# The distribution, kinematics and luminosities of extreme helium stars as
probes of their origin and evolution

A. Philip Monai1,2, P. Martin1,3, C. S. Jeffery1
1Armagh Observatory and Planetarium, College Hill, Armagh, BT61 9DG, UK
2School of Mathematics and Physics, Queen’s University Belfast, Belfast, BT7
1NN, UK
3School of Physics, Trinity College Dublin, College Green, Dublin 2, Ireland
email<EMAIL_ADDRESS>
(Last updated 2023 December 1 ; in original form 2023 September 29)

###### Abstract

Hydrogen deficient stars include the cool R CrB variable (RCBs) and hydrogen-
deficient carbon (HdCs) giants through extreme helium stars (EHes) to the very
hot helium-rich subdwarfs (He-sdO and O(He) stars) and white dwarfs. With
surfaces rich in helium, nitrogen and carbon, their origins have been
identified with the merger of two white dwarfs. Using Gaia to focus on the
EHes, we aim to identify progenitor populations and test the evolution models.
Gaia DR3 measurements and ground-based radial velocities have been used to
compute Galactic orbits using `galpy`. Each orbit has been classified by
population; EHe stars are found in all of the thin disk, thick disk, halo and
bulge, as are RCB, HdC and He-sdO stars. Spectral energy distributions were
constructed for all EHes, to provide angular diameters, and hence radii and
luminosities. The EHes fall into two luminosity groups divided at $L\approx
2500\,{\rm L_{\odot}}$. This supports theory for the origin of EHes, and is
the strongest confirmation so far in terms of luminosity. The lower luminosity
EHes correspond well with the post-merger evolution of a double helium white
dwarf binary. Likewise, the higher luminosity EHes match the post-merger
evolution of a carbon/oxygen plus helium white dwarf binary. In terms of
parent populations, current models predict that double white dwarf mergers
should occur in all Galactic populations, but favour mergers arising from
recent star formation (i.e. thin disk), whereas the statistics favour an older
epoch (i.e. thick disk).

###### keywords:

parallaxes – proper motions – stars: AGB and post-AGB – stars: chemically
peculiar – stars: fundamental parameters – stars: kinematics and dynamics

††pubyear: 2023††pagerange: The distribution, kinematics and luminosities of
extreme helium stars as probes of their origin and evolution–A

##  1 Introduction

Extreme helium stars (EHes) are low-mass stars of spectral types A and B
(Jeffery, 1996). Their low surface gravities indicate high luminosity-to-mass
ratios. Helium dominates the surface composition, with hydrogen contributing
less than one part per thousand (ppt, by number) and carbon between 3 and 30
ppt. Nitrogen, oxygen and other products of nucleosynthesis are also enhanced
(Jeffery et al., 2011). Their radial-velocities and Galactic distribution
suggest an origin in the Galactic bulge (Jeffery et al., 1987). R CrB (RCB)
and O(He) stars have similar surface chemistries and luminosities but lower
and higher surface temperatures respectively (Clayton, 1996; Reindl et al.,
2014). The RCB stars represent the most active members of a larger class of
cool hydrogen-deficient carbon-rich giants (HdC stars) (Crawford et al.,
2023). The surface properties of these three groups are best explained by
evolution following the merger of a helium white dwarf with a carbon-oxygen
white dwarf (Webbink, 1984; Saio & Jeffery, 2002), with their ultimate fate to
become a hot hydrogen-deficient white dwarf. Naively speaking, an origin in
the (old) Galactic bulge should be entirely consistent with the long delay
time associated with the orbital decay of a double white dwarf binary via
gravitational wave radiation.

Several EHes have higher surface gravities than the majority and are better
understood in terms of evolution following the merger of two helium white
dwarfs (Saio & Jeffery, 2000). Such stars will evolve toward the helium main-
sequence where they are observed as helium-rich sdO stars (He-sdOs) (Zhang &
Jeffery, 2012a) associated with the Galactic thick disk (Martin & Jeffery,
2017), and considered younger than the Galactic bulge.

Binary-star population synthesis (BSPS) calculations suggest other pictures.
Zhang et al. (2014) find that double helium white dwarf mergers should come
predominantly from star formation more than 4 Gyr ago and carbon-oxygen +
helium white dwarfs come from star formation between 0.5 and 2 Gyr ago. Yu &
Jeffery (2010, 2011) find that the majority of mergers in the present epoch
should arise from star formation more than 4 Gyr ago. Since actual orbital
decay times depend on the white dwarf masses and initial separations, a
sufficiently large sample of binaries from a given star-formation epoch that
evolve to become double white dwarfs will continue to produce short-lived
exotic stars long after their pre-white dwarf evolution is complete. Hence -
studies of a present day sample of such stars must in fact derive from a long
period of Galactic star formation and reflect a substantial range of actual
ages.

Our main question (1) concerns the progenitor population(s) of EHes; that is,
what are their distributions in position and age? Secondary questions concern
(2) the relationship between EHe stars, HdC and RCB stars, O(He) stars and He-
sdOs, and (3) the validity of the evolution models in terms of EHe masses and
luminosities. Owing to their considerable heliocentric distances (1 – 8 kpc),
reliable answers to (1) have only become accessible since the 3rd release of
data from the Gaia project (Gaia Collaboration et al., 2016, 2023). In
addition, answers to (2) and (3) require additional data for effective
temperatures over a wide range of spectral types.

This paper combines the Gaia positional and proper motion data and ground-
based radial velocity data (§ 2) to obtain full 6-space positions (§,3) and
population classifications (§ 4). These data are supplemented with published
photometry to build complete spectral energy distributions and hence angular
radii and luminosities (§ 5). Masses are inferred from the measured surface
gravities, where these are available. We present this analysis in detail for
the EHes. We have also carried out this analysis for comparison samples of
related objects including RCB, and helium-rich subdwarfs. Since similar
analyses have been carried out in part or in whole elsewhere (Geier, 2020;
Culpan et al., 2022; Tisserand et al., 2022, etc.), they are only discussed
here in summary form.

Table 1: Astrometric data for EHe stars from Gaia including radial velocities, corrected parallax and the computed distance sorted by right ascension. Star | $\alpha$ | $\delta$ | $\mu_{\alpha}$ | $\mu_{\delta}$ | $v$ | $\pi$ | Distance
---|---|---|---|---|---|---|---
| deg | mas yr-1 |  $\mbox{km}\,\mbox{s}^{-1}$ | mas | kpc
BD +37 442 | 29.64 | 38.57 | -10.49$\pm$ | 0.06 | -7.27$\pm$ | 0.07 | -99.4$\pm$ | 25.01 | 0.97$\pm$ | 0.06 | 1.04 | ${}^{+0.06}_{-0.07}$
LSS 99 | 103.69 | -10.81 | 0.09$\pm$ | 0.01 | -0.59$\pm$ | 0.01 | 109.0$\pm$ | 3.02 | 0.17$\pm$ | 0.01 | 5.73 | ${}^{+0.38}_{-0.44}$
BD +37 1977 | 141.11 | 36.71 | 10.86$\pm$ | 0.05 | -11.77$\pm$ | 0.05 | -80.9$\pm$ | 9.91 | 0.64$\pm$ | 0.07 | 1.60 | ${}^{+0.16}_{-0.20}$
BD +10 2179 | 159.73 | 10.06 | -10.37$\pm$ | 0.06 | -4.86$\pm$ | 0.04 | 155.2$\pm$ | 2.82 | 0.52$\pm$ | 0.05 | 1.99 | ${}^{+0.19}_{-0.24}$
BX Cir | 210.40 | -66.17 | -8.34$\pm$ | 0.01 | 2.22$\pm$ | 0.02 | -83.0$\pm$ | 2.03 | 0.31$\pm$ | 0.02 | 3.29 | ${}^{+0.21}_{-0.23}$
HD 124448 | 213.74 | -46.29 | -6.54$\pm$ | 0.04 | -0.05$\pm$ | 0.03 | -65.0$\pm$ | 3.02 | 0.65$\pm$ | 0.03 | 1.56 | ${}^{+0.07}_{-0.08}$
PG 1415+492 | 214.26 | 48.96 | 1.1$\pm$ | 0.03 | -6.55$\pm$ | 0.03 | 54.0$\pm$ | 1.04 | 0.37$\pm$ | 0.03 | 2.76 | ${}^{+0.21}_{-0.25}$
CoD –48 10153 | 234.75 | -48.60 | -6.07$\pm$ | 0.02 | -6.4$\pm$ | 0.02 | -4.5$\pm$ | 2.52 | 0.14$\pm$ | 0.02 | 6.88 | ${}^{+0.81}_{-1.03}$
V2205 Oph | 247.15 | -9.33 | -2.27$\pm$ | 0.03 | 3.06$\pm$ | 0.02 | -69.3$\pm$ | 1.02 | 0.14$\pm$ | 0.03 | 6.85 | ${}^{+0.95}_{-1.26}$
V652 Her | 252.02 | 13.26 | -4.24$\pm$ | 0.04 | 3.76$\pm$ | 0.03 | 2.0$\pm$ | 0.55 | 0.66$\pm$ | 0.05 | 1.55 | ${}^{+0.11}_{-0.13}$
V2076 Oph | 265.46 | -17.90 | -6.25$\pm$ | 0.03 | 2.56$\pm$ | 0.02 | 76.8$\pm$ | 2.62 | 0.56$\pm$ | 0.03 | 1.79 | ${}^{+0.09}_{-0.10}$
CoD –46 11775 | 265.64 | -46.98 | -3.79$\pm$ | 0.03 | -0.95$\pm$ | 0.02 | -90.7$\pm$ | 9.32 | 0.21$\pm$ | 0.03 | 4.91 | ${}^{+0.62}_{-0.81}$
LSS 4357 | 266.11 | -19.63 | -3.51$\pm$ | 0.02 | 1.55$\pm$ | 0.01 | -99.0$\pm$ | 10.02 | 0.15$\pm$ | 0.02 | 6.77 | ${}^{+0.70}_{-0.87}$
V2244 Oph | 267.86 | -1.72 | -0.13$\pm$ | 0.02 | -8.34$\pm$ | 0.01 | -8.3$\pm$ | 2.96 | 0.19$\pm$ | 0.02 | 5.29 | ${}^{+0.43}_{-0.51}$
NO Ser | 270.98 | -1.01 | 0.3$\pm$ | 0.02 | -2.02$\pm$ | 0.02 | -21.1$\pm$ | 4.62 | 0.37$\pm$ | 0.02 | 2.75 | ${}^{+0.12}_{-0.13}$
LS IV+6 2 | 271.73 | 6.37 | -3.01$\pm$ | 0.03 | -8.84$\pm$ | 0.03 | -24.0$\pm$ | 4.02 | 0.63$\pm$ | 0.03 | 1.61 | ${}^{+0.07}_{-0.08}$
PV Tel | 275.81 | -56.63 | -1.24$\pm$ | 0.02 | -7.81$\pm$ | 0.02 | -170.9$\pm$ | 2.32 | 0.27$\pm$ | 0.02 | 3.67 | ${}^{+0.27}_{-0.32}$
LSS 5121 | 280.82 | -18.52 | -2.0$\pm$ | 0.02 | 0.52$\pm$ | 0.02 | -62.0$\pm$ | 6.02 | 0.21$\pm$ | 0.02 | 4.89 | ${}^{+0.38}_{-0.45}$
GALEX J184559.8–413827 | 281.50 | -41.64 | 0.24$\pm$ | 0.04 | 0.1$\pm$ | 0.03 | -57.6$\pm$ | 6.17 | 0.18$\pm$ | 0.04 | 5.56 | ${}^{+0.90}_{-1.27}$
LS IV –14 109 | 284.91 | -14.44 | -0.36$\pm$ | 0.02 | -0.43$\pm$ | 0.02 | -7.3$\pm$ | 2.78 | 0.25$\pm$ | 0.02 | 3.96 | ${}^{+0.29}_{-0.34}$
GALEX J191049.5–441713 | 287.71 | -44.29 | -2.7$\pm$ | 0.05 | -2.93$\pm$ | 0.04 | 1.0$\pm$ | 3.09 | 0.70$\pm$ | 0.05 | 1.45 | ${}^{+0.09}_{-0.11}$
V1920 Cyg | 296.32 | 33.97 | 0.11$\pm$ | 0.02 | -6.24$\pm$ | 0.02 | -89.9$\pm$ | 1.92 | 0.23$\pm$ | 0.02 | 4.39 | ${}^{+0.29}_{-0.33}$
EC 19529–4430 | 299.13 | -44.37 | -6.8$\pm$ | 0.03 | -13.22$\pm$ | 0.03 | 5.0$\pm$ | 3.09 | 0.21$\pm$ | 0.04 | 4.77 | ${}^{+0.71}_{-0.98}$
EC 20111–6902 | 304.04 | -68.89 | 2.65$\pm$ | 0.06 | -1.72$\pm$ | 0.08 | -81.0$\pm$ | 3.09 | 0.19$\pm$ | 0.08 | 5.08 | ${}^{+1.27}_{-1.96}$
EC 20236–5703 | 306.90 | -56.90 | 1.94$\pm$ | 0.04 | -13.34$\pm$ | 0.04 | -74.0$\pm$ | 3.09 | 0.26$\pm$ | 0.04 | 3.94 | ${}^{+0.50}_{-0.67}$
BPS CS 22940–0009 | 307.58 | -59.84 | 2.53$\pm$ | 0.03 | -10.79$\pm$ | 0.03 | 32.7$\pm$ | 2.04 | 0.47$\pm$ | 0.03 | 2.16 | ${}^{+0.15}_{-0.17}$
FQ Aqr | 312.84 | 2.31 | -0.62$\pm$ | 0.02 | -6.18$\pm$ | 0.02 | 23.7$\pm$ | 1.46 | 0.21$\pm$ | 0.02 | 4.84 | ${}^{+0.39}_{-0.46}$
1.de Bruijne & Eilers (2012), 2.Jeffery et al. (1987), 3.Kilkenny et al.
(1999), 4.Martin et al. (2017), 5.Jeffery et al. (2015), 6.Jeffery et al.
(2001a), 7.Kawka et al. (2015), 8.Lawson et al. (1993), 9.Jeffery et al.
(2021)

##  2 Observations

The complete dataset for analysis contains the full 6-space position for every
known member of the different classes of hydrogen-deficient stars together
with spectroscopic and photometric measurements of effective temperature,
surface gravity and interstellar extinction. The EHe sample was based on
compilations by Jeffery et al. (1996); Clayton (1996) and Martin (2019). 111DY
Cen has been excluded from the EHe sample on the basis of its high hydrogen
content and very rapid evolution (Jeffery et al., 2020). HD 144941 has been
excluded as possibly the most extreme member of the magnetic massive helium-
strong stars (Przybilla et al., 2021). In addition, we have included new EHes
discovered as part of the SALT survey of chemically peculiar subdwarfs
(Jeffery et al., 2021). The primary criteria for inclusion are that each star
should be included in Gaia Data Release 3 (DR3) and should have a known radial
velocity.

The majority of EHe radial velocities come from Jeffery et al. (1987) and
Jeffery et al. (2021). The former found no significant variability amongst all
EHes surveyed. With no evidence that any are binaries, Jeffery et al. (1987)
argued that all must have been binaries at some time in the past. Where repeat
observations have been obtained, none of the stars classified by Jeffery et
al. (2021) and identified here as EHes have yet been found to be binaries. A
number are known to pulsate with irregular small-amplitude radial-velocity
variations (Walker & Hill, 1985; Lawson et al., 1993; Jeffery et al., 2001a),
for which we adopt the mean velocity, or with regular large-amplitude radial-
velocity variations (Lynas-Gray et al., 1984; Kilkenny et al., 1999), for
which the system velocity is known precisely. We take the space velocities to
be secure to within the errors shown. For the EHes, the typical error is
$\sim\pm 3\,\mbox{$\mbox{km}\,\mbox{s}^{-1}$}$ and for the secondary sample,
the typical error is $\sim\pm 17\,\mbox{$\mbox{km}\,\mbox{s}^{-1}$}$.

For the EHe sample, an additional criterion was the availability of
measurements for effective temperatures ($T_{\rm eff}$) and surface gravities
($\log g$). These measurements along with the extinction coefficients
($E_{\rm(B-V)}$) are presented in section 5. Table 1 shows the Gaia data
(position, proper motion and parallax) and the radial velocity for the 27
stars in the EHe sample.

We studied the kinematics and the Galactic orbits of these stars and derived
the angular diameters and luminosities from their spectral energy
distributions. To compare this sample with the other groups mentioned above,
we compiled a secondary sample containing HdC, RCB, He-sdO, He-sdOB, and He-
sdB stars based on Clayton (2012); Reindl et al. (2014); Geier (2020);
Tisserand et al. (2020); Culpan et al. (2022); Tisserand et al. (2022) and
Crawford et al. (2023). A list of these stars is provided in Appendix A.

Figure 1: Distribution of sample in the Galactic $X-Z$ plane. The red stars
denote the primary sample and the grey dots denote the secondary sample. The
position of the Sun is denoted by a filled cyan pentagon. The dashed ellipse
shows the estimates of the inner bulge (R $\sim$ 1.5 kpc) and the dashed
rectangle shows the estimates of the bar (X = $\pm$4 kpc, Y = $\pm$ 1.5 kpc, Z
= $\pm$ 1.5 kpc) (Bland-Hawthorn & Gerhard, 2016).

Figure 2: galpy orbits for 6 representative EHe stars computed for 3 Gyrs from
their current positions. The top panels show motion in the $\rm X-Y$ plane,
the bottom panels show motion in the $\rm R-Z$ plane, with the Galactic centre
being at the origin. The panels illustrate thin-disk (HD 124448), thick disk
(BX Cir), halo (BD +10 2179), bulge (LSS 4357), halo (EC 20236–5703), and halo
(V2205 Oph) orbits. Figure 3: Colour magnitude diagram of the whole sample
obtained from the Gaia magnitude and colours as given in S. 3.3.

##  3 Analysis

###  3.1 Distances

Gaia DR3 parallaxes have been used to obtain distances. The zero points of the
parallax measurements have been corrected as described by Lindegren et al.
(2021) and the corrected parallax is given in Table 1.

Inverting a parallax to give a distance is only appropriate when measurement
errors are negligible. As parallax measurements always contain significant
errors, determining distance from parallax becomes an inference problem. Small
absolute errors can translate into large errors in distance (Bailer-Jones,
2015; Luri et al., 2018; Bailer-Jones et al., 2021). Once the fractional
parallax error $\sigma/\pi\geq 0.2$, a simple inversion becomes noisy and
gives an incorrect error estimate. This can be mitigated by the use of a
properly normalised prior. Here an Exponentially Decreasing Space Density
Prior is adopted, with one free parameter, the length scale, fixed at $1.35$
kpc (Luri et al., 2018). Even though a Bayesian approach can give distance
estimates from even a negative parallax measurement, the prior will always
dominate when the fractional error in parallax is high. Three stars in the
primary sample have fractional parallax error $\sigma/\pi\geq 0.2$: EC
20111–6902 (0.42), GALEX J184559.8–413827 (0.22) and V2205 Oph (0.21). We note
that although these errors are significant, they are substantially improved
over Gaia DR2. In particular, V2205 Oph had $\sigma/\pi\geq 0.5$ in Gaia DR2.

Distance measurements obtained for the stars in the primary sample are
reported in Table 1, where the errors correspond to the 68.27% confidence
intervals.

###  3.2 Galactic and orbital parameters

Figure 1 shows the positions of the stars projected onto the Galactic $X-Z$
plane, where $Z$ is the distance from the Galactic plane, and $X$ from the
Galactic Centre (GC). We define the inner disk $R<7$ kpc, the Solar ring
$7<R<11$ kpc and the outer disk $R>11$ kpc from the GC (Bland-Hawthorn &
Gerhard, 2016). Estimates of the extent of the bulge and/or bar are also
shown. Most of the stars in our sample lie between the Sun and the GC. Seven
EHe stars are situated within or close to the bulge or bar. This highlights
the capabilities of Gaia in separating out sources that are close to the
Galactic bulge. This figure also highlights that our sample is subject to
Malmquist bias, or the preferential detection at large distances of
intrinsically brighter objects. The question this observation raises is
whether this constraint causes any bias in our understanding of group
kinematics and further inferences.

Using the observed values of right ascension ($\alpha$), declination
($\delta$), distance, proper motion ($\mu_{\alpha}$ and $\mu_{\delta}$) and
radial velocity ($v$), the Galactic velocity components were calculated
following the method outlined in Randall et al. (2015). The left-handed system
for the velocity components is used here, where $U$ is the Galactic radial
velocity, positive towards the Galactic Centre, $V$ is the Galactic rotational
velocity in the direction of the Galactic rotation and $W$ is the component
positive towards the North Galactic Pole. This calculation assumes the
distance of the Sun from the Galactic Centre to be $8.25\pm 0.33$ kpc (GRAVITY
Collaboration et al., 2021), its motion relative to the LSR to have components
$(v_{x},v_{y},v_{z})=(9.5,17.3,8.56)$ km $\rm s^{-1}$ and the velocity of the
LSR to be $V_{\rm LSR}=233.4\pm 1.5$ km $\rm s^{-1}$ (Drimmel & Poggio, 2018;
Reid & Brunthaler, 2020; GRAVITY Collaboration et al., 2021).

Orbits for individual stars (Fig. 2) have been calculated using
`galpy`222http://github.com/jobovy/galpy, a python package for Galactic-
dynamic calculations (Bovy, 2015). The orbits were computed using the
potential MWPotential 2014; this model is fit to dynamical data of the Milky
Way. Although this is not the best possible current model, it was chosen as it
gives a realistic model of the Milky Way’s gravitational potential that is
simple and easy to use. It consists of a bulge modelled as a power-law density
profile that is exponentially cut off with a power-law exponent of –1.8 and a
cut-off radius of 1.9 kpc, a Miyamoto–Nagai Potential disc (Miyamoto & Nagai,
1975) and a dark-matter halo described by a Navarro–Frenk–White potential
(Navarro et al., 1996). These orbits when integrated over 3 Gyrs give values
for the maximum distance from the GC (apocentre $R_{\rm a}$), minimum distance
to the GC (pericentre $R_{\rm p})$, maximum vertical amplitude ($Z_{\rm max}$)
and the z-component of the angular momentum ($J_{z}$). The quantities $R_{\rm
a}$ and $R_{\rm p}$ are obtained over a revolution of $2\pi$ radians, measured
on the Galactic plane. From these distances, the orbital eccentricity can be
computed as

$e=\frac{R_{\rm a}-R_{\rm p}}{R_{\rm a}+R_{\rm p}}.$ (1)

Using `galpy`, 100 orbits were computed for each star, with starting values
distributed randomly over the range of errors associated with each one so as
to obtain a sample of likely orbits. From this sample, the orbit with the
highest likelihood (mode) was selected with the rest being used to compute the
statistical errors (standard deviation) on the orbital elements. These
quantities are shown in Table 2, along with the stars’ Galactic velocities.

###  3.3 Colour-magnitude diagram

When combined with the extinction coefficient ($E_{\rm B-V}$), Gaia distances
and colours provide us with absolute magnitudes $M_{\rm V}$. These can be
defined in terms of the apparent Gaia magnitude $G$ and colours $G_{\rm
BP}-G_{\rm RP}$ using the Johnson-Cousins relation from Riello et al. (2021):

$V=G+0.02704-0.01424(G_{\rm BP}-G_{\rm RP})+0.2156(G_{\rm BP}-G_{\rm
RP})^{2}\\\ -0.01426(G_{\rm BP}-G_{\rm RP})^{3},$ (2) $M_{\rm
V}=V-5(\log_{10}d-1)-3.1E_{\rm B-V},$ (3)

where $V$ is the apparent visual magnitude and $d$ is the distance in parsecs.

Since Eqn (2) has been derived for stars with hydrogen-rich atmospheres, we
compared the transformed V magnitude with V magnitudes from SIMBAD. The latter
are, on average, $\approx 0.02$ mag larger for $G_{\rm BP}-G_{\rm RP}>0$
decreasing to $\approx 0.05$ mag smaller for $G_{\rm BP}-G_{\rm
RP}\approx-0.4$, with a mean scatter of $\approx\pm 0.02$ mag (1$\sigma$). The
small trend is consistent with a reduced contribution of the Balmer series to
the EHe star colours. The transformed EHe V magnitudes may be improved by
applying the correction

$\delta=0.00759+0.11452(G_{\rm BP}-G_{\rm RP})-0.11589(G_{\rm BP}-G_{\rm
RP})^{2}.$ (4)

The colour-magnitude diagram of the whole sample plotted from the Gaia
colours333Author’s note in proof: Fig. 3 is based on mean Gaia magnitudes. For
RCB and HdC stars observed during a decline, mean Gaia magnitudes do not
reflect the luminosity at maximum light and here applies to RCB and HdC stars
with $M_{\rm V}>-3$. is shown in Fig. 3. This shows a progression from the
cool HdC stars and RCB stars to the hotter EHe and He-SdO stars. There is an
overlap between the coolest EHe stars and the hottest HdCs.

Table 2: Orbital parameters and Galactic velocities of Extreme Helium stars sorted as in Table 1. The last column shows the population classification where TH = thin disk, TK = thick disk, H = halo and B = bulge. $f=p({\rm thick})/p({\rm thin})$ shows the likelihood of a star belonging to the thick or thin disk. The stars for which the orbits were classified by inspection have been marked with a *. Star | $U$ | $V$ | $W$ | $J_{z}$ | $e$ | Ra | Rp | Zmax | $\log(f)$ | pop
---|---|---|---|---|---|---|---|---|---|---
|  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ | kpc $\mbox{km}\,\mbox{s}^{-1}$ |  | kpc | kpc | kpc |  |
BD +37 442 | $-98.1$ | ${}^{+10.5}_{-10.6}$ | $210.1$ | ${}^{+8.5}_{-8.4}$ | $0.9$ | ${}^{+5.7}_{-5.6}$ |  $1971.9$$\pm$ | $75.3$ |  $0.33$$\pm$ | $0.04$ |  $12.03$$\pm$ | $0.19$ |  $6.05$$\pm$ | $0.44$ |  $0.47$$\pm$ | $0.03$ | $-0.82$ | TH
LSS 99 | $10.0$ | ${}^{+1.6}_{-1.8}$ | $175.3$ | ${}^{+0.8}_{-0.8}$ | $-5.0$ | ${}^{+0.2}_{-0.2}$ |  $2352.5$$\pm$ | $31.3$ |  $0.25$$\pm$ | $0.00$ |  $13.19$$\pm$ | $0.20$ |  $7.86$$\pm$ | $0.13$ |  $0.42$$\pm$ | $0.02$ | $-0.85$ | TH
BD +37 1977 | $-20.4$ | ${}^{+4.3}_{-4.5}$ | $114.4$ | ${}^{+4.3}_{-5.1}$ | $-20.8$ | ${}^{+4.3}_{-4.4}$ |  $1646.3$$\pm$ | $44.1$ |  $0.48$$\pm$ | $0.02$ |  $12.89$$\pm$ | $0.28$ |  $4.52$$\pm$ | $0.18$ |  $1.68$$\pm$ | $0.20$ | - | H
BD +10 $2179^{*}$ | $-79.6$ | ${}^{+3.2}_{-4.4}$ | $189.9$ | ${}^{+0.7}_{-0.7}$ | $110.2$ | ${}^{+1.3}_{-1.6}$ |  $1161.0$$\pm$ | $26.1$ |  $0.53$$\pm$ | $0.02$ |  $10.59$$\pm$ | $0.15$ |  $3.26$$\pm$ | $0.17$ |  $3.01$$\pm$ | $0.06$ | - | H
BX Cir∗ | $-130.2$ | ${}^{+3.4}_{-3.4}$ | $280.7$ | ${}^{+2.1}_{-1.8}$ | $114.7$ | ${}^{+1.9}_{-1.9}$ |  $1827.1$$\pm$ | $20.3$ |  $0.17$$\pm$ | $0.01$ |  $9.42$$\pm$ | $0.14$ |  $6.65$$\pm$ | $0.03$ |  $1.66$$\pm$ | $0.06$ | $0.91$ | TK
HD 124448 | $-34.9$ | ${}^{+1.5}_{-1.4}$ | $292.6$ | ${}^{+1.2}_{-1.2}$ | $22.0$ | ${}^{+0.6}_{-0.6}$ |  $2003.4$$\pm$ | $16.7$ |  $0.16$$\pm$ | $0.01$ |  $9.89$$\pm$ | $0.17$ |  $7.14$$\pm$ | $0.03$ |  $0.51$$\pm$ | $0.01$ | $-0.8$ | TH
PG 1415+492 | $-27.1$ | ${}^{+0.6}_{-0.8}$ | $230.3$ | ${}^{+0.9}_{-1.2}$ | $75.4$ | ${}^{+0.7}_{-0.7}$ |  $2094.5$$\pm$ | $7.8$ |  $0.16$$\pm$ | $0.00$ |  $11.90$$\pm$ | $0.08$ |  $8.67$$\pm$ | $0.03$ |  $4.60$$\pm$ | $0.19$ | $13.57$ | TK
CoD –48 10153 | $-140.9$ | ${}^{+3.9}_{-0.9}$ | $0.9$ | ${}^{+11.8}_{-15.9}$ | $7.5$ | ${}^{+0.5}_{-0.5}$ |  $494.0$$\pm$ | $19.9$ |  $0.51$$\pm$ | $0.02$ |  $4.59$$\pm$ | $0.03$ |  $1.50$$\pm$ | $0.09$ |  $0.85$$\pm$ | $0.09$ | - | H
V2205 Oph | $111.3$ | ${}^{+20.1}_{-10.8}$ | $299.7$ | ${}^{+6.6}_{-1.1}$ | $103.5$ | ${}^{+5.2}_{-6.9}$ |  $563.8$$\pm$ | $172.2$ |  $0.57$$\pm$ | $0.07$ |  $9.39$$\pm$ | $0.53$ |  $2.59$$\pm$ | $0.36$ |  $6.87$$\pm$ | $1.47$ | - | H
V652 Her | $4.8$ | ${}^{+0.5}_{-0.6}$ | $269.4$ | ${}^{+0.3}_{-0.5}$ | $50.4$ | ${}^{+0.8}_{-1.1}$ |  $1847.5$$\pm$ | $12.8$ |  $0.14$$\pm$ | $0.01$ |  $9.05$$\pm$ | $0.02$ |  $6.87$$\pm$ | $0.08$ |  $1.31$$\pm$ | $0.06$ | $0.21$ | TK
V2076 Oph | $34.3$ | ${}^{+1.6}_{-1.5}$ | $251.8$ | ${}^{+0.4}_{-0.4}$ | $66.2$ | ${}^{+1.0}_{-1.1}$ |  $1525.8$$\pm$ | $16.4$ |  $0.24$$\pm$ | $0.01$ |  $8.25$$\pm$ | $0.07$ |  $5.04$$\pm$ | $0.06$ |  $0.86$$\pm$ | $0.03$ | $-0.47$ | TH
CoD –46 11775 | $-58.2$ | ${}^{+8.6}_{-9.6}$ | $235.2$ | ${}^{+5.0}_{-4.2}$ | $98.8$ | ${}^{+2.7}_{-4.0}$ |  $910.6$$\pm$ | $98.3$ |  $0.02$$\pm$ | $0.02$ |  $4.20$$\pm$ | $0.36$ |  $4.00$$\pm$ | $0.34$ |  $1.17$$\pm$ | $0.06$ | - | B
LSS 4357 | $135.1$ | ${}^{+18.4}_{-14.9}$ | $234.4$ | ${}^{+13.3}_{-6.0}$ | $142.6$ | ${}^{+4.3}_{-5.6}$ |  $297.6$$\pm$ | $115.8$ |  $0.61$$\pm$ | $0.10$ |  $3.98$$\pm$ | $0.22$ |  $0.98$$\pm$ | $0.35$ |  $1.06$$\pm$ | $0.27$ | - | B
V2244 Oph | $-39.3$ | ${}^{+1.2}_{-1.4}$ | $128.4$ | ${}^{+1.6}_{-2.2}$ | $-85.8$ | ${}^{+2.2}_{-2.7}$ |  $545.7$$\pm$ | $31.7$ |  $0.40$$\pm$ | $0.03$ |  $4.73$$\pm$ | $0.05$ |  $2.04$$\pm$ | $0.13$ |  $1.71$$\pm$ | $0.08$ | - | B
NO Ser | $45.6$ | ${}^{+2.3}_{-2.3}$ | $217.2$ | ${}^{+1.8}_{-1.7}$ | $-11.3$ | ${}^{+0.6}_{-0.6}$ |  $1362.2$$\pm$ | $19.7$ |  $0.15$$\pm$ | $0.01$ |  $6.51$$\pm$ | $0.05$ |  $4.85$$\pm$ | $0.10$ |  $0.55$$\pm$ | $0.02$ | $-0.77$ | TH
LS IV+6 2 | $-25.5$ | ${}^{+1.7}_{-1.8}$ | $195.1$ | ${}^{+1.5}_{-1.5}$ | $-1.6$ | ${}^{+0.5}_{-0.5}$ |  $1331.3$$\pm$ | $20.5$ |  $0.25$$\pm$ | $0.01$ |  $7.17$$\pm$ | $0.03$ |  $4.29$$\pm$ | $0.10$ |  $0.38$$\pm$ | $0.01$ | $-0.87$ | TH
PV Tel | $135.9$ | ${}^{+1.1}_{-1.0}$ | $236.4$ | ${}^{+1.2}_{-1.4}$ | $38.0$ | ${}^{+0.7}_{-0.8}$ |  $1256.8$$\pm$ | $40.2$ |  $0.40$$\pm$ | $0.00$ |  $8.94$$\pm$ | $0.27$ |  $3.84$$\pm$ | $0.09$ |  $2.16$$\pm$ | $0.04$ | $2.23$ | TK
LSS 5121 | $93.5$ | ${}^{+4.0}_{-4.3}$ | $223.2$ | ${}^{+2.3}_{-2.1}$ | $68.6$ | ${}^{+1.3}_{-1.5}$ |  $802.2$$\pm$ | $53.4$ |  $0.32$$\pm$ | $0.02$ |  $5.15$$\pm$ | $0.15$ |  $2.65$$\pm$ | $0.18$ |  $0.98$$\pm$ | $0.04$ | - | B
GALEX J184559.8–413827 | $1.9$ | ${}^{+8.3}_{-6.4}$ | $264.3$ | ${}^{+1.2}_{-1.1}$ | $19.7$ | ${}^{+1.4}_{-1.3}$ |  $847.1$$\pm$ | $155.5$ |  $0.22$$\pm$ | $0.05$ |  $5.28$$\pm$ | $0.26$ |  $3.35$$\pm$ | $0.54$ |  $2.12$$\pm$ | $0.34$ | $2.1$ | TK
LS IV –14 109 | $59.7$ | ${}^{+2.2}_{-2.7}$ | $233.6$ | ${}^{+1.1}_{-1.2}$ | $13.1$ | ${}^{+0.3}_{-0.3}$ |  $1160.5$$\pm$ | $39.4$ |  $0.17$$\pm$ | $0.01$ |  $5.78$$\pm$ | $0.09$ |  $4.08$$\pm$ | $0.17$ |  $0.64$$\pm$ | $0.03$ | $-0.69$ | TH
GALEX J191049.5–441713 | $-23.7$ | ${}^{+1.6}_{-1.6}$ | $228.7$ | ${}^{+0.5}_{-0.6}$ | $20.5$ | ${}^{+0.7}_{-0.7}$ |  $1617.5$$\pm$ | $17.4$ |  $0.09$$\pm$ | $0.01$ |  $7.26$$\pm$ | $0.05$ |  $6.11$$\pm$ | $0.09$ |  $0.58$$\pm$ | $0.02$ | $-0.74$ | TH
V1920 Cyg | $-0.9$ | ${}^{+0.5}_{-0.6}$ | $155.2$ | ${}^{+1.2}_{-1.2}$ | $-64.6$ | ${}^{+1.3}_{-1.5}$ |  $1271.5$$\pm$ | $15.0$ |  $0.33$$\pm$ | $0.01$ |  $7.99$$\pm$ | $0.03$ |  $4.01$$\pm$ | $0.09$ |  $1.48$$\pm$ | $0.10$ | $0.53$ | TK
EC 19529–4430 | $-61.3$ | ${}^{+1.5}_{-2.2}$ | $-61.1$ | ${}^{+13.0}_{-18.2}$ | $98.3$ | ${}^{+4.0}_{-5.4}$ |  $-314.5$$\pm$ | $117.4$ |  $0.64$$\pm$ | $0.15$ |  $5.20$$\pm$ | $0.29$ |  $1.13$$\pm$ | $0.55$ |  $2.99$$\pm$ | $0.22$ | - | H
EC 20111–6902 | $-40.8$ | ${}^{+11.9}_{-13.7}$ | $279.8$ | ${}^{+3.4}_{-2.1}$ | $8.0$ | ${}^{+3.3}_{-5.1}$ |  $1523.0$$\pm$ | $138.9$ |  $0.26$$\pm$ | $0.02$ |  $9.91$$\pm$ | $0.14$ |  $5.86$$\pm$ | $0.29$ |  $4.26$$\pm$ | $0.92$ | $11.47$ | TK
EC 20236–5703 | $127.7$ | ${}^{+4.6}_{-5.7}$ | $67.1$ | ${}^{+6.0}_{-9.1}$ | $36.2$ | ${}^{+1.1}_{-1.2}$ |  $368.5$$\pm$ | $101.0$ |  $0.71$$\pm$ | $0.05$ |  $6.79$$\pm$ | $0.06$ |  $1.15$$\pm$ | $0.27$ |  $3.57$$\pm$ | $0.42$ | - | H
BPS CS 22940–0009 | $-0.5$ | ${}^{+1.2}_{-1.3}$ | $142.4$ | ${}^{+2.1}_{-2.2}$ | $-20.5$ | ${}^{+0.7}_{-0.7}$ |  $982.0$$\pm$ | $39.3$ |  $0.40$$\pm$ | $0.02$ |  $6.94$$\pm$ | $0.06$ |  $2.96$$\pm$ | $0.14$ |  $1.32$$\pm$ | $0.06$ | $0.27$ | TK
FQ Aqr | $-3.9$ | ${}^{+0.4}_{-0.4}$ | $198.7$ | ${}^{+1.2}_{-1.4}$ | $-56.3$ | ${}^{+1.2}_{-1.6}$ |  $1290.5$$\pm$ | $22.3$ |  $0.13$$\pm$ | $0.01$ |  $6.88$$\pm$ | $0.01$ |  $5.28$$\pm$ | $0.08$ |  $2.47$$\pm$ | $0.14$ | $3.2$ | TK
Figure 4: Distribution of the sample in the Z plane plotted as a function of
the galactocentric distance. Red symbols indicate the primary sample of EHes
and the black symbols denote the secondary sample. The sample has been
classified into the disc and spherical components as given in section 4. The
circles represent the spherical components with the filled circles denoting
the bulge and the open circles denoting the halo stars. The stars represent
the disk components with the filled stars denoting the thin disk and the open
circles denoting the thick disk stars. Figure 5: The maximum distance in the Z
direction ($\rm Z_{max}$) is plotted as a function of the maximum distance of
the star from the Galactic center ($\rm R_{a}$). The symbols have the same
meaning as defined in Fig. 4. The dashed line represents the thin disk cut-off
height of 1.2 kpc set to distinguish between the thick and thin disk. Figure
6: The z component of angular momentum plotted as a function of eccentricity.
The symbols have the same meaning as defined in Fig. 4. The dashed regions
indicate estimates for the thin and thick disk stars from Pauli et al. (2003).
Figure 7: Galactic rotational velocity plotted against the total kinetic
energy. The symbols have the same meaning as defined in Fig. 4. The parabolic
curves denote line of equal velocity ($V_{\bot}=(U^{2}+W^{2})^{1/2}$) at
$0,100,300$ and $400\,\mbox{$\mbox{km}\,\mbox{s}^{-1}$}$ respectively. The
histogram with a binsize $=\,20\,\mbox{$\mbox{km}\,\mbox{s}^{-1}$}$ depicts
the Galactic rotational velocities of the whole sample. The red and black bins
refer to their respective samples. The grey dashed line represents $V=0$ with
the stars above it showing retrograde motion and the stars below it showing
prograde motion.  Figure 8: The Toomre diagram shows the kinematics of the
sample. The symbols have the same meaning as defined in Fig. 4. The dotted
lines correspond to predictions of Toomre diagrams from the Besançon Galactic
models (Robin et al., 2003) for the thin disk ($\leq
100\,\,\mbox{$\mbox{km}\,\mbox{s}^{-1}$}$), thick disk ($\leq
180\,\,\mbox{$\mbox{km}\,\mbox{s}^{-1}$}$) and halo stars ($\leq
400\,\,\mbox{$\mbox{km}\,\mbox{s}^{-1}$}$).

##  4 Kinematics

With information about Galactic 3D space velocities and orbits, an attempt may
be made to connect both classes and individual stars with parent populations.
In the following we describe our classification scheme, and then discuss the
classifications in terms of spatial and kinematical distributions.

###  4.1 Classification.

The population classification described in Martin et al. (2017) has been
augmented with a classification for the bulge. We define the extent of the
bulge based on estimates for the bulge and bar from Bland-Hawthorn & Gerhard
(2016) who state that it is difficult to separate the outer bulge from the
bar; we therefore do not distinguish the bar from the bulge.

Broadly:

  1. 1.

Stars with low eccentricity and low inclination orbits are identified with the
Galactic disk. These are further subdivided into

Thin Disk (TH): stars with $Z_{\rm max}\,<1.2$ kpc and falling within the thin
disk regime in the Toomre diagram.

Thick Disk (TK): stars with $Z_{\rm max}\,>1.2$ kpc and falling within the
thick disk regime in the Toomre diagram.

  2. 2.

Stars with high eccentricity orbits and/or high orbital inclination are
identified with spherical components. They are divided into:

Bulge (B): stars with low angular momentum, which come in close proximity to
the Galactic Centre and stay in the inner disk, i.e. $J_{z}<1000$ kpc
$\mbox{km}\,\mbox{s}^{-1}$, $|X|\,\leq 4$ kpc, $|Y|\,\leq 1.5$ kpc and
$|Z|\,\leq 1.5$ kpc, or have $R_{a}<5\,$kpc and $e>0.4$.

Halo (H):  stars with $Z_{\rm max}\ >$ 1.2 kpc and $R_{a}>7$ kpc or stars with
high orbital inclination.

The classifications derived using the above criteria are shown in Table 2. A
justification for these criteria will be given in the following subsection.
The orbits for stars which clearly do not match any of the above categories
were classified by inspection. A similar classification scheme was applied to
the stars in the secondary sample.

###  4.2 Justification.

Figure 4 shows the Z-distribution of the sample members as a function of
galactocentric distance $R$. The EHe sample appears to be centred on the disk
with a Gaussian distribution along the Z axis, skewed slightly to negative Z.
The Z-distribution of stars in all other classes is broadly similar, although
skewed in the opposite sense. The scale height of both Gaussian distributions
appears to exceed 2 kpc, so the samples as a whole (EHe and all others) cannot
belong to the thin disk alone.

The thin and thick discs kinematically overlap one another in a way that makes
it difficult to find a better selection criteria capable of distinguishing
them. Bovy (2011) suggests that there may not be a separation between thin and
thick discs implying that the transition between them is a continuum. Our
adopted definition for the thin disk extent, $|Z_{\rm max}|<1.2$ kpc, is based
on a relationship between the well-established scale heights of the thin disk
and the thick disk (Ma et al., 2017), $W$ values, and their number densities
(Bensby et al., 2014).
We define

$p(z)=n\,e^{-(z/h)^{2}}$ (5)

as the probability of a star being found at height $z$ in a population with a
Gaussian distribution $e^{-(z/h)^{2}}$, where $h$ is the scale height and $n$
is the normalisation fraction of the population. Based on this relationship,
we can obtain the likelihood that a star at $Z_{\rm max}$ belongs to either
the thin disk or the thick disk, such that stars with $|Z_{\rm max}|\,=1.2$
kpc have an equal likelihood $(\sim 1)$ of being either. The $\log$ likelihood
of a star belonging to the thick disk rather than the thin disk, $f=p({\rm
thick})/p({\rm thin})$, is shown in Table 2. Thus, the thin and thick disk
assignments are $>70\%$ secure in all cases except V652 Her, V2076 Oph, and
BPS CS 22940–0009, which all have a $>33\%$ chance of being mis-classified.

Figure 5 shows the apocentric positions of the sample members in terms of
$|Z_{\rm max}|$ and $R_{\rm a}$. This representation helps to separate classes
because it combines the full orbital information with the spatial information.
It clearly distinguishes the thin disk EHes from the thick disk and halo, but
is not so good at separating out thick disk and halo stars, or thin disk and
bulge stars. The same holds for stars in the secondary samples. There is a
deficit of stars with high $\rm Z_{\rm max}$ and low $\rm R_{\rm ap}$. This
‘zone of avoidance’ would correspond to stars in highly inclined orbits which
are not expected to be numerous.

A method frequently used for population classification compares the
Z-component of angular momentum ($J_{z}$) with orbital eccentricity (Fig. 6)
(cf. Pauli et al., 2003). Due to the low eccentricity of the disk stars, they
tend to cluster around $e\approx 0.2\pm 0.1$ and $J_{z}\approx 2000\pm 500$.
This diagram was originally devised to identify thick disk stars in the local
neighbourhood; because our sample volume is much larger than Pauli et al.
(2003), some thick disk EHes lie outside Pauli’s region 2.

Figure 7 shows the kinetic energy $2E_{\rm kin}/m=U^{2}+V^{2}+W^{2}$ as a
function of the rotational component V. Contours show the velocity
perpendicular to Galactic rotation at certain values, where
$V_{\bot}=(U^{2}+W^{2})^{1/2}$. Any value for which $V_{\bot}>$ 100 $\rm
km\,s^{-1}$ implies a non-disk orbit. The higher the value of $2E_{\rm
kin}/m$, the more the orbit deviates from a circular orbit. This highlights
stars which do not belong to the disk. We note a number of stars in retrograde
motion, particularly the EHe star EC 19529–4430.

The Toomre diagram (Figure 8) has been used to classify the stars into their
populations using their space velocities $T\equiv
V_{\bot}=(U^{2}+W^{2})^{1/2}$ versus $V$. Based on the predictions from the
Besançon Galactic models (Robin et al., 2003), we identify stars within 100
$\mbox{km}\,\mbox{s}^{-1}$of the solar motion to be likely thin disk stars,
within 180 $\mbox{km}\,\mbox{s}^{-1}$to be likely thick disk stars and those
within 400 $\mbox{km}\,\mbox{s}^{-1}$to be halo stars.

A useful tool in identifying halo stars with low eccentricities is the
‘normalized z-extent’, which can be substituted as a measure of the orbital
inclination, given by

$z_{\rm n}=\frac{Z_{\rm max}}{R(Z_{\rm max})}$ (6)

where $R(Z_{\rm max})$ is the galactocentric distance when the star is at
$Z_{\rm max}$.

As this paper was being completed, we received a preprint by Tisserand et al.
(2023) presenting a similar analysis for HdC, RCB and EHe stars. Their sample
of 16 EHe stars compares with our sample of 27 EHe stars owing mainly to our
inclusion of recent discoveries from SALT (Jeffery et al., 2021). On
comparison of the population classifications for EHes, both papers agree on
memberships for the thin disk and bulge stars. Tisserand et al. (2023) did not
identify any EHes in the halo, with the possible exception of V2205 Oph. We
classify V2205 Oph as a halo star (Fig. 2) on the basis of its high
eccentricity ($0.57\pm 0.07$) and $R_{a}$ ($9.39\pm 0.53$ kpc). 3 halo stars
in our sample (BD +37 1977, EC 19529–4430 and EC 20236–5703) were not included
by Tisserand et al. (2023). 4 stars, V2076 Oph, CoD –46 11775, BD +10 2179 and
CoD –48 10153, are classified as thick disk by Tisserand et al. (2023). We
classify V2076 Oph as thin disk because of its small $Z_{\rm max}=0.86\pm
0.03$ kpc. CoD -46 11775 lies in the region that we have defined for the bulge
(X = $-3.59^{+0.17}_{-0.21}$ kpc, Y = $-1.32^{+0.05}_{-0.06}$ kpc, Z =
$-0.78^{+0.03}_{-0.03}$ kpc). Although BD +10 2179 falls within the thick disk
region in the Toomre diagram, its high eccentricity ($0.53\pm 0.02$) and
$R_{a}$ ($10.59\pm 0.15$ kpc) make it more likely to be a halo star. Finally,
CoD –48 10153 falls outside the thick disk regime in the Toomre diagram.
However, its highly eccentric orbit ($0.51\pm 0.02$) and a very low Galactic
rotational velocity
($V=0.9^{+11.8}_{-15.9}\,\,\mbox{$\mbox{km}\,\mbox{s}^{-1}$}$) clearly make it
a halo star.

Table 3: Population statistics for various classes of hydrogen-deficient star. Category | N | Thin Disk | Thick Disk | Halo | Bulge
---|---|---|---|---|---
EHe | 27 | 8 | 9 | 6 | 4
RCB | 38 | 9 | 13 | 8 | 8
HdC | 8 | 3 | 3 | 2 | 0
He-sdO | 181 | 41 | 104 | 36 | 0
He-sdOB | 135 | 40 | 47 | 48 | 0
He-sdB | 17 | 13 | 3 | 1 | 0

###  4.3 Statistics.

Table 3 compares the numbers of stars classified as thin or thick disk, halo
or bulge stars within various classes of hydrogen-deficient star. Five
additional subclasses have been classified in exactly the same way as the
EHes. Of these, the helium-rich subdwarfs (He-sdB, He-sdOB, He-sdO) are
intrinsically fainter than the other classes. The absence of bulge stars in
these classes reflects the fact that they are not represented in our sample at
such distances. O(He) and PG1159 subclasses were also considered, but are too
few to provide useful samples.

It is highly significant that the EHe sample includes stars from the thin
disk, the thick disk, the halo and the bulge. We shall return to this in § 5.

Given the sample sizes, the distributions of RCB, HdC and He-sdO stars amongst
the four components are not significantly different from that of the EHes.
They are dominated by thick disk stars, with thin disk, halo and bulge stars
roughly in the ratio 23:53:20:4. The HdC sample shows the largest departure
from this ratio, but is roughly consistent given the sample size. The He-sdO
sample is 7 times larger than the EHe sample. Thus, the hypothesis that EHe
stars may be connected to the RCB, HdC and He-sdO classes cannot be excluded.

The He-sdB sample is heavily dominated by thin disk stars, but the sample size
is small. The He-sdOB sample is balanced across thin disk, thick disk and halo
and is 4 times larger than the EHe sample. It therefore appears that the He-
sdB and He-sdOB samples do not share the characteristics of the EHe and He-sdO
samples. The helium-rich subdwarf samples can be further subdivided into,
inter alia, intermediate helium-rich and extreme-helium rich subclasses
(Jeffery et al., 2021). Detailed analysis of these classes will therefore be
deferred.

##  5 Luminosities and radii

One method to derive the luminosity is to obtain the absolute visual magnitude
(S. 3.3), and then to obtain the absolute bolometric magnitude by applying a
bolometric correction (BC). Since commonly used values for the BC (Weidemann &
Bues, 1967; Lang, 1974; Martins et al., 2005; Nieva, 2013) are derived from
hydrogen-rich stars, these might not be applicable to hydrogen-deficient
stars. An alternative method is to deduce the angular diameter of the star
($\theta$) from the spectral energy distribution (SED), and thence to obtain
the actual diameter by multiplying by the distance. If the effective
temperature is known, the luminosity follows. In order to apply this method, a
theoretical energy distribution from a model atmosphere is convolved with an
extinction function and scaled to fit the observed SED. Principal unknowns are
the effective temperature of the model atmosphere $T_{\rm eff}$, the
extinction coefficient $E_{\rm(B-V)}$ and $\theta$. Other parameters which
affect the theoretical model include surface gravity, metallicity and
microturbulent velocity. In general these cannot be determined from the SED
and must be selected by some other means.

Table 4: Atmospheric parameters, extinction, magnitudes, luminosities and radii for Extreme Helium stars, ordered by effective temperature. The sample has been divided into those stars with $L>2500\mbox{\,$\rm L_{\odot}$}$ above and those with $L<2500\mbox{\,$\rm L_{\odot}$}$ below. The sources cited for $T_{\rm eff}$ are also sources for $\log g$ and extinction $E_{\rm(B-V)}$, where available. ’*’ indicates a missing error for temperature or gravity; we assume $\pm\,2\,\%$ for temperature and $\pm 0.25$ for $\log g$. †indicates an extinction estimated from Schlegel et al. (1998). G and V magnitudes are from Gaia Collaboration et al. (2023). Masses $M_{L}$ and $M_{g}$ obtained from the $M_{c}-L_{s}$ relation for helium-shell burning are shown for the high luminosity stars (Fig. 13). The three low-gravity low-luminosity stars from Fig. 13 are also shown in parenthesis.  Star |  Teff | $E_{\rm(B-V)}$ | G | V | Luminosity | $\log g$ | Radius | $M_{L}$ | $M_{g}$
---|---|---|---|---|---|---|---|---|---
| (K) |  | (mag) | (mag) | (log L⊙) | (cm s-2) | (R⊙) | M⊙ | M⊙
NO Ser | 11750$\pm$ | 2501 | 0.498$\pm$ | 0.010 | 10.11 | 10.25 | 3.60${}^{+0.15}_{-0.01}$ | 2.30$\pm$ | 0.40 | 15.30 | ${}^{+2.07}_{-0.50}$ | $0.60^{+0.03}_{-0.01}$ | $0.53^{+0.05}_{-0.04}$
V2244 Oph | 12750$\pm$ | 2501 | 0.500$\pm$ | 0.020 | 10.85 | 10.94 | 3.81${}^{+0.22}_{-0.02}$ | 1.75$\pm$ | 0.25 | 16.70 | ${}^{+3.80}_{-0.91}$ | $0.66^{+0.05}_{-0.01}$ | $0.67^{+0.08}_{-0.06}$
PV Tel | 13750$\pm$ | 4003 | 0.130$\pm$ | 0.010 | 9.23 | 9.26 | 3.83${}^{+0.17}_{-0.06}$ | 1.60$\pm$ | 0.25 | 14.60 | ${}^{+2.17}_{-0.19}$ | $0.64^{+0.04}_{-0.01}$ | $0.76^{+0.13}_{-0.08}$
LSS 99 | 15330$\pm$ | 5004 | 0.877$\pm$ | 0.038 | 12.05 | 12.27 | 4.03${}^{+0.22}_{-0.22}$ | 1.90$\pm$ | 0.25 | 14.80 | ${}^{+2.99}_{-0.98}$ | $0.69^{+0.08}_{-0.05}$ | $0.71^{+0.10}_{-0.06}$
LSS 4357 | 16130$\pm$ | 5004 | 0.628$\pm$ | 0.040 | 12.43 | 12.54 | 3.84${}^{+0.30}_{-0.05}$ | 2.00$\pm$ | 0.25 | 10.90 | ${}^{+3.25}_{-1.10}$ | $0.65^{+0.08}_{-0.01}$ | $0.70^{+0.10}_{-0.06}$
V1920 Cyg | 16300$\pm$ | 9003 | 0.310$\pm$ | 0.020 | 10.26 | 10.30 | 3.94${}^{+0.19}_{-0.12}$ | 1.70$\pm$ | 0.35 | 11.70 | ${}^{+1.38}_{-0.35}$ | $0.67^{+0.06}_{-0.03}$ | $0.89^{+0.36}_{-0.16}$
CoD –46 11775 | 18300$\pm$ | 4003 | 0.161$\pm$ | 0.015 | 11.17 | 11.20 | 3.57${}^{+0.15}_{-0.22}$ | 2.20$\pm$ | 0.20 | 6.20 | ${}^{+0.72}_{-1.28}$ | $0.61^{+0.03}_{-0.03}$ | $0.71^{+0.08}_{-0.05}$
EC 19529–4430 | 18540$\pm$ | 906 | 0.050$\pm$ | $0.012^{{\dagger}}$ | 11.77 | 11.81 | 3.41${}^{+0.34}_{-0.14}$ | 3.42$\pm$ | 0.04 | 5.00 | ${}^{+2.21}_{-0.86}$ | $0.57^{+0.06}_{-0.02}$ | $0.49^{+0.01}_{-0.01}$
V2205 Oph | 20277$\pm$ | 5507 | 0.300$\pm$ | 0.040 | 10.48 | 10.51 | 4.28${}^{+0.21}_{-0.20}$ | 2.55$\pm$ | 0.10 | 11.60 | ${}^{+1.85}_{-2.27}$ | $0.78^{+0.11}_{-0.08}$ | $0.66^{+0.02}_{-0.02}$
LSS 5121 | 29772$\pm$ | 18307 | 0.650$\pm$ | 0.020 | 13.16 | 13.23 | 3.91${}^{+0.32}_{-0.01}$ | 3.00$\pm$ | 0.50 | 3.40 | ${}^{+0.93}_{-0.39}$ | $0.66^{+0.10}_{-0.01}$ | $0.77^{+0.30}_{-0.14}$
V2076 Oph∗ | 34000$\pm$ | 68013 | 0.450$\pm$ | 0.020 | 9.79 | 9.82 | 4.20${}^{+0.11}_{-0.04}$ | 2.80$\pm$ | 0.25 | 3.65 | ${}^{+0.38}_{-0.07}$ | $0.75^{+0.04}_{-0.02}$ | $1.10^{+0.53}_{-0.25}$
BD +37 $442^{*}$ | 48000$\pm$ | 96015 | 0.090$\pm$ | $0.002^{{\dagger}}$ | 9.94 | 10.01 | 3.72${}^{+0.10}_{-0.07}$ | 4.00$\pm$ | 0.25 | 1.06 | ${}^{+0.10}_{-0.07}$ | $0.62^{+0.02}_{-0.02}$ | $0.67^{+0.09}_{-0.06}$
BD +37 $1977^{*}$ | 48000$\pm$ | 96015 | 0.030$\pm$ | $0.004^{{\dagger}}$ | 10.13 | 10.21 | 3.96${}^{+0.12}_{-0.13}$ | 4.00$\pm$ | 0.25 | 1.39 | ${}^{+0.16}_{-0.17}$ | $0.68^{+0.03}_{-0.03}$ | $0.67^{+0.09}_{-0.06}$
FQ Aqr | 8750$\pm$ | 2501 | 0.100$\pm$ | 0.020 | 9.47 | 9.51 | 2.93${}^{+0.14}_{-0.14}$ | 0.75$\pm$ | 0.25 | 12.90 | ${}^{+1.13}_{-1.46}$ | $\left(0.51^{+0.02}_{-0.01}\right)$ | $\left(0.80^{+0.16}_{-0.1}\right)$
LS IV –14 109 | 9500$\pm$ | 2501 | 0.340$\pm$ | 0.050 | 10.99 | 11.08 | 2.61${}^{+0.12}_{-0.13}$ | 0.90$\pm$ | 0.20 | 7.50 | ${}^{+0.49}_{-0.66}$ | $\left(0.48^{+0.01}_{-0.01}\right)$ | $\left(0.79^{+0.11}_{-0.08}\right)$
CoD –48 10153 | 10600$\pm$ | 2502 | 0.450$\pm$ | 0.040 | 11.33 | 11.44 | 3.04${}^{+0.17}_{-0.18}$ | 1.00$\pm$ | 0.50 | 10.00 | ${}^{+1.35}_{-1.62}$ | $\left(0.52^{+0.02}_{-0.02}\right)$ | $\left(0.85^{+0.85}_{-0.21}\right)$
HD 124448 | 15800$\pm$ | 4003 | 0.092$\pm$ | 0.010 | 9.94 | 9.97 | 2.82${}^{+0.08}_{-0.10}$ | 2.10$\pm$ | 0.25 | 3.43 | ${}^{+0.15}_{-0.22}$ |  |
BD +10 2179 | 17300$\pm$ | 3005 | 0.023$\pm$ | 0.001 | 9.92 | 9.97 | 3.11${}^{+0.15}_{-0.14}$ | 2.80$\pm$ | 0.10 | 4.00 | ${}^{+0.55}_{-0.50}$ |  |
V652 Her | 20950$\pm$ | 708 | 0.060$\pm$ | 0.010 | 10.51 | 10.56 | 2.78${}^{+0.09}_{-0.06}$ | 3.46$\pm$ | 0.05 | 1.88 | ${}^{+0.17}_{-0.14}$ |  |
BX Cir | 23390$\pm$ | 909 | 0.239$\pm$ | 0.008 | 12.54 | 12.57 | 3.13${}^{+0.15}_{-0.04}$ | 3.38$\pm$ | 0.02 | 2.24 | ${}^{+0.40}_{-0.11}$ |  |
GALEX J184559.8–413827 | 26170$\pm$ | 75010 | 0.075$\pm$ | $0.001^{{\dagger}}$ | 14.57 | 14.62 | 2.74${}^{+0.18}_{-0.22}$ | 4.22$\pm$ | 0.10 | 1.02 | ${}^{+0.31}_{-0.08}$ |  |
EC 20236–5703 | 26380$\pm$ | 1306 | 0.055$\pm$ | $0.012^{{\dagger}}$ | 14.75 | 14.80 | 2.26${}^{+0.20}_{-0.06}$ | 4.14$\pm$ | 0.05 | 0.66 | ${}^{+0.14}_{-0.06}$ |  |
LS IV+6 2 | 31800$\pm$ | 80011 | 0.210$\pm$ | 0.020 | 12.12 | 12.16 | 2.85${}^{+0.13}_{-0.05}$ | 4.05$\pm$ | 0.10 | 0.87 | ${}^{+0.09}_{-0.05}$ |  |
PG 1415+492 | 32200$\pm$ | 25012 | 0.011$\pm$ | $0.012^{{\dagger}}$ | 14.27 | 14.34 | 2.21${}^{+0.08}_{-0.10}$ | 4.20$\pm$ | 0.10 | 0.41 | ${}^{+0.03}_{-0.04}$ |  |
EC 20111–6902 | 34100$\pm$ | 1106 | 0.036$\pm$ | $0.012^{{\dagger}}$ | 15.84 | 15.87 | 2.28${}^{+0.61}_{-0.96}$ | 5.68$\pm$ | 0.04 | 0.39 | ${}^{+0.39}_{-0.26}$ |  |
BPS CS 22940–0009 | 34970$\pm$ | 37014 | 0.052$\pm$ | $0.012^{{\dagger}}$ | 13.97 | 14.03 | 2.26${}^{+0.08}_{-0.11}$ | 4.79$\pm$ | 0.17 | 0.37 | ${}^{+0.02}_{-0.04}$ |  |
GALEX J191049.5–441713 | 39690$\pm$ | 906 | 0.085$\pm$ | $0.006^{{\dagger}}$ | 12.93 | 12.98 | 2.58${}^{+0.11}_{-0.04}$ | 5.47$\pm$ | 0.03 | 0.42 | ${}^{+0.05}_{-0.02}$ |  |
1:Pandey et al. (2001), 2:Pandey & Reddy (2006), 3:Pandey et al. (2006),
4:Jeffery et al. (1998), 5:Kupfer et al. (2017), 6:Jeffery et al. (2021),
7:Jeffery et al. (2001a), 8:Jeffery et al. (2001b), 9:Woolf & Jeffery (2002),
10:Jeffery (2017), 11:Jeffery (1998), 12:Ahmad & Jeffery (2003) 13:Rauch
(1996), 14:Snowdon et al. (2022), 15:Jeffery & Hamann (2010)
Figure 9:  SED fit from the broadband photometry of V2244 Oph with $T_{\rm
eff}\,=\,12750\,{\rm K}$ (upper panel). The grey line shows the best-fit model
SED. 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).

Photometric observations from a number of sources were used to fit the SED of
the EHe stars using the model-atmosphere fitting tool
isis444http://www.sternwarte.uni-erlangen.de/gitlab/irrgang/stellar.git (Heber
et al., 2018). These sources include Høg et al. (2000), Cutri et al. (2003,
2021), Denis (2005), McMahon et al. (2013), Henden et al. (2015), Kilkenny et
al. (2016), (Bianchi et al., 2017), Schlafly et al. (2018, 2019), Onken et al.
(2019), Magnier et al. (2020), Drlica-Wagner et al. (2021), Riello et al.
(2021). The theoretical spectra used for the fits were taken from grids of
line-blanketed model atmospheres computed in local thermodynamic equilibrium
with sterne (Behara & Jeffery, 2006). The model grid used for each star was
chosen according to the measured metallicity and microturbulence, where
available, or on the basis of the similarity of the star’s optical spectrum to
those of other EHes.

isis allows us to solve for several parameters at once, or to keep some fixed
and solve for others. For hot stars, $T_{\rm eff}$ and $E_{\rm(B-V)}$ are
almost degenerate, so free solutions for both are difficult to control (cf.
Jeffery et al., 2001a). For consistency, $T_{\rm eff}$ was fixed to the most
recent value obtained from optical spectroscopy wherever possible. isis then
solved for $E_{\rm(B-V)}$ and $\theta$. Hence, we deduce the radius

${R_{\star}}=\theta d/2$ (7)

and the luminosity

$\frac{L_{\star}}{\rm L_{\odot}}=\left(\frac{R_{\star}}{\rm
R_{\odot}}\right)^{2}\,\left(\frac{T_{\rm eff}}{\rm T_{\rm
eff\,\odot}}\right)^{4}.$ (8)

These values have been computed for the EHe stars and are given in Table 4
along with published values for the effective temperatures ($T_{\rm eff}$),
surface gravities ($\log g$) and extinction coefficients ($E_{\rm(B-V)}$).
$T_{\rm eff}$ and $\log g$ have been taken from the most recent spectroscopic
analyses of optical spectra wherever possible and the sources are cited in
Table 4. For measurements that do not have a published error, we have assumed
an error of $\pm\,2\%$ for temperature and $\pm$ 0.25 dex for $\log g$. Some
measurements cited in Table 4 have very small error; these are taken to be
formal errors. To partially account for likely larger systematic errors,
minimum errors of $\pm\,1\%$ and 0.05 dex are adopted for $T_{\rm eff}$ and
$\log g$ respectively for propagation. Figure 9 shows an example of an SED fit
for the cool EHe V2244 Oph. None of the SED fits show any evidence for an
infra-red excess that might indicate an unseen cool companion or a dust shell.

Since we have the surface gravity and radius for each star, we may in
principle deduce the mass

$M_{\star}=\frac{\rm g}{\rm G}\,R_{\star}^{2}.$ (9)

In practice, whilst the errors in radius are usually smaller than $\pm\,10\%$,
their contribution doubles in the derivation of mass and the errors in surface
gravity are mostly between $\pm\,25\%$ and $\pm\,80\%$. Consequently, the mass
errors ($1\sigma$) exceed $100\%$ for half of the EHe sample, and are less
than $50\%$ for only 5 EHes. The deduced masses run from
$0.02^{+0.015}_{-0.003}-2.71^{+3.62}_{-5.44}$ $\rm M_{\odot}$ and 12 cluster
between 0.2 and 0.5  $\rm M_{\odot}$. In view of the errors and the spread, we
attach little confidence to these data. Likely reasons include the difficulty
of measuring surface gravities and the presence of large amplitude pulsations
in these luminous stars; unless angular radii and surface gravities are
obtained at equivalent phases in approximately hydrostatic equilibrium,
significant systematic errors will occur. The issues are examined in detail
for the case of V652 Her by Jeffery et al. (2022).

Figure 10: Luminosities of EHes derived from Gaia distances and SED-based
angular diameters as a function of effective temperature. Symbols represent
the population assignments given in Table 4 (see key). Figure 11: Comparison
between BC adopted from Weidemann & Bues (1967), Lang (1974), Martins et al.
(2005) and Nieva (2013) ($\rm BC_{lit}$) and BC obtained using the spectral
energy distributions (${\rm BC}_{\theta}$) of the EHe stars in the temperature
range 8750 K - 48000 K. The blue dotted line depicts a low order polynomial
fit to the data.

Figure 10 shows the luminosities as a function of effective temperature. This
suggests that EHes may be divided into two luminosity groups, with a dividing
line at $L\approx 2\,500\mbox{\,$\rm L_{\odot}$}$. The more luminous group
$L\approx 2\,500-20\,000\mbox{\,$\rm L_{\odot}$}$ shows roughly similar
luminosity over the entire temperature range. The less luminous group
$L\approx 100-2\,500\mbox{\,$\rm L_{\odot}$}$ shows a progression towards
lower luminosity with increasing temperature. The two groups are also
identified in Table 4. It is significant that both groups include stars from
the thin disk, the thick disk, and the halo.

###  5.1 Bolometric correction for EHe stars

To determine whether the bolometric corrections available in literature for
stars of these temperature ranges could be applicable to EHes, we converted
the SED luminosities to $M_{\rm bol\star}$ using

$M_{\rm bol\star}=-2.5\log_{10}\left(\frac{L_{\star}}{\rm
L_{\odot}}\right)+{\rm M_{\rm bol\odot}}$ (10)

and then compared with the absolute visual magnitude from Eq. 3 to obtain the
bolometric correction

$\rm BC=M_{\rm bol\star}-M_{V}.$ (11)

Figure 11 compares the EHe bolometric corrections with the bolometric
corrections from Weidemann & Bues (1967); Lang (1974); Martins et al. (2005);
Nieva (2013). The correction for helium stars seems to be more positive than
the literature values by about 0.3 mag. This is probably due to the absence of
Balmer line and continuum absorption in the EHe stars. The BC for EHes can be
expressed as a function of $T_{\rm eff}$ by the polynomial fit shown in Fig.
11:

$BC=1.59-1.79\,(T_{\rm eff}/10^{4})+0.122\,(T_{\rm eff}/10^{4})^{2}.$ (12)

This correction can also be used to obtain luminosities for stars with
insufficient photometric data for an SED fit.

Figure 12: A comparison of the post-merger evolution of double white dwarfs
with the observed properties of Extreme Helium stars. Left: the Kiel
($g-T_{\rm eff}$) diagram. The black dotted lines indicate equal L/M ratio as
marked. The grey lines show the post-merger evolution tracks for models of
CO+He WD mergers from Saio & Jeffery (2002) with product masses $0.6+0.2$ and
$0.6+0.3$ $\rm M_{\odot}$. The blue lines show tracks for He+He WD mergers
from Saio & Jeffery (2000) with the dotted line corresponding to $\rm
0.3+0.2\,M_{\odot}$ and solid corresponding to $\rm 0.4+0.3\,M_{\odot}$. The
red line shows the track for a $0.3+0.25\,\rm M_{\odot}$ He+He WD merger from
Zhang & Jeffery (2012a) Right: The Hertszprung-Russell ($L-T_{\rm eff}$)
diagram, plotted with the same evolution tracks. Dark grey lines show CO+He WD
post-merger tracks from Schwab (2019) with final masses 0.69, 0.67 and 0.65
$\rm M_{\odot}$.

##  6 Inferences on Evolution, Age, and Numbers

With spatial and kinematic data, as well as luminosities, we are in a position
to discuss the age, origin and evolution of EHes.

Using their distribution and radial velocity in the Galactic frame, Drilling &
Hill (1986) argued that EHe stars belong to the Galactic bulge. Iben & Tutukov
(1985) derived a scale height 1700 pc for the EHe star population, which would
be commensurate with a thick disk population. The current analysis shows that
EHes include stars representative of all the major Galactic populations,
including the thin and thick disk as well as the bulge and halo. Thus EHes
must arise from star formation at many epochs of Galactic evolution. The Gaia
analysis also shows that EHes form two luminosity groups, implying more than
one formation channel.

###  6.1 Evolution

It has been proposed that RCB and EHe stars form as a result of the merger of
two white dwarfs (WDs) (Webbink, 1984; Saio & Jeffery, 2002). Post-merger
evolution depends on the nature of the WDs involved; for example:

  * •

He+He WD$\xrightarrow{}$ ?? $\xrightarrow{}$ EHe $\xrightarrow{}$ He-sdO
$\xrightarrow{}$ DO WD (Saio & Jeffery, 2000; Zhang & Jeffery, 2012a)555Iben
(1990) proposed that a He+He WD merger would produce an sdB star; in fact,
Iben’s model cannot account for the classical hydrogen-rich sdB stars but is
equivalent to this sequence.

  * •

He+He WD$\xrightarrow{}$ ?? $\xrightarrow{}$ EHe $\xrightarrow{}$ He-sdO
$\xrightarrow{}$ RCB $\xrightarrow{}$EHe $\xrightarrow{}$ He-sdO+
$\xrightarrow{}$ O(He) $\xrightarrow{}$ DO WD (Zhang & Jeffery, 2012b)

  * •

Co+He WD$\xrightarrow{}$ RCB $\xrightarrow{}$ EHe $\xrightarrow{}$ He-sdO+
$\xrightarrow{}$ O(He) $\xrightarrow{}$ DO WD (Webbink, 1984; Saio & Jeffery,
2002; Zhang et al., 2014; Schwab, 2019)

The middle sequence may be impossible to distinguish from either the first or
last sequence, having the characteristics of both. It is not clear what the
immediate product of a He+He WD merger will be; hence ’??’ above. Its lifetime
will be short, being only the lifetime of a helium shell-flash cycle at the
start of core helium burning. It may well be a cool EHe or HdC star. In
contrast, the lifetime of the immediate He+CO WD merger product is relatively
long, being the lifetime for the helium-burning shell to consume available
fuel above the carbon-oxygen core; this may be some 0.3 - 0.4  $\rm
M_{\odot}$. It is reasonable that these may be RCB or HdC stars.

Given the two EHe luminosity groups, it seems likely that the EHe sample
includes post-merger products from both CO+He WD binaries and He+He WD
binaries. The lower luminosity EHes ($L>2\,500\mbox{\,$\rm L_{\odot}$}$) and
He-sdO’s have already been identified with the He+He WD merger sequence (Saio
& Jeffery, 2000; Zhang & Jeffery, 2012a). The higher luminosity EHes
($L>2\,500\mbox{\,$\rm L_{\odot}$}$) are identified with the merger of a CO+He
WD binary (Saio & Jeffery, 2002; Zhang et al., 2014; Schwab, 2019), evolving
via the low gravity hot sdO domain (He-sdO+ and O(He) stars) to become hot
WDs. Clayton et al. (2007) established that the cooler RCBs lie on the same
pathway. A strict boundary cannot be drawn because it is possible to form
He+He systems which are more massive than the lightest CO+He systems, and
because the former can emulate the evolution of the latter after completion of
core helium burning (Zhang & Jeffery, 2012b).

Figure 12 compares post-merger tracks for both He+He and CO+He WD mergers with
the Gaia-derived luminosities as well as the spectroscopic surface gravities
of the EHes.

Figure 13: EHe masses derived from observed luminosities ($M_{L}/\mbox{\,$\rm
M_{\odot}$}$) and surface gravities ($M_{g}/\mbox{\,$\rm M_{\odot}$}$) and the
$M_{c}-L_{s}$ relation appropriate for CO+He WD mergers (Jeffery, 1988).

The intrinsically brighter EHes have luminosities consistent with post-merger
tracks for CO+He WDs in the 0.65 – 0.9 $\rm M_{\odot}$ range, as identified by
Saio & Jeffery (2002); Zhang et al. (2014); Schwab (2019). For these,
evolution proceeds via contraction at constant luminosity, approximately on a
thermal timescale. The luminosity reflects the stars’ masses, as indicated by
the core-mass shell-luminosity ($M_{c}-L_{s}$) relation for helium-shell
burning stars (Jeffery, 1988) which we have verified against the Saio &
Jeffery (2002) and Schwab (2019) evolution tracks.

Systems with $L<2\,500\mbox{\,$\rm L_{\odot}$}$ are more likely to have been
produced in He+He systems with total masses $\leq 0.7\mbox{\,$\rm
M_{\odot}$}$. Whilst initially bright after shell-helium ignition, these stars
contract and dim as the helium-burning shell burns inwards towards the core,
eventually reaching the helium main-sequence.

Estimates for the mass of each EHe star can be obtained from theoretical
evolution tracks (Fig. 12) or from the Jeffery (1988) $M_{c}-L_{s}$ relation
by separately comparing with the observed surface gravity to give mass
$M_{g}$, and luminosity to give $M_{L}$.

Values of $M_{L}$ and $M_{g}$ obtained from the $M_{c}-L_{s}$ relation for
high-$L$ EHes ($L>2\,500\mbox{\,$\rm L_{\odot}$}$) are shown in Table 4 and
compared in Fig. 13. V2244 Oph, LSS 99, LSS 4357, BD+37 442 and BD+37 1977
have $M_{g}$ and $M_{L}$ in good agreement between 0.62 and 0.71  $\rm
M_{\odot}$. LSS 5121, CoD -46 11775 and PV Tel have $M_{L}$ in the range
$0.59-0.66\mbox{\,$\rm M_{\odot}$}$, but $M_{g}$ in the range
$0.71-0.76\mbox{\,$\rm M_{\odot}$}$. NO Ser and EC 19529–4430 have $M_{L}$ in
the range $0.57-0.60\mbox{\,$\rm M_{\odot}$}$, but markedly lower $M_{g}$. For
V2205 Oph, $M_{g}$ is also too low. V1920 Cyg and V2076 Oph have $M_{g}$
substantially higher than the corresponding $M_{L}$. Overall, the Gaia+SED
luminosities support masses for post-merger He+CO white dwarfs in the range
$0.57-0.78\mbox{\,$\rm M_{\odot}$}$. Significant differences between $M_{L}$
and $M_{g}$ should be examined in more detail, particularly with respect to
surface gravity and extinction.

FQ Aqr, LS IV-14 109 and CoD -48 10153 are included in Fig. 13 because their
surface gravities suggest a high luminosity, which is not supported by the
Gaia+SED measurements. The low-$L$ EHes ($L<2\,500\mbox{\,$\rm L_{\odot}$}$)
lie well below the luminosities predicted for CO+He mergers. Masses cannot be
derived from the post-merger evolution tracks for He+He WDs since, for a given
class of model, these are degenerate in $g$ (and $L$) during contraction
toward the helium main-sequence (Zhang & Jeffery, 2012a). Moreover, loops
associated with helium-shell flashes broaden the tracks by more than any
difference caused by a change in mass.

According to Tisserand et al. (2020), the cool group of RCB stars represents
about 2/3 the entire RCB sample, but is under-represented in atmospheric
analyses. With 118 Galactic RCB stars now known (Tisserand et al., 2020),
substantial numbers of accurate $\mbox{\,$T_{\rm eff}$},g$ measurements for
stars within 10 kpc could transform Fig. 12 into a tool that will places
useful constraints on evolution models and stellar physics. Additionally, with
precise bolometric corrections for a larger temperature range, Fig. 12 would
be expanded to include other sets of helium stars, thereby shedding more light
on evolutionary pathways.

###  6.2 Age

The defining timescales for double WD mergers are those of the progenitor
binary followed by the orbital-decay time of the double WD system. Post-merger
evolution timescales are comparatively short, so all current EHes probably
formed within the last 104 – 106 y. From a composite model for the star-
formation history of the Galaxy, Yu & Jeffery (2011) argue that the majority
($>95\%$) of CO+He double WDs currently alive in the Galactic disc were formed
between 4 and 10 Gyr before the present epoch. However, the fraction of these
that contribute to the present-day CO+He WD merger rate is dominated by star
formation between 1 and 3 Gyr before the present. Supporting this, Zhang et
al. (2014) show that, for a single starburst, CO+He WD mergers peak some 1 Gyr
after the starburst, declining exponentially by a factor 10 over 3 Gyr, but
then remaining steady up to at least 10 Gyr after the starburst (i.e. at
$\approx$1/10 the rate for $\approx 10\times$ the time). Thus the majority of
EHes should come from relatively recent star formation. This is supported by
the fact that 2/3 of the sample belong to the thin (8) and thick (9) disks
(Table 3). However, the tail of the distribution, which formed up to 10 Gyr or
more in the past, will continue to provide a significant number of recent
CO+He WD mergers in all Galactic populations.

Table 5: Relative frequency of double white dwarf binary mergers by Galactic population and binary white dwarf class at the current epoch based on Yu & Jeffery (2010, 2011) and normalised to 100 yr-1. The associated total rate for the Galaxy over all merger types is $\sim 2.8\times 10^{-3}$ yr-1.  White Dwarfs | Galaxy | Thin Disk | Thick Disk | Halo | Bulge
---|---|---|---|---|---
He+He | 34 | 17 | 1 | 16 | 8
CO+He | 14 | 7 | 1 | 5 | 2
CO+CO | 46 | 22 | 2 | 10 | 5
ONeMG+X | 6 | 3 | 0 | 1 | 1
All | 100 | 49 | 4 | 32 | 15

###  6.3 Numbers

Predictions for relative numbers of double white dwarf mergers in different
populations have been derived in many studies using the methods of binary star
population synthesis (BSPS) (e.g. Yu & Jeffery, 2010, 2011; Zhang et al.,
2014). Table 5 shows the relative merger rates obtained by combining the rates
per Galactic component (Yu & Jeffery, 2010, Table 2) with the rates per merger
type (Yu & Jeffery, 2011, Tables 2,3), assuming a quasi-exponential star-
formation history for the thin and thick disks, and an instantaneous star-
formation history for the bulge and halo. These statistics include both stable
and unstable mergers (Zhang et al., 2014, Figs. 1,24). Only a subset of the
latter will give rise to EHe stars, a supernova explosion being an alternative
for the most massive mergers. There are significant differences between
merger-rate predictions. Yu & Jeffery (2011, Fig. 11) and Zhang et al. (2014,
Fig. 23) show the same quantities, with qualitatively similar, but
quantitatively different, results. This is not the place to explore the
particulars of different BSPS implementations. Rather, the intent of Table 5
is to compare the contributions of He+He and CO+He merger channels and their
parent populations with observed EHe numbers (Table 3 and Figs. 10,12).

Ideally, merger rates should be combined with the lifetimes of post-merger
products to obtain number densities, and adjusted for completeness in order to
compare with observed numbers. However, even without adjustment, Table 5
clearly shows a shortage of predicted WD mergers in the thick disk relative to
other locations when compared with the observed numbers of EHes, RCBs and He-
sdOs (Table 3). Yu & Jeffery (2010, Table 1) used a model in which the thick
disk has 5% the mass of the thin disk, whilst Bensby et al. (2014, Table A.1)
cite a ratio closer to 11%, but this cannot account for all of the shortage in
predicted numbers. The observed numbers suggest the delay-time distribution
for He+He and CO+He WD mergers is too low in the 3 - 10 Gyr range, and hence
that the distribution of initial periods of post-common-envelope double WDs is
too heavily weighted to short periods. Adjusting the common-envelope ejection
efficiency in binary star evolution models to produce more widely separated
post-common-envelope systems could ameliorate the problem. Another explanation
could be that, since EHes are rare but luminous, they are seen at greater
distances in the thick disk than in the more heavily obscured thin disk; is
there a missing population of EHes close to the Galactic plane? We note that
the kick velocity imparted to the survivor of a double white dwarf merger due
to the destruction of one component is only a few km s-1 (Dan et al., 2014)
and will have little overall effect on the population assignments.

It has been proposed that EHes could alternatively follow canonical stellar
evolution as stripped post-AGB stars or as the remnant of a late thermal pulse
in a post-AGB star (Iben et al., 1983). Whilst neither proposal explains the
absence of binaries and the surface chemistries of EHes, it is useful to
compare with the Galactic distribution of other post-AGB stars. A well-defined
sample is provided by the planetary nebulae (PNe). PNe with [WC]-type central
stars could represent a sequence of late thermal pulse stars (Herwig, 2001;
Blöcker, 2001). PNe in the galactic halo are extremely rare (Clegg, 1987, 3
field PNe). Górny et al. (2004) divided the Strasbourg-ESO catalogue of
Galactic PNe (Acker et al., 1992) into 263 bulge objects and 878 disk objects.
The fraction of [WC]-type PN is similar across both populations at 55/263 for
the bulge and 154/878 for the remainder. However, considering selection
effects, Górny et al. (2004) concluded that the fraction of [WR] PNe is
significantly larger in the bulge than in the disk. The San Pedro Mártir
kinematic catalogue (López et al., 2012) divided the Galactic PNe sample into
405 thin disk, 24 thick disk, 17 halo and 155 bulge PNes. Ali et al. (2013)
found roughly equal numbers of PNe in the thin and thick disks. Crudely, the
available data suggest a distribution of $\approx$ 48:27:1:24 for the thin
disk, thick disk, halo and bulge PNe. Similarly, the Galactic population of
AGB stars is dominated by the thin disk and bulge, with a survey of IRAS-
selected AGB stars finding only 15/6039 stars having $|Z|>2.5$ kpc (Jackson et
al., 2002). The larger fraction of halo EHe and other hydrogen-deficient stars
(Table 3) contrasts starkly with the deficit of halo PNe and AGB stars. It
would appear that halo stars massive enough to produce PNe and, by inference,
a late thermal pulse, have long since completed their evolution. In contrast,
double white dwarfs in the halo can continue to produce mergers on a
timescales commensurate with the age of the Galaxy.

##  7 Conclusions

Gaia DR3 has provided parallaxes and proper motions for hundreds of millions
of stars, including extremely rare hydrogen-deficient stars such as R CrB
variables, hydrogen-deficient carbn giants, extreme helium stars (EHes), and
helium-rich hot subdwarfs.

In conjunction with the ongoing SALT survey of hydrogen-deficient stars
(Jeffery et al., 2021) we have updated the list of known EHes; the focus of
this paper has been to examine their Galactic distribution and kinematics, and
hence learn something about their origin, age, and relationship with other
classes of hydrogen-deficient star.

The Gaia DR3 data have been processed with `galpy` to obtain complete orbital
and spatial information for 27 EHes. We have also analysed comparison samples
of 38 RCBs, 8 HdCs, 181 He-sdOs, 135 He-sdOBs and 17 He-sdBs. These data have
been used to classify the parent populations for each star. EHes can clearly
be found in all of the thin disk, the thick disk, the halo and the bulge of
the Galaxy. The same is true, in similar proportion, for RCBs, HdCs and He-
sdOs, but the largest fraction of all four classes are found in the thick
disk. EHes, RCBs and HdCs are luminous and hence have short lifetimes. Their
presence in all four components of the Galaxy implies that their progenitor
lifetimes must cover a wide range from a few to more than 10 Gyr.

We have combined the Gaia DR3 distances with analyses of the EHe spectral
energy distributions to obtain radii and luminosities. From the luminosities,
we find that the EHes can be divided into two luminosity groups, with the
division at $\log L/{\rm L_{\odot}}\approx 3.4$. Thin and thick disk and halo
populations are all represented in both luminosity groups. The existence and
population characteristics of both groups are best understood if:
a) EHes with lower luminosities ($L<2\,500\mbox{\,$\rm L_{\odot}$}$)
correspond to the post-merger evolution of double white dwarf binaries
containing two helium white dwarfs; these are contracting towards the helium
main-sequence where they will be observed as He-sdOs, and b) EHes with higher
luminosities ($L>2\,500\mbox{\,$\rm L_{\odot}$}$) correspond to the post-
merger evolution of double white dwarf binaries containing a carbon-oxygen and
a helium white dwarf; these are contracting at roughly constant luminosity to
eventually become hot white dwarfs. We have also derived an equation for the
bolometric correction appropriate to hydrogen-deficient stars in the effective
temperature range $7\,000-50\,000$ K.

We have briefly discussed the parent populations for both classes of double
white dwarf merger. Binary star population synthesis predicts that double
white dwarfs capable of merging at the current epoch should exist in all
Galactic populations. However, the predictions favour mergers arising from
recent star formation (i.e. thin disk), whereas the statistics favour an older
epoch (i.e. thick disk). Further analyses of the He-sdO, RCB and HdC
populations will be instructive.

## Acknowledgments

APM and PM acknowledge studentships from the Armagh Observatory and
Planetarium which, in turn, is supported by a core grant from the Northern
Ireland Department for Communities. CSJ acknowledges support from the UK
Science and Technology Facilities Council via UKRI Grant No. ST/V000438/1.

This work has made use of data from the European Space Agency (ESA) mission
Gaia666www.cosmos.esa.int/gaia, processed by the Gaia Data Processing and
Analysis Consortium (DPAC)777www.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.

We thank the referee for very helpful comments.

## Data Availability Statement

The astrometric data underlying this article are available in the Gaia Archive
at ESA and can be accessed via the archive website at
gea.esac.esa.int/archive/. All other data are available in the publications
cited.

## References

  * Acker et al. (1992) Acker A., Marcout J., Ochsenbein F., Stenholm B., Tylenda R., Schohn C., 1992, The Strasbourg-ESO Catalogue of Galactic Planetary Nebulae. Parts I, II.
  * Ahmad & Jeffery (2003) Ahmad A., Jeffery C. S., 2003, A&A, 402, 335
  * Ali et al. (2013) Ali A., Ismail H. A., Snaid S., Sabin L., 2013, A&A, 558, A93
  * Bailer-Jones (2015) Bailer-Jones C. A. L., 2015, PASP, 127, 994
  * Bailer-Jones et al. (2021) Bailer-Jones C. A. L., Rybizki J., Fouesneau M., Demleitner M., Andrae R., 2021, AJ, 161, 147
  * Behara & Jeffery (2006) Behara N. T., Jeffery C. S., 2006, A&A, 451, 643
  * Bensby et al. (2014) Bensby T., Feltzing S., Oey M. S., 2014, A&A, 562, A71
  * Bianchi et al. (2017) Bianchi L., Shiao B., Thilker D., 2017, ApJS, 230, 24
  * Bland-Hawthorn & Gerhard (2016) Bland-Hawthorn J., Gerhard O., 2016, ARA&A, 54, 529
  * Blöcker (2001) Blöcker T., 2001, Ap&SS, 275, 1
  * Bovy (2011) Bovy J., 2011, PhD thesis, New York University
  * Bovy (2015) Bovy J., 2015, ApJ, 216, 29
  * Clayton (1996) Clayton G. C., 1996, PASP, 108, 225
  * Clayton (2012) Clayton G. C., 2012, J. American Assoc. Var. Star Observers, 40, 539
  * Clayton et al. (2007) Clayton G. C., Geballe T. R., Herwig F., Fryer C., Asplund M., 2007, ApJ, 662, 1220
  * Clegg (1987) Clegg R. E. S., 1987, in European Southern Observatory Conference and Workshop Proceedings. pp 543–551
  * Crawford et al. (2023) Crawford C. L., et al., 2023, MNRAS, 521, 1674
  * Culpan et al. (2022) Culpan R., Geier S., Reindl N., Pelisoli I., Gentile Fusillo N., Vorontseva A., 2022, A&A, 662, A40
  * Cutri et al. (2003) Cutri R. M., et al., 2003, VizieR Online Data Catalog, 2246
  * Cutri et al. (2021) Cutri R. M., et al., 2021, VizieR Online Data Catalog, p. II/328
  * Dan et al. (2014) Dan M., Rosswog S., Brüggen M., Podsiadlowski P., 2014, MNRAS, 438, 14
  * Denis (2005) Denis C., 2005, VizieR Online Data Catalog, p. B/denis
  * Drilling & Hill (1986) Drilling J. S., Hill P. W., 1986, in Hunger K., Schönberner D., Kameswara Rao N., eds, Astrophysics and Space Science Library Vol. 128, Hydrogen Deficient Stars and Related Objects, Proceedings of IAU Colloq. 87. D. Reidel Publishing Co, Dordrecht, p. 499
  * Drimmel & Poggio (2018) Drimmel R., Poggio E., 2018, Research Notes of the American Astronomical Society, 2, 210
  * Drlica-Wagner et al. (2021) Drlica-Wagner A., et al., 2021, ApJS, 256, 2
  * GRAVITY Collaboration et al. (2021) GRAVITY Collaboration et al., 2021, A&A, 654, A22
  * Gaia Collaboration et al. (2016) Gaia Collaboration et al., 2016, A&A, 595, A1
  * Gaia Collaboration et al. (2023) Gaia Collaboration et al., 2023, A&A, 674, A1
  * Geier (2020) Geier S., 2020, A&A, 635, A193
  * Górny et al. (2004) Górny S. K., Stasińska G., Escudero A. V., Costa R. D. D., 2004, A&A, 427, 231
  * Heber et al. (2018) Heber U., Irrgang A., Schaffenroth J., 2018, Open Astronomy, 27, 35
  * Henden et al. (2015) Henden A. A., Levine S., Terrell D., Welch D. L., 2015, in American Astronomical Society Meeting Abstracts #225. p. 336.16
  * Herwig (2001) Herwig F., 2001, ApJ, 554, L71
  * Høg et al. (2000) Høg E., et al., 2000, A&A, 355, L27
  * Iben (1990) Iben Jr. I., 1990, ApJ, 353, 215
  * Iben & Tutukov (1985) Iben Jr. I., Tutukov A. V., 1985, ApJS, 58, 661
  * Iben et al. (1983) Iben Jr. I., Kaler J. B., Truran J. W., Renzini A., 1983, ApJ, 264, 605
  * Jackson et al. (2002) Jackson T., Ivezić Ž., Knapp G. R., 2002, MNRAS, 337, 749
  * Jeffery (1988) Jeffery C. S., 1988, MNRAS, 235, 1287
  * Jeffery (1996) Jeffery C. S., 1996, in Jeffery C. S., Heber U., eds, Astronomical Society of the Pacific Conference Series Vol. 96, Hydrogen Deficient Stars. p. 152
  * Jeffery (1998) Jeffery C. S., 1998, MNRAS, 294, 391
  * Jeffery (2017) Jeffery C. S., 2017, MNRAS, 470, 3557
  * Jeffery & Hamann (2010) Jeffery C. S., Hamann W. R., 2010, MNRAS, 404, 1698
  * Jeffery et al. (1987) Jeffery C. S., Drilling J. S., Heber U., 1987, MNRAS, 226, 317
  * Jeffery et al. (1996) Jeffery C. S., Heber U., Hill P. W., Dreizler S., Drilling J. S., Lawson W. A., Leuenhagen U., Werner K., 1996, in Jeffery C. S., Heber U., eds, Astron. Soc. Pac. Conf. Ser. Vol. 96, Hydrogen Deficient Stars. Astronomical Society of the Pacific, San Francisco, p. 471
  * Jeffery et al. (1998) Jeffery C. S., Hamill P. J., Harrison P. M., Jeffers S. V., 1998, A&A, 340, 476
  * Jeffery et al. (2001a) Jeffery C. S., Starling R. L. C., Hill P. W., Pollacco D., 2001a, MNRAS, 321, 111
  * Jeffery et al. (2001b) Jeffery C. S., Woolf V. M., Pollacco D. L., 2001b, A&A, 376, 497
  * Jeffery et al. (2011) Jeffery C. S., Karakas A. I., Saio H., 2011, MNRAS, 414, 3599
  * Jeffery et al. (2015) Jeffery C. S., Ahmad A., Naslim N., Kerzendorf W., 2015, MNRAS, 446, 1889
  * Jeffery et al. (2020) Jeffery C. S., Rao N. K., Lambert D. L., 2020, MNRAS, 493, 3565
  * Jeffery et al. (2021) Jeffery C. S., Miszalski B., Snowdon E., 2021, MNRAS, 501, 623
  * Jeffery et al. (2022) Jeffery C. S., Montañés-Rodríguez P., Saio H., 2022, MNRAS, 509, 1940
  * Kawka et al. (2015) Kawka A., Vennes S., O’Toole S., Németh P., Burton D., Kotze E., Buckley D. A. H., 2015, MNRAS, 450, 3514
  * Kilkenny et al. (1999) Kilkenny D., Koen C., Jeffery C. S., Hill N. C., O’Donoghue D., 1999, MNRAS, 310, 1119
  * Kilkenny et al. (2016) Kilkenny D., Worters H. L., O’Donoghue D., Koen C., Koen T., Hambly N., MacGillivray H., Stobie R. S., 2016, MNRAS, 459, 4343
  * Kupfer et al. (2017) Kupfer T., Przybilla N., Heber U., Jeffery C. S., Behara N. T., Butler K., 2017, MNRAS, 471, 877
  * Lang (1974) Lang K. R., 1974, Astrophysical formulae : a compendium for the physicist and astrophysicist. Springer-Verlag: Berlin Heidelberg New York
  * Lawson et al. (1993) Lawson W. A., Kilkenny D., van Wyk F., Marang F., Pollard K., Ryder S. D., 1993, MNRAS, 265, 351
  * Lindegren et al. (2021) Lindegren L., et al., 2021, A&A, 649, A4
  * López et al. (2012) López J. A., Richer M. G., García-Díaz M. T., Clark D. M., Meaburn J., Riesgo H., Steffen W., Lloyd M., 2012, Rev. Mex. Astron. Astrofis., 48, 3
  * Luri et al. (2018) Luri X., et al., 2018, A&A, 616, A9
  * Lynas-Gray et al. (1984) Lynas-Gray A. E., Schönberner D., Hill P. W., Heber U., 1984, MNRAS, 209, 387
  * Ma et al. (2017) Ma X., Hopkins P. F., Wetzel A. R., Kirby E. N., Anglés-Alcázar D., Faucher-Giguère C.-A., Kereš D., Quataert E., 2017, MNRAS, 467, 2430
  * Magnier et al. (2020) Magnier E. A., et al., 2020, ApJS, 251, 6
  * Martin (2019) Martin P., 2019, PhD thesis, Trinity College Dublin
  * Martin & Jeffery (2017) Martin P., Jeffery C. S., 2017, Open Astronomy, 26, 240
  * Martin et al. (2017) Martin P., Jeffery C. S., Naslim N., Woolf V. M., 2017, MNRAS, 467, 68
  * Martins et al. (2005) Martins F., Schaerer D., Hillier D. J., 2005, Astronomy and Astrophysics, 436, 1049
  * McMahon et al. (2013) McMahon R. G., Banerji M., Gonzalez E., Koposov S. E., Bejar V. J., Lodieu N., Rebolo R., VHS Collaboration 2013, The Messenger, 154, 35
  * Miyamoto & Nagai (1975) Miyamoto M., Nagai R., 1975, PASJ, 27, 533
  * Navarro et al. (1996) Navarro J. F., Frenk C. S., White S. D. M., 1996, ApJ, 462, 563
  * Nieva (2013) Nieva M. F., 2013, Astronomy and Astrophysics, 550
  * Onken et al. (2019) Onken C. A., et al., 2019, Publ. Astron. Soc. Australia, 36, e033
  * Pandey & Reddy (2006) Pandey G., Reddy B. E., 2006, MNRAS, 369, 1677
  * Pandey et al. (2001) Pandey G., Kameswara Rao N., Lambert D. L., Jeffery C. S., Asplund M., 2001, MNRAS, 324, 937
  * Pandey et al. (2006) Pandey G., Lambert D. L., Jeffery C. S., Rao N. K., 2006, ApJ, 638, 454
  * Pauli et al. (2003) Pauli E.-M., Napiwotzki R., Altmann M., Heber U., Odenkirchen M., Kerber F., 2003, A&A, 400, 877
  * Przybilla et al. (2021) Przybilla N., Fossati L., Jeffery C. S., 2021, A&A, 654, A119
  * Randall et al. (2015) Randall S. K., Bagnulo S., Ziegerer E., Geier S., Fontaine G., 2015, A&A, 576, A65
  * Rauch (1996) Rauch T., 1996, in C. S. Jeffery & U. Heber ed., Astron. Soc. Pac. Conf. Ser. Vol. 96, Hydrogen Deficient Stars. Astron. Soc. Pac., San Francisco, pp 174–+
  * Reid & Brunthaler (2020) Reid M. J., Brunthaler A., 2020, ApJ, 892, 39
  * Reindl et al. (2014) Reindl N., Rauch T., Werner K., Kruk J. W., Todt H., 2014, A&A, 566, A116
  * Riello et al. (2021) Riello M., et al., 2021, Astronomy and Astrophysics, 649
  * Robin et al. (2003) Robin A. C., Reylé C., Derrière S., Picaud S., 2003, A&A, 409, 523
  * Saio & Jeffery (2000) Saio H., Jeffery C. S., 2000, MNRAS, 313, 671
  * Saio & Jeffery (2002) Saio H., Jeffery C. S., 2002, MNRAS, 333, 121
  * Schlafly et al. (2018) Schlafly E. F., et al., 2018, ApJS, 234, 39
  * Schlafly et al. (2019) Schlafly E. F., Meisner A. M., Green G. M., 2019, ApJS, 240, 30
  * Schlegel et al. (1998) Schlegel D. J., Finkbeiner D. P., Davis M., 1998, ApJ, 500, 525
  * Schwab (2019) Schwab J., 2019, ApJ, 885, 27
  * Snowdon et al. (2022) Snowdon E. J., Scott L. J. A., Jeffery C. S., Woolf V. M., 2022, MNRAS, 516, 794
  * Tisserand et al. (2020) Tisserand P., et al., 2020, A&A, 635, A14
  * Tisserand et al. (2022) Tisserand P., et al., 2022, A&A, 667, A83
  * Tisserand et al. (2023) Tisserand P., Crawford C. L., Soon J., Clayton G. C., Ruiter A. J., Seitenzahl I. R., 2023, arXiv e-prints, p. arXiv:2309.10148
  * Walker & Hill (1985) Walker H. J., Hill P. W., 1985, A&AS, 61, 303
  * Webbink (1984) Webbink R. F., 1984, ApJ, 277, 355
  * Weidemann & Bues (1967) Weidemann V., Bues I., 1967, Z. Astrophys., 67, 415
  * Woolf & Jeffery (2002) Woolf V. M., Jeffery C. S., 2002, A&A, 395, 535
  * Yu & Jeffery (2010) Yu S., Jeffery C. S., 2010, A&A, 521, A85+
  * Yu & Jeffery (2011) Yu S., Jeffery C. S., 2011, MNRAS, 417, 1392
  * Zhang & Jeffery (2012a) Zhang X., Jeffery C. S., 2012a, MNRAS, 419, 452
  * Zhang & Jeffery (2012b) Zhang X., Jeffery C. S., 2012b, MNRAS, 426, L81
  * Zhang et al. (2014) Zhang X., Jeffery C. S., Chen X., Han Z., 2014, MNRAS, 445, 660
  * de Bruijne & Eilers (2012) de Bruijne J. H. J., Eilers A.-C., 2012, A&A, 546, A61

##  Appendix A Secondary Sample

The stars in the secondary sample defined in Section 2, numbering 383, include
members of various classes of hydrogen-deficient stars and are shown in Table
6. The method used to deduce population membership is the same as that for
EHes (Section 4).

Table 6: Orbital parameters and Galactic velocities of the secondary sample grouped by class and sorted as in Table 1. The population membership has the same meaning as in Table 2. Star | $U$ | $V$ | $W$ | $J_{z}$ | $e$ | Ra | Rp | Zmax | pop | class
---|---|---|---|---|---|---|---|---|---|---
|  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ | kpc $\mbox{km}\,\mbox{s}^{-1}$ |  | kpc | kpc | kpc |  |
V* XX Cam | $33.1$ | $238.3$ | $3.9$ | $2227.4$ | $0.10$ | $10.77$ | $8.82$ | $0.07$ | TH | RCB
V* UX Ant | $-257.9$ | $-93.4$ | $85.8$ | $3964.7$ | $0.11$ | $22.98$ | $18.41$ | $7.97$ | H | RCB
V* UW Cen | $-255.2$ | $185.8$ | $16.2$ | $1610.1$ | $0.08$ | $7.68$ | $6.49$ | $1.16$ | H | RCB
V* Y Mus | $-215.5$ | $123.3$ | $-1.5$ | $1155.9$ | $0.29$ | $6.93$ | $3.80$ | $0.78$ | H | RCB
V* V854 Cen | $-10.9$ | $231.3$ | $-119.3$ | $1462.0$ | $0.43$ | $11.53$ | $4.61$ | $3.18$ | TK | RCB
V* Z UMi | $81.5$ | $173.3$ | $29.0$ | $812.6$ | $0.77$ | $15.25$ | $1.96$ | $4.51$ | TK | RCB
V* S Aps | $-117.0$ | $242.1$ | $85.0$ | $1524.9$ | $0.10$ | $7.51$ | $6.19$ | $1.54$ | TK | RCB
V* R CrB | $-50.3$ | $241.7$ | $34.9$ | $1839.0$ | $0.13$ | $9.12$ | $7.09$ | $0.93$ | TH | RCB
V* IO Nor | $-87.6$ | $175.4$ | $16.7$ | $891.5$ | $0.36$ | $5.84$ | $2.75$ | $0.06$ | TK | RCB
V* RT Nor | $-78.0$ | $154.5$ | $-6.6$ | $808.1$ | $0.23$ | $4.70$ | $2.92$ | $0.76$ | TK | RCB
IRAS 16571-5011 | $-105.0$ | $67.5$ | $-117.3$ | $452.3$ | $0.48$ | $5.15$ | $1.79$ | $2.84$ | H | RCB
V* GV Oph | $49.2$ | $150.2$ | $-41.1$ | $445.3$ | $0.46$ | $4.08$ | $1.52$ | $0.98$ | B | RCB
SV* HV 7863 | $-101.4$ | $226.2$ | $77.0$ | $889.6$ | $0.19$ | $4.84$ | $3.29$ | $0.73$ | TK | RCB
ASAS J171710-2043.3 | $-139.2$ | $65.4$ | $-96.1$ | $23.6$ | $0.91$ | $2.38$ | $0.11$ | $1.86$ | B | RCB
V* V2552 Oph | $-21.0$ | $122.1$ | $-152.0$ | $543.7$ | $0.40$ | $4.75$ | $2.03$ | $1.76$ | B | RCB
Terz V 2637 | $-112.4$ | $37.0$ | $60.5$ | $-56.3$ | $0.49$ | $1.12$ | $0.39$ | $0.42$ | B | RCB
V* V653 Sco | $-246.9$ | $-40.6$ | $99.1$ | $233.1$ | $0.92$ | $13.08$ | $0.51$ | $2.55$ | H | RCB
V* WX CrA | $35.0$ | $88.6$ | $-126.7$ | $210.3$ | $0.46$ | $2.64$ | $0.97$ | $1.46$ | B | RCB
V* VZ Sgr | $459.0$ | $159.2$ | $175.7$ | $171.9$ | $0.78$ | $4.64$ | $0.58$ | $2.46$ | B | RCB
V* RS Tel | $-35.3$ | $72.5$ | $9.7$ | $194.7$ | $0.60$ | $3.60$ | $0.91$ | $1.41$ | B | RCB
V* FH Sct | $14.9$ | $267.1$ | $-106.5$ | $876.5$ | $0.12$ | $4.66$ | $3.68$ | $1.34$ | TK | RCB
V* V CrA | $-5.1$ | $338.5$ | $30.3$ | $3660.8$ | $0.53$ | $35.04$ | $10.85$ | $3.03$ | TK | RCB
V* SV Sge | $25.6$ | $239.9$ | $34.1$ | $1534.7$ | $0.13$ | $7.47$ | $5.73$ | $0.44$ | TH | RCB
V* V1157 Sgr | $-1.7$ | $260.5$ | $34.3$ | $1180.9$ | $0.06$ | $5.52$ | $4.89$ | $1.01$ | TH | RCB
V* RY Sgr | $72.6$ | $252.5$ | $-55.1$ | $1772.2$ | $0.20$ | $9.64$ | $6.41$ | $1.21$ | TK | RCB
V* ES Aql | $-53.1$ | $180.3$ | $72.4$ | $536.9$ | $0.53$ | $5.33$ | $1.66$ | $1.22$ | TK | RCB
V* V482 Cyg | $-14.5$ | $215.0$ | $-18.3$ | $1595.6$ | $0.15$ | $7.95$ | $5.84$ | $0.36$ | TH | RCB
V* UV Cas | $52.4$ | $220.3$ | $4.5$ | $2143.8$ | $0.17$ | $11.17$ | $7.92$ | $0.06$ | TH | RCB
IRAS 00450+7401 | $40.0$ | $170.7$ | $-18.4$ | $3629.5$ | $0.20$ | $21.60$ | $14.50$ | $3.90$ | TK | RCB
V* W Men | $-53.1$ | $55.1$ | $-142.1$ | $425.4$ | $0.62$ | $9.60$ | $2.25$ | $7.98$ | H | RCB
HD 137613 | $-80.8$ | $197.6$ | $5.2$ | $1351.8$ | $0.30$ | $8.09$ | $4.37$ | $0.63$ | TH | HdC
C* 2277 | $-185.7$ | $91.5$ | $50.0$ | $536.6$ | $0.38$ | $4.14$ | $1.87$ | $0.90$ | H | HdC
SOPS IV e-67 | $-17.7$ | $120.0$ | $-123.5$ | $638.4$ | $0.44$ | $6.25$ | $2.43$ | $3.20$ | H | HdC
V* LV TrA | $-33.4$ | $232.1$ | $40.3$ | $1504.5$ | $0.09$ | $7.01$ | $5.89$ | $0.61$ | TH | HdC
V* AC Ser | $-46.8$ | $156.2$ | $19.1$ | $-45.1$ | $0.88$ | $3.07$ | $0.20$ | $1.99$ | H | RCB
UCAC4 325-115052 | $-126.3$ | $283.5$ | $25.9$ | $2899.1$ | $0.50$ | $25.39$ | $8.46$ | $1.10$ | TK | RCB
2MASS J17485129-3306172 | $108.8$ | $336.9$ | $38.3$ | $3662.9$ | $0.60$ | $41.20$ | $10.14$ | $2.63$ | TK | RCB
2MASS J17510712-2423573 | $123.2$ | $-89.0$ | $54.8$ | $-98.5$ | $0.28$ | $1.05$ | $0.59$ | $0.23$ | B | RCB
IRAS 18029-1513 | $-192.8$ | $283.6$ | $33.0$ | $2015.0$ | $0.56$ | $18.85$ | $5.37$ | $0.79$ | H | RCB
ATO J277.4326-19.0462 | $-45.1$ | $266.9$ | $17.1$ | $2507.8$ | $0.21$ | $14.00$ | $9.15$ | $0.39$ | TH | RCB
HD 173409 | $109.3$ | $272.8$ | $-55.3$ | $4788.9$ | $0.45$ | $41.82$ | $16.05$ | $8.14$ | TK | HdC
V* V4152 Sgr | $-52.4$ | $172.9$ | $-34.0$ | $1024.8$ | $0.32$ | $6.48$ | $3.31$ | $0.81$ | TH | RCB
HD 182040 | $73.0$ | $236.6$ | $-7.8$ | $1810.5$ | $0.18$ | $9.33$ | $6.53$ | $0.21$ | TH | HdC
CD-35 13668 | $54.1$ | $360.8$ | $9.2$ | $4427.0$ | $0.66$ | $58.95$ | $12.18$ | $7.87$ | TK | HdC
C* 2891 | $37.0$ | $247.9$ | $-34.2$ | $2386.5$ | $0.07$ | $13.13$ | $11.35$ | $5.35$ | TK | HdC
Ton S 137 | $-17.1$ | $141.7$ | $38.9$ | $1100.9$ | $0.44$ | $8.28$ | $3.23$ | $1.06$ | TK | He-sdO
PG 0016+151 | $-31.8$ | $239.8$ | $-28.7$ | $2113.6$ | $0.12$ | $10.91$ | $8.61$ | $2.21$ | TK | He-sdO
LAMOST J001954.03+510505.6 | $60.2$ | $226.3$ | $35.0$ | $1899.2$ | $0.26$ | $10.95$ | $6.50$ | $0.80$ | TH | He-sdO
PB 6221 | $-87.2$ | $122.3$ | $-8.9$ | $1271.5$ | $0.51$ | $13.30$ | $4.36$ | $6.67$ | H | He-sdO
LAMOST J010223.99+485245.3 | $-28.6$ | $220.1$ | $13.8$ | $2768.5$ | $0.17$ | $15.14$ | $10.78$ | $1.62$ | TK | He-sdO
HS 0110+3222 | $-8.4$ | $118.7$ | $-57.3$ | $1185.0$ | $0.50$ | $11.06$ | $3.68$ | $3.89$ | TK | He-sdO
PG 0113+259 | $59.3$ | $231.1$ | $-14.7$ | $2015.9$ | $0.20$ | $10.89$ | $7.33$ | $0.90$ | TH | He-sdO
PB 6433 | $46.0$ | $125.7$ | $-15.2$ | $1157.7$ | $0.49$ | $9.97$ | $3.45$ | $2.59$ | TK | He-sdO
GALEX J012630.2+503946 | $14.2$ | $253.2$ | $25.9$ | $2804.5$ | $0.17$ | $15.26$ | $10.93$ | $1.42$ | TK | He-sdO
FBS 0132+370 | $18.5$ | $265.3$ | $-36.3$ | $2442.2$ | $0.18$ | $13.32$ | $9.28$ | $1.44$ | TK | He-sdO
LAMOST J015012.51+254747.2 | $-99.9$ | $66.7$ | $76.5$ | $631.0$ | $0.77$ | $12.05$ | $1.59$ | $4.23$ | H | He-sdO
Feige 19 | $42.5$ | $253.3$ | $10.1$ | $2201.5$ | $0.16$ | $11.47$ | $8.38$ | $0.98$ | TH | He-sdO
Star | $U$ | $V$ | $W$ | $J_{z}$ | $e$ | Ra | Rp | Zmax | pop | class
---|---|---|---|---|---|---|---|---|---|---
|  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ | kpc $\mbox{km}\,\mbox{s}^{-1}$ |  | kpc | kpc | kpc |  |
FBS 0212+385 | $31.4$ | $262.3$ | $-39.6$ | $2192.0$ | $0.16$ | $11.50$ | $8.27$ | $0.91$ | TH | He-sdO
LAMOST J021703.37+544752.1 | $-51.1$ | $195.3$ | $17.6$ | $2086.1$ | $0.25$ | $11.93$ | $7.22$ | $0.52$ | TH | He-sdO
LAMOST J023851.64+432309.5 | $-22.7$ | $121.4$ | $1.4$ | $1146.3$ | $0.54$ | $10.11$ | $3.02$ | $0.55$ | TK | He-sdO
Feige 26 | $-26.6$ | $216.3$ | $99.0$ | $2036.4$ | $0.17$ | $11.86$ | $8.46$ | $4.10$ | TK | He-sdO
PG 0310+149 | $37.6$ | $246.0$ | $8.4$ | $2348.2$ | $0.13$ | $12.01$ | $9.27$ | $1.20$ | TH | He-sdO
UCAC4 551-007425 | $27.5$ | $203.3$ | $21.6$ | $2040.6$ | $0.11$ | $10.02$ | $8.11$ | $1.07$ | TH | He-sdO
EC 03505-6929 | $-41.8$ | $244.4$ | $51.0$ | $1921.5$ | $0.14$ | $9.99$ | $7.47$ | $1.65$ | TK | He-sdO
HE 0414-5429 | $-16.7$ | $255.6$ | $16.6$ | $2148.8$ | $0.13$ | $11.09$ | $8.50$ | $1.69$ | TK | He-sdO
GALEX J041536.0+253857 | $-65.2$ | $250.4$ | $31.8$ | $2524.7$ | $0.24$ | $14.87$ | $9.06$ | $1.29$ | TK | He-sdO
EC 04253-8213 | $-52.4$ | $252.6$ | $37.4$ | $1878.7$ | $0.18$ | $10.19$ | $7.07$ | $1.76$ | TK | He-sdO
GALEX J042542.2-060934 | $-12.0$ | $232.3$ | $-8.0$ | $2343.0$ | $0.05$ | $11.13$ | $10.08$ | $1.58$ | TK | He-sdO
BPS CS 22182-0037 | $1.8$ | $288.5$ | $39.1$ | $2554.4$ | $0.28$ | $15.91$ | $9.00$ | $2.05$ | TK | He-sdO
UCAC4 434-007650 | $-55.1$ | $277.4$ | $47.8$ | $2657.3$ | $0.32$ | $17.51$ | $9.11$ | $2.29$ | TK | He-sdO
GALEX J050231.9+091835 | $-11.0$ | $199.7$ | $-0.1$ | $2182.0$ | $0.15$ | $11.26$ | $8.34$ | $0.91$ | TH | He-sdO
GALEX J050325.3+641909 | $-32.1$ | $214.2$ | $-7.3$ | $2362.5$ | $0.14$ | $12.14$ | $9.20$ | $0.92$ | TH | He-sdO
GALEX J050650.6+193055 | $-44.5$ | $198.0$ | $20.2$ | $1980.6$ | $0.24$ | $11.27$ | $6.84$ | $0.62$ | TH | He-sdO
GALEX J051157.7+235610 | $-6.3$ | $172.0$ | $38.5$ | $2004.2$ | $0.24$ | $11.55$ | $7.12$ | $1.52$ | TK | He-sdO
UCAC4 535-014568 | $41.8$ | $218.6$ | $27.0$ | $2194.4$ | $0.05$ | $10.18$ | $9.17$ | $0.74$ | TH | He-sdO
UCAC4 630-027754 | $18.8$ | $191.9$ | $13.8$ | $1881.4$ | $0.16$ | $9.52$ | $6.96$ | $0.32$ | TH | He-sdO
KPD 0552+1903 | $-31.6$ | $180.9$ | $-15.1$ | $1849.1$ | $0.27$ | $10.74$ | $6.17$ | $0.29$ | TH | He-sdO
LAMOST J055814.17+464025.3 | $13.9$ | $231.4$ | $2.0$ | $2403.6$ | $0.03$ | $11.01$ | $10.28$ | $0.50$ | TH | He-sdO
UCAC4 498-020345 | $-110.5$ | $264.8$ | $27.7$ | $2580.6$ | $0.44$ | $20.08$ | $7.80$ | $1.03$ | TK | He-sdO
LAMOST J060806.00+461001.4 | $19.8$ | $190.8$ | $2.5$ | $2763.9$ | $0.12$ | $14.32$ | $11.18$ | $1.37$ | TK | He-sdO
GALEX J061205.9+473125 | $-1.0$ | $165.8$ | $30.7$ | $2105.3$ | $0.22$ | $12.07$ | $7.66$ | $1.83$ | TK | He-sdO
LAMOST J061924.34+234639.8 | $-43.4$ | $248.6$ | $-22.6$ | $2560.4$ | $0.08$ | $12.52$ | $10.56$ | $0.85$ | TH | He-sdO
UCAC4 555-028073 | $-1.6$ | $243.0$ | $18.7$ | $2803.0$ | $0.10$ | $14.08$ | $11.48$ | $0.69$ | TH | He-sdO
LAMOST J062812.03+374234.5 | $-21.0$ | $204.2$ | $-11.7$ | $2670.9$ | $0.13$ | $13.90$ | $10.64$ | $1.21$ | TK | He-sdO
KUV 06290+2813 | $25.1$ | $201.1$ | $41.7$ | $2145.4$ | $0.08$ | $10.36$ | $8.89$ | $1.41$ | TK | He-sdO
UCAC4 566-028577 | $-33.2$ | $139.4$ | $-50.0$ | $1339.2$ | $0.45$ | $10.31$ | $3.94$ | $1.65$ | TK | He-sdO
GALEX J063452.6+371110 | $37.5$ | $151.9$ | $6.2$ | $2584.1$ | $0.28$ | $16.06$ | $9.10$ | $1.95$ | TK | He-sdO
TYC 1337-283-1 | $-61.4$ | $253.2$ | $3.3$ | $2172.1$ | $0.23$ | $12.20$ | $7.62$ | $0.10$ | TH | He-sdO
FBS 0649+403 | $102.4$ | $210.8$ | $40.8$ | $2116.4$ | $0.28$ | $12.89$ | $7.25$ | $1.47$ | TK | He-sdO
SDSS J065256.41+120300.8 | $-76.0$ | $254.4$ | $-49.7$ | $3846.2$ | $0.12$ | $21.60$ | $17.03$ | $5.60$ | TK | He-sdO
HS 0657+5333 | $174.2$ | $22.7$ | $57.4$ | $583.3$ | $0.80$ | $12.53$ | $1.41$ | $3.18$ | H | He-sdO
2MASS J07024049+1147418 | $-8.0$ | $213.0$ | $4.1$ | $2309.7$ | $0.09$ | $11.18$ | $9.28$ | $0.44$ | TH | He-sdO
LAMOST J070801.51+103510.1 | $-4.9$ | $247.2$ | $3.9$ | $2795.5$ | $0.09$ | $13.86$ | $11.59$ | $0.72$ | TH | He-sdO
GALEX J071503.2+750140 | $-119.6$ | $-106.2$ | $-21.6$ | $-671.8$ | $0.85$ | $18.55$ | $1.55$ | $4.33$ | H | He-sdO
GALEX J072516.9+283831 | $8.6$ | $263.1$ | $18.9$ | $2391.6$ | $0.13$ | $12.20$ | $9.31$ | $0.64$ | TH | He-sdO
LAMOST J072628.27+083747.9 | $-105.9$ | $104.5$ | $-72.4$ | $1413.5$ | $0.60$ | $17.36$ | $4.32$ | $7.88$ | H | He-sdO
LAMOST J072835.11+280239.1 | $2.0$ | $232.7$ | $15.1$ | $2604.5$ | $0.04$ | $12.24$ | $11.39$ | $1.34$ | TK | He-sdO
UCAC4 453-037143 | $-15.8$ | $198.9$ | $-28.7$ | $2019.5$ | $0.33$ | $13.51$ | $6.79$ | $2.69$ | TK | He-sdO
LAMOST J073409.31+523028.6 | $-22.0$ | $-92.3$ | $-3.5$ | $-278.4$ | $0.91$ | $12.27$ | $0.58$ | $1.56$ | H | He-sdO
HS 0735+4026 | $22.5$ | $171.8$ | $22.9$ | $2192.6$ | $0.17$ | $11.93$ | $8.53$ | $2.24$ | TK | He-sdO
HS 0736+3953 | $38.6$ | $123.5$ | $32.0$ | $2758.5$ | $0.26$ | $18.80$ | $11.02$ | $7.14$ | TK | He-sdO
FBS 0742+337 | $-54.6$ | $275.9$ | $-30.3$ | $2641.5$ | $0.11$ | $13.74$ | $11.03$ | $2.48$ | TK | He-sdO
GALEX J075234.2+161604 | $-34.7$ | $244.2$ | $-2.7$ | $2220.4$ | $0.07$ | $10.50$ | $9.08$ | $0.60$ | TH | He-sdO
GALEX J075250.0+305936 | $40.4$ | $25.9$ | $11.5$ | $755.8$ | $0.75$ | $12.84$ | $1.85$ | $3.32$ | TK | He-sdO
BD+75 325 | $-22.6$ | $243.7$ | $0.8$ | $2018.3$ | $0.10$ | $9.60$ | $7.92$ | $0.11$ | TH | He-sdO
GALEX J082751.0+410925 | $-17.7$ | $322.1$ | $12.8$ | $1759.6$ | $0.39$ | $13.25$ | $5.85$ | $3.90$ | TK | He-sdO
$\rm[CW83]\,0832-01$ | $10.8$ | $235.9$ | $26.3$ | $2109.4$ | $0.11$ | $10.35$ | $8.29$ | $0.68$ | TH | He-sdO
PG 0838+133 | $-69.2$ | $253.4$ | $-22.5$ | $2230.2$ | $0.19$ | $12.10$ | $8.28$ | $1.13$ | TH | He-sdO
US 1993 | $4.1$ | $58.9$ | $9.3$ | $609.0$ | $0.76$ | $10.65$ | $1.46$ | $1.97$ | TK | He-sdO
GALEX J090253.0+073533 | $25.4$ | $-32.3$ | $-17.4$ | $306.3$ | $0.91$ | $16.08$ | $0.75$ | $6.47$ | H | He-sdO
$\rm[CW83]\,0904-02$ | $-84.0$ | $315.3$ | $-18.1$ | $2189.9$ | $0.17$ | $11.69$ | $8.26$ | $1.24$ | TK | He-sdO
PG 0912+119 | $-71.9$ | $118.9$ | $-16.5$ | $924.8$ | $0.62$ | $10.34$ | $2.45$ | $2.21$ | TK | He-sdO
PG 0914-037 | $-166.9$ | $152.7$ | $-71.1$ | $971.9$ | $0.47$ | $9.93$ | $3.55$ | $5.26$ | H | He-sdO
Ton 414 | $-4.0$ | $176.0$ | $4.5$ | $1850.6$ | $0.25$ | $10.77$ | $6.40$ | $1.26$ | TK | He-sdO
SBSS 0934+495 | $13.5$ | $137.4$ | $31.6$ | $1715.3$ | $0.33$ | $12.29$ | $6.17$ | $4.39$ | TK | He-sdO
TYC 4895-599-1 | $-98.9$ | $292.6$ | $28.9$ | $1856.0$ | $0.35$ | $12.25$ | $5.93$ | $1.37$ | TK | He-sdO
GD 300 | $-109.9$ | $99.8$ | $-0.1$ | $-405.3$ | $0.84$ | $11.18$ | $0.96$ | $2.55$ | TK | He-sdO
GALEX J095601.7+091138 | $-54.8$ | $217.1$ | $-7.9$ | $1887.0$ | $0.17$ | $10.00$ | $7.06$ | $1.33$ | TK | He-sdO
GALEX J095648.5+142241 | $-124.9$ | $265.4$ | $-48.6$ | $1922.5$ | $0.06$ | $9.53$ | $8.52$ | $2.68$ | TK | He-sdO
Ton 1137 | $-73.5$ | $204.0$ | $-4.3$ | $1463.8$ | $0.36$ | $10.25$ | $4.84$ | $2.65$ | TK | He-sdO
PG 1034+001 | $-51.8$ | $277.8$ | $59.9$ | $1725.4$ | $0.28$ | $10.15$ | $5.70$ | $0.54$ | TH | He-sdO
GALEX J104033.8+562206 | $-7.5$ | $188.4$ | $33.6$ | $1665.4$ | $0.26$ | $10.20$ | $5.96$ | $2.49$ | TK | He-sdO
PG 1038+510 | $-128.7$ | $205.8$ | $108.0$ | $-250.5$ | $0.95$ | $21.02$ | $0.50$ | $3.76$ | TK | He-sdO
Star | $U$ | $V$ | $W$ | $J_{z}$ | $e$ | Ra | Rp | Zmax | pop | class
---|---|---|---|---|---|---|---|---|---|---
|  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ | kpc $\mbox{km}\,\mbox{s}^{-1}$ |  | kpc | kpc | kpc |  |
GALEX J105759.3+470307 | $-1.0$ | $215.2$ | $16.4$ | $2121.7$ | $0.05$ | $10.45$ | $9.46$ | $2.76$ | TK | He-sdO
SDSS J110215.45+024034.1 | $-138.1$ | $100.0$ | $-60.3$ | $832.6$ | $0.68$ | $12.44$ | $2.34$ | $5.17$ | H | He-sdO
PG 1102+499 | $-53.9$ | $210.7$ | $-19.6$ | $1627.2$ | $0.23$ | $9.37$ | $5.91$ | $1.96$ | TK | He-sdO
CBS 432 | $-95.0$ | $193.2$ | $29.6$ | $1141.1$ | $0.50$ | $10.90$ | $3.62$ | $4.20$ | TK | He-sdO
PG 1125-055 | $-224.4$ | $5.5$ | $172.6$ | $-782.5$ | $0.61$ | $10.10$ | $2.48$ | $4.83$ | H | He-sdO
PG 1134+463 | $-88.8$ | $227.3$ | $35.2$ | $1216.1$ | $0.46$ | $9.79$ | $3.59$ | $1.97$ | TK | He-sdO
HS 1203+6650 | $-17.9$ | $249.0$ | $41.6$ | $1496.1$ | $0.45$ | $11.99$ | $4.57$ | $2.95$ | TK | He-sdO
GALEX J123808.7+053318 | $-191.3$ | $173.9$ | $5.3$ | $830.5$ | $0.51$ | $8.66$ | $2.82$ | $4.08$ | H | He-sdO
$\rm[BFS85]\,12h30\,2B1$ | $-100.4$ | $209.5$ | $-4.7$ | $1499.3$ | $0.24$ | $10.23$ | $6.21$ | $4.75$ | H | He-sdO
Ton 102 | $-11.2$ | $208.5$ | $93.8$ | $1857.0$ | $0.11$ | $10.04$ | $8.03$ | $3.40$ | TK | He-sdO
Ton 109 | $-233.6$ | $126.0$ | $-94.8$ | $240.0$ | $0.56$ | $9.33$ | $2.63$ | $8.93$ | H | He-sdO
PG 1249+762 | $-9.1$ | $232.3$ | $50.7$ | $1541.8$ | $0.37$ | $10.58$ | $4.86$ | $1.75$ | TK | He-sdO
SDSS J125301.62+394622.2 | $-86.0$ | $64.9$ | $-111.5$ | $905.1$ | $0.71$ | $14.29$ | $2.39$ | $5.30$ | H | He-sdO
PG 1251+019 | $-109.8$ | $-11.9$ | $-143.2$ | $118.4$ | $0.97$ | $15.16$ | $0.27$ | $6.56$ | H | He-sdO
PB 4363 | $-306.5$ | $207.1$ | $81.0$ | $837.0$ | $0.46$ | $10.95$ | $4.04$ | $8.13$ | H | He-sdO
Ton 143 | $-108.5$ | $360.2$ | $83.2$ | $1658.6$ | $0.55$ | $17.39$ | $5.00$ | $6.37$ | H | He-sdO
PG 1316+212 | $-249.7$ | $106.6$ | $-18.8$ | $-165.9$ | $0.88$ | $8.40$ | $0.53$ | $4.58$ | H | He-sdO
PG 1318+062 | $-110.3$ | $304.4$ | $86.9$ | $1636.3$ | $0.31$ | $10.48$ | $5.57$ | $2.27$ | TK | He-sdO
PB 166 | $-36.8$ | $267.3$ | $-0.5$ | $1694.9$ | $0.25$ | $9.75$ | $5.81$ | $1.07$ | TH | He-sdO
PG 1325+054 | $-48.9$ | $310.7$ | $37.5$ | $1967.9$ | $0.25$ | $11.56$ | $6.97$ | $1.79$ | TK | He-sdO
GALEX J134738.3+043427 | $-165.8$ | $181.7$ | $29.6$ | $767.8$ | $0.40$ | $8.00$ | $3.44$ | $5.26$ | H | He-sdO
CD-46 8926 | $-3.0$ | $321.3$ | $-45.4$ | $2035.4$ | $0.43$ | $15.59$ | $6.28$ | $2.77$ | TK | He-sdO
SDSS J135707.35+010454.4 | $-279.3$ | $115.0$ | $49.2$ | $81.3$ | $0.90$ | $7.67$ | $0.41$ | $5.74$ | H | He-sdO
PG 1401+289 | $-94.2$ | $150.3$ | $-64.2$ | $875.9$ | $0.50$ | $8.52$ | $2.81$ | $3.32$ | TK | He-sdO
GALEX J140715.4+033147 | $-191.9$ | $207.7$ | $73.5$ | $678.0$ | $0.51$ | $7.56$ | $2.45$ | $3.95$ | H | He-sdO
PG 1412+613 | $-20.8$ | $202.4$ | $-20.0$ | $1692.1$ | $0.17$ | $8.97$ | $6.42$ | $1.61$ | TK | He-sdO
FBS 1412+004 | $-173.7$ | $111.0$ | $-12.9$ | $377.6$ | $0.69$ | $7.61$ | $1.39$ | $4.87$ | H | He-sdO
PG 1427+196 | $-43.2$ | $228.1$ | $17.2$ | $1609.9$ | $0.11$ | $7.97$ | $6.37$ | $1.36$ | TK | He-sdO
PG 1442+346 | $-23.0$ | $173.7$ | $-90.5$ | $945.6$ | $0.32$ | $8.26$ | $4.27$ | $5.12$ | H | He-sdO
PG 1444+076 | $-414.9$ | $31.7$ | $80.7$ | $-1228.6$ | $0.32$ | $7.83$ | $4.08$ | $1.50$ | H | He-sdO
GALEX J144738.3+615033 | $-10.1$ | $232.4$ | $77.2$ | $1724.5$ | $0.22$ | $11.22$ | $7.11$ | $4.82$ | TK | He-sdO
GALEX J145134.2+252221 | $18.3$ | $207.9$ | $-91.2$ | $1389.4$ | $0.19$ | $8.58$ | $5.87$ | $3.67$ | TK | He-sdO
PG 1502+129 | $-8.5$ | $270.8$ | $22.6$ | $1284.1$ | $0.38$ | $9.71$ | $4.37$ | $3.31$ | TK | He-sdO
PG 1507-015 | $-63.9$ | $259.7$ | $62.1$ | $1401.8$ | $0.12$ | $7.28$ | $5.72$ | $1.96$ | TK | He-sdO
GALEX J151415.6-012925 | $-164.2$ | $180.1$ | $56.2$ | $587.4$ | $0.60$ | $6.79$ | $1.72$ | $1.83$ | TK | He-sdO
PG 1528+029 | $-87.7$ | $229.7$ | $56.9$ | $1141.2$ | $0.26$ | $6.96$ | $4.08$ | $1.75$ | TK | He-sdO
PG 1534-018 | $66.6$ | $252.0$ | $-53.4$ | $1957.4$ | $0.26$ | $11.91$ | $6.92$ | $2.28$ | TK | He-sdO
PG 1539+442 | $-118.9$ | $218.6$ | $72.4$ | $1315.3$ | $0.24$ | $9.33$ | $5.69$ | $4.84$ | H | He-sdO
PG 1539+043 | $-180.0$ | $254.6$ | $137.5$ | $-92.0$ | $0.81$ | $6.65$ | $0.69$ | $6.01$ | H | He-sdO
SDSS J154801.15-023452.3 | $-130.2$ | $130.0$ | $16.7$ | $-256.4$ | $0.47$ | $6.30$ | $2.27$ | $5.79$ | H | He-sdO
PG 1554+222 | $-11.1$ | $221.5$ | $13.9$ | $1288.8$ | $0.32$ | $8.10$ | $4.21$ | $1.25$ | TK | He-sdO
PG 1555+504 | $28.5$ | $254.5$ | $99.6$ | $1344.0$ | $0.49$ | $11.86$ | $4.11$ | $3.50$ | TK | He-sdO
PG 1555+489 | $-54.1$ | $222.6$ | $76.6$ | $1202.2$ | $0.34$ | $8.63$ | $4.25$ | $3.03$ | TK | He-sdO
GALEX J160053.0-044132 | $-98.6$ | $195.8$ | $44.1$ | $874.7$ | $0.47$ | $7.11$ | $2.53$ | $0.95$ | TK | He-sdO
GALEX J160152.8-040949 | $84.3$ | $133.8$ | $-205.8$ | $1089.9$ | $0.53$ | $12.63$ | $3.85$ | $7.02$ | H | He-sdO
PG 1607+228 | $-37.3$ | $224.1$ | $25.7$ | $1299.7$ | $0.13$ | $7.08$ | $5.41$ | $2.26$ | TK | He-sdO
PG 1610+043 | $-65.6$ | $227.4$ | $44.9$ | $1157.1$ | $0.19$ | $6.53$ | $4.40$ | $1.70$ | TK | He-sdO
PG 1611+041 | $-136.3$ | $176.0$ | $24.4$ | $792.2$ | $0.47$ | $6.88$ | $2.46$ | $1.84$ | TK | He-sdO
GALEX J161627.1-002933 | $-81.1$ | $217.9$ | $32.2$ | $1101.4$ | $0.20$ | $6.38$ | $4.22$ | $1.84$ | TK | He-sdO
Ton 257 | $-182.5$ | $172.3$ | $97.8$ | $113.4$ | $0.92$ | $7.20$ | $0.31$ | $3.35$ | H | He-sdO
GALEX J162411.5+312252 | $74.4$ | $166.3$ | $80.7$ | $-234.8$ | $0.87$ | $11.16$ | $0.81$ | $8.21$ | H | He-sdO
PG 1624+382 | $-27.9$ | $241.8$ | $53.5$ | $1561.5$ | $0.12$ | $7.99$ | $6.24$ | $1.78$ | TK | He-sdO
GALEX J162626.2+333314 | $19.7$ | $231.4$ | $81.6$ | $920.2$ | $0.51$ | $9.13$ | $2.96$ | $3.70$ | TK | He-sdO
PG 1624+085 | $-37.5$ | $198.8$ | $-2.4$ | $1224.5$ | $0.27$ | $7.22$ | $4.11$ | $0.96$ | TH | He-sdO
PG 1625-034 | $42.3$ | $232.6$ | $6.3$ | $1342.2$ | $0.32$ | $8.37$ | $4.35$ | $1.09$ | TH | He-sdO
GALEX J170045.5+604307 | $49.1$ | $246.5$ | $82.8$ | $2065.0$ | $0.30$ | $15.11$ | $8.10$ | $6.62$ | TK | He-sdO
PG 1700+198 | $-88.5$ | $240.3$ | $103.5$ | $1124.4$ | $0.26$ | $7.13$ | $4.15$ | $2.27$ | TK | He-sdO
PG 1703+355 | $2.5$ | $241.8$ | $89.4$ | $1356.4$ | $0.32$ | $8.92$ | $4.63$ | $2.26$ | TK | He-sdO
GALEX J171720.5+094131 | $-37.6$ | $126.5$ | $-43.5$ | $576.8$ | $0.57$ | $6.33$ | $1.73$ | $1.70$ | TK | He-sdO
GALEX J174516.3+244348 | $-76.3$ | $120.9$ | $-109.2$ | $717.6$ | $0.53$ | $8.10$ | $2.49$ | $4.01$ | H | He-sdO
GALEX J175548.5+501210 | $63.6$ | $200.6$ | $8.0$ | $1549.3$ | $0.30$ | $9.29$ | $4.96$ | $0.33$ | TH | He-sdO
LAMOST J181712.86+053202.7 | $-41.7$ | $205.8$ | $12.5$ | $1010.3$ | $0.27$ | $5.92$ | $3.39$ | $0.61$ | TH | He-sdO
GALEX J182208.6+103745 | $72.0$ | $281.3$ | $17.8$ | $1217.4$ | $0.18$ | $6.79$ | $4.71$ | $1.85$ | TK | He-sdO
UCAC4 687-068720 | $14.2$ | $277.3$ | $9.7$ | $2210.4$ | $0.19$ | $11.90$ | $8.16$ | $0.82$ | TH | He-sdO
LAMOST J193312.83+380154.6 | $-48.6$ | $237.2$ | $21.4$ | $1670.1$ | $0.16$ | $8.54$ | $6.17$ | $0.80$ | TH | He-sdO
BPS CS 22896-0128 | $43.1$ | $213.0$ | $42.1$ | $1115.5$ | $0.12$ | $6.01$ | $4.69$ | $1.98$ | TK | He-sdO
Star | $U$ | $V$ | $W$ | $J_{z}$ | $e$ | Ra | Rp | Zmax | pop | class
---|---|---|---|---|---|---|---|---|---|---
|  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ | kpc $\mbox{km}\,\mbox{s}^{-1}$ |  | kpc | kpc | kpc |  |
LAMOST J202546.17+092158.7 | $-29.2$ | $221.5$ | $56.6$ | $1173.3$ | $0.23$ | $6.97$ | $4.34$ | $1.88$ | TK | He-sdO
LAMOST J202610.56+055413.9 | $22.0$ | $194.3$ | $-8.6$ | $1361.8$ | $0.21$ | $7.28$ | $4.77$ | $0.65$ | TH | He-sdO
LAMOST J210936.02+362337.5 | $-41.3$ | $227.9$ | $4.5$ | $1892.2$ | $0.15$ | $9.56$ | $7.08$ | $0.56$ | TH | He-sdO
HS 2108+1413 | $-39.0$ | $273.8$ | $-15.9$ | $2108.2$ | $0.20$ | $11.41$ | $7.64$ | $0.66$ | TH | He-sdO
PG 2110+001 | $-103.0$ | $206.2$ | $25.2$ | $1298.7$ | $0.34$ | $8.62$ | $4.24$ | $1.73$ | TK | He-sdO
LAMOST J211624.57+132338.7 | $99.8$ | $19.5$ | $28.2$ | $209.4$ | $0.88$ | $11.70$ | $0.73$ | $8.23$ | H | He-sdO
GALEX J211832.4+233416 | $-48.1$ | $218.1$ | $9.3$ | $1652.4$ | $0.18$ | $8.60$ | $5.95$ | $0.63$ | TH | He-sdO
PG 2116+008 | $35.9$ | $224.3$ | $-8.2$ | $1568.9$ | $0.11$ | $7.86$ | $6.25$ | $1.54$ | TK | He-sdO
GALEX J211925.9+202155 | $24.5$ | $128.7$ | $-73.7$ | $1014.1$ | $0.42$ | $8.00$ | $3.28$ | $2.40$ | TK | He-sdO
GALEX J212356.6+153323 | $63.0$ | $90.5$ | $-42.9$ | $718.7$ | $0.61$ | $8.05$ | $1.94$ | $1.56$ | TK | He-sdO
GALEX J212504.4+212957 | $13.8$ | $244.6$ | $21.9$ | $1868.4$ | $0.05$ | $8.78$ | $8.00$ | $1.66$ | TK | He-sdO
GALEX J212544.4+202812 | $-61.1$ | $237.9$ | $9.7$ | $1844.4$ | $0.18$ | $9.64$ | $6.64$ | $0.38$ | TH | He-sdO
UCAC4 648-107111 | $-22.2$ | $254.9$ | $-5.9$ | $2089.3$ | $0.12$ | $10.26$ | $8.07$ | $0.24$ | TH | He-sdO
GALEX J214106.6+252832 | $-92.7$ | $239.8$ | $0.3$ | $1886.5$ | $0.29$ | $11.25$ | $6.23$ | $0.47$ | TH | He-sdO
SDSS J214226.13+091307.5 | $140.4$ | $50.0$ | $53.4$ | $408.0$ | $0.78$ | $9.03$ | $1.09$ | $3.73$ | H | He-sdO
GALEX J214540.8-012807 | $2.1$ | $83.9$ | $7.4$ | $589.6$ | $0.65$ | $7.54$ | $1.59$ | $1.46$ | TK | He-sdO
UCAC4 637-113968 | $4.7$ | $314.8$ | $-50.9$ | $2573.2$ | $0.37$ | $18.22$ | $8.31$ | $1.89$ | TK | He-sdO
PHL 149 | $-72.0$ | $179.7$ | $32.1$ | $1282.8$ | $0.35$ | $8.39$ | $4.08$ | $1.23$ | TK | He-sdO
PG 2158+082 | $-196.5$ | $260.6$ | $-72.6$ | $1998.7$ | $0.58$ | $20.97$ | $5.55$ | $4.84$ | H | He-sdO
PG 2201+145 | $-7.2$ | $227.7$ | $-34.7$ | $1786.7$ | $0.04$ | $8.14$ | $7.58$ | $1.18$ | TH | He-sdO
SDSS J220819.50+060255.4 | $-73.3$ | $183.2$ | $26.8$ | $1310.5$ | $0.33$ | $9.48$ | $4.73$ | $3.58$ | TK | He-sdO
BPS CS 22956-0090 | $16.3$ | $120.0$ | $69.5$ | $817.5$ | $0.52$ | $7.68$ | $2.45$ | $2.09$ | TK | He-sdO
BPS CS 22892-0051 | $151.3$ | $134.4$ | $94.6$ | $1000.4$ | $0.51$ | $10.38$ | $3.39$ | $4.99$ | H | He-sdO
BPS CS 22881-0069 | $48.7$ | $256.4$ | $26.5$ | $1927.0$ | $0.18$ | $10.33$ | $7.11$ | $1.21$ | TK | He-sdO
GALEX J223455.5+312325 | $56.9$ | $182.7$ | $63.9$ | $1592.0$ | $0.23$ | $9.49$ | $5.93$ | $2.60$ | TK | He-sdO
PHL 364 | $-7.8$ | $167.8$ | $-49.2$ | $1291.0$ | $0.28$ | $8.05$ | $4.54$ | $2.03$ | TK | He-sdO
PG 2244+153 | $130.3$ | $120.4$ | $26.9$ | $963.2$ | $0.60$ | $10.14$ | $2.54$ | $1.82$ | TK | He-sdO
PG 2249+220 | $11.7$ | $188.0$ | $11.7$ | $1605.4$ | $0.20$ | $8.90$ | $5.93$ | $1.76$ | TK | He-sdO
BPS CS 22938-0044 | $20.3$ | $230.2$ | $52.2$ | $1531.2$ | $0.15$ | $8.26$ | $6.12$ | $2.28$ | TK | He-sdO
GALEX J230124.7+325943 | $50.9$ | $87.8$ | $37.9$ | $831.7$ | $0.66$ | $11.02$ | $2.27$ | $3.69$ | TK | He-sdO
FBS 2307+338 | $10.8$ | $213.8$ | $30.8$ | $1864.7$ | $0.08$ | $8.88$ | $7.56$ | $1.11$ | TH | He-sdO
BPS CS 22938-0073 | $-33.5$ | $128.8$ | $17.8$ | $865.0$ | $0.53$ | $7.73$ | $2.41$ | $1.07$ | TK | He-sdO
PG 2333-002 | $76.1$ | $137.3$ | $74.5$ | $1114.1$ | $0.35$ | $9.40$ | $4.53$ | $5.04$ | H | He-sdO
GALEX J233913.9+134215 | $117.1$ | $113.0$ | $-84.8$ | $960.5$ | $0.63$ | $12.31$ | $2.76$ | $4.83$ | TK | He-sdO
PG 2343+267 | $26.2$ | $224.4$ | $13.7$ | $2145.5$ | $0.06$ | $10.48$ | $9.31$ | $2.30$ | TK | He-sdO
GALEX J235050.1+194628 | $56.8$ | $205.0$ | $47.6$ | $2056.4$ | $0.13$ | $11.87$ | $9.22$ | $4.85$ | TK | He-sdO
PG 2352+181 | $105.6$ | $190.9$ | $-22.2$ | $1548.4$ | $0.40$ | $10.84$ | $4.63$ | $0.80$ | TK | He-sdO
GALEX J014640.5+411826 | $23.8$ | $264.3$ | $9.3$ | $2746.5$ | $0.19$ | $15.39$ | $10.44$ | $1.51$ | TK | He-sdB
UCAC4 450-010156 | $8.1$ | $243.1$ | $5.8$ | $2219.6$ | $0.05$ | $10.18$ | $9.26$ | $0.38$ | TH | He-sdB
GALEX J062038.5-570538 | $-16.2$ | $272.9$ | $5.9$ | $2229.0$ | $0.16$ | $11.56$ | $8.44$ | $0.64$ | TH | He-sdB
GALEX J064024.8+444720 | $-3.1$ | $249.6$ | $13.4$ | $2474.0$ | $0.10$ | $12.26$ | $9.99$ | $0.75$ | TH | He-sdB
GALEX J064918.3+235440 | $34.5$ | $226.9$ | $25.5$ | $2495.9$ | $0.07$ | $11.96$ | $10.47$ | $0.97$ | TH | He-sdB
FBS 0654+366 | $-3.5$ | $286.1$ | $-4.2$ | $2391.1$ | $0.19$ | $12.92$ | $8.85$ | $0.45$ | TH | He-sdB
HZ 38 | $-83.2$ | $264.7$ | $-21.6$ | $1538.0$ | $0.25$ | $9.05$ | $5.44$ | $1.80$ | TK | He-sdB
GALEX J145817.5+022807 | $-36.9$ | $240.8$ | $16.9$ | $874.4$ | $0.11$ | $7.86$ | $6.32$ | $6.29$ | H | He-sdB
PG 1607+174 | $-39.0$ | $228.0$ | $12.4$ | $1684.5$ | $0.12$ | $8.13$ | $6.41$ | $0.48$ | TH | He-sdB
FBS 1749+373 | $21.4$ | $193.2$ | $4.7$ | $1416.2$ | $0.28$ | $8.25$ | $4.61$ | $0.40$ | TH | He-sdB
UCAC4 657-066324 | $3.4$ | $232.4$ | $3.8$ | $1791.1$ | $0.04$ | $7.99$ | $7.37$ | $0.46$ | TH | He-sdB
2MASS J19230068+3715044 | $-68.6$ | $247.0$ | $-32.9$ | $1832.1$ | $0.22$ | $10.12$ | $6.49$ | $0.98$ | TH | He-sdB
GALEX J213308.4+064701 | $-76.8$ | $287.1$ | $52.6$ | $2991.3$ | $0.39$ | $23.22$ | $10.31$ | $6.43$ | TK | He-sdB
UCAC4 653-107038 | $-29.6$ | $212.6$ | $-5.9$ | $1817.2$ | $0.15$ | $9.14$ | $6.74$ | $0.46$ | TH | He-sdB
2MASS J21391157+4539155 | $-72.3$ | $182.6$ | $-17.8$ | $1815.0$ | $0.32$ | $11.38$ | $5.82$ | $0.70$ | TH | He-sdB
JL 87 | $-24.2$ | $264.9$ | $8.7$ | $2043.0$ | $0.15$ | $10.45$ | $7.67$ | $0.59$ | TH | He-sdB
BPS CS 22956-0094 | $63.8$ | $184.2$ | $21.7$ | $1232.8$ | $0.48$ | $9.66$ | $3.41$ | $0.51$ | TH | He-sdB
UCAC4 685-001272 | $-4.8$ | $231.1$ | $26.0$ | $2073.9$ | $0.05$ | $9.48$ | $8.64$ | $0.64$ | TH | He-sdOB
GALEX J001306.4+491149 | $114.6$ | $58.2$ | $29.8$ | $-20.8$ | $0.98$ | $12.99$ | $0.11$ | $1.44$ | H | He-sdOB
GALEX J002433.0+264910 | $-4.2$ | $226.2$ | $16.2$ | $2145.4$ | $0.04$ | $10.12$ | $9.34$ | $1.82$ | TK | He-sdOB
FBS 0035+343 | $35.7$ | $302.5$ | $-41.4$ | $2604.3$ | $0.35$ | $17.68$ | $8.61$ | $1.67$ | TK | He-sdOB
PG 0039+135 | $-22.8$ | $191.0$ | $72.8$ | $1607.6$ | $0.19$ | $8.96$ | $6.08$ | $2.10$ | TK | He-sdOB
PB 6244 | $188.0$ | $102.9$ | $55.4$ | $994.0$ | $0.63$ | $15.49$ | $3.53$ | $9.76$ | H | He-sdOB
PB 6275 | $163.0$ | $-22.4$ | $-116.1$ | $-219.4$ | $0.92$ | $13.70$ | $0.58$ | $7.41$ | H | He-sdOB
GALEX J011928.8+490109 | $13.1$ | $239.5$ | $-9.6$ | $2048.5$ | $0.05$ | $9.28$ | $8.46$ | $0.25$ | TH | He-sdOB
GALEX J014326.2+323439 | $-11.7$ | $50.0$ | $68.6$ | $385.4$ | $0.82$ | $9.94$ | $0.95$ | $3.72$ | TK | He-sdOB
PG 0216+246 | $-38.3$ | $250.8$ | $8.7$ | $2480.3$ | $0.16$ | $13.40$ | $9.64$ | $1.79$ | TK | He-sdOB
GALEX J022125.9+085919 | $-86.3$ | $161.6$ | $-14.2$ | $1884.2$ | $0.37$ | $14.76$ | $6.76$ | $5.92$ | TK | He-sdOB
Star | $U$ | $V$ | $W$ | $J_{z}$ | $e$ | Ra | Rp | Zmax | pop | class
---|---|---|---|---|---|---|---|---|---|---
|  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ | kpc $\mbox{km}\,\mbox{s}^{-1}$ |  | kpc | kpc | kpc |  |
PG 0221+217 | $-122.6$ | $151.6$ | $-16.9$ | $1336.9$ | $0.52$ | $11.52$ | $3.65$ | $1.26$ | TK | He-sdOB
GALEX J022422.2+000313 | $21.2$ | $-33.8$ | $-39.2$ | $-297.3$ | $0.89$ | $12.93$ | $0.78$ | $6.54$ | H | He-sdOB
GALEX J023254.0+370419 | $-75.1$ | $218.0$ | $1.1$ | $1949.4$ | $0.26$ | $11.23$ | $6.62$ | $0.45$ | TH | He-sdOB
PG 0240+046 | $32.6$ | $164.2$ | $93.0$ | $1482.0$ | $0.20$ | $8.84$ | $5.87$ | $3.04$ | TK | He-sdOB
KUV 02445+3633 | $21.1$ | $295.9$ | $-90.1$ | $2562.5$ | $0.35$ | $18.10$ | $8.79$ | $4.03$ | TK | He-sdOB
GALEX J031842.4+340554 | $-19.9$ | $202.6$ | $9.7$ | $1875.7$ | $0.17$ | $9.65$ | $6.87$ | $0.45$ | TH | He-sdOB
KPD 0319+4553 | $78.9$ | $255.8$ | $-12.8$ | $2293.9$ | $0.27$ | $13.59$ | $7.87$ | $0.33$ | TH | He-sdOB
HD 275347 | $-35.6$ | $230.9$ | $2.8$ | $1998.0$ | $0.12$ | $9.77$ | $7.65$ | $0.13$ | TH | He-sdOB
BPS CS 22190-0003 | $-73.8$ | $277.7$ | $-6.5$ | $2399.4$ | $0.26$ | $14.49$ | $8.42$ | $1.49$ | TK | He-sdOB
HZ 3 | $-18.8$ | $232.2$ | $35.4$ | $2006.8$ | $0.10$ | $9.65$ | $7.97$ | $0.74$ | TH | He-sdOB
GALEX J041700.7+350717 | $34.4$ | $239.0$ | $12.2$ | $2356.8$ | $0.10$ | $11.51$ | $9.44$ | $0.45$ | TH | He-sdOB
UCAC4 633-017614 | $31.3$ | $167.9$ | $17.5$ | $1578.5$ | $0.28$ | $9.14$ | $5.18$ | $0.39$ | TH | He-sdOB
KUV 04456+1502 | $22.4$ | $203.2$ | $16.9$ | $1990.2$ | $0.10$ | $9.58$ | $7.83$ | $0.60$ | TH | He-sdOB
GALEX J045027.6+155910 | $32.5$ | $218.7$ | $5.1$ | $2216.0$ | $0.07$ | $10.45$ | $9.08$ | $0.59$ | TH | He-sdOB
GALEX J052300.5+182727 | $43.7$ | $196.7$ | $14.0$ | $2004.2$ | $0.13$ | $10.00$ | $7.62$ | $0.46$ | TH | He-sdOB
SDSS J052933.85+040720.0 | $-98.9$ | $186.6$ | $-11.1$ | $1837.3$ | $0.39$ | $12.77$ | $5.57$ | $0.74$ | TK | He-sdOB
GALEX J053656.5+395516 | $15.6$ | $203.5$ | $12.9$ | $1868.9$ | $0.12$ | $9.05$ | $7.14$ | $0.26$ | TH | He-sdOB
LAMOST J054711.59+170919.5 | $7.3$ | $213.9$ | $12.9$ | $2074.6$ | $0.07$ | $9.67$ | $8.37$ | $0.29$ | TH | He-sdOB
ATO J089.4285+27.7808 | $215.1$ | $196.7$ | $14.9$ | $2195.6$ | $0.61$ | $23.07$ | $5.66$ | $0.71$ | H | He-sdOB
LAMOST J060000.23+112836.6 | $-56.1$ | $213.6$ | $-28.0$ | $2030.4$ | $0.19$ | $10.85$ | $7.42$ | $0.81$ | TH | He-sdOB
EC 05593-5901 | $-39.2$ | $249.0$ | $57.7$ | $2148.3$ | $0.25$ | $12.93$ | $7.80$ | $2.60$ | TK | He-sdOB
Lan 11 | $-80.0$ | $248.8$ | $-6.5$ | $2211.4$ | $0.25$ | $12.72$ | $7.66$ | $0.20$ | TH | He-sdOB
LAMOST J062830.43+112018.4 | $4.8$ | $237.8$ | $8.4$ | $2313.4$ | $0.02$ | $10.38$ | $9.91$ | $0.13$ | TH | He-sdOB
LAMOST J062836.51+325031.5 | $-11.9$ | $198.0$ | $-17.1$ | $1855.7$ | $0.18$ | $9.70$ | $6.70$ | $0.44$ | TH | He-sdOB
LAMOST J063650.09+291925.0 | $26.0$ | $225.9$ | $13.2$ | $2745.2$ | $0.06$ | $13.23$ | $11.68$ | $0.90$ | TH | He-sdOB
LAMOST J064701.65+690625.2 | $58.5$ | $187.0$ | $5.6$ | $2113.6$ | $0.24$ | $12.39$ | $7.53$ | $1.76$ | TK | He-sdOB
LAMOST J070828.40+442534.8 | $-1.1$ | $144.2$ | $-40.8$ | $1283.4$ | $0.44$ | $9.75$ | $3.80$ | $1.52$ | TK | He-sdOB
GALEX J071319.6+380740 | $88.5$ | $84.4$ | $3.4$ | $960.6$ | $0.65$ | $10.98$ | $2.35$ | $0.88$ | TK | He-sdOB
GALEX J071401.4+693321 | $-14.8$ | $-70.7$ | $-96.1$ | $-742.3$ | $0.63$ | $10.64$ | $2.44$ | $5.73$ | H | He-sdOB
$\rm[CW83]\,0711+22$ | $-41.8$ | $246.9$ | $-11.5$ | $2036.6$ | $0.10$ | $9.77$ | $7.98$ | $0.28$ | TH | He-sdOB
GALEX J071856.2+102637 | $-17.0$ | $227.1$ | $6.3$ | $2098.4$ | $0.09$ | $9.96$ | $8.36$ | $0.28$ | TH | He-sdOB
GALEX J072315.6+183457 | $26.2$ | $208.3$ | $6.7$ | $2150.4$ | $0.19$ | $11.66$ | $7.86$ | $0.82$ | TH | He-sdOB
GALEX J072824.7+414953 | $-31.5$ | $205.0$ | $-11.2$ | $2159.8$ | $0.17$ | $11.50$ | $8.11$ | $1.15$ | TH | He-sdOB
GALEX J073220.1+270408 | $77.1$ | $189.6$ | $18.6$ | $1773.4$ | $0.40$ | $12.49$ | $5.34$ | $0.91$ | TH | He-sdOB
GALEX J074125.1+125020 | $-23.8$ | $217.2$ | $16.9$ | $2601.7$ | $0.17$ | $14.14$ | $10.12$ | $1.78$ | TK | He-sdOB
LAMOST J075139.26+064604.8 | $-41.0$ | $225.9$ | $-11.2$ | $1937.3$ | $0.13$ | $9.52$ | $7.38$ | $0.37$ | TH | He-sdOB
SDSS J075733.11+235828.1 | $29.1$ | $166.9$ | $42.9$ | $2230.8$ | $0.21$ | $13.24$ | $8.71$ | $3.69$ | TK | He-sdOB
GALEX J075807.5-043203 | $-94.0$ | $293.7$ | $-16.8$ | $2558.3$ | $0.45$ | $20.06$ | $7.65$ | $0.51$ | TK | He-sdOB
KUV 07564+3723 | $-16.1$ | $226.7$ | $-3.6$ | $2163.1$ | $0.06$ | $10.12$ | $9.05$ | $1.00$ | TH | He-sdOB
$\rm[CW83]\,0825+15$ | $-55.4$ | $283.5$ | $-17.9$ | $2178.0$ | $0.12$ | $10.87$ | $8.46$ | $0.61$ | TH | He-sdOB
Ton 927 | $-6.5$ | $163.2$ | $3.5$ | $1611.4$ | $0.29$ | $9.60$ | $5.23$ | $0.52$ | TH | He-sdOB
Ton 380 | $-23.7$ | $223.8$ | $-0.9$ | $2056.3$ | $0.11$ | $10.13$ | $8.11$ | $0.95$ | TH | He-sdOB
PG 0902+057 | $-48.6$ | $241.3$ | $4.6$ | $1732.0$ | $0.21$ | $9.30$ | $6.12$ | $0.63$ | TH | He-sdOB
GALEX J094044.0+004759 | $-122.9$ | $259.4$ | $-22.6$ | $2118.2$ | $0.07$ | $10.42$ | $9.08$ | $2.25$ | TK | He-sdOB
PG 0950+158 | $-105.3$ | $138.6$ | $-67.6$ | $1187.3$ | $0.52$ | $11.07$ | $3.45$ | $3.10$ | TK | He-sdOB
Ton 554 | $-52.9$ | $-3.7$ | $-108.7$ | $695.3$ | $0.85$ | $19.28$ | $1.57$ | $4.23$ | H | He-sdOB
PG 1127+019 | $-85.3$ | $245.1$ | $-26.9$ | $1730.7$ | $0.11$ | $8.52$ | $6.89$ | $1.37$ | TK | He-sdOB
Feige 46 | $-208.3$ | $219.7$ | $77.2$ | $470.3$ | $0.80$ | $9.58$ | $1.07$ | $0.56$ | H | He-sdOB
Feige 49 | $-171.6$ | $208.7$ | $58.6$ | $870.6$ | $0.58$ | $8.62$ | $2.26$ | $0.71$ | H | He-sdOB
GALEX J120521.5+224702 | $-193.3$ | $264.9$ | $161.0$ | $1157.7$ | $0.64$ | $16.48$ | $3.66$ | $8.77$ | H | He-sdOB
CBS 461 | $-180.5$ | $262.7$ | $83.2$ | $437.7$ | $0.85$ | $12.71$ | $1.02$ | $4.47$ | H | He-sdOB
CBS 58 | $-95.0$ | $192.3$ | $180.8$ | $1032.9$ | $0.32$ | $9.70$ | $5.01$ | $6.60$ | H | He-sdOB
GALEX J124552.8+175111 | $-224.3$ | $188.3$ | $140.5$ | $410.8$ | $0.78$ | $9.11$ | $1.11$ | $3.85$ | H | He-sdOB
PG 1258+012 | $-117.2$ | $310.0$ | $76.1$ | $1762.7$ | $0.28$ | $11.08$ | $6.30$ | $2.55$ | TK | He-sdOB
PB 146 | $-64.2$ | $139.9$ | $-17.7$ | $1309.1$ | $0.45$ | $10.28$ | $3.93$ | $2.13$ | TK | He-sdOB
Cl* NGC 5139 LEID 49021 | $-179.6$ | $27.8$ | $35.1$ | $91.5$ | $0.93$ | $9.15$ | $0.32$ | $0.87$ | H | He-sdOB
2QZ J132542.4-014655 | $-90.3$ | $223.9$ | $10.5$ | $1406.0$ | $0.15$ | $7.81$ | $5.72$ | $2.46$ | TK | He-sdOB
Cl* NGC 5139 LEID 40026 | $-174.1$ | $42.6$ | $60.8$ | $262.9$ | $0.90$ | $10.46$ | $0.58$ | $1.57$ | H | He-sdOB
Cl* NGC 5139 LEID 31031 | $-86.5$ | $-227.3$ | $-181.5$ | $-819.1$ | $0.13$ | $9.97$ | $7.65$ | $8.87$ | H | He-sdOB
NGC 5139 5596 | $-156.4$ | $68.9$ | $53.3$ | $457.9$ | $0.81$ | $9.75$ | $1.04$ | $1.23$ | H | He-sdOB
Cl* NGC 5139 LEID 42032 | $-143.2$ | $86.8$ | $87.7$ | $762.1$ | $0.71$ | $11.76$ | $1.97$ | $3.83$ | H | He-sdOB
2MASS J13260202-4737234 | $-102.4$ | $-203.4$ | $-152.5$ | $-518.2$ | $0.14$ | $8.35$ | $6.29$ | $7.81$ | H | He-sdOB
NGC 5139 4465 | $-175.6$ | $36.7$ | $52.3$ | $197.4$ | $0.92$ | $9.95$ | $0.44$ | $1.21$ | H | He-sdOB
NGC 5139 6139 | $-194.9$ | $-61.8$ | $-41.7$ | $-385.2$ | $0.73$ | $7.21$ | $1.11$ | $2.75$ | H | He-sdOB
Cl* NGC 5139 LEID 56042 | $-100.3$ | $121.3$ | $119.9$ | $1447.2$ | $0.52$ | $15.37$ | $4.89$ | $7.57$ | H | He-sdOB
Cl* NGC 5139 LEID 54050 | $-119.1$ | $109.0$ | $115.5$ | $1177.5$ | $0.58$ | $14.10$ | $3.75$ | $6.85$ | H | He-sdOB
Star | $U$ | $V$ | $W$ | $J_{z}$ | $e$ | Ra | Rp | Zmax | pop | class
---|---|---|---|---|---|---|---|---|---|---
|  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ |  $\mbox{km}\,\mbox{s}^{-1}$ | kpc $\mbox{km}\,\mbox{s}^{-1}$ |  | kpc | kpc | kpc |  |
Cl* NGC 5139 LEID 48062 | $-180.7$ | $41.1$ | $62.9$ | $195.7$ | $0.92$ | $9.93$ | $0.42$ | $1.46$ | H | He-sdOB
Cl* NGC 5139 LEID 58063 | $-128.0$ | $94.1$ | $83.1$ | $921.4$ | $0.65$ | $12.15$ | $2.54$ | $3.70$ | H | He-sdOB
Cl* NGC 5139 LEID 49227 | $-131.6$ | $99.4$ | $81.2$ | $862.3$ | $0.66$ | $11.21$ | $2.26$ | $3.04$ | H | He-sdOB
Cl* NGC 5139 LEID 56098 | $-184.5$ | $30.8$ | $56.7$ | $113.2$ | $0.95$ | $9.69$ | $0.24$ | $1.24$ | H | He-sdOB
NGC 5139 4547 | $-117.5$ | $112.5$ | $81.3$ | $1034.6$ | $0.60$ | $11.42$ | $2.87$ | $3.21$ | TK | He-sdOB
Cl* NGC 5139 LEID 34202 | $-161.3$ | $66.1$ | $55.4$ | $428.5$ | $0.82$ | $9.90$ | $0.99$ | $1.27$ | H | He-sdOB
Cl* NGC 5139 LEID 56132 | $-131.6$ | $92.2$ | $92.8$ | $958.5$ | $0.67$ | $13.13$ | $2.63$ | $4.82$ | H | He-sdOB
Cl* NGC 5139 LEID 56141 | $-105.5$ | $104.7$ | $95.4$ | $1438.7$ | $0.59$ | $16.42$ | $4.27$ | $6.41$ | TK | He-sdOB
Cl* NGC 5139 LEID 50311 | $-156.4$ | $72.2$ | $66.5$ | $526.1$ | $0.79$ | $10.47$ | $1.23$ | $1.89$ | H | He-sdOB
Cl* NGC 5139 LEID 37330 | $-199.1$ | $-12.2$ | $16.4$ | $-213.4$ | $0.88$ | $8.23$ | $0.54$ | $0.72$ | H | He-sdOB
NGC 5139 3595 | $-186.5$ | $-17.4$ | $-17.2$ | $-202.1$ | $0.89$ | $8.07$ | $0.46$ | $1.00$ | H | He-sdOB
NGC 5139 4373 | $-190.3$ | $3.3$ | $11.8$ | $-97.6$ | $0.92$ | $8.23$ | $0.34$ | $0.80$ | H | He-sdOB
SDSS J133449.25+041014.8 | $-185.8$ | $132.8$ | $-2.9$ | $479.7$ | $0.68$ | $7.95$ | $1.49$ | $3.76$ | H | He-sdOB
GALEX J134352.1+394008 | $-213.6$ | $174.0$ | $130.1$ | $139.5$ | $0.89$ | $9.25$ | $0.51$ | $6.75$ | H | He-sdOB
UM 610 | $-127.5$ | $139.2$ | $-35.1$ | $757.4$ | $0.55$ | $8.11$ | $2.37$ | $3.18$ | TK | He-sdOB
GALEX J134621.2+224835 | $-141.3$ | $249.9$ | $102.2$ | $971.1$ | $0.47$ | $9.21$ | $3.32$ | $4.16$ | H | He-sdOB
GALEX J135150.6+035718 | $-248.1$ | $91.4$ | $31.3$ | $243.1$ | $0.75$ | $9.26$ | $1.32$ | $7.91$ | H | He-sdOB
PB 1353 | $-110.2$ | $170.9$ | $61.6$ | $1080.5$ | $0.37$ | $9.53$ | $4.43$ | $5.42$ | H | He-sdOB
PG 1413+114 | $-98.9$ | $236.0$ | $50.8$ | $1182.0$ | $0.25$ | $7.65$ | $4.54$ | $2.85$ | TK | He-sdOB
GALEX J143729.2-021507 | $-59.4$ | $271.8$ | $41.5$ | $1523.9$ | $0.22$ | $8.53$ | $5.45$ | $1.43$ | TK | He-sdOB
GALEX J145522.9+045802 | $-62.0$ | $209.6$ | $1.7$ | $1249.4$ | $0.22$ | $7.25$ | $4.62$ | $1.84$ | TK | He-sdOB
GALEX J145614.5+165740 | $-274.3$ | $147.9$ | $104.2$ | $-63.9$ | $0.96$ | $7.47$ | $0.17$ | $3.75$ | H | He-sdOB
GALEX J152208.0+342503 | $-124.7$ | $172.4$ | $12.2$ | $1210.7$ | $0.41$ | $10.77$ | $4.53$ | $5.46$ | H | He-sdOB
CSO 1099 | $-53.9$ | $244.8$ | $73.3$ | $1343.7$ | $0.24$ | $8.16$ | $4.95$ | $2.36$ | TK | He-sdOB
SDSS J153419.42+372557.2 | $-71.7$ | $229.1$ | $64.4$ | $1373.9$ | $0.22$ | $7.97$ | $5.09$ | $2.03$ | TK | He-sdOB
GALEX J155202.7+261542 | $-51.7$ | $189.7$ | $0.2$ | $1035.3$ | $0.37$ | $7.43$ | $3.44$ | $2.02$ | TK | He-sdOB
PG 1559+048 | $-22.5$ | $242.4$ | $28.2$ | $1602.8$ | $0.16$ | $8.13$ | $5.84$ | $0.54$ | TH | He-sdOB
PG 1614+270 | $-107.4$ | $231.1$ | $41.7$ | $1609.4$ | $0.30$ | $10.32$ | $5.59$ | $2.55$ | TK | He-sdOB
GALEX J162051.0+375059 | $-42.5$ | $233.6$ | $47.7$ | $1452.2$ | $0.13$ | $7.79$ | $6.05$ | $2.41$ | TK | He-sdOB
GALEX J163150.9+480431 | $82.8$ | $107.3$ | $-100.3$ | $718.1$ | $0.45$ | $9.15$ | $3.44$ | $6.69$ | H | He-sdOB
SDSS J164042.90+311734.6 | $-207.6$ | $239.6$ | $220.8$ | $524.0$ | $0.38$ | $7.92$ | $3.54$ | $6.76$ | H | He-sdOB
Ton 261 | $66.4$ | $203.0$ | $-50.6$ | $1540.7$ | $0.14$ | $8.05$ | $6.11$ | $1.90$ | TK | He-sdOB
PG 1652+159 | $-21.5$ | $215.9$ | $21.1$ | $1284.1$ | $0.22$ | $7.13$ | $4.55$ | $1.11$ | TH | He-sdOB
GALEX J170045.1+391830 | $-131.8$ | $308.8$ | $92.1$ | $1578.8$ | $0.21$ | $11.79$ | $7.71$ | $7.19$ | H | He-sdOB
PG 1715+273 | $-27.8$ | $228.9$ | $16.0$ | $1465.2$ | $0.10$ | $7.23$ | $5.90$ | $1.46$ | TK | He-sdOB
UCAC4 530-064631 | $-42.1$ | $257.1$ | $24.9$ | $1685.3$ | $0.12$ | $8.42$ | $6.57$ | $1.28$ | TK | He-sdOB
GALEX J172034.1+145940 | $-246.4$ | $11.3$ | $-33.1$ | $-557.2$ | $0.72$ | $8.61$ | $1.43$ | $1.78$ | H | He-sdOB
GALEX J172533.3+523321 | $-45.1$ | $187.1$ | $-3.9$ | $1366.9$ | $0.30$ | $8.47$ | $4.54$ | $1.39$ | TK | He-sdOB
GALEX J181102.8+173759 | $255.4$ | $-21.6$ | $-60.2$ | $-219.9$ | $0.91$ | $13.69$ | $0.68$ | $5.02$ | H | He-sdOB
HS 1837+5913 | $-46.8$ | $277.4$ | $-7.2$ | $2287.4$ | $0.26$ | $13.54$ | $7.93$ | $0.84$ | TH | He-sdOB
2MASS J19271504+3827186 | $-27.9$ | $236.6$ | $-28.7$ | $1811.7$ | $0.10$ | $8.68$ | $7.10$ | $0.71$ | TH | He-sdOB
2MASS J19380163+4649446 | $0.0$ | $331.0$ | $56.6$ | $4101.1$ | $0.37$ | $31.64$ | $14.59$ | $7.55$ | TK | He-sdOB
2MASS J19565555+4350171 | $-8.7$ | $271.2$ | $-17.2$ | $2195.7$ | $0.17$ | $11.51$ | $8.15$ | $0.35$ | TH | He-sdOB
BPS CS 22940–0009 | $1.2$ | $138.3$ | $-20.9$ | $873.5$ | $0.43$ | $6.79$ | $2.70$ | $1.38$ | TK | He-sdOB
GALEX J211000.6+152913 | $-13.3$ | $165.6$ | $17.9$ | $1194.3$ | $0.35$ | $7.71$ | $3.75$ | $0.84$ | TH | He-sdOB
GALEX J211148.7+132529 | $66.1$ | $-96.7$ | $-145.9$ | $-526.0$ | $0.56$ | $8.35$ | $2.35$ | $5.95$ | H | He-sdOB
SDSS J212330.46+004238.8 | $33.4$ | $196.4$ | $50.5$ | $1359.7$ | $0.18$ | $7.54$ | $5.19$ | $1.90$ | TK | He-sdOB
GALEX J213054.5-004116 | $-18.6$ | $210.9$ | $-0.3$ | $1409.2$ | $0.13$ | $7.35$ | $5.69$ | $1.92$ | TK | He-sdOB
PG 2129+151 | $62.9$ | $224.1$ | $-70.2$ | $1803.0$ | $0.17$ | $9.70$ | $6.83$ | $1.75$ | TK | He-sdOB
GALEX J215541.6+300340 | $-15.2$ | $192.8$ | $21.3$ | $1559.0$ | $0.21$ | $8.40$ | $5.47$ | $0.71$ | TH | He-sdOB
GALEX J215956.5+141804 | $-42.2$ | $260.4$ | $23.2$ | $2014.9$ | $0.17$ | $10.61$ | $7.54$ | $1.11$ | TH | He-sdOB
PG 2204+071 | $8.3$ | $238.0$ | $-26.5$ | $1858.5$ | $0.03$ | $8.38$ | $7.90$ | $1.03$ | TH | He-sdOB
PG 2218+052 | $40.2$ | $201.0$ | $-52.5$ | $1601.4$ | $0.18$ | $8.51$ | $5.93$ | $1.34$ | TK | He-sdOB
FBS 2255+404 | $-44.0$ | $193.7$ | $15.5$ | $1797.8$ | $0.24$ | $10.10$ | $6.24$ | $0.85$ | TH | He-sdOB
PG 2321+214 | $70.9$ | $233.7$ | $-67.9$ | $1901.5$ | $0.25$ | $11.29$ | $6.78$ | $2.08$ | TK | He-sdOB
LAMOST J232812.94+295333.5 | $-127.0$ | $-26.9$ | $55.3$ | $-329.2$ | $0.86$ | $12.19$ | $0.95$ | $4.27$ | H | He-sdOB
GALEX J232856.6+492806 | $-25.0$ | $194.3$ | $-32.4$ | $2138.2$ | $0.16$ | $11.28$ | $8.17$ | $1.41$ | TK | He-sdOB
Ton S 103 | $65.5$ | $193.9$ | $164.4$ | $1475.3$ | $0.18$ | $10.67$ | $7.45$ | $6.56$ | H | He-sdOB