ABSTRACT
The existence of intermediate-mass black holes (IMBHs) is crucial for understanding various astrophysical phenomena, yet their existence remains elusive, except for the LIGO-Virgo detection. We report the discovery of a high-velocity star J0731+3717, whose backward trajectory about 21 Myr ago intersected that of globular cluster M15 within the cluster tidal radius. Both its metallicity [Fe/H] and alpha-to-iron abundance ratio [
/Fe] are consistent with those of M15. Furthermore, its location falls right on the fiducial sequence of cluster M15 on the color-absolute magnitude diagram, suggesting similar ages. These findings support the notion that J0731+3717 was originally associated with M15 at a confidence level of ‘seven nines’. We find that such a high-velocity star (
km s
) was most likely tidally ejected from as close as one astronomical unit to the center of M15, confirming an IMBH (
with a credibility of 98%) as the exclusive nature of the central unseen mass proposed previously.
Keywords: intermediate-mass black hole, Hills mechanism, hypervelocity star, globular cluster, large-scale survey
This paper reports the discovery of a high-velocity star J07 ejected from globular cluster M15 approximately 21 million years ago, providing strong evidence for the presence of an IMBH constrained to within a few AU of the central region of M15.
INTRODUCTION
Intermediate-mass black holes (IMBHs) in the mass range of 
–
solar masses (
) may fill the gap between BHs formed as stellar remnants and supermassive BHs (SMBHs) found in the centers of galaxies [1]. Except for LIGO-Virgo detection [2,3], their existence, however, is still uncertain despite extensive search efforts. Discovering IMBHs and characterizing their mass functions in this range are therefore of great interest for many reasons [1].
Globular clusters (GCs), dense and massive dynamical systems, have long been considered promising places to harbor IMBHs. Both theory and numerical simulations suggest that IMBHs can form either through the repeated mergers of stellar black holes (‘slow mode’) [4], remnants of massive stars that sink to the center, or through the explosion of a very massive star resulting from runaway mergers of stars during an early phase of cluster core collapse (‘fast mode’) [5]. The ‘slow mode’ is a competitive scenario to explain the LIGO-Virgo-detected IMBHs [2,3] that arise from mergers of binary BHs.
Extensive efforts have indeed found a large central unseen mass in some globular clusters using velocity dispersion [6,7] or pulsar timing measurements [8], but such a mass can be either an IMBH or a cluster of stellar remnants within a few thousand astronomical units [9–11]. To exclude the latter possibility, we need to limit the central mass to a much smaller volume. One approach is to search for hyper/high-velocity stars ejected from globular clusters. If they exist, they are largely linked to the tidal interaction between an IMBH and a binary system for a close encounter, typically within one astronomical unit (AU).
RESULTS AND DISCUSSION
A high-velocity star ejected from globular cluster M15
To discover high-velocity stars ejected from globular clusters, backward orbital integrations are carried out for 934 high-velocity (
km s
) halo stars in a searching volume of 5 kpc from the Sun [12] and 145 Galactic globular clusters [13–15]. Both the trajectories of the stars and globular clusters are traced back 250 Myr (in about one orbital period at solar position) using a common-adopted model of steady-state Galactic potential [16]. The closest distance for each high-velocity star and globular cluster pair is calculated from their backward trajectories. Amongst the hundred thousand pairs, only J0731+3717 has a closest distance smaller than the tidal radius of M15, making it a rare candidate for a cluster-ejected high-velocity star (see Sections A–F within the online supplementary material (SM) for more technical details).
Table 1 summarizes the information on J0731+3717 and M15. J0731+3717 is a high-velocity star with 
km s
at a heliocentric distance of 
kpc. M15 is a 12.5-billion-year-old globular cluster [17] located in the constellation Pegasus with a heliocentric distance of 
kpc [14] and a mass of 
[18]. M15 is believed to host an IMBH of 1700–3200 
based on velocity dispersion measurements [6,19], albeit with debate [9,20,21], especially the 
upper limit of 980 M
placed by the non-detection from ultra-deep radio observations at the cluster core [22]. While J0731+3717 is currently 11.5 kpc away from M15, their backward trajectories intersected with each other 21 Myr ago with a relative velocity of 
km s
and a closest distance of 58 pc (Fig. 1a), smaller than the cluster tidal radius of 132 pc. The intersection locations and their uncertainties in three-dimensional space are estimated with one million Monte Carlo (MC) trajectory simulations to be 
pc, 
pc and 
pc, as shown in Fig. 1b&d.
Table 1.
The measured parameters of J0731+3717 and M15.
| Parameter | J0731+3717 | M15 | Units |
|---|---|---|---|
| RA (J2000) | 07:31:27.26 | 21:29:58.33 | hh:mm:ss.ss |
| Dec (J2000) |
37:17:04.3 |
12:10:01.2 |
dd:mm:ss.s |
| Gaia DR3 source_id | 898707303799931392 | N/A | N/A |
Gaia DR3 proper motion 
|
|
|
mas yr
|
Gaia DR3 proper motion 
|
|
|
mas yr
|
| Gaia DR3 parallax |
|
|
mas |
Gaia DR3  -band magnitude |
|
N/A | mag |
Gaia DR3 
|
|
N/A | mag |
SDSS  -band magnitude |
|
N/A | mag |
SDSS  -band magnitude |
|
N/A | mag |
SDSS  -band magnitude |
|
N/A | mag |
SDSS  -band magnitude |
|
N/A | mag |
SDSS  -band magnitude |
|
N/A | mag |
| Distance |
|
|
pc |
|
0.047 | 0.08 | mag |
| Heliocentric radial velocities HRV |
|
|
km s
|
Effective temperature 
|
|
N/A | K |
Surface gravity log 
|
|
N/A | dex |
| Metallicity [Fe/H] |
|
(syst.) |
dex |
-element-to-iron ratio [ /Fe] |
|
|
dex |
Total velocity 
|
|
|
km s
|
| Age |
|
|
Gyr |
| Mass |
|
|
|
Figure 1.
Backward orbital analysis of J0731+3717 and M15. (a) Three-dimensional representation of the backward orbits of J0731+3717 and the globular cluster M15. The blue and magenta lines with arrows mark the backward orbits of J0731+3717 and M15, respectively. The triangle and inverted triangle mark the encounter positions, which occurred 21 Myr ago, for M15 and J0731+3717. The black dots represent the locations of the Galactic center and the Sun, as labeled. The solar circle (
kpc) is shown with a dashed black line. (b) The distributions of the closest distance between J0731 and the center of M15 along 
(green), 
(yellow) and 
(purple) at encounter, estimated with one million MC trajectory simulations (see SM-B). (c, d) Density of the relative positions (J0731+3717 with respect to M15) at encounter, again estimated with one million MC trajectory calculations, in the (c) 
-
and (d) 
-
planes. The normalized number density is color coded, as shown by the right color bar. The white contours mark the 
confidence region. The green dashed circle represents the size of the tidal radius of M15. The black star represents the relative location at closest distance derived directly using the observational parameters listed in Table 1.
In addition to the orbital connection, J0731+3717 exhibits rare chemical fingerprints consistent with those of M15. The SEGUE spectrum [23] clearly shows that J0731+3717 is a very metal-poor late F-type star, as plotted in Fig. 2a, with effective temperature 
K, metallicity [Fe/H] = 
and alpha-to-iron abundance ratio 
(see SM-E). The old globular cluster M15 has well measured 
and 
[24,25]. Their chemical parameters are consistent with each other within errors, and both are located in a region with very few stars in the [Fe/H]-[
/Fe] plane. Only 
of all halo stars within the 5-kpc searching volume with reliable abundances are located in such a region, as shown in Fig. 2b. The rare chemical similarity implies that J0731+3717 was originally associated with the cluster, in line with the suggestion of orbital analysis.
Figure 2.
Optical spectrum, chemical properties and color-absolute magnitude diagram of J0731+3717 and M15. (a) Optical spectrum (in black) of J0731+3717 from the SEGUE survey. Two synthetical spectra (degraded to SEGUE spectral resolution) are plotted on top of each other for comparison (see SM-E). The red spectrum has stellar parameters 
K, log 
, 
and 
, similar to those of J0731+3717, while the blue spectrum is 0.5 dex richer in metallicity (i.e. 
) with the other parameters unchanged. The insets show enlarged views of the Ca ii H (
3968) and K (
3933) lines, and the Ca ii triplet lines at 
8498, 8542, 8662. (b) [Fe/H]–[
/Fe] diagram for J0731+3717 (blue dot) and globular cluster M15 (magenta dot). The dashed magenta box marks the region within two times the measurement uncertainties of [Fe/H] and [
/Fe] for M15. For comparison purposes, the background shows the density of APOGEE-targeted stars with reliable determinations of [Fe/H] and [
/Fe] (see SM-H). (c) Plot of 
versus 
for globular cluster M15 and J0731+3717. The background gray dots are photometric observations of M15 from the Galactic globular and open clusters study based on the Sloan Digital Sky Survey by An et al. [26], by adopting a cluster distance of 10.71 kpc and an 
value of 0.08 (Table 1). The magenta squares denote the cluster fiducial sequence derived from the background gray dots by An et al. [26]. The dashed magenta lines are shifted from the fiducial sequence by 
mag in 
. The diamonds are field halo stars from the existing spectroscopic surveys with chemical fingerprints (defined by the magenta box shown in panel (b)) similar to M15 (see SM-H).
The association of J0731+3717 with M15 can be further supported by their similar ages as derived from isochrone fitting. Broadband photometric measurements for M15 and J0731+3717 are taken from the Galactic globular and open clusters study based on the Sloan Digital Sky Survey (SDSS) [26] and SDSS DR12 [27], respectively. Both their absolute magnitudes and colors are corrected for extinction values along their separate lines of sight. As shown in Fig. 2c, J0731+3717 falls right on the cluster fiducial sequence of M15; subsequently, its isochrone age as estimated from the Bayesian approach is 
Gyr, almost identical to the age obtained for M15
(see SM-F & G). In comparison, 37% of the field halo stars with chemical abundances similar to M15 (defined by the box in Fig. 2b) actually deviate from its fiducial sequence by more than 0.05 mag (the maximal error) in color direction, implying significantly different ages.
It is extremely unlikely for the association of J0731+3717 and M15 to be by pure chance, given the probability for random association and chemical and age similarities. To quantitatively determine the probability of random high-velocity halo stars encountering M15, we ran MC simulations to generate about one million high-velocity halo stars with 
km s
in such a searching volume (see SM-H). Only 12 high-velocity stars have had close encounters with M15 within its tidal radius in the past 250 Myr. This means that the probability of an unphysical orbital encounter between J0731+3717 and M15 is 
. Considering the orbital link, together with the chemical and age similarities, one high-velocity halo star in our searching volume is coincidentally linked to M15 by a pure chance of only 
. In other words, J0731+3717 is a true former member of M15 at a confidence level of ‘seven nines’.
Interpretation as a Hills ejection via an IMBH
An energetic ejection mechanism is required to kick-off J0731+3717 from M15 with an ejection velocity up to 
km s
; in comparison, the cluster central escape velocity is only 62 km s
(the escape velocity at the cluster half-mass radius is 27 km s
; see [28]). The Hills mechanism [29] invokes three-body exchange interactions between stellar binary and super-massive BHs to eject hypervelocity stars from the Galactic center; such a mechanism can naturally eject high-velocity stars from IMBHs in the center of globular clusters. If this mechanism is at work in this case, the ejection velocity would constrain the mass of the central BH in M15 to be 726 
for a binary separation 
AU and 5804 
for 
AU. A stellar-mass BH smaller than 
can also eject a star up to around 550 km s
if 
AU, but the probability is only a few percent based on our MC simulations of two hundred million Hills ejections (see SM-I and Fig. 3). Thus, the ejection of J0731+3717 from M15 requires an IMBH (
with a credibility of 98%) at the center of the cluster; the encounters mostly occurred (93%) within 2 AU from the cluster center. This confirms that the previously claimed aggregated mass of more than a few thousand solar masses [6,19,22] is indeed an IMBH rather than a cluster of stellar remnants [20,21].
Figure 3.
Ejection velocities predicted by the Hills mechanism. The lines represent the most probable ejection velocities, calculated using Equations S7 and S8 within the SM-I, as a function of the black hole mass under different binary separations ranging from 0.01 to 0.1 AU (from left to right). In the calculation, the binary is assumed to contain two J0731+3717-like stars, each with a mass of 
. The color of the lines indicates the ejection probability (see the color bar shown on the right), derived using Equation S9 within the SM-I. Here the closest distance that the binary can approach the black hole is set to 0.5 AU. The horizontal dashed line with a shaded 
uncertainty indicates the reported ejection velocity (
km s
) of J0731+3717. The vertical shaded region represents the mass of the black hole (1700-3200 
) of M15 dynamically derived from velocity dispersion measurements [6,19]. The black line represents the cumulative probability of the ejection of 0731+3717-like stars at different black hole masses, calculated through Monte Carlo simulations (see SM-I).
Excluding alternative explanations
A competing mechanism to eject high-velocity stars (even up to 2000 km s
) in a globular cluster is the single star–binary interaction involving compact objects. Observations reveal the presence of a binary neutron star, possibly a remnant from these encounters in M15 [30]. However, the ejection rate, as derived by a recent comprehensive Monte Carlo 
-body simulation [31], for producing J0731+3717-like high-velocity stars remains remarkably low, 
yr
in the present day, which is three orders of magnitude lower than that of the aforementioned IMBH-binary encounters (see SM-J). The same simulation shows that no J0731+3717-like high-velocity stars with 
km 
were kicked from M15 through this channel in the past 10 Gyr (let alone the past 250 Myr).
A high ejection velocity can be obtained through several alternative scenarios. First, a star can be ejected through a normal single star–binary interaction [32] without compact objects involved or exchange collision with a massive star [33] (similar to the Hills mechanism but for massive stars), but the typical ejection velocity is within 200 km s
. To eject a J0731+3717-like star with an ejection velocity above 550 km s
, interaction between a very massive star (50–100 
) and a hard massive binary is required [33], which cannot have recently occurred in such an old cluster like M15. Second, a star can be ejected by the core-collapse supernova explosion of its former massive companion in a binary scenario [34]. However, this is unlikely to have recently occurred in M15 in light of its old age; moreover, the maximum kick velocity by supernova would be largely within 300-400 km s
[35]. At present, only type-Ia supernovae from a white dwarf plus helium star (hot subdwarf) or the dynamically driven double-degenerate double-detonation [36,37] channels can eject the surviving helium star or white dwarf with velocity even up to 1000 km s
like US 708 [38] or like D6-1 to D6-3 [37]. One possible such ejection associated with the GC was recently reported in the nearby galaxy NGC 5353 [39]. The late F-type nature of J0731+3717 certainly rules out the possibility of a fast helium star or white dwarf ejected by a type-Ia supernova explosion. Third, a star can be stripped from the cluster when the latter experiences tidal shock from interactions with giant molecular clouds [40], the Galactic disk [41], the spiral arm [42] or perigalactic passages [41]. Apparently, J0731+3717 is not such a case since the ejection position (at 
kpc below the Galactic disk plane; see Fig. 1a) is far away from the Galactic disk, known giant molecular clouds or the last pericenter of M15. In summary, the above alternative ejection mechanisms are not viable to kick off J0731+3717 from M15.
CONCLUSION
Our discovery of J0731+3717 ejected by an IMBH in M15 thus proves that the existence of IMBHs can be disclosed by high-velocity stars ejected from clusters via the Hills mechanism, unambiguously as compared to previous velocity dispersion measurements [6,9,20,21]. Such a method can be applied to find more cases like J0731+3717 in our Galaxy. Simulations of the 145 globular clusters in the past 14 Gyr led to around 500 J0731+3717-like high-velocity stars ejected into the current 5-kpc searching volume (see SM-J), although only 50 of them were ejected in the past 250 Myr that can be traced back to their cluster origin under current measurement uncertainties. With the increasing power of ongoing Gaia and large-scale spectroscopic surveys, we expect to discover dozens of cases within the 5-kpc volume and ten times more within a 10-kpc volume, which should shed light on understanding the evolutionary path from stellar-mass BHs to SMBHs.
METHODS
Detailed methods are available in the online supplementary material.
Supplementary Material
ACKNOWLEDGEMENTS
This work presents results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. The Gaia mission website is available at https://www.cosmos.esa.int/gaia. The Gaia archive website is available at https://archives.esac.esa.int/gaia.
Contributor Information
Yang Huang, School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China; National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China.
Qingzheng Li, Yunnan Observatories, Chinese Academy of Sciences, Kunming 650011, China.
Jifeng Liu, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China; New Cornerstone Science Laboratory, National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China; Institute for Frontiers in Astronomy and Astrophysics, Beijing Normal University, Beijing 102206, China.
Xiaobo Dong, Yunnan Observatories, Chinese Academy of Sciences, Kunming 650011, China.
Huawei Zhang, Department of Astronomy, School of Physics, Peking University, Beijing 100871, China; Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China.
Youjun Lu, School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China; National Astronomical Observatories, Chinese Academy of Sciences, Beijing 100012, China.
Cuihua Du, School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China.
DATA AVAILABILITY
All data used in this study are publicly available. This work 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). The stellar parameters of J0731+3717 are available from the SDSS-II/III SEGUE archive at https://data.sdss.org/sas/dr12/sdss/sspp/ssppOut-dr12.fits. The SDSS photometric and spectroscopic data can be found at http://skyserver.sdss.org/dr12/en/tools/search/radial.aspx. The photometric catalog of M15 is available from http://das.sdss.org/va/osuPhot/v1_0/. The stellar isochrones can be found at http://stellar.dartmouth.edu/models. The data supporting the plots in this paper and other findings of this study are available from the corresponding authors upon reasonable request.
We used standard data analysis tools in Python environments. Specifically, the orbital analysis was carried out with Python package Gala and galpy, which are publicly available at http://gala.adrian.pw/en/v1.6.1/getting_started.html and www.galpy.org.
FUNDING
This work is supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB0550103). Y.H. acknowledges the National Natural Science Foundation of China (12422303, 11903027 and 11833006) and the National Key R&D Program of China (2023YFA1608303 and 2019YFA0405503). J.L. acknowledges support from the National Natural Science Foundation of China (11988101 and 11933004), and the New Cornerstone Science Foundation through the New Cornerstone Investigator Program and the XPLORER PRIZE. X.D. acknowledges support from the National Natural Science Foundation of China (12373013). H.Z. acknowledges the National Natural Science Foundation of China (11973001, 12090040 and 12090044) and the National Key R&D Program of China (2019YFA0405504).
AUTHOR CONTRIBUTIONS
Y.H. led this project and wrote the paper; Q.L. contributed to the sample preparation, systematic search, data analysis and wrote the manuscript together with Y.H.; J.L. contributed to the interpretation of the results and writing the text; H.Z. and X.D. contributed to the project planning, discussions and text revisions; Y.L. and C.D. contributed to the interpretation and revisions of the text.
Conflict of interest statement
None declared.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
All data used in this study are publicly available. This work 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). The stellar parameters of J0731+3717 are available from the SDSS-II/III SEGUE archive at https://data.sdss.org/sas/dr12/sdss/sspp/ssppOut-dr12.fits. The SDSS photometric and spectroscopic data can be found at http://skyserver.sdss.org/dr12/en/tools/search/radial.aspx. The photometric catalog of M15 is available from http://das.sdss.org/va/osuPhot/v1_0/. The stellar isochrones can be found at http://stellar.dartmouth.edu/models. The data supporting the plots in this paper and other findings of this study are available from the corresponding authors upon reasonable request.
We used standard data analysis tools in Python environments. Specifically, the orbital analysis was carried out with Python package Gala and galpy, which are publicly available at http://gala.adrian.pw/en/v1.6.1/getting_started.html and www.galpy.org.