The match between the data and the isochrone model across the wavelengths is well demonstrated by Fig. 2. Red points with error bars shown on multiple panels of Fig. 3 mark the parameter values measured from spectroscopic analysis of S5-HVS1 (Section 3.1). The measurements from photometric data only are broadly consistent with the spectroscopic analysis, as the error bars overlap with the high probability parts of the posterior. Although there is possibly a small discrepancy in temperature of ∼200 K and/or [Fe/H]

of ∼0.2 dex between purely spectroscopic and photometric measurements, we believe this level of disagreement is well within the systematic errors of our spectroscopic and isochrone modelling.

Since the photometric and spectroscopic analyses are consistent, we also show in the figure the posterior from the combination of the spectroscopic and photometric analyses (Model SP) as green contours. As expected, the combination of the data sets shrinks the posteriors considerably, i.e. the combined mass estimate is 2.35 ± 0.06 M_⊙ and distance estimate is logDhel1kpc=0.936±0.015

⁠. The posterior estimates for these and other parameters from the Model SP are also provided in Table 2. Throughout the paper, we use both the photometric and photometric+spectroscopic sets of estimates, where we will interpret the photometric-only constraints as being more conservative.⁸ As we will discuss in the next section, the kinematics of S5-HVS1 are consistent with ejection from the GC if the star has a very specific heliocentric distance of ∼8.8 kpc. Pink lines on Fig. 3 show the heliocentric distance to the star that is consistent with ejection from the GC (see Section 5), and we remark that this distance agrees perfectly with both the photometric and spectrophotometric analyses.

While the isochrone modelling performed so far did include the horizontal branch phase, the posterior on the stellar parameters indicates that the photometry of S5-HVS1 is inconsistent with it being a BHB star. However, it is still worth specifically addressing the possibility that S5-HVS1 is a BHB, because this is quite feasible given the star’s colour of g − r ∼ −0.27 (most BHB stars have colours of −0.3 ≲ g − r ≲ 0; Yanny et al. 2000). We therefore perform an independent check to assess the BHB hypothesis by looking at measurements of g − r and i − z colours. This colour combination is known to be sensitive to the surface gravity of stars due to the Paschen break contribution to the z-band, and therefore allows us to separate BHB from BS/MS stars (see e.g. Vickers, Grebel & Huxor 2012; Belokurov & Koposov 2016). With colours of (g − r) = −0.27 and (i − z) = −0.13, S5-HVS1 sits significantly below the line separating the BHB from BS/MS (see the right-hand panel of fig. 11 and equation 5 of Li et al. 2019) further confirming that S5-HVS1 is a main-sequence star. Additionally, when looking at the distribution of surface gravities and effective temperatures (the left-hand panel of fig. 11 of Li et al. 2019) S5-HVS1 lies on the BS side of the distribution. Thus for future analysis, unless specified otherwise, we will adopt the main-sequence–based distance constraints determined in this section.

4 KINEMATICS OF S5-HVS1

The extreme radial velocity of S5-HVS1 as measured from the observed spectra makes it one of the fastest stars known in the Galaxy and thus warrants a detailed investigation of its orbit and origin. Summarizing the phase-space information available for S5-HVS1, the position of the star on the sky is known very precisely, as is the radial velocity. The proper motion of the star is available in the Gaia DR2 catalogue and, because of the star’s brightness G ∼ 16, it is also very precise (μ_αcos δ, μ_δ) = (35.328 ± 0.084, 0.587 ± 0.125) masyr−1

⁠.⁹ The only phase space parameter that is poorly constrained is the heliocentric distance, as discussed in Section 3.3. This is why we expect that most of the orbital inferences for S5-HVS1 should show a 1D degeneracy corresponding to a range of possible heliocentric distances. Even with the more conservative (Model P) distance estimates, it is clear from combining the radial velocity and proper motions that the S5-HVS1 velocity in the Galactic frame is in excess of ∼1200 kms−1⁠: V3D=1470+166−147 kms−1

⁠.

As a first step in modelling the orbit of S5-HVS1, we perform a backward integration of its current phase space coordinates to infer a possible ejection site of the star. Since the current total velocity of S5-HVS1 is at least 1200 kms−1

⁠, one of the key questions we are interested in is whether the star has been ejected from the GC, the MW disc, or some other system such as a globular cluster or satellite galaxy. While some fast moving stars have been associated with other galaxies like the Large Magellanic Cloud (Edelmann et al. 2005; Gualandris & Portegies Zwart 2007; Boubert & Evans 2016; Boubert et al. 2017; Irrgang et al. 2018; Erkal et al. 2019); in this paper, we will focus only on ejection from the MW disc and the GC.

To infer a possible ejection point and velocity of S5-HVS1, we integrate the orbit of the star backwards in time in the gravitational potential of the Milky Way until the star intersects the Galactic plane Z = 0 at the location X_pl, Y_pl. Throughout the paper when doing orbit integrations, unless specified otherwise, we adopt the gravitational potential from McMillan (2017), the distance from the Sun to GC of 8.178 kpc (Gravity Collaboration et al. 2019), and Solar velocity of (U⊙,V⊙,W⊙)=(11.1,245,7.25)kms−1

(Schönrich, Binney & Dehnen 2010; McMillan 2017). To take into account the observational uncertainties in our inference of the ejection site X_pl, Y_pl, when integrating back the orbit of S5-HVS1 we sample the observed uncertainties in radial velocity from S⁵, proper motion from Gaia and the distance posterior derived in Section 3.3. The resulting distributions of the Galactic plane ejection coordinates X_pl, Y_pl together with current heliocentric distance D_hel and current velocity in the Galactocentric frame V_3D,now are shown in Fig. 4. The two sets of distributions shown with green and blue correspond to the photometric only distance (Model P) and spectro-photometric distance (Model SP) constraints. We remark that the current heliocentric distance D_hel distribution is exactly the same as the posterior on D_hel determined in Section 3.3. While the figure shows the Monte Carlo sampling of uncertainties, it is mathematically equivalent to the posterior distribution of P(X_pl, Y_pl, D_hel, V_3D,now|Data) under the model where the star was ejected from MW disc plane (and uninformative priors on X_pl, Y_pl and ejection velocity).

As expected, the posterior on the S5-HVS1 ejection point is very elongated (almost one dimensional) due to the negligible uncertainties in all parameters but the heliocentric distance. However, we also see that the usage of spectrophotometric distances alleviates this problem somewhat. The current total velocity of the star in the Galactic rest frame is constrained to be V3D,now=1470+170−150

kms−1 for Model P and V3D,now=1687+39−37 kms−1 for Model SP, while the ejection velocity of the star from the Galactic disc is Vej=1550+190−160 kms−1 for Model P, and Vej=1755+45−44 kms−1 for Model SP, very similar to the current velocity. The difference between the current velocities and the ejection velocities is small (∼50 kms−1⁠) because the impact of the Galactic potential on such a fast moving star is minimal. The inferred ejection point based on the photometric only distance (Model P) is Xpl=−2.63+1.72−1.54 kpc, Ypl=−0.22+0.15−0.10 kpc, where the values and uncertainties come from 50 per cent and 16 per cent, 84 per cent percentiles of 1D marginal distributions. However, the constraints on X_pl, Y_pl are strongly non-Gaussian and elongated. Most importantly we see that the GC (X, Y) = (0, 0) (shown on Fig. 4 by pink dashed lines) is located within the 90 per cent probability contour of the X_pl, Y_pl distribution. While the peak of the posterior for the ejection point X_pl, Y_pl is shifted by 2.5 kpc from the GC, the fact that the very thin probability contour covers the GC is highly informative and suggestive of a GC origin. If we instead consider the contours for Model SP based on spectrophotometric distances, we see that the inference of X_pl, Y_pl is significantly tighter Xpl=−0.37+0.40−0.39 kpc, Ypl=−0.03+0.05−0.04

 kpc, and thus our backward integrations point almost unambiguously at the GC (X_pl, Y_pl) = (0, 0) as the origin of S5-HVS1.¹⁰

The Bayes factor is K = 81 when we use photometric distances (Model P), and K = 354 for the spectrophotometric distances (Model SP). This constitutes strong (Model P) or overwhelming (Model SP) evidence in favour of the GC origin. In the calculation, we assumed the same (uniform) priors over ejection velocities, direction and traveltime in both hypotheses. An intuitive explanation of a Bayes factor of 354 is that if before observing S5-HVS1 the odds ratio in favour of the GC origin versus disc origin was 50/50, then after observing S5-HVS1 we would have to update the odds to be 354/1.

The evidence that S5-HVS1 is coming from the GC is almost definitive and is much stronger than for any other hyper-velocity star we know. To illustrate this, we take the list of stars from Boubert et al. (2018, augmented with LAMOST-HVS4 from Li et al. 2018, and J01020100 from Massey et al. 2018) and perform the calculation of the ejection point X_pl, Y_pl within the plane of the disc (identically to that performed on S5-HVS1), given the existing observational constraints on those stars (position, distances, proper motions, and radial velocities). The right-hand panel of Fig. 5 shows the 90 per cent confidence contours for a subset of the stars where those contours overlapped significantly with the 30 × 30 kpc² region (for many stars in the list, e.g. HVS1, the contours are larger than the whole plot). The figure shows that there are stars that could be associated with the GC based on their phase space coordinates (for instance, HVS20 and HVS24), but their confidence region of origin includes the whole Milky Way disc as well. Among other stars with tighter constraints on the point of origin, only J01020100 (Massey et al. 2018) seems to cover the GC (but note that J01020100 is believed to be a disc runaway due its meagre velocity of 296 kms−1

⁠). The contour showing the region of origin of S5-HVS1 around the GC is almost invisible compared to the other stars.

Concluding this section, based on strong orbital evidence that points at a region of ∼50 × 1000 pc² around the GC as the origin of S5-HVS1 (Fig. 5) and the large velocity of S5-HVS1 V_3D,now ∼ 1500–1700 kms−1

that is impossible for a disc runaway star of ∼2 M_⊙ (see Tauris 2015), we can conclude that S5-HVS1 was ejected from the GC. It is the first star with such a confident identification. In the next section, we will analyse what inferences can made based on this assumption.

5 GC ORIGIN

Assuming that S5-HVS1 was ejected from the GC, we can now investigate the kinematics of the star further. First, we determine the exact ejection velocity and time of flight from the GC required to match the observations of S5-HVS1, by ejecting the star from the centre of the MW in the potential of McMillan (2017) (without considering the potential of the SMBH itself). This gives a prediction of α, δ, μ_α, μ_δ, RV, D_hel as a function of the ejection velocities V_x, V_y, V_z, and traveltime T. We then write a Normal likelihood function using the observed position, distance, proper motion, and RV of S5-HVS1 and their uncertainties (we use a Gaussian approximation to the log₁₀D_hel posterior from Section 3.3). We adopt non-informative uniform priors on all the parameters and then sample the posterior using an ensemble sampler. Fig. 6 shows the posterior. This model implies an ejection speed of 1798.6 ± 3.1 kms−1

with the z-component of the velocity being the largest and a total traveltime from the GC to the current position of 4.801 ± 0.009 Myr. We note that the constraints on the ejection velocities are now much tighter compared to Fig. 4. The reason for this is that postulating that the star is coming from the GC strongly constrains the current distance to S5-HVS1 to be D_hel = 8884 ± 11 pc and thus makes our spectro-photometric measurement mostly irrelevant.¹¹ We also remark that the measured ejection speed of 1798.6 ± 3.1 kms−1 from the GC was computed while ignoring the potential of the SMBH, and thus represents the ejection velocity outside the sphere of influence of the black hole (≳1 pc). The actual ejection speed of the star depends on how close to the BH the ejection happened, and could easily be as high as ∼8000 kms−1 if the ejection happened at a distance of 100 au from the BH. Assuming a GC origin also allows us to improve the proper motion precision from the one delivered by Gaiaμαcosδ=35.333±0.081masyr−1 and μδ=0.617±0.011masyr−1

⁠. While the μ_αcos δ precision did not improve much, the error bar on the predicted μ_δ is 8 times smaller than Gaia’s. Since the full phase space position of S5-HVS1 becomes very precise when we adopt the GC origin hypothesis, we can look at the geometric position of S5-HVS1 in the Galaxy. This is shown in Fig. 7. We see that, as expected, S5-HVS1 is mostly moving downwards away from the disc and that the Sun, GC, and S5-HVS1 form an almost equilateral triangle with ∼8–9 kpc edges.

In this section, we will further use the phase space observations of S5-HVS1 to constrain the gravitational potential of the MW, location, and kinematics of the Sun in the Galaxy, and assess the possible connection of S5-HVS1 to the stars in the vicinity of Sgr A*.

5.1 Constraining the position and motion of the Sun

away from the GC. Therefore, assuming that S5-HVS1 originates in the GC constrains R₀ and possibly other Galactic parameters. The idea of constraining the Solar motion as well as the distances to the GC have been discussed previously, most notably by Hattori et al. (2018b). To determine these constraints, we construct a forward model where we eject the star from the GC with velocity V_x, V_y, V_z, and let it travel in the Galactic potential of McMillan (2017) for the time T. We then observe it from the Sun located at a distance of R₀ from the GC and moving with the velocity U_⊙, V_⊙, W_⊙ kms−1 (this includes both the speed of the Local Standard of Rest and the peculiar velocity of the Sun). The likelihood of the model is then constructed using the observed 6D phase measurements of S5-HVS1: position, proper motion, distance, and radial velocity. This leads to the following posterior distribution:  

where ψ is the shorthand for all the model parameters V_x, V_y, V_z, T, R₀, U_⊙, V_⊙, W_⊙. For this model, we focus on constraining R₀ and V_⊙, so we adopt broad uninformative priors on the distance of the Sun to the GC R01kpc∼U(6,9)⁠, and V⊙1kms−1∼U(200,290) and informed Normal priors on the other two components of Solar velocity U⊙1kms−1∼N(11.1,0.5)⁠, W⊙1kms−1∼N(7.25,0.5) (Schönrich et al. 2010). For the rest of parameters V_x, V_y, V_z, T we adopt uninformative uniform priors. In principle the model that we have described has a valid posterior that we could sample. However, we have discovered that this posterior is extremely degenerate along one dimension and narrow in another dimension. This is in fact a direct consequence of the elongated contour shape for the constraint on the ejection point X_pl, Y_pl seen in Fig. 5. This contour shape and the fact that simultaneous changes of V_⊙ and R₀ give two degrees of freedom for ‘moving’ the high probability contour in (X_pl, Y_pl) space while still covering the GC explains the long degeneracy ridge in the posterior. Furthermore, the posterior is also extremely narrow along the time axis, as the orbit needs to pass very close to the precisely known observed position on the sky. It turns out that those features of the posterior make it extremely challenging to sample, so we were unable to do it efficiently using either multinest, dynesty, ensemble or ensemble parallel tempering samplers (emcee). Our solution to this problem was to adopt an approximation to the posterior where we approximately marginalize over the traveltime of the star:  

where ψ is the shorthand for the model parameters V_x, V_y, V_z, R₀, U_⊙, V_⊙, W_⊙, and  

The left-hand panel of Fig. 8 shows the 2D marginalized posterior on two of the parameters – heliocentric distance to the GC and the Y component of the Solar velocity (V_⊙). As before blue lines correspond to Model P (photometric only distance), and green lines to Model SP (spectrophotometric distance). The red bands show the 1σ constraints from Gravity Collaboration et al. (2019). As expected the figure shows a degeneracy between parameters that is almost complete when using the less constrained photometric only distances; however, with spectrophotometric distances the degeneracy is significantly reduced.

We note that even with the spectrophotometric distances of S5-HVS1 we cannot strongly constrain both V_⊙ and R₀ (as the green contours on Fig. 8 are quite large). However, if we adopt the prior on the Galactocentric distance from Gravity Collaboration et al. (2019), we obtain the posterior on V_⊙ shown on the right-hand panel of the figure. V_⊙ is constrained to be 246.1 ± 5.3 kms−1

⁠. Those constraints also do not depend significantly on whether we use spectrophotometric or photometric only distances as we slice the posterior shown on the left-hand panel of the figure across the distance degeneracy. The V_⊙ measurement is competitive with and entirely independent from the 247.4 ± 1.4 kms−1

constraint from Gravity Collaboration et al. (2019). If we instead use the prior on V_⊙ from Gravity Collaboration et al. (2019) to constrain the distance to the GC (marginalizing over the x-axis on Fig. 8), we obtain R₀ = 8.12 ± 0.23 kpc.

While Fig. 8 may look somewhat underwhelming compared to the Gravity Collaboration et al. (2019) measurements, we highlight that our measurement was done with one single star. The shape of the degeneracy in U_⊙, V_⊙, W_⊙, R₀ space is specific to the position of the star on the sky, and so if we had a second star then the combined constraints would be significantly more precise and likely comparable in precision to Gravity Collaboration et al. (2019).¹² Another reason for optimism is that future Gaia data releases and high-resolution spectroscopic follow-up will narrow the uncertainties on the proper motion and distance of S5-HVS1 and thus tighten our constraints on the Solar motion and position in the Galaxy.

5.2 Constraints on the Galactic potential

As we showed in the previous section, S5-HVS1 strongly constrains the Galactic position and velocity of the Sun. On top of that we expect that – under the assumption that the star comes from the GC – the observed properties of the star should also constrain the gravitational potential of the MW. This idea was first proposed by Gnedin et al. (2005), who suggested using individual HVS with accurate phase-space positions to measure the MW Dark Matter (DM) halo flattening. This idea has been extended to the modelling of the HVS population as a whole as it is being deflected by the disc and flattened MW halo away from an initial distribution over angles (Yu & Madau 2007; Contigiani, Rossi & Marchetti 2019).

It turns out, however, that while the proximity of S5-HVS1 was essential for precise measurements of its properties and its detection, the short flight time of ∼5 Myr from the GC makes the orbit of the star barely sensitive to the MW potential. To gain an intuition for this, it is useful to look at the inferred position where the star crosses the MW plane P(Xpl,Ypl)

in Figs 4 and 5, when we were backtracking the current phase-space coordinates to the Galactic plane. The reason why the potential could be constrained by the S5-HVS1 is because when we change the gravitational potential, the distribution of X_pl, Y_pl changes, and high probability contours are shifted away from (X_pl, Y_pl) = (0, 0) making such potentials less likely under the hypothesis that the GC is the origin of the S5-HVS1. However even if we turn-off the MW potential completely, the offset in the point of the Galactic plane crossing X_pl, Y_pl for orbits that backtrack from the current phase space position of the star to approximately the GC is a mere ∼15 pc, which is less than the width of the distribution X_pl, Y_pl. Similarly, setting the MW disc mass to zero causes a shift in X_pl, Y_pl of ∼13 pc. If we take the potential of McMillan (2017) and vary the flattening (in density) of the Navarro–Frenk–White (Navarro, Frenk & White 1997) DM halo from default q_DM,halo = 1 to 0.5 or 2 that results in offsets of only ∼7 and 18 pc respectively.

This lack of sensitivity to the DM halo flattening was confirmed when we obtained the formal posterior on P(qDM,halo|D)

under the hypothesis of ejection from the GC and found that it was consistent with the prior. This shows that with the current proper motion precision, S5-HVS1 cannot yet be used to constrain the MW gravitational potential. One additional reason for the current lack of constraining power from S5-HVS1 is that, because we do not know the actual ejection velocity from the BH, we do not constrain the total deceleration of the star, but only deviations of the trajectory from a straight line. For meaningful potentials consistent with the existing data, the deviations from a straight line for a ∼2000 kms−1

star flying for ∼5 Myr are within a few tens of parsecs (listed above) and thus within the current uncertainties of the S5-HVS1 trajectory. With the improvement in proper motion precision from future Gaia data we expect, however, that constraints on the MW halo flattening will be possible.

5.3 S5-HVS1 ejection by Sgr A*

Given an almost certain GC origin of S5-HVS1, here we discuss possible implications for the ejection by Sgr A*. We focus on the Hills (1988) mechanism involving a three-body interaction of a stellar binary with the SMBH, leading to one star being ejected. There are other mechanisms involving binary black holes (Yu & Tremaine 2003; Levin 2006) and an SMBH surrounded by a cluster of stellar mass black holes (O’Leary & Loeb 2008), and we will discuss some of them later.

The first question we address is what are the expected properties of the binary required to produce the very high ejection speed of S5-HVS1. To infer this we use the results of Bromley et al. (2006), who parametrized the distribution of ejection velocities as a function of the black hole mass and binary parameters (see equations 1–4 of Bromley et al. 2006). We adopt a black hole mass of 4.1 × 10⁶ M_⊙ from Gravity Collaboration et al. (2018), fix the mass of S5-HVS1 to the observed value 2.35 M_⊙ (see Table 2) and adopt an ejection velocity of 1798 ± 3 kms−1

⁠. The remaining parameters required to compute the ejection velocity distribution are the semimajor axis of the binary a, the mass of the second star M₂, and the minimum approach distance R_min between the binary and the SMBH. We adopt a log-uniform distribution over the binary separation and the Chabrier (2005) IMF prior on the mass of the secondary, and π

(R_min) ∼ R_min prior for the minimum approach distance (see Bromley et al. 2006 for details). We require that the semimajor axis of the binary is larger than 2.5R_⊙, which is approximately the expected radius of a star with a mass of ∼2.35 M_⊙ (Boyajian et al. 2013), and that the radius of S5-HVS1 is smaller than its tidal radius at the closest approach between the binary and the SMBH (R_min). This limits the minimal separation of the binary and the SMBH R_min to be ≳1.4 au.

Fig. 9 shows our inferred probability distribution of the semimajor axis of the binary and mass of the second star. The distribution shows that in order to produce S5-HVS1 we need a former binary companion with mass 0.9 M_⊙ ≲ M₂ ≲ 16 M_⊙, where low-mass secondaries require an extremely tight separation of only ∼0.06 au, while if the secondary is massive, the semi-major can be as much as ∼0.63 au. The orbital periods of these binaries would range from 3 to 40 d. These ranges correspond to the 68 per cent confidence interval of the posterior. The binary parameters that we obtain are certainly possible (see e.g. Raghavan et al. 2010; Moe & Di Stefano 2013); however, we expect these binaries to be quite rare.

5.4 S5-HVS1 and stars around Sgr A*

Given the certainty of the S5-HVS1 association with the GC, it is interesting to assess if S5-HVS1 is related to any other structures known around the GC. The main stellar structure near the centre of the MW is the nuclear star cluster (Becklin & Neugebauer 1968; Launhardt, Zylka & Mezger 2002) with the Sgr A* SMBH at the centre. The central part of the star cluster consists of the so-called S-stars whose dynamics are dominated by the SMBH and that orbit around it with periods from a few years to a few hundred years (Ghez et al. 2005; Gillessen et al. 2009). These stars are known to be massive and young (Genzel, Eisenhauer & Gillessen 2010; Lu et al. 2013) and we do not yet know how they came to be where they are. Furthermore, the cluster of stars around Sgr A* is known to have substructure in the form of a coherently rotating small disc of young stars (the so-called clock-wise or CW disc) (Levin & Beloborodov 2003; Paumard et al. 2006; Bartko et al. 2009; Yelda et al. 2014; Gillessen et al. 2017).

The reason why S5-HVS1 can be potentially associated to some structures in the centre is that if the star has been produced by the Hills mechanism, then we expect that the direction of HVS’s flight should be approximately aligned (Lu, Zhang & Yu 2010; Zhang, Lu & Yu 2010) with (i) the orbital plane of the original binary around the SMBH; and (ii) the orbital plane of the secondary star captured by the SMBH after the binary disruption (unless the secondary was swallowed by the black hole and/or produced a tidal disruption event). Thus, we can hope to either identify a possible progenitor population of the S5-HVS1 binary or perhaps directly pinpoint the star that was previously paired to S5-HVS1 and still orbits Sgr A*.

To check for possible association with the S-stars, we consider a set of possible orbital planes around the black hole that are aligned with the S5-HVS1 direction of flight. This set is clearly a 1D manifold, as there are infinitely many planes aligned with the vector pointing from the GC to S5-HVS1. In Fig. 10, we show the distribution of poles (or angular momentum directions) for this set of orbits by a red curve. The coordinate system of the figure is the positional angle of the ascending node of the orbit and the angle between the orbital plane with respect to the vector from the Sun to the GC. Therefore, the orbits seen edge-on from the Sun would occupy the equator on the figure, while face-on orbits would correspond to either the north or the south pole of the figure depending on the direction of rotation. In this figure, we also overplot by blue circles the orientations of orbits (specifically the direction of their angular momenta) for stars around Sgr A* from Gillessen et al. (2017). Thus if the S5-HVS1 has been produced by the Hills mechanism and the secondary star was captured on an orbit around the BH, then the red curve should pass near the current orbital plane of the secondary star. In this figure, we also mark by a grey circle the concentration of orbital poles corresponding to the disc of young stars observed around the GC (Bartko et al. 2009; Yelda et al. 2014). We see that the red line comes close to many S stars, which is not surprising and is expected to happen by chance. However, we see that the red curve also crosses the concentration of blue points marked by the grey circle, meaning that S5-HVS1 flies within the orbital plane of young stars around the GC. This is potentially very interesting, because it may mean that the binary responsible for S5-HVS1 has the same origin as the young stellar disc. Several formation scenarios for it exist, that either involve the infall of a gas cloud on the GC with subsequent star formation (Bonnell & Rice 2008), or star formation in the disc around the SMBH (Nayakshin, Cuadra & Springel 2007). This disc could then potentially be the source of the S5-HVS1 binary (i.e. due to orbit instabilities discovered by Madigan, Levin & Hopman 2009) and S5-HVS1 would provide us with an opportunity of studying the stars in disc without all the complexities of observing through tens of magnitudes of extinction. In this scenario, the secondary of the S5-HVS1 could still be in the disc and thus could be potentially identified.

Alternatively, the young disc may consist of captured secondary stars from binaries disrupted in the Hills mechanism, in which case the previous partner of S5-HVS1 may be still in that disc. We note, however, that the young stellar age of the stars in the disc of a few Myr (Lu et al. 2013), and the low eccentricities of stars in the disc (Yelda et al. 2014) make this scenario unlikely because the captured stars in Hills mechanism are expected to have high eccentricities (Hills 1988).

6 DISCUSSION

Here we address the multiple open questions that the discovery of S5-HVS1 poses. First, we compare S5-HVS1 to the other HVS. The main property that distinguishes S5-HVS1 from the rest of the hyper-velocity stars is its unusually high velocity. If we exclude the recently discovered D⁶ WDs produced in SNIa-like explosions (Shen et al. 2018), the velocity of S5-HVS1 is almost a factor of two larger than the velocity of any other known HVS. Fig. 11 shows the distribution of likely ejection velocities from the GC for other HVS. Here we use the same set of stars from Boubert et al. (2018) as shown on Fig. 5, and select a subset of those which can be well described (χ² < 20) as being ejected from the GC based on proper motion, position, distance and radial velocity. The figure shows how much of an outlier S5-HVS1 is, in particular because of the apparent clumping of previously known HVS at 800–1000 kms−1

⁠, which begs the question whether S5-HVS1 was produced using the same mechanism as other HVS. Another difference between S5-HVS1 and other HVS is that it is an A-type star, and thus is somewhat cooler, lower mass and later spectral type than the classical B-type hyper-velocity stars (Brown 2015). It is also brighter and much more nearby than the majority of the faint, blue HVS that have been discovered in the Northern sky.

One possible interpretation of these differences between S5-HVS1 and previously known HVS is that S⁵ was just very lucky to stumble on a very rare object. However, the other explanation may be related to the somewhat lower mass and redder colour of S5-HVS1 g − r = −0.27, which is close to the colour boundary g − r ∼ −0.3 of dedicated searches (Brown et al. 2006; Brown, Geller & Kenyon 2009); this boundary minimizes contamination because MS and BHB stars start to overlap at this colour. This may be the reason why previous spectroscopic searches missed lower mass/redder stars like S5-HVS1. However, since the Sloan Digital Sky Survey (SDSS; York et al. 2000; Yanny et al. 2009) did observe a large number of blue A-type stars in the range −0.4 < g − r < 0 and did not find anything close to S5-HVS1, it is useful to compare the number of objects spectroscopically observed by SDSS to S⁵. In fact, surprisingly, SDSS (DR9; Ahn et al. 2012) has observed spectroscopically only ∼7 times more blue, distant (with small parallax π < 3σ_π) stars in the −0.4 < g − r < −0.2 and 16 < g < 18 colour–magnitude range than S⁵ did (1445 versus 202). Thus, the SDSS non-detection of an S5-HVS1-like star is not in significant disagreement with the S⁵ discovery.

Another possible explanation of the S5-HVS1 discovery has to do with its proximity, as the star is closer by a factor of several compared to other HVS. Why would closer HVSs be potentially noticeably faster or have a different velocity distribution? For this to happen it would require that the ejection mechanism of HVS is not operating at a constant rate and/or does not eject the same spectrum of HVS over time. In the canonical Hills (1988) mechanism where the loss cone of the SMBH is populated by slow scattering processes, such rapid changes would be problematic. However, as the presence of young (only few Myr old) stars and substructures near the GC indicate, the GC has had a very active recent history; e.g. it is likely that the GC had an accretion event of a giant molecular cloud a few Myr ago that formed new stars (Bonnell & Rice 2008; Lucas et al. 2013) that were then distributed in a disc around the SMBH. If that is the case, that accretion event could have been a source of binaries for the Hills mechanism, producing an excess of stars in the orbital plane of accretion and an increased rate of HVS ejections a few Myr ago. In such a scenario, HVSs like S5-HVS1 could serve as timers and indicators of orientation of large accretion events happening near the GC. To test this hypothesis we will, however, need to find more stars with similar travel times as S5-HVS1. It is remarkable that the age of S5-HVS1 ejection is close to both the age of the disc of young stars around the GC (Lu et al. 2013) and the age of the Fermi bubbles (Bland-Hawthorn & Cohen 2003; Su, Slatyer & Finkbeiner 2010) which have been potentially associated with the recent accretion event in the GC (Zubovas, King & Nayakshin 2011; Guo & Mathews 2012), thus potentially linking these different astrophysical objects.

An alternative scenario that would naturally produce a time-variable HVS spectrum is that involving an Intermediate Mass Black Hole (IMBH) orbiting the GC (Yu & Tremaine 2003; Levin 2006). In this mechanism, during the inspiral of the IMBH, the HVS production rate peaks and then subsides due to dynamical friction around the SMBH (Baumgardt, Gualandris & Portegies Zwart 2006; Darbha et al. 2019), with the fastest HVS being ejected in the final phase of the in-spiral. This mechanism produces a strongly anisotropic distribution with the fastest stars in the orbital plane of the IMBH (Rasskazov et al. 2019). There is also some indication that the HVSs produced by this mechanism tend to have higher velocities and a flatter velocity spectrum than the classical Hills mechanism (Sesana, Haardt & Madau 2007). While there is currently not much evidence for the presence of an IMBH in the GC (Gualandris & Merritt 2009) other than a shallow stellar density slope that can be produced by an IMBH scattering (Baumgardt et al. 2006), if an IMBH inspiral happened a few Myr ago, then it would produce an excess of nearby and fast HVSs with a narrow range of ejection times. To test for this possibility we need to search for other nearby HVS and see if there is an excess of stars that were ejected at roughly the same time as S5-HVS1 (∼5 Myr ago), are strongly anisotropic and that have a velocity spectrum inconsistent with the Hills mechanism.

An interesting consequence of the fact that S5-HVS1 has lower mass than most other HVS in the halo is that its expected lifetime given the stellar mass of ∼2.3 M_⊙ is quite long – around a 1 Gyr. By the end of its life the star would have travelled a distance of ∼2 Mpc, traversing a large fraction of the Local Group. This suggests that searching for such ejected stars at large distances from the MW or Andromeda (Sherwin, Loeb & O’Leary 2008) is quite promising. On top of being well separated in colour–magnitude space from other contaminants, an S5-HVS1-like star would eventually evolve on to the red giant branch and thus be detectable much more easily. Searches for S5-HVS1-like stars within the whole Local Group will be possible with upcoming deep imaging surveys like LSST (LSST Science Collaboration et al. 2009).

In this paper, we tried to use the position–velocity information on S5-HVS1 to constrain the distance from the Sun to the GC and the Galactic Solar velocity. We have not been able to constrain those simultaneously, mainly due to the precision of the distance determination to S5-HVS1. However, in the future, the combination of such constraints from multiple S5-HVS1-like stars (see Fig. 8) will resolve the existing degeneracies and should provide extremely precise measurements of the geometric and kinematic Galactic parameters. We believe that with the upcoming Gaia DR3 as well as future spectroscopic surveys like WEAVE (Dalton et al. 2014), 4MOST (de Jong et al. 2014), and DESI (DESI Collaboration et al. 2016), the discovery of more HVS similar to S5-HVS1 is guaranteed. Furthermore, while with S5-HVS1 we were currently not able to put constraints on the gravitational potential due to the very short flight time and loose proper motion constraint, with the next Gaia data release that will increase the proper motion precision by a factor of few as well as deliver new HVSs, we think we will be able to start constraining the potential with individual HVS as predicted by Gnedin et al. (2005).

One other interesting prospect for the future of HVS science that we did not explore in this paper, but which may be promising, is that HVS could become probes of substructure and particularly DM substructure in the Galaxy, similar to stellar streams (Yoon, Johnston & Hogg 2011; Erkal et al. 2016) or lensing (Vegetti et al. 2012). The reason for this is that for HVS that were ejected from the GC we know the orbit exactly, as it must connect to the GC. Thus if we imagine a large collection of HVS travelling throughout the Galaxy, we expect that some of those trajectories will be affected by various external perturbations, including massive perturbers such as the Large Magellanic Cloud or Sagittarius Dwarf Spheroidal Galaxy, but also potentially smaller DM haloes and globular clusters in the halo. Although we expect the effect of these perturbations to be quite small due the high velocity of the stars, if we have enough of these stars and they have high accuracy phase-space measurements, then we could say something about the mass substructure in the Galaxy. As an example, a 10⁸ M_⊙ point-mass perturbing a hyper-velocity star travelling at 2000 kms−1

with an impact parameter of 0.5 kpc will produce a velocity offset of ∼1 kms−1

(Binney & Tremaine 2011) perpendicular to the trajectory of the HVS, or equivalently an offset of ∼ a few parsecs in the trajectory. While these offsets are small, the velocity accuracy is within what Gaia proper motions will provide for objects brighter than G ∼ 17 within 10 kpc.

Finally, let us consider the effect of future Gaia data releases on S5-HVS1. The main improvement will come from much higher precision parallax and proper motions, which are expected to better constrain the orbit of S5-HVS1. In advance of Gaia DR3, we predict that the true proper motions and parallax of S5-HVS1 are μ_αcos δ = 35.333 ± 0.080masyr−1

⁠, μ_δ = 0.617 ± 0.011masyr−1⁠, and π

 = 0.11 mas (corresponding to a distance of 8.828 kpc). Time will tell whether these predictions based on the assumption of a GC origin will hold.

7 CONCLUSIONS

• Using data from the S⁵ spectroscopic survey we have identified a star with a radial velocity of ∼1020 kms−1

• without any signs of binarity across a year of observations.

• Analysis of the spectra and photometry of the star shows that it is likely an A-type ∼2.35 M_⊙ main- sequence metal-rich star at a distance of ∼9 kpc.

• Given the measured distance, proper motion and radial velocity, the total velocity of the star in the Galactic rest frame is 1755+55−45

kms−1

• ⁠, making it the third fastest hyper-velocity (unbound) star in the Galaxy after the D⁶ WDs (Shen et al. 2018).

• Backtracking the current phase-space position of S5-HVS1 to the MW disc points at a small elongated region of ∼50 × 1000 pc² that contains the GC. This provides incredibly strong evidence that the star was ejected from the GC at speed of ∼1800 kms−1

• around ∼4.8 Myr ago.

• If S5-HVS1 was ejected from the GC then we can constrain the distance to the GC and the Solar velocity. If we assume the Gravity Collaboration et al. (2019) prior on R₀, then our constraint on the y-component of solar velocity is V⊙=246.1±5.3kms−1

• ⁠, and, vice versa, if the Gravity Collaboration et al. (2019) prior is used on V_⊙, it leads to an R₀ constraint of 8.12 ± 0.23 kpc. Due to the short flight time and non-negligible proper motion uncertainties, the star currently cannot yet constrain the MW gravitational potential.

• The direction of the S5-HVS1 ejection is curiously aligned with the disc of young stars around the Sgr A*, suggesting a possible connection. This may mean that the star has been ejected in the same event that leads to the disc’s formation.

• The fact that S5-HVS1 was ejected with a velocity almost twice that of all other known HVS potentially originating from the GC poses two questions: were all the known HVS produced by the same mechanism and has the HVS velocity spectrum been constant in time?

ACKNOWLEDGEMENTS

This paper includes data gathered with AAT in Australia under programme A/2018B/09. 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.

This work has made use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC; https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.

SK is partially supported by NSF grants AST-1813881, AST-1909584, and Heising-Simons foundation grant 2018-1030. DB is grateful to Magdalen College for his Fellowship by Examination and the Rudolf Peierls Centre for Theoretical Physics for providing office space and travel funds. TSL and APJ are supported by NASA through Hubble Fellowship grant HST-HF2-51439.001 and HST-HF2-51393.001, respectively, awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. JDS, SLM, and DBZ acknowledge the support of the Australian Research Council(ARC) through Discovery Project grant DP180101791. GSDaC also acknowledges ARC support through Discovery Project grant DP1501013294. Parts of this research were supported by the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. We also thank the referee Ulrich Heber for a detailed report.

Software: numpy (van der Walt, Colbert & Varoquaux 2011), scipy (Jones et al. 2001), matplotlib (Hunter 2007), astropy (Astropy Collaboration et al. 2013; Price-Whelan et al. 2018), emcee (Foreman-Mackey et al. 2013), gala (Price-Whelan 2017), q3c (Koposov & Bartunov 2006), isochrones (Morton 2015) fastkde (O’Brien et al. 2016), dynesty (Speagle 2019), pymultinest (Buchner et al. 2014), ipython (Perez & Granger 2007), chainconsumer (Hinton 2016), rebound (Rein & Liu 2012), multinest (Feroz, Hobson & Bridges 2009), rvspecfit (Koposov 2019), schwimmbad (Price-Whelan & Foreman-Mackey 2017)

Footnotes

REFERENCES