Non-Local Thermodynamic Equilibrium abundance analyses of the extreme helium stars: V652 Her and HD 144941
Gajendra Pandey David L. Lambert






Indian Institute of Astrophysics;
Bangalore, 560034 India
pandey@iiap.res.in

The W.J. McDonald Observatory and Department of Astronomy, University of Texas at Austin; Austin,
TX 78712-1083
dll@astro.as.utexas.edu



 Optical high-resolution spectra of V652 Her and HD 144941, the two extreme helium stars with 
exceptionally low C/He ratios, have been subjected to a non-LTE abundance analysis using the tools 
TLUSTY and SYNSPEC. Defining atmospheric parameters were obtained from a grid of non-LTE atmospheres 
and a variety of spectroscopic indicators including He i and He ii line profiles, 
ionization equilibrium of ion pairs such as C ii/C iii and N ii/N iii. 
The various indicators provide a consistent set of atmospheric parameters: 
T_ eff=25000±300K, log g = 3.10±0.12(cgs), and ξ=13±2  km s^-1 are
provided for V652 Her, and T_ eff=22000±600K, log g = 3.45±0.15 (cgs), 
and ξ=10  km s^-1 are provided for HD 144941. In contrast to the non-LTE analyses, 
the LTE analyses – LTE atmospheres and a LTE line analysis – with the available indicators do not 
provide a consistent set of atmospheric parameters. The principal non-LTE effect on the elemental 
abundances is on the neon abundance. It is generally considered that these extreme helium stars with 
their very low C/He ratio result from the merger of two helium white dwarfs. Indeed, the derived composition 
of V652 Her is in excellent agreement with predictions by Zhang & Jeffery (2012) who model the slow merger 
of helium white dwarfs; a slow merger results in the merged star having the composition of the accreted white dwarf.  
In the case of HD 144941 which appears to have evolved from metal-poor stars a slow merger is incompatible with 
the observed composition but variations of the merger rate may account for the observed composition.  
More detailed theoretical studies of the merger of a pair of helium white dwarfs are to be encouraged.









§ INTRODUCTION


Extreme helium stars (EHes) are very hydrogen poor stars with effective temperatures 
of about 10000 K to 30000 K (i.e., spectral types A and B) with surface gravities of 
log g ∼ 1 for the coolest stars and increasing to ∼ 3 for the hottest stars. 
A majority of EHes populate a locus of roughly constant log L/M ∼ 4.5 where the 
luminosity L and mass M are in solar units. This locus most likely represents an 
evolutionary track with stars evolving at about constant luminosity from low to high temperatures. Such EHes thought 
to form from the merger of a helium white dwarf with a carbon-oxygen white dwarf have 
carbon-to-helium ratios by number of about 0.6 % with presently analyzed stars exhibiting 
C/He ratios by number in the range 0.3 % to 1.0 %. The carbon is provided by the surface 
of the C-O white dwarf and the helium primarily by the helium white dwarf.

At the time of  <cit.>'s succinct review of EHes, 
about 20 Galactic EHes were known. Two are set apart from the majority highlighted above 
by a much lower 
C/He ratio. V652 Her according to <cit.> and an LTE analysis 
has the low C/He ratio of 0.006 % and HD 144941 according to <cit.>'s 
LTE abundance analysis has the even lower C/He ratio of 0.0017 %. Both ratios are 
sharply lower than the C/He ratio of the majority of the EHes. In addition, V652 Her 
and HD 144941 have higher surface gravities than the majority EHes of the same 
effective temperature and thus correspond to a log L/M smaller by about a factor of 1.3 dex than the majority.
These differences especially the low C/He ratio suggest a different origin, namely the merger 
of a helium white dwarf with another helium white dwarf. Again, see <cit.>'s 
review for further details.

In this paper, we describe a non-LTE analysis of new high-quality optical spectra of both 
V652 Her and HD 144941 primarily in order to determine how non-LTE effects influence the 
C/He ratio but also to measure the effects of departures from LTE on the abundances of other 
elements. The paper follows our similar analyses of non-LTE effects on several EHes
having C/He ratios characteristic of the majority  EHes <cit.>.



§ OBSERVATIONS


 High-resolution optical spectra of V652 Her and HD 144941
were obtained on 2011 May 13 at the coudé focus of the 
W.J. McDonald Observatory's Harlan J. Smith 2.7-m telescope
with the Robert G. Tull cross-dispersed échelle spectrograph
<cit.> at a resolving power of R = 60,000. Three
thirty minutes exposures were recorded for each of these stars.
The observing procedure and the wavelength coverage is same as 
described in <cit.>.
The Image Reduction and Analysis Facility (IRAF) software package 
was used to reduce these recorded spectra. HD 144941's spectrum obtained
from Anglo-Australian Telescope (AAT), and analysed by <cit.>,
was made available by Simon Jeffery (private communication) for comparison. 

The sample wavelength interval shown in Figure 1  displays
the extracted spectrum from each exposure of the observed EHes.
All spectra were aligned to the rest wavelengths of well-known lines. 
Inspection of the Figure 1 shows that the line profiles are not always symmetric.
Note the obvious asymmetry in the two exposures of V652 Her attributable to
atmospheric pulsations <cit.>. V652 Her pulsates with a period of
2.592 hours <cit.> and  a radial velocity amplitude of about 
70 km s^-1 <cit.>. For the abundance analysis, we have used the spectrum of V652 Her,
showing symmetric profiles with signal-to-noise ratio of about 140 per pixel at 5600Å. 
The line profiles of HD 144941 for each exposure appear symmetric and show extremely weak metal lines. 
Hence, these exposures were coadded to enhance the signal-to-noise ratio for 
the abundance analyses; the signal-to-noise ratio is about 280 per pixel at 5600Å.

The pure absorption line spectrum of V652 Her 
is dominated by contributions from the following species: H i, He i, N ii,
N iii, O ii, Ne i, Al iii, Si ii,
Si iii, S ii, S iii, and Fe iii.
However, the absorption line spectrum of HD 144941 is dominated by 
H i, and He i lines and a small collection of weak lines from other species.
Revised Multiplet Table (RMT) <cit.>, tables of spectra
of H, C, N, and O <cit.> and the NIST Atomic Spectra
Database[http://www.nist.gov/pml/data/asd.cfm] (ver. 5.3) were used for line identification. 

The primary objective is to determine reliable atmospheric parameters (effective temperature, surface gravity 
and microturbulence) and then the chemical composition of V652 Her and HD 144941.




§ QUANTITATIVE FINE ANALYSES


Non-LTE line-blanketed model atmospheres are used to determine the atmospheric parameters
and the chemical composition. The effective temperature T_ eff and 
surface gravity g are obtained from  intersecting loci in the T_ eff 
versus log g plane. These loci represent the ionization equilibrium of 
available ion pairs such as 
C ii/C iii, N ii/N iii, Si ii/Si iii, Si iii/Si iv and
S ii/S iii and loci  derived from the best fits to the
Stark-broadened profiles of He i and He ii lines. 
The microturbulent velocity ξ is obtained from both  the N ii and
the O ii lines with each ion providing lines spanning a range in equivalent width.

In principle, the chemical composition of the adopted model atmosphere
must match the composition derived from a spectrum. This match is achieved
iteratively. Note that model atmospheres computed with
C/He of 0.003 - 0.03% and H/He of 0.0001 and 0.1 have the same
atmospheric structure and so provide the same atmospheric parameters including the
composition. This helpful aide to the abundance analysis arises because neutral He is
the dominant opacity source for the two EHes.

Since  photoionization of 
neutral helium is the main source of continuous opacity,
lines of another species, say C ii, are sensitive to the
C/He abundance ratio. Abundances are given as logϵ(X)
and normalized with respect to logΣμ_ Xϵ(X) = 12.15
where μ_ X is the atomic weight of element X. Since all elements but He have a
very low abundance, the logarithmic He abundance is 11.54.


Our abundance analyses were carried with non-LTE model atmospheres and non-LTE
(and LTE) line formation for all major elements. For a few  minor elements, the abundance
analysis could be done only in LTE. 
Partially line-blanketed non-LTE model atmospheres were computed with the 
code TLUSTY <cit.> using atomic data and model atoms
provided on the TLUSTY home page[http://nova.astro.umd.edu/index.html], 
as described in <cit.>. These model atmospheres included opacity from
both bound-free and 
bound-bound transitions of H, He, C, N, O, Ne, Mg, Si, S, and Fe in
non-LTE. The adopted model atoms with their number of levels given in parentheses, are:
H i(9), He i(14), He ii(14), C i(8), C ii(11), C iii(12),
C iv(13), N i(13), N ii(6), N iii(11), N iv(12), O i(22),
O ii(29), O iii(29), Ne i(35), Ne ii(32), Ne iii(34),
Mg ii(14), Si ii(16), Si iii(12), Si iv(13), S ii(14),
S iii(20), Fe ii(36), and Fe iii(50). Of the model atoms available in TLUSTY,
these choices each refer to the smallest of the available atoms for many ions. Use of these model 
atoms suffices for the calculations of model atmospheres but, as we describe below, larger model atoms 
are used for the calculations of equivalent widths of lines.

Model atmospheres in LTE were also computed using TLUSTY.  Model grid in non-LTE and LTE
were computed covering the ranges T_ eff = 20 000 (1 000) 30 000 K 
and log g = 3.0 (0.1) 4.5 cgs. 



In this paper, we have used TLUSTY and SYNSPEC for calculating LTE and
non-LTE model atmospheres and line profiles <cit.>.
Stellar atmospheric parameters provided in Table 1 are
determined from the spectra of V652 Her and HD 144941 on the assumption
of both non-LTE and LTE using the lines given in Tables 2 and 3.
Except where noted, the gf-values of the lines are taken from the
NIST database[http://www.nist.gov/pml/data/asd.cfm] (ver. 5.3).
A few other sources consulted for gf-values are given in footnotes to the
relevant tables.













TLUSTY model atmospheres are calculated with line opacity provided by the smallest of
the available model atoms for many ions, as detailed above. In many cases, the observed lines are
not contained within these model atoms. In order to extend the non-NLTE calculations to more of
the observed lines, we ran the statistical equilibrium calculations with larger model atoms
available in TLUSTY as described in <cit.>. Results are provided for the following model atoms:
C ii(22), C iii(23), N ii(42), N iii(32), O ii(29),
Ne i(35), and  Si iii(30). Lines with both the upper and lower level within the 
model atom are marked by * in Table 2 and 3.
We note that, our non-LTE abundance analysis using model atmospheres with extended (more levels) model atoms is
fairly consistent in terms of the ionization balance and the derived abundances when compared with
the analysis using small (less levels) model atoms; the mean abundances differ by
about 0.05 to 0.3 dex, and that individual line abundances differ by typically ≤0.3 dex. 
However, for most of the ions, we notice that the larger model atoms
provide relatively less line-to-line scatter in the derived abundances.














For the elements H to Fe, identification of lines suitable for analysis
is not a major issue for V652 Her. In particular, a good selection of clean lines
representing the ions of key elements is available. For HD 144941, lines of H, He, N, and O are available in good number but
 fewer lines are present for C, Ne, Al, Si, and S with Fe represented only by upper limits to equivalent widths of the most promising lines of Fe iii.
<cit.> is the primary source of wavelengths and
classifications for these lines.



 §.§ V652 Her




  §.§.§ Non-LTE analyses


The Non-LTE code SYNSPEC <cit.> was adopted to compute the line profiles and the
theoretical equivalent widths using the non-LTE model atmospheres. The observed absorption profile or 
its measured equivalent width was matched with the SYNSPEC prediction to obtain the 
non-LTE abundance. The unresolved blends of two or more lines were dealt by
synthesizing and then matching to the observed feature by adjustment of abundances.

For determining the T_ eff, log g and ξ, a standard procedure is followed.
The microturbulent velocity ξ is estimated from N ii and O ii lines as they 
show a wide range in equivalent width. To minimise the temperature dependence, N ii lines 
with similar lower excitation potentials (LEP) were used: N ii lines were used with LEPs 
about 18, 21, 23, and 25 eV. ξ was found from the requirement that the derived abundance is
independent of the measured equivalent width. A microturbulent velocity 
ξ=13±2  km s^-1 is obtained from N ii and O ii lines.

Ionization equilibrium is imposed, using model atmospheres computed with small model atoms, to provide loci in 
the (T_ eff, log g) plane for the following pairs of ions:
C ii/C iii, N ii/N iii, S ii/S iii, 
and Si iii/Si iv but low weight is given to the last ratio because the Si abundances from the Si iii lines show
a large line-to-line scatter. 

Fits to the Stark-broadened wings of He i and He ii line profiles provide additional loci
in the (T_ eff, log g) plane. The line broadening coefficients are from TLUSTY/SYNSPEC which
adopts the line broadening coefficients for He i 4471Å, 4388Å, and 4026Å 
from <cit.>. For He i 4009Å, TLUSTY/SYNSPEC uses an approximate Stark broadening
treatment. For He ii 4686Å, TLUSTY/SYNSPEC uses a broadening table from 
Schoening (private communication to I. Hubeny). The predicted line profiles depend on the
electron densities and, therefore, on the temperature and surface gravity.
Observed profiles of the He i 4471Å, 4388Å, 4026Åand 4009Å lines and the He ii 4686Å were used in the analysis.

Sample observed profiles of the He i and He ii 4686Åline are shown in Figure 2 with predicted non-LTE profiles for a non-LTE
atmosphere of T_ eff=25000K and three different surface gravities. The He i and He ii
loci were obtained by fitting the line profiles for a range of effective temperatures.
Note that, the predicted profiles have been convolved with the instrumental profile
and the stellar rotation profile. A projected rotation velocity of 10-12 km s^-1 was obtained
from fits of synthetic spectra to clean O ii lines with an allowance for the instrumental
profile. 









The loci derived from the application of ionization equilibrium to C, N, Si, and S ions are
also added to the loci from the He i and He ii profiles.
Figure 3 shows these loci. Their intersection suggests the best non-LTE model
atmosphere has T_ eff=25000±300K and log g = 3.10±0.12.

H i observed profiles at 4102Å, 4340Å and 4861Å were chosen for
estimating the non-LTE hydrogen abundance by spectrum synthesis.
The line wings of 4340Å and 4861Åprofiles are mainly used for this purpose. It is noted that the best fitting theoretical profile for each line
does not have an emission core but
such cores appear for theoretical profiles of higher H abundance.
Less weight is given to the NLTE hydrogen abundance derived from the poor signal-to-noise profile
of 4102Å line. The hydrogen model atoms and the
line broadening coefficients adopted from <cit.> are from TLUSTY.
Observed profiles of the 4102Å, 4340Å, and 4861Åare shown in Figure 4 with predicted non-LTE profiles for a non-LTE
atmosphere of T_ eff=25000K and log g = 3.10 for three different
hydrogen abundances.

The abundances of all elements were derived for the adopted model atmosphere
(T_ eff, log g, ξ)=(25000, 3.10, 13.0), computed with extended model atoms. The final photospheric line by line
non-LTE abundances including the mean abundance
and the line-to-line scatter are given in Table 2.



The abundance rms errors due to uncertainty in T_ eff and log g, from
C ii, C iii, N ii, N iii, O ii,
Ne i, Mg ii, Si iii, Si iv, S ii, S iii, and
Fe iii are 0.03, 0.13, 0.03, 0.16, 0.04, 0.02, 0.04, 0.05, 0.13, 0.05, 0.05, and
0.03 dex, respectively.




  §.§.§ LTE analyses


Analysis of the line spectrum was repeated with the TLUSTY LTE models and LTE line
analysis. This LTE analysis uncovers several inconsistencies arising from substantial
non-LTE effects on some of the lines. These inconsistencies demand worrying compromises
in selecting the atmospheric parameters and, thus, in determining the elemental abundances.

Among the concerns are the fits to the He i and He ii line profiles. Observed profiles of He i and the 
He ii 4686 Å lines are shown in Figure 5 with predicted LTE profiles for the LTE 
atmosphere of T_ eff = 25300 K and three different surface gravities. The predicted 
He i profiles fail to reproduce the observed cores but are acceptable fits to 
the line wings. Note that the non-LTE profiles provide a satisfactory fit  both to  the cores and 
the wings (Figure 2). In LTE, the fit to the He ii 4686 Å line requires a much higher 
surface gravity at a given temperature than other indicators. Figure 6, the LTE counterpart to Figure 3,
shows the He i and He ii loci, as well as those corresponding to ionization equilibrium. 

The loci set by ionization equilibrium for C, N and Si are almost coincident and each is only slightly shifted from
their non-LTE location in the T_ eff,log g plane. However, the locus set by S ii/S iii is shifted away
from other ionization equilibrium loci because of the large non-LTE effect on the S iii lines.

Other species subject to appreciable non-LTE effects do not enter into consideration in determining the
atmospheric parameters. The species most obviously affected by non-LTE effects is Ne i .





An enthusiast dedicated to LTE analyses with Nelsonian eyesight might adopt the LTE model (see Figure 6)
with T_ eff = 25300±300 K,  log g = 3.25±0.12 and a microturbulence of 13 km s^-1.
The LTE abundances for this adopted LTE TLUSTY model are given in Table 2. The abundance rms errors,
due to uncertainty in T_ eff and log g, from Al iii, Si ii, P iii,
and Ar ii are 0.05, 0.07, 0.03, and 0.04 dex, respectively. The abundance rms errors for the
rest of the species are very similar to those estimated for the appropriate non-LTE model atmosphere. Of course,
such errors do not recognize that the choice of the LTE model atmosphere involves compromises.





 §.§ HD 144941




  §.§.§ Non-LTE analyses


Essentials of the  procedure  discussed in Section 3 for V652 Her were adopted for the non-LTE analyses of HD 144941.
A microturbulent velocity ξ=10  km s^-1 is used as suggested by <cit.>.
Except for the observed H i and He i lines, all lines in the observed spectrum are
weak.  Of course, the derived abundances from these weak lines are almost independent of the adopted
microturbulence.

Fits to the Stark-broadened wings of He i and He ii line profiles provide loci
in the (T_ eff, log g) plane. Unfortunately, the He ii 4686Å line profile is not
detected on our spectrum but the upper limit to its presence provides a limiting locus 
in the (T_ eff, log g) plane. Figure 7 shows the
sample observed profiles with predicted non-LTE profiles for a non-LTE atmosphere of 
T_ eff=22000K and three different surface gravities.

The only locus obtained from ionization balance is through sulphur ions:
S ii/S iii but this is based on just one weak S ii and two weak S iii lines. 

Figure 8 shows the loci obtained from the fits to the He i and He ii profiles
and the ionization balance of S ii/S iii using model atmospheres computed with small model atoms. 
These intersecting loci are used in determining 
the final model parameters of T_ eff=22000±600K and 
log g = 3.45±0.15.

Observed profiles of the 4102Å, 4340Å, and 4861Å are shown in Figure 9 with predicted
non-LTE profiles for a non-LTE atmosphere of T_ eff=22000K and log g = 3.45 for three different
hydrogen abundances. The line-wings are mainly used for this purpose as the predicted profiles show 
emission in the line-core. Unlike V652 Her, the best fits to the wings are 
affected by emission in the core with the intensity of emission increasing from Hδ to Hβ.
However, the predicted profiles by <cit.> match the 
observations (the wings as well as the core) fairly well.
 For comparison, observed profiles of the 4102Å, 4340Å, and 4861Å lines for three different H abundances
are shown in Figure 10 with predicted
non-LTE profiles for a non-LTE atmosphere with the stellar parameters, T_ eff=22000K and log g = 4.15
adopted by <cit.>: 
(logϵ( H) = 10.1 is the non-LTE abundance estimated by <cit.> and <cit.>.





The non-LTE abundances for the adopted non-LTE TLUSTY model 
(T_ eff, log g, ξ)=(22000, 3.45, 10.0), computed with small model atoms, are given in Table 3.
The abundance rms errors, due to uncertainty in T_ eff and log g, from
C ii, N ii, O ii, Ne i, Mg ii, Si iii, S ii, S iii,
and Fe iii are 0.06, 0.06, 0.05, 0.04, 0.07, 0.06, 0.08, 0.06, and 0.04 dex, respectively.



  §.§.§ LTE analyses


Inconsistencies among atmospheric parameter indicators when using LTE model atmospheres and
LTE line analysis techniques may be expected to resemble those inconsistencies
identified as present for V652 Her. The lower abundances of many elements in 
HD 144941 relative to V652 Her may effect the radiation
field in HD 144941's atmosphere even though opacity at many wavelengths including the optical
region is dominated by helium.

Observed profiles of the He i and He ii 4686Åline are shown in Figure 11 with predicted LTE profiles for a LTE
atmosphere of T_ eff=21000K and three different surface gravities.
As anticipated, the predicted LTE He i profiles for HD 144941
fail to reproduce the observed line-core but the line-wings are well reproduced but the predicted
non-LTE He i profiles successfully reproduce the observed core as well as the wings 
with the adopted non-LTE TLUSTY model (see Figure 7).

The He ii 4686Å line is not
positively detected on our spectra. Predicted profiles of this line provide a limiting locus with significantly
higher gravities than other indicators, a similar situation occurs for V652 Her (Figure 6).

Figure 12 shows the loci obtained from the fits to the He i and He ii profiles
and ionization equilibria which are provided by the the following pairs of ions:
Si ii/Si iii and S ii/S iii. The Si locus appears in Figure 12 but not Figure 8 because
TLUSTY lacks an adequate model Si^+ atom.
The final compromise LTE model parameters are 
T_ eff=21000±600K and log g = 3.35±0.15.

LTE abundances for the adopted LTE model are given in Table 3.
Observed profiles of the Balmer lines 4102Å, 4340Å, and 4861Å are shown in Figure 13 with predicted
LTE profiles for a LTE atmosphere of T_ eff=21000K and log g = 3.35 for three different
hydrogen abundances. The abundance rms errors,
due to uncertainty in T_ eff and log g, from Al iii, and Si ii
are 0.06, and 0.11 dex, respectively. The abundance rms errors for the
rest of the species are very similar to those estimated for the appropriate non-LTE model atmosphere.
In comparing non-LTE - LTE abundance differences in Table 2 for V652 Her and in Table 3 for
HD 144941, it must be noted that the compromise LTE model for V652 Her is 300 K hotter and
0.15 dex greater in log g than its non-LTE model but the LTE model for HD 144941 is 1000 K cooler
and 0.10 dex lower in log g than its non-LTE model. 




§ DISCUSSION - CHEMICAL COMPOSITION


Tables 4 and 5 summarize our derived non-LTE and LTE abundances for V652 Her and HD 144941, respectively.
Mean elemental abundances are given for elements represented by more than a single stage of
ionisation. Composition of the solar photosphere is given 
in the final column <cit.>.




 §.§ V652 Her


Inspection of the abundances for V652 Her offers three pointers to the star's
history: i) most obviously, it is  H-poor by a factor of about 300, ii) CNO-cycling was
most likely responsible for conversion of H to He because, as first noted by <cit.>,
the star is N-rich and relatively C and O poor, and iii) the overall metallicity of the
star is approximately solar, as judged by the abundances of elements from Mg to Fe. Before
connecting these points to the star's evolutionary status, brief remarks are made on the previous LTE abundance analysis
of this star.

<cit.> obtained a time series of optical spectra at a resolving power of 10000.
Results of a LTE abundance analysis when this pulsating star was near maximum radius were
given. This LTE atmosphere had parameters T_ eff = 22000 K, log g = 3.25 and
a microturbulence of 9 km s^-1. This model is 3000 K cooler than our LTE model and differs slightly in
surface gravity and microturbulence. A direct comparison of LTE abundances (our Table 4 and their Table 2)
gives differences of less than ±0.3 dex for all elements except C, Ne and P for which differences in the
sense (us - them) are -0.4, +0.6 and -0.9 dex, respectively. Jeffery et al. isolate their P abundance
estimate for comment and recommend that `The older value [as provided by <cit.>]
should be preferred for the present.' This older value for P is within 0.1 dex of our LTE value. 
When the 1999 values for H to Fe are adopted, the (us - them) differences are within ±0.3 dex except
for S at 0.4 dex. The 1999 LTE model atmospheres corresponded to
T_ eff = 24550±500 K, log g = 3.68±0.05 and a microturbulence 5 km s^-1. In short, 
our and published LTE abundance analyses are in good agreement but this should be hardly surprising given
the similarities of spectra and analytical tools.









 <cit.> provided a hybrid non-LTE analysis (i.e., a non-LTE analysis of absorption lines was
made using a LTE model atmosphere) of a selection of lines measured off the spectrum used by <cit.>.
The atmosphere was very similar to that used by <cit.> and, thus, 3000 K cooler  but of similar surface
gravity to our chosen non-LTE model atmosphere. The abundances of H, C, N, O, Mg and S differ in the
sense (Us - Prz) by +0.3, -0.4, +0.2, -0.5, -0.8 and -0.3 dex, respectively. C, Mg and S were represented 
by very few lines. With the exception of the Mg abundance from the 
Mg ii 4481 Å feature (the sole Mg indicator), the non-LTE - LTE
corrections are within  ±0.2 dex. This independent non-LTE analysis fully confirms the result 
that V652 Her's atmosphere is now highly enriched in CNO-cycled material.

What is new here is the demonstration that adoption of a set of non-LTE atmospheres and the
chosen collection of non-LTE line tools reveal inconsistencies in the 
indicators previously employed to determine the
appropriate atmospheric parameters and corrections to LTE abundances for non-LTE effects which
can for some species (e.g., Ne i) be considerable. At the present time, the non-LTE abundances
should be used to discuss the three pointers mentioned in this section's opening paragraph.
   
Even if V652 Her is the result of a merger of two He white dwarfs, it is very likely to have
retained the metallicity - say, Ne to Fe abundances - of the two stars from which the white
dwarfs evolved with mass loss and mass exchange playing major roles. For the five elements
(Ne, Mg, Si, S and Fe) with non-LTE abundances, the mean difference (V652 Her - Sun) is -0.1 which
suggests a near-solar initial composition. (The differences of -0.5 for Mg and Fe are intriguing.) 
Thus, V652 Her is a member of the thin disk.

V652 Her's high N abundance is 0.8 dex above the solar value. This coupled with the high H deficiency
and sub-solar values of C and O point to CNO-cycling as the primary process for conversion of
H to He. The CNO-cycles preserve the total number of C, N and O nuclei. The non-LTE
CNO-sum is 8.78 and the solar sum is 8.92. Almost fortuitously, the expected sum for a mix corresponding
to a metal deficiency of -0.1 dex is 8.82!.  












 §.§ HD 144941


Comparison of the non-LTE and solar abundances (Table 5) shows a near-uniform difference (star - Sun)
for elements from C to Fe. With the exception of Ne and S, the mean difference is -1.6 with individual
values ranging from -1.4 to -1.8.  (The LTE Al abundance gives a difference of -1.4.)
The difference for Fe is ≤ -0.9. The Fe line at 5156Å is present in all  three exposures, and clearly seen in Figure 14 but since this is
the sole positive detection and not confirmed by other lines,  we assign an upper limit to the Fe abundance. 
Adopting the Fe abundance
from IUE spectra and the LTE analysis  by <cit.>, the difference
is -1.8, a value consistent with our much higher limit. Their logarithmic Fe abundance of 5.7±0.2 and our
non-LTE abundances, except for the α-elements: Ne and S, are consistent with the composition of metal-poor stars, 
residents of the Galactic thick disk or halo, which show α-element enhancements of approximately
+0.3 for O, Mg and Si. Moreover, the abundances of C, N and O are consistent with the difference
of -1.6, and, hence, the H-deficiency is not obviously attributable to CNO-cycling, as is the case for
V652 Her.

As just noted, Ne and S provide striking exceptions to the run of (star - Sun) differences offered by
other elements. These elements give differences of -0.7 for Ne and -0.9 for S. There are no
convincing nucleosynthetic reasons for these differences. (Just conceivably, N-rich He-rich
material could have been heated and a considerable amount for N burnt to Ne by two
successive alpha-captures. The total initial sum of CNO abundances could have been about
7.3 but the Ne abundance of 7.2 implies a near perfect conversion of CNO to Ne.) The Ne i
lines appear to be secure identification - see Figure 14 for the strongest Ne i line. The primary
suspect for the high S abundance are systematic errors associated with the identification of
the weak S ii and S iii lines. The gf-values and non-LTE treatment are less likely
sources of errors as the measured lines are among a larger set used for V652 Her. 

Our LTE abundances are in good agreement with the previous LTE analysis of an optical spectrum
by <cit.> using the model atmosphere T_ eff = 23200 K, log g = 3.9 and
a microturbulence of 10 km s^-1.  The abundance differences (us - them) are within  ±0.25
dex limits. Unfortunately, Harrison & Jeffery did not include Ne and S. Their Fe abundance of 6.4 was
lowered to 5.7 by their synthesis of lines in IUE spectra <cit.>. Our non-LTE abundances are also in
good agreement but for Mg with results from <cit.>'s hybrid non-LTE analysis: differences (Us - Pry) are 
+0.3, 0.0, -0.3, -0.4 and -0.8 dex for H, C, N, O and Mg, respectively. Our corrections (Non-LTE - LTE) are in 
agreement to within ±0.15 dex including for Mg ii with those found by <cit.>. The model atmosphere
used by <cit.> has the same effective temperature but a higher surface gravity (log g = 4.15 rather our 3.45). 
<cit.> selected lines from the optical spectrum used by <cit.>. 



§ CONCLUDING REMARKS


A possible origin for extreme He stars such as V652 Her and HD 144941 involves, as noted in the Introduction, the merger of two He
white dwarfs. The white dwarfs themselves began life as main sequence stars in a binary system which then experienced two mass  exchange
and mass loss episodes  to form the pair of low-mass He white dwarfs. Emission of gravitational radiation causes the white dwarfs to slowly approach
each other.  White dwarf binaries which can merge in a Hubble time or less are candidates to account for V652 Her and HD 144941.
<cit.> present evolutionary tracks for the merger of two white dwarfs. Three modes of merger are discussed: slow, fast and
composite.  Since their calculations are most extensive for Z=0.02 white dwarfs,  V652 Her is discussed first.

In the slow merger (see also <cit.>), the lower mass white dwarf loses its mass in a few minutes to  form a disk around the more
massive white dwarf.  Accretion from the disk by the surviving white dwarf may last several million years and completes the merger. The composite
star is initially a luminous red giant  which evolves to become a hot subdwarf before entering the white dwarf cooling track.  Along this evolutionary
track, the star may appear as an EHe.  Zhang & Jeffery's calculations predict that the surface composition of the merged star (i.e., the EHe) is that of the less massive white dwarf; there is no mixing between the accreted material and the accreting star. The recipe for setting the compositions of the He white dwarfs as described by Zhang & Jeffery proves insensitive to the less massive star's assumed mass (see Figure 2 from <cit.> for Z = 0.02 star). The stars are predicted to be N-rich (N/C ∼ 100 and N/O ∼ 10) with C/He ∼ 0.01%. This pattern for He, C, N, O and also Ne matches to within a factor of about two, the observed composition of V652 Her (Table 4). (Oddly, the predicted mass fraction of ^24Mg is about an order
of magnitude higher than observed.) Predicted evolutionary tracks in the (T_  eff, log g) plane about the EHe domain are coincident for
masses of 0.5-0.7M_⊙ with tracks for higher masses occurring at lower surface gravities (see Figure 15 from 
<cit.>). (The tracks
at T_ eff≤ 40000 K appear insensitive to the initial composition; Z= 0.02 was generally adopted, i.e., slightly supra-solar.) With
non-LTE parameters from Table 1, V652 Her falls on the predicted 0.8M_⊙ track which is only 0.6 dex lower in log g than the 0.5-0.7M_⊙
tracks.  Since <cit.> estimate V652 Her's mass at 0.6±0.2M_⊙, we consider the observed star fits the predicted evolutionary track
for a slow merger of two He white dwarfs. This fit is echoed by the correspondence between predicted and observed compositions.  In short, V652 Her
may be the result of a slow merger of two low-mass He white dwarfs.

In a fast merger, accretion is considered to be complete in a few minutes. In Zhang & Jeffery's simulations the envelope resembles a hot
corona with carbon produced by He-burning and N destroyed by ^14N(α,γ)^18O and at higher temperatures α-capture
converts the ^18O to ^22Ne. Burning in a He-shell occurs in flashes. Zhang & Jeffery conclude description of fast mergers with
the remark that `For all the fast merger models the surface composition is rich in  ^12C, ^18O and ^22Ne but there is almost
no ^14N for models with initial composition of Z = 0.02. (Of course, it is frustrating that isotopic wavelength shifts for atomic lines with 
stellar line widths do not permit determinations of the isotopic mix of C, O and Ne.) For slow mergers with Z = 0.02, the predicted N/C ratio is about 100 and independent of the final mass as noted above, but for fast mergers the N/C is predicted to run from 0.01 for a final mass of 0.5M_⊙ to 10^-9 for a final mass of 0.8M_⊙ (see Figure 19 of Zhang & Jeffery).  Clearly V652 Her is not the result of a fast merger.

In the composite model, as envisaged by Zhang & Jeffery, the first phase of accretion transfers about half of the mass as a fast merger
with the second half transferred via a disk as in the case of a slow merger. For mergers resulting in a total mass of less than about 0.6M_⊙
(apparently, resulting from roughly equal masses for the two white dwarfs), the surface convection zone is absent and, thus, the surface
composition resulting from accretion from the disk is that of the accreted white dwarf, i.e., the predicted composition is equivalent to that of a slow
merger (see Figure 20 from Zhang & Jeffery). At total masses above 0.6M_⊙ the predicted compositions tend in the direction to those predicted by a
fast merger; the N/C ratio is about 0.3 for a mass 0.8M_⊙ but the prediction for a fast merger is 10^-11. V652 Her may
have resulted from a composite merger (effectively, a slow merger) with a total mass less than about 0.6M_⊙. 
 
In brief, V652 Her's  composition and location in the (T_ eff,log g) plane encourage the idea that the star resulted from the
merger of two Helium white dwarfs. As modeled by Zhang & Jeffery,  the star resulted from a slow or a composite merger with a rather
relaxed constraint on the masses of the white dwarfs. A fast merger, as defined by Zhang & Jeffery, leads to a star with N/C less than
unity in sharp conflict with the observed N/C ratio of 50. Significantly, V652 Her's composition and position in the (T_ eff,log g) plane
can be met by a range of slow or composite mergers. In contrast to V652 Her, the picture of a merger of He white dwarfs is not so
obviously readily applicable to HD 144941. 

An initial impression of HD 144941's composition (Table 5) is that the C, N and O are consistent with the initial abundances for a star
with [Fe/H] of about -1.6 or Z ∼ 0.0004 but such a consistency surely sits uneasily with the messy conversion of a main sequence star to a highly-evolved H-poor star. Moreover, the star's Ne abundance is about 1 dex greater than anticipated for a normal metal-poor star. Thus, we have sought possible solutions in Zhang & Jeffery's paper. It is worthy of note that with respect to the (T_ eff,log g) plane, HD 144941's non-LTE parameters provide an excellent fit to Zhang & Jeffery's evolutionary tracks for merging white dwarfs from stars with Z=0.001. Observed and predicted compositions are more difficult to reconcile. For slow mergers at Z = 0.001, models predict products with a much lower C/He ratio than observed and a very high N/C ratio (see Figure 20 from Zhang & Jeffery), say N/C ∼ 200 but the observed ratio is N/C ∼ 0.3. Fast mergers invert the N/C ratio and but are likely to provide a N abundance declining steeply with increasing total mass such that a match to HD 144941 will be found only for a narrow range of masses. A composite merger may match the observed He, C and N abundances with adjustments to Zhang & Jeffery's recipe for this merger process. Introduction of a period of
fast merging is expected to increase the Ne (as ^22Ne) abundance and so possibly match the observed Ne abundance. (An episode of fast merging
may also provide abundant ^18O.) Expansion of the parameter space considered by Zhang & Jeffery is highly desirable. 


Our abundance analysis shows that the use of non-LTE effects in the construction of model atmospheres and analyses of absorption lines for He-rich warm stars leads to significant changes in the defining atmospheric abundances and in certain elemental abundances relative to the assumption of LTE for
model atmospheres and abundance analysis. Judged by our determinations of composition and location in the (T_ eff,log g) plane, V652 Her  is likely to have resulted from the merger of two helium white dwarfs. HD 144941's location in the  (T_ eff,log g) plane is similarly consistent with the merger hypothesis. Its composition may also be consistent with formation through a merger but additional theoretical predictions seem required. These conclusions are based on Zhang & Jeffery's bold and exploratory calculations of the merging process.  Perhaps, our analyses will not only encourage refinements to the study of white dwarf mergers but also a search for additional EHe stars with the very low C/He ratio that is a characteristic feature of V652 Her and HD 144941.

Quite fortuitously, after submission of the paper,  <cit.> reported the discovery of a third EHe star with a low C/He (= 0.0023%) ratio. The star
GALEX J184559.8-413827 according to the LTE abundance analysis by <cit.>  has a subsolar (-0.4)  metallicity with  C, N and O  abundances
similar to that of V652 Her, i.e., the atmosphere of the new discovery is rich in CNO-cycled material. Our abundance analyses of V652 Her  show that a non-LTE
reanalysis of J184559.8-413827 will not alter this conclusion.  



We thank Simon Jeffery and Mike Montgomery for helpful email exchanges. We also thank
Ivan Hubeny for helping us in using the TLUSTY and SYNSPEC codes. We would like to thank 
the anonymous referee for the constructive comments.
DLL acknowledges the support of the Robert A. Welch Foundation of Houston, Texas through grant F-634.
































llcccc

0pt
7
Summary of atmospheric parameters

          T_ eff     log g     ξ    
v sin i

Star     Analyses     (K)     (cgs units)     (km s^-1)    
(km s^-1)
V652 Her     non-LTE     25000±300      3.10±0.12     13±2     10 - 12  

V652 Her     LTE     25300±300      3.25±0.12     13±2     10 - 12  

HD 144941     non-LTE     22000±600      3.45±0.15     10     10  

HD 144941     LTE     21000±600      3.35±0.15      10     10  




lccrcc


0pt
7


Measured equivalent widths (W_λ) and NLTE/LTE photospheric line abundances
for V652 Her.

     χ          W_λ    
2clog ϵ( X)

5-6 

Line     (eV)     log gf     (mÅ)    
NLTEa     LTEb
H i λ 4101.734     10.199     -0.753     Synth     9.42      9.65     

H i λ 4340.462     10.199     -0.447     Synth     9.47      9.64     

H i λ 4861.323     10.199     -0.020     Synth     9.52      9.69     

                                                                                

Mean...                  9.47±0.05      9.66±0.03 

                                                                                

C ii λ 3920.681*     16.333     -0.232     35      7.21      6.94     

                                                                                

C ii λ 4267.001*     18.046     +0.563                                

C ii λ 4267.183*     18.046     +0.716                                

C ii λ 4267.261*     18.046     -0.584     125     7.29      6.94     

                                                                                

C ii λ 6578.050*     14.449     -0.026     69      7.04      6.86     

C ii λ 6582.880*     14.449     -0.327     45      7.08      6.90     

                                                                                

Mean...                 7.16±0.12     6.91±0.04 

                                                                                

C iii λ 4647.418*     29.535    +0.070     25      6.86     6.88 

C iii λ 4650.246*     29.535    -0.151     22      6.92     7.02 

                                                                                

Mean...                 6.90±0.04     6.95±0.10 

                                                                                

N ii λ 3955.851*     18.466     -0.849     139                8.56 

N ii λ 3994.997*     18.497     +0.163     308      8.75      8.99 

N ii λ 4227.736*     21.600     -0.061     153                8.64 

N ii λ 4459.937*     20.646     -1.476      28      8.77      8.63 

N ii λ 4507.560*     20.666     -0.817      74                8.54 

N ii λ 4564.760*     20.409     -1.589      30                8.73 

N ii λ 4601.478*     18.466     -0.452     220      8.73      8.87 

N ii λ 4607.153*     18.462     -0.522     206      8.73      8.83 

N ii λ 4613.868*     18.466     -0.665     194      8.79      8.86 

N ii λ 4621.393*     18.466     -0.538     215      8.79      8.91 

N ii λ 4630.539*     18.483     +0.080     316      8.78           

N ii λ 4643.086*     18.483     -0.371     222      8.55      8.82 

N ii λ 4654.531*     18.497     -1.506      85                8.83 

N ii λ 4667.208*     18.497     -1.646      65                8.79 

N ii λ 4674.908*     18.497     -1.553      80                8.84 

N ii λ 4718.377     27.746     -0.042      33                8.91 

N ii λ 4774.244*     20.646     -1.280      51                8.78 

N ii λ 4779.722*     20.646     -0.587     106                8.60 

N ii λ 4781.190*     20.654     -1.337      40                8.70 

N ii λ 4788.138*     20.654     -0.363     120                8.49 

N ii λ 4803.287*     20.666     -0.113     160                8.57 

N ii λ 4810.299*     20.666     -1.084      54                8.63 

N ii λ 4987.376*     20.940     -0.584      87                8.53 

N ii λ 4991.243*     25.491     -0.180      50                8.81 

N ii λ 4997.224*     25.491     -0.657      28                8.96 

N ii λ 5002.703*     18.462     -1.022     126                8.65 

N ii λ 5023.053*     25.507     -0.165      60                8.91 

N ii λ 5045.099*     18.483     -0.407     245      8.66      8.83 

N ii λ 5073.592*     18.497     -1.550      85                8.91 

                                                                                

N ii λ 5179.344     27.980     +0.497                             

N ii λ 5179.521     27.746     +0.675      95                8.71 

                                                                                

N ii λ 5183.200     27.980     -0.090      26                8.94 

N ii λ 5184.961     27.739     -0.044      26                8.84 

N ii λ 5452.070*     21.148     -0.881      60      8.74      8.66 

N ii λ 5454.215*     21.153     -0.782      97      8.88      8.91 

N ii λ 5478.086*     21.153     -0.930      40                8.47 

N ii λ 5480.050*     21.160     -0.711      56                8.45 

N ii λ 5495.655*     21.160     -0.220     106                8.43 

N ii λ 5526.234*     25.491     -0.312      45      8.58      8.93 

N ii λ 5530.242*     25.498     +0.113      81      8.48      8.90 

                                                                                

N ii λ 5535.347*     25.507     +0.398                             

N ii λ 5535.383*     25.491     -0.204     135      8.43      8.98 

                                                                                

N ii λ 5540.061*     25.491     -0.557      32      8.65      8.98 

N ii λ 5543.471*     25.498     -0.092      68      8.59      8.98 

N ii λ 5551.922*     25.507     -0.189      63      8.64      9.03 

N ii λ 5676.020*     18.462     -0.367     236      8.77      9.06 

N ii λ 5710.770*     18.483     -0.518     199      8.87      8.88 

N ii λ 5730.660*     18.483     -1.703      51                8.77 

N ii λ 5747.300*     18.497     -1.091     116                8.77 

N ii λ 5767.450*     18.497     -1.447      95                8.95 

N ii λ 6136.890*     23.132     -1.124      23                8.89 

N ii λ 6150.750*     23.125     -1.086      24                8.87 

N ii λ 6167.750*     23.142     +0.025     122                8.86 

N ii λ 6170.160*     23.125     -0.311      73                8.75 

N ii λ 6173.310*     23.132     -0.126     100                8.82 

N ii λ 6340.580*     23.246     -0.192      79                8.73 

N ii λ 6346.860*     23.239     -0.901      37                8.96 

N ii λ 6379.620*     18.466     -1.191     103      8.60      8.81 

N ii λ 6482.050*     18.497     -0.311     229      8.82      9.04 

N ii λ 6504.610*     23.246     -0.626      55                8.93 

                                                                                

Mean...                 8.70±0.12     8.80±0.16 

                                                                                

N iii λ 4514.850*     35.671     +0.221      46                9.13 

N iii λ 4634.130*     30.459     -0.086      78      8.52      8.81 

N iii λ 4640.640*     30.463     +0.168     100      8.41      8.81 

                                                                                

Mean...                 8.50±0.10     8.92±0.18 

                                                                                

O ii λ 4345.560*     22.979     -0.346       62     7.64      7.67 

O ii λ 4366.895*     22.999     -0.348       60     7.60      7.64 

O ii λ 4414.899*     23.441     +0.172      104     7.53      7.64 

O ii λ 4416.975*     23.419     -0.077      107     7.78      7.91 

O ii λ 4452.378*     23.442     -0.788       23     7.56      7.65 

O ii λ 4590.974*     25.661     +0.350       70     7.79      7.68 

O ii λ 4596.177*     25.661     +0.200       52     7.72      7.63 

O ii λ 4638.856*     22.966     -0.332       64     7.64      7.69 

O ii λ 4649.135*     22.999     +0.308      140     7.64      7.74 

O ii λ 4650.838*     22.966     -0.362       38     7.35      7.40 

O ii λ 4661.632*     22.979     -0.278       62     7.57      7.62 

O ii λ 4676.235*     22.999     -0.394       42     7.44      7.50 

                                                                                

O ii λ 4699.011*     28.510     +0.418                             

O ii λ 4699.218*     26.225     +0.270       36     7.37      7.30 

                                                                                

O ii λ 4705.346*     26.249     +0.477       44     7.43      7.40 

O ii λ 5206.651*     26.561     -0.266       15     7.73      7.69 

                                                                                

Mean...                 7.59±0.14     7.61±0.15 

                                                                                

Ne i λ 5852.488*     16.848     -0.490      20                8.51 

Ne i λ 6143.063*     16.619     -0.100      53      8.13      8.62 

Ne i λ 6163.594*     16.715     -0.620      24      7.98      8.72 

Ne i λ 6266.495*     16.715     -0.370      25      7.75      8.50 

Ne i λ 6334.428*     16.619     -0.320      40      8.23      8.69 

Ne i λ 6382.991*     16.671     -0.240      40      8.13      8.62 

Ne i λ 6402.246*     16.619     +0.330      104     8.09      8.72 

Ne i λ 6506.528*     16.671     -0.030      52      8.07      8.58 

Ne i λ 6598.953*     16.848     -0.360      22      7.97      8.48 

Ne i λ 7032.413*     16.619     -0.260      40      8.16      8.67 

                                                                                

Mean...                 8.06±0.14     8.61±0.09 

                                                                                

Mg ii λ 4481.126*      8.864     +0.749                             

Mg ii λ 4481.150*      8.864     -0.553                             

Mg ii λ 4481.325*      8.864     +0.594      211     7.09      7.48 

                                                                                

Al iii λ 4149.913     20.555     +0.620                             

Al iii λ 4149.968     20.555     -0.680                             

Al iii λ 4150.173     20.555     +0.470      103               6.40 

                                                                                

Al iii λ 4479.885     20.781     +0.900c                              

Al iii λ 4479.971     20.781     +1.020c                              

Al iii λ 4480.009     20.781     -0.530c      75                5.93 

                                                                                

Al iii λ 4512.565     17.808     +0.410      89                6.24 

                                                                                

Al iii λ 4528.945     17.818     -0.290                             

Al iii λ 4529.189     17.818     +0.660      146               6.34 

                                                                                

Al iii λ 5696.604     15.642     +0.230      169               6.67 

Al iii λ 5722.730     15.642     -0.070      126               6.60 

                                                                                

Mean...                                   6.36±0.27 

                                                                                

Si ii λ 4128.054      9.837     +0.359       30               7.19 

                                                                                

Si ii λ 4130.872      9.839     -0.783                             

Si ii λ 4130.894      9.839     +0.552       34               7.04 

                                                                                

Si ii λ 5041.024     10.066     +0.029       35               7.67 

Si ii λ 5055.984     10.074     +0.523       44               7.30 

                                                                                

Mean...                                   7.30±0.27 

                                                                                

Si iii λ 3796.124*     21.730     +0.407                             

Si iii λ 3796.203*     21.730     -0.703      167     7.18      7.04 

                                                                                

Si iii λ 3806.526*     21.739     +0.679                             

Si iii λ 3806.700*     21.739     -0.071      307     7.60      7.69 

                                                                                


Si iii λ 4567.840*     19.016     +0.068      285     7.40      7.85 

Si iii λ 4574.757*     19.016     -0.409      204     7.34      7.57 

Si iii λ 4716.654*     25.334     +0.491       83     7.46      7.15 

Si iii λ 4813.333*     25.979     +0.708       85     7.04      7.11 

                                                                                

Si iii λ 4819.712*     25.982     +0.937                             

Si iii λ 4819.814*     25.982     -0.354      116     7.01      7.24 

                                                                                

Si iii λ 4828.951*     25.987     +0.937                             

Si iii λ 4829.111*     25.980     -0.354      120     7.03      7.16 

                                                                                

Si iii λ 5739.734*     19.722     -0.096      226     7.36      7.76 

                                                                                

Mean...                 7.27±0.21     7.40±0.32 

                                                                                

Si iv λ 4088.862*     24.050     +0.194      185     7.63      7.75 

Si iv λ 4116.104*     24.050     -0.110      120     7.48      7.44 

                                                                                

Mean...                 7.56±0.11     7.60±0.22 

                                                                                

P iii λ 4222.198     14.610     +0.210       80               5.42 

P iii λ 4246.720     14.610     -0.120       65               5.61 

                                                                                

Mean...                                   5.52±0.13 

                                                                                

S ii λ 5032.434     13.672     +0.188       40               7.35 

S ii λ 5103.332     13.672     -0.457       25               7.76 

S ii λ 5212.620     15.068     +0.316       25     7.21      7.33 

S ii λ 5320.723     15.068     +0.431       27     7.12      7.26 

S ii λ 5428.655*     13.584     -0.177       20     7.57      7.37 

S ii λ 5432.797*     13.617     +0.205       35     7.46      7.27 

S ii λ 5509.705*     13.617     -0.175       20     7.56      7.37 

S ii λ 5564.958     13.672     -0.336       33               7.80 

S ii λ 5606.151     13.733     +0.124       25               7.22 

                                                                                

S ii λ 5639.977     14.067     +0.258                             

S ii λ 5640.346     13.701     -0.036       45               7.23 

                                                                                

S ii λ 5660.001     13.677     -0.222       17               7.37 

                                                                                

Mean...                 7.38±0.21     7.39±0.20 

                                                                                

S iii λ 4253.589*     18.244     +0.107      174     7.46      7.18 

S iii λ 4284.979*     18.193     -0.233      103     7.28      6.90 

S iii λ 4332.692*     18.188     -0.564       66     7.26      6.88 

S iii λ 4354.566*     18.311     -0.959       53     7.49      7.15 

S iii λ 4361.527*     18.244     -0.606       68     7.32      6.95 

S iii λ 4364.747*     18.318     -0.805       34     7.07      6.74 

S iii λ 4499.245*     18.294     -1.640       16     7.52      7.20 

                                                                                

Mean...                 7.34±0.16     7.00±0.18 

                                                                                

Ar ii λ 4806.021     16.644     +0.210       32                6.91 

                                                                                

Fe iii λ 4137.764     20.613     +0.630c       42      6.74      7.05 

Fe iii λ 4164.731     20.634     +0.923c       83      6.91      7.20 

                                                                                

Fe iii λ 4296.851     22.860     +0.418c                              

Fe iii λ 4296.851     22.860     +0.879c       30      6.71      7.02 

                                                                                

Fe iii λ 4310.355     22.869     +0.189c                              

Fe iii λ 4310.355     22.869     +1.156c       45      6.76      7.05 

                                                                                

Fe iii λ 4395.755      8.256     -2.595c       39      7.04      7.34 

Fe iii λ 4419.596      8.241     -2.218c       81      7.15      7.38 

Fe iii λ 4431.019      8.248     -2.572c       38      7.02      7.30 

Fe iii λ 5063.421      8.648     -2.950c       18      7.14      7.42 

Fe iii λ 5086.701      8.659     -2.590c       40      7.17      7.46 

Fe iii λ 5127.387      8.659     -2.218c      100                7.66 

Fe iii λ 5156.111      8.641     -2.018c      100      7.31      7.46 

Fe iii λ 5235.658     18.266     -0.107c       33                7.18 

Fe iii λ 5243.306     18.270     +0.405c       71                7.13 

Fe iii λ 5276.476     18.264     -0.001c       36                7.13 

Fe iii λ 5282.297     18.266     +0.108c       43                7.12 

Fe iii λ 5299.926     18.261     -0.166c       31                7.21 

Fe iii λ 5302.602     18.262     -0.120c       31                7.17 

Fe iii λ 5460.799     14.178     -1.519c       30      6.88      7.59 

Fe iii λ 5485.517     14.176     -1.469c       30      6.83      7.54 

Fe iii λ 5573.424     14.175     -1.390c       42      6.92      7.64 

Fe iii λ 5833.938     18.509     +0.616c       66                6.96 

Fe iii λ 5891.904     18.509     +0.498c       54                6.96 

Fe iii λ 5929.685     18.509     +0.351c       48                7.04 

                                                                                

Mean...                 7.05±0.16     7.30±0.22 

a(T_ eff, log g, ξ)=(25000, 3.10, 13.0)
b(T_ eff, log g, ξ)=(25300, 3.25, 13.0)
cKurucz gf-value
*The lines covered by the adopted model atom, including the
extended model atom with more levels, for the ions providing the ionization balance and some other ions





lccrcc


0pt
7


Measured equivalent widths (W_λ) and NLTE/LTE photospheric line abundances
for HD 144941.

     χ          W_λ    
2clog ϵ( X)

5-6 

Line     (eV)     log gf     (mÅ)     NLTEa    
LTEb
H i λ 4101.734     10.199     -0.753     Synth    10.47     10.41     

H i λ 4340.462     10.199     -0.447     Synth    10.32     10.32     

H i λ 4861.323     10.199     -0.020     Synth    10.24     10.19     

                                                                                

Mean...                 10.37±0.09     10.35±0.05 

                                                                                

C ii λ 6578.050*     14.449     -0.026     88      6.88      6.64     

C ii λ 6582.880*     14.449     -0.327     52      6.84      6.58     

                                                                                

Mean...                 6.86±0.03     6.61±0.04 

                                                                                

N ii λ 3994.997*     18.497     +0.163      74      6.68      6.98 

N ii λ 4447.030*     20.409     +0.221      22      6.50      6.72 

N ii λ 4601.478*     18.466     -0.452      16      6.49      6.75 

N ii λ 4607.153*     18.462     -0.522      15      6.54      6.80 

N ii λ 4621.393*     18.466     -0.538      15      6.54      6.81 

N ii λ 4630.539*     18.483     +0.080      35      6.36      6.64 

                                                                                

N ii λ 4994.360*     25.498     -0.164                             

N ii λ 4994.370*     20.940     -0.098       8      6.55      6.75 

                                                                                

N ii λ 5001.474*     20.654     +0.435      24      6.47      6.69 


N ii λ 5025.659*     20.666     -0.558       8      6.94      7.15 

N ii λ 5045.099*     18.483     -0.407      16      6.49      6.76 

N ii λ 5666.630*     18.466     -0.080      12      6.10      6.37 

N ii λ 5676.020*     18.462     -0.367       8      6.19      6.47 

N ii λ 5679.560*     18.483     +0.250      24      6.11      6.39 

N ii λ 6482.050*     18.497     -0.311       7      6.17      6.45 

                                                                                

Mean...                 6.44±0.23     6.70±0.22 

                                                                                

O ii λ 4414.899*     23.441     +0.172       19     6.94      6.87 

O ii λ 4416.975*     23.419     -0.077       16     7.10      7.02 

O ii λ 4590.974*     25.661     +0.350       14     7.24      7.10 

O ii λ 4596.177*     25.661     +0.200       11     7.26      7.12 

O ii λ 4638.856*     22.966     -0.332        8     6.94      6.86 

O ii λ 4649.135*     22.999     +0.308       37     7.15      7.08 

O ii λ 4650.838*     22.966     -0.362        7     6.91      6.83 

                                                                                

Mean...                 7.08±0.15     6.98±0.13 

                                                                                

Ne i λ 6143.063*     16.619     -0.100      12      7.26      7.49 

Ne i λ 6402.246*     16.619     +0.330      28      7.26      7.50 

Ne i λ 6506.528*     16.671     -0.030      10      7.14      7.38 

                                                                                

Mean...                 7.22±0.07     7.46±0.07 

                                                                                

Mg ii λ 4481.126*      8.864     +0.749                             

Mg ii λ 4481.150*      8.864     -0.553                             

Mg ii λ 4481.325*      8.864     +0.594       51     5.77      5.88 

                                                                                





Al iii λ 4479.885     20.781     +0.900c                              

Al iii λ 4479.971     20.781     +1.020c                              

Al iii λ 4480.009     20.781     -0.530c      20                5.11  

                                                                                

Al iii λ 4512.565     17.808     +0.410      21                5.22 

                                                                                

Al iii λ 4528.945     17.818     -0.290                             

Al iii λ 4529.189     17.818     +0.660      33                5.17 

                                                                                

Al iii λ 5696.604     15.642     +0.230      21                4.96 

Al iii λ 5722.730     15.642     -0.070      11                4.95 

                                                                                

Mean...                                   5.08±0.12 

                                                                                

Si ii λ 5041.024     10.066     +0.029        8               6.11 

Si ii λ 5055.984     10.074     +0.523       15               5.90 

                                                                                

Mean...                                   6.01±0.15 

                                                                                

Si iii λ 4552.622*     19.016     +0.292       70     6.11      5.93 

Si iii λ 4567.840*     19.016     +0.068       46     6.03      5.85 

Si iii λ 4574.757*     19.016     -0.409       20     6.01      5.84 

                                                                                

Si iii λ 4819.712*     25.982     +0.937                             

Si iii λ 4819.814*     25.982     -0.354       12     5.75      5.99 

                                                                                

Si iii λ 4828.951*     25.987     +0.937                             

Si iii λ 4829.111*     25.980     -0.354       16     5.90      6.15 

                                                                                

Si iii λ 5739.734*     19.722     -0.096       23     6.16      5.95 

                                                                                

Mean...                 5.99±0.15     5.95±0.11 

                                                                                

S ii λ 5432.797     13.617     +0.205       12     6.08      6.09 


                                                                                



S iii λ 4253.589*     18.244     +0.107       30     6.30      5.71 

S iii λ 4284.979*     18.193     -0.233       17     6.31      6.11 

S iii λ 4332.692*     18.188     -0.564       ≤15     ≤6.59      ≤6.39 

                                                                                

Mean...                 6.31±0.01     5.91±0.28 

                                                                                

Fe iii λ 4395.755      8.256     -2.595c       ≤19      ≤7.09      ≤6.79 

Fe iii λ 4419.596      8.241     -2.218c       ≤29      ≤6.96      ≤6.62 

Fe iii λ 4431.019      8.248     -2.572c       ≤16      ≤6.99      ≤6.68 

Fe iii λ 5127.387      8.659     -2.218c       ≤20      ≤6.98      ≤6.59 

Fe iii λ 5156.111      8.641     -2.018c       ≤14      ≤6.60      ≤6.21 

                                                                                

Mean...                 ≤6.60±0.00     ≤6.21±0.00 

a(T_ eff, log g, ξ)=(22000, 3.45, 10.0)
b(T_ eff, log g, ξ)=(21000, 3.35, 10.0)
cKurucz gf-value
*The lines covered by the adopted model atom, including the
extended model atom with more levels, for the ions providing the ionization balance and some other ions





lccc


0pt
4


Summary of V652 Her's photospheric abundances

Element     non-LTE     LTE    
Suna
H        9.5      9.7     12.0 

He      11.5     11.5     10.9 

C       7.0     6.9      8.4 

N       8.7     8.9      7.8 

O       7.6     7.6      8.7 

Ne      8.1     8.6      7.9 

Mg      7.1     7.5      7.6 

Al          6.4      6.5 

Si      7.4     7.4      7.5 

P          5.5      5.4 

S      7.4     7.2      7.1 

Ar          6.9      6.4 

Fe      7.1     7.3      7.5 

a<cit.>



lccc


0pt
4


Summary of HD 144941's photospheric abundances

Element     non-LTE     LTE    
Suna
H        10.4     10.4      12.0 

He       11.5     11.5      10.9 

C        6.9      6.6        8.4 

N        6.4      6.7        7.8 

O        7.1      7.0        8.7 

Ne       7.2      7.5        7.9 

Mg       5.8      5.9        7.6 

Al           5.1     6.5 

Si       6.0      6.0        7.5 

S        6.2      6.0        7.1 

Fe       ≤6.6     ≤6.2     7.5 

a<cit.>











25
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