ Sco and $\upsilon$ Ori, we obtained abundances from three
ionization stages, C ii/C iii/C iv. C ii/C iii ionization equilibrium is
achieved in $\tau$ Sco, however the abundance from C iv lines is lower,
although still consistent within 2$\sigma$. C ii/C iv ionization equilibrium
is achieved in $\upsilon$ Ori, however the abundance from C iii lines gives a
higher abundance than that from the C ii and C iv lines, by 0.23 and 0.22 dex,
respectively. In both stars, the abundances from C iii lines are higher
compared to C ii and C iv. For $\phi^{1}$ Ori, $\lambda$ Lep, $\tau$ Sco the
NLTE abundances derived from the C ii and C iii lines agree within the error
bars, while in LTE, the abundance differences can reach up to 0.72 dex.

We obtained an averaged abundance of carbon log $\epsilon_{\rm
C}$=8.36$\pm$0.08 from twenty B-type stars from all lines listed in Table 3.
The resulting value is lower by $\sim$0.07 dex compared to the solar carbon
NLTE abundance, log $\epsilon_{\rm C}$=8.43, which are obtained with this
model atom from C i atomic lines in Alexeeva & Mashonkina (2015). Our result
is in line with the present-day Cosmic Abundance Standard (Nieva & Przybilla,
2012), where log $\epsilon_{\rm C}$=8.33$\pm$0.04 is presented.

###  3.3 Determination of carbon abundances in O-stars

Here, we derive the carbon abundances of two O-type stars from emission and
absorption C iii and absorption C iv lines by spectrum fitting. In Table 4, we
present the abundances derived from absorption and emission lines in two
O-type stars. Best NLTE fits of C iii 5695, 6744, 8500, and 9701–17 Å and C iv
5801, 5811 Å in HD 42088 and 15 Mon are presented on Figure 10. Everywhere
NLTE provides smaller line-to-line scatter that is illustrated by Fig. 9
(right panel). The abundances derived from emission and absorption C iii are
slightly lower (by $\sim$0.14 dex) compared to C iv, although still consistent
within the error bars. In both stars, NLTE provides consistent values within
0.14 dex abundances from the two ionization stages, C iii and C iv, while the
LTE abundance difference can be up to 1.34 dex in the absolute value. It
should be noticed that emission lines of C iii 9705–17 Å tend to be stronger
in our modeling, that leads to lower abundances from this line in both stars.
After excluding C iii 9705–17 Å lines, we obtained log $\epsilon_{\rm
C}$=8.31$\pm$0.11 in HD 42088 and log $\epsilon_{\rm C}$=8.27$\pm$0.08 in 15
Mon from the lines of both ionization stages.

Figure 9: Carbon LTE and NLTE abundances of program stars derived from lines
of C i, C ii (left panel) and C iii, C iv (right panel). The horizontal axis
corresponds to the serial number of star, according to Table 2. The error bars
correspond to the dispersion in the single-line measurements about the mean.
In each panel, the dashed line represents the NLTE abundance averaged over all
C i, C ii, C iii, and C iv lines, log $\epsilon_{\rm C}$=8.36. The solid line
represents the solar value, log $\epsilon_{\rm C}$=8.43.  Table 3: NLTE and
LTE Carbon abundances in 20 B-type stars.

$\lambda$ (Å ) | NLTE | LTE | NLTE | LTE | NLTE | LTE | NLTE | LTE | NLTE | LTE | NLTE | LTE | NLTE | LTE | NLTE | LTE | NLTE | LTE | NLTE | LTE
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| 18 Peg |  $\iota$ Her | HR 1820 | HIP 26000 | $o$ Tau |  $\zeta$ Cas |  $\chi$ Cen |  $\delta$ Cet |  $\nu$ Eri |  $\gamma$ Peg
Cı |
9078 |  $\cdots$ |  $\cdots$ |  8.62 | $e$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
9088 |  $\cdots$ |  $\cdots$ |  8.51 | $e$ |  $\cdots$ |  $\cdots$ |  8.40 | $e$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
9094 |  $\cdots$ |  $\cdots$ |  8.39 | $e$ |  8.49 | $e$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.29 | $e$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
9111 |  $\cdots$ |  $\cdots$ |  8.47 | $e$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.23 | $e$ |  8.29 | $e$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
9405 |  $\cdots$ |  $\cdots$ |  8.47 | $e$ |  $\cdots$ |  $\cdots$ |  8.30 | $e$ |  $\cdots$ |  $\cdots$ |  8.24 | $e$ |  8.33 | $e$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
9658 |  $\cdots$ |  $\cdots$ |  8.29 | $e$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
Mean |  $\cdots$ |  $\cdots$ |  8.47 |  $\cdots$ |  8.49 |  $\cdots$ |  8.35 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.24 |  $\cdots$ |  8.30 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
$\sigma$ |  $\cdots$ |  $\cdots$ |  0.11 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  0.07 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  0.01 |  $\cdots$ |  0.02 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
C ii |
3918 |  8.30 |  8.35 |  8.33 |  8.50 |  8.24 |  8.24 |  8.24 |  8.24 |  $\cdots$ |  $\cdots$ |  8.30 |  8.32 |  8.21 |  8.16 |  8.11 |  8.10 |  8.43 |  8.09 |  8.26 |  8.15
3920 |  8.30 |  8.24 |  8.28 |  8.51 |  8.23 |  8.30 |  8.24 |  8.28 |  $\cdots$ |  $\cdots$ |  8.25 |  8.34 |  8.20 |  8.23 |  8.09 |  8.09 |  $\cdots$ |  $\cdots$ |  8.26 |  8.21
4267 |  8.05 |  8.24 |  8.23 |  8.42 |  8.08 |  8.12 |  8.08 |  8.02 |  8.14 |  8.03 |  8.21 |  7.96 |  8.09 |  7.90 |  8.14 |  7.72 |  8.14 |  7.63 |  8.30 |  7.83
5132 |  8.43 |  8.46 |  8.52 |  8.54 |  8.42 |  8.41 |  8.43 |  8.44 |  8.34 |  8.34 |  8.41 |  8.39 |  8.32 |  8.30 |  8.30 |  8.24 |  8.42 |  8.35 |  8.46 |  8.38
5137 |  $\cdots$ |  $\cdots$ |  8.54 |  8.53 |  8.44 |  8.46 |  8.40 |  8.41 |  8.35 |  8.31 |  8.48 |  8.44 |  8.41 |  8.41 |  8.31 |  8.25 |  8.44 |  8.19 |  8.47 |  8.39
5139 |  $\cdots$ |  $\cdots$ |  8.47 |  8.47 |  8.44 |  8.40 |  8.34 |  8.35 |  8.35 |  8.35 |  8.43 |  8.35 |  8.28 |  8.23 |  8.29 |  8.23 |  8.42 |  8.22 |  8.46 |  8.37
5143 |  8.48 |  8.58 |  8.53 |  8.57 |  8.44 |  8.45 |  8.43 |  8.44 |  8.36 |  8.39 |  8.44 |  8.42 |  8.34 |  8.33 |  8.37 |  8.31 |  8.42 |  8.36 |  8.47 |  8.45
5145 |  8.46 |  8.49 |  8.55 |  8.63 |  8.43 |  8.49 |  8.49 |  8.51 |  8.36 |  8.43 |  8.49 |  8.45 |  8.36 |  8.37 |  8.39 |  8.33 |  8.44 |  8.36 |  8.47 |  8.47
5151 |  8.48 |  8.50 |  8.53 |  8.56 |  8.41 |  8.41 |  8.44 |  8.46 |  8.35 |  8.36 |  8.44 |  8.43 |  8.35 |  8.36 |  8.35 |  8.29 |  8.45 |  8.38 |  8.46 |  8.45
5648 |  $\cdots$ |  $\cdots$ |  8.46 |  8.59 |  8.46 |  8.55 |  8.40 |  8.49 |  8.39 |  8.48 |  8.37 |  8.47 |  8.38 |  8.44 |  8.26 |  8.36 |  8.31 |  8.45 |  8.35 |  8.44
5662 |  $\cdots$ |  $\cdots$ |  8.43 |  8.52 |  8.37 |  8.45 |  8.32 |  8.41 |  8.26 |  8.34 |  8.24 |  8.35 |  8.21 |  8.29 |  8.15 |  8.27 |  8.25 |  8.42 |  8.30 |  8.40
6151 |  8.44 |  8.51 |  8.45 |  8.28 |  8.32 |  8.09 |  8.30 |  8.03 |  8.25 |  8.04 |  8.08 |  7.80 |  8.19 |  7.98 |  7.90∗ |  7.58∗ |  8.26 |  7.80 |  8.23 |  7.77
6461 |  8.44 |  8.14 |  8.74∗ |  8.17∗ |  8.32 |  7.86 |  8.30 |  7.85 |  8.21 |  7.84 |  7.97 |  7.59 |  8.34 |  7.92 |  $\cdots$ |  $\cdots$ |  8.19 |  7.50 |  7.84∗ |  7.44∗
6578 |  8.23 |  8.66 |  8.36 |  9.13 |  8.18 |  8.94 |  8.31 |  8.79 |  8.39 |  8.81 |  8.59 |  8.93 |  8.26 |  8.70 |  8.62 |  8.82 |  $\cdots$ |  $\cdots$ |  8.67 |  8.65
6582 |  8.26 |  8.66 |  8.42 |  9.12 |  8.22 |  8.79 |  8.37 |  8.73 |  8.45 |  8.72 |  8.67 |  8.83 |  8.33 |  8.59 |  8.72 |  8.65 |  $\cdots$ |  $\cdots$ |  8.77 |  8.62
6779 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.40 |  8.35 |  8.46 |  8.42 |  8.41 |  8.36 |  8.45 |  8.39 |  8.36 |  8.29 |  8.33 |  8.23 |  8.28 |  8.30 |  8.47 |  8.36
6780 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.40 |  8.35 |  8.46 |  8.44 |  8.41 |  8.36 |  8.45 |  8.39 |  8.36 |  8.29 |  8.33 |  8.23 |  8.28 |  8.30 |  8.47 |  8.36
6783 |  $\cdots$ |  $\cdots$ |  8.61 |  8.63 |  8.53 |  8.47 |  8.59 |  8.52 |  8.49 |  8.44 |  8.62 |  8.51 |  8.40 |  8.35 |  8.47 |  8.35 |  8.42 |  8.40 |  8.59 |  8.46
6800 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.40 |  8.36 |  8.46 |  8.41 |  8.41 |  8.36 |  8.47 |  8.39 |  8.35 |  8.31 |  8.32 |  8.23 |  8.36 |  8.38 |  8.42 |  8.32
9903 |  $\cdots$ |  $\cdots$ |  8.50 | $e$ |  8.29 | $e$ |  8.68 | $e$ |  8.54 | $e$ |  8.50 | $e$ |  8.33 | $e$ |  8.61 | $e$ |  8.44 | $e$ |  8.37 | $e$
Mean |  8.37 |  8.47 |  8.46 |  8.65 |  8.36 |  8.44 |  8.41 |  8.43 |  8.37 |  8.41 |  8.42 |  8.44 |  8.31 |  8.33 |  8.38 |  8.34 |  8.36 |  8.26 |  8.45 |  8.36
$\sigma$ |  0.14 |  0.17 |  0.11 |  0.24 |  0.11 |  0.22 |  0.13 |  0.23 |  0.10 |  0.23 |  0.17 |  0.31 |  0.08 |  0.20 |  0.17 |  0.28 |  0.10 |  0.29 |  0.14 |  0.30
C iii |
4647 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.39 |  8.49 |  8.39 |  8.58 |  $\cdots$ |  $\cdots$ |  8.23 |  8.47 |  8.24 |  8.39 |  8.24 |  8.47 |  8.41 |  8.78 |  $\cdots$ |  $\cdots$
4650 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.49 |  8.67 |  $\cdots$ |  $\cdots$ |  8.30 |  8.53 |  8.26 |  8.42 |  8.31 |  8.55 |  $\cdots$ |  $\cdots$ |  8.17 |  8.43
4651 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.36 |  8.53 |  $\cdots$ |  $\cdots$ |  8.34 |  8.57 |  $\cdots$ |  $\cdots$ |  8.25 |  8.44
5696 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.34 |  8.35
Mean |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.39 |  8.49 |  8.44 |  8.63 |  $\cdots$ |  $\cdots$ |  8.30 |  8.51 |  8.25 |  8.41 |  8.30 |  8.53 |  8.41 |  8.78 |  8.26 |  8.41
$\sigma$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  0.07 |  0.06 |  $\cdots$ |  $\cdots$ |  0.07 |  0.03 |  0.01 |  0.02 |  0.05 |  0.05 |  $\cdots$ |  $\cdots$ |  0.09 |  0.05
|  $\alpha$ Pix | HR 1781 | HR 1886 | HR 2928 | HR 1861 |  $\theta^{2}$ Ori B |  $\phi^{1}$ Ori |  $\lambda$ Lep | $\tau$ Sco | $\upsilon$ Ori
C ii |
3918 |  8.36 |  8.26 |  8.19 |  8.09 |  8.29 |  8.13 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.26 |  8.18 |  $\cdots$ |  $\cdots$ |  8.25 |  8.25 | 8.31 | 8.26
3920 |  $\cdots$ |  $\cdots$ |  8.19 |  8.13 |  8.20 |  8.06 |  8.15 |  7.93 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
4267 |  8.41 |  7.70 |  8.33 |  7.72 |  8.41 |  7.64 |  8.24 |  7.54 |  8.27 |  7.55 |  8.22 |  7.58 |  8.19 |  7.75 |  8.22 |  7.71 |  8.15 |  7.82 |  8.14 |  8.03
5132 |  8.42 |  8.33 |  8.49 |  8.38 |  8.54 |  8.35 |  8.33 |  8.14 |  8.51 |  8.32 |  8.51 |  8.30 |  8.34 |  8.17 |  8.48 |  8.31 |  8.39 |  8.24 |  $\cdots$ |  $\cdots$
5137 |  8.43 |  8.42 |  8.52 |  8.40 |  8.54 |  8.34 |  8.31 |  8.14 |  8.47 |  8.29 |  8.47 |  8.27 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
5139 |  8.42 |  8.34 |  8.45 |  8.34 |  8.55 |  8.34 |  8.27 |  8.09 |  8.45 |  8.27 |  8.53 |  8.33 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
5143 |  8.44 |  8.33 |  8.55 |  8.44 |  8.55 |  8.37 |  8.36 |  8.19 |  8.55 |  8.37 |  8.53 |  8.34 |  8.39 |  8.16 |  8.49 |  8.36 |  8.37 |  8.29 |  $\cdots$ |  $\cdots$
5145 |  8.44 |  8.42 |  8.54 |  8.43 |  8.54 |  8.40 |  8.36 |  8.19 |  8.53 |  8.33 |  8.54 |  8.34 |  8.37 |  8.19 |  8.49 |  8.36 |  8.41 |  8.29 |  8.25 |  8.18
5151 |  8.42 |  8.32 |  8.47 |  8.35 |  8.54 |  8.43 |  8.29 |  8.11 |  8.47 |  8.28 |  8.52 |  8.32 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.41 |  8.28 |  8.24 |  8.18
5648 |  8.31 |  8.38 |  8.35 |  8.42 |  8.42 |  8.40 |  8.29 |  8.34 |  8.33 |  8.33 |  8.33 |  8.37 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.17 |  8.24 |  $\cdots$ |  $\cdots$
5662 |  8.21 |  8.35 |  8.32 |  8.36 |  8.31 |  8.32 |  8.08 |  8.12 |  8.21 |  8.27 |  8.27 |  8.34 |  $\cdots$ |  $\cdots$ |  8.28 |  8.31 |  8.12 |  8.22 |  $\cdots$ |  $\cdots$
6151 |  8.24 |  7.64 |  8.19 |  7.51 |  8.54 |  7.35 |  8.28 |  7.31 |  8.39 |  7.16 |  8.29 |  $e$ |  8.22 | $e$ |  8.36 | $e$ |  8.24 | $e$ |  8.19 | $e$
6461 |  8.24 |  7.23 |  8.04 |  7.14 |  8.64 |  $e$ |  8.64 |  $e$ |  8.74∗ |  $e$ |  8.29 |  $e$ |  8.09 | $e$ |  8.19 | $e$ |  8.24 | $e$ |  8.19 | $e$
6578 |  8.32 |  8.52 |  8.62 |  8.41 |  8.54 |  8.24 |  8.32 |  8.09 |  8.42 |  8.19 |  8.16 |  7.93 |  8.04 |  7.69 |  $\cdots$ |  $\cdots$ |  8.14 |  7.92 |  8.09 |  7.69
6582 |  8.41 |  8.41 |  8.71 |  8.36 |  8.63 |  8.18 |  8.39 |  7.99 |  8.49 |  8.16 |  $\cdots$ |  $\cdots$ |  8.09 |  7.74 |  $\cdots$ |  $\cdots$ |  8.18 |  7.96 |  8.18 |  7.85
6779 |  8.40 |  8.40 |  8.42 |  8.34 |  8.40 |  8.34 |  8.17 |  8.11 |  8.29 |  8.22 |  8.25 |  8.23 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
6780 |  8.39 |  8.27 |  8.37 |  8.35 |  8.40 |  8.34 |  8.17 |  8.11 |  8.29 |  8.22 |  8.25 |  8.23 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
6783 |  8.54 |  8.40 |  8.59 |  8.45 |  8.51 |  8.42 |  8.17 |  8.15 |  8.37 |  8.31 |  8.31 |  8.31 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
6800 |  8.40 |  8.29 |  8.41 |  8.34 |  8.44 |  8.32 |  8.18 |  8.14 |  8.28 |  8.22 |  8.31 |  8.31 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$
9903 |  8.42 |  $e$ |  8.48 |  $e$ |  8.28 |  $e$ |  7.98 |  $e$ |  8.15 |  $e$ |  8.19 |  $e$ |  8.06 | $e$ |  8.25 | $e$ |  8.16 | $e$ |  8.14 | $e$
Mean |  8.39 |  8.30 |  8.44 |  8.30 |  8.45 |  8.28 |  8.28 |  8.09 |  8.40 |  8.22 |  8.37 |  8.25 |  8.22 |  8.04 |  8.36 |  8.26 |  8.26 |  8.18 |  8.20 |  8.07
$\sigma$ |  0.08 |  0.35 |  0.17 |  0.36 |  0.12 |  0.29 |  0.14 |  0.25 |  0.12 |  0.33 |  0.13 |  0.27 |  0.14 |  0.26 |  0.14 |  0.28 |  0.11 |  0.18 |  0.07 |  0.22
C iii |
4056 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.43 |  8.33 |  8.15 |  8.12 |  8.35 |  8.33 |  8.31 |  8.31 |  8.34 |  8.34 |  8.43 |  8.44 |  8.32 |  8.32 |  8.34 |  8.37
4153 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.42 |  8.36 |  $\cdots$ |  $\cdots$ |  8.39 |  8.37 |  8.31 |  8.31 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.31 |  8.41 |  8.39 |  8.58
4163 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.34 |  8.45 |  $\cdots$ |  $\cdots$ |  8.30 |  8.38 |  8.44 |  8.65
4647 |  8.20 |  8.65 |  8.30 |  8.61 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.47 |  9.22 |  8.49 |  9.15 |  $\cdots$ |  $\cdots$ |  8.42 |  9.18
4650 |  $\cdots$ |  $\cdots$ |  8.31 |  8.62 |  8.11 |  8.44 |  8.10 |  8.46 |  8.17 |  8.63 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.17 |  8.78 |  8.44 |  9.24
4651 |  $\cdots$ |  $\cdots$ |  8.34 |  8.60 |  8.19 |  8.39 |  8.10 |  8.32 |  8.21 |  8.55 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.30 |  8.65 |  8.46 |  9.27
4664 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.27 |  8.27 |  8.36 |  8.47 |  8.33 |  8.33 |  8.41 |  8.38
4666 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.29 |  8.33 |  8.39 |  8.43 |  8.39 |  8.39 |  8.49 |  8.59 |  8.33 |  8.35 |  8.51 |  8.51
5696 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.26 |  8.38 |  8.22 |  8.42 |  8.29 |  8.41 |  8.25 |  8.34 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.18 |  8.12 |  8.39 |  8.07
6731 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.47 |  8.22 |  8.49 |  8.11
6744 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.44 |  8.96 |  $\cdots$ |  $\cdots$ |  8.41 |  8.12 |  8.53 |  7.94
8500 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.44 |  8.51 |  $\cdots$ |  $\cdots$ |  8.34 |  8.34 |  8.54 |  8.93 |  8.23 |  8.67 |  8.32 |  8.92
Mean |  8.20 |  8.65 |  8.32 |  8.60 |  8.30 |  8.38 |  8.15 |  8.41 |  8.31 |  8.46 |  8.34 |  8.35 |  8.38 |  8.76 |  8.47 |  8.81 |  8.31 |  8.45 |  8.43 |  8.83
$\sigma$ |  $\cdots$ |  $\cdots$ |  0.02 |  0.01 |  0.14 |  0.04 |  0.06 |  0.14 |  0.10 |  0.12 |  0.06 |  0.06 |  0.07 |  0.41 |  0.07 |  0.31 |  0.09 |  0.22 |  0.06 |  0.46
C iv |
5801 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.00 |  8.41 |  8.16 |  8.70
5811 |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.12 |  8.49 |  8.26 |  8.71
Mean |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  8.06 |  8.45 |  8.21 |  8.71
$\sigma$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  $\cdots$ |  0.08 |  0.06 |  0.07 |  0.01

Note. — Notes. Emission lines are marked by symbol $e$. Lines and abundances,
which were not used in mean calculations are marked by (*). $\sigma$ means
standard deviation.

Figure 10: Best NLTE fits (solid curves) of C iii 4647, 5695, 6744, 7037,
8500, and 9701–17 Å and C iv 5801, 5811 Å in HD 42088 and 15 Mon. The observed
spectra are shown by open circles. Table 4: NLTE and LTE Carbon abundances in
two O-type stars

$\lambda$ (Å ) | NLTE | LTE | NLTE | LTE
---|---|---|---|---
| HD 42088 | 15 Mon
C iii |
4163 | 8.17 | 8.60 | – | –
4647 | 8.39 | 7.57 | 8.28 | 7.73
8500 | 8.40 | 8.63 | 8.16 | 8.63
Mean | 8.33 | 8.46 | 8.22 | 8.38
$\sigma$ | 0.13 | 0.60 | 0.08 | 0.64
5695 | 8.21 | $e$ | 8.31 | $e$
6744 | 8.15 | $e$ | 8.14 | $e$
7037 | 8.29 | $e$ | 8.31 | $e$
9705–17 | 8.04 | $e$ | 8.09 | $e$
Mean | 8.18 | – | 8.22 | –
$\sigma$ | 0.11 | – | 0.11 | –
Mean C iii | 8.25 | 8.46 | 8.22 | 8.38
$\sigma$ | 0.13 | 0.60 | 0.10 | 0.64
C iv |
5801 | 8.37 | 9.86 | 8.32 | 9.74
5811 | 8.41 | 9.72 | 8.35 | 9.56
Mean C iv | 8.39 | 9.80 | 8.34 | 9.66
$\sigma$ | 0.03 | 0.10 | 0.02 | 0.13

Note. — Notes. Emission lines are marked by symbol $e$.

Table 5:  The Carbon NLTE abundances obtained from emission and absorption lines of four ionization stages  Number | Star | Name | log $\epsilon_{\rm C}$
---|---|---|---
1 | HD 209008 | 18 Peg | 8.37$\pm$0.14
2 | HD 160762 |  $\iota$ Her | 8.46$\pm$0.11
3 | HD 35912 | HR 1820 | 8.37$\pm$0.11
4 | HD 36629 | HIP 26000 | 8.40$\pm$0.12
5 | HD 35708 |  $o$ Tau | 8.37$\pm$0.10
6 | HD 3360 |  $\zeta$ Cas | 8.40$\pm$0.16
7 | HD 122980 |  $\chi$ Cen | 8.30$\pm$0.07
8 | HD 16582 |  $\delta$ Cet | 8.37$\pm$0.16
9 | HD 29248 |  $\nu$ Eri | 8.36$\pm$0.10
10 | HD 886 |  $\gamma$ Peg | 8.40$\pm$0.11
11 | HD 74575 |  $\alpha$ Pix | 8.39$\pm$0.08
12 | HD 35299 | HR 1781 | 8.43$\pm$0.17
13 | HD 36959 | HR 1886 | 8.46$\pm$0.14
14 | HD 61068 | HR 2928 | 8.26$\pm$0.14
15 | HD 36591 | HR 1861 | 8.37$\pm$0.11
16 | HD 37042 |  $\theta^{2}$ Ori B | 8.36$\pm$0.12
17 | HD 36822 |  $\phi^{1}$ Ori | 8.29$\pm$0.13
18 | HD 34816 |  $\lambda$ Lep | 8.40$\pm$0.12
19 | HD 149438 |  $\tau$ Sco | 8.28$\pm$0.10
20 | HD 36512 |  $\upsilon$ Ori | 8.32$\pm$0.13
21 | HD 47839 | 15 Mon AaAb | 8.27$\pm$0.11
22 | HD 42088 |  | 8.31$\pm$0.11

###  3.4 Discussions

We examine the reliability of carbon abundances obtained from C ii 4267, 9903
Å and C iii 5695 Å lines. The C ii 4267, 9903 Å lines reach a maximum strength
around $T_{\rm eff}$ $\sim$21 000 and ∼30 000 K, respectively. The C iii 5695
Å line reaches a maximum strength in absorption at $T_{\rm eff}$ $=$33 400 K,
and is still in emission at $T_{\rm eff}$ $=$38 000 K.

It is known from the observations of the CHANDRA satellite (Nazé et al.,
2011), that the X-ray fluxes in O-B stars can be higher than theoretical one,
that can lead to underestimation of radiation in the far UV and, as a result,
to the underestimation of the degree of ionization, that can lead to lower
abundances dependent on the temperature. Our stars have effective temperatures
lying in the range 15 800–38 000 K. No trend between the abundances from C ii
4267, 6578, 6582 Å and C iii 5695 Å lines and effective temperature is
apparent (Fig. 11).

The obtained abundances from C ii 4267 Å line are systematically lower by 0.20
$-$ 0.30 dex compared to other C ii lines in the stars with $T_{\rm eff}$
$\leq$ 22 000 K. The C ii 4267 Å line provides consistent abundances at the
temperature range from 22 900 K to 30 000 K only, where the agreement between
C ii 4267 Å and the other carbon lines is within 0.14 dex.

Other two classical strong lines of C ii 6578/82 Å show too high abundances in
several of the cooler sample stars, switching to too low abundance in some of
the higher temperature stars, that well demonstrated on Figure 11. However,
for eight stars in our sample, $\iota$ Her, HIP 26000, $o$ Tau, $\chi$ Cen,
$\alpha$ Pix, HR 1886, HR 2928, HR 1861, the discrepancies between C ii 6578 Å
and other carbon lines do not exceed 0.10 dex. We have noticed that the line C
ii 6578 Å shows systematically lower abundance by about 0.07 dex compared to
the C ii 6582 Å in all sample stars, however both of them belong to same
multiplet.

The prominent discrepancies between C ii 4267 Å and C ii 6582 Å were found in
the most of the stars, except for six of them, HR 1820, $\alpha$ Pix,
$\phi^{1}$ Ori, $\lambda$ Lep, $\tau$ Sco in which the value, log
$\epsilon_{\rm C}(6582)$ $-$ log $\epsilon_{\rm C}(4267)$, is lower than 0.14
dex. For six stars, HR 1820, $\alpha$ Pix, HR 2928, $\theta^{2}$ Ori B, $\tau$
Sco, and $\upsilon$ Ori, the abundances from C ii 4267 Å and C ii 6578 Å are
found to be consistent within 0.10 dex.

We have found that the mean abundance from emission C ii 9903 Å line in the
stars with $T_{\rm eff}$$<$25 000 K is log $\epsilon_{\rm C}$=8.48$\pm$0.12,
while in the stars with $T_{\rm eff}$$>$25 000 K is log $\epsilon_{\rm
C}$=8.16$\pm$0.10 (Fig. 11). We find a small (within 3 $\sigma$) temperature
dependence in the C abundances between hot and cool stars. The most probable
reason for this apparent difference is our treatment of the model atom, in
which R-matrix calculations for effective collision strengths (dependent on
temperature) have been carried out only for 30 lowest fine-structure levels of
C ii available in the literature.

Figure 11: Carbon NLTE abundances in program stars derived from lines of C ii
at 4267, 6578, 6582, and 9903 Å and of C iii at 5695 Å in a wide temperature
range. The solid line represents solar value, log $\epsilon_{\rm C}$=8.43. The
dashed line represents the NLTE abundance averaged over all C i, C ii and C
iii lines, log $\epsilon_{\rm C}$=8.36.

###  3.5 Comparison with previous studies

We obtained log $\epsilon_{\rm C}$=8.36$\pm$0.08 from twenty B-type stars,
that is in a good agreement with present-day Cosmic abundance standard (Nieva
& Przybilla, 2012), where log $\epsilon_{\rm C}$=8.33$\pm$0.04 was obtained in
twenty B-stars. It is not surprising, because the sixteen stars in our sample
are common with Nieva & Przybilla (2012) and our methods of calculations are
similar. However, there are some differences in the used model atom. Nieva &
Przybilla (2008) performed the NLTE calculations for C ii/C iii/C iv on the
basis of the ATLAS9 model atmosphere using Maxwellian-averaged collision
strengths for electron-impact excitation among the lowest 24 terms of C iii
from the R-matrix computations of Mitnik et al. (2003), and effective
collision strengths for the lowest 24 fine-structure levels of C iv from
Aggarwal & Keenan (2004). The departure coefficients computed for the
atmosphere with 32 000 / 4.3, corresponding to $\tau$ Sco (Fig. 4 for the
levels of C ii and C iii and Fig. 5 for C iv) are similar to departure
coefficients in Nieva & Przybilla (2008). We briefly comment on some
individual stars as follows.

HD 160762 ($\iota$ Her). In Alexeeva et al. (2016), the star was found to have
log $\epsilon_{\rm C}$=8.43$\pm$0.10 from emission C i and absorption C ii
lines (totally 20 lines), that is in agreement with this work, log
$\epsilon_{\rm C}$=8.46$\pm$0.11, where we added the abundance from emission C
ii 9903 Å line. Nieva & Przybilla (2012) obtained log $\epsilon_{\rm
C}$=8.40$\pm$0.07 from 13 lines of C ii, that is consistent with both Alexeeva
et al. (2016) and this work.

HD 36512 ($\upsilon$ Ori). In this star, we obtained log $\epsilon_{\rm
C}$=8.32$\pm$0.13 from 23 lines of three ionization stages, C ii, and C iii,
and C iv. Carneiro et al. (2018) derived a carbon abundance of log
$\epsilon_{\rm C}$=8.25$\pm$0.22 with NLTE atmosphere code fastwind, that is
slightly lower than our result, although still consistent within the error
bars. Our result is consistent with Martins et al. (2015c), who obtained log
$\epsilon_{\rm C}$=8.38$\pm$0.12 with the code cmfgen that computes NLTE and
spherical models. Our result is in line with Nieva & Przybilla (2012), in
which they obtained 8.35$\pm$0.14 from 19 lines of three ionization stages.

HD 47839 (15 Mon AaAb). 15 Monocerotis is a bright O-type star (mV = 4.64) in
a spectroscopic binary system that belongs to an open cluster NGC 2264 located
at about $d$ $\approx$ 720 pc from the Sun (Cvetković et al., 2010; Maíz
Apellániz, 2019). An orbital period of 25 years was estimated by Gies et al.
(1993). Recent astrometric calculations based on the GAIA DR2 indicate a
period of 108 years (Maíz Apellániz, 2019). The difference in magnitude
between Aa and Ab is 1.2 mag (Maíz Apellániz et al., 2018), which indicates
that Ab is likely to be a late-O or an early-B star, but there is no spatially
separated spectroscopy to confirm that. Gies et al. (1993) showed that the
broad component of He i 5876 Å line in the spectrum of the primary component
can be potentially associated with the companion. For the secondary component,
they estimated spectral type 09.5 V and quite a large projected rotational
velocity $v$ sin $i$ = 350$\pm$40 km s-1 based on the shape of the wings. The
domination of the primary component to the line flux, in combination with such
a large rotational velocity, complicates the detection of the secondary by the
spectral observations. In the case of 15 Mon AaAb, we do not notice any broad
features originating from the secondary in the wings of the investigated
carbon lines, even in the strong C iii 5695 and C iv 5801, 5811 Å (Fig. 10).
Due to the high rotational velocity of the secondary, other weak lines would
be broad and shallow and almost indistinguishable from the continuum level.
Even then, abundance results can be affected by the spectroscopic binarity.
When the spectrum of the primary is diluted by that of the rapidly rotating
secondary, spectral lines on the normalized continuum might be apparently
weakened. Then, abundances obtained by assuming a single star may contain some
errors. However, we are presently unable to quantify the effect of the
secondary star to the normalized continuum and to estimate the resulting
errors quantitatively. We obtained a carbon abundance in this star and our
mean value, log $\epsilon_{\rm C}$=8.27$\pm$0.11, is lower by 0.16 dex than
the solar value. We find no previous study on the carbon abundance in this
star.

HD 42088. It is a Blue Straggler and a member of Gem OB1 stellar association
(Schild & Berthet, 1986). It also is considered as a peculiar star with
nitrogen overabundance (Schild & Berthet, 1986). The derived carbon abundance
for HD 42088 ($T_{\rm eff}$ = 38 000, log $g$ = 4.0), log $\epsilon_{\rm
C}$=8.31$\pm$0.11, is consistent with Martins et al. (2015c), who obtained log
$\epsilon_{\rm C}$=8.30$\pm$0.06 using the code cmfgen with NLTE model
including wind, line-blanketing and spherical geometry. Our line-by-line
scatter is higher, because we used a different set of lines. For example, such
lines as C iii 4647, 8500, 5695, 7037, 9705$-$9717 Å, and C iv 5801, 5811 Å,
were not included in analysis of Martins et al. (2015c).

##  4 Conclusions

We present a model atom for C i–C ii–C iii–C iv using the most up-to-date
atomic data and evaluated the non-local thermodynamic equilibrium (NLTE) line
formation in classical 1D atmospheric models of O-B-type stars with the code
detail. The model atom allows the absorption and emission lines of C i, C ii,
C iii, and C iv to be analyzed in the atmospheres of O-B type stars with
effective temperature 15 800 $\leq$ $T_{\rm eff}$$\leq$ 38 000 K and surface
gravity 3.60 $\leq$ log $g$ $\leq$ 4.30.

Our modeling predicts the emission lines of C ii 9903 and 18 535 Å that appear
at effective temperature of $T_{\rm eff}$$\geq$ 17 500 K, those of C ii 6151
and 6461 Å that appear at effective temperature of $T_{\rm eff}$$>$ 25 000 K,
and the emission lines of C iii 5695, 6728–44, 9701–17 Å that appear at
effective temperature of $T_{\rm eff}$$\geq$ 35 000 K (log $g$=4.0). These
emission lines form in the stellar atmosphere, and NLTE effects are
responsible for the formation of emission. A pre-requisite of the emission is
the depletion of population in a minority species, where the photoionization-
recombination mechanism provides an inversion of populations of energy levels.
Our detailed analysis shows that the upper levels of the transitions at C ii
9903 and 18 535 Å are mainly populated from C iii reservoir through the
Rydberg states. Photon losses in UV transitions at 885, 1308, and 1426–28 Å
that become optically thin in the photosphere drive the extra depopulation of
the lower levels of transitions at C iii 5695, 6728–44 Å. The upper levels of
transitions at C iii 9701–17 Å are mainly populated due to spontaneous
deexcitation at C iii 1577 and 1923 Å. The emission lines of C ii 6151, 6461,
9903, 18 535 Å and C iii 5695, 6728–44, 9701–17 Å in the spectra of main-
sequence O-B-type stars is the result of atomic processes taking place between
levels. We confirm that the emission can be obtained without the external
mechanisms of excitation, the hypothesis of extended envelopes, atmospheric
expansion and supplemental non-radiative influxes of energy.

We analysed the lines of C i, C ii, C iii, and C iv in twenty-two O-B-type
stars with temperature range 15 800 $\leq$ $T_{\rm eff}$$\leq$ 38 000 K taking
the advantages of their observed high-resolution, high SN ratio, and broad
wavelength coverage spectra, where SN ratio is higher than 1000 for some of
them. Stellar parameters of our stars were reliably determined by Nieva &
Przybilla (2012); Nieva & Simón-Díaz (2011); Markova et al. (2004); Martins et
al. (2015c). The emission line C ii 9903 Å was predicted theoretically and
well-reproduced in the observations of B-stars for the first time.

We examine the reliability of carbon abundances determined from the absorption
C ii line at 4267 Å and the emission line of C ii at 9903 Å in B-stars and the
line C iii at 5695 Å in O-type stars. There is no hint of a trend between the
abundances from C ii 4267 and C iii 5695 Å lines and effective temperature in
the investigated temperature range. Although, we found a hint on the trend
between the abundances from emission C ii 9903 Å line and effective
temperature, where the mean abundance from C ii 9903 Å line in the stars with
$T_{\rm eff}$$<$25 000 K is 8.48$\pm$0.12, while in the stars with $T_{\rm
eff}$$>$25 000 K is 8.16$\pm$0.10. Though the agreement is within 3$\sigma$,
we might attribute the apparent discrepancy to be due to the shortcoming of
our model atom, where in the $R$-matrix calculations for effective collision
strengths are not available in the literature, except for the 30 lowest fine-
structure levels in C ii. The C ii 4267 Å line provides reliable abundances at
the temperature range from 22 900 K to 30 000 K only, while for cooler stars,
with $T_{\rm eff}$ $\leq$ 22 000 K, the abundances from C ii 4267 Å line are
systematically lower by 0.20$-$0.30 dex compared to other C ii lines.

We conclude that the abundances from emission lines of C i, C ii and C iii do
not differ significantly from absorption ones, that makes them potential
abundance indicator as well. Consistent abundances from emission lines of C i
and absorption lines of C ii have been found for $\iota$ Her, HIP 26000 and
$\chi$ Cen, while for other stars, HR 1820 and $\zeta$ Cas, the agreement is
still within 1$\sigma$. Consistent abundances within the error bars from C ii
emission and C ii absorption lines were found in $\iota$ Her, HR 1820, $\zeta$
Cas, $\chi$ Cen, $\nu$ Eri, $\gamma$ Peg, $\alpha$ Pix, HR 1781, $\lambda$
Lep, $\tau$ Sco, and $\upsilon$ Ori. Consistent abundances within the error
bars from C iii emission and C iii absorption lines were found in 15 Mon and
HD 42088, however the abundance from C iii emission lineas at 9705$-$17 are
systematically lower by about 0.20 dex.

For each star, NLTE leads to smaller line-to-line scatter. The NLTE must be
taken into account since the deviations from LTE are strong in the
investigated temperature regime. For example, in C iv lines at 5801 and 5811 Å
among O-type stars, the difference between NLTE and LTE abundances,
$\Delta_{\rm NLTE}$, can reach up to $-$1.49 dex. In the LTE assumption, we
only can recommend the C ii 5132–5151 Å lines as carbon abundance indicator in
the stars with 15 000 $\leq$ $T_{\rm eff}$$\leq$ 21 000 K, due to small NLTE
effects for these lines. For stars with 26 000 $\leq$ $T_{\rm eff}$$\leq$ 32
000 K, the C iii 4056 Å line can be used in a LTE analysis. We obtained log
$\epsilon_{\rm C}$=8.36$\pm$0.08 from twenty B-type stars in the solar
vicinity, which is in a good agreement with a present-day Cosmic abundance
standard (Nieva & Przybilla, 2012). The obtained carbon abundances in 15 Mon
and HD 42088 are 8.27$\pm$0.11 and 8.31$\pm$0.11, that is lower by 0.16 dex
and 0.12 dex than the solar value, respectively.

.

We thank the anonymous referee for valuable suggestions and comments. This
work was supported by the National Natural Science Foundation of China and
Chinese Academy of Sciences joint fund on astronomy under grants No. U1331102,
U1631105 and by the Sino-German Science Foundation under project No. GZ1183.
This work is also partly supported by the Young Scholars Program of Shandong
University (No. 20820162003). S.A. is grateful to the China Postdoctoral
international exchange program (ISS-SDU) for financial support. This research
is based on observations obtained with MegaPrime/MegaCam, a joint project of
CFHT and CEA/IRFU, at the Canada-France-Hawaii Telescope (CFHT) which is
operated by the National Research Council (NRC) of Canada, the Institut
National des Science de l Univers of the Centre National de la Recherch
Scientifique (CNRS) of France, and the University of Hawaii. We made use of
the NORAD-Atomic-Data, NIST, SIMBAD, VALD, and UK APAP Network databases.

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