# EC 19529–4430: SALT identifies the most carbon- and metal-poor extreme
helium star

C. S. Jeffery1, L. J. A. Scott1, A. Philip Monai1,2, B. Miszalski3 and V. M.
Woolf4
1Armagh Observatory and Planetarium, College Hill, Armagh, BT61 9DG, UK
2School of Mathematics and Physics, Queen’s University Belfast, Belfast, BT7
1NN, UK
3Australian Astronomical Optics - Macquarie, Faculty of Science and
Engineering, Macquarie University, North Ryde, NSW 2113, Australia
4Physics Department, University of Nebraska at Omaha, 6001 Dodge St, Omaha,
NE, 68182, USA email<EMAIL_ADDRESS>
(Accepted …. Received …; in original form …)

###### Abstract

EC 19529$-$4430 was identified as a helium-rich star in the Edinburgh-Cape
Survey of faint-blue objects and subsequently resolved as a metal-poor extreme
helium (EHe) star in the SALT survey of chemically-peculiar hot subdwarfs.
This paper presents a fine analysis of the SALT high-resolution spectrum.  EC
19529$-$4430 has $T_{\rm eff}=20\,700\pm 250$ K, $\log g/{\rm
cm\,s^{-2}}=3.49\pm 0.03$, and an overall metallicity some 1.3 dex below
solar; surface hydrogen is $\approx 0.5\%$ by number. The surface CNO ratio
1:100:8 implies that the surface consists principally of CNO-processed helium
and makes  EC 19529$-$4430 the coolest known carbon-poor and nitrogen-rich EHe
star. Metal-rich analogues include V652 Her and  GALEX J184559.8$-$413827.
Kinematically, its retrograde orbit indicates membership of the galactic halo.
No pulsations were detected in TESS photometry and there is no evidence for a
binary companion.  EC 19529$-$4430 most likely formed from the merging of two
helium white dwarfs, which themselves formed as a binary system some 11 Gyr
ago.

###### keywords:

stars: abundances, stars: fundamental parameters, stars: chemically peculiar,
stars: individual (EC 19529–4430),

††pagerange: EC 19529–4430: SALT identifies the most carbon- and metal-poor
extreme helium star–B††pubyear: 2014 Figure 1: The RSS spectrum of  EC
19529$-$4430 (black) with the best-fit model (red) having $T_{\rm
eff}=20\,650\pm 130$ K, $\log g/{\rm cm\,s^{-2}}=3.51\pm 0.02$, and $n_{\rm
H}=0.0053\pm 0.0002$ ($\log y=2.27\pm 0.02$) (formal errors). The lower panel
shows the residuals. Hydrogen Balmer and neutral helium absorption lines are
marked in red and blue, respectively.

##  1 Introduction

Extreme helium stars (EHes) are characterised by their spectral types A and B,
weakness or absence of hydrogen Balmer lines, and strength of neutral helium
lines. Being rare and luminous, their lifetimes must be short, and yet they
are located in all major components of the galaxy (Philip Monai et al., 2023).
High carbon and/or nitrogen abundances indicate evolved surfaces revealed
through a catastrophic event in their history, generally thought to be the
merger of two white dwarfs (Saio & Jeffery, 2000, 2002). Their surface
composition and distribution suggest a connection with other hydrogen-
deficient stars including the cooler R Coronae Borealis variables (RCB)
(Jeffery, 1994), dustless hydrogen-deficient carbon stars (dlHdC) (Warner,
1967; Crawford et al., 2023; Tisserand et al., 2023) and the hotter hydrogen-
deficient hot subdwarfs (Hesd) (Saio & Jeffery, 2000; Zhang & Jeffery, 2012)
and O(He) stars (Reindl et al., 2014).

Following a spectroscopic survey of luminous blue stars (Drilling, 1980,
1983), the number of confirmed EHes remained at roughly 17 from the early
1980s until the commencement of the Southern African Large Telescope (SALT)
survey of chemically-peculiar hot subdwarfs in 2016 (Jeffery et al., 2021)
(SALT1 hereafter). The Edinburgh-Cape (EC) survey of faint blue stars (Stobie
et al., 1997; Kilkenny et al., 1997; O’Donoghue et al., 2013; Kilkenny et al.,
2015; Kilkenny et al., 2016) classified a number of stars as He-sdB, a
classification which overlaps the sdOD stars identified by Green et al. (1986)
and the EHe stars as discussed by Drilling et al. (2013). SALT1 observations
of He-sdB stars from the EC and other surveys revealed 3 new low-gravity
B-type EHe stars, namely  GALEX J184559.8$-$413827(=J1846$-$4138),  EC
19529$-$4430, and EC 20236–5703 (Jeffery, 2017; Jeffery et al., 2021).
Concurrently, the Tisserand et al. (2022) survey of dustless hydrogen-
deficient carbon stars identified 2 new A-type EHes, namely A208
(J182447.94–221429.1) and A798 (J183357.03+052917.0). Meanwhile, several
helium-rich subdwarfs were recognised to have properties similar to the hot
high-gravity EHe star LS IV$+6^{\circ}2$ (Jeffery, 1998) including PG 1415+492
(Ahmad & Jeffery, 2003) and PG 0135+243 (Moehler et al., 1990). Stars such as
BPS CS 22940–0009 (Snowdon et al., 2022), EC 20187–4939 (Scott et al., 2023),
and others (Naslim et al., 2010), suggest that a continuous sequence extends
to the helium-rich sdO stars.

A preliminary analysis of  EC 19529$-$4430 ($\alpha_{2000}=19{\rm h}\,56{\rm
m}\,30.7{\rm s}$, $\delta_{2000}=-44^{\circ}\,22\arcmin\,19\arcsec$, showed it
to be the coolest star in SALT1. At low-resolution, the spectrum “shows no
ionized helium lines (including Heii 4686 Å) and Balmer lines much weaker than
the neutral helium lines. A defining feature is the weakness of all metal
lines and the narrow wings of the H and He I lines” (Jeffery et al., 2021).
Philip Monai et al. (2023) found  EC 19529$-$4430 to be a halo object in a
retrograde orbit. The weak metal-lined spectrum and low surface gravity
demands a more careful analysis with model atmospheres of appropriate
composition and regard to possible departures from LTE. The likely age and
retrograde orbit deserve further discussion in terms of origin and evolution.

The observations on which this analysis is based are described in § 2. The
model atmospheres underlying the analysis are described in § 3. The spectral
analysis itself is presented in § 4. § 5 discusses the distance and
kinematics. § 6 discusses the overall properties and evolutionary status and
concludes the paper.

Table 1: Radial velocities measured from blue HRS spectra of  EC 19529$-$4430. “RSS” shows the measurement reported in SALT1. Radial velocities for individual observations are measured in two wavelength ranges relative to an average spectrum. “Mean” shows the averages and standard deviations. “Template” shows the velocities of the average spectrum relative to a model, and the bottom line indicates the adopted barycentric mean velocity.  Date | Run | JD | $\sigma_{4540}$ |  $\delta V$(4500-4700Å) |  $\delta V$(4300-4500Å)
---|---|---|---|---|---
|  |  |  |  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$
20180516 | RSS |  |  |  $5\pm 3$ (SALT1)
20190323 | H0049 | 2458566.631215 | 0.010 | $0.290\pm 0.035$ | $-0.531\pm 0.301$
20190329 | H0021 | 2458572.619016 | 0.009 | $-0.117\pm 0.032$ | $-0.234\pm 0.315$
20190329 | H0022 | 2458572.631412 | 0.011 | $-0.151\pm 0.047$ | $-0.200\pm 0.353$
20210801 | H0015 | 2459428.269282 | 0.030 | $-1.863\pm 0.115$ | $-0.320\pm 0.116$
20210823 | H0025 | 2459450.464167 | 0.058 | $0.889\pm 0.057$ | $0.467\pm 0.112$
20210825 | H0018 | 2459452.458264 | 0.060 | $0.696\pm 0.099$ | $2.120\pm 0.196$
20210829 | H0017 | 2459456.446146 | 0.051 | $-0.913\pm 0.254$ | $-0.601\pm 0.172$
| Mean |  |  | $-0.17\pm 0.96$ | $0.10\pm 0.96$
| Template |  | 0.006 | $+9.73\pm 0.57$ | $+11.38\pm 1.02$
|  |  |  | $10.32\pm 0.70$

##  2 Observations

Observations were obtained in 2019 March and April with SALT using both the
High Resolution Spectrograph (HRS) and the Robert Stobie Spectrograph (RSS).
These are described in Section 2 and Appendix A of SALT1. The methods used for
data reduction are described in SALT1 (RSS) and by Snowdon et al. (2022)
(HRS). Additional short exposure HRS observations were obtained during 2021
August and September in order to establish radial-velocity behaviour. For
these and for all the red-arm HRS observations we have used the SALT pipeline
reductions as described by Kniazev (2016).

The RSS spectrum and a model fit is shown in Fig. E.1 of SALT1. Fig. 1 shows
the same spectrum together with a revised model solution which will be
discussed below. The He i absorption lines are readily apparent and everywhere
narrower than in helium-rich hot subdwarfs, but less sharp than in the lowest-
gravity extreme helium stars. The Balmer lines are stronger than in most EHe
stars, but similar in strength to those seen in J1846$-$4138 (Jeffery, 2017).
There are no detectable Heii lines in the RSS spectrum. The spectrum bears
similarities to EHe star V652 Her (Jeffery et al., 2001, 2015), including in
particular the extremely rich spectrum of singly-ionized nitrogen (Fig. 1).

The wavelength range covered by the HRS spectrum is 3860 – 5519 Å and has a
S/N ratio in the range 140 – 200 at a resolution of $\approx 37,000$. The
orders were rectified, mapped onto a common logarithmically spaced wavelength
grid, and merged. The observed spectrum was further renormalised using
appropriate models to guide the location of the local continuum in regions
where strong lines overlap and to facilitate the measurement of abundances
from narrow and weak lines.

Equivalent widths were measured for a substantial list of lines anticipated in
early-type stellar spectra. For each predicted line, a region of spectrum is
displayed and nearby continuum regions are identified manually. The upper and
lower limits of the line itself are then identified, and the area of the line
under the continuum is integrated and converted to an equivalent width
($W_{\lambda}$) The error is estimated from the variance of data in the local
continuum, as described by Snowdon et al. (2022). Measurements used in
subsequent analyses are shown in Appendix B.

Radial velocities of  EC 19529$-$4430 were measured from the HRS spectra as
follows and are reported in Table 1. The signal-to-noise ratio of each
spectrum is represented by $\sigma_{4540}$, the variance around the mean
continuum between 4531 and 4548Å. A mean spectrum was formed from the sum of
the first three HRS observations. Velocities were measured by cross-
correlation relative to this mean spectrum in two wavelength ranges, namely
4300–4500Å which includes several broad Hei lines and 4500–4700Å which
contains only sharp lines. Barycentric velocity corrections were applied prior
to analysis. The heliocentric radial velocity of the mean spectrum was
measured relative to a laboratory template (“Template” in Table 1).

With a standard deviation $<1$ $\mbox{km}\,\mbox{s}^{-1}$ over 7 observations
on timescales of hours, days, weeks and years, there is no evidence for
variability that would indicate membership of a close binary or of surface
pulsations (“Mean” in Table 1). The mean HRS velocity is close enough to the
RSS velocity to be unremarkable.

Photometric observations were obtained by the TESS spacecraft during cycles 13
and 27. These show no periodic variation at any frequency between 0.2 and 50
d-1 with an amplitude $>0.02\%$ (4$\sigma$) of the mean flux. Pulsations are
not expected for low-metallicity extreme helium stars with the properties of
EC 19529$-$4430, where sufficient iron is necessary to drive pulsations
(Jeffery & Saio, 1999).

##  3 Model Atmospheres and Spectrum Synthesis

Analyses of astronomical spectra require the use of theoretical models
adjusted to match the observations. In the present case we consider the
spectrum to be formed in the atmosphere of a star which is in hydrostatic and
radiative equilibrium. Other physics assumptions are implicit in the choice of
computer code used to construct the models; for these we refer below to papers
associated with the codes adopted.

Most of our models are computed with the codes sterne and spectrum described
by Behara & Jeffery (2006) and Jeffery et al. (2001). These assume local
thermodynamic equilibrium (LTE) for the atomic level populations, but depart
from strict LTE111Strict LTE assumes that the local source function is given
by the Planck function. in that they include electron scattering in the
radiative transfer calculation for the source function. Bound-free opacities
are included using data from the Opacity and Iron Projects (Seaton et al.,
1994; Hummer et al., 1993). Line opacities due to 559316 lines (Kurucz & Bell,
1995) are also included. Pressure broadening in the H, Hei and Heii lines is
treated using the tables of Vidal et al. (1973), Beauchamp et al. (1997) and
Schöning & Butler (1989), respectively. At low densities, the Beauchamp et al.
(1997) tables are supplemented by Voigt profiles using Stark broadening
coefficients from Dimitrijevic & Sahal-Brechot (1984, 1990). Behara & Jeffery
(2006) and Kupfer et al. (2017) compared models computed with sterne and
atlas9 and atlas12 (Kurucz, 1993, 1996) respectively. They found differences
of up to 2–3% in the line forming region, likely due to differences in the
opacities and other model assumptions.

Analyses of the EHe stars V652 Her (Przybilla et al., 2005; Pandey & Lambert,
2017) and BD$+10^{\circ}2179$ (Pandey & Lambert, 2011; Kupfer et al., 2017)
showed departures from LTE to be small except for very strong lines. In both
analyses of V652 Her, the non-LTE hydrogen measurement was improved by almost
eliminating line-to-line discrepancies, whilst the surface gravity measured
from Hei lines was lower by $\sim 0.5$ dex than found previously (Hill et al.,
1981; Lynas-Gray et al., 1984; Jeffery et al., 1999a, 2001). In contrast, the
surface gravity measured by Kupfer et al. (2017) for BD$+10^{\circ}2179$
increased by $\sim 0.3$ dex relative to previous LTE and non-LTE analyses by
Heber (1983); Pandey et al. (2006); Pandey & Lambert (2011). This is likely
due to the adoption of an improved treatment of metal-line blanketing in the
atlas12 model atmosphere and an improved model for the Hei atom in the line
profile treatment.

On the basis of these previous studies, we have assumed for  EC 19529$-$4430
that departures from LTE will also be small except for very strong lines.
However, since the strong lines affect the measurement of major parameters,
our analysis included the effect of departures from LTE on the profiles of
hydrogen and helium lines. First, we computed sterne equivalent models in LTE
using version 208 of the code tlusty (Hubeny & Lanz, 1995, 2017a, 2017b,
2017c; Hubeny et al., 2021). These tlusty (LTE) models are consistent with the
sterne (LTE) models, as established by comparing the temperature structures of
the converged models (see § 4.3).

Using the structure of the previously converged LTE model, we used tlusty to
solve the statistical equilibrium equations for H, Hei and Heii without
computing any additional temperature corrections. Thus, we computed departure
coefficients for the H, Hei and Heii ions with model atoms using 9, 24 and 20
energy levels respectively. These model ions, sourced from the tlusty
website,222http://tlusty.oca.eu/Tlusty2002/tlusty-frames-data.html used
oscillator strengths and photoionisation cross sections from the Opacity
Project database (Cunto et al., 1993), and level energies from NIST (Ralchenko
& Kramida, 2020). Hence, using the formal solution code synspec version 54
(Hubeny & Lanz, 1995, 2017a, 2017b, 2017c; Hubeny et al., 2021), we computed
grids of emergent spectra with these ions in non-LTE (synspec non-LTE). This
approach mirrors that used by, for example, Przybilla et al. (2005) in their
analysis of the extreme helium star V652 Her.

Figure 2: Solutions for $T_{\rm eff}$ and $\log g$ for  EC 19529$-$4430 for
both RSS (top) and HRS spectra (middle). The bottom panel shows solutions for
the HRS spectrum with $n_{\rm H}=0.008$. Labels m20, m10 (‘$\times$’) and p00
indicate fits using the second iteration sterne (LTE) $+$ spectrum (LTE) grid,
with $\xi_{\rm turb}=0$ $\mbox{km}\,\mbox{s}^{-1}$. Labels v00, v05
(‘$\square$’), v10 and v15 indicate fits using the third iteration sterne
(LTE) $+$ spectrum (LTE) grid (m13n10), with $\xi_{\rm turb}=0$, 5, 15 and 15
$\mbox{km}\,\mbox{s}^{-1}$. Heavy symbols indicate fits using the tlusty (LTE)
$+$ synspec (non-LTE) grids m10n and m13n. The violet symbol, labelled m13s,
refers to a fit using the tlusty (LTE) $+$ synspec (LTE) grid (m13n10), with
$\xi_{\rm turb}=5$ $\mbox{km}\,\mbox{s}^{-1}$. Formal errors are shown for the
RSS fits. Formal errors for the HRS fits are too small to show.  Figure 3: The
HRS spectrum of  EC 19529$-$4430 (histogram) in the vicinity of Heii4686
compared with equivalent synspec (top) and sterne (bottom) models (red) having
$T_{\rm eff}$ = 16 kK (dots), 18 kK (long dashes), 20 kK (short dashes) and 22
kK (solid). The thick grey curve shows the HRS spectrum smoothed with a 0.1Å
FWHM Gaussian filter.

##  4 Stellar Atmosphere Analysis

###  4.1 Model atmosphere grids.

In the process of fine analysis, atmospheric parameters are obtained by
finding a best-fit model spectrum, usually by interpolation in an appropriate
grid. Typically, an estimate is made for the metal content and microturbulent
velocity $\xi_{\rm turb}$, and then a grid of model atmospheres is computed to
span a range of effective temperature $T_{\rm eff}$, surface gravity $g$ and
hydrogen abundance $n_{\rm H}$ (fractional abundance by number). Since the
composition and $\xi_{\rm turb}$ are not known ab initio, the process is
iterative. The first (SALT1) iteration used solar metallicity grids (p00)
(Jeffery et al., 2021), from which $T_{\rm eff}\approx 18\,500$K, $\log
g/({\rm cm\,s^{-2}})\approx 3.4$ and $n_{\rm H}\approx 0.01$ was deduced.
Alternatively, $\log y\equiv\log n_{\rm He}/n_{\rm H}\approx 2$. Predominantly
weak metal lines suggested adoption of a metallicity scaled to 1/10 of the
solar abundance (m10). $\xi_{\rm turb}=0$ $\mbox{km}\,\mbox{s}^{-1}$ was
assumed. sterne models were calculated on grids defined by:
$T_{\rm eff}=16,18,20,22$ kK,
$\log g/({\rm cm\,s^{-2}})=2.50,2.75,3.00,3.25,3.50,3.75$, and
$n_{\rm H}=0.00,0.01,0.03$.
For completeness, model grids were also calculated with metallicity scaled to
1/100 (m20) and 1 times solar (p00).

The second iteration provided estimates of $T_{\rm eff}\approx 20\,000$K,
$\log g/({\rm cm\,s^{-2}})\approx 3.5$ and $n_{\rm H}\approx 0.01$. From this,
abundance estimates were obtained from measured equivalent widths, indicating
an overall metallicity 1/20 times solar ($-1.3$ dex = m13), with the exception
of nitrogen being close to $1\times$ solar (n10). New models were calculated
on the same grid as above using this custom mixture (m13n10) and with
$\xi_{\rm turb}=0$, 5, 10 and 15 $\mbox{km}\,\mbox{s}^{-1}$(abbreviated: v00,
v05, v10 and v15). Abundances obtained from this third iteration were within
0.3 dex of those used as inputs, so the process was deemed to have converged.

LTE models were computed using tlusty on the same grids and mixtures as the
sterne m10 and m13n10 grids. $\xi_{\rm turb}=5$ $\mbox{km}\,\mbox{s}^{-1}$ was
adopted throughout. Departure coefficients were computed for hydrogen and
helium, and hence model spectra were obtained with hydrogen and helium out of
LTE. All other atoms were treated in LTE throughout. The resulting grids are
labelled m10_nlte (or m10n) and m13n10_nlte (or m13n).

Figure 4: Comparison of temperature structures of tlusty and sterne model
atmospheres in the sense $1-(T_{\rm STERNE}/T_{\rm TLUSTY})$ as a function of
optical depth. Models are compared for $T_{\rm eff}=20\,000$ K, $\log g/({\rm
cm\,s^{-2}})=3.5$, $n_{\rm H}=0.01$, $\xi_{\rm turb}=5$
$\mbox{km}\,\mbox{s}^{-1}$.  Figure 5: The HRS spectrum of  EC 19529$-$4430 in
the vicinity of several Hei lines compared with the best-fit non-LTE model
(bold red) and the best-fit LTE models computed with tlusty+synspec (dotted
red) and sterne+spectrum (solid violet). The best-fit non-LTE model has
$T_{\rm eff}=20\,680\pm 40$ K, $\log g/{\rm cm\,s^{-2}}=3.49\pm 0.01$, and
$n_{\rm H}=0.0042\pm 0.0001$ ($\log y=2.37\pm 0.01$) (formal errors). Each Hei
line is labelled by its transition. The cores of strong lines are duplicated
above, with the wavelength scale expanded by a factor 5. Lines observed but
not shown include $2^{3}P^{0}-4^{3}P^{0}$ 4517.4Å, $2^{1}S-4^{1}P^{0}$
3964.7Å, $2^{1}P^{0}-8^{1}S$ 3935.9Å, and $2^{1}P^{0}-8^{1}D$ 3926.5Å.

###  4.2 Effective temperature and surface gravity.

We use the $\chi^{2}$ minimizer sfit (Jeffery et al., 2001) to optimise for
$T_{\rm eff}$, $\log g$ and $n_{\rm H}$ within a model grid, as defined by a
given metal mixture and $\xi_{\rm turb}$. Other factors which affect the fit
include the choice of wavelength range, bad data points, and local
normalisation. The overall wavelength ranges used for the $\chi^{2}$
minimisation were 3900 – 5070Å (RSS) and 3900 – 5200 Å (HRS). Both spectra
include many strong neutral helium and 4 hydrogen Balmer lines; the latter
includes 2 additional strong Hei lines. The Caii interstellar lines and other
notably noisy regions of spectrum were excluded from the fit by setting very
small weights to those regions. Key lines sensitive to temperature, gravity
and hydrogen abundance were given extra weight in the HRS fits. These include
H$\beta$, H$\gamma$, Hei 4471, 4388Å, Heii 4686Å, Siii 4128, 4131Å, and Siiii
4553, 4568, 4575Å.

Solutions for $T_{\rm eff}$ and $\log g$ for each model grid and for each
spectrum are shown in Fig. 2. The fits for $\log g$ are dominated by the
pressure sensitive Hei lines and hence strongly correlate with $T_{\rm eff}$.
$T_{\rm eff}$ is constrained by various line strengths and is sensitive to the
model grid assumptions (metallicity, microturbulent velocity, etc).

The top panel shows the position of the best fits to the RSS spectrum for 3
different model grids including a first generation sterne+spectrum grid (m10),
a second generation sterne+spectrum grid (m13n10v05 $\equiv$ v05), and a
tlusty+synspec grid (m13n).

The light red triangles in the middle panel show positions of best fits to the
HRS spectrum obtained with the same three grids (m10, v05, m13n), and also
positions of best fits with each of the other grids. These show the
progression of fits as a function of metallicity (first generation: p00, m10,
m20), and microturbulent velocity (second generation: v00, v05, v10, v15).
They thus demonstrate the magnitude of systematic errors arising from an
incorrect metallicity or microturbulent velocity in the models. The bolder red
triangles represent the three tlusty+synspec grids (m10n, m13n, m13s).

The bottom panel shows positions of the best fits to the HRS spectrum for each
of the three reference grids (m10, v05, m13n), but with the hydrogen abundance
increased to 0.8%.

The general shape of the $\chi^{2}$ surface for each model grid is a narrow
valley with a poorly-defined minimum. In addition to H and Hei, other lines
affect precisely where the $\chi^{2}$ minimum occurs and hence fix  Teff.
Examples include Heii 4686Å and Siii 4128, 4131Å as well as the large number
of Nii lines. The Heii 4686Å line in  EC 19529$-$4430 is weak, with an
equivalent width of $4.8\pm 2.4$ mÅ. Nevertheless, its presence provides an
important constraint on $T_{\rm eff}$. Fig. 3 compares the Heii 4686Å with
models from the LTE m13n10 grid and from the non-LTE m10 grid covering $T_{\rm
eff}=16,18,20$ and 22 kK; $\xi_{\rm turb}=5$ $\mbox{km}\,\mbox{s}^{-1}$in both
cases. In the LTE grid, $T_{\rm eff}\approx 18$ kK, whereas in the non-LTE
grid, $T_{\rm eff}\approx 21$ kK. These values are broadly consistent with the
results in Fig. 2.

Figure 6:  The HRS spectrum of  EC 19529$-$4430 in the vicinity of four Balmer
lines compared with models for (a) a best-fit hydrogen abundance ($n_{\rm
H}\approx 0.004$; thin lines) and (b) a fixed value of the hydrogen abundance
($n_{\rm H}=0.008$; thick lines). Solid red lines show the best-fit with non-
LTE hydrogen and helium ($\mbox{\,\em T${}_{\rm eff}$}=20.7$ kK, $\mbox{\,log
$g$}=3.5$). Dotted violet lines show H and He in LTE ($\mbox{\,\em T${}_{\rm
eff}$}=19.8$ kK, $\mbox{\,log $g$}=3.4$). The strong narrow line at 3968.5Å is
due to interstellar calcium.

###  4.3 Departures from LTE

A criticism of the LTE approximation is that it does not perform well in the
cores of strong lines (Przybilla et al., 2005; Pandey & Lambert, 2011; Kupfer
et al., 2017; Pandey & Lambert, 2017). This problem is mitigated by the use of
models in which the hydrogen and helium level populations are treated in non-
LTE (bold symbols in Fig. 2). For mixture m13n10 and $\xi_{\rm turb}=5$
$\mbox{km}\,\mbox{s}^{-1}$, the non-LTE solution (m13n) for the HRS spectrum
is some 1400 K hotter than the equivalent LTE solution (v05). It is also
successful in fitting the Hei line cores much better than the LTE solution
(Fig. 5).

Since the underlying models are computed with independent codes, it is
necessary to verify that the difference comes primarily from the non-LTE
treatment of H and He lines, and not from other differences between the
underlying models. Fig. 4 compares the temperature structures of models
computed with sterne and tlusty for identical input parameters. Within the
line-forming region ($10^{-4}<\tau_{4000}<1$) the temperatures differ by less
than 1%. A separate grid of models for the mixture mixture m13n10 and
$\xi_{\rm turb}=5$ $\mbox{km}\,\mbox{s}^{-1}$was computed using tlusty and
synspec in which the H and He lines were treated in LTE. Fitting the HRS
spectrum to this grid gave a solution almost identical to that for the
equivalent grid calculated with sterne and spectrum. This solution is labelled
‘m13s’ in Fig. 2. Equivalence between the tlusty+synspec and sterne+spectrum
solutions in LTE is also demonstrated in Fig. 5, particularly in the cores of
the diffuse ($2P^{0}-nD$) lines.

To address the question of how much the line cores affect the fits, the
central 2Å of all Hei lines were excluded. For the reference sterne$+$spectrum
grid m13n10 (v05), $T_{\rm eff}$ and $g$ increased to almost exactly the
values given by the tlusty and synspec (non-LTE) grid with the line cores
included. However, excluding the line cores from the non-LTE grid increased
$T_{\rm eff}$ by a similar amount $\approx 1\,000$ K, implying that the line
wings are also significantly different.

###  4.4 Formal and systematic errors

It is difficult to assign confidences to our solutions; small changes in fit
settings, such as wavelength range, wavelength weighting and normalization,
can produce changes an order of magnitude larger than the formal errors in the
$\chi^{2}$ minimization. In most cases, we check for global minima by
restarting the fit with different initial estimates and checking that same
solutions are obtained. The formal errors for the HRS solutions have maxima of
50 K in $T_{\rm eff}$ and 0.01 dex in $g$. The correlation between $T_{\rm
eff}$ and $g$ is robust over different spectra and different model grids.

Microturbulent velocity is not too important for the $T_{\rm eff},g$ solution
so long as some line broadening is included; the results for v05, v10 and v15
(mix m13n10) are almost coincident, whilst being substantially hotter than for
${\bf v00}$. HRS results for m20, m10 and p00 in Fig. 2 are diverse for
decadal changes in metallicity but, if the metallicity is about right, other
factors are probably more important. The LTE results for m10 and m13n10 (v05)
are comparable, as are the non-LTE results for the same mixtures.

###  4.5 RSS

Solutions were obtained for the same model grids and for the RSS spectrum; for
clarity only three solutions are shown in Fig. 2 (black diamonds), being for
the m13n10 (diamond+square), m10 (diamond+cross) and m13n10_nlte (bold
diamond) grids.

In comparing HRS and RSS results, the influence of weak lines at lower
resolution is reduced; exactly why this favours higher $T_{\rm eff}$ and $g$
is unclear. Excluding Balmer lines and sharp Hei and H lines from the HRS fits
reduced $T_{\rm eff}$ by 400 K, with no effect on gravity.

Both the LTE and non-LTE RSS results are consistent with the non-LTE HRS
results. The former seems counter-intuitive, but a test using the fully LTE
tlusty $+$ synspec grid gave a much lower $T_{\rm eff}\approx 18\,900$ K,
suggesting that systematic errors in fitting the RSS spectrum remain
significant.

###  4.6 Hydrogen abundance.

In a free solution, the hydrogen abundance measured from
H$\beta,\gamma,\delta$ and $\epsilon$ is $\approx 0.5\%$ by number. Forcing
the solution to fit H$\gamma$ yields $\approx 0.8\%$. However, in both LTE and
non-LTE solutions, the Balmer line fits are inconsistent in the sense that, if
a model spectrum matches at H$\gamma$, the model for H$\beta$ is too weak and
the models for H$\delta$ and H$\epsilon$ are increasingly too strong (Fig. 6).

The blue squares in Fig. 2 represent fits to the HRS spectrum in which $n_{\rm
H}=0.008$ was held fixed. Otherwise the symbols match the corresponding red
triangles; i.e. ‘$\times$’ = m10, ‘$\square$’ = m13n10 v05, and a bold symbol
= m13n10_nlte.

Both Przybilla et al. (2005) and Pandey & Lambert (2017) were able to resolve
this ‘Balmer-line’ problem through the use of non-LTE models. This has not
been possible in the current case.

Figure 7:  The HRS spectrum of  EC 19529$-$4430 in the vicinity of Mgii 4481Å
and Nii 5001Å doublets compared with a model spectrum for 3 different values
of projected rotation velocity $v_{\rm rot}\sin i$ (top - blue) and
microturbulent velocity $\xi_{\rm turb}$ (bottom - red). Values are indicated
by dots $=0$ $\mbox{km}\,\mbox{s}^{-1}$, solid lines $=5$
$\mbox{km}\,\mbox{s}^{-1}$and dashes $=10$ $\mbox{km}\,\mbox{s}^{-1}$.

Figure 8: Top: Abundances derived from Nii lines as a function of equivalent
width for microturbulent velocities of $\xi_{\rm turb}=0,5,10$ and 15
$\mbox{km}\,\mbox{s}^{-1}$. The base model atmospheres used were
m13n10/h01he99/t200g350 with input $\xi_{\rm turb}=0$, 5, 10 and 15
$\mbox{km}\,\mbox{s}^{-1}$. The solid lines show a linear regression for each
value of $\xi_{\rm turb}$. Bottom: The same for $\xi_{\rm turb}=7$
$\mbox{km}\,\mbox{s}^{-1}$, with the Nii lines separated into 3 groups ordered
by $E_{\rm l}$

###  4.7 Rotation.

The Mgii 4481Å doublet is unresolved but asymmetric; a projected rotation
velocity $v\sin i=5\pm 2$ $\mbox{km}\,\mbox{s}^{-1}$ is sufficient to match
the observed profile (Fig. 7).

###  4.8 Microturbulent velocity.

Two methods have been considered to estimate the microturbulent velocity
$\xi$. Looking at line profiles, the resolved Nii 5001 Å doublet requires a
value of $\xi_{\rm turb}$ between 5 and 10 $\mbox{km}\,\mbox{s}^{-1}$ (Fig.
7). The larger value produces profiles that are broader than observed; the
lower value matches the line wings but over-resolves the doublet core.
Alternatively, $\xi_{\rm turb}$ can be adjusted so that all of the Nii lines
yield a consistent nitrogen abundance across the full range of measured
equivalent widths. This method indicates $\xi_{\rm turb}=15\pm 5$
$\mbox{km}\,\mbox{s}^{-1}$(Fig. 8, upper panel). The conflict between these
methods is partially resolved if the Nii lines are considered according to the
excitation potential of the lower energy level of the transition $E_{l}$. The
lines fall naturally into three groups, namely lines with (1) $E_{\rm
l}<19$eV, (2) $19{\rm eV}<E_{\rm l}<22$eV, and (3) $E_{\rm l}>22$eV. A value
$\xi_{\rm turb}=7\pm 1$ $\mbox{km}\,\mbox{s}^{-1}$ minimizes the absolute
gradient ${\rm d}\log n_{\rm N}/{\rm d}W_{\lambda}$ averaged over all three
groups (Fig. 8: lower panel). However, the inconsistency between lines of
different $E_{l}$ suggests that the temperature structure of the atmosphere is
still not fully solved or that some lines may show non-LTE effects.

Since the parameters derived from the spectral fits are relatively insensitive
to $\xi_{\rm turb}>5$ $\mbox{km}\,\mbox{s}^{-1}$, this value is deemed
acceptable for the model atmosphere calculation. Its principal effect on the
model structure is through line opacity in the ultraviolet which is reduced by
the relatively low metallicity of the star.

For measuring abundances, errors will not be too large if a low value of
$\xi_{\rm turb}$ is adopted, so long as the line equivalent widths are small
(e.g. $W_{\lambda}<50$mÅ). This would certainly be necessary if a spectral
synthesis approach were to be used because otherwise the model profiles would
be too broad to fit the observed profiles. On the basis of Fig. 8, we have
used $\xi_{\rm turb}=7$ $\mbox{km}\,\mbox{s}^{-1}$ to measure abundances
directly from measured equivalent widths using the individual line curve-of-
growth method (Table B.2). For reference, the majority of lines used in our
analysis have equivalent widths $<100$mÅ. The minimum measurable equivalent
width depends on the local signal-to-noise ratio which varies throughout the
èchelle spectrum, but generally $W_{\lambda}>4$mÅ. This corresponds roughly to
the line detection threshold
$W_{\lambda}>n^{2}\sigma_{a}^{2}/\delta\lambda=6.9$mÅ (Snowdon et al., 2022)
for $\sigma_{4540}=0.006$ (Table 1), pixel width $\delta\lambda=0.05$Å and a
confidence level of 99% ($n=3$).

###  4.9 Adopted solution.

The final surface properties measured for  EC 19529$-$4430 are $T_{\rm
eff}=20\,700\pm(40,250)$ K and $\log g/{\rm cm\,s^{-2}}=3.49\pm(0.01,0.03)$,
$n_{\rm H}=0.008\pm(0.0001,0.002)$ with $v\sin i=5\pm 2$
$\mbox{km}\,\mbox{s}^{-1}$. These are taken from the fit of the HRS spectrum
to the tlusty $+$ synspec grid with mixture m13n10 and $\xi_{\rm turb}=5$
$\mbox{km}\,\mbox{s}^{-1}$. All elements are treated in LTE in the tlusty
models. H and He are treated in non-LTE in the synspec formal solutions; other
elements are in LTE. 1$\sigma$ errors are given in the form (statistical,
systematic).

Table 2: Atmospheric abundances of  EC 19529$-$4430, helium stars with similar
$L/M$ ratios, and the Sun. Abundances are given as $\log\epsilon$, normalised
to $\log\Sigma\mu\epsilon=12.15$. A colon indicates an uncertain value. Ratios
relative to the Sun are shown for  EC 19529$-$4430 beneath.

Star | H | He | C | N | O | Ne | Mg | Al | Si | P | S | Ar | Fe | Ref
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
$\log\epsilon$ |  |  |  |  |  |  |  |  |  |  |  |  |  |
EC 19529$-$4430 | 9.24 | 11.54 | 5.60 | 7.76 | 6.67 |  | 6.50 | 4.95 | 5.89 |  | 5.99 |  | 6.11 |
$\pm$ | 0.10 |  | 0.22 | 0.19 | 0.12 |  | 0.12 | 0.15 | 0.12 |  | 0.25 |  | 0.11 |
V652 Her | 9.61 | 11.54 | 7.29 | 8.69 | 7.58 | 7.95 | 7.80 | 6.12 | 7.47 | :6.42 | 7.05 | 6.64 | 7.04 | 1,2
V652 Hera | 9.5 | 11.5 | 7.0 | 8.7 | 7.6 | 8.1 | 7.1 |  | 7.4 |  | 7.4 |  | 7.1 | 3
J1846$-$4138 | 9.56 | 11.54 | 6.91 | 8.69 | 7.78 | 8.29 | 7.91 | 6.44 | 7.61 | 5.62 | 6.93 |  | 7.07 | 4
BX Cir | 8.1 | 11.5 | 9.02 | 8.4 | 8.0 |  |  | 7.2 | 6.0 | 6.8 | 5.0 | 6.6 | 6.6 | 5
BD $+10^{\circ}2179$ | 8.36 | 11.53 | 9.75 | 8.03 | 7.51 | 8.00 | 6.97 | 5.84 | 7.14 |  | 6.84 |  | 6.55 | 6
Sun | 12 | 10.93 | 8.43 | 7.83 | 8.69 | 7.93 | 7.60 | 6.45 | 7.51 | 5.45 | 7.12 | 6.40 | 7.50 | 7
$\log\epsilon/\epsilon_{\odot}$ |  |  |  |  |  |  |  |  |  |  |  |  |  |
EC 19529$-$4430 | $-2.76$ | 0.61 | $-2.83$ | $-0.07$ | $-2.02$ |  | $-1.10$ | $-1.50$ | $-1.62$ |  | $-1.13$ |  | $-1.39$ |

References. 1 Jeffery et al. (1999b), 2: Jeffery et al. (2001), 3: Pandey &
Lambert (2017), 4: Jeffery (2017), 5: Drilling et al. (1998), 6: Kupfer et al.
(2017), 7: Asplund et al. (2009).

Note. (a) non-LTE measurements

###  4.10 Elemental Abundances

Elemental abundances were computed for each measured absorption line using
individual curves-of-growth computed with spectrum. Two values were calculated
for each line with model atmospheres from grid m13n10 having $\mbox{\,$T_{\rm
eff}$}=20\,000$ and $22\,000$ K, and otherwise $\log g=3.50$, $n_{H}=0.01$ and
$\xi_{\rm turb}=5$ $\mbox{km}\,\mbox{s}^{-1}$. Abundances were computed with
$\xi_{\rm turb}=7$ $\mbox{km}\,\mbox{s}^{-1}$, as indicated in § 4.8, and
errors were propagated from the equivalent width errors to the abundances on a
line-by-line basis. Line abundances and errors were interpolated to
$\mbox{\,$T_{\rm eff}$}=20\,700$ K. Results for each line and each ion are
shown in Appendix B (Table B.4)333 Abundances are given in the form
$\log\epsilon_{i}=\log n_{i}+c$ where $\log\Sigma_{i}a_{i}\epsilon_{i}=12.15$,
$n_{i}$ are relative abundances by number with $\Sigma_{i}n_{i}=1$, $a_{i}$
are atomic weights, and $c=\log\Sigma_{i}\epsilon_{i}$. This conserves values
of $\epsilon_{i}$ for elements whose abundances do not change, even when the
mean atomic mass of a mixture changes substantially, and conforms to the
convention that $\log\epsilon_{\rm H}\equiv 12$ for the Sun and other
hydrogen-normal stars..

The overall elemental abundances of measured species are given in Table 2 and
are compared with abundances for other relatively high-gravity extreme helium
stars and the Sun. Where lines from more than one ion species are present, the
overall elemental abundance is calculated from the weighted mean over all
lines of that element.

We note the very low abundances of magnesium, aluminium, silicon, sulphur and
iron, indicative of a systemically low metallicity,
$-1.53<\log\epsilon_{i}/\epsilon_{\odot}<-0.87$, ${\rm
Z}_{i}\in$(Mg,Al,Si,S,Fe). We have adopted $-1.3$ as an indicative mean.

We also note the ratio C : N : O $\approx 1:100:8$. This ratio is $4:90:7$ in
V652 Her, and $1:88:11$ in J1846$-$4138.

Fluorine is an important stellar evolution tracer (Pandey, 2006; Bhowmick et
al., 2020). The crucial Fii lines in the optical ultraviolet were undetectable
in V652 Her; Bhowmick et al. (2020) could only deduce an upper limit of 10
times the solar abundance. Our spectrum does not reach these lines.

An independent check on the effective temperature is provided by the
ionization equilibria of species where lines from more than one ion are
present. Equilibrium is defined as the model effective temperature where the
abundances derived from each ion would be equal. This was computed for Si
ii/iii yielding $T_{\rm ion}=21\,550\pm 820$ K and for S ii/iii yielding
$T_{\rm ion}=20\,000\pm 570$ K.

Figure 9: galpy orbit for  EC 19529$-$4430 computed for 3 Gyrs from its
current positions. The panels show motion in the $\rm X-Y$ (left) and $\rm
R-Z$ (right) planes, with the Galactic centre being at the origin.  Figure 10:
The spectral energy distribution of  EC 19529$-$4430 and model fit (grey line)
with $T_{\rm eff}=20\,700\,{\rm K}$ (upper panel). The lower panel shows the
residuals. Photometry is taken from: Bianchi et al. (2017)(FUV,NUV), Høg et
al. (2000)(BT,VT), Henden et al. (2015)(B,V), Riello et al. (2021)($\rm
G_{BP},\,G,\,G_{RP}$), Onken et al. (2019)(u,v,g,r,i,z), Denis (2005)(I,J),
Cutri et al. (2003)(J,H) and Schlafly et al. (2019)(W2).

##  5 Distance and Kinematics

###  5.1 Kinematics

From an analysis of EHe kinematics using Gaia eDR3 (Gaia Collaboration et al.,
2016; Gaia Collaboration, 2021) data, Pandey et al. (2021) found that EHes
belong to a spherical population that is more extended than the R CrB stars
(RCBs) to which they were being compared. Extending earlier work by Martin
(2019) and using positions and proper motions from Gaia DR3 (Gaia
Collaboration et al., 2016; Gaia Collaboration, 2023), Philip Monai et al.
(2023) presented a more detailed study of EHe kinematics, distinguishing
between the disk (thin/thick disk stars) and the spherical components
(halo/bulge stars). They found that EHes are present in all Galactic
populations. Tisserand et al. (2023) studied a large sample of RCBs, dustless
hydrogen-deficient carbon stars (HDCs) and EHes. They came to no conclusion
about the RCB distribution due to uncertainties arising from the Gaia point-
spread function, but concurred that HdCs and RCBs are to be found in all four
Galactic components. Both Philip Monai et al. (2023) and Tisserand et al.
(2023) support the idea that EHes formed recently from double white-dwarf
mergers that arise originally from binary star formation over a range of
epochs.

Philip Monai et al. (2023) obtained a distance to  EC 19529$-$4430 of
$4.4^{+1.2}_{-0.8}$ kpc. Although the error is non-negligible ($\approx
22\%$), its retrograde orbit clearly makes  EC 19529$-$4430 a halo member
(Fig. 9). This is consistent with its low overall metallicity.

###  5.2 Spectral Energy Distribution

Philip Monai et al. (2023) used measurements of the spectral energy
distribution (SED) to obtain radii and luminosities for all of the EHes. These
measurements have been repeated for  EC 19529$-$4430 using a more appropriate
grid of model atmospheres (m13n10) and  $T_{\rm eff}$ and  log $g$ as given by
the model atmosphere analysis (Fig. 10). The results are only marginally
different to those given by Philip Monai et al. (2023). With color excess
$E(44-55)=0.067\pm 0.011$mag being the only free parameter in the SED fit, the
angular diameter is given as $\log\theta/{\rm rad}=-10.494\pm 0.007$. At the
Gaia distance, this yields a median radius of $3.4^{+1.0}_{-0.6}$ $\rm
R_{\odot}$ and luminosity $1.9^{+1.2}_{-0.6}\times 10^{3}$ $\rm L_{\odot}$.
With substantial errors in both distance and gravity, the median mass of
$1.3^{+0.8}_{-0.5}$ $\rm M_{\odot}$is not well constrained. Using modes rather
than medians reduces all of the above values by some 30%.

Philip Monai et al. (2023) concluded that EHes may be divided into high- and
low-luminosity groups, which may be associated with different types of
progenitor, namely CO+He and He+He double white dwarf mergers respectively.
Both groups include members from the galactic thin disk, the galactic thick
disk and the galactic halo.

EC 19529$-$4430 is marginal in terms of luminosity, being at the upper limit
of the low-luminosity group. However, its high nitrogen abundance strongly
suggests that  EC 19529$-$4430 belongs to the low luminosity group, which also
includes the N-rich EHe stars V652 Her and J1846$-$4138\. C-poor and N-rich
surfaces are only expected for some He+He mergers, and not for He+CO mergers.
C-rich and N-rich surfaces are expected for He+CO mergers and the more massive
He+He mergers (Zhang & Jeffery, 2012).

Figure 11: The $g-T_{\rm eff}$ diagram for  EC 19529$-$4430 with reference to
other known extreme helium stars. The positions of the Eddington limit
(Thomson scattering: dashed), luminosity-to-mass contours (solar units:
dotted) and lower boundaries for pulsation instability (metallicities $Z$ =
0.004, 0.01, 0.03: dot-dashed) (Jeffery et al., 1999b) are also shown.
Variable EHes are shown in purple (cool), blue (hot) and green (V652 Her like
variables). Non-variables are black. Data for $T_{\rm eff},g$ are as in
Jeffery (2008), (Ahmad & Jeffery, 2003) or Jeffery et al. (2021), except for
BD+10∘2179 (Kupfer et al., 2017),  GALEX J184559.8$-$413827 (Jeffery, 2017),
BPS CS 22940–0009 (Snowdon et al., 2022) and  EC 19529$-$4430. Post-merger
evolution tracks for models of He+He white dwarf mergers (Zhang & Jeffery,
2012, 0.30+0.25 and 0.30+0.30 $M_{\odot}$) are shown in red. Stars from Table
2 and other selected stars from the low-mass sequence identified by Philip
Monai et al. (2023) are labelled.

##  6 Conclusion

We have presented a fine analysis of the spectrum of the recently discovered
extreme helium star  EC 19529$-$4430. In doing so, we have examined the impact
of several assumptions inherent in the model atmosphere approach, including
the metallicity, the microturbulent velocity and departures from LTE. All
three, if not correctly treated, can have a significant impact on the final
result, amounting cumulatively in this case to over 3 000 K (or $>10\%$) in
$T_{\rm eff}$. Treating the neutral helium lines in non-LTE, and metal line-
blanketing with an appropriate metallicity and microturbulent velocity, we
obtain a solution for  $T_{\rm eff}$ and  log $g$ which is consistent over
several discriminants. Citing the systematic errors, we conclude that $T_{\rm
eff}=20\,700\pm 250$ K and $\log g/{\rm cm\,s^{-2}}=3.49\pm 0.03$. The surface
hydrogen abundance cannot be obtained consistently from all four Balmer lines
measured; 0.8% by number is given by the H$\gamma$ line, but a mean value
between 0.45% and 1% is possible. Otherwise, the surface composition is
predominantly metal-poor, with $\log\epsilon_{\rm Fe}/\epsilon_{\odot}=-1.39$,
or $\langle\log\epsilon_{i}/\epsilon_{\odot}\rangle\approx-1.3$ for ${\rm
Z}_{i}\in$(Mg,Al,Si,S,Fe). For such a metal-poor mixture, nitrogen is 1.2 dex
overabundant. Since carbon and oxygen are 1.5 and 0.7 dex underabundant,
respectively, with respect to the mean metallicity, the surface appears to be
composed primarily of CNO-processed helium. Kinematically,  EC 19529$-$4430 is
a galactic halo star in a retrograde orbit.

Fig. 11 shows  EC 19529$-$4430 relative to other EHes in a $\log
g-\log\mbox{\,$T_{\rm eff}$}$ diagram. Contours of similar $L/M$ ratio run
diagonally across this figure. Philip Monai et al. (2023) argued that the
distribution of EHes in this figure suggests the presence of low and high
$L/M$ sequences. The former are consistent with evolutionary tracks for
merging He+He white dwarfs (Zhang & Jeffery, 2012). These form originally from
binary star systems in which both components expand at the end of core-helium
burning. If sufficiently close, they will interact in a common envelope. One
or more common-envelope phases will remove material from both stars and shrink
the orbit to leave a double white dwarf (DWD) binary. The overall age of  EC
19529$-$4430 is thus dominated by the main-sequence lifetime of the progenitor
binary and the gravitational wave radiation timescale between DWD formation
and merging. Both are determined by the mass ratios and separations of the
initial main-sequence stars and of the two white dwarfs. On the basis of
binary-star population synthesis calculations by Yu & Jeffery (2010, 2011),
Philip Monai et al. (2023) argued that approximately 50% of EHes formed in the
current epoch should come from He+He WD binaries in the galactic halo. Zhang &
Jeffery (2012) demonstrated that the more massive He+He merger products should
be carbon-rich and nitrogen-rich, whilst the less massive products would red
carbon-poor and nitrogen-rich. This model therefore provides a good
description of  EC 19529$-$4430, consistent with its surface composition,
galactic orbit, and position in the $\log g-\log\mbox{\,$T_{\rm eff}$}$
diagram.

EC 19529$-$4430 is the most metal-poor EHe star known. It is the coolest
member of the carbon-poor group, of which V652 Her and J1846-4138 are slightly
warmer metal-rich analogues. Hotter carbon-poor EHe stars are found as
subdwarfs. The non-detection of pulsations is probably associated with the
iron abundance being too low to drive pulsations. There is no evidence for a
binary companion either from radial velocities or the spectra energy
distribution. It is most likely that  EC 19529$-$4430 formed from the merging
of two helium white dwarfs, which themselves formed as a binary system some 11
Gyr ago, and that it will evolve to become a core helium-burning EHe subdwarf.
It will be important to identify cooler N-rich EHe stars, additional metal-
poor EHe stars, and to study other chemical species, such as neon, to better
understand the He+He WD merger process.

## Acknowledgments

The authors thank the referee for valuable comments and in particular for
helping to resolve a discrepancy between two different measurements of the
microturbulent velocity.

The Armagh Observatory and Planetarium is funded by direct grant from the
Northern Ireland Department for Communities. CSJ and LJS acknowledge support
from the UK Science and Technology Facilities Council (STFC) Grant No.
ST/M000834/1.

The spectroscopic observations reported in this paper were obtained using the
Southern African Large Telescope (SALT) under programs 2018-2-SCI-033,
2018-2-SCI-033 and 2021-1-MLT-005 (PI: Jeffery). The authors are indebted to
the work of the entire SALT team.

This paper reports on data collected with the TESS mission, obtained from the
MAST data archive at the Space Telescope Science Institute (STScI). Funding
for the TESS mission is provided by the NASA Explorer Program. STScI is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS 5-26555.

## Data Availability

The SALT and TESS data reported in this paper are available in their
respective public archives (ssda.salt.ac.za, and archive.stsci.edu/missions-
and-data/tess). Theoretical model atmospheres and spectra generated for this
paper will be made available on reasonable request to the principal author.

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##  Appendix A Model Atmosphere Grids

Details for each of the model atmosphere grids used in § 4 are given in Table
A.3.

Table A.3: Identifiers, chemical composition and other parameters for model atmosphere grids used in § 4. Where different, labels used in Fig. 2 are given in parentheses. Label | Code | $n_{\rm N}$ | [Fe/H] | $\xi_{\rm turb}$ | Lines | Comment
---|---|---|---|---|---|---
p00 | sterne+spectrum | $\odot$ | 0.0 | 5 |  | LTE + scattering
m10 | sterne+spectrum | $\odot/10$ | $-1.0$ | 5 |  | LTE + scattering
m20 | sterne+spectrum | $\odot/100$ | $-2.0$ | 5 |  | LTE + scattering
m13n10v00 (v00) | sterne+spectrum | $\odot$ | $-1.3$ | 0 |  | LTE + scattering
m13n10v05 (v05) | sterne+spectrum | $\odot$ | $-1.3$ | 5 |  | LTE + scattering
m13n10v10 (v10) | sterne+spectrum | $\odot$ | $-1.3$ | 10 |  | LTE + scattering
m13n10v15 (v15) | sterne+spectrum | $\odot$ | $-1.3$ | 15 |  | LTE + scattering
m10_nlte (m10n) | tlusty+synspec | $\odot/10$ | $-1.0$ | 5 |  |  model LTE, H + Hei lines nLTE
m13n10_nlte (v05n) | tlusty+synspec | $\odot$ | $-1.3$ | 5 |  |  model LTE, H + Hei lines nLTE
m13n10_lte (v05s) | tlusty+synspec | $\odot$ | $-1.3$ | 5 |  | LTE
Table B.4:  Equivalent widths and scaled abundances for unblended absorption lines in the spectrum of  EC 19529$-$4430.  Ion | Reference |  |  |  |
---|---|---|---|---|---
$\lambda$ | $E_{\rm l}$ | $\log gf$ | $W_{\lambda}$ | $\sigma_{W_{\lambda}}$ | $\log\epsilon_{i}$ | $\sigma_{\log\epsilon_{i}}$
Å | eV |  | mÅ | mÅ |  |
N ii | Becker & Butler (1989) |
3919.01 | 20.410 |  $-$0.335 | 36 | 20 | 7.70 | 0.38
3955.85 | 18.466 |  $-$0.780 | 50 | 20 | 7.85 | 0.31
3995.00 | 18.498 | 0.225 | 122 | 26 | 7.78 | 0.29
4035.08 | 23.120 | 0.597 | 30 | 12 | 7.38 | 0.25
4041.31 | 23.128 | 0.830 | 53 | 21 | 7.57 | 0.31
4056.90 | 23.140 |  $-$0.461 | 11 | 8 | 7.89 | 0.36
4073.05 | 23.124 |  $-$0.160 | 20 | 11 | 7.89 | 0.32
4082.27 | 23.132 | 0.150 | 19 | 11 | 7.55 | 0.34
4171.60 | 23.196 | 0.280 | 14 | 7 | 7.31 | 0.27
4173.57 | 23.240 |  $-$0.457 | 5 | 4 | 7.57 | 0.38
4176.16 | 23.196 | 0.600 | 33 | 10 | 7.49 | 0.21
4179.67 | 23.250 |  $-$0.204 | 13 | 8 | 7.76 | 0.30
4195.97 | 23.242 |  $-$0.290 | 8 | 6 | 7.61 | 0.36
4199.98 | 23.246 | 0.030 | 16 | 7 | 7.63 | 0.24
4227.74 | 21.600 |  $-$0.089 | 26 | 12 | 7.62 | 0.29
4236.93 | 23.239 | 0.383 | 46 | 13 | 7.96 | 0.22
4237.05 | 23.242 | 0.553 | 45 | 13 | 7.79 | 0.22
4241.18 | 23.240 |  $-$0.336 | 9 | 5 | 7.73 | 0.29
4241.76 | 23.242 | 0.210 | 47 | 12 | 7.54 | 0.20
4242.44 | 23.240 |  $-$0.336 | 6 | 4 | 7.51 | 0.32
4417.10 | 23.415 |  $-$0.340 | 9 | 5 | 7.84 | 0.29
4427.24 | 23.420 |  $-$0.004 | 8 | 9 | 7.45 | 0.54
4431.82 | 23.410 |  $-$0.152 | 5 | 4 | 7.36 | 0.39
4432.74 | 23.410 | 0.595 | 29 | 10 | 7.53 | 0.22
4433.48 | 23.420 |  $-$0.028 | 15 | 5 | 7.77 | 0.19
4442.02 | 23.420 | 0.324 | 14 | 5 | 7.39 | 0.21
4447.03 | 20.411 | 0.238 | 64 | 10 | 7.70 | 0.14
4530.40 | 23.470 | 0.671 | 36 | 6 | 7.65 | 0.13
4601.48 | 18.468 |  $-$0.385 | 71 | 14 | 7.90 | 0.19
4607.16 | 18.464 |  $-$0.483 | 64 | 15 | 7.90 | 0.21
4613.87 | 18.468 |  $-$0.607 | 51 | 11 | 7.85 | 0.17
4621.29 | 18.468 |  $-$0.483 | 62 | 10 | 7.88 | 0.13
4630.54 | 18.484 | 0.093 | 113 | 10 | 7.96 | 0.12
4643.09 | 18.484 |  $-$0.385 | 72 | 10 | 7.93 | 0.13
4667.21 | 18.497 |  $-$1.580 | 10 | 4 | 7.87 | 0.18
4678.14 | 23.572 | 0.434 | 13 | 4 | 7.34 | 0.16
4694.70 | 23.570 | 0.111 | 15 | 5 | 7.74 | 0.19
4774.24 | 20.650 |  $-$1.055 | 5 | 2 | 7.57 | 0.25
4779.72 | 20.650 |  $-$0.577 | 20 | 6 | 7.82 | 0.17
4788.13 | 20.650 |  $-$0.388 | 28 | 8 | 7.83 | 0.18
4803.29 | 20.660 |  $-$0.135 | 38 | 8 | 7.79 | 0.14
4987.38 | 20.940 |  $-$0.630 | 17 | 4 | 7.90 | 0.15
5001.13 | 20.646 | 0.282 | 55 | 8 | 7.72 | 0.23
5001.47 | 20.654 | 0.452 | 60 | 9 | 7.62 | 0.13
5002.70 | 18.480 |  $-$1.086 | 31 | 6 | 8.06 | 0.12
5007.33 | 20.940 | 0.161 | 42 | 7 | 7.69 | 0.13
5010.62 | 18.470 |  $-$0.611 | 53 | 12 | 7.95 | 0.18
5025.66 | 20.666 |  $-$0.438 | 17 | 5 | 7.65 | 0.17
5045.09 | 18.460 |  $-$0.389 | 65 | 14 | 7.90 | 0.19
5073.59 | 18.497 |  $-$1.280 | 20 | 7 | 7.99 | 0.20
|  |  |  |  | 7.76 | 0.19
|  |  |  |  | $\mathrm{\Delta}\epsilon=-0.011$
Table B.4: (cont.) Ion | Reference |  |  |  |
---|---|---|---|---|---
$\lambda$ | $E_{\rm l}$ | $\log gf$ | $W_{\lambda}$ | $\sigma_{W_{\lambda}}$ | $\log\epsilon_{i}$ | $\sigma_{\log\epsilon_{i}}$
Å | eV |  | mÅ | mÅ |  |
C ii | Yan & Seaton (1987) |
4267.02$\rceil$ | 18.047 | 0.559 |  |  |  |
4267.27$\rfloor$ | 18.047 | 0.734 | 18 | 8 | 5.60 | 0.22
|  |  |  |  | 5.60 | 0.22
|  |  |  |  | $\mathrm{\Delta}\epsilon=0.005$
O ii | Bell et al. (1994) |
3973.26 | 23.442 |  $-$0.015 | 8 | 11 | 6.81 | 1.07
4072.15 | 25.650 | 0.552 | 5 | 5 | 6.58 | 0.90
|  |  |  |  | 6.67 | 0.12
|  |  |  |  | $\mathrm{\Delta}\epsilon=-0.016$
Mg ii | Wiese et al. (1969) |
4481.13$\rceil$ | 8.863 | 0.568 |  |  |  |
4481.15 $\arrowvert$ | 8.864 |  $-$0.560 |  |  |  |
4481.33$\rfloor$ | 8.863 | 0.732 | 110 | 15 | 6.50 | 0.12
|  |  |  |  | 6.50 | 0.12
|  |  |  |  | $\mathrm{\Delta}\epsilon=0.035$
Al iii | Cunto et al. (1993) |
4512.54 | 17.808 | 0.405 | 12 | 5 | 5.14 | 0.21
4529.20 | 17.740 | 0.660 | 12 | 4 | 4.84 | 0.16
|  |  |  |  | 4.95 | 0.15
|  |  |  |  | $\mathrm{\Delta}\epsilon=-0.004$
Si ii | Becker & Butler (1990) |
4128.07 | 9.837 | 0.369 | 18 | 9 | 6.02 | 0.28
4130.87 | 9.839 |  $-$0.824 | 22 | 9 | 5.93 | 0.21
5041.03 | 10.070 | 0.262 | 6 | 3 | 5.73 | 0.26
5055.98 | 10.070 | 0.517 | 8 | 3 | 5.60 | 0.22
|  |  |  |  | 5.81 | 0.19
|  |  |  |  | $\mathrm{\Delta}\epsilon=0.031$
Si iii | Becker & Butler (1990) |
4552.62 | 19.018 | 0.283 | 77 | 12 | 6.36 | 0.14
4567.82 | 19.018 | 0.061 | 55 | 10 | 6.31 | 0.14
4574.76 | 19.018 |  $-$0.416 | 30 | 7 | 6.34 | 0.14
4716.65 | 25.330 | 0.491 | 3 | 2 | 5.96 | 0.34
4813.30 | 25.980 | 0.702 | 4 | 2 | 6.05 | 0.28
4819.72 | 25.980 | 0.814 | 5 | 2 | 5.99 | 0.26
|  |  |  |  | 6.27 | 0.15
|  |  |  |  | $\mathrm{\Delta}\epsilon=-0.008$
S ii | Wiese et al. (1969) |
4815.55 | 13.672 | 0.177 | 7 | 3 | 5.87 | 0.17
5032.41 | 13.668 | 0.176 | 9 | 4 | 6.01 | 0.19
|  |  |  |  | 5.93 | 0.07
|  |  |  |  | $\mathrm{\Delta}\epsilon=0.037$
S iii | Hardorp & Scholz (1970) |
4253.59 | 18.244 | 0.400 | 17 | 7 | 5.80 | 0.26
4284.98 | 18.193 | 0.110 | 12 | 6 | 5.87 | 0.27
4332.69 | 18.188 |  $-$0.240 | 4 | 4 | 5.67 | 0.46
|  |  |  |  | 5.81 | 0.08
|  |  |  |  | $\mathrm{\Delta}\epsilon=-0.011$
Fe iii | Kurucz & Petryemann (1975) |
4164.73 | 20.634 | 0.972 | 5 | 4 | 5.95 | 0.38
4419.60 | 8.241 |  $-$2.207 | 10 | 5 | 6.18 | 0.24
|  |  |  |  | 6.11 | 0.11
|  |  |  |  | $\mathrm{\Delta}\epsilon=0.011$

##  Appendix B Line Abundance Measurements

Table B.4 shows the abundances obtained from individual absorption lines in
the spectrum of  EC 19529$-$4430. Columns 1 and 4 give wavelengths and
equivalent widths ($W_{\lambda}$) for identified absorption lines. Multiplets
treated as blends are grouped by a square bracket ”]” following the
wavelength. Columns 2 and 3 give the excitation potential of the lower level
($E_{\rm l}$) and the oscillator strength ($\log gf$) for each transition.
Column 5 gives the $1\sigma$ error in $W_{\lambda}$, as described by Snowdon
et al. (2022). Lines with abundances $>2\sigma$ from the mean were rejected
and omitted, and the means recalculated. The sources of oscillator strengths
($gf$) are given with the ion designation. Column 7 gives the abundance
$\log\epsilon_{i}$ deduced from each line. Column 8 gives the error in the
line abundance obtained by propagating $\sigma_{W_{\lambda}}$ through the
abundance derivation in spectrum. The mean abundance for each ion is given as
the weighted mean of all lines shown. Errors on the mean abundance per ion are
given as the weighted standard deviation where the number of lines $n>2$, the
semi-range where $n=2$, or the line measurement error where $n=1$. The change
in abundance due to a systematic error $\delta\mbox{\,$T_{\rm eff}$}=+250$K is
shown beneath the mean abundance in the form $\mathrm{\Delta}\epsilon={\rm
d}\log\epsilon_{i}/{\rm d}T_{\rm eff}\times 250{\rm K}$.

Abundances were calculated at the adopted temperature of $T_{\rm eff}=20\,700$
K by interpolation, between LTE models with $\log g/{\rm cm\,s^{-2}}=3.50$,
$\xi_{\rm turb}=7$ $\mbox{km}\,\mbox{s}^{-1}$, and $T_{\rm eff}$ of 20 000 and
22 000 K.

The Nii lines fall into three natural groups by $E_{\rm l}$ (see Fig. 8) with
each group yielding a slightly different mean abundance. We compared the
weighted mean from all lines taken together with the weighted mean for each
group, namely lines with (1) $E_{\rm l}<19$eV, (2) $19{\rm eV}<E_{\rm
l}<22$eV, and (3) $E_{\rm l}>22$eV and also groups (1)+(2) combined. Relative
to the overall mean, the mean abundance for each group was (1) +0.21, (2)
+0.01, (3) -0.10 and (1)+(2) +0.11 dex. Although it contains the largest
number of lines, group (3) is dominated by weak lines with large abundance
errors; it therefore has a smaller impact on the overall mean. Rather than
reject any group of Nii lines, we have adopted the overall mean for the
nitrogen abundance

Abundances for sulphur and silicon are available for 2 ions in each case. The
abundances for Sii and Siii differ by 0.12 dex, which is within the scatter of
individual line measurements and less than the error in any individual line
abundance. The abundances for Siii and Siiii differ by 0.46 dex; the
individual line abundance errors are less than this whilst the scatter for
each ion is $\approx 0.4$ dex. On this basis, Table 2 gives the overall
sulphur and silicon abundances from the weighted mean of all lines of both
species . Since the silicon abundance is dominated by the strong Siiii lines
at 4553, 4568, and 4575Å, which frequently do show strong non-LTE effects, we
note that the silicon abundance may be overestimated.