1. Introduction
Hypervelocity stars (HVS) are rare stellar objects first identified by Brown et al. (Reference Brown, Geller, Kenyon and Kurtz2005) as young (B-type) stars travelling at velocities of several hundred to over one thousand km s
$^{-1}$
, exceeding the escape velocity of the Milky Way. A promising explanation is the Hills mechanism (Hills Reference Hills1988), in which a binary star undergoes a close encounter with an SMBH: capturing one component while the other star gets ejected at high velocity. The required presence of an SMBH is in agreement with the current observations of the Galactic Center, which hosts a single SMBH, Sagittarius A* (Sgr A*), with a mass of
$\sim 4 \times 10^6\,M_\odot$
(GRAVITY Collaboration 2022) and a population of young, massive stars on tight orbits-the so-called S-stars-has been detected within 0.01–0.1 pc of Sgr A* (Ghez et al. Reference Ghez, Duchêne, Matthews, Hornstein, Tanner, Larkin, Morris, Becklin, Salim, Kremenek, Thompson, Soifer, Neugebauer and McLean2003; Gillessen et al. Reference Gillessen, Eisenhauer, Trippe, Alexander, Genzel, Martins and Ott2009).
At larger radii, a disk of young stars has been observed in the central region (Paumard et al. Reference Paumard, Genzel, Martins, Nayakshin, Beloborodov, Levin, Trippe, Eisenhauer, Ott, Gillessen, Abuter, Cuadra, Alexander and Sternberg2006; Bartko et al. Reference Bartko, Martins, Fritz, Genzel, Levin, Perets, Paumard, Nayakshin, Gerhard, Alexander, Dodds-Eden, Eisenhauer, Gillessen, Mascetti, Ott, Perrin, Pfuhl, Reid, Rouan, Sternberg and Trippe2009; von Fellenberg et al. Reference von Fellenberg, Gillessen, Stadler, Bauböck, Genzel, de Zeeuw, Pfuhl, Amaro Seoane, Drescher, Eisenhauer, Habibi, Ott, Widmann and Young2022), which may represent the remnants of a molecular cloud infall and fragmentation event (Mapelli et al. Reference Mapelli, Hayfield, Mayer and Wadsley2012; Bonnell and Rice Reference Bonnell and Rice2008). These structures provide natural initial conditions for studying the joint origin of HVS and S-stars. Previous work by Šubr and Haas (Reference Šubr and Haas2016) has explored such a setup with N-body simulations and showed that HVS together with S stars could have originated in a disc-like stellar structure similar to the stellar disc we currently observe in the Galactic Center. However, the currently observed HVS in the Galactic Center halo cannot have originated from the current disc, but may have some counterparts in the S stars. This leaves an unanswered question: where are the HVSs originating from the current disc?
We expand on previous works by testing this model with a notable recent observation, the HVS, S5-HVS1 (Koposov et al. Reference Koposov, Boubert, Li, Erkal, Da Costa, Zucker, Ji, Kuehn, Lewis, Mackey, Simpson, Shipp, Wan, Belokurov, Bland-Hawthorn, Martell, Nordlander, Pace, De Silva and Wang2020). Its velocity vector points almost directly away from the Galactic Center, with an inferred flight time of
$\sim 4.8$
Myr. In this work, we investigate whether a young stellar disk around the SMBH can account for the observed properties of S5-HVS1. Using direct N-body simulations of binaries embedded in an eccentric disk, we follow the dynamical evolution of stars over several Myr and track both ejected and bound populations. We demonstrate that the Kozai-Lidov mechanism (Kozai Reference Kozai1962; Lidov Reference Lidov1962) operating in a stellar disk, in conjunction with the Hills mechanism, can account for the observations of S5-HVS1, providing a unified framework for the stellar dynamics of the Galactic center.
2. Methods
In order to study the origins of HVS and S stars in the Galactic center, we perform numerical integrations of mutually gravitationally interacting point masses in a disk configuration orbiting around a supermassive black hole. We use values guided by observations of our Galactic center, starting with the central SMBH, mimicking Sgr A*, of mass
$ M_{\bullet} =4 \times 10^6 M_\odot$
. We sample 2000 stars from a power-law distribution function
$n_m \propto m^{-1.5}$
with
$1 M_\odot \lt m \lt 150 M_\odot$
which gives us a disk mass of
$M_d=24500 M_\odot$
. We pair all stars to form binaries with a mass ratio as close to unity as possible. The binaries are in circular orbits, with the orbital angular momentum aligned to be parallel to the angular momentum of the disk. We sample the binary’s semimajor axis from the Öpik distribution function,
$n_{a_b} \propto a_b^{-1}$
where
$a_b$
is in the range
$0.05 - 100$
au (Kobulnicky and Fryer Reference Kobulnicky and Fryer2007; Ling et al. Reference Ling, Magdalena and Prieto2004).
The binary systems are orbiting the SMBH on Keplerian orbits with semimajor axis following a power law distribution
$n_a \propto a^{-1}$
with
$a_\textrm{in}=0.04 \text{ pc} \leq a \leq a_\textrm{out}=0.4 \text{ pc} $
. These orbits are inclined following the distribution function
$n_i \propto \sin{i}$
with
$i \in \langle 0,2.5^\circ \rangle$
. The eccentricity of the orbits of the center of masses of the binaries follows a radial gradient according to
$e=0.9(a-a_{in})/(a_{out}-a_{in})$
from Šubr and Haas (Reference Šubr and Haas2016). The eccentricity vectors of the orbits are parallel, which means the ellipses are mutually aligned and not randomly oriented. This is motivated by works of Mapelli et al. (Reference Mapelli, Hayfield, Mayer and Wadsley2012) and Bonnell and Rice (Reference Bonnell and Rice2008), which model star formation in the vicinity of an SMBH from an infalling gas cloud.
This system does not include the spherical cluster of the old star due to computational constraints. We use NBODY 6 to perform the numerical integration of this system (Aarseth Reference Aarseth2003). A thorough explanation of the simulation methodology and technical details is provided in Šubr and Haas (Reference Šubr and Haas2016).
3. Results
Šubr and Haas (Reference Šubr and Haas2016) demonstrated that hypervelocity stars can form as counterparts to the S-stars via the Hills mechanism. They also found that the ejected stars by the Hills mechanism are preferentially launched within the plane of the stellar disk and show a preferred azimuthal direction of escape. This anisotropy provides a potential diagnostic tool for tracking observed HVS back to their origin. The rate of ejections is not constant over time. We find that ejections peak at
$T \approx 1.5$
Myr after disk formation, which corresponds to the timescale for Kozai-Lidov oscillations to drive binaries to high eccentricities (Šubr and Haas Reference Šubr and Haas2016). At this stage, close passages by the SMBH efficiently disrupt binaries, producing both unbound hypervelocity stars and tightly bound S-star counterparts.
To test the consistency of our model with the observation of S5-HVS1, we evolved the ejected stellar population forward in time within the compound potential of the SMBH and a spherical potential of the galaxy (Kenyon et al. Reference Kenyon, Bromley, Geller and Brown2008). We project the distribution of ejected stars onto the plane of the sky. The left panel of Fig. 1 shows that after 4.8 Myr of evolution, after the ejections peak at 1.5 Myr, the simulated HVS population shows a spatial distribution confined to a narrow band defined by the disk plane. The location of S5-HVS1 is denoted by a white star and the galactic plane with the red line. Since the spatial distribution is dependent on the disk orientation, we do a parameter search for all possible disk orientations. A heatmap of all disk orientations in the phase space of its longitude of ascending node (
$\Omega$
) and inclination (i) with respect to the galactic plane is shown in the right panel of Fig. 1. The colour denotes the number of stars in a 5-degree window after projection around the observed S5-HVS1. The orientation of the currently observed clockwise disk is marked with a black dot.
Left: Shows the heatmap of the number of HVS after projection of the 3D simulation onto our night sky. A disk orientation of
$\Omega = 360 ^\circ$
and
$i=72^\circ$
. The red line is the galactic plane, and the white star is the observed location of S5-HVS1. Right: A heatmap of the different disk orientations possible, with the colour representing the number of stars observed in a 5-degree window around S5-HVS1 in a projection shown like the left panel. The black dot represents the current location of the clockwise disk.
Figure 1 Long description
Panel A: A heatmap shows the number of hypervelocity stars projected onto the night sky. The x-axis represents Right Ascension in degrees, and the y-axis represents Declination in degrees. The color scale indicates the logarithm of the number of stars per square degree, ranging from -2 to 2. A red line marks the galactic plane, and a white star indicates the observed location of S5-HVS1. Panel B: Another heatmap displays different disk orientations, with the x-axis representing the inclination angle (i) in degrees and the y-axis representing the position angle (Omega) in degrees. The color scale shows the number of stars observed in a 5-degree window around S5-HVS1, ranging from 0 to 0.09. A black dot marks the current location of the clockwise disk.
However, in the galactic center, we also have the circumnuclear disk (CND), a massive torus of gas and dust at
$\sim 1.5$
pc from Sag A* (Martín et al. Reference Martín, Martín-Pintado, Montero-Castaño, Ho and Blundell2012). The massive CND can perturb the young stellar disk over time, causing it to precess and evolve its orientation (Šubr et al. 2009). Thus, our results indicate that both the timing and geometry of S5-HVS1 is compatible with an origin in the young stellar disk of the Galactic Center.
4. Conclusions
Our simulations in conjunction with results from Šubr and Haas (Reference Šubr and Haas2016) show that the Hills mechanism and Kozai–Lidov mechanism acting on binaries in a young stellar disk can simultaneously produce hypervelocity stars and tightly bound S-stars near Sgr A* in the Galactic Center.
The observed properties of S5-HVS1, including its trajectory and
$\sim$
4.8 Myr flight time, are consistent with this scenario. The agreement could be affected when precession due to torques exerted by the circumnuclear disk onto the clockwise disk are taken into account.
These results support a common origin for both HVS and S-stars in the Galactic Center. Future work will extend the models by including stellar collisions, which should reduce the number of observed HVS originating from the Galactic Center, and provide an answer for the lack of observed HVS like S5-HVS1. We also want to study and compare our model with the growing sample of HVS identified by future surveys.
Ω=360∘
i=72∘
Open access
