# 591 high velocity stars in the Galactic halo selected from LAMOST DR7 and
Gaia DR2

Yin-Bi Li CAS Key Laboratory of Optical Astronomy, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, China  A-Li Luo∗
CAS Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences, Beijing 100101, China  School of Astronomy and
Space Science, University of Chinese Academy of Sciences, Beijing 100049,
China  You-Jun Lu∗ CAS Key Laboratory of Optical Astronomy, National
Astronomical Observatories, Chinese Academy of Sciences, Beijing 100101, China
School of Astronomy and Space Science, University of Chinese Academy of
Sciences, Beijing 100049, China  Xue-Sen Zhang  ExtantFuture (Beijing)
Technology Co., Ltd, Beijing 100102, People′ Republic of China  Jiao Li CAS
Key Laboratory of Optical Astronomy, National Astronomical Observatories,
Chinese Academy of Sciences, Beijing 100101, China  Yunnan observatories,
Chinese Academy of Sciences, Kunming 650011, China  Rui Wang CAS Key
Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese
Academy of Sciences, Beijing 100101, China  Fang Zuo  CAS Key Laboratory of
Optical Astronomy, National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100101, China  School of Astronomy and Space Science,
University of Chinese Academy of Sciences, Beijing 100049, China  Maosheng
Xiang Max-Planck Institute for Astronomy, Konigstuhl 17, D-69117 Heidelberg,
Germany  Yuan-Sen Ting Institute for Advanced Study, Princeton, NJ 08540, USA
Department of Astrophysical Sciences, Princeton University, Princeton, NJ
08540, USA  Observatories of the Carnegie Institution of Washington, 813 Santa
Barbara Street, Pasadena, CA 91101, USA  Research School of Astronomy &
Astrophysics, Australian National University, Cotter Rd., Weston, ACT 2611,
Australia  T.Marchetti  Leiden Observatory, Leiden University, PO Box 9513
2300 RA Leiden, the Netherlands  Shuo Li  CAS Key Laboratory of Optical
Astronomy, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100101, China  School of Astronomy and Space Science, University of
Chinese Academy of Sciences, Beijing 100049, China  You-Fen Wang  CAS Key
Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese
Academy of Sciences, Beijing 100101, China  Shuo Zhang Department of
Astronomy, School of Physics, Peking University, Beijing 100871, China  Kavli
Institute for Astronomy and Astrophysics, Peking University, Beijing 100871,
China  Kohei Hattori  Department of Astronomy, University of Michigan, 1085 S.
University Ave., Ann Arbor, MI 48109, USA  Yong-Heng Zhao  CAS Key Laboratory
of Optical Astronomy, National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100101, China  School of Astronomy and Space Science,
University of Chinese Academy of Sciences, Beijing 100049, China  Hua-Wei
Zhang Department of Astronomy, School of Physics, Peking University, Beijing
100871, China  Kavli Institute for Astronomy and Astrophysics, Peking
University, Beijing 100871, China  Gang Zhao∗ CAS Key Laboratory of Optical
Astronomy, National Astronomical Observatories, Chinese Academy of Sciences,
Beijing 100101, China  School of Astronomy and Space Science, University of
Chinese Academy of Sciences, Beijing 100049, China

###### Abstract

In this paper, we report 591 high velocity star candidates (HiVelSCs) selected
from over 10 million spectra of the data release seven (DR7) of the Large Sky
Area Multi-object Fiber Spectroscopic Telescope and the second Gaia data
release, with three-dimensional velocities in the Galactic rest-frame larger
than $445$ km s-1. We show that at least 43 HiVelSCs are unbound to the Galaxy
with escape probabilities larger than 50$\%$, and this number decreases to
eight if the possible parallax zero-point error is corrected. Most of these
HiVelSCs are metal-poor and slightly $\alpha$-enhanced inner halo stars. Only
14$\%$ of them have [Fe/H] $>$ -1, which may be the metal-rich “in situ” stars
in halo formed in the initial collapse of the Milky Way or metal-rich stars
formed in the disk or bulge but kinematically heated. The low ratio of 14$\%$
implies that the bulk of stellar halo was formed from the accretion and tidal
disruption of satellite galaxies. In addition, HiVelSCs on the retrograde
orbits have a slightly lower metallicities on average compared with these on
the prograde orbits, meanwhile metal-poor HiVelSCs with [Fe/H] $<$ -1 have an
even faster mean retrograde velocity compared with metal-rich HiVelSCs. To
investigate the origins of HiVelSCs, we perform orbit integrations and divide
them into four types, i.e., hypervelocity stars, hyper-runaway stars, runaway
stars and fast halo stars. A catalog for these 591 HiVelSCs, including radial
velocities, atmospheric parameters, Gaia astrometric parameters, spatial
positions, and velocities, etc., is available at http://paperdata.china-
vo.org/LYB/lamostdr7_gaiadr2_hvs_591.csv.

Galaxy: kinematic and dynamics — Galaxy: stellar content — Galaxy: halo

††journal: ApJS

##  1 Introduction

High velocity stars are moving fast, and they mark the presence of extreme
dynamical and astrophysical processes, especially when a star approaches or
even exceeds the escape velocity of the Galaxy at its position (Hills, 1988;
Yu & Tremaine, 2003; Bromley et al., 2006; Abadi et al., 2009; O’Leary & Loeb,
2008; Capuzzo-Dolcetta & Fragione, 2015; Marchetti et al., 2019). These stars
provide probes for a wide range of Galactic science, on scales from a few
parsecs near the central Massive Black Hole (MBH) to the distant Galactic
halo. They can provide insights to the dynamical mechanisms that produce their
extreme velocities (Zhang et al., 2010; Hawkins et al., 2015), and for
example, their distributions in space and velocity can reveal the existence of
a binary MBH (Zhang et al., 2010; Brown, 2015; Fragione et al., 2018; Fragione
& Gualandris, 2018). They are powerful tracers used to probe the mass
distribution of the Galaxy since they travel large distances across the Galaxy
(Gnedin et al., 2005; Kenyon et al., 2008), and their trajectories can also be
used to probe the shape of the dark matter halo of the Galaxy (Kenyon et al.,
2008; Yu & Madau, 2007).

In general, there are four subclasses for high velocity stars including
“hypervelocity star” (HVS), “runaway star” (RS), “hyper-runaway star” (HRS),
and “fast halo star” (OUT), and they have different origins. The fastest stars
in our Galaxy are HVSs, and their proposed ejection mechanisms include: the
tidal breakup of binary stars by a single MBH in the Galactic center (GC)
(Hills, 1988; Yu & Tremaine, 2003; Bromley et al., 2006); single star
encounters with a binary MBH (Yu & Tremaine, 2003; Sesana et al., 2006, 2007);
single star encounters with a cluster of stellar mass black holes around the
MBH (O’Leary & Loeb, 2008); the interaction between a globular cluster with a
single or binary MBH in the GC (Capuzzo-Dolcetta & Fragione, 2015; Fragione &
Capuzzo-Dolcetta, 2016). RSs are the second subclass of high velocity stars,
and they are thought to have formed in the disk and then were ejected into the
halo. RSs can be produced through two main formation mechanisms: supernova
explosions in stellar binary systems (e.g., Blaauw, 1961; Gvaramadze et al.,
2009; Wang & Han, 2009; Wang et al., 2013); dynamical interactions due to
multi-body encounters in dense stellar systems (e.g., Gvaramadze et al., 2009;
Bromley et al., 2009). If a RS has such an extremely high velocity that it can
escape from the Galaxy, it belongs to the third subclass of high velocity
stars, i.e., to the HRS (Perets & Šubr, 2012; Brown, 2015; Li et al., 2018).
The last subclass of high velocity stars is the fast halo stars, and they can
be produced by the tidal interactions of dwarf galaxies near the GC (Abadi et
al., 2009), or from other galaxies in the Local group (Sherwin et al., 2008;
Teyssier et al., 2009), for example from the center of the Large Magellanic
Cloud (LMC, Boubert & Evans, 2016; Boubert et al., 2017).

The first hypervelocity star (HVS1) was serendipitously discovered by Brown et
al. (2005), and it is a late-B type star with a heliocentric distance $\sim$71
kpc and radial velocity ($RV$) $\sim$853 km s-1. Since then, the number of
high velocity star candidates (HiVelSCs) has ballooned, and there are nearly
500 candidates in the literature before Gaia DR2 (Hirsch et al., 2005;
Edelmann et al., 2005; Brown et al., 2006, 2009, 2012, 2014; Heber et al.,
2008; Kollmeier et al., 2009; Tillich et al., 2009; Li et al., 2012; Zheng et
al., 2014; Zhong et al., 2014; Li et al., 2015; Favia et al., 2015; Huang et
al., 2017; Vennes et al., 2017). Most of these stars are late type high proper
motion stars, and about two dozens of them are faint and blue stars in the
halo and were classified as HVSs based only on their extreme $RV$s.

After Gaia DR2 release, new high velocity stars were searched for with more
precise astrometric parameters (Li et al., 2018; Shen et al., 2018; Hattori et
al., 2018; Irrgang et al., 2018a; Bromley et al., 2018; Irrgang et al., 2019;
Raddi et al., 2019; de la Fuente Marcos & de la Fuente Marcos, 2019; Caffau et
al., 2020; Koposov et al., 2020; Li et al., 2020). For example, Li et al.
(2018) found a new late-B type hyper-runaway star from the Large Sky Area
Multi-object Fiber Spectroscopic Telescope (LAMOST) with Gaia DR2 proper
motions, and it has a total Galactocentric velocity of $\sim$ 586 km s-1.
Hattori et al. (2018) reported the discovery of 30 old metal-poor stars with
extreme velocities ($>$ 480 km s-1) in Gaia DR2, up to three of these stars
were purported to be ejected from the LMC, and one or two stars originated
from the GC. Marchetti et al. (2019) found 20 stars that have probabilities
$>$ 80$\%$ of being unbound from the Galaxy, seven of them are hyper-runaway
stars, and other 13 stars may not have their origins in the Galaxy. Shen et
al. (2018) found three hyper-runaway white dwarfs in Gaia DR2, which have
total Galactocentric velocities between 1000 and 3000 km s-1. Except for these
newly discovered high velocity stars, previously known HVSs were also
revisited to further investigate their possible origins by tracing their
orbits back in time with new Gaia astrometric parameters (Brown et al., 2018;
Boubert et al., 2018; Erkal et al., 2019; Irrgang et al., 2018a; Kreuzer et
al., 2020). For example, Erkal et al. (2019) reanalyzed 26 previously known
HVSs and found that the third hypervelocity star (HE 0437-5439 or HVS3) is
likely to be coming almost from the center of the LMC, and Boubert et al.
(2018) found that almost all previously known late type high velocity stars
are likely bound to the Milky Way and only one late-type object (LAMOST
J115209.12+120258.0) is unbound from the Galaxy (Li et al., 2018).

Du et al. (2018a) and Du et al. (2018b) successively searched for HiVelSCs
from the early data version of LAMOST and Gaia, and the second work only
focuses on spectra also having Gaia $RV$s (LAMOST provides $RV$s data for all
stellar spectra, but Gaia provides these data only for a small fraction of
spectral types), which is a sample smaller than that corresponding to the
LAMOST data they used. As mentioned in Boubert et al. (2019) and Li et al.
(2020), $RV$s of Gaia DR2 could be spurious if there exists light
contamination from a nearby bright star. To avoid this problem, we only use
LAMOST $RV$s to estimate spatial velocities, and search for HiVelSCs from the
latest data version of LAMOST (data release seven) and Gaia (data release
two). Besides, different target selection method, and distance and velocity
estimation methods are adopted in this work, which leads to a different search
result of HiVelSCs.

Up to now, only a few studies have used both the chemical and kinematic
information of high velocity stars to determine where they were produced and
how did they achieve such high velocities (Hawkins et al., 2015; Geier et al.,
2015; Du et al., 2018a, b; Irrgang et al., 2018b; Marchetti et al., 2019). In
this paper, we use the chemistry and kinematics simultaneously to investigate
the possible origins and stellar populations for high velocity stars, and find
a few possible “in situ” halo stars. We also analyze the kinematic properties
for metal-poor and metal-rich stars, respectively, and the chemical properties
for prograde and retrograde stars.

The paper is organized as follows. In Section 2, we describe the method that
we used to search for HiVelSCs. In Section 3, we analyze the spatial position
and velocity distributions of our HiVelSCs, their stellar population, and
their chemical and kinematic properties. In Section 4, we calculate orbit
parameters for HiVelSCs, and investigate their possible origins. In Section 5,
we discuss the impact of a -0.029 mas global parallax zero-point, and the
results that adopt more conservative criteria to select HiVelSCs. Finally, the
conclusions are presented in Section 6.

##  2 Data

###  2.1 LAMOST and Gaia

LAMOST is a 4m quasi-meridian reflective Schmidt telescope, which is equipped
with 4000 fibers and can observe up to 4000 targets per exposure
simultaneously (Wang et al., 1996; Su & Cui, 2004; Zhao et al., 2006, 2012;
Luo et al., 2012; Cui et al., 2012). From 2011 to 2018, LAMOST has completed
its first stage low resolution spectroscopic survey ($R$ $\sim$ 1800), and
obtained more than 9 million spectra 111http://dr5.lamost.org/. Since October
2018, LAMOST started the second stage survey (LAMOST II), which contains both
low- and medium-resolution spectroscopic surveys. LAMOST II takes about 50$\%$
nights to continue the previous low-resolution survey, and the other 50$\%$
nights (bright/gray nights) for medium-resolution survey (Liu et al., 2020).
In March 2020, DR7 of Low-Resolution Spectroscopic Survey provided 10,608,416
low resolution spectra 222http://dr7.lamost.org/, and these spectra cover the
wavelength range of 3690$-$9100 Å with a resolution of $R$ $\sim$ 1800
respectively at 4750 Å (blue) and 7350 Å (red). The LAMOST Stellar Parameter
Pipeline (LASP) estimates atmospheric parameters and $RV$, and it has an
accuracy of about 150 K, 0.25 dex, 0.15 dex, 5.0 km s-1 for the effective
temperature ($T_{\rm eff}$), surface gravity (log $g$), metallicity ([Fe/H])
and $RV$, respectively (Luo et al., 2015; Xiang et al., 2015), for spectra of
signal to noise ratios higher than 10.

Gaia is a space-based mission in the science programme of the European Space
Agency (ESA) launched in 2013, and its main aim is to measure astrometric
parameters of stars, and to understand the formation, structure, and evolution
of the Milky Way (see review from Bland-Hawthorn $\&$ Gerhard, 2016). On 2018
April 25, Gaia delivered its second date release (Gaia DR2, Gaia Collaboration
et al., 2016, 2018a), and it provides precise positions ($\alpha$, $\delta$),
proper motions ($\mu_{\alpha^{*}}$, $\mu_{\delta}$), parallaxes ($\varpi$) and
photometries for over 1.3 billion stars brighter than magnitude 21 (Gaia
Collaboration et al., 2018a, b). The median uncertainty in parallax and
position (at the reference epoch J2015.5) is about 0.04 mas at $G<$ 14 mag,
0.1 mas at $G$ = 17 mag, and 0.7 mas at $G$ = 20 mag, and the corresponding
uncertainties of the proper motion components are 0.05, 0.2, and 1.2 mas yr-1,
respectively (Lindegren et al., 2018).

###  2.2 Distance and Total Velocity Determination

Using the five astrometric parameters in Gaia DR2 catalogue and $RV$ in LAMOST
catalogue, Galactocentric distance ($r_{\rm GC}$) and total velocity ($V_{\rm
GC}$) are computed based on the following assumptions: 1) the distance between
the Sun and the GC is $d_{\odot}$ = 8.2 kpc, and the Sun has an offset above
the stellar disk of $z_{\odot}$ = 25 pc (Bland-Hawthorn $\&$ Gerhard, 2016);
2) the motion of the local standard of rest (LSR) is 238 km s-1, and the
velocity of the Sun with respect to the LSR is [U⊙, V⊙, W⊙] = [14.0, 12.24,
7.25] km s-1 (Schönrich et al., 2010; Schönrich, 2012; Bland-Hawthorn $\&$
Gerhard, 2016); 3) the distribution of equator coordinates, parallax and
proper motions is a multivariate Gaussian with a mean vector m = [$\alpha$,
$\delta$, $\varpi$, $\mu_{\alpha^{*}}$, $\mu_{\delta}$], and a

covariance matrix:

$\displaystyle\Sigma=\begin{pmatrix}\sigma^{2}_{\rm\alpha}&\quad\sigma_{\rm\alpha}\sigma_{\rm\delta}\rho(\alpha,\delta)&\quad\sigma_{\rm\alpha}\sigma_{\rm\varpi}\rho(\alpha,\varpi)&\quad\sigma_{\rm\alpha}\sigma_{\rm\mu_{\alpha^{*}}}\rho(\alpha,\mu_{\alpha^{*}})&\quad\sigma_{\rm\alpha}\sigma_{\rm\mu_{\delta}}\rho(\alpha,\mu_{\delta})\\\
\sigma_{\rm\delta}\sigma_{\rm\alpha}\rho(\delta,\alpha)&\quad\sigma^{2}_{\rm\delta}&\quad\sigma_{\rm\delta}\sigma_{\rm\varpi}\rho(\delta,\varpi)&\quad\sigma_{\rm\delta}\sigma_{\rm\mu_{\alpha^{*}}}\rho(\delta,\mu_{\alpha^{*}})&\quad\sigma_{\rm\delta}\sigma_{\rm\mu_{\delta}}\rho(\delta,\mu_{\delta})\\\
\sigma_{\rm\varpi}\sigma_{\rm\alpha}\rho(\varpi,\alpha)&\quad\sigma_{\rm\varpi}\sigma_{\rm\delta}\rho(\varpi,\delta)&\quad\sigma^{2}_{\rm\varpi}&\quad\sigma_{\rm\varpi}\sigma_{\rm\mu_{\alpha^{*}}}\rho(\varpi,\mu_{\alpha^{*}})&\quad\sigma_{\rm\varpi}\sigma_{\rm\mu_{\delta}}\rho(\varpi,\mu_{\delta})\\\
\sigma_{\rm\mu_{\alpha^{*}}}\sigma_{\rm\alpha}\rho(\mu_{\alpha^{*}},\alpha)&\quad\sigma_{\rm\mu_{\alpha^{*}}}\sigma_{\rm\delta}\rho(\mu_{\alpha^{*}},\delta)&\quad\sigma_{\rm\mu_{\alpha^{*}}}\sigma_{\rm\varpi}\rho(\mu_{\alpha^{*}},\varpi)&\quad\sigma^{2}_{\rm\mu_{\alpha^{*}}}&\quad\sigma_{\rm\mu_{\alpha^{*}}}\sigma_{\rm\mu_{\delta}}\rho(\mu_{\alpha^{*}},\mu_{\delta})\\\
\sigma_{\rm\mu_{\delta}}\sigma_{\rm\alpha}\rho(\mu_{\delta},\alpha)&\quad\sigma_{\rm\mu_{\delta}}\sigma_{\rm\delta}\rho(\mu_{\delta},\delta)&\quad\sigma_{\rm\mu_{\delta}}\sigma_{\rm\varpi}\rho(\mu_{\delta},\varpi)&\quad\sigma_{\rm\mu_{\delta}}\sigma_{\rm\mu_{\alpha^{*}}}\rho(\mu_{\delta},\mu_{\alpha^{*}})&\quad\sigma^{2}_{\rm\mu_{\delta}}\end{pmatrix}$
(1)

where $\rho$($i$, $j$) is the correlation coefficient between the astrometric
parameters $i$ and $j$, and is provided by the Gaia DR2. LAMOST $RV$ is
uncorrelated to the astrometric parameters, thus we assume it follows a
Gaussian distribution, which is centered on $RV$ and with a standard deviation
of $\sigma_{\rm RV}$ (uncertainty on $RV$, Marchetti et al., 2019).

To estimate $r_{\rm GC}$ and $V_{\rm GC}$, the Monte Carlo (MC) method is
applied. For each star, 1000 MC samplings on its five astrometric parameters
and $RV$ are performed, and 1000 $r_{\rm GC}$ and $V_{\rm GC}$ can be obtained
according to above assumptions. The Galactic Cartesian coordinate system
adopted here is centered on the GC. The X-axis points from the Sun to the GC,
the Y-axis points in the direction of Galactic rotation, and the Z-axis points
toward the Northern Galactic Pole (Johnson & Soderblom, 1987; Li et al.,
2012). We use the median (50th percentile) and the 16th and 84th percentiles
as the computed parameters and their lower and upper uncertainties,
respectively (Marchetti et al., 2019; de la Fuente Marcos & de la Fuente
Marcos, 2019).

Lindegren et al. (2018) pointed that Gaia DR2 parallax has a global zero-point
of -0.029 mas, which indicates that the parallaxes are underestimated and
hence the distances are overestimated if the usual inverse relationship is
adopted. However, both Lindegren et al. (2018) and Arenou et al. (2018)
explicitly discouraged a global zero-point correction, particularly in cases
where the sample is not well distributed over the entire sky. In addition,
Arenou et al. (2018) showed that the parallax offset is partly dependent on
the scanning pattern of Gaia, which makes it a function of the coordinates.
Taking these into account, we do not correct the parallaxes zero-point here,
and discuss the changes on distances and velocities if the zero-point
correction were to be considered in Section 5.

###  2.3 Sample Selection

Using the parallax in Gaia DR2 catalogue, the heliocentric distance can be
determined just by inverting the parallax: $d=1/\varpi$. However, Bailer-Jones
(2015) discussed that this naive approach fails for non-positive parallaxes,
and can induce strong biases for fractional parallax errors, i.e.,
$f_{\rm\varpi}=\sigma_{\varpi}/\varpi$, larger than about 20$\%$. In this
paper, we only focus on stars with positive parallaxes ($\varpi>0$) and
smaller fractional parallax errors of $f_{\rm\varpi}\leq 0.2$ (the “low-f”
samples).

Using the TOPCAT 333http://www.star.bris.ac.uk/ mbt/topcat/, cross-match of
LAMOST DR7 with Gaia DR2 were performed with a radius of 5 arc sec, and
outputs a catalogue (LAMOST-Gaia hereafter) consisting of over 10 million
entries, which includes both LAMOST and Gaia parameters, for example, $RV$,
five Gaia astrometric parameters, magnitudes, and correlation coefficients. In
LAMOST-Gaia catalogue, there are over 8.48 million “low-f” entries, and their
$r_{\rm GC}$ and $V_{\rm GC}$ are estimated as described in Section 2.2. Seven
Galactic potential models (Paczynski, 1990; Gnedin et al., 2005; Xue et al.,
2008; Koposov et al., 2010; Kenyon et al., 2014; Bovy, 2015; Watkins et al.,
2019, hereinafter Paczynski+1990, Gnedin+2005, Xue+2008, Koposov+2010,
Kenyon+2014, MWPotential2014, and Watkins+2019) are adopted here to estimate
the escape velocities, and 31,440 samples are picked out with the condition of
either escaping from our Galaxy under at least one potential model or bound
but at least with total velocities of $V_{\rm GC}\geq 450$ km s-1 as used in
Marchetti et al. (2019) to select HivelSCs. We then check the spectral
qualities and only retain spectra with the highest signal to noise ratios for
stars with multiple observations, and 1761 stars are left. In previous steps,
we use the $RV$ provided by the LAMOST 1D pipeline ($RV_{\rm 1D}$) to
calculate the total velocity, and did not consider the reliability of RV. To
select candidates with reliable $RV$s, we inspect the spectra for 1761 stars
to check whether the spectral line shift is consistent with $RV_{\rm 1D}$, and
591 HiVelSCs with reliable $RV_{\rm 1D}$s are finally selected.

In the public stellar parameter catalog of LAMOST, $RV$ and atmospheric
parameters, radial velocity, and their errors were determined by the LASP
using the method mentioned in Luo et al. (2020). This work not only consider
the calculation error of the LASP but also include the errors introduced by
observation and data processing. Thus, the calculation of LASP $RV$ ($RV_{\rm
LASP}$) error takes into account more factors, which may make the outcome
closer to the true $RV$ errors. To be consistent with the public LAMOST
parameter catalog and use more reasonable RV uncertainties, we adopt the
$RV_{\rm LASP}$ as our final $RV$s for 591 HiVelSCs.

Then we correct the zero-point of $RV_{\rm LASP}$ for all HiVelSCs using a
catalog of 18080 radial velocity standard stars (Huang et al., 2018) selected
from the APO Galactic Evolution Experiment data, and it is also used to
investigate the consistency of $RV_{\rm 1D}$ and $RV_{\rm LASP}$. We cross-
match the catalog of radial velocity standard stars with LAMOST DR7, and
obtain 2125 common stars. For these stars, the distribution of difference
between $RV_{\rm 1D}$ and $RV_{\rm LASP}$ is shown in the left panel of Figure
1, and we can see that these stars yield a mean difference of $\mu=-0.01$ km
s-1 and a standard deviation of $\sigma=0.07$ km s-1, which represents that
$RV_{\rm 1D}$ is well consistent with $RV_{\rm LASP}$. The distribution of
difference between $RV_{\rm LASP}$ and $RV$ in the catalog of radial velocity
standard stars ($RV_{\rm Huang}$) for these common stars is shown in the right
panel of Figure 1, and we see that there exists a mean difference of
$\mu=-5.40$ km s-1 and a standard deviation of $\sigma=4.65$ km s-1, which
means that the zero-point of $RV_{\rm LASP}$ is $-$5.4 km s-1. After a zero-
point correction of $-$5.4 km s-1 for $RV_{\rm LASP}$, we recalculate the
spatial velocities for 591 HiVelSCs, and find that the recalculated median
$V_{\rm GC}$ are all larger than 445 km s-1.

Figure 1: Cross-match between a catalog of radial velocity standard stars
provided by Huang et al. (2018) and LAMOST DR7 catalog were performed, and
obtained 2125 common stars. These stars were used to investigate the
consistency ofradial velocities given by the LAMOST 1D pipeline ($RV_{\rm
1D}$) and by the LAMOST Stellar Parameter Pipeline ($RV_{\rm LASP}$) and the
radial velocity zero-point, and about 93$\%$ of their spectra have signal to
noise ratios larger than 40. Left panel: the difference between $RV_{\rm 1D}$
and $RV_{\rm LASP}$. Right panel: the difference between $RV_{\rm 1D}$ and
radial velocities in the radial velocity standard star catalog ($RV_{\rm
Huang}$). A mean difference of $\mu=-0.01$ km s-1 represents the $RV_{\rm 1D}$
is consistent with $RV_{\rm LASP}$, which is used to recalculate
Galactocentric total velocity ($V_{\rm GC}$) for 592 high velocity star
candidates (HiVelSCs), and $RV_{\rm LASP}$ is shown in our high velocity star
candidate catalog instead of $RV_{\rm 1D}$. A mean difference $\mu=-5.40$ km
s-1 implies the zero-point of $RV_{\rm LASP}$ is $-$5.40 km s-1, which is used
to perform the zero-point correction for 592 HiVelSCs.

###  2.4 High Velocity Star Candidates

After the above steps in Section 2.3, 591 HiVelSCs are finally selected from
the LAMOST-Gaia catalogue, and only 14 of them were reported in the current
version of the open fast stars catalog (OFSC) 444https://faststars.space/
(Boubert et al., 2018), which contains a collection of 558 HiVelSCs in the
literature. Du et al. (2018a) and Du et al. (2018b) reported 16 (Du1) and 24
(Du2) high velocity stars, respectively, which were both found from LAMOST and
Gaia with different data, and nine of them in total were also reported in the
OFSC. We cross-match 591 HiVelSCs with Du1 and Du2 in a radius of 3 arc sec,
respectively, and find that 12 out of our 591 HiVelSCs were already reported
in Du2.

We construct a catalogue including 93 columns to list various parameters for
these 591 HiVelSCs, i.e., “LAMOSTDR7-GAIADR2-HiVelSC”, and Table
LABEL:tab:general_catalog explains each column of this table in detail. The
4th to 21st columns of Table LABEL:tab:general_catalog are listed in Table 1
for the 20 fastest HiVelSCs, such as equatorial coordinate, Gaia parallax and
magnitude, and the 26th to 61st columns are listed in Table 2 also for the 20
fastest HiVelSCs.

Table 1: Basic parameters for the 20 fastest High velocity star candidates
(HiVelSCs)

ID | R.A. | decl. |  $S/N$_ra | Classb | $RV_{\rm LASP}^{c}$ | pmrad | pmdecd | parallaxe | $G^{f}$ | $G_{\rm BP}^{f}$ | $G_{\rm RP}^{f}$ | astrometric_flagg
---|---|---|---|---|---|---|---|---|---|---|---|---
| (deg) | (deg) |  |  | (km s-1) | (mas yr-1) | (mas yr-1) | (mas) | (mag) | (mag) | (mag) |
Hivel1 | 240.3374980 | 41.16681800 | 158 | G7 | -179$\pm$5 | -25.759$\pm$0.025 | -9.745$\pm$0.040 | 0.118$\pm$0.016 | 13.01 | 13.00 | 15.21 | 0
Hivel2 | 193.4372560 | 55.05813200 | 29 | F9 | -225$\pm$14 | -23.742$\pm$0.042 | -39.545$\pm$0.041 | 0.197$\pm$0.029 | 15.63 | 13.19 | 13.89 | 1
Hivel3 | 102.4840100 | 46.83601200 | 33 | K5 | -75$\pm$6 | 142.070$\pm$0.091 | -285.151$\pm$0.084 | 1.345$\pm$0.092 | 14.39 | 16.20 | 16.92 | 0
Hivel4 | 171.7747380 | 42.40792700 | 135 | A1V | 109$\pm$4 | -39.672$\pm$0.054 | -26.943$\pm$0.076 | 0.214$\pm$0.042 | 14.62 | 12.69 | 13.25 | 0
Hivel5 | 212.4778050 | 33.71299000 | 34 | F6 | -252$\pm$10 | -17.612$\pm$0.019 | -16.573$\pm$0.034 | 0.105$\pm$0.019 | 13.09 | 12.51 | 13.51 | 1
Hivel6 | 240.5153620 | 9.52531900 | 153 | G2 | 172$\pm$8 | -3.737$\pm$0.035 | -24.323$\pm$0.023 | 0.126$\pm$0.024 | 13.63 | 12.35 | 12.54 | 1
Hivel7 | 214.9762830 | 37.66936600 | 31 | F0 | -245$\pm$15 | -42.914$\pm$0.038 | -17.258$\pm$0.050 | 0.222$\pm$0.035 | 15.83 | 19.25 | 19.17 | 1
Hivel8 | 194.7713607 | -2.54662930 | 127 | G7 | 92$\pm$5 | 26.920$\pm$0.140 | -134.331$\pm$0.068 | 0.723$\pm$0.063 | 13.61 | 13.07 | 14.00 | 0
Hivel9 | 231.8486900 | 36.03446500 | 174 | G5 | -89$\pm$4 | -15.238$\pm$0.027 | -14.224$\pm$0.041 | 0.103$\pm$0.020 | 11.19 | 10.37 | 11.98 | 0
Hivel10 | 329.7058060 | 1.35603100 | 24 | F7 | -52$\pm$12 | -21.883$\pm$0.068 | -30.680$\pm$0.056 | 0.213$\pm$0.036 | 14.03 | 12.97 | 13.95 | 0
Hivel11 | 190.6504160 | 52.56223400 | 72 | G6 | 99$\pm$6 | -12.198$\pm$0.022 | -13.476$\pm$0.022 | 0.092$\pm$0.015 | 13.42 | 15.90 | 18.79 | 1
Hivel12 | 187.4196460 | 24.50598100 | 153 | G3 | 241$\pm$6 | -15.178$\pm$0.035 | -15.656$\pm$0.026 | 0.111$\pm$0.022 | 13.37 | 12.75 | 13.84 | 1
Hivel13 | 256.3047540 | 19.94524300 | 65 | G3 | -146$\pm$7 | -8.992$\pm$0.021 | -26.154$\pm$0.024 | 0.146$\pm$0.017 | 13.91 | 15.39 | 17.83 | 1
Hivel14 | 288.3732000 | 42.08276000 | 84 | G7 | -316$\pm$10 | -4.459$\pm$0.031 | 12.781$\pm$0.031 | 0.092$\pm$0.017 | 14.39 | 16.17 | 16.80 | 0
Hivel15 | 250.9465099 | 43.60750040 | 59 | F5 | -70$\pm$13 | -16.454$\pm$0.070 | -36.536$\pm$0.106 | 0.231$\pm$0.042 | 16.03 | 15.51 | 18.34 | 1
Hivel16 | 216.9762060 | 29.84803200 | 115 | F0 | -40$\pm$9 | -10.328$\pm$0.034 | -28.546$\pm$0.037 | 0.159$\pm$0.021 | 13.38 | 12.96 | 13.64 | 1
Hivel17 | 244.1838800 | 17.86343200 | 57 | F0 | 23$\pm$16 | -49.937$\pm$0.052 | -19.192$\pm$0.049 | 0.291$\pm$0.049 | 15.54 | 12.51 | 13.81 | 1
Hivel18 | 258.1346050 | 40.47350100 | 90 | G3 | -218$\pm$11 | -20.574$\pm$0.035 | 4.683$\pm$0.040 | 0.123$\pm$0.021 | 12.68 | 14.89 | 18.18 | 1
Hivel19 | 182.5150380 | 0.98761100 | 91 | G7 | 223$\pm$7 | -22.117$\pm$0.055 | -30.106$\pm$0.036 | 0.195$\pm$0.033 | 13.08 | 13.61 | 14.68 | 1
Hivel20 | 207.1676590 | 52.84460600 | 57 | F2 | -103$\pm$15 | -24.004$\pm$0.036 | -24.524$\pm$0.034 | 0.179$\pm$0.025 | 15.23 | 12.36 | 13.51 | 1

Note. — The 4th to 21st columns of Table LABEL:tab:general_catalog are listed
here for the 20 fastest HiVelSCs, and the measurement values and the
uncertainties are shown in the same column in this table but separated into
two columns in Table LABEL:tab:general_catalog. a r band signal to noise ratio
from LAMOST; b Spectral type given by the LAMOST 1D pipeline; c $RV$ given by
the LASP, which is corrected a radial velocity zero-point of $-$5.4 km s-1
mentioned in the last two paragraphs of Section 2.3; d Proper motions from
Gaia; e Parallax from Gaia; f $G$, $G_{\rm BP}$ and $G_{\rm RP}$ magnitudes
from Gaia; g A flag to show whether a candidate has more conservative
astrometric parameters.

Table 2: Spatial Positions and Velocities of the 20 fastest HiVelSCs

ID |  $x$a |  $y$a |  $z$a |  $r_{\rm GC}$b |  $V_{\rm x}$c |  $V_{\rm y}$c |  $V_{\rm z}$c |  $V_{\rm GC}$d | $e^{e}$ |  $Z_{\rm max}$f |  $r_{\rm min}$g | E-$\Phi$($\infty$)h
---|---|---|---|---|---|---|---|---|---|---|---|---
| (kpc) | (kpc) | (kpc) | (kpc) | (km s-1) | (km s-1) | (km s-1) | (km s-1) |  | (kpc) | (kpc) | (kpc2 Myr-2)
Hivel1 | -5.9${}_{-0.3}^{+0.4}$ | 5.1${}_{-0.6}^{+0.8}$ | 6.4${}_{-0.8}^{+1.0}$ | 10.1${}_{-0.6}^{+0.9}$ | -88${}_{-8}^{+7}$ | -717${}_{-127}^{+104}$ | 573${}_{-85}^{+108}$ | 922${}_{-136}^{+168}$ | $-$ | $-$ | 13.7${}_{-1.4}^{+1.9}$ | 0.0033${}_{-0.0013}^{+0.0019}$
Hivel2 | -9.4${}_{-0.2}^{+0.2}$ | 2.0${}_{-0.3}^{+0.4}$ | 4.5${}_{-0.6}^{+0.8}$ | 10.6${}_{-0.4}^{+0.6}$ | 56${}_{-5}^{+4}$ | -850${}_{-182}^{+132}$ | 256${}_{-60}^{+85}$ | 888${}_{-142}^{+197}$ | $-$ | $-$ | 19.1${}_{-1.4}^{+1.8}$ | 0.0030${}_{-0.0012}^{+0.0020}$
Hivel3 | -8.9${}_{-0.0}^{+0.0}$ | 0.1${}_{-0.0}^{+0.0}$ | 0.3${}_{-0.0}^{+0.0}$ | 8.9${}_{-0.0}^{+0.1}$ | -78${}_{-14}^{+12}$ | -866${}_{-80}^{+72}$ | 110${}_{-8}^{+10}$ | 876${}_{-73}^{+81}$ | $-$ | $-$ | 8.9${}_{-0.1}^{+0.1}$ | 0.0028${}_{-0.0007}^{+0.0007}$
Hivel4 | -10.0${}_{-0.4}^{+0.3}$ | 0.5${}_{-0.1}^{+0.1}$ | 4.4${}_{-0.7}^{+1.0}$ | 10.9${}_{-0.5}^{+0.8}$ | -613${}_{-137}^{+95}$ | -621${}_{-206}^{+142}$ | -41${}_{-36}^{+24}$ | 874${}_{-168}^{+247}$ | $-$ | $-$ | 92.9${}_{-54.6}^{+184.4}$ | 0.0026${}_{-0.0012}^{+0.0026}$
Hivel5 | -6.7${}_{-0.2}^{+0.4}$ | 2.5${}_{-0.4}^{+0.6}$ | 9.0${}_{-1.3}^{+2.0}$ | 11.5${}_{-0.9}^{+1.6}$ | -73${}_{-11}^{+7}$ | -857${}_{-237}^{+145}$ | 66${}_{-43}^{+70}$ | 862${}_{-147}^{+242}$ | $-$ | $-$ | 74.4${}_{-6.4}^{+7.4}$ | 0.0028${}_{-0.0013}^{+0.0025}$
Hivel6 | -2.6${}_{-0.9}^{+1.2}$ | 2.1${}_{-0.4}^{+0.5}$ | 5.3${}_{-0.9}^{+1.2}$ | 6.3${}_{-0.4}^{+0.8}$ | 639${}_{-84}^{+113}$ | -454${}_{-168}^{+126}$ | -109${}_{-51}^{+39}$ | 791${}_{-142}^{+199}$ | $-$ | $-$ | 195.7${}_{-105.9}^{+541.8}$ | 0.0018${}_{-0.0010}^{+0.0018}$
Hivel7 | -7.6${}_{-0.1}^{+0.1}$ | 1.5${}_{-0.2}^{+0.3}$ | 4.2${}_{-0.6}^{+0.8}$ | 8.8${}_{-0.2}^{+0.4}$ | -382${}_{-73}^{+48}$ | -676${}_{-168}^{+112}$ | 138${}_{-50}^{+73}$ | 789${}_{-126}^{+194}$ | $-$ | $-$ | 18.2${}_{-1.9}^{+2.2}$ | 0.0020${}_{-0.0010}^{+0.0016}$
Hivel8 | -7.8${}_{-0.0}^{+0.0}$ | -0.6${}_{-0.1}^{+0.0}$ | 1.2${}_{-0.1}^{+0.1}$ | 7.9${}_{-0.0}^{+0.0}$ | 606${}_{-44}^{+51}$ | -334${}_{-51}^{+43}$ | -357${}_{-40}^{+35}$ | 778${}_{-69}^{+81}$ | $-$ | $-$ | $-$ | 0.0018${}_{-0.0005}^{+0.0007}$
Hivel9 | -5.3${}_{-0.5}^{+0.7}$ | 4.6${}_{-0.8}^{+1.1}$ | 8.0${}_{-1.3}^{+2.0}$ | 10.6${}_{-1.0}^{+1.7}$ | 172${}_{-31}^{+46}$ | -631${}_{-205}^{+139}$ | 349${}_{-68}^{+102}$ | 741${}_{-156}^{+236}$ | $-$ | $-$ | 20.1${}_{-3.4}^{+4.6}$ | 0.0018${}_{-0.0012}^{+0.0019}$
Hivel10 | -6.4${}_{-0.3}^{+0.4}$ | 3.1${}_{-0.4}^{+0.7}$ | -2.9${}_{-0.6}^{+0.4}$ | 7.7${}_{-0.1}^{+0.3}$ | 705${}_{-102}^{+154}$ | -214${}_{-96}^{+61}$ | 16${}_{-10}^{+8}$ | 737${}_{-114}^{+174}$ | $-$ | $-$ | 176.9${}_{-65.1}^{+177.2}$ | 0.0015${}_{-0.0008}^{+0.0015}$
Hivel11 | -10.9${}_{-0.6}^{+0.4}$ | 3.8${}_{-0.5}^{+0.8}$ | 9.8${}_{-1.4}^{+2.0}$ | 15.2${}_{-1.2}^{+2.0}$ | -221${}_{-43}^{+28}$ | -583${}_{-181}^{+119}$ | 371${}_{-37}^{+58}$ | 727${}_{-123}^{+186}$ | $-$ | $-$ | 19.0${}_{-4.0}^{+5.8}$ | 0.0018${}_{-0.0010}^{+0.0015}$
Hivel12 | -8.6${}_{-0.1}^{+0.1}$ | -0.8${}_{-0.2}^{+0.1}$ | 9.0${}_{-1.4}^{+2.3}$ | 12.5${}_{-1.0}^{+1.8}$ | -215${}_{-56}^{+35}$ | -675${}_{-232}^{+144}$ | 160${}_{-23}^{+15}$ | 726${}_{-138}^{+230}$ | $-$ | $-$ | 27.7${}_{-10.3}^{+24.4}$ | 0.0016${}_{-0.0010}^{+0.0018}$
Hivel13 | -3.8${}_{-0.4}^{+0.6}$ | 3.7${}_{-0.4}^{+0.5}$ | 3.6${}_{-0.4}^{+0.5}$ | 6.4${}_{-0.1}^{+0.3}$ | 508${}_{-59}^{+79}$ | -503${}_{-89}^{+69}$ | -87${}_{-4}^{+4}$ | 718${}_{-87}^{+121}$ | $-$ | $-$ | $-$ | 0.0013${}_{-0.0007}^{+0.0010}$
Hivel14 | -5.2${}_{-0.5}^{+0.7}$ | 10.1${}_{-1.6}^{+2.4}$ | 2.6${}_{-0.4}^{+0.6}$ | 11.6${}_{-1.2}^{+2.0}$ | -593${}_{-120}^{+82}$ | -9${}_{-11}^{+13}$ | 395${}_{-72}^{+109}$ | 713${}_{-108}^{+160}$ | $-$ | $-$ | 10.1${}_{-1.3}^{+2.3}$ | 0.0014${}_{-0.0008}^{+0.0015}$
Hivel15 | -7.0${}_{-0.2}^{+0.3}$ | 3.0${}_{-0.5}^{+0.7}$ | 2.9${}_{-0.4}^{+0.7}$ | 8.1${}_{-0.1}^{+0.3}$ | 614${}_{-94}^{+147}$ | -277${}_{-116}^{+73}$ | 212${}_{-39}^{+60}$ | 705${}_{-121}^{+191}$ | $-$ | $-$ | 16.1${}_{-1.4}^{+2.0}$ | 0.0013${}_{-0.0008}^{+0.0014}$
Hivel16 | -6.6${}_{-0.2}^{+0.2}$ | 1.6${}_{-0.2}^{+0.2}$ | 5.9${}_{-0.7}^{+0.9}$ | 9.0${}_{-0.3}^{+0.5}$ | 397${}_{-46}^{+58}$ | -566${}_{-119}^{+94}$ | 90${}_{-17}^{+20}$ | 698${}_{-104}^{+132}$ | $-$ | $-$ | 37.3${}_{-5.8}^{+8.3}$ | 0.0013${}_{-0.0007}^{+0.0012}$
Hivel17 | -6.0${}_{-0.4}^{+0.4}$ | 1.4${}_{-0.2}^{+0.3}$ | 2.3${}_{-0.4}^{+0.4}$ | 6.6${}_{-0.1}^{+0.2}$ | -21${}_{-13}^{+13}$ | -474${}_{-143}^{+117}$ | 512${}_{-80}^{+95}$ | 697${}_{-137}^{+165}$ | $-$ | $-$ | 6.8${}_{-0.0}^{+0.1}$ | 0.0010${}_{-0.0007}^{+0.0013}$
Hivel18 | -5.4${}_{-0.4}^{+0.6}$ | 6.0${}_{-0.8}^{+1.3}$ | 4.7${}_{-0.6}^{+1.0}$ | 9.3${}_{-0.6}^{+1.1}$ | -328${}_{-52}^{+38}$ | -304${}_{-76}^{+57}$ | 538${}_{-92}^{+139}$ | 697${}_{-110}^{+170}$ | $-$ | $-$ | 8.8${}_{-1.0}^{+1.6}$ | 0.0013${}_{-0.0008}^{+0.0014}$
Hivel19 | -7.7${}_{-0.1}^{+0.1}$ | -2.4${}_{-0.5}^{+0.3}$ | 4.6${}_{-0.7}^{+1.0}$ | 9.3${}_{-0.3}^{+0.6}$ | -81${}_{-25}^{+17}$ | -659${}_{-177}^{+118}$ | -207${}_{-87}^{+62}$ | 696${}_{-131}^{+198}$ | $-$ | $-$ | 195.7${}_{-186.0}^{+283.0}$ | 0.0012${}_{-0.0008}^{+0.0015}$
Hivel20 | -8.8${}_{-0.1}^{+0.1}$ | 2.5${}_{-0.3}^{+0.4}$ | 5.0${}_{-0.6}^{+0.8}$ | 10.5${}_{-0.4}^{+0.6}$ | -31${}_{-9}^{+8}$ | -609${}_{-136}^{+103}$ | 324${}_{-55}^{+69}$ | 691${}_{-118}^{+149}$ | $-$ | $-$ | 13.8${}_{-1.2}^{+1.9}$ | 0.0012${}_{-0.0007}^{+0.0012}$

Note. — The 26th to 61st columns of Table LABEL:tab:general_catalog are listed
here for the 20 fastest HiVelSCs, which includes spatial positions and
velocities. The median value, the lower uncertainty, and the upper uncertainty
of each parameter are shown in the same column in this table but separated
into three columns in Table LABEL:tab:general_catalog (from 26th to 61st
columns). a Galactocentric spatial position ($x$, $y$, $z$); b Galactocentric
distance; c Galactocentric spatial velocity ($V_{\rm x}$, $V_{\rm y}$, $V_{\rm
z}$); d Galactocentric total velocity; e Orbit eccentricity e, “$-$”
represents e is not provided; f Orbital maximum height above the Galactic
disk, “$-$” represents Zmax is not provided; g Minimum crossing radius during
the orbital trace back; h Energy difference between orbital energy and
potential energy at infinity; i For a star, if less than 1$\%$ orbits of a
Monte-Carlo simulation with N realizations intersect with the Galactic disk,
we do not provide $r_{\rm min}$ and its errors, which is represented by the
“$-$”.

Note that, we only provide e and Zmax for 246 bound HiVelSCs with Z${}_{\rm
max}\leq 200$ kpc, and “$-$” represents e and Zmax are not provided.

The spatial distribution of the 591 HiVelSCs in Galactic coordinates is
plotted in Figure 2, and the black solid dots are 558 stars in the OFSC. The
red and blue solid dots represent 591 HiVelSCs, and the blue solid dots are 92
conservative HiVelSCs, which are introduced in detail in Section 5.2. The
dashed magenta rectangle shows the region of LAMOST Galactic anticentre survey
(Yuan et al., 2015), which collects over 3.6 million spectra accounting for at
least 34$\%$ of all DR7 released spectra, but only about 10 HiVelSCs are found
in this region, which account for about $1.7\%$ of all HiVelSCs.

Figure 2: The spatial distribution of 591 HiVelSCs in the Galactic
coordinates. The black solid dots are 558 stars in the open fast stars
catalog, and the red and blue solid dots represent 591 HiVelSCs, 92 of which
are conservative HiVelSCs shown by blue solid dots and selected by more
conservative criteria described in Section 5.2.

The $G$ magnitude distribution of Gaia DR2 is shown in Figure 3, and the black
histogram is the distribution for 558 stars in the the open fast stars
catalog. The red histogram is the distribution for 591 HiVelSCs, and the green
one is for 92 conservative HiVelSCs introduced in Section 5.2. From this
figure, we can clearly see that our HiVelSC sample contains relatively more
objects in the magnitude range from 13 mag to 16.5 mag, and we miss the second
mode at the faint end of magnitude distribution of the open fast stars catalog
because LAMOST is magnitude limited.

Figure 3: $G$ magnitude distribution of Gaia DR2. The black and red histograms
are the $G$ magnitude distributions for 558 stars in the open fast stars
catalog and 591 HiVelSCs, respectively, and the green one is for 92
conservative HiVelSCs introduced in Section 5.2. The red and greed
distributions miss the second mode at the faint end of magnitude distribution
of OFSC because LAMOST is magnitude limited (SDSS $r$-band magnitude less than
17.8 mag (Du et al., 2018a)).

Figure 4 shows the Hertzsprung-Russell diagram for 591 HiVelSCs (green and
blue x-marks) and over 8 million “low-f” spectra introduced in Section 2.3
(black solid dots). The x-axis represents the color index in the Gaia Blue
Pass (BP) and Red Pass (RP) bands (BP-RP), and the y-axis gives the absolute
magnitude of Gaia G band. It should be noted that we do not consider
extinction when construct the HR diagram, because of the caveats using the
extinction in the G band for individual sources (Andrae et al., 2018). From
this figure, we can see that the majority of 591 HiVelSCs are giant stars.

Figure 4: The Hertzsprung-Russell diagram for all the 591 HiVelSCs (green and
blue x-marks), 92 of which are conservative HiVelSCs (blue x-marks) introduced
in Section 5.2. The black solid dots represent over 8.48 million “low-f”
spectra mentioned in Section 2.3.

As mentioned in Section 2.3, seven Galactic potential models are used to
estimate escape velocities for 591 HiVelSCs, and Table A1 lists these escape
velocities for the 20 fastest HiVelSCs. In this table, $V_{\rm esc}$(W),
$V_{\rm esc}$(G), $V_{\rm esc}$(Ke), $V_{\rm esc}$(Ko), $V_{\rm esc}$(P),
$V_{\rm esc}$(M), and $V_{\rm esc}$(X) are escape velocities estimated by
using the seven potential models of Watkins+2019, Gnedin+2005, Kenyon+2014,
Koposov+2010, Paczynski+1990, MWPotential2014, and Xue+2008, respectively.
Meanwhile, we estimate the probability $P_{\rm ub}$ of being unbound from the
Milky Way, which is defined as the percentage of $V_{\rm GC}$ larger than
escape velocity in 1000 MC realizations of $r_{\rm GC}$ and $V_{\rm GC}$, and
the Table A2 lists these probabilities for the 20 fastest HiVelSCs. In this
table, $P_{\rm ub}$(W), $P_{\rm ub}$(G), $P_{\rm ub}$(Ke), $P_{\rm ub}$(Ko),
$P_{\rm ub}$(P), $P_{\rm ub}$(M), and $P_{\rm ub}$(X) are unbound
probabilities estimated by using the above seven potential models. Table 3
lists the number of HiVelSCs with $P_{\rm ub}>50\%$ under each potential
model, and we can see that at least 43 HiVelSCs have $P_{\rm ub}>50\%$ of
being unbound in Watkins+2019 potential model, and at most 304 HiVelSCs have
$P_{\rm ub}>50\%$ of being unbound in Xue+2008 potential model, and the amount
of unbound HiVelSCs with $P_{\rm ub}>50\%$ in other potential models is given
by a number that is within the range (43, 304), i.e., larger than 43 and less
than 304.

Table 3: The number of HiVelSCs with probabilities of being unbound larger than 50$\%$ ($P_{\rm ub}\geq 50\%$) in each of the seven potential models | Watkins+2019 | Gnedin+2005 | Kenyon+2014 | Koposov+2010 | Paczynski+1990 | MWPotential2014 | Xue+2008
---|---|---|---|---|---|---|---
$P_{\rm ub}\geq 50\%$ | 43 | 52 | 59 | 97 | 149 | 211 | 304

To highlight visually possibly unbound HiVelSCs, we plot the total velocities
in the Galactic rest frame $V_{\rm GC}$ as a function of Galactocentric
distances $r_{\rm GC}$ for 591 HiVelSCs (black and red solid dots) in Figure
5, and also plot escape velocities at different $r_{\rm GC}$ with color short
dashed lines based on the above seven potential models. Considering the total
velocity uncertainties, there are at least 43 stars in Figure 5 that can
escape from the Galaxy in the most conservative Watkins+2019 potential model
(resulting in the largest escaping velocities) with $P_{\rm ub}>50\%$, and 287
stars are bound in the least conservative potential model of Xue+2008
(resulting in the smallest escaping velocities) with $P_{\rm ub}\leq 50\%$.
Whether the remaining 261 stars are marginally unbound with $P_{\rm ub}>50\%$
or not depends on the potential model used.

Figure 5: Total velocities in the Galactic rest-frame ($V_{\rm GC}$) as a
function of Galactocentric distances ($r_{\rm GC})$ for 591 HiVelSCs. The
seven dashed curves in different colors are escape velocities at different
distances $r_{\rm GC}$ determined by seven Galactic potential models
(Paczynski, 1990; Gnedin et al., 2005; Xue et al., 2008; Koposov et al., 2010;
Kenyon et al., 2014; Bovy, 2015; Watkins et al., 2019), and the black and red
solid dots are 591 HiVelSCs, 92 of which are conservative HiVelSCs (red solid
dots) introduced in Section 5.2.

In order to mark HiVelSCs with high quality Gaia astrometry, here we adopted
equations (C.1), (C.2), and the latter two criteria of selection A in Appendix
C of Lindegren et al. (2018), and the equality cuts from (i) to (iv) in
Section 4 of Marchetti et al. (2019). The “astrometric_flag” column in Table 1
is used to determine the quality of astrometric parameters, and the value of
“1” represents a HiVelSC that satisfies all above criteria. Using the
“astrometric_flag” column, 476 HiVelSCs have conservative high quality
astrometric parameters of equatorial coordinates, parallaxes, and proper
motions.

##  3 Properties of High Velocity Star Candidates

###  3.1 Distribution of Spatial Positions and Velocities

The spatial distribution of 591 HiVelSCs is shown in Figure 6. The upper
panels are the distribution on the Galactic disk and the (X, Z) plane, and the
bottom panel is the distribution in the Galactocentric cylindrical coordinates
(R, Z). From the upper panels, we can see that all the 591 HiVelSCs are
located on the side of the sun having negative $X$, whereas majority of them
have positive $Y$ ($\sim$$80.7\%$) and $Z$ ($\sim$$91\%$). From the bottom
panel, we note that about half (49$\%$) of our HiVelSCs lie away from the
stellar disk with $|Z|\geq 3$ kpc, which is the edge of the thick disk
(Carollo et al., 2010).

Figure 7 shows the Galactocentric velocity components of our HiVelSCs, showing
that they are not clumped in velocity. These stars show symmetry in the
$V_{\rm x}$ \- $V_{\rm z}$ plane but an obvious asymmetry in the $V_{\rm x}$
\- $V_{\rm y}$ plane, and most of HiVelSCs have negative values of $V_{\rm
y}$. There are at most 304 out of 591 HiVelSCs unbound to the Galaxy with
$P_{\rm ub}>50\%$ and 251 ($\sim$$82.6\%$) of them have negative values of
$V_{\rm y}$, assuming the Xue+2008 potential model (The number of unbound ones
is smaller if we assume other potential models.) Such an asymmetry in the
$V_{\rm x}$ \- $V_{\rm y}$ plane is consistent with the discussion in de la
Fuente Marcos & de la Fuente Marcos (2019), and negative $V_{\rm y}$
components (retrograde) tend to be significantly larger than the positive
counterparts (prograde). But this could be a side effect of the large
uncertainties in heliocentric distances (de la Fuente Marcos & de la Fuente
Marcos, 2019; Schönrich et al., 2011). In order to further exclude stars with
large uncertainties on distances, we use “astrometric_flag” to single out 245
stars with more conservative Gaia astrometry out of all 304 unbound HiVelSCs
mentioned above, and 206 ($\sim$$84\%$) of them still have retrograde $V_{\rm
y}$. This result is consistent with that in de la Fuente Marcos & de la Fuente
Marcos (2019), but the ratio of HiVelSCs with negative values of $V_{\rm y}$
is much higher. As discussed in literature (de la Fuente Marcos & de la Fuente
Marcos, 2019; Marchetti et al., 2019; Cicone et al., 2016), most unbound
HiVelSCs having negative values of $V_{\rm y}$ suggest that a population of
high velocity stars that may have an extragalactic provenance.

Figure 6: The spatial distribution of 591 HiVelSCs. Upper left panel: the
distribution on the Galactic plane . Upper right panel: the distribution in
the (X, Z) plane. Bottom panel: the distribution in the Galactocentric
cylindrical coordinates (R, Z). The Sun and GC are marked by a red solid
circle and a red plus, respectively. The black and green solid dots represent
591 HiVelSCs, and the green solid dots are 92 conservative HiVelSCs introduced
in Section 5.2.  Figure 7: Galactocentric velocity distribution of 591
HiVelSCs. The black and red solid dots represent 591 HiVelSCs, and the red
solid dots are 92 conservative HiVelSCs introduced in Section 5.2.

###  3.2 Halo or Disk Stars?

Figure 8 shows the Toomre diagram for 591 HiVelSCs, which has been widely used
to distinguish the thin-disk, thick-disk, and halo stars. On the x axis, we
plot the component $V_{\rm LSR}$ of the space total velocity ($V_{\rm total}$)
with respect to the LSR, and on the y axis the perpendicular component to it,
$\sqrt{U_{\rm LSR}^{2}+W_{\rm LSR}^{2}}$. The magenta and blue dashed
semicircles are dividing lines between halo and disk stars, which were defined
by Bonaca et al. (2017) and Nissen & Schuster (2010), respectively. The
magenta dashed semicircle can be represented by $|V_{\rm total}|\geq 220$ km
s-1 (Bonaca et al., 2017), and the blue one can be defined as $|V_{\rm
total}|\geq 180$ km s-1 (Nissen & Schuster, 2010). Here, we adopt the more
conservative magenta dashed semicircle as the dividing line of halo and disk
stars. As shown in this figure, all HiVelSCs are located outside of the
magenta dashed semicircle, which means that all the 591 HiVelSCs have halo-
like kinematic properties.

Figure 8: Toomre diagram for 591 HiVelSCs, and ($U_{\rm LSR}$, $V_{\rm LSR}$,
$W_{\rm LSR}$) is the three dimensional velocity with respect to the Local
Rest Frame. The magenta and blue dashed semicircles represent $V_{\rm
total}=\sqrt{U_{\rm LSR}^{2}+V_{\rm LSR}^{2}+W_{\rm LSR}^{2}}=220$ km s-1 and
$V_{\rm total}=\sqrt{U_{\rm LSR}^{2}+V_{\rm LSR}^{2}+W_{\rm LSR}^{2}}=180$ km
s-1, respectively, and they can be used to distinguish halo stars from disk
stars. The black and green solid dots represent 591 HiVelSCs, and the green
solid dots are 92 conservative HiVelSCs introduced in Section 5.2.

Following Bensby et al. (2003), we estimate the relative probabilities for the
thick-disk-to-halo (TD/H) membership using equations (1) - (3), which can also
be used to distinguish stellar population, and the result shows that relative
probabilities of all 591 HiVelSCs of not being halo stars are far less than
0.1 and nearly equal to 0. Such a result indicates that all the 591 HiVelSCs
are halo stars with extremely high probabilities, and it is consistent with
the result obtained by using the Toomre diagram.

Besides the kinematic methods, chemistry is usually used together with
kinematics to study the stellar population and possible origin places, and we
use the method of data-driven Payne (DD-Payne) described in Xiang et al.
(2019) (see also Ting et al., 2017) to determine $\alpha$ element abundance
([$\alpha$/Fe]) in this work since it was not provided by the LASP. The DD-
Payne method also provides atmospheric parameters for 591 HiVelSCs, and these
parameters are included in our “LAMOSTDR7-GAIADR2-HiVelSC” catalogue together
with LASP atmospheric parameters. Table A3 shows these parameters for the 20
fastest HiVelSCs, where $T_{\rm eff}$_LASP, log $g$_LASP, and [Fe/H]$\\_$LASP
are atmospheric parameters determined by the LASP, and $T_{\rm eff}$_DD-Payne,
log $g$_DD-Payne, [Fe/H]$\\_$DD-Payne and [$\rm\alpha$/Fe]$\\_$DD-Payne are
parameters obtained by the DD-Payne method.

The left panel of Figure 9 plots the distribution of 591 HiVelSCs on the DD-
Payne ($\rm\alpha$, [Fe/H]) plane, and the mean and standard deviation of the
$\alpha$-abundances of our HiVelSCs are about +0.23 dex and 0.07 dex. This is
consistent with the results in Du et al. (2018b) and Hawkins et al. (2015),
which have mean $\alpha$ abundances of $\rm\alpha=+0.22~{}dex$ and
$\rm\alpha=+0.24~{}dex$, respectively. The right panel shows the
[Fe/H]$\\_$DD-Payne distribution of these stars, which peaks at near [Fe/H]
$\sim$ $-$1.2 and has a wide range from near [Fe/H] $\sim$ $-$3.5 to [Fe/H]
$\sim$ +0.5. From this figure, the 591 kinematically selected halo stars are
mostly metal-poor and slightly $\alpha$-enhanced. In addition, their [Fe/H]
distribution and its peak value at about [Fe/H] $\sim$ -1.2 are consistent
with the distribution of inner halo stars in Conroy et al. (2019) and Liu et
al. (2018). While the mean or peak values of metallicity distributions of
inner halo in some research works (Carollo et al., 2010, 2007; Xue et al.,
2015; Das & Binney, 2016; Mackereth et al., 2019; Youakim et al., 2020;
Allende Prieto et al., 2014; An et al., 2013; Zuo et al., 2017) can shift
towards more metal poor for several reasons such as bias in halo stars
selection as discussed in Conroy et al. (2019), the metallicity distribution
of our 591 HiVelSCs is nonetheless broadly consistent with that of the inner
halo in these works.

Figure 9: Left panel: The distribution of 591 HiVelSCs on the ([$\alpha$/Fe],
[Fe/H]) plane. The horizontal and vertical axes are the metallicity
([Fe/H]_DD-Payne) and the $\alpha$ element abundance ([$\alpha$/Fe]_DD-Payne),
respectively, and they are estimated by the method of data-driven Payne (DD-
Payne). Right panel: the distribution of [Fe/H]_DD-Payne for 591 HiVelSCs,
which peaks at about [Fe/H] $\sim$ $-$1.2 and has a wide range from near
[Fe/H] $\sim$ $-$3.5 to [Fe/H] $\sim$ +0.5. The black and red solid dots in
the left panel represent 591 HiVelSCs, and the red solid dots are 92
conservative HiVelSCs introduced in Section 5.2. The black histogram are the
distribution of [Fe/H]_DD-Payne for 591 HiVelSCs, and the red one is the
distribution of [Fe/H]_DD-Payne for 92 conservative HiVelSCs.

As mentioned in recent works (Conroy et al., 2019; Bonaca et al., 2017; Du et
al., 2018a), a fraction of kinematically defined metal-rich halo stars are in
situ components of the local stellar halo, which display thick-disk chemistry
on halo-like orbits and are confined to the range of $|z|\leq 10$ kpc and
$R_{\rm gal}\leq 20$ kpc. Such in situ halo stars are considered to be formed
in the initial collapse of the Milky Way or formed in the disk or bulge and be
kinematically heated subsequently (Conroy et al., 2019; Bonaca et al., 2017;
Du et al., 2018a). In our 591 HiVelSCs, 83 ($\sim$14$\%$) of them are metal-
rich halo stars with [Fe/H]${}_{\rm DD-Payne}>$-1, and their vertical height
and Galactocentric radius are limited in the range of $|z|\leq 10$ kpc and
$R_{\rm gal}\leq 20$ kpc. Thus, they may be the in situ halo stars (Nissen &
Schuster, 2010; Conroy et al., 2019), and such a lower ratio of about 14$\%$
(but 30$\%$ from Du et al. (2018a) and 50$\%$ from Bonaca et al. (2017)) is
consistent with the result in Conroy et al. (2019) that the bulk of the
stellar halo formed from the accretion and tidal disruption.

In recent studies of the Galactic halo’s metallicity distribution (Zuo et al.,
2017; Liu et al., 2018; Conroy et al., 2019), the majority of the retrograde
stars are more metal-poor than the prograde stars. We thus divide our HiVelSCs
into two groups, i.e., prograde and retrograde HiVelSCs, and plot their
distribution on the ([Fe/H], $R$) plane in the upper panels of Figure 10. We
further divide them into another two types, i.e., metal-rich ([Fe/H] $>$ $-$1)
and metal-poor ([Fe/H] $\leq$ $-$1) HiVelSCs, and plotted them on the ($V_{\rm
y}$, $R$) plane in the bottom panels. In this figure, we show the mean values
of horizontal and vertical axes as red solid dots.

From the upper panels, we can see that retrograde HiVelSCs have slightly low
mean value of [Fe/H] ($\langle$[Fe/H]$\rangle$ = $-$1.4), and this is
consistent with the results in the above literature (Zuo et al., 2017; Liu et
al., 2018; Conroy et al., 2019). In the bottom panels, about 75$\%$ metal-rich
HiVelSCs are retrograde, and the ratio for metal-poor HiVelSCs is about
80$\%$. Thus, the majority of our HiVelSCs tend to be retrograde no matter if
they are metal-rich or metal-poor. From the bottom panels, we can see that
metal-poor HiVelSCs tend to have significantly faster mean retrograde
velocities Vy ($\langle$Vy$\rangle$ = $-$186 km s-1). Although the results
here combining chemistry and kinematics are consistent with recent studies,
further verification is needed because the number of stars in our HiVelSCs
samples is small and the precisions for chemical and kinematic parameters need
further improvement, especially the precisions that correspond to the
metallicity and $RV$ from LAMOST low resolution spectra, as well as those of
parallaxes and proper motions from Gaia DR2.

Figure 10: Upper panels: Metallicity ([Fe/H]) vs. Galactocentric radius ($R$)
separated according to the y-components ($V_{\rm y}$) of the Galactocentric
total velocities. The red solid dot marks the mean values of [Fe/H] and $R$.
Upper left and right panels are for prograde and retrograde HiVelSCs,
respectively. Bottom panels: Distribution of 591 HiVelSCs on the (Vy, $R$)

plane separated by [Fe/H]. The red solid dot marks the mean values of Vy and
$R$. Bottom left and right panels are for HiVelSCs with [Fe/H] $>$ $-$1 and
[Fe/H] $\leq$ $-$1, respectively. The green solid dots in each panel represent
92 conservative HiVelSCs introduced in Section 5.2.

##  4 Orbital Integration and Origin

In order to better understand the ejection locations of our HiVelSCs, we
perform numerical orbit integrations and trace their trajectories back in time
using the python package Galpy (Bovy, 2015). For each star, weperform 1000
random MC samplings of the equatorial coordinate, $RV$, proper motion, and
parallax considering the measurement errors as discussed in Section 2.2, and
trace each orbit back to 10 Gyr ago, with a fixed time-step of 10 Myr, using
the MWPotential2014 potential of the Galpy package which consists of a bulge
modeled as a power-law density profile that is exponentially cut-off, a
MiyamotoNagaiPotential disk, and a NFW dark-matter halo (Bovy, 2015).

We estimate for each HiVelSC the maximum distance above the Galactic plane
($Z_{\rm max}$), the eccentricity ($e$), the minimum crossing radius ($r_{\rm
min}$), and the energy ($E$) of each orbit during the 1000 MC realizations,
and record the Galactocentric coordinates ($x_{\rm c}$, $y_{\rm c}$) at the
instant when $z$ = 0, and define the crossing radius ($r_{\rm c}$) as $r_{\rm
c}=\sqrt{x_{\rm c}^{2}+y_{\rm c}^{2}}$ (Marchetti et al., 2019). In the case
of multiple disk crossing for each orbit, $r_{\rm min}$ is defined as the
minimum $r_{\rm c}$. In order to determine unbound or bound orbits, we
calculate the energy of $E-\Phi(\infty)$, in which $E$ is the orbit energy and
$\Phi(\infty)$ is the energy of the convergence potential MWPotential2014 at
infinity.

In Figure 11, we plot $Z_{\rm max}$ as a function of $e$ only for 246 bound
HiVelSCs with $Z_{\rm max}\leq 200$ kpc, solid dots show the median values of
$Z_{\rm max}$ and $e$, and the error bars mark their standard deviations. This
plot has the ability to sort out stars of similar orbits like the Toomre
diagram, because eccentricity $e$ represents the shape of the orbit and
$Z_{\rm max}$ represents the amplitude of the orbit vertical oscillation
(Boeche et al., 2013). From this figure, we can see that the range of e and
Zmax are [0.898, 0.996] and [12 kpc, 200 kpc], respectively, and the median
values of $e$ and $Z_{\rm max}$ are 0.978 and 105 kpc, respectively. These
results represent that the 246 HiVelSCs stars are on highly eccentric orbits,
and all of them have $e$ above 0.6 and $Z\rm_{max}>3~{}kpc$, which represents
that they are kinematically consistent with the halo population (Hawkins et
al., 2015; Boeche et al., 2013; Kordopatis et al., 2013a, b). Table 2 lists
$e$, $Z_{\rm max}$, $r_{\rm min}$, and $E-\Phi(\infty)$ in the last four
columns, and Table LABEL:tab:general_catalog explains the four orbit
parameters in detail. For unbound HiVelSCs and bound HiVelSCs with $Z_{\rm
max}>200$ kpc, Table 2 and LABEL:tab:general_catalog does not provide e and
Zmax.

Figure 11: The maximum height above the Galactic plane $|Z_{\rm max}|$ as a
function of eccentricity $e$, and the y-axis is in log scale. The black solid
dots represent 246 bound HiVelSCs with $Z_{\rm max}\leq 200$ kpc, and the
green solid dots represent 55 conservative HiVelSCs with $Z_{\rm max}\leq 200$
kpc. The conservative HiVelSCs are introduced in Section 5.2.

In Figure 12, we plot $r_{\rm min}$ as a function of the energy
$E-\Phi(\infty)$, and the red dashed line is the separation region between
bound and unbound HiVelSCs. In this figure, there are 240 (41$\%$) HiVelSCs
with remarkably high values of the energy and traveling on unbound orbits
($E-\Phi(\infty)>0$).

Figure 12: Minimum crossing radius $r_{\rm min}$ as a function of energy
$E-\Phi(\infty)$, and the y-axis is in log scale. The dashed red line
separates unbound ($E-\Phi(\infty)>0$) from bound ($E-\Phi(\infty)<0$) orbits.
The black and green solid dots are 591 HiVelSCs, and the green solid dots
represent 92 conservative HiVelSCs introduced in Section 5.2.

After tracing the orbit back, we derive the origins of 591 HiVelSCs from the
positions of these stars crossing the disk (Marchetti et al., 2019). Using the
minimum crossing radius $r_{min}$, we obtain the probability that a star is
ejected from the GC ($P_{\rm gc}$) which is defined as the fraction of orbits
with $r_{\rm min}<1$ kpc in 1000 MC orbits, and the probability that a star is
ejected from the Galaxy ($P_{\rm MW}$) that is defined as the fraction of
orbits with $r_{\rm min}<25$ kpc (Xu et al., 2015; Du et al., 2018b, 2019).
Using $P_{\rm gc}$, $P_{\rm MW}$, and the unbound probability of $P_{\rm ub}$
defined in Section 2.4, the HiVelSCs are divided into four types, and the
classified criteria are shown in Table 4. In this table, “HVS” represents the
fastest hypervelocity stars in the Galaxy; “HRS” represents hyper-runaway
stars; “RS” represents the runaway stars; and “OUT” represents fast halo
stars. In our “LAMOSTDR7-GaiaDR2-HiVelSC” catalog, the column
“Origin$\\_$Class” records the result of this classification, and the last
column of the Table A2 lists the classification results for the 20 fastest
HiVelSCs. Following the classification criteria in Table 4, our HiVelSCs are
divided into 91 “HVS” candidates, 107 “HRS” candidates, 221 “RS” candidates,
and 172 “OUT” candidates. The “HVS” and “OUT” candidates are considered to be
stripped from the GC and dwarf galaxies, respectively, and both “HRS” and “RS”
stars were ejected from the Galactic disk.

The origins of our HiVelSCs from their tracing back orbits might suggest that
a fraction (71$\%$) of them were ejected from the Galactic disk or bulge, and
others were originated from dwarf galaxies. This appears to be in
contradiction with that inferred from the metallicities of these HiVelSCs,
i.e., only a small fraction (14$\%$) HiVelSCs were originated from the
Galactic disk or bulge as explained in Section 3.2. The main reason for such a
difference is that although the orbits of these stars can cross the Galactic
disk or bulge, it does not necessarily mean that they must be ejected from
disk or bulge. Besides, uncertainties of kinematic parameters and the
selection of Galactic potential model will affect the orbits.

Table 4: The classification criteria of HiVelSCs  Class | $P_{\rm gc}$ | $P_{\rm MW}$ | $P_{\rm ub}$
---|---|---|---
HVS candidates |  $>$ 0.16 |  $-$ |  $-$
HRS candidates |  $<$ 0.16 |  $>$ 0.5 |  $>$ 0.5
RS candidates |  $<$ 0.16 |  $>$ 0.5 |  $<$ 0.5
OUT candidates |  $<$ 0.16 |  $<$ 0.5 |  $-$

In Figure 13, we plot the distribution of $P_{\rm gc}$, $P_{\rm MW}$, and
$P_{\rm ub}$ for “HVS”, “HRS”, “RS”, and “OUT” candidates, respectively. In
the upper left panel, most “HVS” candidates are located in the region with
$P_{\rm gc}\leq 0.5$, $P_{\rm ub}\leq 0.5$ and $P_{\rm MW}>0.5$, and it
implies that our criterion might be too optimistic in the sense that we might
over-estimate the number of ”HVS” stars. A fraction of ”HVS” candidates will
be proved to be other three types of stars (“HRS”, “RS” or “OUT” stars). A
similar conclusion can be drawn from other three panels of this figure, which
indicates that the classification criteria in Table 4 used in this work and
other literature (Du et al., 2018b, 2019; Marchetti et al., 2019) might not be
sufficient to determine the origin places of our HiVelSCs. In near future,
more precise measurements of atmospheric parameters (in particular the
metallicity, parallax, proper motions and improved Galactic potential models)
will be available, a detailed orbit analysis to further investigate the origin
places for our HiVelSCs will be carried out as needed.

Figure 13: The distribution of probability that a star is ejected from the GC
($P_{\rm gc}$), probability that a star is ejected from the Galaxy ($P_{\rm
MW}$), and unbound probability ($P_{\rm ub}$) for hypervelocity stars (“HVS”),
hyper-runaway stars (“HRS”), runaway stars (“RS”), and fast halo stars
(“OUT”), respectively. $P_{\rm gc}$ and $P_{\rm MW}$ are defined in Section 4,
and $P_{\rm ub}$ is defined in Section 2.4.

##  5 Discussion

###  5.1 The Zero-Point Correction of Parallax

In this Section, we discuss the impact of a -0.029 mas global parallax zero-
point mentioned in Lindegren et al. (2018) for 591 HVCSs, derived from distant
quasars. Being a negative offset, it leads to lower inferred distance, and
therefore smaller total velocity. We repeat the calculations described in
Section 2.2 but using the mean vector $m=[\alpha,\delta,\varpi+\varpi_{\rm
zp},\mu_{\alpha^{*}},\mu_{\delta}$] to estimate Galactocentric distance and
total velocity, where $\rm\varpi_{zp}=0.029~{}mas$.

After such a parallax zero-point correction, both Galactocentric distances
$r_{\rm GC}$ and total velocities$V_{\rm GC}$ are reduced for 591 HiVelSCs.
The maximum, minimum, and mean value of $r_{\rm GC}$ reduction are 4.0 kpc,
0.2 pc, and 0.4 kpc, respectively, and those of $V_{\rm GC}$ reduction are 241
km s-1, 0.15 km s-1, and 66 km s-1 respectively. Unbound probabilities in the
seven potential models mentioned in Section 2.4 are also re-estimated, and we
find that the number of unbound HiVelSCs in Watkins+2019 potential model with
$P_{\rm ub}\geq 50\%$ decreased from 43 to 8, the number of bound HiVelSCs
with $P_{\rm ub}<50\%$ in Xue+2008 potential model increase from 284 to 492,
and whether other 99 HiVelSCs are unbound with $P_{\rm ub}\geq 50\%$ or not
depend on the potential model used.

###  5.2 Selecting HiVelSCs with More Conservative Criteria

In Section 2.3, we describe the selection criteria of 591 HiVelSCs, and here
we focus on more stringent selection criteria and show the corresponding
results in Table 5. The first column of each row in this table lists the
selection criteria, and the second to sixth columns show the corresponding
results of using these criteria, which are the total number ($\leq 591$) of
the HiVelSCs, the number of HiVelSCs unbound in Watkins+2019 potential model
with $P_{\rm ub}\geq 50\%$, the number of HiVelSCs unbound in the Xue+2008
potential model with $P_{\rm ub}\geq 50\%$, the number of HiVelSCs bound in
the Xue+2008 potential model with $P_{\rm ub}<50\%$, and the maximum value of
total Galactocentric velocities for HiVelSCs selected by the criteria in the
first column, respectively. As a comparison, the results using the selection
method in Section 2.3 are listed in the first row, and the results using other
more conservative criteria are listed from the second to fifth rows.

From the second row of Table 5, we can see that 476 HiVelSCs have conservative
high quality astrometric parameters, i.e., astrometric$\\_$flag = 1, and 34 of
them are still unbound in Watkins+2019 potential model with $P_{\rm ub}\geq
50\%$. If we focus on HiVelSCs with more precise parallaxes, from the third
row we can see that only 120 HiVelSCs satisfy this criteria, and only two of
them are unbound in Watkins+2019 potential model with $P_{\rm ub}\geq 50\%$.
If we focus on HiVelSCs with more precise total velocities VGC, from the
fourth row we can see that only 247 HiVelSCs are left, and three of them are
unbound in Watkins+2019 potential model with $P_{\rm ub}\geq 50\%$.

Finally, if we use all criteria listed in the first column from the second to
fourth rows, we can see in the fifth row that only 92 HiVelSCs are left, and
none of them are unbound in Watkins+2019 potential model with $P_{\rm ub}\geq
50\%$, but there are 26 HiVelSCs unbound in Xue+2008 potential model with
$P_{\rm ub}\geq 50\%$. In Figures 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12, we
also show the distribution of 92 conservative HiVelSCs. Besides, in our
“LAMOSTDR7-GAIADR2-HiVelSC” catalogue, the “conservative$\\_$result” column is
used to select the 92 conservative HiVelSCs by using “conservative$\\_$result
= 1”.

Table 5: The results using more stringent selection criteria

Criteria a | N1 b | N2c | N3d | N4e | Maximum V${}_{\rm GC}^{f}$
---|---|---|---|---|---
|  |  |  |  | (km s-1)
only criteria mentioned in Sect. 2.3 used | 591 | 43 | 304 | 287 | 922
astrometric$\\_$flag = 1 | 476 | 34 | 245 | 231 | 888
$f_{\rm\varpi}=\sigma_{\varpi}/\varpi\leq 0.1$ | 120 | 2 | 38 | 82 | 876
$\rm\sigma_{V_{GC}}/V_{\rm GC}\leq$ 0.2 | 247 | 3 | 87 | 160 | 876
above criteria are all used | 92 | 0 | 26 | 66 | 595

a Selection criteria. The criteria from the second to fifth rows are adopted
after using the criteria in the first row. b Total number of HiVelSCs
satisfied the selection criteria listed in the first column c The number of
HiVelSCs unbound in Watkins+2019 potential model with $P_{\rm ub}\geq 50\%$; d
The number of HiVelSCs unbound in Xue+2008 potential model with $P_{\rm
ub}\geq 50\%$; e The number of HiVelSCs bound in Xue+2008 potential model with
$P_{\rm ub}<50\%$; f The maximum Galactocentric velocities for all HiVelSCs
selected by the criteria in the first column;

##  6 Conclusion

In this paper, we cross-match LAMOST DR7 with Gaia DR2 to find more high
velocity stars, and obtain a catalog consisting of over 10 million spectra
(LAMOST-Gaia). Galactocentric distances $r_{\rm GC}$ and total velocities
$V_{\rm GC}$ are estimated for over 8.48 million “low-f” entries in the
LAMOST-Gaia catalog, which have positive Gaia parallax and low fractional
parallax errors ($f_{\rm\varpi}=\sigma_{\rm\varpi}/\varpi\leq 0.2$). We define
our sample of high velocity stars as those, who can escape from the Galaxy in
at least one of the seven Galactic potential models adopted in this work, or
have total velocities in the Galactic rest frame larger than 450 km s-1, and
result in a total of 591 high velocity star candidates (HiVelSCs) found from
the LAMOST-Gaia catalog. Their total velocities $V_{\rm GC}$ are then
recalculated using the radial velocities determined by the LAMOST Stellar
Parameter Pipeline (LASP), because their $RV$ uncertainties given by the LASP
not only consider the calculation error caused by LASP algorithm but also take
into account the error introduced from the process of spectra observation and
data processing. After the recalculation, the total velocities for all
HiVelSCs are still $>445$ km s-1, and our main conclusions are:

(i) Among 591 HVCs, the majority of them are giant stars, and 14 of them have
been already collected in the open fast stars catalog (OFSC) (Boubert et al.,
2018). In this paper, we construct a catalogue of “LAMOSTDR7-GAIADR2-HiVelSC”
to collect parameters for 591 HiVelSCs, including 93 columns such as LAMOST
radial velocity, atmospheric parameters, and five Gaia astrometry parameters,
and 476 HiVelSCs have conservative high quality astrometric parameters of Gaia
DR2, which satisfy the criteria introduced in Section 2.4.

(ii) Using seven Galactic potential models, 43 HiVelSCs can escape from the
Galaxy with unbound probabilities of $P_{\rm ub}>50\%$ in the potential model
of Watkins et al. (2019) (Watkins+2019; resulting in the largest escaping
velocities), 304 HiVelSCs are unbound in the potential model of Xue et al.
(2008) (Xue+2008; resulting in the smallest escaping velocities) with $P_{\rm
ub}>50\%$, and other 287 HiVelSCs are bound in Xue+2008 potential model with
P${}_{\rm ub}\leq 50\%$. As mentioned in Lindegren et al. (2018) and Arenou et
al. (2018), there is a negative zero-point for Gaia parallax, and we attempt
to correct the zero-point of -0.029 for 591 HiVelSCs, which leads to a
decrease in the number of HiVelSCs unbound in Watkins+2019 potential model
with P${}_{\rm ub}>50\%$, from 43 to 8. At the end of this work, we also
discuss the effect if more conservative criteria are adopted to select
HiVelSCs. The conclusion is that there are in total 92 HiVelSCs satisfying all
of the three more conservative selection criteria, and they are referred to as
92 conservative HiVelSCs in the main text. Among them, there is no HiVelSCs
unbound in Watkins+2019 potential model with P${}_{\rm ub}>50\%$ when all
criteria listed in Table 5 are used, but there are 26 HiVelSCs have P${}_{\rm
ub}>50\%$ of being unbound in Xue+2019 potential model, and the maximum value
of Galactocentric velocities $V_{\rm GC}$ for 92 conservative HiVelSCs is 595
km s-1.

(iii) Using the Toomre diagram, probabilities for the thick-disk-to-halo
(TD/H) and the distribution on the (eccentricity, $z_{\rm max}$) plane, we
find that all 591 HiVelSCs are kinematically associated to the halo
population, which confirms the assumptions, that high velocity stars in the
solar vicinity mostly belong to the halo, adopted in previous works (Schuster
& Nissen, 1988; Ryan & Smith, 2003; Schuster et al., 2006). The 591 HiVelSCs
have a mean $\alpha$ abundance of $\alpha=+0.22$ dex, and their metallicities
[Fe/H] peak at near [Fe/H] $\sim$ $-$1.2 and have a wide range from near
[Fe/H] $\sim$ $-$3.5 to [Fe/H] $\sim$ +0.5, which also indicates that on the
whole they are metal-poor slightly $\alpha$-enhanced inner halo stars.

Among the 591 HiVelSCs, about 14$\%$ of them are metal-rich halo stars with
[Fe/H]$>-$1, and they may be the in situ halo stars (Nissen & Schuster, 2010;
Conroy et al., 2019). These in situ halo stars are considered to be formed in
the initial collapse of the Milky Way or formed in the disk or bulge and be
kinematically heated subsequently (Conroy et al., 2019; Bonaca et al., 2017;
Du et al., 2018a), and the low ratio of them indicates that the bulk of the
stellar halo formed as a consequence of the accretion and tidal disruption
processes as mentioned in Conroy et al. (2019).

(iv) Considering both their kinematics and chemistries, we find that most of
our HiVelSCs have retrograde velocities of Vy, and retrograde HiVelSCs have a
slightly lower mean value of [Fe/H], which is consistent with the results in
the literature (Zuo et al., 2017; Liu et al., 2018; Conroy et al., 2019),
meanwhile metal-poor ([Fe/H] $<$ -1) HiVelSCs tend to have faster mean
retrograde velocities $V_{\rm y}$.

(v) There are 304 HiVelSCs unbound in Xue+2008 potential model with $P_{\rm
ub}>50\%$, and most of them move on retrograde ($V_{\rm y}<0$) orbit, which
means, as it has been suggested in the literature, that a population of
unbound stars may have an extragalactic provenance (de la Fuente Marcos & de
la Fuente Marcos, 2019; Marchetti et al., 2019; Cicone et al., 2016). In order
to further investigate their origin, we track the orbits of 591 HiVelSCs back
in time, and they are divided into four types, i.e., “HVS”, “HRS”, “RS” and
“OUT”, according to their unbound probabilities ($P_{\rm ub}$), and the
probabilities of being ejected from the GC ($P_{\rm gc}$) and Galactic disk
($P_{\rm MW}$). We find that $\sim$15$\%$ of stars are from the GC,
$\sim$55$\%$ of stars are from the Galactic disk, and $\sim$30$\%$ of stars
have extragalactic origins, but we caution that due to the uncertainty in the
phase space measurement, further investigation is needed to confirm their
origins.

##  Appendix A Tables

Here, we list four tables. Table A1 and A2 list escape velocities $V_{\rm
esc}$ and unbound probabilities $P_{\rm ub}$ (defined in Section 2.4 ) for the
20 fastest HiVelSCs in the seven potential models (Paczynski, 1990; Gnedin et
al., 2005; Xue et al., 2008; Koposov et al., 2010; Kenyon et al., 2014; Bovy,
2015; Watkins et al., 2019) mentioned in Section 2.4, and Table A3 lists their
atmospheric parameters (effective temperature $T_{\rm eff}$, surface gravity
log $g$, and metallicity [Fe/H]) and $\alpha$ element abundances
([$\alpha$/Fe]). As mentioned in Section 2.4, we construct the catalogue of
“LAMOSTDR7-GAIADR2-HiVelSC” including 93 columns to list various parameters
for 591 HiVelSCs, and Table LABEL:tab:general_catalog explains each column of
this table in detail.

Table A1: Escape velocities of the 20 fastest HiVelSCs in the seven Galactic
potential models

ID |  $r_{\rm GC}$a |  $V_{\rm GC}$a |  $V_{\rm esc}$(W)b |  $V_{\rm esc}$(G)b |  $V_{\rm esc}$(Ke)b |  $V_{\rm esc}$(Ko)b |  $V_{\rm esc}$(P)b |  $V_{\rm esc}$(M)b |  $V_{\rm esc}$(X)b
---|---|---|---|---|---|---|---|---|---
| (kpc) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (km s-1)
Hivel1 | 10.1${}_{-0.6}^{+0.9}$ | 922${}_{-136}^{+168}$ | 598 | 587 | 573 | 543 | 512 | 491 | 474
Hivel2 | 10.6${}_{-0.4}^{+0.6}$ | 888${}_{-142}^{+197}$ | 595 | 585 | 570 | 542 | 511 | 486 | 469
Hivel3 | 8.9${}_{-0.0}^{+0.1}$ | 876${}_{-73}^{+81}$ | 615 | 601 | 590 | 567 | 533 | 503 | 483
Hivel4 | 10.9${}_{-0.5}^{+0.8}$ | 874${}_{-168}^{+247}$ | 593 | 584 | 568 | 540 | 509 | 484 | 468
Hivel5 | 11.5${}_{-0.9}^{+1.6}$ | 862${}_{-147}^{+242}$ | 585 | 579 | 561 | 530 | 501 | 479 | 464
Hivel6 | 6.3${}_{-0.4}^{+0.8}$ | 791${}_{-142}^{+199}$ | 634 | 617 | 610 | 576 | 544 | 535 | 508
Hivel7 | 8.8${}_{-0.2}^{+0.4}$ | 789${}_{-126}^{+194}$ | 611 | 598 | 586 | 557 | 525 | 504 | 484
Hivel8 | 7.9${}_{-0.0}^{+0.0}$ | 778${}_{-69}^{+81}$ | 624 | 608 | 600 | 573 | 540 | 514 | 492
Hivel9 | 10.6${}_{-1.0}^{+1.7}$ | 741${}_{-156}^{+236}$ | 592 | 583 | 568 | 537 | 507 | 486 | 469
Hivel10 | 7.7${}_{-0.1}^{+0.3}$ | 737${}_{-114}^{+174}$ | 623 | 606 | 599 | 569 | 537 | 516 | 493
Hivel11 | 15.2${}_{-1.2}^{+2.0}$ | 727${}_{-123}^{+186}$ | 561 | 558 | 535 | 507 | 480 | 453 | 442
Hivel12 | 12.5${}_{-1.0}^{+1.8}$ | 726${}_{-138}^{+230}$ | 578 | 573 | 553 | 524 | 495 | 471 | 457
Hivel13 | 6.4${}_{-0.1}^{+0.3}$ | 718${}_{-87}^{+121}$ | 636 | 616 | 612 | 580 | 548 | 533 | 506
Hivel14 | 11.6${}_{-1.2}^{+2.0}$ | 713${}_{-108}^{+160}$ | 588 | 575 | 563 | 537 | 506 | 478 | 462
Hivel15 | 8.1${}_{-0.1}^{+0.3}$ | 705${}_{-121}^{+191}$ | 619 | 603 | 594 | 566 | 534 | 511 | 489
Hivel16 | 9.0${}_{-0.3}^{+0.5}$ | 698${}_{-104}^{+132}$ | 607 | 596 | 583 | 552 | 521 | 502 | 482
Hivel17 | 6.6${}_{-0.1}^{+0.2}$ | 697${}_{-137}^{+165}$ | 637 | 617 | 612 | 583 | 550 | 531 | 504
Hivel18 | 9.3${}_{-0.6}^{+1.1}$ | 697${}_{-110}^{+170}$ | 606 | 592 | 581 | 552 | 520 | 499 | 479
Hivel19 | 9.3${}_{-0.3}^{+0.6}$ | 696${}_{-131}^{+198}$ | 606 | 594 | 581 | 552 | 521 | 499 | 479
Hivel20 | 10.5${}_{-0.4}^{+0.6}$ | 691${}_{-118}^{+149}$ | 596 | 586 | 571 | 542 | 512 | 488 | 471

Note. — The 62th to 68th columns of Table LABEL:tab:general_catalog are listed
here for the 20 fastest HiVelSCs, which mainly includes the escape velocities
estimated by the seven Galactic potential models (Paczynski, 1990; Gnedin et
al., 2005; Xue et al., 2008; Koposov et al., 2010; Kenyon et al., 2014; Bovy,
2015; Watkins et al., 2019). The median value, lower uncertainty, and upper
uncertainty of Galactocentric distance ($r_{\rm GC}$) are shown in the same
column (the second column) in this table but separated into three columns,
respectively, in Table LABEL:tab:general_catalog (from 35th to 37th columns).
The median value, lower uncertainty, and upper uncertainty of Galactocentric
total velocity ($V_{\rm GC}$) are shown in the same column (the third column)
in this table but separated into three columns, respectively, in Table
LABEL:tab:general_catalog (from 47th to 49th columns). a Galactocentric
distance and total velocity; b Escape velocities in the seven Galactic
potential models;

Table A2: Unbound probabilities of the 20 fastest HiVelSCs in the seven
potential models

ID |  $P_{\rm gc}$a |  $P_{\rm MW}$b |  $P_{\rm ub}$(W)c |  $P_{\rm ub}$(G)c |  $P_{\rm ub}$(Ke)c |  $P_{\rm ub}$(Ko)c |  $P_{\rm ub}$(P)c |  $P_{\rm ub}$(M)c |  $P_{\rm ub}$(X)c | Origin$\\_$Classd
---|---|---|---|---|---|---|---|---|---|---
Hivel1 | 0.000 | 1.000 | 0.996 | 0.998 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | HRS
Hivel2 | 0.000 | 0.993 | 0.995 | 0.999 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | HRS
Hivel3 | 0.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | HRS
Hivel4 | 0.000 | 0.039 | 0.969 | 0.973 | 0.978 | 0.991 | 0.996 | 0.999 | 0.999 | OUT
Hivel5 | 0.000 | 0.000 | 0.975 | 0.981 | 0.984 | 0.990 | 0.997 | 0.999 | 1.000 | OUT
Hivel6 | 0.000 | 0.002 | 0.861 | 0.898 | 0.904 | 0.951 | 0.981 | 0.989 | 0.997 | OUT
Hivel7 | 0.000 | 0.994 | 0.928 | 0.947 | 0.953 | 0.981 | 0.995 | 0.998 | 1.000 | HRS
Hivel8 | 0.000 | 0.000 | 0.992 | 0.997 | 0.999 | 1.000 | 1.000 | 1.000 | 1.000 | OUT
Hivel9 | 0.000 | 0.852 | 0.804 | 0.831 | 0.852 | 0.912 | 0.935 | 0.951 | 0.969 | HRS
Hivel10 | 0.001 | 0.003 | 0.837 | 0.874 | 0.894 | 0.939 | 0.972 | 0.989 | 0.999 | OUT
Hivel11 | 0.000 | 0.848 | 0.900 | 0.913 | 0.940 | 0.961 | 0.983 | 0.994 | 0.996 | HRS
Hivel12 | 0.000 | 0.415 | 0.843 | 0.854 | 0.886 | 0.929 | 0.965 | 0.980 | 0.988 | OUT
Hivel13 | 0.000 | 0.000 | 0.821 | 0.868 | 0.876 | 0.942 | 0.979 | 0.987 | 0.997 | OUT
Hivel14 | 0.000 | 0.997 | 0.863 | 0.885 | 0.910 | 0.942 | 0.982 | 0.994 | 0.996 | HRS
Hivel15 | 0.000 | 0.995 | 0.759 | 0.790 | 0.809 | 0.871 | 0.931 | 0.959 | 0.978 | HRS
Hivel16 | 0.000 | 0.009 | 0.800 | 0.830 | 0.855 | 0.923 | 0.965 | 0.984 | 0.993 | OUT
Hivel17 | 0.000 | 1.000 | 0.659 | 0.713 | 0.732 | 0.797 | 0.864 | 0.915 | 0.953 | HRS
Hivel18 | 0.000 | 1.000 | 0.782 | 0.816 | 0.839 | 0.908 | 0.961 | 0.979 | 0.990 | HRS
Hivel19 | 0.000 | 0.022 | 0.736 | 0.775 | 0.798 | 0.857 | 0.909 | 0.938 | 0.962 | OUT
Hivel20 | 0.000 | 0.999 | 0.779 | 0.809 | 0.837 | 0.904 | 0.946 | 0.975 | 0.983 | HRS

Note. — The 69th to 78th columns of Table LABEL:tab:general_catalog are listed
here for the 20 fastest HiVelSCs, which include the unbound probabilities in
the seven potential models (Paczynski, 1990; Gnedin et al., 2005; Xue et al.,
2008; Koposov et al., 2010; Kenyon et al., 2014; Bovy, 2015; Watkins et al.,
2019), and the classification results of their origin. a The probability that
a star is derived from the GC; b The probability that a star origins from the
Galactic disk; c The unbound probabilities in the seven Galactic potential
models; d ;

Table A3: Atmospheric parameters for the 20 fastest HiVelSCs

ID |  $T_{\rm eff}$_LASPa | log $g$_LASPa | [Fe/H]$\\_$LASPa |  $T_{\rm eff}$_DD-Payneb | log $g$_DD-Payneb | [Fe/H]$\\_$DD-Payneb | [$\alpha$/Fe]$\\_$DD-Payneb
---|---|---|---|---|---|---|---
| (K) | (dex) | (dex) | (K) | (dex) | (dex) | (dex)
Hivel1 | 4803$\pm$19 | 1.89$\pm$0.03 | -1.40$\pm$0.02 | 4919$\pm$38 | 37.62$\pm$2.22 | -1.25$\pm$0.06 | 0.28$\pm$0.02
Hivel2 | 5384$\pm$84 | 2.82$\pm$0.14 | -1.54$\pm$0.08 | 5813$\pm$47 | 46.96$\pm$3.66 | -1.24$\pm$0.07 | 0.24$\pm$0.04
Hivel3 | 4615$\pm$228 | 4.86$\pm$0.36 | -1.48$\pm$0.21 | 4801$\pm$51 | 50.95$\pm$4.93 | -1.09$\pm$0.09 | 0.17$\pm$0.04
Hivel4 | 6553$\pm$12 | 4.10$\pm$0.02 | -2.30$\pm$0.02 | 7190$\pm$49 | 48.50$\pm$4.02 | -1.87$\pm$0.10 | 0.16$\pm$0.03
Hivel5 | 4835$\pm$121 | 1.54$\pm$0.19 | -2.20$\pm$0.11 | 5366$\pm$81 | 80.92$\pm$2.37 | -1.84$\pm$0.13 | 0.22$\pm$0.10
Hivel6 | 5415$\pm$32 | 2.78$\pm$0.05 | -1.10$\pm$0.03 | 5443$\pm$29 | 29.04$\pm$2.53 | -1.12$\pm$0.05 | 0.28$\pm$0.02
Hivel7 | 6238$\pm$214 | 3.97$\pm$0.34 | -1.60$\pm$0.20 | 6175$\pm$90 | 89.67$\pm$3.35 | -1.88$\pm$0.18 | 0.30$\pm$0.07
Hivel8 | 5401$\pm$29 | 4.16$\pm$0.05 | -0.46$\pm$0.03 | 5362$\pm$24 | 24.47$\pm$4.08 | -0.41$\pm$0.04 | 0.09$\pm$0.01
Hivel9 | 4243$\pm$42 | 0.75$\pm$0.07 | -1.29$\pm$0.04 | 4290$\pm$21 | 21.40$\pm$1.17 | -1.22$\pm$0.04 | 0.10$\pm$0.02
Hivel10 | 6151$\pm$260 | 4.06$\pm$0.41 | -0.79$\pm$0.24 | $-$ | $-$ | $-$ | -0.29$\pm$0.02
Hivel11 | 4650$\pm$48 | 1.53$\pm$0.08 | -1.43$\pm$0.05 | 4798$\pm$50 | 49.53$\pm$1.92 | -1.25$\pm$0.07 | 0.27$\pm$0.03
Hivel12 | 4928$\pm$26 | 2.13$\pm$0.04 | -1.34$\pm$0.02 | 5058$\pm$35 | 34.58$\pm$2.36 | -1.20$\pm$0.05 | 0.26$\pm$0.02
Hivel13 | 5010$\pm$59 | 2.31$\pm$0.10 | -1.38$\pm$0.06 | 5054$\pm$57 | 57.30$\pm$2.32 | -1.28$\pm$0.08 | 0.26$\pm$0.03
Hivel14 | 5013$\pm$39 | 2.26$\pm$0.06 | -1.97$\pm$0.04 | 5111$\pm$40 | 40.42$\pm$3.06 | -1.94$\pm$0.06 | 0.01$\pm$0.02
Hivel15 | 6159$\pm$108 | 4.17$\pm$0.18 | -0.97$\pm$0.10 | 6118$\pm$36 | 36.28$\pm$4.14 | -1.07$\pm$0.07 | 0.18$\pm$0.04
Hivel16 | 6336$\pm$29 | 4.14$\pm$0.05 | -1.21$\pm$0.03 | 6151$\pm$27 | 27.28$\pm$3.18 | -1.31$\pm$0.05 | 0.16$\pm$0.02
Hivel17 | 6181$\pm$129 | 4.05$\pm$0.21 | -1.51$\pm$0.12 | 6220$\pm$55 | 54.78$\pm$3.95 | -1.55$\pm$0.10 | 0.18$\pm$0.06
Hivel18 | 4660$\pm$50 | 1.40$\pm$0.08 | -2.04$\pm$0.05 | 5009$\pm$47 | 46.74$\pm$2.19 | -1.70$\pm$0.06 | 0.24$\pm$0.03
Hivel19 | 4930$\pm$49 | 2.36$\pm$0.08 | -1.22$\pm$0.05 | 5024$\pm$50 | 49.61$\pm$2.52 | -1.16$\pm$0.07 | 0.25$\pm$0.03
Hivel20 | 5271$\pm$95 | 2.76$\pm$0.16 | -2.21$\pm$0.09 | 5435$\pm$54 | 53.93$\pm$3.08 | -2.00$\pm$0.10 | 0.27$\pm$0.06

Note. — The 79th to 92nd columns of Table LABEL:tab:general_catalog are listed
here for the 20 fastest HiVelSCs, which are atmospheric parameters and
$\alpha$ abundance estimated by the the LASP and the method of data-driven
Payne (DD-Payne), respectively. The measurements and uncertainties are shown
in the same column in this table but separated into two columns in Table
LABEL:tab:general_catalog. a Atomespheric parameters estimated by the LASP; b
Atomespheric parameters calculated by the method of data-driven Payne (DD-
Payne) in Xiang et al. (2019);

Table A4: Description of our HiVelSCs catalog. Parameters measured by this work such as distances and velocities correspond to the median of the distribution, and lower and upper uncertainties are derived respectively from the 16th and 84th percentiles of the distribution. Entries labelled1 are from the LAMOST catalog, entries labelled2 are taken from the Gaia DR2 catalogue (Gaia Collaboration et al., 2018a), and entries labelled3 are derived in this paper. Column | Name | Units | Description
---|---|---|---
1 | ID | $-$ | High Velocity star identifier 3
2 | specid | $-$ | LAMOST DR7 identifier 1
3 | Gaia_designation | $-$ | Gaia DR2 identifier 2
4 | R.A. | deg | Right ascension 2
5 | e_R.A. | deg | Right ascension error 2
6 | decl. | deg | Declination 2
7 | e_decl. | deg | Declination error 2
8 | S/N_r | $-$ | r-band spectral signal to noise ratio 1
9 | Class | $-$ | spectral type 1
10 | RV_LASP | km s-1 | Radial velocity measured by the LASP 1
11 | e_RV_LASP | km s-1 | Radial velocity error given by the LASP 1
12 | pmra | mas yr-1 | Proper motion in right ascension 2
13 | e_pmra | mas yr-1 | Standard uncertainty in pmra 2
14 | pmdec | mas yr-1 | Proper motion in declination 2
15 | e_pmdec | mas yr-1 | Standard uncertainty in pmdec2
16 | parallax | mas | Parallax 2
17 | e_parallax | mas | Standard uncertainty in parallax 2
18 | G | mag | G band mean magnitude 2
19 | G_BP | mag | G$\\_$BP band mean magnitude 2
20 | G_RP | mag | G$\\_$RP band mean magnitude 2
21 | astrometric_flag | $-$ | A flag to mark whether a star has reliable astrometric parameters 3
22 | RV_LASP_Calibrate | km s-1 | LASP radial velocity corrected the zero-point 1
23 | r | kpc | Heliocentric distance 3
24 | el_r | kpc | Lower uncertainty on r 3
25 | eu_r | kpc | Upper uncertainty on r 3
26 | x | kpc | Cartesian Galactocentric x coordinate 3
27 | el_x | kpc | Lower uncertainty on x 3
28 | eu_x | kpc | Upper uncertainty on x 3
29 | y | kpc | Cartesian Galactocentric y coordinate 3
30 | el_y | kpc | Lower uncertainty on y 3
31 | eu_y | kpc | Upper uncertainty on y 3
32 | z | kpc | Cartesian Galactocentric z coordinate3
33 | el_z | kpc | Lower uncertainty on z 3
34 | eu_z | kpc | Upper uncertainty on z 3
35 | r_GC | kpc | Galactocentric distance 3
36 | el_r_GC | kpc | Lower uncertainty on r$\\_$GC 3
37 | eu_r_GC | kpc | Upper uncertainty on r$\\_$GC 3
38 | Vx | km s-1 | Cartesian Galactocentric x velocity 3
39 | el_Vx | km s-1 | Lower uncertainty on Vx 3
40 | eu_Vx | km s-1 | Upper uncertainty on Vx 3
41 | Vy | km s-1 | Cartesian Galactocentric y velocity 3
42 | el_Vy | km s-1 | Lower uncertainty on Vy 3
43 | eu_Vy | km s-1 | Upper uncertainty on Vy 3
44 | Vz | km s-1 | Cartesian Galactocentric z velocity 3
45 | el_Vz | km s-1 | Lower uncertainty on Vz 3
46 | eu_Vz | km s-1 | Upper uncertainty on Vz 3
47 | V_GC | km s-1 | Cartesian Galactocentric total velocity 3
48 | el_V_GC | km s-1 | Lower uncertainty on V$\\_$GC 3
49 | eu_V_GC | km s-1 | Upper uncertainty on V$\\_$GC 3
50 | e | $-$ | Orbit eccentricirty 3
51 | el_e | $-$ | Lower uncertainty on e 3
52 | eu_e | $-$ | Upper uncertainty on e 3
53 | Zmax | kpc | Orbit maximum height above the Galactic disk 3
54 | el_Zmax | kpc | Lower uncertainty on Zmax 3
55 | eu_Zmax | kpc | Upper uncertainty on Zmax 3
56 | r_min | kpc | Minimum crossing radius 3
57 | el_r_min | kpc | Lower uncertainty on r$\\_$min 3
58 | eu_r_min | kpc | Upper uncertainty on r$\\_$min 3
59 | E_Phi_Infinity | kpc2 Myr-2 | The difference between orbit energy E and potential energy at infinity 3
60 | el_E_Phi_Infinity | kpc2 Myr-2 | Lower uncertainty on E$\\_$Phi$\\_$Infinity 3
61 | eu_E_Phi_Infinity | kpc2 Myr-2 | Upper uncertainty on E$\\_$Phi$\\_$Infinity 3
62 | Vesc(W) | km s-1 | Escape velocity estimated by the potential model in Watkins et al. (2019) 3
63 | Vesc(G) | km s-1 | Escape velocity estimated by the potential model in Gnedin et al. (2005) 3
64 | Vesc(Ke) | km s-1 | Escape velocity estimated by the potential model in Kenyon et al. (2014) 3
65 | Vesc(Ko) | km s-1 | Escape velocity estimated by the potential model in Koposov et al. (2010) 3
66 | Vesc(P) | km s-1 | Escape velocity estimated by the potential model in Paczynski (1990) 3
67 | Vesc(M) | km s-1 | Escape velocity estimated by the potential model in Bovy (2015) 3
68 | Vesc(X) | km s-1 | Escape velocity estimated by the potential model in Xue et al. (2008) 3
69 | Pgc | $-$ | Probability of ejecting from the GC 3
70 | PMW | $-$ | Probability of ejecting from the Galactic disk 3
71 | Pub(W) | $-$ | Unbound probability in the potential model in Watkins et al. (2019) 3
72 | Pub(G) | $-$ | Unbound probability in the potential model in Gnedin et al. (2005) 3
73 | Pub(Ke) | $-$ | Unbound probability in the potential model in Kenyon et al. (2014) 3
74 | Pub(Ko) | $-$ | Unbound probability in the potential model in Koposov et al. (2010) 3
75 | Pub(P) | $-$ | Unbound probability in the potential model in Paczynski (1990) 3
76 | Pub(M) | $-$ | Unbound probability in the potential model in Bovy (2015) 3
77 | Pub(X) | $-$ | Unbound probability under the potential model in Xue et al. (2008) 3
78 | Origin_Class | $-$ | Origin classification including “HVS”, “HRS”, “RS” and “OUT” 3
79 | Teff_LASP | K | Effective temperature estimated by the LASP 3
80 | e_Teff_LASP | K | Uncertainty on Teff$\\_$LASP 3
81 | log $g$_LASP | dex | Surface gravity estimated by the LASP 3
82 | e_log $g$_LASP | dex | Uncertainty on log$(g)\\_$LASP 3
83 | [Fe/H]_LASP | dex | Metallicity estimated by the LASP 3
84 | e_[Fe/H]_LASP | dex | Uncertainty on [Fe/H]$\\_$LASP 3
85 | Teff_DD-Payne | K | Effective temperature estimated by the method of data-driven Payne 3
86 | e_Teff_DD-Payne | K | Uncertainty on Teff$\\_$DD-Payne 3
87 | log $g$_DD-Payne | dex | Surface gravity estimated by the method of data-driven Payne 3
88 | e_log $g$_DD-Payne | dex | Uncertainty on log$(g)\\_$DD-Payne 3
89 | [Fe/H]_DD-Payne | dex | Metallicity estimated by tthe method of data-driven Payne 3
90 | e_[Fe/H]_DD-Payne | dex | Uncertainty on [Fe/H]$\\_$DD-Payne 3
91 | Alpha_Fe_DD-Payne | dex |  $\alpha$ abudance estimated by the method of data-driven Payne 3
92 | e_Alpha_Fe_DD-Payne | dex | Uncertainty on Alpha$\\_$Fe$\\_$DD-Payne 3
93 | conservative_result | $-$ | HiVelSCs satisfy all more conservative criteria in Section 5.2 3

[1] For unbound HiVelSCs and bound HiVelSCs with Z${}_{\rm max}>200$ kpc, we
do not provide eccentricity $e$ and the maximum height above the Galactic disk
$Z_{\rm max}$. [2] “$-$” represents null.

We would like to thank an anoymous referee for helpful comments and
suggestions. We thank Bovy Jo, Fu Xiao-Ting, Du Bing, Yan Hong-Liang, Shi
Jian-Rong, Hou Wen, Chen Jian-Jun,Yuan Hai-Long, Guo Yan-Xin, Xue Xiang-Xiang,
and Zhang Lan for helpful discussions. This work is supported by National Key
R$\&$D Program of China (No. 2019YFA0405502), the National Natural Science
Foundation of China (Nos. U1931209, 11873056, 11991052, 11988101 and
11890694), and the National Key Program for Science and Technology Research
and Development (Grant No. 2016YFA0400704). YST is supported by the NASA
Hubble Fellowship grant HST-HF2-51425.001 awarded by the Space Telescope
Science Institute. Cultivation Project for LAMOST Scientific Payoff and
Research Achievement of CAMS-CAS. Guoshoujing Telescope (the Large Sky Area
Multi-Object Fiber Spectroscopic Telescope, LAMOST) is a National Major
Scientific Project built by the Chinese Academy of Sciences. Funding for the
project has been provided by the National Development and Reform Commission.
LAMOST is operated and managed by the National Astronomical Observatories,
Chinese Academy of Sciences.

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