11institutetext:  Dr. Karl Remeis-Observatory & ECAP, Friedrich-Alexander
University Erlangen-Nürnberg, Sternwartstr. 7, 96049 Bamberg, Germany 11email:
<EMAIL_ADDRESS>22institutetext: Institut für Physik und Astronomie,
Universität Potsdam, Haus 28, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm,
Germany 33institutetext: Armagh Observatory and Planetarium, College Hill,
Armagh BT61 9DG, Northern Ireland 44institutetext: Department of Physics,
University of Nebraska at Omaha, 6001 Dodge St, Omaha, NE 68182-0266, USA

# EC 22536$-$5304: A lead-rich and metal-poor long-period binary

M. Dorsch 1,21,2 C. S. Jeffery 33 A. Irrgang, V. Woolf, U. Heber 114411

(Received ; accepted )

Helium-burning hot subdwarf stars of spectral types O and B (sdO/B) are
thought to be produced through various types of binary interactions. The
helium-rich hot subdwarf star EC 22536$-$5304 was recently found to be
extremely enriched in lead. Here, we show that EC 22536$-$5304 is a binary
star with a metal-poor subdwarf F-type (sdF) companion. We performed a
detailed analysis of high-resolution SALT/HRS and VLT/UVES spectra, deriving
metal abundances for the hot subdwarf, as well as atmospheric parameters for
both components. Because we consider the contribution of the sdF star, the
derived lead abundance for the sdOB, $+6.3\pm 0.3$ dex relative to solar, is
even higher than previously thought. We derive $T_{\mathrm{eff}}$ = $6210\pm
70$ K, $\log g$ = $4.64\pm 0.10$, [Fe/H] = $-1.95\pm 0.04$, and
[$\alpha/\mathrm{Fe}$] = $+0.40\pm 0.04$ for the sdF component. Radial
velocity variations, although poorly sampled at present, indicate that the
binary system has a long orbital period of about 457 days. This suggests that
the system was likely formed through stable Roche lobe overflow (RLOF). A
kinematic analysis shows that EC 22536$-$5304 is on an eccentric orbit around
the Galactic centre. This, as well as the low metallicity and strong alpha
enhancement of the sdF-type companion, indicate that EC 22536$-$5304 is part
of the Galactic halo or metal-weak thick disc. As the first long-period hot
subdwarf binary at [Fe/H] $\lesssim$ $-1$, EC 22536$-$5304 may help to
constrain the RLOF mechanism for mass transfer from low-mass, low-metallicity
red giant branch (RGB) stars to main-sequence companions.

###### Key Words.:

stars: individual (EC 22536$-$5304) — subdwarfs — stars: abundances

##  1 Introduction

Hot subdwarf stars form a heterogeneous class of evolved stars located at the
hot end of the horizontal branch or beyond (for reviews, see Heber, 2009,
2016). This implies that they burn helium either in the core or in a shell,
while their hydrogen envelope is very thin or almost absent. Accordingly,
their masses are close to half that of the Sun. Most B-type subdwarf stars
(sdB) have helium-poor atmospheres due to atmospheric diffusion (Hu et al.,
2011; Michaud et al., 2011). In contrast, the hotter sdO stars are often found
to be extremely enriched in helium. There is also an intermediate class of hot
subdwarf stars, termed intermediate helium sdOB (iHe-sdOB). Their effective
temperature and helium abundances are intermediate between the cooler helium
poor sdBs and those of the hotter helium-rich sdO stars (e.g. Németh et al.,
2012; Jeffery et al., 2021). Recently, several members of this small
population have been found to be extremely enriched in heavy elements such as
strontium, yttrium, zirconium, or lead (e.g. Naslim et al., 2011; Jeffery et
al., 2017; Dorsch et al., 2020). The hot component of EC 22536$-$5304 was
identified as an extremely lead-rich iHe-sdOB by Jeffery & Miszalski (2019);
in fact, it is the most lead-rich star known to date. Like the depletion of
helium observed in the photospheres of most sdB stars, the strong enrichment
in heavy metals is usually attributed to diffusion and selective radiative
acceleration. However, quantitative predictions are still lacking for atomic
diffusion in the atmospheres of iHe-sdOB stars.

A close inspection of new high-resolution spectra taken with SALT/HRS reveals
a second component in the spectrum of EC 22536$-$5304: a metal-poor, subdwarf-
F-type (sdF) main-sequence (MS) star, which was not considered in the previous
analysis. Many helium-poor sdB stars are found in binary systems with low-mass
MS stars or white dwarfs at short orbital periods of the order of ten days or
fewer (Kupfer et al., 2015). They are thought to be formed following a common
envelope (CE) phase, in which the red giant progenitor to the sdB has lost
most of its hydrogen-rich envelope, just before it ignites helium burning in
the core (Han et al., 2002).

The orbital properties of all 23 solved helium-poor sdB stars in long-period
binaries have recently been published by Vos et al. (2019). They find that the
orbital periods of these sdB + F/G/K-type systems range from about 500 to 1400
days. The hot subdwarf stars in such systems are the result of a stable Roche
overflow (RLOF) as the progenitor star to the sdB reaches the tip of the red
giant branch (RGB, Han et al., 2003; Chen et al., 2013). Only two helium-rich
subdwarf stars in long-period binary systems are known: the post-asymptotic
giant branch (AGB) He-sdO HD 128220 B (Rauch, 1993) and the He-sdO HD 113001
B, a visually resolved binary with a very long orbital period that has likely
not undergone mass transfer (Tomley, 1970; Goy, 1980; Orlov et al., 2010).
Very recently, Németh et al. (2021) have found the He-poor sdOB component of
the long-period binary system SB 744 to be extremely enhanced in lead.

EC 22536$-$5304 is the first helium-rich heavy-metal subdwarf found to be in a
binary system (long- or short-period). As we show in the following, EC
22536$-$5304 is likely to be a long-period binary, and the first such system
found at a metallicity below about $\mathrm{[Fe/H]}=-1$. It therefore presents
a unique opportunity to study the RLOF evolutionary scenario, especially once
additional spectra become available that will further constrain the orbital
parameters of the system.

In this paper, we present a detailed analysis of high-resolution spectra of EC
22536$-$5304\. The presence of the cool component is confirmed by an analysis
of the spectral energy distribution (SED), which is described in Sect. 2. The
available spectroscopic data are summarised in Sect. 3. Results from the SED
and spectroscopic analysis (Sect. 4) are combined with the parallax
measurement provided by the Gaia mission to derive stellar masses, radii, and
luminosities in Sect. 5. Because the cool companion (hereafter EC 22536$-$5304
B) contributes significantly in the optical range, we updated the metal
abundances derived for the hot component (hereafter EC 22536$-$5304 A). A
detailed account of the metal abundance analysis for the sdOB is given in
Sect. 6. The radial velocities derived from the currently available spectra
are used to perform a kinematic analysis in Sect. 7. The Galactic orbit of the
system is characterised in Sect. 8. We summarise our results in Sect. 9.

##  2 Spectral energy distribution

Figure 1: Photometric fit for EC 22536$-$5304\. Filter-averaged fluxes are shown as coloured data points that were converted from observed magnitudes. Filter widths are indicated by dashed horizontal lines. The grey line visualises the combined model spectrum while individual contributions are shown in blue (A) and red (B). The residual panels on the bottom and right side respectively show the differences between synthetic and observed magnitudes and colours. The following colour codes are used to identify the photometric systems: Tycho (brown, Høg et al., 2000), Johnson-Cousins (blue, Henden et al., 2015; Kilkenny et al., 2016), SDSS (yellow, Henden et al., 2015), SkyMapper (dark yellow, Wolf et al., 2018), Gaia (cyan, Riello et al., 2021), DENIS (orange, DENIS Consortium, 2005), DES (bright yellow, Abbott et al., 2018), VISTA (dark red, McMahon et al., 2013), 2MASS (bright red, Cutri et al., 2003), and WISE (magenta, Cutri et al., 2021).  Table 1: SED fit and spectroscopic fit results for the hot (A) and cool (B) components of EC 22536$-$5304. | SED fit | Spectral fit
---|---|---
$\log\Theta_{\mathrm{A}}\,\mathrm{(rad)}$ | $-11.09^{+0.09}_{-0.05}$ | –
$T_{\mathrm{eff,A}}$ (K) | $38000^{+5000}_{-7000}$ | $38000\pm 400$
$\log g_{\mathrm{A}}$ |  | $\phantom{+}5.81\pm 0.04$
$\log n(\mathrm{He})/n(\mathrm{H})$ |  | $-0.15\pm 0.04$
$v_{\mathrm{tb,A}}$ (km s-1) |  | $\phantom{+}2.1\pm 0.2$
$v_{\mathrm{rot}}\sin i\leavevmode\nobreak\ _{\mathrm{A}}$ (km s-1) | – | $0.0^{+1.0}_{-0.0}$
$T_{\mathrm{eff,B}}$ (K) | $6460^{+90}_{-190}$ | $6210\pm 70$
$\log g_{\mathrm{B}}$ |  | $\phantom{+}4.64\pm 0.10$
[Fe/H]B |  | $-1.95\pm 0.04$
[$\alpha/\mathrm{Fe}$]B |  | $+0.40\pm 0.04$
$v_{\mathrm{tb,B}}$ (km s-1) |  | $\phantom{+}1.83\pm 0.05$
$v_{\mathrm{rot}}\sin i\leavevmode\nobreak\ _{\mathrm{B}}$ (km s-1) | – | $15.3\pm 0.2$
Surface ratio | $34\pm 9$ | $34\pm 5$

Due to the large difference in their effective temperatures, both components
of EC 22536$-$5304 are easily distinguished in the SED of the system. To
obtain an initial estimate for the atmospheric parameters of both components,
a first photometric fit was performed before the spectral analysis. We
obtained apparent magnitudes from the ultraviolet to the infrared to construct
the SED of EC 22536$-$5304\. A general description of the $\chi^{2}$
minimisation method used for the SED fit is given by Heber et al. (2018). In
short, model spectra of both components were converted to filter-averaged
magnitudes and scaled to match the observed magnitudes. Free fit parameters
were the effective temperatures of both components, the angular diameter of
the sdOB $\Theta_{\mathrm{A}}$, and the surface ratio
$A_{\mathrm{sdF}}/A_{\mathrm{sdOB}}$. Here, we used the same large model grids
as for the spectroscopic analysis, which are described in Sect. 4.
Interstellar reddening was considered as by Fitzpatrick et al. (2019),
assuming an extinction parameter of $R(55)=3.02$. Since no reliable UV
magnitudes are available, we constrained the colour excess not to exceed the
line-of-sight value given by Schlegel et al. (1998), $E(B-V)=0.126$ mag, which
is reached in the fit. The first fit was later refined by fixing the helium
abundance of the hot component, the metallicity and alpha enhancement of the
cool component, and both surface gravities to values derived from the spectral
analysis. The final SED fit is shown in Fig. 1. Table 1 compares results of
the SED fit with parameters derived from the spectral fit (see Sect. 4).

Several heavy metal subdwarfs have been found to show peculiar low-amplitude
photometric variability: the zirconium-rich LS IV$-$14$°$116, Feige 46, and
PHL 417 (Ahmad & Jeffery, 2005; Latour et al., 2019b; Østensen et al., 2020),
as well as the lead-rich UVO 0825+15 (Jeffery et al., 2017). It would
therefore be interesting to search for photometric variability in EC
22536$-$5304 as well.

##  3 Spectroscopic observations

Table 2: Spectroscopic data available for EC 22536$-$5304aa$a$The signal-to-
noise ratio is the maximum reached in a combined spectrum..

Spectrograph | Range / Å | $R$ | $n_{\mathrm{exp}}$ | S/N
---|---|---|---|---
HRS/blue | $3895-5520$ | 43000 | 25 | 200
HRS/red | $5500-8870$ | 41000 |  09 | 120
RSS | $3850-5100$ | 1.6 Åbb$b$The resolution for RSS is given as $\Delta\lambda$. |  02 | 100
UVES/blue | $3740-4525$ | 41000 |  03 |  050
UVES/red | $5655-9463$ | 42000 |  02 |  025
111

The spectroscopic data available for EC 22536$-$5304 are summarised in Table
$a$. EC 22536$-$5304 has been observed extensively with the Southern African
Large telescope (SALT) using both the Robert Stobie Spectrograph (RSS) and the
High Resolution Spectrograph (HRS). The setups used for both spectrographs are
described in detail in Jeffery & Miszalski (2019). They used two long-slit RSS
spectra taken in June 2018, as well as HRS spectra taken on 2017 May 18 and
2018 November 15, with exposure times of $2\times 2000$ s on both occasions.
These individual HRS spectra have mean signal-to-noise ratios (S/N) of about
30. Twenty-one additional blue HRS spectra were taken between 2019 May 9 and
23, increasing the combined S/N to about 200. The HRS spectra consist of short
échelle orders, which make order merging difficult. We used a technique that
normalises all orders simultaneously, ensuring continuity across the order
overlaps, before stitching the individual orders together. Some residual
anomalies persist, so we re-normalised the order-merged spectra before
performing the spectral analysis. As a result, broad hydrogen and helium lines
in these spectra could not be used to estimate atmospheric parameters. The HRS
spectra remained essential for the detection of weak metal lines of both
components, as well as the Mg i triplet. Coverage of the Mg i triplet is
especially important because it is sensitive to the metallicity, alpha-
enhancement, and surface gravity of the F-type companion.

In addition to the blue HRS spectra, nine red HRS spectra of sufficient
quality are available. These spectra were taken on the same dates as the blue
HRS spectra. Their near infrared coverage is especially useful since it
includes the Ca ii triplet of the F-type star, as well as He i 6678, 7065, and
7281 Å for the sdOB, all of which help to constrain the surface ratio.

We also make use of archival UVES spectra, which were obtained in October and
December 2011 by M. R. Schreiber under Programme ID 088.D-0364(A). Because
normalisation issues are less pronounced in the blue UVES spectra than in the
HRS spectra, UVES spectra proved to be valuable for the determination of
atmospheric parameters from broad hydrogen and helium lines, despite their
lower S/N.

##  4 Spectral analysis and atmospheric parameters

Figure 2:  Mg i triplet in the HRS spectrum of EC 22536$-$5304 (grey). The
combined model spectrum (red) is the sum of the contributions of the sdOB and
F-type star at the best fit. The dashed spectrum was computed at $\log g_{2}$
= 4.9, while the dotted spectrum uses $\log g_{2}$ = 4.55.

Figure 3: Top: Examples of prominent helium and hydrogen lines in an
individual UVES spectrum of EC 22536$-$5304 (grey). The combined model
spectrum (red) is the sum of the contributions of the sdOB (blue) and F-type
star (dark red). Bottom: Similarly, the strongest calcium lines in blue and
red UVES spectra.

To model the contribution of the sdOB component, we used fully line-blanketed,
plane-parallel, homogeneous, hydrostatic, non-local thermodynamic equilibrium
(NLTE) synthetic spectra computed with Tlusty and Synspec, in particular the
most recent public versions (for detailed descriptions, see Hubeny & Lanz,
2017a, b, c). Heavy metals were included in LTE in the spectrum synthesis as
described by Latour et al. (2019a). A first estimate of the atmospheric
parameters was obtained using a large grid of synthetic spectra that was
computed using the model atoms of Lanz & Hubeny (2003). This grid covers the
full He-sdO/B parameter space in $T_{\mathrm{eff}}$, $\log g$, and helium
abundance $\log n(\mathrm{He})/n(\mathrm{H})$. A smaller grid was then
constructed around the best-fit parameters for the sdOB obtained with the
first grid. To be consistent with the models used for the metal abundance
analysis performed in Sect. 6, this second grid uses the largest model atoms
distributed with Tlusty 205\. Because these model atoms include more energy
levels, optical transitions that involve high-lying levels were treated in
NLTE. The grid considers H, He, C, N, O, Ne, Mg, Al, Si, P, S, Ar, Ca, Fe, and
Ni in NLTE at abundances close to those derived for the sdOB. The abundances
of metals that could not be determined from the available spectra (most
importantly Fe and Ni) were set to the values derived for the iHe-sdOB HZ 44
(Dorsch et al., 2019).

Similarly, the cool companion was initially modelled using a large grid of
model spectra. Here, we used LTE model atmospheres and synthetic spectra
computed with Atlas12 (Kurucz, 1996) and Synthe (Kurucz, 1993). The initial
grid extends from $T_{\mathrm{eff}}$ = 4000 to 8000 K, $\log g$ = 2.0 to 5.2,
[Fe/H] = $-2.0$ to $+0.5$ dex, and covers microturbulent velocities of
$v_{\mathrm{tb}}=0$, 1, and 2 km s-1. A solar helium abundance was assumed.
The F-type companion is metal poor ([Fe/H] = $-1.9$) and strongly alpha
enhanced, which is typical for halo stars (e.g. Fuhrmann, 1998). The initial
grid was therefore computed using a fixed alpha enhancement of
$[\alpha/\mathrm{Fe}]=0.4$ dex relative to the photospheric solar values of
Asplund et al. (2009). As for the sdOB component, a second, smaller grid was
constructed around the best-fit parameters. This grid also uses Atlas12 and
Synthe model spectra, but it was additionally allowed to vary in alpha
enhancement. The dimensions of all four grids of synthetic spectra used in
this analysis are summarised in Table 7.

It is challenging to determine the surface gravity of the F-type companion
accurately. The wings of hydrogen lines, which are typically used to determine
the surface gravity of sdB stars, are less useful for F-type stars because
they are less sensitive to the density and correlate strongly with
temperature. In EC 22536$-$5304, this is further complicated by the
contribution of the sdOB, which has very broad hydrogen lines. The strength of
the bluest Balmer and Paschen lines is sensitive to the surface gravity due to
level dissolution. Unfortunately, our spectra lack coverage of these high
Balmer lines, while the high Paschen lines are below the detection limit. The
observed Balmer series, from Hα up to H11, excludes surface gravities $\log
g_{\mathrm{B}}$ ¡ $4.0$. Instead, the surface gravity of cool (F/G-type) stars
is often derived from the Fe i-ii ionisation equilibrium, which also depends
on the effective temperature. The strengths of the Mg i triplet and the Ca ii
3934, 3968 Å resonance lines are sensitive to the surface gravity and the
respective abundances. As shown in Fig. 2, the Mg i triplet in EC 22536$-$5304
is well reproduced at $\log g_{\mathrm{B}}$ = $4.7$, assuming an alpha
enhancement of 0.4 dex.

We performed global spectral fits in order to consider all sensitive
absorption lines in the observed spectra. Examples for strong hydrogen,
helium, and calcium lines are shown in Fig. 3. The atmospheric parameters of
both components and the surface ratio were varied simultaneously. The
individual UVES and HRS exposures were not stacked but evaluated at the same
time. This is necessary because the radial velocity difference between both
components is not constant over more than a few days. Spectral regions that
were not well reproduced were removed before performing the final fit. This
includes metal lines with uncertain atomic data, as well as the cores of Ca ii
resonance and hydrogen Balmer lines, which are poorly modelled in our LTE
models for the cool component. After a first fit using large model grids, a
second global fit was performed that used tailored grids for both components,
as described above.

The atmospheric parameters derived from the final spectral fit are listed in
Table 1. They are consistent with the results obtained from the SED fit in
Sect. 2, but more precise. We use 1-$\sigma$ intervals for the statistical
uncertainties. Due to the high resolution and high total S/N of our spectra,
purely statistical uncertainties are small. The total uncertainties are
dominated by systematic effects, such as deficiencies in the synthetic spectra
or limited accuracy in the normalisation of our spectra. We estimate
systematic uncertainties of 1% in $T_{\mathrm{eff}}$, as well as 0.04 in $\log
g_{\mathrm{A}}$, $\log n(\mathrm{He})/n(\mathrm{H})$, [Fe/H]B, and
[$\alpha/\mathrm{Fe}$]B. These systematic uncertainties were added in
quadrature to the smaller statistical errors. We used a higher systematic
uncertainty of 0.10 dex for the surface gravity of the cool component, $\log
g_{\mathrm{B}}$, for two reasons. First, there is no spectral feature that is
strongly dependent on $\log g_{\mathrm{B}}$. Second, $\log g_{\mathrm{B}}$ is
strongly correlated with other free parameters such as $T_{\mathrm{eff,B}}$,
the surface ratio, and the alpha enhancement.

We find a significant projected rotational velocity of $15.3\pm 0.2$ km s-1
for the sdF-type companion. This rotation is relatively slow compared to the
values Vos et al. (2018) found for the cool companions in their sample of nine
long-period sdB + F/G/K-type systems. EC 22536$-$5304 A is consistent with no
rotation, which is not unusual since most hot subdwarfs are slow rotators,
including stars found in wide binaries (Geier & Heber, 2012).

##  5 Mass, radius, and luminosity

Table 3: Stellar parameters for EC 22536$-$5304 as derived by combining the SED, spectroscopic, and parallax measurements. The mode and the highest density interval of each quantity are given for 1-$\sigma$ probability (see Bailer-Jones et al., 2018). | A | B
---|---|---
$R/R_{\odot}$ | $0.132\pm 0.007$ | $0.75\pm 0.07$
$M/M_{\odot}$ | $0.40\pm 0.06$ | $0.84^{+0.29}_{-0.23}$
$L/L_{\odot}$ | $32\pm 4$ | $0.74^{+0.15}_{-0.14}$

Figure 4: Main-sequence evolutionary tracks from MIST (Choi et al., 2016) for
[Fe/H] = $-2.1$ (dashed), $-1.9$ (solid), and $-1.6$ (dash-dotted), as well as
for four initial masses. The upper panel shows the Kiel diagram, while the
Hertzsprung-Russell diagram is shown in the lower panel. The dotted grey lines
indicate equal age and are labelled in Gyr. The parameters of EC 22536$-$5304
B and their uncertainties are marked by the cross.

Stellar parameters can be derived using the precise parallax measurement
provided by the Early Data Release 3 (EDR3) of the Gaia mission (Gaia
Collaboration et al., 2016, 2021), $\varpi$ = $1.40\pm 0.04$ mas. We corrected
the parallax for its zero-point offset following Lindegren et al. (2021) and
inflated the corresponding uncertainty using the function suggested by El-
Badry et al. (2021). Stellar radii are then given as $R$ = $\Theta/(2\varpi)$.
Here, $\Theta$ refers to the individual angular diameters determined from the
SED. In contrast to the SED fit performed in Sect. 2, the angular diameter
used here, $\log\Theta_{\mathrm{A}}/{\rm rad}$ = $-11.078^{+0.018}_{-0.022}$,
was obtained while keeping all atmospheric parameters fixed to the more
precise spectroscopic values as listed in Table 1. Combining the radii with
the spectroscopic surface gravities then allowed us to derive the stellar
masses $M$ = $gR^{2}/G$, where $G$ is the gravitational constant. Stellar
luminosities are given as $L/L_{\odot}$ =
$(R/R_{\odot})^{2}(T_{\mathrm{eff}}/T_{\mathrm{eff},\odot})^{4}$. The stellar
parameters for both components are listed in Table 3. We used a Monte Carlo
method to propagate the uncertainties.

Due to the high uncertainty in surface gravity and surface ratio, the mass for
the sdF component is poorly constrained. As discussed in Sect. 7, it is likely
that the EC 22536$-$5304 system formed through Roche-lobe overflow. However,
the transferred mass is expected to be less than 0.03 $M_{\odot}$ (Vos et al.,
2018). It is likely that the transferred mass for EC 22536$-$5304 B is
significantly below this value, given its relatively slow projected rotation.
We can therefore derive an evolutionary mass for the sdF based on its
spectroscopic effective temperature and surface gravity. Figure 4 shows
single-star evolutionary tracks from the MIST project (Choi et al., 2016) for
metallicities of $\mathrm{[Fe/H]}$ = $-1.9\pm 0.3$. In the Kiel diagram (Fig.
4; upper panel), our atmospheric parameters of EC 22536$-$5304 B are
consistent with masses between about 0.8 and 0.7 $M_{\odot}$. We cannot
estimate an evolutionary age directly from the atmospheric parameters since
our surface gravity puts EC 22536$-$5304 B close to the predicted zero-age MS.
Given the low metallicity of EC 22536$-$5304 B, one would expect an age of the
order of about 10 Gyr or more. The spectroscopic surface gravity for the sdF
may therefore be slightly overestimated.

It is useful to consider the position of EC 22536$-$5304 B in the Hertzsprung-
Russell diagram (luminosity vs. $T_{\mathrm{eff}}$), given that the luminosity
is (almost) independent of the spectroscopic surface gravity. As shown in the
bottom panel of Fig. 4, our estimates for the luminosity and effective
temperature of the sdF are consistent with a lower evolutionary mass, about
0.7 $M_{\odot}$. While this mass would be consistent with the expected age,
the uncertainties are large.

It is not possible to directly derive an evolutionary mass for the sdOB
because too many evolutionary tracks cross its position in the
$T_{\mathrm{eff}}$ \- $\log g$ plane. However, the mass expected for a sdOB
that was formed through RLOF is close to the core mass that is required for
the helium-flash at the top of the RGB, or about 0.49 $M_{\odot}$ at
$\mathrm{[Fe/H]}\approx-2$ (Dorman et al., 1993). Although higher than the
$0.40\pm 0.06$ $M_{\odot}$ found for EC 22536$-$5304 A, the lower value
observed is still consistent with it being a core helium burning star.

##  6 Metal abundance analysis

Table 4: Metal abundance results for EC 22536$-$5304 A by number fraction ($\log\epsilon=\log n_{\mathrm{X}}/\sum_{i}n_{i}$) and number fraction relative to solar ($\log\epsilon/\epsilon_{\odot}$, Asplund et al., 2009). The number of resolved lines used per ionisation stage is given in the last column (with equivalent widths $>$ 10 mÅ).  Element | $\log\epsilon$ | $\log\epsilon/\epsilon_{\odot}$ | $N_{\mathrm{lines}}$
---|---|---|---
C ii-iv | $-2.88\pm 0.20$ | $0.73\pm 0.21$ | 19/45/2
N ii-iii | $-3.73\pm 0.20$ | $0.48\pm 0.21$ | 22/9
O ii-iii | $-3.46\pm 0.20$ | $-0.11\pm 0.21$ | 46/4
Mg ii | $-5.07\pm 0.30$ | $-0.64\pm 0.30$ | 1
Si iii-iv | $-5.52\pm 0.25$ | $-0.99\pm 0.25$ | 1/2
P iii-iv | $-5.92\pm 0.30$ | $0.70\pm 0.30$ | 1/1
S iii-iv | $-5.76\pm 0.30$ | $-0.84\pm 0.30$ | 1/1
Ar | ¡$-5.80^{+0.40}$ | ¡$-0.17^{+0.41}$ |
Ca | ¡$-5.42^{+0.40}$ | ¡$0.27^{+0.40}$ |
Ti | ¡$-5.84^{+0.50}$ | ¡$1.24^{+0.50}$ |
Fe | ¡$-4.30^{+0.30}$ | ¡$0.23^{+0.30}$ |
Zn | ¡$-5.36^{+0.40}$ | ¡$2.11^{+0.40}$ |
Ga | ¡$-5.82^{+0.40}$ | ¡$3.18^{+0.40}$ |
Ge | ¡$-5.89^{+0.40}$ | ¡$2.50^{+0.40}$ |
Kr | ¡$-4.89^{+0.40}$ | ¡$3.90^{+0.40}$ |
Sr | ¡$-5.27^{+0.40}$ | ¡$3.90^{+0.40}$ |
Y | ¡$-5.76^{+0.40}$ | ¡$4.07^{+0.40}$ |
Zr | ¡$-6.71^{+0.40}$ | ¡$2.75^{+0.40}$ |
Sn | ¡$-6.44^{+0.40}$ | ¡$3.56^{+0.40}$ |
Pb iii-iv | $-4.01\pm 0.30$ | $6.27\pm 0.32$ | 5/7

The atmospheric parameters of both components were kept fixed for the metal
abundance analysis. The spectrum of the cool companion was modelled using
Atlas12/Synthe using the final best-fit atmospheric parameters. We used the
global $\chi^{2}$ fitting procedure developed by Irrgang et al. (2014) to
simultaneously determine the abundances for all metals that show sufficiently
strong lines in the hot component (C, N, O, Mg, Si, P, Pb). A grid of
synthetic spectra that include lines of one metal only was computed for each
metal using Synspec, always based on the same Tlusty atmosphere. This model
atmosphere was calculated for the best-fit atmospheric parameters derived in
Sect. 4. To allow an estimation of the microturbulent velocity, each grid was
calculated for microturbulent velocities of 0 and 3 km s-1. The full synthetic
spectrum was then constructed by multiplication of all individual metal
spectra, which were interpolated to the desired abundances. This method is
well tested for sdB and other B-type stars (e.g. Schaffenroth et al., 2021;
Irrgang et al., 2020). It assumes that small changes in the metal abundances
do not influence the atmospheric structure and that there are few intrinsic
blends between lines of different metals. The abundance fitting procedure was
repeated using a Tlusty atmosphere that consistently includes the abundances
from a first fit. As before, spectral regions that were not well reproduced
were removed from the fit.

Because the observed lines that originate from the sdOB component show no
strong signs of a microturbulent velocity, the best-fit
$v_{\mathrm{tb,A}}=2.1\pm 0.2$ km s-1 can be considered as an upper limit.
The final abundance pattern for EC 22536$-$5304 A is listed in Table 4 and
shown in Fig. 5. Upper limits were derived by eye. They are stated as best-fit
values, with an uncertainty that indicates at which abundance the predicted
lines become clearly too strong. The analysis of individual metal abundances
is described in the following.

Figure 5: Photospheric abundances for EC 22536$-$5304 A relative to solar
values from Asplund et al. (2009). Abundance measurements are shown as black
dots, while upper limits are marked with grey arrows. Solid red lines show the
corresponding metal abundances adopted in our model for EC 22536$-$5304 B, as
given by the best-fit [Fe/H] and [$\alpha/\mathrm{Fe}$]. The solar reference
is indicated by the dashed grey line.

Plenty of strong C ii-iv, N ii-iii, and O ii-iii lines are present in the
spectrum of EC 22536$-$5304 A. The C ii atom was updated to use resonance-
averaged photo-ionisation cross-sections using data from TOPbase (Cunto et
al., 1993). This slightly changes the strengths of C ii lines, but it has
little effect on the general atmospheric structure because C ii represents a
small fraction of all carbon ions throughout the atmosphere (¡ 2 %). The sdOB
star is enriched in carbon and nitrogen and has an approximately solar oxygen
abundance. The carbon, nitrogen, and oxygen lines in the spectrum of the
F-type companion are too weak to be detected. The Mg ii 4481 Å doublet is
present in both components, but the contribution of the sdOB is larger,
despite its sub-solar magnesium abundance. This is because the flux
contribution of the sdOB star is more than twice that of the F-type companion
in this specific range. The derived silicon abundance for the sdOB, about one-
tenth solar, is mostly based on the strong Si iv 4088.9, 4116.1 Å lines and
the weaker Si iii 4552.6 Å line. The only detected silicon line that
originates from the cool companion, Si i 3905.52 Å, is consistent with an
alpha-enhancement of 0.4 dex. Two weak phosphorus lines in the spectrum of the
sdOB, P iii 4222.2 Å and P iv 4249.7 Å, are clearly identified. They are best
reproduced at an abundance of about five times solar. All detected calcium
lines originate from the cool component. Most notably, the Ca i 4226.7 Å
resonance line and the Ca ii 8498, 8542, 8662 Å triplet are well reproduced at
an alpha-enhancement of 0.4 dex.

Figure 6: Very strong lead lines in the HRS spectrum of EC 22536$-$5304
(grey). The combined model spectrum (red) is the sum of the contributions of
the sdOB (blue) and F-type star (dark red). Table 5:  Lead lines detected in
the spectrum of EC 22536$-$5304\. References for the oscillator strengths are
stated in the last column.

Ion |  $\lambda$ / Å | $\log gf$ | Ref.
---|---|---|---
Pb iii | 3854.080 | $+0.302$ | 1
Pb iii | 4272.660 | $-0.462$ | 1
Pb iii | 4571.219 | $+0.029$ | 1
Pb iii | 4761.120 | $+0.012$ | 1
Pb iii | 4798.590 | $-0.356$ | 1
Pb iv | 3962.467 | $-0.047$ | 2
Pb iv | 4049.832 | $-0.065$ | 2
Pb iv | 4174.478 | $-0.444$ | 3
Pb iv | 4496.223 | $-0.437$ | 3
Pb iv | 4534.447 | $+1.190$ | 3
Pb iv | 4534.917 | $+1.102$ | 3
Pb iv | 4605.400 | $-0.991$ | 3
222 (1) Alonso-Medina et al. (2009); (2) Safronova & Johnson (2004); (3)
Alonso-Medina et al. (2011).

As shown in Fig. 6, strong Pb iv lines are present at rest wavelengths of
3962.5, 4049.8, 4174.5, 4496.2, 4534.4, 4534.9, and 4605.4 Å. Although weaker,
Pb iii lines at 3854.1, 4272.7, 4571.2, 4761.1, and 4798.6 Å are clearly
detected. All identified lead lines are listed in Table 5. The 2019 HRS
spectra were shifted to the rest frame of the sdOB and co-added to update the
wavelengths of newly observed lead lines. This co-added spectrum was not used
for the abundance fit, which, as before, was performed using all individual
spectra. All modelled lead lines are reasonably well reproduced at an
abundance between one and two million times solar, or 100 million times larger
than the scaled solar value using the metallicity deduced from the cool
companion. This is significantly more than the 4.8 dex enrichment derived by
Jeffery & Miszalski (2019), who were unaware of any flux contribution from a
companion.

Table 4 also lists upper limits for several elements, which had been detected
in other iHe sdOBs, in particular Feige 46 and LS IV$-$14$°$116 (Dorsch et
al., 2020). Since no lines from these elements are detected, any ’best-fit’
abundance obtained from a $\chi^{2}$ fit would strongly depend on the location
of the continuum. We therefore prefer to obtain upper limits by eye. All lines
used to derive upper limits for EC 22536$-$5304 A up to iron are known to be
well reproduced in our models of other He-sdOB stars. For sulphur, we used the
weak S iv 4485.7, 4504.2 Å lines, which seem to be just below the detection
limit of the HRS and UVES spectra of EC 22536$-$5304\. The only usable
predicted argon line is Ar iii 4183.0 Å. The upper limits for calcium and
titanium are based on Ca iii 4233.7, 4240.7 Å, and Ti iv 4618.2, 5398.9,
5492.5 Å, respectively. The upper limit for iron is based on the non-detection
of Fe iii 4164.7, 4304.8, and 4310.4 Å. In addition to lead, we also searched
for heavy metals that have been detected in optical spectra of the
intermediate He-sdOBs Feige 46 and LS IV$-$14$°$116: Zn, Ga, Ge, Kr, Sr, Y,
Zr, and Sn. Upper limits for these elements are based on the non-detection of
Zn iii 4818.9, 5075.2 Å, Ga iii 4380.6, 4381.8, 4993.9 Å, Ge iii 4179.1,
4260.9 Å, Kr iii 4067.4, 4226.6 Å, Sr iii 3936.4 Å, Y iii 4039.6, 4040.1 Å, Zr
iv 4198.3, 5462.4 Å, and Sn iv 4216.2 Å. We used the same atomic data as
Dorsch et al. (2020) for these ions. The resulting upper limits rule out
extreme enrichments as observed for lead, but would still be consistent with
strong enrichment compared to solar or even mean sdB values. Ultraviolet
spectra would enable us to determine abundances for most of these heavy
metals, but they are not presently available. A small number of lines in the
UVES and HRS spectra remain unidentified. The identification of these lines is
complicated by the composite nature of EC 22536$-$5304, since the lines of the
F-type companion are only slightly more broadened by rotation than those of
the sdOB. Table 8 lists the rest wavelengths of all detected unidentified
lines, assuming that they originate from the sdOB component. We only list
lines that are present in both coadded HRS and coadded UVES spectra, or are
strong enough to be identified in single exposures.

The overall abundance pattern for EC 22536$-$5304 A is similar to that derived
by Jeffery & Miszalski (2019), but shifted to higher abundances due to the
contribution of the sdF star (unaccounted for previously). Carbon, nitrogen,
and phosphorus are enhanced relative to solar values, while the oxygen
abundance is about solar. Magnesium, silicon, and sulphur are sub-solar. With
respect to the primordial metallicity plus alpha enhancement, all detected
elements would be enhanced. Similar patterns for these light metals have been
observed in other heavy-metal iHe-sdOBs: the zirconium-rich Feige 46 and LS
IV$-$14$°$116 (Naslim et al., 2011; Dorsch et al., 2020), the zirconium- and
lead-rich HE 2359-2844 and HE 1256-2738 (Naslim et al., 2013), the lead-rich
PG 1559+048 and FBS 1749+373 (Naslim et al., 2020), as well as PG 0909+276 and
UVO 0512-08 (Edelmann et al., 2003; Wild & Jeffery, 2018), which are extremely
enriched in iron-group elements. Unlike the hotter lead-rich iHe-sdOBs UVO
0825+15 (Jeffery et al., 2017), HZ 44, and HD 127493 (Dorsch et al., 2019), EC
22536$-$5304 A does not show the distinct CNO-cycle pattern (strong N, weak C
and O). Notably, the metal abundance pattern is not shifted to lower values
when compared to other heavy-metal iHe-sdOBs. This indicates that the metal
abundance patterns observed for iHe-sdOB stars are not strongly dependent on
the initial metallicity. The abundances derived for C, N, O, and Si are almost
identical to those of HE 1256-2738, an apparently single lead-rich iHe-sdOB
found to be a Galactic halo member by Martin et al. (2017).

EC 22536$-$5304 A does not seem to share the extreme zirconium abundance
observed in some iHe-sdOBs or the extreme enrichment in iron-group elements
with respect to the Sun found in others, although our upper limits are high.
The latter may be due to the very low primordial metallicity of the system.
The lead enhancement of EC 22536$-$5304 A is the most extreme found in any hot
subdwarf, or, to our knowledge, in any star. The strong enrichment of heavy
metals in the photospheres of heavy-metal sdOBs is usually discussed in terms
of selective radiative levitation. In this picture, the strong heavy metal
lines observed in the emergent spectrum are the result of a chemically
stratified envelope, in which a thin metal-rich layer overlaps with the line-
forming region. As mentioned by Jeffery & Miszalski (2019), atmospheric models
that include a physical treatment of stratification by diffusion are required
to estimate the total amount of lead in the enriched layers. These models
would then have to be compared with lines that form at various optical depths,
ideally using both far-UV and optical spectra.

The flux contribution of the sdF only overtakes that of the sdOB at about 7200
Å in our best-fit model. Therefore, and due to the low metallicity, relatively
few metal lines that originate from the sdF component are detectable in our
spectra. Most of them are well reproduced at the best-fit metallicity and
alpha-enhancement. The strongest metal lines detected include transitions in
the Na i, Mg i, Al i, Si i, Ca i-ii, Ti ii, Cr i, Mn i, Fe i-ii, and Ni i
atoms. The strontium lines Sr ii 4077.7, 4215.5 Å seem to be well reproduced
at the scaled solar abundance. We also detect Ba ii 4554.0, 4934.1 Å, which
are somewhat too weak in our models at the scaled solar abundance. This
discrepancy may be due to a weak enrichment in barium, but may also be caused
by deficiencies in our synthetic spectra, such as uncertain atomic data or
NLTE effects. The existence of dwarf barium stars is usually explained with
pollution through wind accretion or RLOF from an AGB star (Jorissen & Boffin,
1992; Gray et al., 2011). Given that EC 22536$-$5304 A is likely still on the
horizontal branch, it seems unlikely that the sdF component is a barium star.

It is likely that the present EC 22536$-$5304 system formed through mass
transfer from a RGB star to the sdF companion. One might therefore expect at
least some pollution of the sdF companion by material processed in the CNO-
cycle, although diluted by convection. Unfortunately, no carbon, nitrogen, or
oxygen lines that originate from the sdF are detectable in our spectra.

##  7 Analysis of the radial velocity curve

Figure 7: Elliptic orbits fit to the radial velocities of both EC 22536$-$5304 A (black) and B (red). Asterisks indicate UVES measurements, while HRS data from 2017, 2018, and 2019 are marked by crosses, squares, and diamonds, respectively.  Table 6: Orbital parameters for EC 22536$-$5304\. The gravitational redshift $\varv_{\mathrm{grav}}$ is calculated from the stellar parameters listed in Table 3. Parameter | Value
---|---
Period $P$ |  $457.0^{+1.2}_{-1.5}$ d
Epoch of periastron $T_{\mathrm{periastron}}$ |  $56160^{+21}_{-17}$ MJD
Eccentricity $e$ | $0.22^{+0.13}_{-0.08}$
Longitude of periastron $\omega$ |  $276^{+21}_{-18}$ deg
Velocity semiamplitude $K_{A}$ |  $15.5^{+1.7}_{-1.6}$ km s-1
Velocity semiamplitude $K_{B}$ |  $10.7\pm 1.4$ km s-1
Gravitational redshift $\varv_{\mathrm{grav_{A}}}$ |  $1.95^{+0.22}_{-0.20}$ km s-1
Gravitational redshift $\varv_{\mathrm{grav_{B}}}$ |  $0.72^{+0.21}_{-0.17}$ km s-1
Systemic velocity $\gamma$ |  $-3.3\pm 0.4$ km s-1
Derived parameter | Value
Mass ratio $q=K_{B}/K_{A}=M_{A}/M_{B}$ | $0.69^{+0.06}_{-0.05}$
Projected semimajor axis $a_{A}\sin(i)$ |  $0.63\pm 0.05$ au
Projected semimajor axis $a_{B}\sin(i)$ |  $0.44\pm 0.04$ au

A total of 27 HRS and UVES spectra are of sufficient quality to measure the
radial velocities for both components, which are listed in Table 9. These
spectra cover a time span of $\Delta t=2880$ days, but they were taken in only
five observing runs, the longest of which was just two weeks. This coverage is
too irregular to precisely determine the orbital parameters of the EC
22536$-$5304 system. We initially searched for orbital periods by fitting
circular orbits to all available radial velocities, corrected for the
gravitational redshifts. A unique best orbital period, $P$ $\approx$ 457 days,
was obtained by finely sampling orbital frequencies between 1/330 and 1/550
d-1 with steps of $0.01/\Delta t=3.6\times 10^{-6}$ $\mathrm{d}^{-1}$. Fitting
eccentric orbits resulted in a somewhat eccentric orbit with the same 457-day
period and velocity semi-amplitudes of $K_{A}=15.5\pm 1.7$ km s-1 and
$K_{B}=10.7\pm 1.4$ km s-1 (see Table 6). The phased radial velocity curves
are shown in Fig. 7. More observations are required to improve the orbital
solution, in particular for the eccentricity.

Since the orbital period of EC 22536$-$5304 is certainly longer than 50 days,
it is likely that the system was formed through stable Roche-lobe overflow.
Vos et al. (2017) discovered a positive correlation between the eccentricity
and orbital period for post-RLOF systems. Given the orbital period of about
457 days, one would expect a low eccentricity for the orbit of EC
22536$-$5304\. We find an eccentricity of $e=0.22^{+0.13}_{-0.08}$, which,
however, strongly depends on the radial velocities derived from the HRS
spectra taken in 2017.

A correlation between orbital period and mass ratio of post-RLOF sdB+MS
binaries was found by Vos et al. (2019). Subsequently, Vos et al. (2020)
showed that the observed relation can be explained in terms of the system
metallicity. Orbital periods of sdB+MS systems decrease with metallicity,
because low-metallicity donor stars have smaller radii at the top of the RGB.
In order to produce a sdB, the mass transfer must happen close to the top of
the RGB, so that the RGB star can ignite helium burning in its core. Low-
metallicity systems therefore have shorter initial periods, which leads to
shorter final periods once the mass transfer has stopped. For halo systems at
[Fe/H] = $-1.8\pm 0.5$, Vos et al. (2020) predicted orbital periods of 300 to
500 days and mass ratios $q=M_{\mathrm{sdB}}/M_{\mathrm{MS}}$ of 0.6 to 0.8,
which is consistent with our (preliminary) result for EC 22536$-$5304,
$q=K_{B}/K_{A}=M_{A}/M_{B}=0.69\pm 0.06$. Assuming a canonical mass of
$M_{\mathrm{sdB}}=0.49$ $M_{\odot}$ for the sdOB, the mass ratio would put the
mass of the sdF at $0.71\pm 0.06$ $M_{\odot}$.

##  8 Kinematics

Figure 8:  Toomre diagram showing space velocities with respect to the
Galactic centre. The velocity component $V$ is measured in the direction of
the rotation of the Galaxy, $U$ towards the Galactic centre, and $W$
perpendicular to the plane. The position of EC 22536$-$5304, the Sun, and the
local standard of rest (LSR) are marked by the red cross, yellow circled dot,
and black plus sign, respectively. The grey, green, and blue dashed lines
indicate 2-$\sigma$ velocity dispersions from Robin et al. (2003) for the
halo, thick disc, and old thin disc, respectively. Stars from the sample of
intermediate He-sdO/Bs studied by Martin et al. (2017), updated using Gaia
EDR3 parallaxes and proper motions are shown in grey. Probable halo stars are
labelled.

Proper motions and the parallax from Gaia EDR3 combined with the system’s
radial velocity can be used to derive the present 3D space velocity of EC
22536$-$5304\. The Galactic orbit of EC 22536$-$5304 can then be traced back
using a model for the Galactic potential: here, for 10 Gyr. We used Model I of
Irrgang et al. (2013) for the Galactic potential, which is a revision of the
Allen & Santillan (1991) potential. Given the sparse coverage of our radial
velocities, we adopted an uncertainty of 5 km s-1 on the system’s radial
velocity. The resulting orbit for EC 22536$-$5304 has a low angular momentum
perpendicular to the Galactic disc $J_{Z}=930\pm 40$ kpc km s-1, but a
relatively high eccentricity of $e=0.53\pm 0.02$. The current velocity towards
the Galactic centre $U$, perpendicular to the disc $W$, and in the direction
of Galactic rotation $V$ can be used to place EC 22536$-$5304 in the Toomre
diagram. When compared to the Toomre parameters predicted from Besançon
Galactic models (Robin et al., 2003), the location of EC 22536$-$5304 in this
diagram is consistent with either a thick-disc or halo origin (see Fig. 8).
Although most hot subdwarf stars seem to be part of the thin disc, several
intermediate He-sdO/Bs in the sample of Martin et al. (2017) have been
classified as thick discs or halos. To facilitate the comparison with EC
22536$-$5304, we repeated the orbit calculation for iHe-sdOBs from this sample
using reliable Gaia EDR3 proper motions and parallaxes
($\sigma_{\varpi}/\varpi$ ¡ $10\,\%$). The heavy-metal iHe-sdOBs Feige 46 and
HZ 44 (Dorsch et al., 2019, 2020) were considered in addition. We corrected
the proper motions provided by Gaia EDR3 for bright stars ($G<13$ mag),
following Cantat-Gaudin & Brandt (2021). As before, we applied corrections to
the parallax measurements (Lindegren et al., 2021) and their uncertainty (El-
Badry et al., 2021). The resulting orbital parameters are summarised in Table
10.

Given the low metallicity of EC 22536$-$5304, the system may be part of the
low-metallicity tail of the thick disc, also termed metal-weak thick disc
(MWTD). According to Chiba & Beers (2000), the low-metallicity cut-off of the
MWTD is close to [Fe/H] = $-2$, comparable to the metallicity of EC
22536$-$5304 B. At this low metallicity, the halo population in their sample
dominates even at small distances from the Galactic disc, such as the
$Z=-593^{+13}_{-16}$ pc observed for EC 22536$-$5304\. However, is not
possible to discern between a MWTD or halo origin for any particular system
that shows disc-like kinematics (see e.g. Reddy & Lambert, 2008).

##  9 Conclusions

We performed a detailed analysis of high-resolution spectra of EC
22536$-$5304and can confirm that the system contains an extremely lead-rich
intermediate He-sdOB, as found by Jeffery & Miszalski (2019). However, we find
a second component in its spectrum: a strongly alpha-enhanced and metal-poor
F-type subdwarf. EC 22536$-$5304 A is the first heavy-metal sdOB found in a
binary system. Our updated metal abundances for the sdOB component are similar
to those derived in the previous analysis, but shifted to higher abundances.
EC 22536$-$5304 A therefore remains the most lead-rich hot subdwarf known to
date. Although the initial metallicity of the system is low, the abundances
for the hot component are quite similar to those of other iHe-sdOB stars, some
of which probably have significantly higher initial metallicities, given that
they belong to the younger thin-disc population (such as PG 1559+048, see
Sect. 8). The observed abundance pattern of EC 22536$-$5304 A is likely the
result of strong diffusion processes. Ultraviolet spectroscopy would enable us
to derive a more complete abundance pattern for the sdOB component.

EC 22536$-$5304 A is the first hot subdwarf found in a long-period binary with
a known metallicity [Fe/H] ¡ $-1$. The low metallicity ([Fe/H]B = $-1.95$) and
strong alpha enhancement ([$\alpha/\mathrm{Fe}$]B = 0.4) derived for the sdF
component indicate that the system is part of the Galactic halo or metal-weak
thick disc. The system is therefore likely old ($\gtrsim$10 Gyr, e g. Helmi,
2020). Other hot subdwarfs with a low known metallicity are part of globular
clusters, but they are typically not found in binary systems (Latour et al.,
2018). Still, the stellar evolution models of Han (2008) predict a significant
fraction of old sdO/Bs to have been formed through stable RLOF, which seems to
be the case for EC 22536$-$5304.

To determine the stellar parameters mass, radius, and luminosity for both
components, we combined the parallax provided by Gaia EDR3 with the angular
diameter derived from a SED fit and our spectroscopic atmospheric parameters.
The resulting mass for EC 22536$-$5304 A, $0.40\pm 0.06$ $M_{\odot}$, is
consistent with the range of masses expected for hot subdwarf stars on the
extreme horizontal branch. The spectroscopic mass for EC 22536$-$5304 B,
$0.84^{+0.29}_{-0.23}$ $M_{\odot}$, is associated with a high uncertainty
because its surface gravity is not easily determined. In fact, the comparison
of MIST evolutionary tracks with our effective temperature and luminosity
points to a lower mass for the sdF, about 0.7 $M_{\odot}$. This mass would be
consistent with an evolutionary age of about 10 Gyr.

Radial velocity variations suggest that the system is likely a wide binary
with an orbital period of about 457 days. An eccentric fit to the radial
velocities results in a mass ratio $q=M_{A}/M_{B}=0.69\pm 0.06$. Vos et al.
(2019) recently found a strong relation between the orbital period and mass
ratio for long-period hot subdwarf binaries. This relation could be explained
by a correlation between the final orbital period and metallicity of such
systems found by Vos et al. (2020), which results from different radii of the
progenitors at the tip of the RGB, when mass transfer started. Given the low
metallicity of EC 22536$-$5304, the system helps to constrain these relations
at much lower metallicity than before. The current results for the orbital
period, mass ratio, and metallicity are consistent with the predictions of Vos
et al. (2020) for post-RLOF systems. Additional spectra that sample the full
orbital period are required to obtain reliable orbital parameters.

We also performed a kinematic analysis, based on the system radial velocity
determined from the current radial velocity curve. EC 22536$-$5304 is on an
eccentric orbit around the Galactic centre, which is consistent with a halo or
thick-disc membership. Several heavy-metal iHe-sdOB stars have been found in
the Galactic halo. From the Gaia EDR3 data, we can confirm that the zirconium-
rich Feige 46 and LS IV$-$14$°$116 (Latour et al., 2019b; Dorsch et al., 2020)
are halo members.

###### Acknowledgements.

We thank the referee for the careful reading and comments that improved this
paper. A.I., U.H. and M.D.  acknowledge funding by the Deutsche
Forschungsgemeinschaft (DFG) through grants IR190/1-1, HE1356/70-1 and
HE1356/71-1. This research made use of the lmfit python package developed by
Newville et al. (2014). Based on observations obtained with the Southern
African Large Telescope (SALT) under programmes 2017-1-SCI-004,
2018-2-SCI-033, and 2019-1-MLT-003. Based on observations collected at the
European Southern Observatory under ESO programme 088.D-0364(A). This work has
made use of data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This publication makes use
of data products from the Wide-field Infrared Survey Explorer, which is a
joint project of the University of California, Los Angeles, and the Jet
Propulsion Laboratory/California Institute of Technology, funded by the
National Aeronautics and Space Administration. This research has made use of
NASA’s Astrophysics Data System. The Armagh Observatory and Planetarium are
funded by direct grant from the Northern Ireland Department for Communities.

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##  Appendix A Additional material

Table 7: Dimensions for the four grids of synthetic spectra used for the spectroscopic and SED analyses. For each parameter, the maximum and minimum values, as well as the step width are stated. As described in Sect. 4, the large and small Tlusty/Synspec grids were each computed using a fixed metal abundance pattern. |  Tlusty/Synspec |  Atlas12/Synthe
---|---|---
Parameter | large | small | large | small
{3*[$T_{\mathrm{eff}}$ (K) ] | 27500 | 37300 | 4000 | 6150
| 47500 | 38800 | 8000 | 6275
| 1250 | 500 | 200 | 25
{3*[$\log g$ ] | 4.750 | 5.60 | 2.00 | 4.50
| 6.125 | 6.00 | 5.20 | 4.80
| 0.125 | 0.20 | 0.20 | 0.10
{3*[$\log n(\mathrm{He})/n(\mathrm{H})$ ] | $-1.00$ | $-0.23$ | $-1.07$ | $-1.07$
| $+2.00$ | $+0.07$ | $-1.07$ | $-1.07$
| 0.25 | 0.15 | – | –
{3*[[Fe/H] ] | – | – | $-2.00$ | $-2.05$
| – | – | $+0.50$ | $-1.85$
| – | – | 0.50 | 0.20
{3*[[$\alpha/\mathrm{Fe}$] ] | – | – | 0.40 | 0.33
| – | – | 0.40 | 0.44
| – | – | – | 0.11
{3*[$v_{\mathrm{tb}}$ (km s-1) ] | 5.0 | 0.0 | 0.0 | 1.5
| 5.0 | 3.0 | 2.0 | 2.5
| – | 3.0 | 1.0 | 1.0
Table 8:  Unidentified lines in the HRS and UVES spectra of EC 22536$-$5304\. Equivalent widths are stated for the composite spectrum. Rest wavelengths assume that lines originate from the sdOB.  $\lambda$ / Å | EW / mÅ | Comment
---|---|---
4081.692 | 19 | sharp
4182.414 | 11 | sharp
4273.738 | 12 |
4400.840 | 10 |
4450.986 | 8 |
4581.979 | 25 | broad
4664.656 | 13 | broad
4802.251 | 12 |
5021.613 | 27 | artifact?
5094.107 | 15 |
5438.381 | 22 |
7298.346 | 78 |
Table 9:  Radial velocities with barycentric correction applied. The gravitational redshifts have not been corrected. The typical uncertainty is of the order of 2 km s-1, depending on S/N. There may be a small systematic trend in the radial velocities derived from HRS spectra that were taken in 2019.  MJD |  $v_{\mathrm{rad,B}}$ / km s-1 |  $v_{\mathrm{rad,A}}$ / km s-1 | Spectrograph
---|---|---|---
55846.1 | 4.0 |  $-$14.6 | UVES
55846.1 | 4.1 |  $-$15.7 | UVES
55849.1 | 6.0 |  $-$12.2 | UVES
55849.1 | 4.0 |  $-$13.0 | UVES
55908.0 |  $-$1.2 |  $-$5.0 | UVES
57891.0 |  $-$11.7 | 13.5 | HRS
57891.0 |  $-$11.5 | 11.6 | HRS
58437.0 |  $-$3.3 |  $-$3.2 | HRS
58437.0 |  $-$4.2 |  $-$0.3 | HRS
58612.0 | 2.4 |  $-$10.5 | HRS
58612.0 | 2.6 |  $-$9.4 | HRS
58616.0 | 1.9 |  $-$10.7 | HRS
58616.0 | 2.1 |  $-$11.0 | HRS
58617.0 | 2.0 |  $-$8.3 | HRS
58617.0 | 2.3 |  $-$8.8 | HRS
58619.0 | 4.1 |  $-$10.0 | HRS
58619.0 | 2.9 |  $-$7.5 | HRS
58620.0 | 2.5 |  $-$7.6 | HRS
58620.0 | 4.9 |  $-$8.0 | HRS
58621.0 | 3.9 |  $-$8.4 | HRS
58621.0 | 3.8 |  $-$9.0 | HRS
58624.0 | 3.4 |  $-$8.4 | HRS
58624.0 | 3.0 |  $-$7.4 | HRS
58625.0 | 3.4 |  $-$7.4 | HRS
58625.0 | 4.1 |  $-$7.3 | HRS
58626.0 | 3.3 |  $-$7.9 | HRS
58626.0 | 4.1 |  $-$7.2 | HRS

Table 10:  Orbital parameters for a sample of intermediate He sdOB stars studied by (Martin et al. 2017) and recent additions (HZ 44, Feige 46, EC 22536$-$5304). The quantities $R_{\mathrm{max}}$, $R_{\mathrm{min}}$, and $Z_{\mathrm{max}}$ refer to the maximum and minimum distance from the Galactic centre, as well as the maximum distance from the Galactic disc. Known zirconium- or lead-rich stars are marked by †.  Star | $v_{\mathrm{rad}}$ | $\pm$ | $R_{\mathrm{max}}$ | $\pm$ | $R_{\mathrm{min}}$ | $\pm$ | $Z_{\mathrm{max}}$ | $\pm$ | $V$ | $\pm$ | $U$ | $\pm$ | $W$ | $\pm$ | $J_{Z}$ | $\pm$ | $e$ | $\pm$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| km s-1 |  | kpc |  | kpc |  | kpc |  | km s-1 |  | km s-1 |  | km s-1 |  | Mpc km s-1 |  |  |
PG 0909+276 | $20.0$ | 2.0 | 9.23 | 0.18 | 8.59 | 0.05 | 0.42 | 0.03 | $249.1$ | $2.1$ | $-0.3$ | $1.9$ | $22.0$ | $1.5$ | $2.19$ | $0.02$ | 0.04 | $0.01$
HD 127493† | $-17.0$ | 3.0 | 8.42 | 0.08 | 7.60 | 0.13 | 0.10 | 0.01 | $234.2$ | $2.4$ | $13.3$ | $2.5$ | $-3.2$ | $1.8$ | $1.98$ | $0.02$ | 0.05 | $0.01$
UVO 0512$-$08 | $11.0$ | 3.3 | 9.46 | 0.20 | 8.24 | 0.07 | 0.44 | 0.03 | $248.1$ | $2.5$ | $-21.0$ | $2.9$ | $-25.2$ | $1.6$ | $2.17$ | $0.03$ | 0.07 | $0.02$
HE 1238$-$1745 | $-7.9$ | 2.8 | 9.18 | 0.15 | 7.19 | 0.12 | 0.96 | 0.07 | $240.2$ | $2.8$ | $39.1$ | $3.1$ | $15.6$ | $2.1$ | $1.97$ | $0.03$ | 0.12 | $0.01$
PG 1559+048† | $-26.7$ | 0.9 | 8.15 | 0.06 | 6.22 | 0.12 | 0.54 | 0.03 | $217.0$ | $2.3$ | $27.9$ | $1.6$ | $18.1$ | $1.3$ | $1.75$ | $0.02$ | 0.13 | $0.01$
CPD $-$20 1123 | $-6.3$ | 1.2 | 9.71 | 0.12 | 7.54 | 0.09 | 0.17 | 0.01 | $238.9$ | $2.2$ | $-41.4$ | $1.5$ | $8.4$ | $0.7$ | $2.10$ | $0.02$ | 0.13 | $0.01$
SB 705 | $4.0$ | 12.0 | 10.46 | 0.27 | 7.95 | 0.11 | 0.99 | 0.09 | $255.5$ | $3.8$ | $40.1$ | $2.5$ | $5.7$ | $11.4$ | $2.20$ | $0.03$ | 0.14 | $0.01$
JL 87 | $-6.1$ | 2.3 | 10.24 | 0.20 | 7.76 | 0.06 | 0.56 | 0.02 | $266.7$ | $2.5$ | $-27.6$ | $1.9$ | $5.7$ | $1.5$ | $2.17$ | $0.02$ | 0.14 | $0.01$
UVO 0825+15† | $56.4$ | 0.5 | 9.63 | 0.10 | 7.18 | 0.10 | 0.16 | 0.01 | $232.0$ | $2.1$ | $46.8$ | $1.3$ | $6.4$ | $0.8$ | $2.04$ | $0.02$ | 0.15 | $0.01$
PG 0229+064 | $7.6$ | 4.0 | 9.16 | 0.08 | 6.67 | 0.14 | 0.67 | 0.05 | $210.8$ | $2.6$ | $31.1$ | $3.0$ | $19.1$ | $3.1$ | $1.90$ | $0.02$ | 0.16 | $0.02$
HE 2357$-$3940 | $-18.4$ | 14.2 | 9.59 | 0.21 | 6.95 | 0.12 | 0.96 | 0.12 | $236.1$ | $2.6$ | $54.5$ | $5.1$ | $9.6$ | $13.4$ | $1.97$ | $0.03$ | 0.16 | $0.02$
TON 414 | $2.7$ | 0.5 | 10.08 | 0.12 | 6.75 | 0.16 | 1.44 | 0.13 | $207.8$ | $3.6$ | $-54.1$ | $3.0$ | $35.5$ | $1.8$ | $1.96$ | $0.03$ | 0.20 | $0.02$
HE 1310$-$2733 | $41.5$ | 1.9 | 9.12 | 0.09 | 5.95 | 0.12 | 0.94 | 0.05 | $221.4$ | $2.4$ | $-67.9$ | $2.7$ | $19.2$ | $1.4$ | $1.77$ | $0.03$ | 0.21 | $0.01$
FBS 1749+373† | $-73.6$ | 0.2 | 8.34 | 0.05 | 4.74 | 0.09 | 0.39 | 0.01 | $182.6$ | $2.1$ | $39.2$ | $1.3$ | $-2.5$ | $0.8$ | $1.51$ | $0.02$ | 0.28 | $0.01$
HE 1136$-$2504 | $59.4$ | 9.3 | 8.40 | 0.05 | 4.63 | 0.33 | 0.68 | 0.04 | $176.0$ | $7.8$ | $-30.4$ | $1.6$ | $5.6$ | $5.5$ | $1.48$ | $0.07$ | 0.29 | $0.04$
TYC 3519-907-1 | $-62.7$ | 0.2 | 9.30 | 0.08 | 5.12 | 0.09 | 0.30 | 0.01 | $195.5$ | $2.1$ | $73.5$ | $2.2$ | $2.7$ | $0.9$ | $1.66$ | $0.02$ | 0.29 | $0.01$
PG 0240+046 | $63.4$ | 2.0 | 10.57 | 0.11 | 5.36 | 0.13 | 0.57 | 0.03 | $196.9$ | $3.1$ | $93.4$ | $2.8$ | $0.6$ | $2.1$ | $1.78$ | $0.03$ | 0.33 | $0.02$
HZ 44† | $-12.7$ | 0.4 | 9.30 | 0.07 | 4.48 | 0.11 | 0.41 | 0.02 | $177.3$ | $2.7$ | $76.8$ | $2.3$ | $10.2$ | $0.8$ | $1.52$ | $0.02$ | 0.35 | $0.02$
EC 22133$-$6446 | $-21.0$ | 10.0 | 9.30 | 0.20 | 3.58 | 0.26 | 0.44 | 0.05 | $159.1$ | $7.9$ | $101.3$ | $8.7$ | $-2.9$ | $7.2$ | $1.31$ | $0.07$ | 0.44 | $0.04$
EC 22536$-$5304† | $-3.3$ | 5.0 | 8.21 | 0.05 | 2.51 | 0.13 | 1.50 | 0.12 | $113.2$ | $4.2$ | $-26.4$ | $2.8$ | $58.3$ | $4.3$ | $0.93$ | $0.04$ | 0.53 | $0.02$
Feige 46† | $90.0$ | 4.0 | 9.64 | 0.09 | 1.13 | 0.12 | 0.68 | 0.04 | $63.5$ | $5.2$ | $115.5$ | $3.7$ | $13.8$ | $4.4$ | $0.55$ | $0.04$ | 0.79 | $0.03$
LS IV$-$14$°$116† | $-154.0$ | 1.0 | 8.15 | 0.05 | 0.66 | 0.14 | 0.24 | 0.02 | $-42.5$ | $6.8$ | $21.2$ | $2.7$ | $0.1$ | $2.9$ | $-0.35$ | $0.06$ | 0.85 | $0.03$

##  Appendix B Full spectral comparisons

This section presents the full spectral comparison between the observed
spectra of EC 22536$-$5304 and our final synthetic spectra. We show the co-
added 2019 HRS spectra and two examples for the UVES spectra. The 2019 HRS
spectra were shifted to a common radial velocity for the sdOB component before
they were co-added. Lines that originate from the sdF component are therefore
very slightly broadened in this spectrum. The observations were normalised to
match the continuum levels of our synthetic spectra. Telluric lines in the red
spectra were removed using the grid of transmission spectra provided by
Moehler et al. (2014). The strongest metal lines for the sdOB are labelled on
top, while lines of the sdF are labelled at the bottom. The combined model is
shown in red, while the contributions of the sdOB and sdF components are shown
in blue and dark red, respectively.

Figure 9: HRS spectrum of EC 22536$-$5304 (grey) and the combined (red) and
individual models. Figure 10: Blue HRS spectrum of EC 22536$-$5304 (grey) and
the combined (red) and individual models. Figure 11: Blue HRS spectrum of EC
22536$-$5304 (grey) and the combined (red) and individual models. Figure 12:
Red HRS spectrum of EC 22536$-$5304 (grey) and the combined (red) and
individual models. Figure 13: Red HRS spectrum of EC 22536$-$5304 (grey) and
the combined (red) and individual models. Figure 14: Blue UVES spectrum of EC
22536$-$5304 (grey) and the combined (red) and individual models. Figure 15:
Blue UVES spectrum of EC 22536$-$5304 (grey) and the combined (red) and
individual models. Figure 16: Blue UVES spectrum of EC 22536$-$5304 (grey) and
the combined (red) and individual models. Figure 17: Red UVES spectrum of EC
22536$-$5304 (grey) and the combined (red) and individual models. Figure 18:
Red UVES spectrum of EC 22536$-$5304 (grey) and the combined (red) and
individual models.