The Origin of High-velocity Stars Considering the Impact of the Large Magellanic Cloud

Utilizing astrometric parameters sourced from Gaia Data Release 3 and radial velocities obtained from various spectroscopic surveys, we identify 519 high-velocity stars (HiVels) with a total velocity in the Galactocentric rest frame greater than 70% of their local escape velocity under the Gala MilkyWayPotential. Our analysis reveals that the majority of these HiVels are metal-poor late-type giants, and we show nine HiVels that are unbound candidates to the Galaxy with escape probabilities of 50%. To investigate the origins of these HiVels, we classify them into four categories and consider the impact of the Large Magellanic Cloud (LMC) potential on their backward-integration trajectories. Specifically, we find that one of the HiVels can track back to the Galactic center, and three HiVels may originate from the Sagittarius dwarf spheroidal galaxy (Sgr dSph). Furthermore, some HiVels appear to be ejected from the Galactic disk, while others formed within the Milky Way or have an extragalactic origin. Given that the LMC has a significant impact on the orbits of Sgr dSph, we examine the reported HiVels that originate from the Sgr dSph, with a few of them passing within the half-light radius of the Sgr dSph.


INTRODUCTION
The existence of high-velocity stars (HiVels) implies the presence of extreme dynamics.In the literature, these stars are typically divided into four categories: hypervelocity stars (HVSs), hyperrunaway stars (HRSs), runaway stars (RSs), and high velocity halo stars (Li et al. 2021;Quispe-Huaynasi et al. 2022).The first two types of HiVels are unbound stars, with speeds exceeding the escape velocity of the Milky Way (MW).The classic origin of HVSs, as theorized by Hills (1988), involves a close encounter between a stellar binary and a massive black hole (MBH).A star that is ejected by a MBH and has an unbound velocity is defined as an HVS by Brown (2015).The Southern Stellar Stream Spectroscopic Survey (S 5 ) discovered the fastest HVS (Koposov et al. 2020), which is an A-type star with a total velocity of 1755 km s −1 .This star was ejected by the MBH at the Galactic Center, providing strong evidence for the Hills mechanism.HRSs are another type of unbound HiVels and are also considered as RSs with extreme velocities.One of the most plausible mechanisms for generating HRSs is the thermonuclear explosion in double white dwarf binaries (Shen et al. 2018).The first confirmed HRS is HD 271791 originating from the outer disk (Heber et al. 2008), with a total velocity of 630 km s −1 .
The last two types of HiVels are stars that are bound by the Galactic potential.RSs were initially introduced as O-and B-type stars with high velocities (Blaauw 1961).It is believed that RSs form in the disk and then are ejected into the halo.There are generally two main mechanisms for the formation of RSs: supernova explosions in stellar binary systems (e.g., Blaauw 1961;Portegies Zwart 2000;Wang & Han 2009;Wang et al. 2013) and dynamical encounters resulting from multi-body interactions in dense stellar systems (e.g., Bromley et al. 2009;Gvaramadze et al. 2009).Highvelocity halo stars are another type of bound HiVels that could be an in-situ population of stars formed within the MW (Di Matteo et al. 2019;Belokurov et al. 2020) or an extragalactic source.Numerical simulations by Abadi et al. (2009) have shown that disrupted dwarf galaxies may contribute halo stars with high velocities.In addition to the mechanisms mentioned above, the dense environments in the cores of globular clusters facilitate many strong dynamical encounters among stellar objects (Cabrera & Rodriguez 2023).HiVels could also be ejected through the close interaction of a globular cluster and a supermassive black hole (Capuzzo-Dolcetta & Fragione 2015), or through the formation of three-body binaries in globular clusters (Weatherford et al. 2023).
Recently, a significant number of candidate HiVels originating from the Sagittarius dwarf spheroidal galaxy (Sgr dSph) have been identified.The first candidate HVS (J1443+1453) that likely originated from the Sgr dSph was discovered by Huang et al. (2021).Subsequently, Li et al. (2022) reported 60 candidate HiVels (including 2 HVS candidates) that may also come from the Sgr dSph, and Li et al. (2023) found 15 extreme velocity stars that have had close encounters with the Sgr dSph.However, both Huang et al. (2021) and Li et al. (2023) did not consider the impact of the Large Magellanic Cloud (LMC), and Li et al. (2022) disregarded the dynamical friction from the Milky Way (MW) on the LMC.It is important to mention that the HVS3 (or HE 0437-5439) has a 40% probability of passing within 5 kpc of the LMC, taking into account the LMC's influence (Edelmann et al. 2005;Erkal et al. 2019b).It is fortunate that the Gaia Data Release 3 (Gaia DR3) provides precise proper motion measurements for HVS3.Consequently, it is necessary to investigate the origin of these HiVels.
The aim of the work is to search for more HiVels, and determine their origins considering the impact of the LMC.This paper is organized as follows: Section 2 provides a description of the observation sample.In section 3, we obtain 519 HiVels with a total velocity in the Galactocentric restframe greater than 70% of the local escape velocity.Section 4 focuses on the analysis of the origin of these HiVels.Finally, a summary is provided in Section 5.

OBSERVATION SAMPLE
The Gaia DR3 provides astrophysical parameters for 470 million stars (Gaia Collaboration et al. 2023), 34 million radial velocities (RVs) (Katz et al. 2023).To select stars with accurately measured parallax, proper motion and spectroscopic data, we applied the following criteria: RUWE < 1.4, ϖ − ϖ ZP > 0, ϖ − ϖ ZP > 5σ ϖ and S/N > 10.RUWE is Renormalized Unit Weight Error to assess the goodness-of-fit of the astrometric solution for a particular star (Lindegren et al. 2021b).We use the approach described in Lindegren et al. (2021a) to correct Gaia DR3 parallaxes by the parallax zero point ϖ ZP .To obtain precise RVs, we cross-matched the Gaia DR3 catalog with other large-scale Galactic Surveys, such as GALAH DR3 (De Silva et al. 2015;Buder et al. 2021), LAMOST DR10 (Cui et al. 2012;Zhao et al. 2012), RAVE DR6 (Steinmetz et al. 2020), APOGEE DR17 (Majewski et al. 2017), and S 5 (Li et al. 2019)).The weighted mean RV was computed using the following equation: where rv represents the calculated radial velocity, w i = 1/σ2 i is the weight corresponding to each measurement with uncertainty σ i , and N is the total number of measurements.We removed stars for which |rv − rv Gaia | ⩾ 3σ Gaia .In the context of this analysis, rv, rv Gaia , and rv Survey correspond to the corrected radial velocity, the radial velocity from Gaia, and the radial velocity from other surveys, respectively.Figure 1 demonstrates that the difference in radial velocities among the 519 HiVels is minimal, with a majority falling within 15 km s −1 .Using the Gaia's parameters such as phot variable flag, and classprob dsc combmod star flag which represents the probability of being a single star (but not a white dwarf) from DSC-Combmod (which classifies objects using BP/RP spectrum, photometry and astrometry features), we removed all variable stars and the 519 HiVels are single stars.
Adopting the same method as Du et al. (2019), we use Bayesian analysis to determine heliocentric distances (d) and velocities in the R.A. and Decl.direction (ν α and ν δ ).The posterior consists of likelihood with a three-dimensional Gaussian distribution and prior with the three-parameter generalized Gamma distribution (Bailer-Jones et al. 2021): where .74047, and C χ is covariance matrix.

HIVELS SAMPLE
In order to determine the origin of the HiVels, we rewind them in the combined presence of the gravitational field of the MW and LMC.For the MW, we adopt the Gala potential MilkyWayPotential (Price-Whelan 2017), including the Hernquist (Hernquist 1990) bulge and nucleus, the Miyamoto-Nagai (Miyamoto & Nagai 1975) stellar disk, and the Navarro-Frenk-White (Navarro et al. 1996) dark matter halo.For the LMC, we consider a Plummer profile with a mass of 1.38 × 10 11 M ⊙ (Erkal  et al. (2016).We have set the half-mass radius to 5 kpc for definiteness.The scale radius is set at 17 kpc, computed based on an enclosed mass of 1.7 × 10 10 M ⊙ within 8.7 kpc (van der Marel & Kallivayalil 2014).The analysis is conducted with the LMC's position, radial velocity and proper motions from Erkal et al. (2019b).The dynamical friction and LMC's gravitational potential use the ChandrasekharDynamicalFrictionForce function and MovingObjectPotential function implemented in galpy (Bovy 2015), respectively.We then integrate the backward orbit using galpy over a total time of 3 Gyr with a time step of 0.1 Myr .If a star is ejected from the Galactic disk, its backward-integral trajectory passes through the Galactic midplane (Z GC = 0 kpc plane) with a maximum distance of 25 kpc from the node to the Galactic Center (Marchetti 2021).In addition, a HiVel tracking back to the Galactic Center should intersect the Galactic midplane only once, and its backward-integral trajectory pass within 1 kpc of the Galactic Center (Liao et al. 2023).For HiVels originating from the Sgr dSph, their backward-integral trajectories are expected to pass within the Sgr dSph's half-light radius of 2.587 kpc (McConnachie 2012).In the case of a HiVel originating from a globular cluster, it needs to pass within the Plummer scale radius of that cluster (Vasiliev & Baumgardt 2021).The probabilities were calculated by tallying the frequency of occurrence in the 4000 MC realizations conducted in this study.
The HiVels sample is defined as stars with total velocities (ν GC ) in the Galactocentric restframe exceeding 70% of the escape velocity (ν GC > 0.7 ν esc ).From this definition, a final sample of 519 HiVels with astrometric parameters and radial velocities was derived, including 9 unbound candidates (P ub > 0.5).The density distribution of these stars in ν GC and r GC is shown in Figure 2. The number of HiVels is the highest at a distance of 8.1 kpc and gradually decreases on both sides.This aligns with the observed number of stars.As the Sun is positioned at a distance of 8.12 kpc (GRAVITY Collaboration et al. 2018), the count of observed stars gradually diminishes towards the outer regions.We also plot the Hertzsprung-Russell diagram of these stars' astrophysical parameters (T eff , log g, [Fe/H]) in Figure 3.Most of them are the metal-poor late-type giants with [Fe/H] < −0.8 dex and T eff < 7300 K. Table 1 gives the classification criteria of HiVels.Detailed information about 9 unbound stars (8 for the first time, and 2 reported by Marchetti (2021) and Li et al. (2021)) is provided in Table 2. Two of these stars exhibit retrograde motion relative to the direction of the MW's rotation (ν ϕ < 0), and their trajectories do not track back to the Galactic disk (P disk < 0.5), suggesting a possible extragalactic origin.Furthermore, 57 bound HiVels (P ub < 0.5) exhibit prograde motion and cluster at high metallicity, and their trajectories track back to the galactic disk (P disk > 0.5), indicating they are likely the runaway stars (RSs) that form in the disk and then are ejected into the halo but not the typical OB type runaway stars.The remaining 453 HiVels are classified as high-velocity halo stars that may form within the MW or have extragalactic origins.Note-The last two rows list the stars that have been reported by Marchetti (2021); Li et al. (2021).

A HiVel track back to the Galactic Center
We found a HiVel that crosses over the Galactic midplane (Z GC = 0 kpc plane) only once and has a backwards-integrated trajectory passing within 1 kpc of the Galactic Center.Table 3 shows the detailed information.Since the Galactic field is a classically collisionless system, particularly at the high speeds typical of HiVels, we neglect the perturbative influence of other bodies on these orbits.According to the Hills mechanism ejection probability proposed by Bromley et al. (2006), the HiVel is not close enough to the Galactic Center, making it unlikely to be ejected by this mechanism.We computed the trajectories of 150 globular clusters from Vasiliev (2019) using proper motions from Vasiliev & Baumgardt (2021), but this star does not pass within their Plummer scale radius.Interestingly, the star is similar in metallicity and age to the VVV CL002 ([Fe/H] = −0.4± 0.2, age > 6.5 Gyr) (Moni Bidin et al. 2011), which is the closest globular cluster to the Galactic Center Note-P cross and r closest are the probability of crossing over the Galactic midplane only once and the distance of the backward-integral trajectory closest to the Galactic center, respectively.The last five rows of data come from GALAH DR3.(Minniti et al. 2021).However, due to the lack of radial velocity information for this globular cluster, it is unknown whether the star passed within its Plummer scale radius.

HiVels originated from the Sgr dSph and the LMC
In our sample of HiVels, three HiVels (2 for the first time, and 1 reported by Li et al. (2022); Li et al. ( 2023)) show potential origin from the Sgr dSph.Their backward-integrated trajectories can track back to the Sgr dSph (P Sgr > 0.5) and other parameters are listed in Table 5.The chemical abundance ([Fe/H]= −1.12 ± 0.02, [α/Fe]= 0.27 ± 0.01) of Gaia DR3 3702750168409332864 is consistent with the members stars of the Sgr stream which are taken from an analysis based on the LAMOST K gaints (Huang et al. 2021;Yang et al. 2019).The color-magnitude (BP-RP = 0.96, M G = 0.21) of Gaia DR3 3653273996289384832 is most similar to both the Sgr and Sgr stream (e.g., Li et al. 2022;Vasiliev & Belokurov 2020;Vasiliev et al. 2021) It is evident that the LMC significantly influences the orbit of the Sgr dSph as shown in Figure 4.As the HiVels that reported to originate from the Sgr dSph (Li et al. 2022;Huang et al. 2021;Li et al. 2023) did not consider the impact or the dynamical friction from the MW on the LMC, we recalculated the probabilities P Sgr of their trajectories passing within the half-light radius of the Sgr dSph.Among them, the HiVels with P Sgr > 0.5 are listed in Table 5.We also calculated the   trajectory of HVS3 (Erkal et al. 2019b) using the proper motion provided by Gaia DR3, and related parameters are listed in Table 4. HVS3 has a 37% probability passing within 5 kpc of the LMC, and we show contours of the time of closest approach to the LMC and the velocity during this closest approach in Figure 5.  Liao et al.

SUMMARY AND DISCUSSION
In this study, we identify a total of 519 high-velocity stars (HiVels) through a cross-matching process between the Gaia DR3 and other Large-scale Galactic Surveys.A catalog of the properties of these stars is available on China-VO: doi:10.12149/101304.These HiVels consist of 9 unbound candidates under the Gala MilkyWayPotential, 57 runaway stars (not the typical OB type runaway stars), and 453 high-velocity halo stars.In our sample, 78 HiVels have been reported by Li et al. (2021), a candidate HiVel originating from the Sgr dSph has been reported by Li et al. (2022), and 440 have been reported for the first time.
The Gaia G-band magnitudes of these HiVels are less than 15 and majority of these stars are metal-poor late-type giants.Although we employ geometric distances rather than photogeometric or photo-astrometric distances, they are very similar at G < 15 as shown in Anders et al. (2022).The backwards-integraed trajectory of a HiVel can track back to the Galactic Center but there is insufficient evidence for the VVV CL002 origin.Notably, based on the color-magnitude or chemical analysis, as well as the trajectories, three HiVels could be the member stars of the Sgr dSph.If the LMC has not been taken into account in the orbital analysis, we still obtain the same results for the four stars, as they are far from the LMC (over 50 kpc) and have a short time to their pericenter (57 Myr ago).Considering the impact of the LMC, only a small number of reported HiVels pass within the half-light radius of the Sgr dSph.This is because the LMC has a significant impact on the orbit of the Sgr dSph and HiVels originating from the Sgr dSph are required to pass within the half-light radius of the Sgr dSph.Using the Gaia DR3's proper motion, HVS3 may still come from the LMC.In the near future, we anticipate the radial velocity of VVV CL002 to be observed, which will enable us to calculate its orbit to determine the origin of the HiVel tracking back to the Galactic Center.We also expect that the future surveys will provide a rich source of more HiVels to provide new insights for understanding the presence of an extreme dynamic in the Galaxy.
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.Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions.SDSS-IV acknowledges support and resources from the Center for High Performance Computing at the University of Utah.The SDSS website is www.sdss.org.Based on data acquired at the Anglo-Australian Telescope.We acknowledge the traditional owners of the land on which the AAT stands, the Gamilaraay people, and pay our respects to elders past and present.

APPENDIX
A. CATALOG FORMAT Table 6 describes the format of the full table for the 519 HiVels with a total velocity in the Galactocentric restframe greater than 70% of the local escape velocity.It is available in a machinereadable format in the online Journal and in China-VO.Note-Table 6 is published in its entirety in the machine-readable format.A portion is shown here for guidance regarding its form and content.It is also available on China-VO: doi:10.12149/101304

Figure 1 .
Figure 1.Distribution of radial velocity differences (|rv − rv Gaia |, |rv Survey − rv Gaia |, |rv − rv Survey |) for the 519 HiVels.The corrected radial velocities, the radial velocities from Gaia, and the radial velocities from other surveys are represented by rv, rv Gaia , and rv Survey , respectively.For reference, a vertical blue line is plotted at a difference of 15 km s −1 .

Figure 2 .
Figure 2. The density distribution of total velocity ν GC vs. Galactocentric distance r GC for the final sample 519 HiVels with ν GC > 0.7 ν esc , including 9 unbound candidates (P ub > 0.5) with error bars under the Gala (Price-Whelan 2017) MilkyWayPotential.The four different colored dashed lines are the escape velocity curves derived from the four different Milky Way potential models (McMillan 2017; Price-Whelan 2017; Cautun et al. 2020; Bovy 2015), respectively.The purple dashed line represents 70 % of the escape velocity curve from the Gala.

Figure 4 .
Figure4.The left panel illustrates the orbits without dynamical friction from the MW on the Sgr dSph and with dynamical friction, showing minimal differences.In contrast, the right panel shows the orbits without and with the potential of the LMC, displaying significant differences in the orbits caused by the LMC's gravitational potential.

Figure 5 .
Figure 5. Distribution of the velocity and time at closest approach to LMC.The dashed lines show the 16,50,84 percentiles of 1D distribution.The velocity is 790 +59 −63 km s −1 .The backward time is 24.9 +5.7 −7.3 Myr.
point correction, after Lindegren et al. (2021b) pmRA mas.yr-1Proper motion in right ascension direction, Gaia DR3 e pmRA mas.yr-1Error of pmRA pmDE mas.yr-1Proper motion in declination direction, Gaia DR3 e pmDE mas.yr-1Error of pmDE plx pmra-corr -Correlation between parallax and proper motion in right ascension, Gaia DR3 plx pmdec-corr -Correlation between parallax and proper motion in declination, Gaia DR3 pmra pmdec-corr -Correlation between proper motion in right ascension and in declination, color, Gaia DR3 [phot bp mean mag -phot rp mean mag] cross-match-sur -Cross-match the name of survey id surveyid -Unique ID in the survey [survey id] Teff K Effective temperature, the cross-match survey

FeH
in equation 2, after Bailer-Jones et al. (2021) GGDalpha -Corresponding to α in equation 2, after Bailer-Jones et al. (2021) GGDbeta -Corresponding to β in equation 2, after Bailer-Jones et al. (2021) Dist kpc Heliocentric distance (after Du et al. (2019)) star tracking back to the disk , this work P-sgr -Probablity of the star tracking back to the Sgr, this work var-flag -Flag indicating if variability was identified in the photometric data,

Table 1 .
Li et al. (2023)on criteria of HiVels Note-The formula ν ϕ = −276.7 × [Fe/H] − 97.78, proposed byLi et al. (2023), serves as an empirical demarcation line for distinguishing between the disk stars and the halo stars.P ub and P disk represent the probability of exceeding the Galactic escape velocity curves and the probability of tracking back to the Galactic disk, respectively.

Table 3 .
Detailed information about the star with probable origin in the center of the Galaxy.

Table 4 .
The related parameters of HVS3

Table 6 .
Catalog Format