11institutetext: Universitat Politècnica de Catalunya, Departament de Física,
c/ Esteve Terrades 5, 08860 Castelldefels, Spain 22institutetext: Dr. Karl
Remeis-Observatory & ECAP, Astronomical Institute, Friedrich-Alexander
University Erlangen-Nuremberg (FAU), Sternwartstr. 7, 96049 Bamberg, Germany

# Runaway blue main-sequence stars at high Galactic latitudes

Target selection with Gaia and spectroscopic identification

Roberto Raddi , 1122<EMAIL_ADDRESS>Andreas Irrgang 22 Ulrich Heber 22
David Schneider 22 Simon Kreuzer 22

(Received xx; accepted yyy)

###### Abstract

Context. The ESA Gaia mission is a remarkable tool for stellar population
analysis through its accurate Hertzsprung-Russell diagram. Its precise
astrometry has propelled detailed kinematic studies of the Milky Way and the
identification of high-velocity outliers.

Aims. Motivated by the historical identification of runaway main-sequence (MS)
stars of early spectral type at high Galactic latitudes, we test the
capability of Gaia at identifying new such stars.

Methods. We have selected $\approx 2300$ sources with Gaia magnitudes of
$G_{\rm BP}-G_{\rm RP}\leq 0.05$, compatible with the colors of low-extinction
MS stars earlier than mid-A spectral type, and obtained low-resolution optical
spectroscopy for 48 such stars. By performing detailed photometric and
spectroscopic analyses, we derive their atmospheric and physical parameters
(effective temperature, surface gravity, radial velocity, interstellar
reddening, spectrophotometric distance, mass, radius, luminosity, and age).
The comparison between spectrophotometric and parallax-based distances enables
us to disentangle the MS candidates from older blue horizontal branch (BHB)
candidates.

Results. We identify 12 runaway MS candidates, with masses between 2 and 6 M☉.
Their trajectories are traced back to the Galactic disc to identify their most
recent Galactic plane crossings and the corresponding flight times. All 12
candidates are ejected from the Galactic disc within 2 to 16.5 kpc from the
Galactic center and possess flight times that are shorter than their
evolutionary ages, compatible with a runaway hypothesis. Three MS candidates
have ejection velocities exceeding 450 km s-1, thus, appear to challenge the
canonical ejection scenarios for late B-type stars. The fastest star of our
sample also has a non-negligible Galactic escape probability if its MS nature
can be confirmed. We identify 27 BHB candidates, and the two hottest stars in
our sample are rare late O and early B type stars of low mass evolving towards
the white dwarf cooling sequence.

Conclusions. The combination of Gaia parallaxes and proper motions can lead to
the efficient selection of runaway blue MS candidates up to 10 kpc away from
the Sun. High resolution spectra are needed to confirm the MS status, via
precise measurements of projected rotational velocities and chemical
compositions.

###### Key Words.:

Stars: early-type, horizontal-branch, fundamental parameters, kinematics and
dynamics

##  1 Introduction

The presence of short-lived, early-type main sequence (MS) stars at high
Galactic latitudes has long been a puzzle that, now more than ever,
demonstrates the existence of violent astrophysical phenomena, which lead to
the ejection of these stars from their birth places such as open clusters and
OB associations.

In the classical picture, Galactic runaway stars are accelerated through
variations of the binary supernova mechanism (Blaauw, 1961) and dynamical
ejection from open clusters (Poveda et al., 1967). In the first case, the
runaway star is ejected subsequently to the core-collapse supernova of a more
massive companion; in the second case, binary interactions in massive clusters
provide the ejection mechanism. Both phenomena are seen to take place early in
the stellar lifetime, within the same regions of high-mass star formation
(Hoogerwerf et al., 2001). The predicted ejection velocity distribution of
these mechanisms ranges from a few tens of km s-1 up to 400–500 km s-1,
strongly depending both on the mass of the runaway star and on the kind of
interactions (Portegies Zwart, 2000; Gvaramadze et al., 2009; Tauris, 2015;
Renzo et al., 2019; Evans et al., 2020). The binary ejection mechanism is
highly efficient at forming runaway stars if a “birth kick” is imparted as
consequence of asymmetric supernova explosions (see discussions by Renzo et
al., 2019; Evans et al., 2020). For the dynamical ejection scenario, the birth
rate of runaway stars is seen to strongly correlate with increasing cluster
density and stellar mass (Perets & Šubr, 2012; Oh & Kroupa, 2016). The fastest
runaway stars are expected to form mostly via the binary supernova mechanism
and to reach no further away than a few tens of kilo-parsecs above the
Galactic plane, implying that just a negligible fraction of them might escape
from the Milky Way.

The literature is rich with works focusing on the identification and
classification of runaway stars. Notably, Silva & Napiwotzki (2011) produced a
large systematic study of previously known runaway blue stars, arguing that
their ejection velocity distribution is compatible with the binary supernova
ejection scenario, although suggesting that a small contribution could also
arise from the dynamical ejection from open clusters. The assortment of
runaway early-type MS stars is not just populated by former Galactic disc
members. In fact, there are extra-galactic visitors like HE 0437$-$5439 (also
known as HVS 3) that seems to have been ejected from the Large Magellanic
Cloud
(Edelmann et al., 2005; Irrgang et al., 2018a; Erkal et al., 2019b). In
addition, other more energetic phenomena have also been suggested to operate
in the Milky Way. One of them is the Hills mechanism (Hills, 1988), which
could be responsible for the formation of the hyper-velocity stars through the
interaction of binaries with the supermassive black hole at the center of our
Galaxy. With ejection velocities in the range $1000$ km s-1, these stars could
also escape the Milky Way (see Brown, 2015, for a review).

Wider samples of runaway stars have recently become more accessible thanks to
the ESA Gaia astrometric mission (Gaia Collaboration et al., 2016). Following
the promising search for runaway stars in the first data release of Gaia (Maíz
Apellániz et al., 2018), the second data release (DR2; Gaia Collaboration et
al., 2018b) has been the real game changer, due to the high precision of its
space-based proper motions, parallaxes, broad-band photometry, and radial
velocities (e.g. Boubert et al., 2018; Brown et al., 2018; Irrgang et al.,
2018a; Shen et al., 2018; Hattori et al., 2018; Raddi et al., 2018, 2019;
Koposov et al., 2020; Kreuzer et al., 2020).

In this manuscript, we present a selection of blue stars at high Galactic
latitudes, guided by the Gaia Hertzsprung-Russell diagram (Sect. 2), with the
goal of testing the prospects for the identification of blue MS runaway
candidates in our Galaxy. We obtained low-resolution optical spectra for 48
stars (Sect. 3), which enable us to determine effective temperatures, surface
gravities, and radial velocities. We classify 12 likely MS stars, 27 blue
horizontal branch (BHB) stars, and two very hot evolved stars via the
agreement between spectrophotometric and parallax-based distances (Sect. 4).
We determine the Galactic orbits of the MS candidates (Sect. 5), and discuss
their key properties in the context of runaway MS stars (Sect. 6). The results
of this work suggest future improvements for the identification of runaway
stars by exploiting the synergy between Gaia and optical spectroscopy.

##  2 Target selection

Figure 1: Gaia Hertzsprung-Russell diagram of candidate blue stars at high
Galactic latitudes (grey cross symbols). The observed targets are shown as
large circles. Solid curves represent the zero-age and terminal-age MS, while
the evolutionary tracks for representative initial masses are plotted as
dashed curves (Choi et al., 2016). The light-blue strip represents the
horizontal branch (Dorman, 1992). The reddening vector and typical error bars
of the observed targets are displayed at the top edge of the figure. Figure 2:
The relative parallax uncertainties and tangential velocities of early-type
star candidates (cross symbols) and observed targets (circles with error bars)
are plotted against the parallax-based distance in the top and bottom panels,
respectively.

We queried the Gaia DR2 in order to identify candidate MS runaway stars with
masses above 2 M☉ at high Galactic latitudes ($|b|\geq 15^{\circ}$). We
required that parallaxes are measured with a precision of better than 30%, and
we applied color and absolute magnitude cuts of $G_{\rm BP}-G_{\rm RP}\leq
0.05$ mag and $M_{G}=G+5-5\log{(1000/\varpi)}\leq 3.7$ mag, respectively,
where $G$, $G_{\rm BP}$, and $G_{\rm RP}$ are the Gaia magnitudes, and
$\varpi$ is the parallax given in mas yr-1. We filtered the Gaia photometry
and astrometry, requiring high quality data as prescribed by Lindegren et al.
(2018) and the Gaia Collaboration et al. (2018a). In addition, we requested
that our selection had re-normalized unit weight error (ruwe) smaller than 1.4
(Lindegren, 2018). This procedure delivered 10 342 objects. The adql code used
to perform our query is given in Appendix A.

We note that the $G$ magnitude distribution of the selected candidates is
double peaked at $\approx 8.5$ and 14.5 mag, and that apparently brighter
objects present relatively small tangential velocities in a heliocentric
reference frame. In order to reduce contamination from objects that are less-
likely runaway stars, we applied an additional cut defined via the tangential
velocity as:

$\varv_{\rm
tan}=4.74\times\frac{\sqrt{{\mu^{*}_{\alpha}}^{2}+\mu_{\delta}^{2}}}{\varpi}\geq
150\,\mathrm{km}\,\mathrm{s}^{-1};$ (1)

where $\mu^{*}_{\alpha}=\mu_{\alpha}\cos{\delta}$ and $\mu_{\delta}$ are the
proper motion components along the right ascension and declination directions,
respectively. This velocity cut delivers 2392 objects that are displayed in
Fig. 1, along with the 48 stars for which we have collected follow-up
spectroscopy.

Focusing on blue stars, our selection does not overlap with previous work
(e.g. Hattori et al., 2018), which targeted cool stars for which six-
dimensional data were delivered by Gaia DR2, including radial velocities that
are not available for stars bluer than early-F spectral type, but also have
their pitfalls (Boubert et al., 2019). Instead, we note that towards the lower
edge of Fig. 1, i.e. the faint absolute magnitude cut, our candidates overlap
with the hot subluminous star candidates identified by Geier et al. (2019),
which we avoided as much as possible in our spectroscopic follow-up. In
addition, we note that our target selection of blue stars at high Galactic
latitudes would contain a large fraction of BHB stars and field blue
stragglers (Brown et al., 2010) out of which we aim to disentangle MS runaway
candidates.

##  3 Observations

The time allocation for our follow-up observations consisted of five nights at
the New Technology Telescope (NTT) on 2019 August 15–20, with the ESO Faint
Object Spectrograph and Camera (EFOSC2; Buzzoni et al., 1984).

Based on the on-sky visibility of suitable targets, we defined our priority
list according to two empirical criteria. First, we favored objects having
colors and absolute magnitudes that place them in the proximity of the
unreddened MS (Fig. 1). Second, we covered a wide range of tangential
velocities so not to solely favor stars with the highest apparent motion, as
this quantity is negatively affected by larger parallax uncertainties (Fig.
2). Due to the time allocation in August, we observed 48 stars with right
ascension between 16.5 h and 3 h. Figure 3 shows the spatial distribution of
all the identified candidates and observed targets, which are compared to
known runaway stars (Silva & Napiwotzki, 2011). The relevant Gaia data for the
observed targets are listed in Table 1.

All the stars were observed with grism #7 and $2\times 2$ CCD binning, taking
two exposures that ranged between 5–30 min, followed by one He-Ar arc exposure
at the same position of the observed star. We typically observed three white
dwarf flux standards per night (GD 50, LAWD 74, and LTT 7987). Our
observations were undertaken near to full moon and the weather conditions were
generally stable, frequently reaching sub-arcsec seeing; the sole exception
was the first night, when thick clouds disrupted the second half of the night.

We used standard iraf (Tody, 1986, 1993) procedures for the reduction of long-
slit spectra (Massey et al., 1992; Massey, 1997), which we bias subtracted,
flat-field corrected, and wavelength and flux calibrated.

The observing setup delivered a useful spectral coverage between 3650$-$5050
Å, with a dispersion of $1.9$ Å/pixel (that translates to $\approx 120$ km s-1
at H$\beta$). Because the point-spread-function of the spectral trace was
smeared due to tracking limitations, the resolving power is strictly
determined by the slit width. We measured a spectral resolution of
$\Delta\lambda=6.5$ Å from the full width at half maximum of the He-Ar lines
of the calibration lamp. The residuals of the wavelength solution have a root-
mean-square of 0.2 Å. Given that no strong emission line from the night sky is
detectable within the wavelength range of our spectra, we assessed the
accuracy of the wavelength calibration by measuring the radial velocities of
the white dwarf standards GD 50 and LTT 7987. Following the line-fitting
technique adopted by Napiwotzki et al. (2020), we used their analysis
software, fitsb2, to measure the radial velocity, $\varv_{\rm rad}$, of the
white dwarf standards by iteratively combining synthetic spectra (Koester,
2010) with Gaussian and/or Lorentzian functions. From this procedure, we
estimated an average systematic uncertainty of $\pm 25$ km s-1 with respect to
the values published by Napiwotzki et al. (2020), which we will add in
quadrature to that obtained for the radial measurements of our science
targets.

Figure 3: On-sky distribution of Gaia-selected candidate blue stars at high
Galactic latitude (grey ’+’ symbols). The 48 observed targets (circles) and
known MS runaway stars (red ’x’ symbols; Silva & Napiwotzki, 2011) are also
shown. Table 1: Gaia DR2 data for the observed 48 targets.

Gaia DR2 | $\alpha$ | $\delta$ | $\mu^{*}_{\alpha}$ | $\mu_{\delta}$ | $\varpi$ | $G$ | $G_{\rm BP}$ | $G_{\rm RP}$ | Short name | Observing date
---|---|---|---|---|---|---|---|---|---|---
| (hms) | (dms) |  (mas yr-1) |  (mas yr-1) | (mas) | (mag) | (mag) | (mag) |  (hhmm$\pm$ddmm) | (yyyy-mm-dd)
4907042024497066752 | 00:35:19.19 |  $-$59:00:22.35 | $12.35\,\pm\,0.05$ | $-8.92\,\pm\,0.04$ | $0.12\pm 0.03$ | 14.47 | 14.46 | 14.44 |  0035$-$5900 | 2019-08-16
4901793883699014912 | 00:37:24.77 |  $-$61:54:55.17 | $4.29\,\pm\,0.07$ | $5.15\,\pm\,0.06$ | $0.17\pm 0.04$ | 14.64 | 14.56 | 14.71 |  0037$-$6154 | 2019-08-20
4707068828231737856 | 00:38:16.76 |  $-$66:12:17.46 | $21.22\,\pm\,0.05$ | $-12.31\,\pm\,0.05$ | $0.23\pm 0.03$ | 13.86 | 13.85 | 13.84 |  0038$-$6612 | 2019-08-16
4992937934442887296 | 00:39:20.74 |  $-$42:01:22.10 | $20.70\,\pm\,0.04$ | $-12.06\,\pm\,0.05$ | $0.23\pm 0.04$ | 14.04 | 13.99 | 14.05 |  0039$-$4201 | 2019-08-16
4921153294167369856 | 00:49:49.34 |  $-$53:56:30.65 | $20.97\,\pm\,0.04$ | $-10.96\,\pm\,0.04$ | $0.24\pm 0.03$ | 13.79 | 13.77 | 13.75 |  0049$-$5356 | 2019-08-16
4692515142570804608 | 01:22:35.90 |  $-$67:59:13.95 | $17.26\,\pm\,0.07$ | $-10.09\,\pm\,0.05$ | $0.21\pm 0.03$ | 14.71 | 14.62 | 14.77 |  0122$-$6759 | 2019-08-16
4714790492235234176 | 02:05:56.74 |  $-$59:38:35.84 | $6.14\,\pm\,0.07$ | $2.11\,\pm\,0.06$ | $0.15\pm 0.04$ | 13.07 | 12.97 | 13.15 |  0205$-$5938 | 2019-08-20
5050539802435511552 | 02:45:48.67 |  $-$34:18:56.36 | $48.43\,\pm\,0.04$ | $-9.93\,\pm\,0.06$ | $0.51\pm 0.04$ | 12.41 | 12.40 | 12.36 |  0245$-$3418 | 2019-08-18
5153423785504601216 | 02:59:01.73 |  $-$17:04:59.96 | $0.67\,\pm\,0.06$ | $-6.63\,\pm\,0.07$ | $0.17\pm 0.04$ | 13.58 | 13.52 | 13.63 |  0259$-$1705 | 2019-08-20
5768566765625082112 | 16:21:57.93 |  $-$83:50:56.96 | $2.77\,\pm\,0.07$ | $6.87\,\pm\,0.08$ | $0.18\pm 0.04$ | 14.01 | 13.83 | 14.20 |  1621$-$8350 | 2019-08-20
4568776103982893056 | 17:15:28.48 | +23:41:27.05 | $1.39\,\pm\,0.04$ | $-25.74\,\pm\,0.05$ | $0.26\pm 0.03$ | 14.27 | 14.21 | 14.30 | 1715+2341 | 2019-08-18
6414065681237630720 | 18:39:12.47 |  $-$75:15:41.08 | $-0.63\,\pm\,0.06$ | $-16.08\,\pm\,0.09$ | $0.20\pm 0.05$ | 16.03 | 15.95 | 16.09 |  1839$-$7515 | 2019-08-19
6655084093244687872 | 18:51:05.60 |  $-$50:36:39.75 | $2.62\,\pm\,0.06$ | $-10.83\,\pm\,0.06$ | $0.16\pm 0.04$ | 15.04 | 15.01 | 15.01 |  1851$-$5036 | 2019-08-19
6421018924052925952 | 19:00:44.83 |  $-$70:32:03.13 | $-12.38\,\pm\,0.04$ | $-22.21\,\pm\,0.05$ | $0.28\pm 0.03$ | 13.37 | 13.37 | 13.32 |  1900$-$7032 | 2019-08-18
6421018717894498048 | 19:00:33.66 |  $-$70:33:35.28 | $5.70\,\pm\,0.05$ | $-2.46\,\pm\,0.06$ | $0.15\pm 0.04$ | 13.83 | 13.71 | 13.96 |  1900$-$7033 | 2019-08-20
6446292607565372800 | 19:19:54.92 |  $-$59:38:28.88 | $5.21\,\pm\,0.06$ | $-21.40\,\pm\,0.05$ | $0.22\pm 0.05$ | 14.45 | 14.43 | 14.41 |  1919$-$5938 | 2019-08-17
4180161033474768640 | 19:39:22.50 |  $-$16:40:43.31 | $1.43\,\pm\,0.11$ | $-8.85\,\pm\,0.09$ | $0.23\pm 0.05$ | 12.66 | 12.56 | 12.70 |  1939$-$1640 | 2019-08-19
6683685723576804992 | 19:44:12.51 |  $-$46:28:58.22 | $-0.38\,\pm\,0.08$ | $-36.87\,\pm\,0.07$ | $0.30\pm 0.05$ | 13.32 | 13.19 | 13.40 |  1944$-$4628 | 2019-08-16
6374275970335856512 | 20:19:00.99 |  $-$71:07:53.49 | $6.13\,\pm\,0.05$ | $-37.38\,\pm\,0.06$ | $0.39\pm 0.04$ | 12.74 | 12.72 | 12.71 |  2019$-$7107 | 2019-08-17
6846204709077343872 | 20:24:00.16 |  $-$27:25:25.22 | $-11.54\,\pm\,0.07$ | $-22.39\,\pm\,0.05$ | $0.29\pm 0.04$ | 13.99 | 13.96 | 13.98 |  2024$-$2725 | 2019-08-18
6855907796113999872 | 20:28:33.90 |  $-$22:18:19.49 | $-10.38\,\pm\,0.10$ | $-28.60\,\pm\,0.06$ | $0.31\pm 0.07$ | 12.38 | 12.37 | 12.33 |  2028$-$2218 | 2019-08-17
6901493616919722496 | 20:34:40.08 |  $-$11:08:05.94 | $-13.81\,\pm\,0.10$ | $-5.86\,\pm\,0.06$ | $0.34\pm 0.06$ | 12.45 | 12.37 | 12.50 |  2034$-$1108 | 2019-08-19
6474092762640262016 | 20:34:20.66 |  $-$53:07:06.23 | $-6.54\,\pm\,0.06$ | $-18.68\,\pm\,0.06$ | $0.19\pm 0.04$ | 13.43 | 13.41 | 13.40 |  2034$-$5307 | 2019-08-17
6854645866004127872 | 20:40:17.89 |  $-$23:36:47.22 | $-23.18\,\pm\,0.07$ | $-29.89\,\pm\,0.05$ | $0.38\pm 0.04$ | 13.36 | 13.33 | 13.33 |  2040$-$2336 | 2019-08-17
6805531918539239040 | 20:54:36.95 |  $-$25:26:12.89 | $-4.22\,\pm\,0.09$ | $-5.34\,\pm\,0.05$ | $0.18\pm 0.05$ | 13.43 | 13.33 | 13.52 |  2054$-$2526 | 2019-08-19
6470192756241354240 | 20:58:10.82 |  $-$54:07:33.00 | $1.14\,\pm\,0.06$ | $-28.15\,\pm\,0.06$ | $0.29\pm 0.05$ | 13.11 | 13.10 | 13.05 |  2058$-$5407 | 2019-08-18
6456376915897827456 | 21:03:25.75 |  $-$58:15:35.28 | $-15.18\,\pm\,0.06$ | $-20.15\,\pm\,0.06$ | $0.26\pm 0.04$ | 13.48 | 13.46 | 13.46 |  2103$-$5815 | 2019-08-18
6802706551612738432 | 21:10:28.12 |  $-$27:00:29.36 | $-2.31\,\pm\,0.08$ | $-25.71\,\pm\,0.05$ | $0.27\pm 0.06$ | 13.28 | 13.28 | 13.23 |  2110$-$2700 | 2019-08-18
6401710125478435200 | 21:14:02.00 |  $-$64:38:47.32 | $16.33\,\pm\,0.04$ | $-17.01\,\pm\,0.04$ | $0.24\pm 0.03$ | 13.97 | 13.93 | 13.98 |  2114$-$6438 | 2019-08-17
6479124127849108736 | 21:19:11.03 |  $-$48:27:17.63 | $16.91\,\pm\,0.08$ | $-11.78\,\pm\,0.06$ | $0.21\pm 0.05$ | 14.53 | 14.51 | 14.47 |  2119$-$4827 | 2019-08-17
6467153298080614400 | 21:25:20.11 |  $-$48:34:50.08 | $2.13\,\pm\,0.06$ | $-19.70\,\pm\,0.06$ | $0.19\pm 0.05$ | 14.11 | 14.09 | 14.09 |  2125$-$4834 | 2019-08-20
6403485802397156992 | 21:27:10.30 |  $-$63:00:27.09 | $12.34\,\pm\,0.03$ | $-16.52\,\pm\,0.04$ | $0.17\pm 0.03$ | 13.86 | 13.85 | 13.81 |  2127$-$6300 | 2019-08-18
6593248963749480320 | 21:45:10.70 |  $-$30:22:26.73 | $1.00\,\pm\,0.07$ | $-25.95\,\pm\,0.07$ | $0.25\pm 0.05$ | 13.66 | 13.64 | 13.63 |  2145$-$3022 | 2019-08-20
6619758674426791936 | 22:07:39.31 |  $-$26:45:05.56 | $11.25\,\pm\,0.11$ | $2.16\,\pm\,0.09$ | $0.24\pm 0.07$ | 12.11 | 12.04 | 12.18 |  2207$-$2645 | 2019-08-19
6568272908586299136 | 22:07:29.23 |  $-$43:29:30.49 | $17.90\,\pm\,0.04$ | $-25.14\,\pm\,0.05$ | $0.21\pm 0.04$ | 13.30 | 13.27 | 13.28 |  2207$-$4329 | 2019-08-19
6559602950163581952 | 22:07:25.53 |  $-$50:21:05.38 | $-8.77\,\pm\,0.05$ | $-26.38\,\pm\,0.07$ | $0.28\pm 0.04$ | 13.72 | 13.69 | 13.69 |  2207$-$5021 | 2019-08-19
6409382345817774080 | 22:08:51.34 |  $-$60:26:11.43 | $0.49\,\pm\,0.04$ | $-12.51\,\pm\,0.06$ | $0.27\pm 0.04$ | 13.82 | 13.74 | 13.86 |  2208$-$6026 | 2019-08-19
6568081112526763648 | 22:13:57.49 |  $-$43:57:43.72 | $8.19\,\pm\,0.05$ | $-11.90\,\pm\,0.06$ | $0.29\pm 0.04$ | 13.67 | 13.59 | 13.73 |  2213$-$4357 | 2019-08-19
6566677242336303360 | 22:14:14.76 |  $-$46:20:06.71 | $7.46\,\pm\,0.05$ | $-16.93\,\pm\,0.06$ | $0.17\pm 0.04$ | 14.77 | 14.71 | 14.79 |  2214$-$4620 | 2019-08-16
6623822705625945472 | 22:39:37.70 |  $-$24:55:02.94 | $55.31\,\pm\,0.12$ | $-24.94\,\pm\,0.12$ | $0.59\pm 0.08$ | 12.50 | 12.42 | 12.59 |  2239$-$2455 | 2019-08-18
6505572880055200896 | 22:50:15.10 |  $-$56:25:17.08 | $13.58\,\pm\,0.04$ | $-16.19\,\pm\,0.04$ | $0.15\pm 0.03$ | 14.42 | 14.41 | 14.38 |  2250$-$5625 | 2019-08-20
6514882651165295232 | 22:59:35.83 |  $-$49:31:18.23 | $8.68\,\pm\,0.04$ | $-27.30\,\pm\,0.06$ | $0.27\pm 0.06$ | 14.29 | 14.28 | 14.27 |  2259$-$4931 | 2019-08-20
6543384947494107392 | 23:04:43.81 |  $-$40:21:07.52 | $2.04\,\pm\,0.05$ | $-5.30\,\pm\,0.06$ | $0.14\pm 0.04$ | 13.89 | 13.86 | 13.87 |  2304$-$4021 | 2019-08-20
6556633886515772544 | 23:07:12.20 |  $-$31:57:38.11 | $20.57\,\pm\,0.10$ | $-9.06\,\pm\,0.07$ | $0.35\pm 0.05$ | 12.30 | 12.24 | 12.36 |  2307$-$3157 | 2019-08-19
6493693515910526208 | 23:09:26.75 |  $-$56:23:02.24 | $8.79\,\pm\,0.05$ | $-9.18\,\pm\,0.06$ | $0.32\pm 0.04$ | 13.53 | 13.47 | 13.56 |  2309$-$5623 | 2019-08-20
6391197660443817984 | 23:09:32.88 |  $-$67:29:14.43 | $6.16\,\pm\,0.04$ | $-23.25\,\pm\,0.05$ | $0.20\pm 0.03$ | 13.72 | 13.70 | 13.70 |  2309$-$6729 | 2019-08-18
6503103617457504000 | 23:13:52.61 |  $-$48:58:15.92 | $15.52\,\pm\,0.03$ | $-10.51\,\pm\,0.04$ | $0.19\pm 0.03$ | 14.09 | 14.08 | 14.04 |  2313$-$4858 | 2019-08-18
6389351133744091648 | 23:48:08.84 |  $-$66:12:17.59 | $2.88\,\pm\,0.05$ | $-9.08\,\pm\,0.05$ | $0.15\pm 0.03$ | 15.41 | 15.38 | 15.40 |  2348$-$6612 | 2019-08-20

111The short name is based on the Gaia RA and Dec, expressed in sexagesimal
units. 1900$-$7033 and 2239$-$2455 were previously known as JL 6 and PHL 5382,
respectively.

##  4 Data analysis

For the atmospheric characterization of the observed targets, we follow a
three-step approach. First, we perform model fitting of their entire spectral
energy distributions (SED) that consist of the available ground-based and
space-borne broad-band photometry, from which we estimate the atmospheric
parameters of each star, i.e., effective temperature and surface gravity, as
well as the interstellar reddening and angular diameter ($T_{\rm eff}$,
$\log{g}$, $E(44-55)$, and $\Theta$). Here, $E(44-55)$ is the monochromatic
reddening measured at 4400 and 5500 Å, which is closely related to the more
traditional band-integrated color excess $E(B-V)$, following the definition of
Fitzpatrick et al. (2019). Second, we use the photometric estimates as initial
guesses for the spectral analysis of flux calibrated spectra. Third, we re-
determine $E(44-55)$ and $\Theta$, by employing the spectroscopic best-fit
model in the SED-fitting procedure.

###  4.1 Grids of synthetic spectra

Due to the low resolution of the spectra in hand, only stellar parameters such
as $T_{\rm eff}$ and $\log{g}$ can reliably be measured, while rotation,
metallicity, and helium abundance are very poorly constrained, especially in
the late-B/early-A spectral type transition, where many candidates are found.
In this region of the Hertzsprung-Russell diagram, MS and BHB stars can not be
distinguished on the basis of their atmospheric parameters alone (see Fig. 1),
but additional information on the chemical composition and rotation of the
stars is needed (see e.g. Heber et al., 2008b). Because the lack of spectral
resolving power does not allow us to accurately obtain this auxiliary
information, we perform the analysis of the SEDs and spectra for all targets
twice by using two different grids of synthetic models, one being appropriate
for MS stars and one being tailored to BHB stars, see below. The distinction
between MS and BHB nature is then made based on the agreement of their
spectrophotometric and parallax-based distances (see Sect. 4.4).

For MS stars it is self-evident to adopt a solar chemical composition. In
contrast, the abundance patterns of BHB stars are diverse. Because the targets
were selected to have high tangential velocities, BHB candidates are likely
halo stars and thus metal poor. However, the stars’ chemical composition also
varies along the horizontal branch. The morphology of BHBs of globular
clusters reveals a universal discontinuity at $T_{\rm eff}\sim 11\,500$ K
(Grundahl et al., 1999; Brown et al., 2016), which coincides with a drastic
change in the chemical composition. While BHB stars cooler than 11 500K have
the same metal content as the bulk of the stars of the host cluster, the
abundance pattern of the hotter stars is peculiar, with helium depletion and
iron enrichment (Behr, 2003). These chemical pecularities have been attributed
to atomic diffusion, that is, to an interplay of gravitational settling and
radiative levitation. The former leads to helium depletion and the latter
causes the iron enrichment. The onset of atomic diffusion coincided with the
disappearance of surface convection (Sweigart, 2002; Michaud et al., 2011).
Because we can not determine the abundance pattern of the individual BHB
stars, we calculate model atmospheres and synthetic spectra assuming a
metalicity of one tenth solar for all BHB stars, but different helium
abundances, that is, solar helium content for stars cooler than 11 500 K and
1/10 solar for the hotter ones.

Both grids span $T_{\rm eff}=7200$–$33\,000$ K and $\log{g}=3.0$–$4.6$. For
$T_{\rm eff}\geq 9000$ K, we adopt the hybrid approach “ADS” (Przybilla et
al., 2011; Irrgang et al., 2014), which combines Atlas12 (Kurucz, 1996) to
compute hydrostatic model atmospheres in local thermodynamic equilibrium (LTE)
with Detail (Giddings, 1981) to account for non-LTE effects; the Surface
software (Giddings, 1981) is used to produce the synthetic spectrum. Another
set of models, which extends below $10\,000$ K, has been generated by
accounting only for LTE by means of the Atlas12 and synthe software (Kurucz,
1993). All models include the recent improvements introduced by Irrgang et al.
(2018b) for the computation of level dissolution in proximity of the Balmer
jump. The synthetic photometry is based on SEDs computed with Atlas12 using a
ten times finer frequency grid, which were convolved with the appropriate
transmission profile of each band-pass and subsequently shifted to the
respective zero point.

Figure 4: Examples for SED fits, from top left to bottom right: the MS
candidates 0259$-$1705, 1900$-$7033, 2207$-$4329, and 2259$-$4931; the BHB
candidate 1851$-$5036; and the binary 1944$-$4628\. In each plot, the top
panels show the measurements (color-coded by photometric system) as well as
the best-fitting model spectra (gray), while the bottom panels show the error-
normalized best-fit residuals, $\chi=(O_{i}-M_{i})/\sigma_{i}$, for each band-
pass. The object 1944$-$4628 requires a composite SED fit, which is the
combination of a $T_{\rm eff}\approx 24\,400$ K and a $T_{\rm eff}\approx
5900$ K component (blue and red curve, respectively).

###  4.2 SED fitting

We use the stilts software (Taylor, 2006) to query all the major photometric
surveys that are available through the Table Access Protocol (TAP) of the
VizieR online service (Ochsenbein, 2019), which is hosted by the Strasbourg
Astronomical Data Center. For most of the stars, in addition to Gaia
photometry, there is reliable coverage from the ultraviolet (GALEX; Bianchi et
al., 2017) through the optical (APASS and SkyMapper; Henden et al., 2015; Wolf
et al., 2018, as well as SDSS and PanSTARRS, for targets with
$\delta\gtrsim-30$ deg; Alam et al. 2015; Chambers et al. 2016) and infrared
(VHS, 2MASS, and WISE; McMahon et al., 2013; Skrutskie et al., 2006; Cutri &
et al., 2014; Schlafly et al., 2019) We adopt the most recent calibration of
GALEX (Wall et al., 2019), well-validated zero points and uncertainties for
the other photometric surveys222SkyMapper (Casagrande et al., 2019), SDSS
(Holberg & Bergeron, 2006), PanSTARRS (Tonry et al., 2012), 2MASS (Maíz
Apellániz et al., 2018), UKIDDS (Hewett et al., 2006), VHS (González-Fernández
et al., 2018), WISE (Jarrett et al., 2011)., as well as suggested corrections
of Gaia DR2 photometry and the corresponding filter transmission profiles
(Evans et al., 2018; Maíz Apellániz & Weiler, 2018).

The SED fitting procedure follows the methods outlined by Heber et al. (2018),
allowing to directly estimate the four parameters: $\Theta$, $T_{\rm eff}$,
$\log{g}$, and $E(44-55)$. We adopt the monochromatic extinction law by
Fitzpatrick et al. (2019) with the total-to-selective extinction coefficient
$R(55)=3.02$, as typical for the interstellar medium. The best-fit is found by
matching observed and synthetic photometry via $\chi^{2}$ minimization. Each
stellar SED is fitted with both model grids described in the previous section.
Six examples are displayed in Fig. 4.

The preliminary SED fitting does not only provide an initial guess for the
spectroscopic analysis, but is also crucial for identifying problematic
objects like binary stars that exhibit composite SEDs. Indeed, we find that a
single stellar component is not sufficient to model the SED of 1944$-$4628,
which is likely an evolved low-mass star with an infrared excess due to a
cooler binary companion (Fig. 4). Last but not least: photometric temperature
estimates provide an important consistency check for our spectroscopic
analysis, see the following section.

Figure 5: Comparisons between photometric $T_{\rm eff}$, measured via SED
fitting, and spectroscopic $T_{\rm eff}$. The result for MS (top left panel)
and BHB models (top right panel) are shown. The dashed lines represent the
equality curves. The residuals are displayed as function of photometric
$T_{\rm eff}$ in the lower panels. The gray shaded area represent the 4%
systematic uncertainty assumed for the spectroscopic results. Figure 6:
Observed spectra, sorted by decreasing $T_{\rm eff}$.

Figure 7: Examples of spectroscopic best-fits for four MS candidates (Sect.
4.4) with error-normalized residuals; from top left to bottom right:
1900$-$7033, 0259$-$1705, 2207$-$4329, and 2259$-$4931\. The normalized
spectra and the best-fit solar-metallicity models are shown in black and red,
respectively. The two top panels show ADS models, while the bottom ones are
obtained from the Atlas12/synthe grid. H and He lines are labeled at the
corresponding wavelengths. The Ca ii lines are masked out during the fitting
procedure due to possible interstellar contamination, which is recognizable in
the spectrum of 1900$-$7033; masked regions are plotted using lighter colors.
We note that the He i lines of 1900$-$7033 are stronger than those of our
solar-metallicity model (c.f. Sect. 4.3 for a discussion on this star). The
second star, 0259$-$1705, shows an excellent agreement between observed and
model spectrum. In contrast, the Ca ii H lines of the two coolest stars in the
bottom panels and the Mg ii 4481 line of 2259$-$4931 are weaker than those of
the best-fit MS model. This issue, although to a lesser extent, also
characterizes the best-fit obtained with sub-solar metallicity models.

###  4.3 Spectroscopic fitting

The analysis of flux-calibrated spectra follows the methods outlined by
Irrgang et al. (2014), where the best-fits are determined via $\chi^{2}$
statistics through comparison with our model grids. We preferentially use ADS
models, but we switch to the Atlas12/synthe grid in order to avoid
extrapolation at the edge of the ADS grids. We ignore macroturbulence and
assume a microturbulence of 2 km s-1. As stated in Sect. 4.1, the low
resolution of our spectra makes it difficult to measure detailed metal
abundances and stellar rotation, hence, our approach is to fit the spectra
with both the solar composition and the metal-deficient grids, respectively.

Mg and Si are the only elements for which the individual abundances are
allowed to independently vary when using the ADS grids. However, we note that
most measurements are poorly constrained and do not deliver reliable
abundances, which is why we refrain from giving those numbers. Although we
keep the projected rotational velocity, $\varv\sin{i}$, as a free parameter,
it can be hardly resolved from our low-resolution spectra ($\Delta\varv\approx
400$ km s-1). The spectra are corrected for the barycentric velocity and the
radial velocity, $\varv_{\rm rad}$, is independently determined from each
exposure. Statistical uncertainties affecting $T_{\rm eff}$ and $\log{g}$ are
numerically inconspicuous. The systematic uncertainties dominating the error
budget of $T_{\rm eff}$ and $\log{g}$ are estimated to the level of 4% and 0.1
dex, respectively. The error budget of $\varv_{\rm rad}$ is also dominated by
systematic uncertainties, which are estimated from the difference between the
measured values of the two available exposures for each star ($\lesssim 10$ km
s-1) and the 25 km s-1 error, determined by comparing the $\varv_{\rm rad}$ of
the white dwarf standards to values from the literature (Sect. 3).

The main results of our analysis are presented in Fig. 5, which displays the
comparison between photometric and spectroscopic $T_{\rm eff}$ for the MS and
BHB model analyses. The good agreement seen in Fig. 5 confirms the robustness
of the SED and spectroscopic analyses, but also suggests that an additional
method (like the distance comparison discussed in the following section) is
necessary to distinguish between MS and BHB candidates.

Two stars, 1621$-$8350 and 1944$-$4628, are considerably hotter than the bulk
of the sample, and are not included in Fig. 5. 1621$-$8350 is the only star
that shows a He ii line (at 4685.8 Å) in its spectrum (Fig. 6), which leads to
the classification of an O type star that is consistent with a high $T_{\rm
eff}\approx 30\,000$ K. 1944$-$4628 is an early B-type star in a binary system
(Fig. 4) at $T_{\rm eff}\approx 24\,400$ K. Both stars are discussed
separately in Sect. 4.4.

A spectral atlas of our program stars is presented in Fig. 6, while examples
of spectroscopic best-fits are shown in Fig. 7 for four stars (0259$-$1705,
1900$-$7033, 2207$-$4329, and 2259$-$4931) that are later classified as MS
candidates based on their spectrophotometric distances (Sect. 4.4). In this
figure, we exhibit three typical temperature regimes of our sample. We note
that for hot stars like 1900$-$7033, shown in Fig. 7, and 1939$-$1640 and
2054$-$2526, it would be in fact possible to have more reliable He abundance
measurements rather than assuming solar composition, but this exercises is
beyond the scope of the paper. For cool objects like 2207$-$4329 and
2259$-$4931, we can see just a few weak metal lines. In these specific cases,
both MS and BHB models seem to overestimate the intensity of the Ca ii H line,
hinting at a sub-solar abundance that could be better investigated with
higher-resolution spectra. The intensity of the Mg ii 4481 line of 2207$-$4329
is also overestimated. The star with an intermediate temperature, 0259$-$1705,
shows an excellent agreement with the model.

Finally, we report that three stars were previously studied by other authors:

1900$-$7033: Kilkenny (1989) determined $T_{\rm eff}=18\,000$ K and
$\log{g}=4.0$ with 10 % errors from 3 Å-resolution spectra, in agreement with
our results. This author proposed the star to be mildly He-rich ($n$He/$n$H
$\sim 0.3$). This finding is supported by our observations, because the He
lines appear slightly deeper than those of the best-fit model with solar
$\log{({\rm He/H})}=-1.01$ (see Fig. 7). Kilkenny (1989) also measured
$\varv\sin{i}=175$ km s-1 from the He lines, while the H$\gamma$ and H$\delta$
fits delivered smaller $\varv\sin{i}\approx 75$ and $100$ km s-1,
respectively. If we keep He as a free parameter, the best-fit result favors
slightly super-solar He, but the line cores of the observed spectrum are still
deeper than the model. Given that we cannot disentangle the effect of stellar
rotation due to the low resolution of our spectra, we adopt the atmospheric
parameters obtained for solar He abundance. Finally, Kilkenny (1989) reported
a previous measurement of $\varv_{\rm rad}\approx-95$ km s-1 that is at 2
$\sigma$ from our result.

2239$-$2455: Kilkenny (1987) used Strömgren photometry to classify this star
as B7V, which is compatible with our spectral analysis. Ortiz et al. (2007)
obtained 1.2 Å-resolution spectra over the H$\beta$–H$\epsilon$ spectral
range, from which they suggest $T_{\rm eff}>17\,000$ K and $\log{g}=4.5\pm
0.5$ via measurements of equivalent widths and depths of the Balmer lines.

2307$-$3157: Ortiz et al. (2007) determined $T_{\rm eff}=8500$–10 000 K and
$\log{g}=3$–3.5 with errors of 500 K and 0.5 dex, respectively, that roughly
agree with our results.

Figure 8: Kiel diagrams showing the atmospheric parameters of the observed
stars as determined via the spectroscopic best-fit with model spectra
representing MS and BHB stars (top and bottom panels, respectively). Top
panel: Evolutionary tracks for rotating MS stars are plotted in black (Ekström
et al., 2012). The initial masses of each model are noted below the zero-age
MS (thick solid curve), while the stellar ages for selected evolutionary
points along the tracks are given in mega years. Bottom panel: The horizontal
branch is represented by the gray shaded area, and the evolutionary tracks for
post-horizontal branch stars of different masses are drawn as solid curves
(Dorman, 1992). Figure 9: Comparison between spectrophotometric distances and
three different parallax-based distance estimates. Upper panels: MS candidates
(blue colored symbols) are identified via the 1 $\sigma$ agreement, which is
represented by the dashed equality line and the shaded gray area. Lower
panels: as for the upper panels, BHB candidates are represented by orange
filled symbols. Note that three stars are classified both as MS and BHB
candidates, hence they are color-colored in both the upper and lower panels.

###  4.4 Distance-driven classification and physical parameters

Figure 10: Theoretical Hertzsprung-Russell diagrams. The top panel shows our
candidate MS stars over-plotted on Ekström et al. (2012) evolutionary tracks
for rotating stars. The masses of each model are plotted in correspondence of
the zero-age MS. The luminosities are derived by adopting the
spectrophotometric distances. The bottom panel shows our candidate BHB stars
over-plotted on the horizontal branch that is represented by a grey-shaded
area and the evolutionary tracks for post-horizontal branch stars of given
masses (Dorman, 1992; Dorman et al., 1993). Note that three stars are
classified both as MS and BHB candidates, hence they feature in both panels
with the appropriate parameters.

Figure 8 displays the $T_{\rm eff}$ and $\log{g}$ distribution of the observed
stars in the Kiel diagram,as derived from the spectral analysis with synthetic
spectra representing MS and BHB stars. For reference, we plot the theoretical
evolutionary tracks for MS rotating stars (Ekström et al., 2012), and the
horizontal branch and post-horizontal branch tracks (Dorman, 1992; Dorman et
al., 1993). Given the degeneracy between MS stars of 3–4 M☉ and BHB stars,
whose evolutionary tracks overlap in the Kiel diagram, and the lack of
additional information such as $\varv\sin{i}$ and metal abundances, it is a
priori impossible to classify the majority of stars in our sample by just
using $T_{\rm eff}$ and $\log{g}$.

Hence, to assess the nature of our program stars, we proceed in a different
fashion, by comparing the Gaia parallaxes to the spectrophotometric distances,
$D({\rm SpT})$, determined under the assumption that the observed stars are
either MS or BHB stars. In order to estimate $D({\rm SpT})$ under the MS-star
assumption, we first determine the stellar masses, radii, and luminosities via
interpolation of the Ekström et al. (2012) tracks shown in Fig. 8 onto the
$T_{\rm eff}$ and $\log{g}$ obtained via the spectroscopic fitting with the
solar-metallicity grid. The spectrophotometric distance is then computed from
the resulting stellar radius and the angular diameter determined via SED-
fitting: $D({\rm SpT})=2R/\Theta$. In the BHB-star assumption, we assume a
canonical BHB-star mass of $M=0.5\pm 0.1$ M☉ from which we infer the stellar
radius as $R=\sqrt{GM/g}$, where $G$ is the gravitational constant and $g$ is
the surface gravity measured with the representative metal-poor model grid.
Then, the $D({\rm SpT})$ is calculated as above using the appropriate
$\Theta$.

Figure 9 displays the comparison between parallax-based distance estimators,
$D(\varpi)$, and spectrophotometric distances for the MS and BHB results. The
simplest estimator that we consider is $D(\varpi)=1/\varpi$, where $D(\varpi)$
is the median of the $1/\varpi$ distribution. We also consider the effect of a
global zero-point shift of +0.03 mas, identified by Lindegren et al. (2018)
from the analysis of an all-sky sample of extra-galactic sources – but these
authors also noted that such an offset has relatively large variations over
degree-wide scales. Finally, as advised by Bailer-Jones et al. (2018) and Luri
et al. (2018), we also compare their prior-based distance estimate,
$D$(Bailer-Jones), against $D({\rm SpT})$.

MS and BHB stars are expected to lie on the identity lines depicted in Fig. 9,
when the $D({\rm SpT})$ computed from the corresponding models agree with the
parallax-based distance estimates. From this comparison, we identify 15 MS
candidates that have $D({\rm SpT})$ in agreement within 1 $\sigma$ with one of
the three $D(\varpi)$ estimators (top panels of Fig. 9). The same comparisons
for BHB estimates deliver 29 candidates (lower panels in Fig. 9). We note that
three stars (0035$-$5900, 2127$-$6300, and 2304$-$4021) are both identified as
MS and BHB candidates, while all the others are uniquely classified either as
MS or BHB candidates. Among the 29 BHB candidates, there are 1621$-$8350 and
1944$-$4628 too, which we discuss in more detail below as evolved extreme
horizontal branch stars (post-EHB). Seven stars of our sample do not fit in
any of the two proposed classification schemes.

In general, we note that all MS candidates agree with the $1/\varpi$ estimator
and that the other two estimators tend to bring the parallax-based distances
closer to the Sun. This effect is more extreme for the $D$(Bailer-Jones)
estimator of stars that have larger spectrophotometric distances, and it is
also noticeable for the BHB candidates. The overlap between the MS and BHB
candidates is limited to three stars, reinforcing the validity of this method.
Nevertheless, this ambiguity and the presence of seven unclassified stars
suggests the use of higher-resolution spectroscopy for future analysis in
addition to improved parallaxes from future Gaia releases. Finally, we note
that unclassified objects may point towards the presence of either unresolved
binaries or other kinds of stars, like field blue stragglers (Brown et al.,
2010) that we do not account for. Note that Brown et al. (2010) estimate that
74% of their blue halo star sample are BHBs and 26% are blue stragglers, which
comes close to the 27 BHB stars versus 7 unclassified objects in our sample.

Table 3 lists the atmospheric parameters corresponding to the spectroscopic
best-fit models implied by the unique distance-driven classification as MS/BHB
candidates, along with the signal-to-noise ratio (S/N) of the stacked spectra
and the $E(44-55)$. In passing, we note that the 7 unclassified stars cluster
around $T_{\rm eff}\approx 10\,000$ K and $\log{g}=3.6$. For the remainder of
the manuscript, we take a conservative approach by considering as runaway MS
candidates at high Galactic latitudes the 12 stars that uniquely agree within
1 $\sigma$ of the identity line in either of the top panels of Fig. 9,
assuming the three stars with ambiguous classification as BHB candidates.

The spectra of the two hottest stars previously mentioned (1621$-$8350 and
1944$-$4628) resemble those of MS objects of late O- and early B-type (see
Fig. 6). However, the respective spectroscopic distances would be about 30 and
10 kpc, which is at variance with their Gaia parallaxes (top panels of Fig.
9). Therefore, they must be evolved low-mass stars that mimic hot massive
stars. Such stars are rare but do exist, e.g., the B-type star HZ 22 of
$T_{\rm eff}=29\,200$ K and $\log{g}=4.04$ (Saffer et al., 1997) and the
O-type star PG2 120+062 (Moehler et al., 1994). HZ 22, in fact, is a binary
orbited by an unseen white dwarf, which allowed its mass to be estimated at
0.39 M☉ (Schönberner, 1978). Hence, those stars are likely post-RGB or post-
AGB stars. For a brief account of such so-called UV-bright stars see also
Heber (2016).

While the SED of 1621$-$8350 can be matched by a single hot star model, this
is not the case for 1944$-$4628, which shows an infrared excess indicative of
a cool companion (Fig. 4). Adding a grid of SEDs from Husser et al. (2013),
the infrared excess can well be matched by a composite model SED that includes
a companion of $T_{\rm eff}$ = 5900${}^{+1300}_{-1200}$ K with a radius of
1.34${}^{+0.60}_{-0.35}$ R⊙. Although uncertainties are large, the derived
radius and luminosity of the companion are consistent with those of a G-type
MS star.

We list the physical parameters of the 12 MS candidates in Table LABEL:t:ms.
The physical parameters of the 27 BHB candidates as well as those of the two
post-EHB candidates and the late-type companion of 1944$-$4628 are given in
Table 4.4.

To conclude this section, we present the results of our classification in the
two theoretical Hertzsprung-Russell diagrams of Fig. 10, displaying the MS and
BHB candidates with their appropriate evolutionary tracks. A few MS candidates
appear to be fairly evolved, with evolutionary timescales, $\tau_{\rm evo}$,
in the range of 300–400 Myr. The BHB candidates are mostly distributed along
their main locus. From Fig. 8–10, we conclude that the positions of
1621$-$8350 and 1944$-$4628 are well matched by the evolution of EHB stars
(subluminous B stars) after core helium exhaustion (Dorman et al., 1993).

Table 2: Spectroscopic parameters of the sample derived from model spectra, as
appropriate for their classification (MS or BHB candidate, respectively).
Unclassified stars are listed at the bottom with their parameters derived from
models with sub-solar composition.

Short name | S/N | $T_{\rm eff}$ | $\log{g}$ | $\varv_{\rm rad}$ | $E(44-55)$ | MS
---|---|---|---|---|---|---
|  | (K) | $\log{({\rm cm\,s}^{-2})}$ |  (km s-1) | (mag) |
0035$-$5900 | 180 | $8900$ | 3.19 | $141\,\pm\,31$ | $0.02\,\pm\,0.02$ | ✓✗
0037$-$6154 | 230 | $11\,900$ | 4.05 | $138\,\pm\,26$ | $<\,0.01$ | ✓
0038$-$6612 | 220 | $8900$ | 3.18 | $233\,\pm\,26$ | $<\,0.01$ | ✗
0039$-$4201 | 220 | $10\,300$ | 3.58 | $144\,\pm\,25$ | $<\,0.02$ | ✗
0049$-$5356 | 240 | $9300$ | 3.42 | $-109\,\pm\,26$ | $<\,0.02$ | ✗
0122$-$6759 | 140 | $12\,800$ | 3.91 | $272\,\pm\,27$ | $<\,0.01$ | ✗
0205$-$5938 | 380 | $12\,300$ | 3.81 | $109\,\pm\,27$ | $0.00$ | ✓
0245$-$3418 | 370 | $9300$ | 3.47 | $123\,\pm\,28$ | $<\,0.06$ | ✗
0259$-$1705 | 370 | $12\,100$ | 4.07 | $185\,\pm\,26$ | $0.04\,\pm\,0.02$ | ✓
1621$-$8350a | 210 | $29\,400$ | 4.00 | $115\,\pm\,39$ | $0.08\,\pm\,0.02$ | ✗
1715+2341 | 190 | $12\,700$ | 3.83 | $1\,\pm\,26$ | $0.04\,\pm\,0.02$ | ✗
1839$-$7515 | 50 | $18\,100$ | 4.53 | $65\,\pm\,26$ | $0.12\,\pm\,0.03$ | ✗
1851$-$5036 | 120 | $10\,500$ | 3.38 | $-28\,\pm\,26$ | $0.05\,\pm\,0.03$ | ✗
1900$-$7032 | 340 | $9800$ | 3.58 | $-46\,\pm\,28$ | $0.05\,\pm\,0.04$ | ✓✗
1900$-$7033 | 250 | $16\,800$ | 4.19 | $-38\,\pm\,26$ | $0.02\,\pm\,0.02$ | ✓
1919$-$5938 | 160 | $10\,300$ | 3.61 | $-88\,\pm\,25$ | $0.06\,\pm\,0.04$ | ✗
1939$-$1640 | 200 | $18\,300$ | 4.20 | $224\,\pm\,26$ | $0.12\,\pm\,0.01$ | ✓
1944$-$4628a,b | 260 | $22\,300$ | 4.02 | $261\,\pm\,26$ | $0.16\,\pm\,0.02$ | ✗
2019$-$7107 | 320 | $10\,100$ | 3.60 | $109\,\pm\,26$ | $0.05\,\pm\,0.03$ | ✓✗
2024$-$2725 | 180 | $10\,700$ | 3.67 | $123\,\pm\,26$ | $0.05\,\pm\,0.03$ | ✗
2028$-$2218 | 380 | $10\,000$ | 2.84 | $79\,\pm\,25$ | $0.05\,\pm\,0.03$ | ✗
2034$-$1108 | 250 | $12\,400$ | 4.00 | $-74\,\pm\,28$ | $0.02\,\pm\,0.02$ | ✓
2034$-$5307 | 280 | $9800$ | 3.61 | $123\,\pm\,28$ | $0.04\,\pm\,0.03$ | ✓
2054$-$2526 | 220 | $16\,000$ | 3.97 | $65\,\pm\,26$ | $0.05\,\pm\,0.02$ | ✓
2110$-$2700 | 270 | $9800$ | 3.48 | $-3\,\pm\,33$ | $0.06\,\pm\,0.03$ | ✗
2114$-$6438 | 160 | $10\,400$ | 3.53 | $17\,\pm\,28$ | $0.02\,\pm\,0.02$ | ✗
2119$-$4827 | 120 | $10\,400$ | 3.16 | $27\,\pm\,25$ | $0.10\,\pm\,0.03$ | ✗
2125$-$4834 | 230 | $10\,000$ | 3.61 | $8\,\pm\,26$ | $0.04\,\pm\,0.03$ | ✗
2145$-$3022 | 280 | $9700$ | 3.53 | $179\,\pm\,27$ | $0.04\,\pm\,0.04$ | ✗
2207$-$2645 | 340 | $12\,200$ | 3.78 | $51\,\pm\,26$ | $0.02\,\pm\,0.02$ | ✓
2207$-$4329 | 150 | $9700$ | 3.62 | $-170\,\pm\,26$ | $0.02\,\pm\,0.02$ | ✓
2207$-$5021 | 190 | $9800$ | 3.61 | $75\,\pm\,26$ | $0.03\,\pm\,0.03$ | ✗
2208$-$6026 | 250 | $12\,000$ | 3.76 | $356\,\pm\,25$ | $<\,0.03$ | ✗
2213$-$4357 | 250 | $12\,100$ | 3.67 | $64\,\pm\,29$ | $<\,0.01$ | ✗
2214$-$4620 | 160 | $10\,400$ | 3.62 | $112\,\pm\,26$ | $0.01\,\pm\,0.01$ | ✗
2239$-$2455 | 320 | $12\,700$ | 3.83 | $-43\,\pm\,29$ | $<\,0.01$ | ✗
2250$-$5625 | 220 | $8800$ | 3.20 | $118\,\pm\,26$ | $<\,0.01$ | ✗
2259$-$4931 | 250 | $9200$ | 4.16 | $244\,\pm\,27$ | $<\,0.01$ | ✓
2307$-$3157 | 320 | $11\,100$ | 3.94 | $-2\,\pm\,29$ | $0.01\,\pm\,0.01$ | ✓
2313$-$4858 | 210 | $8700$ | 3.22 | $-183\,\pm\,29$ | $<\,0.01$ | ✗
2348$-$6612 | 130 | $10000$ | 3.51 | $225\,\pm\,26$ | $<\,0.04$ | ✗
2040$-$2336 | 260 | $10\,200$ | 3.92 | $56\,\pm\,26$ | $0.05\,\pm\,0.03$ |
2058$-$5407 | 300 | $9700$ | 3.60 | $-8\,\pm\,30$ | $0.06\,\pm\,0.03$ |
2103$-$5815 | 300 | $10\,000$ | 3.60 | $121\,\pm\,27$ | $0.03\,\pm\,0.03$ |
2127$-$6300 | 220 | $9100$ | 3.26 | $99\,\pm\,26$ | $<\,0.03$ |
2304$-$4021 | 300 | $8800$ | 2.99 | $27\,\pm\,27$ | $0.00$ |
2309$-$5623 | 340 | $9900$ | 3.21 | $186\,\pm\,27$ | $0.00$ |
2309$-$6729 | 290 | $9800$ | 3.52 | $126\,\pm\,32$ | $0.02\,\pm\,0.02$ |
333Signal-to-noise ratio, effective temperature, surface gravity, radial
velocity, and interstellar reddening, and MS-candidate classification of the
observed stars. Systematic uncertainties are of the order of 4% and 0.1 dex
for $T_{\rm eff}$ and $\log{g}$, respectively. $a$$a$footnotetext: This star
is a hot evolved star (see Sect. 4.3); based on solar-metallicity models.
$b$$b$footnotetext: The result may be affected by the presence of an infrared
excess (see Fig. 4).

Table 3: Physical parameters of the MS candidates: mass, radius, luminosity,
age, and spectrophotometric distance.

Short name |  $M$/M☉ |  $R$/R☉ | $\log{L/{\rm L}_{\sun}}$ | $\tau_{\rm evo}$ |  $D$(SpT)
---|---|---|---|---|---
|  |  |  | (Myr) | (kpc)
0037$-$6154 | $3.17^{+0.32}_{-0.17}$ | $2.77^{+0.54}_{-0.40}$ | $2.13^{+0.18}_{-0.15}$ | $213^{+28}_{-79}$ | $8.34^{+1.80}_{-1.30}$
0205$-$5938 | $3.91^{+0.38}_{-0.29}$ | $4.07^{+0.79}_{-0.64}$ | $2.53^{+0.19}_{-0.17}$ | $152^{+25}_{-22}$ | $6.19^{+1.35}_{-1.05}$
0259$-$1705 | $3.42^{+0.24}_{-0.21}$ | $2.83^{+0.51}_{-0.43}$ | $2.19^{+0.17}_{-0.15}$ | $148^{+57}_{-66}$ | $5.04^{+0.98}_{-0.80}$
1900$-$7033 | $5.04^{+0.36}_{-0.25}$ | $3.00^{+0.54}_{-0.44}$ | $2.81^{+0.15}_{-0.14}$ | $38^{+20}_{-24}$ | $8.19^{+1.57}_{-1.25}$
1939$-$1640 | $5.81^{+0.36}_{-0.35}$ | $3.16^{+0.55}_{-0.47}$ | $3.00^{+0.15}_{-0.15}$ | $27^{+16}_{-20}$ | $4.72^{+0.86}_{-0.73}$
2034$-$1108 | $3.58^{+0.28}_{-0.24}$ | $3.14^{+0.58}_{-0.48}$ | $2.32^{+0.17}_{-0.16}$ | $165^{+26}_{-36}$ | $3.48^{+0.68}_{-0.56}$
2034$-$5307 | $3.00^{+0.37}_{-0.11}$ | $4.51^{+0.94}_{-0.60}$ | $2.23^{+0.19}_{-0.14}$ | $317^{+48}_{-59}$ | $6.01^{+1.34}_{-0.85}$
2054$-$2526 | $5.21^{+0.48}_{-0.36}$ | $3.91^{+0.74}_{-0.60}$ | $2.95^{+0.17}_{-0.15}$ | $63^{+9}_{-13}$ | $8.22^{+1.68}_{-1.33}$
2207$-$2645 | $3.90^{+0.26}_{-0.21}$ | $4.20^{+0.75}_{-0.62}$ | $2.54^{+0.15}_{-0.14}$ | $171^{+23}_{-21}$ | $3.96^{+0.75}_{-0.61}$
2207$-$4329 | $2.97^{+0.31}_{-0.12}$ | $4.45^{+0.88}_{-0.60}$ | $2.21^{+0.17}_{-0.14}$ | $329^{+50}_{-58}$ | $5.71^{+1.21}_{-0.81}$
2259$-$4931 | $2.17^{+0.18}_{-0.20}$ | $2.03^{+0.38}_{-0.33}$ | $1.43^{+0.16}_{-0.21}$ | $462^{+160}_{-212}$ | $3.97^{+0.80}_{-0.79}$
2307$-$3157 | $3.15^{+0.29}_{-0.24}$ | $3.14^{+0.60}_{-0.49}$ | $2.13^{+0.17}_{-0.16}$ | $236^{+26}_{-36}$ | $3.01^{+0.61}_{-0.49}$

Table 4: Physical parameters of BHB and post-EHB candidates computed adopting
the atmospheric parameters derived from metal deficient atmospheric models and
a mass of $M=0.5\pm 0.1$ M☉. The two hot post-EHB stars are listed at the end.
1944$-$4628B denotes the cool companion of 1944$-$4628.

Short name |  $R$/R☉ | $\log{L/{\rm L}_{\sun}}$ |  $D$(SpT)
---|---|---|---
|  |  | (kpc)
0035$-$5900 | $2.94^{+0.48}_{-0.44}$ | $1.68^{+0.15}_{-0.16}$ | $5.84^{+1.03}_{-0.92}$
0038$-$6612 | $2.97^{+0.48}_{-0.44}$ | $1.70^{+0.15}_{-0.16}$ | $4.54^{+0.78}_{-0.70}$
0039$-$4201 | $1.88^{+0.31}_{-0.29}$ | $1.56^{+0.15}_{-0.16}$ | $3.61^{+0.62}_{-0.55}$
0049$-$5356 | $2.28^{+0.37}_{-0.34}$ | $1.54^{+0.15}_{-0.16}$ | $3.48^{+0.58}_{-0.53}$
0122$-$6759 | $1.29^{+0.21}_{-0.20}$ | $1.60^{+0.15}_{-0.16}$ | $4.15^{+0.70}_{-0.64}$
0245$-$3418 | $2.15^{+0.36}_{-0.32}$ | $1.50^{+0.15}_{-0.16}$ | $1.70^{+0.28}_{-0.26}$
1715+2341 | $1.41^{+0.23}_{-0.21}$ | $1.67^{+0.15}_{-0.16}$ | $3.51^{+0.59}_{-0.54}$
1839$-$7515 | $0.63^{+0.12}_{-0.10}$ | $1.59^{+0.17}_{-0.17}$ | $4.27^{+0.79}_{-0.68}$
1851$-$5036 | $2.37^{+0.38}_{-0.35}$ | $1.78^{+0.15}_{-0.16}$ | $6.82^{+1.12}_{-1.01}$
1900$-$7032 | $1.88^{+0.31}_{-0.28}$ | $1.47^{+0.15}_{-0.16}$ | $2.35^{+0.40}_{-0.35}$
1919$-$5938 | $1.83^{+0.30}_{-0.27}$ | $1.52^{+0.15}_{-0.16}$ | $3.87^{+0.64}_{-0.58}$
2019$-$7107 | $1.84^{+0.30}_{-0.28}$ | $1.50^{+0.15}_{-0.16}$ | $1.83^{+0.30}_{-0.28}$
2024$-$2725 | $1.71^{+0.28}_{-0.26}$ | $1.54^{+0.15}_{-0.16}$ | $3.16^{+0.52}_{-0.49}$
2028$-$2218 | $4.41^{+0.71}_{-0.66}$ | $2.24^{+0.15}_{-0.16}$ | $3.61^{+0.59}_{-0.55}$
2110$-$2700 | $2.13^{+0.35}_{-0.31}$ | $1.57^{+0.15}_{-0.16}$ | $2.56^{+0.43}_{-0.38}$
2114$-$6438 | $1.99^{+0.34}_{-0.30}$ | $1.62^{+0.15}_{-0.16}$ | $3.69^{+0.63}_{-0.56}$
2119$-$4827 | $3.04^{+0.53}_{-0.45}$ | $1.99^{+0.16}_{-0.16}$ | $6.51^{+1.14}_{-0.98}$
2125$-$4834 | $1.84^{+0.31}_{-0.28}$ | $1.48^{+0.15}_{-0.16}$ | $3.38^{+0.56}_{-0.51}$
2145$-$3022 | $2.01^{+0.33}_{-0.30}$ | $1.50^{+0.15}_{-0.16}$ | $2.91^{+0.49}_{-0.44}$
2207$-$5021 | $1.83^{+0.31}_{-0.28}$ | $1.45^{+0.15}_{-0.16}$ | $2.76^{+0.47}_{-0.42}$
2208$-$6026 | $1.54^{+0.25}_{-0.23}$ | $1.64^{+0.15}_{-0.16}$ | $3.06^{+0.52}_{-0.47}$
2213$-$4357 | $1.70^{+0.28}_{-0.25}$ | $1.75^{+0.15}_{-0.16}$ | $3.29^{+0.55}_{-0.50}$
2214$-$4620 | $1.81^{+0.30}_{-0.27}$ | $1.53^{+0.15}_{-0.16}$ | $4.89^{+0.83}_{-0.74}$
2239$-$2455 | $1.41^{+0.23}_{-0.21}$ | $1.66^{+0.15}_{-0.16}$ | $1.64^{+0.27}_{-0.24}$
2250$-$5625 | $2.91^{+0.48}_{-0.44}$ | $1.65^{+0.15}_{-0.16}$ | $5.58^{+0.99}_{-0.90}$
2313$-$4858 | $2.87^{+0.48}_{-0.43}$ | $1.63^{+0.15}_{-0.16}$ | $4.61^{+0.84}_{-0.73}$
2348$-$6612 | $2.04^{+0.35}_{-0.32}$ | $1.56^{+0.16}_{-0.17}$ | $7.02^{+1.22}_{-1.11}$
1621$-$8350a | $1.16^{+0.20}_{-0.18}$ | $3.09^{+0.18}_{-0.19}$ | $5.22^{+0.92}_{-0.82}$
1944$-$4628a | $1.14^{+0.19}_{0.17}$ |  2.46 ${}^{+0.16}_{-0.16}$ | $2.56^{+0.44}_{-0.38}$
1944$-$4628Ba |  1.34${}^{+0.60}_{-0.35}$ |  -0.06 ${}^{+0.68}_{-0.90}$ |
444$a$$a$footnotetext: Based on solar-metallicity models.

##  5 Galactic orbit simulation

To model the trajectories of our MS candidates in the Milky Way’s
gravitational potential, we use the python package galpy for galactic dynamics
(Bovy, 2015). We adopt the Model I potential of Irrgang et al. (2013), which
is implemented in galpy in a simplified fashion that serves our purposes. This
potential is a revised version of that described by Allen & Santillan (1991).
The Sun is located at $R_{\sun}=8.4$ kpc from the Galactic center, around
which it orbits with $\varv_{0}=242$ km s-1. The local escape velocity is
$\varv_{\sun,\,{\rm esc}}=614.4$ km s-1. We note that the galpy reference
potential, MWPotential2014, accounts for a lower-mass Galactic halo model
that, however, has relatively small impact in determining the past
trajectories of the youngest and nearest runaway candidates in our sample. The
mass of the Milky Way’s halo can be relevant for the study of unbound stars,
as we discuss in the following section.

The past and future trajectories of the runaway candidates are determined in a
statistical fashion, as we randomly sample the observed quantities ($\alpha$,
$\delta$, $\mu^{*}_{\alpha}$, $\mu_{\delta}$, $D(\rm SpT)$, $\varv_{\rm rad}$)
by adopting their uncertainties and relevant correlations. We draw 10 000
initial conditions, which are evolved for 10 Gyr in the future and traced back
in the past for sufficiently large time (i.e. up to $\tau_{\rm evo}$). For
each star, we note the rest-frame velocity, $\varv_{\rm rf}$, the past and
future Galactic cartesian coordinates, and the corresponding velocity
components. We estimate the escape probability from the Milky Way, $P_{\rm
esc}$, for each star as the fraction of initial conditions where $(\varv_{\rm
rf}-\varv_{\rm esc})>0$. We determine the vertical component of the angular
momentum, $L_{Z}$, which indicates the direction towards which the star has
been ejected. We also numerically estimate the eccentricity, $e$, the median
orbital apocenter and pericenter, $R_{\rm apo}$ and $R_{\rm peri}$, and the
maximum vertical displacement, $Z_{\rm max}$. The most recent Galactic plane
crossings, $R(Z=0)$, are recorded and used to determine the flight time from
such locations, $\tau_{\rm flight}$. The ejection velocity, $V_{\rm ej}$, is
determined as the velocity possessed by the star at $R(Z=0)$, corrected for
the solar motion and the Galactic rotation.

Table 5 lists the relevant orbital quantities for the 12 MS runaway candidates
in a Galactocentric reference system that is left-handed, i.e., with the $x$\-
and $y$-axis pointing, respectively, from the Milky Way’s center towards the
Sun and along the direction of the Galactic rotation.

Table 5: Orbital parameters of our MS candidates.

Short name | $X$ | $Y$ | $Z$ | $\varv_{Z}$ | $\varv_{\rm rf}$ | $P_{\rm esc}$ | $e$ | $L_{Z}$ | $R_{\rm peri}$ | $R_{\rm apo}$ | $Z_{\rm max}$ | $R(Z=0)$ | $\varv_{\rm ej}$ | $\tau_{\rm flight}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (kpc) | (kpc) | (kpc) |  (km s-1) |  (km s-1) |  |  |  (kpc km s-1) | (kpc) | (kpc) | (kpc) | (kpc) |  (km s-1) | (Myr)
0037$-$6154 | $5.63^{+0.50}_{-0.53}$ | $-3.86^{+0.70}_{-0.74}$ | $-6.82^{+1.24}_{-1.31}$ | $-231^{+31}_{-32}$ | $380^{+42}_{-38}$ | $0.0$ | $0.7$ | $2100$ | $8.24^{+0.91}_{-0.62}$ | $40.6^{+29.0}_{-15.0}$ | $31.5^{+25.0}_{-12.7}$ | $8.9^{+1.6}_{-1.1}$ | $330^{+31}_{-37}$ | $24^{+3}_{-3}$
0205$-$5938 | $7.40^{+0.19}_{-0.20}$ | $-3.41^{+0.66}_{-0.67}$ | $-5.07^{+0.98}_{-1.00}$ | $-61^{+22}_{-23}$ | $194^{+18}_{-12}$ | $0.0$ | $0.4$ | $1300$ | $4.81^{+0.88}_{-0.66}$ | $11.49^{+1.86}_{-1.36}$ | $6.17^{+1.71}_{-1.28}$ | $5.2^{+0.7}_{-0.5}$ | $273^{+84}_{-47}$ | $37^{+6}_{-6}$
0259$-$1705 | $10.85^{+0.43}_{-0.43}$ | $-0.93^{+0.16}_{-0.16}$ | $-4.30^{+0.76}_{-0.76}$ | $-178^{+22}_{-23}$ | $204^{+18}_{-16}$ | $0.0$ | $0.2$ | $1000$ | $7.90^{+0.75}_{-0.66}$ | $12.65^{+1.10}_{-0.83}$ | $11.22^{+1.64}_{-1.69}$ | $10.5^{+0.7}_{-0.6}$ | $276^{+27}_{-27}$ | $21^{+4}_{-4}$
1900$-$7033 | $2.43^{+1.01}_{-1.03}$ | $-4.23^{+0.72}_{-0.73}$ | $-3.60^{+0.61}_{-0.63}$ | $-183^{+37}_{-38}$ | $363^{+30}_{-28}$ | $0.0$ | $0.5$ | $1300$ | $5.77^{+0.60}_{-0.23}$ | $19.41^{+9.36}_{-5.21}$ | $15.20^{+9.70}_{-5.72}$ | $7.9^{+1.0}_{-0.8}$ | $295^{+25}_{-39}$ | $16^{+1}_{-1}$
1939$-$1640 | $4.27^{+0.69}_{-0.69}$ | $1.75^{+0.29}_{-0.29}$ | $-1.44^{+0.24}_{-0.25}$ | $-166^{+19}_{-19}$ | $340^{+25}_{-25}$ | $0.0$ | $0.5$ | $1100$ | $4.12^{+0.19}_{-0.11}$ | $11.79^{+3.10}_{-2.33}$ | $6.77^{+1.60}_{-1.23}$ | $5.9^{+0.6}_{-0.6}$ | $259^{+23}_{-23}$ | $8^{+0}_{-1}$
2034$-$1108 | $5.87^{+0.45}_{-0.45}$ | $1.74^{+0.31}_{-0.31}$ | $-1.62^{+0.29}_{-0.29}$ | $188^{+29}_{-29}$ | $253^{+28}_{-24}$ | $0.0$ | $0.4$ | $900$ | $3.64^{+0.31}_{-0.27}$ | $9.15^{+1.63}_{-1.06}$ | $6.19^{+1.62}_{-1.30}$ | $3.8^{+0.4}_{-0.3}$ | $409^{+30}_{-42}$ | $93^{+19}_{-13}$
2034$-$5307 | $3.75^{+0.83}_{-0.83}$ | $-1.22^{+0.22}_{-0.22}$ | $-3.57^{+0.64}_{-0.64}$ | $102^{+35}_{-36}$ | $339^{+96}_{-94}$ | $0.0$ | $0.5$ | $-1200$ | $4.89^{+0.06}_{-0.45}$ | $14.0^{+21.0}_{-6.6}$ | $9.1^{+18.4}_{-5.2}$ | $13.2^{+15.0}_{-6.3}$ | $371^{+63}_{-48}$ | $68^{+45}_{-19}$
2054$-$2526 | $2.30^{+1.09}_{-1.12}$ | $2.28^{+0.42}_{-0.41}$ | $-4.98^{+0.89}_{-0.92}$ | $48^{+22}_{-22}$ | $221^{+25}_{-21}$ | $0.0$ | $0.3$ | $700$ | $3.85^{+1.15}_{-0.68}$ | $7.75^{+1.51}_{-0.75}$ | $6.48^{+1.73}_{-1.37}$ | $6.9^{+1.7}_{-1.2}$ | $262^{+16}_{-17}$ | $50^{+11}_{-7}$
2207$-$2645 | $6.26^{+0.36}_{-0.37}$ | $0.95^{+0.16}_{-0.16}$ | $-3.17^{+0.54}_{-0.55}$ | $-152^{+28}_{-29}$ | $342^{+25}_{-23}$ | $0.0$ | $0.6$ | $1600$ | $4.41^{+0.72}_{-0.66}$ | $20.36^{+5.25}_{-3.63}$ | $9.56^{+3.61}_{-2.71}$ | $4.4^{+0.7}_{-0.6}$ | $272^{+47}_{-44}$ | $16^{+1}_{-1}$
2207$-$4329 | $5.00^{+0.60}_{-0.60}$ | $-0.26^{+0.05}_{-0.05}$ | $-4.57^{+0.81}_{-0.81}$ | $-50^{+41}_{-40}$ | $638^{+140}_{-138}$ | $0.4$ | … | $-2300$ | $6.78^{+0.18}_{-2.06}$ | $...$ | $...$ | $16.5^{+5.9}_{-5.4}$ | $802^{+129}_{-115}$ | $32^{+4}_{-3}$
2259$-$4931 | $6.50^{+0.37}_{-0.38}$ | $-0.73^{+0.14}_{-0.15}$ | $-3.38^{+0.67}_{-0.68}$ | $-114^{+28}_{-30}$ | $350^{+93}_{-82}$ | $0.0$ | $0.5$ | $-2100$ | $7.25^{+0.03}_{-0.06}$ | $20.9^{+33.5}_{-10.8}$ | $11.2^{+19.0}_{-4.9}$ | $9.0^{+2.8}_{-1.0}$ | $541^{+40}_{-54}$ | $22^{+6}_{-5}$
2307$-$3157 | $7.26^{+0.21}_{-0.21}$ | $0.30^{+0.05}_{-0.06}$ | $-2.77^{+0.51}_{-0.51}$ | $-101^{+34}_{-33}$ | $230^{+40}_{-32}$ | $0.0$ | $0.9$ | $200$ | $0.63^{+0.69}_{-0.48}$ | $12.92^{+3.13}_{-1.93}$ | $6.17^{+5.33}_{-2.35}$ | $2.0^{+1.4}_{-1.2}$ | $469^{+170}_{-106}$ | $18^{+2}_{-2}$

555The meaning of the columns from left to right is: current $XYZ$
Galactocentric Cartesian coordinates, vertical component of Galactocentric
rest-frame velocity, Galactocentric rest-frame velocity, escape probability,
orbit eccentricity, vertical component of the angular momentum, median
pericenter and apocenter, maximum vertical displacement from the plane,
Galactocentric radius at the most recent intersection of past trajectories
with the $Z=0$ plane, ejection velocity from $Z=0$, and flight time from
$Z=0$.

##  6 Properties of the runaway candidates

###  6.1 Orbit analysis

As expected for nearby runaway MS stars, all but one candidate are bound to
the Milky Way’s potential, since they have $\varv_{\rm rf}$ that is on average
two times smaller than $\varv_{\rm esc}$ at their Galactic coordinates. The
only exceptions is 2207$-$4329 that has an escape probability $P_{\rm
esc}=0.4$, defined as the fraction of simulated trajectories with $\varv_{\rm
rest}>\varv_{\rm esc}$.

Due to our selection cut of $\varv_{\rm tan}>150$ km s-1 (Eq. 1), all stars in
our sample (both the MS and BHB candidates) resulted to have $|\varv_{\rm
rad}|\lesssim\varv_{\rm tan}$ within the error bars. Three stars, 2034$-$5307,
2207$-$4329, and 2259$-$4931, have the largest $\varv_{\rm tan}\gtrsim 450$ km
s-1 of all MS candidates. This unusual feature can be also noted in the Toomre
diagram of Fig. 11, where the three stars have large negative Galactic
cartesian $V$ components (i.e. they lag behind the Milky Way’s rotation), as
it is more typically seen for the majority of BHB candidates in our sample.
The remaining MS candidates, instead, have moderate tangential velocities of
$\varv_{\rm tan}\simeq 200$ km s-1. The mostly retrograde motions of the BHB
stars implies that they belong to the halo population. In the future,
additional runaway candidates could be selected on the basis of their location
in the Galactic Cartesian velocity space, as depicted by the Toomre diagram
(Fig. 11).

Following the general direction of the Galactic rotation most MS candidates
have $L_{Z}>0$ kpc km s-1, with the exception of the three more extreme stars
that have large negative, Cartesian velocity $V$ components. While our
distance-based method entirely classify them as MS stars, these three stars
appear to possess kinematics that are more typical of BHB stars. We note that
2034$-$5307 and 2207$-$4329 have $T_{\rm eff}$ and $\log{g}$ in the
overlapping region of MS tracks and the horizontal branch (Fig. 8). Instead,
2259$-$4931 has a larger $\log{g}$ that excludes a BHB nature. As already
mentioned in Sect. 4, our distance-based method identifies MS candidates for
which we envisage higher-resolution spectroscopy for a more detailed
assessment of their nature.

All the MS candidates are found below the Galactic plane and are currently
moving away from it, with the exception of three stars, 2034$-$1108,
2034$-$5307, and 2054$-$2526, that are approaching the plane. The orbits of
the observed runaway candidates cover a wide range of eccentricities,
$e=0.2$–0.9, that is larger than the typical values for thin disc stars. All
the runaway candidates have their orbital apocenters roughly between the solar
circle and $R_{\rm apo}=20$ kpc, with a few exceptions potentially reaching
out to very far Galactic radii. Their orbits are typically enclosed within
$Z_{\rm max}=4$–40 kpc from the Galactic plane.

The trajectories of 2307$-$3157 have their orbital pericenters relatively
close to the Galactic center ($R_{\rm peri}<1$ kpc); hence, its motion could
be affected by the shape and orientation of the Galactic bar, which is not
accounted for in our Galactic potential model. The trajectories of stars
reaching beyond $R_{\rm apo}\gtrsim 20$ kpc, instead, might experience
gravitational perturbations due to the Large Magellanic Cloud (Kenyon et al.,
2018; Erkal et al., 2019a), which our Galactic model also does not account
for.

Finally, we do not list the orbital parameters ($e$, $R_{\rm peri}$, $R_{\rm
apo}$, and $Z_{\rm max}$) of 2207$-$4329 in Table 5, for they are
unconstrained due to its non-zero probability of escaping the Milky Way. For
this star, a significant fraction of simulated trajectories reaches extremely
large Galatocentric radii without returning back, within the 10 Gyr time-frame
of our simulation. As for the other stars, the parallax uncertainty has a
major role in determining the agreement with the spectrophotometric distance
and its classification as MS candidate. For the time being, we note that the
adopted potential (Model I of Irrgang et al., 2013) delivers a
$\varv_{\sun,\,{\rm esc}}$ that is already a few tens of km s-1 larger than
more recent Gaia-based estimates (Monari et al., 2018; Deason et al., 2019),
suggesting a real chance for this star to escape the Milky Way if confirmed as
MS candidate.

Figure 11: The positions of the program stars in the Toomre diagram. The
quantity $V$ is the velocity component in direction of Galactic rotation, $U$
towards the Galactic center, and $W$ perpendicular to the Galactic plane. The
local standard of rest (LSR) is marked by a yellow asterisk. The dashed
circles centered around the LSR represent boundaries for three restframe
velocities. The observed stars are plotted with error bars. Blue symbols
correspond to MS candidates, while orange symbols are used for the BHB stars.
All the targets identified in Sect. 2 are plotted as gray crosses, adopting
$\varv_{\rm rad}=0$ km s-1.

###  6.2 Birth place and flight times

The birth places of B-type MS stars are open clusters and associations within
the thin disc of the Milky Way. Although short compared to that of lower mass
stars, the MS life of late-B and early-A type stars can span from several 10
Myr up to $\sim 1$ Gyr, making the identification of their birth places a
relatively complex issue.

In Sect. 5, we have determined the most recent crossings of the Galactic plane
for the MS candidates, from which we estimate the flight times. To confirm the
runaway hypothesis, the flight times need to be shorter than the ages
estimated from evolutionary tracks ($\tau_{\rm flight}\leq\tau_{\rm evo}$). In
the case of ejection via the binary supernova mechanism, a runaway star could
be rejuvenated due to mass-transfer prior to the core-collapse explosion of
the primary (Schneider et al., 2015); hence, it could even appear slightly
younger than the flight time.

In Fig. 12, we show the comparison between these two quantities, noting that –
within the error bars – all the candidates are below or overlap with the solid
curve representing the identity line. Two thirds of our runaway candidates
have ages that are more than 2 times longer than the flight times. This result
poses the question of whether the reported crossing locations of the Galactic
plane, $R(Z=0)$, identify the real birth places and flight times. In fact, we
note that all candidates with $\tau_{\rm evo}>100$ Myr, with the exclusion of
2207$-$4329, could have crossed the Galactic plane two or more times in the
past. If the mechanisms that caused their runaway status occurred early in
their lifetime, as it is generally accepted for the binary supernova and
dynamical ejection scenarios, the most recent $R(Z=0)$ do not constrain their
$\tau_{\rm flight}$.

The various ejection mechanisms have intrinsic timescales. For example, the
canonical binary ejection mechanism necessarily occurs on very short
timescales of a few Myr, which are driven by the core-collapse supernova
(Portegies Zwart, 2000), and the dynamical ejection from clusters can produce
runaway stars for several hundred Myr (Moyano Loyola & Hurley, 2013).
Therefore, future intermediate- and high-resolution spectroscopy would enable
an improved understanding, e.g. via the detection of polluting elements from
supernova ejecta (Pan et al., 2012) as found for the hyper-runaway giant HD
271971 (Przybilla et al., 2008) or via the comparison of measured abundances
with the average elemental abundances of specific locations in the Galactic
disc (Irrgang et al., 2010).

Of all MS candidates, the possibly unbound runaway, 2207$-$4329, also has the
Galactic plane crossing radius that is the furthest from the Galactic center
at $R(Z=0)=16.5^{+5.9}_{-5.4}$. Such a large distance is similar to the case
of HD 271791 also originating from the outer Galactic disk (Heber et al.,
2008a; Przybilla et al., 2008), the ejection velocity of which, however, is
much lower ($390\pm 4$ km s-1; Irrgang et al., 2019). If the MS classification
of 2207$-$4329 is confirmed by future Gaia data releases and higher-resolution
spectroscopy, alternative birth places above the Galactic plane (e.g. the
tidal stream of a satellite galaxy colliding with the Milky Way; Abadi et al.,
2009) or other exotic scenarios involving intermediate-mass black holes
(Fragione & Gualandris, 2019) should also be investigated.

Figure 12: Comparison of flight times and stellar ages for the runaway MS
candidates. The solid line represents the identity curve. The dashed lines
mark the ranges where $\tau_{\rm evo}=2,\,5$, and 10 times $\tau_{\rm
flight}$.

###  6.3 Ejection velocity distribution

Figure 13: Ejection velocities of runaway stars are plotted against their
masses. Our 12 MS runaway candidates are represented by blue circles with
error bars (note that two stars have very similar masses and, thus,
overlapping symbols). The runaway stars studied by Silva & Napiwotzki (2011)
are plotted as squares. More recently discovered high-velocity runaway stars
as listed by Irrgang et al. (2019) are plotted as triangles, with masses
updated from Kreuzer et al. (2020) when available.

Silva & Napiwotzki (2011) described the relation between stellar mass and
ejection velocity, with reference to their compiled sample of runaway stars,
as mostly determined by the binary supernova mechanism. They also noted that
the dynamical ejection from clusters could contribute to the low-ejection
velocity population. On the contrary, the fastest runaway stars could have an
overlap with the slowest hyper-velocity stars.

In Fig. 13, our runaway candidates occupy a lower mass range with respect to
the Silva & Napiwotzki (2011) and Irrgang et al. (2019) samples. The increase
of ejection velocities towards lower masses that characterize our sample
appears to be in agreement with the predictions for binary supernova ejections
in the most extreme scenarios (Tauris, 2015; Evans et al., 2020). However,
Renzo et al. (2019) suggest that the dominant fraction of runaway stars with
large ejection velocities could be mostly formed via dynamical interactions in
open clusters, or more exotic scenarios. Interestingly, the ejection
velocities of three runaway candidates, 2207$-$4329, 2259$-$4931, and
2307$-$3157, could largely exceed $400$–$500$ km s-1, which would be
challenging the classical runaway scenarios (Irrgang et al., 2018a, 2019). Of
the three stars, 2207$-$4329 is by far the fastest (802${}^{+129}_{-115}$ km
s-1). 2259$-$4931, which is the least massive star of our sample, is the
second fastest one, ejected at 541${}^{+40}_{-54}$ km s-1 from near the solar
circle. If confirmed as a MS star, 2207$-$4329 would be the fastest known
hyper-runaway star (cf. Table 5 of Irrgang et al., 2019). Its ejection
velocity would exceed that of HVS 5 (640${}^{+50}_{-40}$ km s-1; Irrgang et
al., 2019), even when we allow for the rather large uncertainty of the former.
2259$-$4931 would also gain a prominent position in the list of Galactic disc
runaways with the largest ejection velocities, next to the well studied PG
1610+062 (550$\pm$20 km s-1).

##  7 Conclusions

We have presented the selection of bright early-type MS candidates at high
Galactic latitudes, relying on the Gaia DR2 astrometry and photometry, with
the goal of identifying new runaway stars. To test our selection we have
followed-up 48 stars obtaining low-resolution optical spectroscopy. By
comparing spectrophotometric distances and parallax-based distance estimators,
we propose 12 stars as MS candidates. Of the remaining stars, 27 are likely
BHB stars, two are rare highly evolved hot stars, and seven yet unclassified
stars could be binaries or blue stragglers.

The newly identified runaway candidates are mostly found within the 2–4 M☉
range. We numerically trace the past trajectories of these stars, identifying
their nearest Galactic disc crossings locations, flight times, and ejection
velocities. Most stars have ejection velocities between 200–450 km s-1. Three
stars exceed the 450 km s-1 upper limit of classical ejection scenarios (see
Irrgang et al., 2019) such as the binary supernova mechanism and dynamical
ejection from open clusters and, thus, call for a yet unknown ejection process
(see also Evans et al., 2020). One of the three stars has a non-negligible
escape probability, but more precise and accurate astrometry is required to
check whether they are bound to the Galaxy. According to their kinematics the
BHB stars belong to the halo population.

We remark that high-resolution spectroscopy is crucial to asses precise
rotational velocities and abundances, which are necessary to confirm the MS
nature of these candidates and shed light on their ejection mechanisms and
birth places. We also envisage an improved kinematic analysis and stellar
classification of the wider target lists, arising from the future Gaia data
releases. More accurate and precise parallaxes will make it possible to extend
the current volume beyond $\sim$10 kpc, which is currently limited by the
parallax precision and accuracy.

###### Acknowledgements.

RR, AI, and UH acknowledge funding by the German Science foundation (DFG)
through grants HE1356/71-1 and IR190/1-1. DS was supported by the Deutsche
Forschungsgemeinschaft (DFG) under grants HE1356/70-1 and IR190/1-1. RR has
received funding from the postdoctoral fellowship programme Beatriu de Pinós,
funded by the Secretary of Universities and Research (Government of Catalonia)
and by the Horizon 2020 programme of research and innovation of the European
Union under the Maria Skłodowska-Curie grant agreement No 801370. We thank I.
Condor for his support during the NTT observing run. This work has made use of
data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. Based on observations
collected at the European Organisation for Astronomical Research in the
Southern Hemisphere under ESO programme 0103.D-0530. This research has made
use of the VizieR catalogue access tool, CDS, Strasbourg, France (DOI :
10.26093/cds/vizier). The original description of the VizieR service was
published in 2000, A&AS 143, 23 This work made use of the IPython package
(Pérez & Granger, 2007) This publication makes use of data products from the
Two Micron All Sky Survey, which is a joint project of the University of
Massachusetts and the Infrared Processing and Analysis Center/California
Institute of Technology, funded by the National Aeronautics and Space
Administration and the National Science Foundation. Based on observations made
with the NASA Galaxy Evolution Explorer. GALEX is operated for NASA by the
California Institute of Technology under NASA contract NAS5-98034. This
publication makes use of data products from the Wide-field Infrared Survey
Explorer (Wright et al., 2010), which is a joint project of the University of
California, Los Angeles, and the Jet Propulsion Laboratory/California
Institute of Technology, funded by the National Aeronautics and Space
Administration.

##  Appendix A Gaia archive query

We performed the following query via the online service offered by the
Astronomisches Rechen-Institut of the Heidelberg
University666http://gaia.ari.uni-heidelberg.de/:

    SELECT *
    FROM gaiadr2.gaia_source
    WHERE parallax_error/parallax<=0.3
       AND parallax  > 0
       AND phot_g_mean_mag + 5 -
           5*log10(1000/parallax)<= 3.7
       AND ABS(b)>=15 AND bp_rp<=0.05
       AND phot_bp_rp_excess_factor
           <= 1.3 + 0.06*power(bp_rp,2)
       AND phot_bp_rp_excess_factor
           >= 1.0 + 0.015*power(bp_rp,2)
       AND visibility_periods_used >= 8
       AND phot_g_mean_flux_over_error >= 50
       AND phot_bp_mean_flux_over_error >= 20
       AND phot_rp_mean_flux_over_error >= 20
       AND ruwe <= 1.4

In addition, we filtered the data with the prescription of Eq.1.

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