High Velocity Runaway Binaries from Supernovae in Triple Systems
aa r X i v : . [ a s t r o - ph . S R ] M a y MNRAS , 1–6 (2019) Preprint 31 May 2019 Compiled using MNRAS L A TEX style file v3.0
High Velocity Runaway Binaries from Supernovae in TripleSystems
Yan Gao, , , ⋆ Jiao Li, , , Shi Jia, , , Yunnan Observatories, Chinese Academy of Sciences, Kunming 650011, China Key Laboratory for the Structure and Evolution of Celestial Objects, Chinese Academy of Sciences, Kunming 650011, China University of Chinese Academy of Sciences
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Recent studies on hypervelocity stars (HVSs) have generated a need to understand thehigh velocity limits of binary systems. If runaway binary systems with high movementspeeds well in excess of 200km/s were to exist, it would have implications on howHVS candidates are selected, and our current understanding of how they form needsto be reinforced. In this paper, we explore the possibility that such high velocityrunaway binaries (HVRBs) can be engendered by supernova explosions of the tertiaryin close hierarchical triple systems. We find that such explosions can lead to significantremnant binary velocities, and demonstrate via constraining the velocity distributionof such HVRBs that this mechanism can lead to binaries with centre of mass velocitiesof 350 km/s or more, relative to the original centre of mass of the progenitor triplesystem. This translates into potential observations of binaries with velocities highenough to escape the Galaxy, once the Galactic rotational velocity and objects ofLarge Magellanic Cloud origins are considered.
Key words: celestial mechanics, (stars:) binaries (including multiple): close, stars:evolution
The recent release of Gaia DR2 (Gaia Collaboration et al.2018) has enhanced, among other things, our under-standing of hypervelocity stars (HVSs), stars whichhave velocities in the Galactic reference frame thatare high enough to achieve escape velocity. The break-throughs were mainly due to spectroscopic radial veloci-ties archived in the catalogue, which led to the discov-ery and identification of many candidates for such ob-jects that were previously unknown (e.g. Bromley et al.2018; Hattori et al. 2018; Irrgang, Kreuzer, & Heber 2018;Marchetti, Rossi, & Brown 2018; Shen et al. 2018). Furtherdiscussion of the advances consequently made in the fieldof HVS studies is beyond the scope of this paper, and willtherfore be omitted here.While performing these studies, some authors have con-sidered the possibility that the HVS candidates they wereprocessing are actually unresolved binaries masqueradingas single stars. If this were the case, binary orbital mo-tion would contaminate the catalogued radial velocities,leading to noise in the final derived velocities. Noting this ⋆ E-mail: [email protected] potential source of error, alongside many others, the au-thors adjusted their candidate selection criteria accordingly(e.g. Marchetti, Rossi, & Brown 2018). Some of these crite-ria could have been further optimised if the velocity distribu-tion of runaway binaries were known. For instance, considera hypothetical object travelling at a very high velocity, forwhich binarity cannot be ruled out by traditional methods.If we were to assume that it is, in fact, part of a binary, wecould constrain the centre-of-mass velocity for the binarysystem, by accounting for any potential contamination dueto binary orbital motion. If this constraint leads to the ve-locity lying beyond the velocity range expected for binarysystems, then the possibility of a binary companion couldbe disregarded for this particular object. However, if insuf-ficient information is available on the expected velocities ofbinary systems, which is currently the case, then it wouldbe prudent to eliminate this object from the sample, whichis what would have happened in all studies to date.Refining data processing techniques aside, it cer-tainly seems legitimate to speculate that some currentor future HVS candidates could be binaries in disguise.Widmark, Leistedt, & Hogg (2018), who studied the issueof binary and triple contamination in the Gaia DR1 gen-eral stellar sample, found that many binaries have indeed © Y. Gao et al. been misidentified as single stars, forming a “binary mainsequence” roughly 0.75 magnitudes above the main sequencewhen plotted in an HR diagram. Upon visual inspectionof HVS candidates, it is found that several lie on this “bi-nary main sequence”, including but not necessarily limited to
Gaia
DR2 1540013339194597376, which can be identified tobe a HVS candidate via its proper motion of 900 km/s alone(Bromley et al. 2018), and
Gaia
DR2 1976597452042003072,with a proper motion of 500 km/s. The list would have goneon, if not for recent issues with Gaia DR2 radial velocities(Boubert et al. 2019). The natural question to ask, then,would be whether it is possible that a binary can be accel-erated to such velocities.For single stars, numerous theories have been pre-sented in the past on how high velocities can be at-tained. Binary systems interacting with the Galactic cen-tral black hole can have one of its stellar components con-sumed by the latter, ejecting the remaining component atvelocities sufficient to become unbound (e.g. Hills 1988;Yu & Tremaine 2003); supernovae occurring in close bi-naries can impart to their companions velocities of hun-dreds of km/s (e.g. Blaauw 1961; Wang & Han 2009), someof which exceed escape velocity, depending on their po-sition in the Galactic potential; dynamical ejection frommultiple systems can also lead to extremely high veloci-ties, especially for low-mass stars in globular clusters (e.g.Gvaramadze, Gualandris, & Portegies Zwart 2009). Yet ofall these mechanisms, none can explain a hypothetical bi-nary system travelling at, say, 200 km/s relative to the back-ground Galactic orbital motion - the first two require thedestruction of one component of a binary system, whereasthe third can rarely eject intact binaries at even moderatelyhigh velocities, with the number of binary systems at a givenvelocity having a sharp cutoff at ∼
150 km/s (Perets & ˇSubr2012). It follows that the production of binaries travelling athigher velocities requires triple systems, and indeed it wasfound that binaries travelling at such velocities consisting ofa main-sequence star and a neutron star can arise in smallquantities from hierarchical triples where the tertiary is asupermassive black hole (Lu & Naoz 2019). It should alsobe easy to imagine that, in a hierarchical triple, the innerbinary may achieve a certain velocity if the outer star ex-plodes as a supernova, but an analysis of such a system hasyet to be made, which is the motivation for this paper.In this paper, we investigate the velocity distribution ofremnant binaries after a tertiary explodes as a core-collapsesupernova in a triple system, in order to provide constraintson the velocity distributions of high velocity runaway bina-ries (HVRBs), which other authors may take advantage of toprobe the hypothesis that such binaries can have sufficientlyhigh velocities consistent with the narrative that some GaiaHVS candidates could be binaries in disguise. Our methodsand results are presented in the next section, while a dis-cussion of the implications of our work is conducted in thelast.
When a supernova explodes in a multiple stellar system, thevelocity of the surrounding matter is modified in three ways(Tauris & Takens 1998). (i) The star that exploded as a su- pernova now has most (core-collapse) or all (thermonuclear)of its mass dispersed, and can no longer hold the surroundingmaterial in orbit around itself. The original orbital velocityof the surrounding matter therefore now leads it to moveaway from its original position. (ii) In the case of a core-collapse supernova, the supernova may leave behind its corein the form of a neutron star, which can have a very highvelocity due to the “kick” imparted upon it by the host su-pernova, which interacts with the remnant system. (iii) Thematerial driven out by the supernova shock and the shock it-self may interact with the surrounding matter. For the rest ofthis paper, we consider only the influence of orbital velocityand the presence of the remnant neutron star, while omit-ting the effects of neutron star kicks and supernova shocks -we shall later see that the effects of this omission are easilyaccounted for.The following work is divided into two parts. In thefirst part, we establish our hierarchical triple model, andintroduce a set of Monte Carlo simulations, from which wegenerate a sample of hierarchical triples with small innerbinary separations, and calculate their initial orbital velocitydistribution. In the second part, we calculate the final HVRBvelocity distribution generated from that sample.
In a hierarchical triple system consisting of three main se-quence (MS) stars of masses m , m and m , where the innerbinary consists of m and m , the outer tertiary m wouldeventually evolve into a core-collapse supernova if it has asuitable initial mass, and if mass tranfer between the bodiescan be disregarded. When this happens, most of the massof m dissipates, leaving behind a neutron star roughly atenth of the original MS star’s mass (see Heger et al. 2003;Margalit & Metzger 2017). Note that we later model thisremnant neutron star as a point mass exactly a tenth of theoriginal MS star’s mass.Since the velocity of the final remnant binary is heavilydependent upon its outer orbital velocity, we require a closetriple system with a small outer binary separation a toproduce a HVRB. For a given inner binary separation a ,the smallest a that does not lead to an unstable system is a , crit = . a (cid:20) ( + q ) + e √ − e (cid:21) . (cid:18) − . i π (cid:19) (1)where q = m /( m + m ) is the mass ratio of the outer or-bit, e is the eccentricity of the outer orbit, and i is theinclination angle between the inner and outer orbits in ra-dians (Mardling & Aarseth 2001, He & Petrovich 2018, seealso Eggleton & Kiseleva 1995). As the minimum value of a is proportional to a , we consider only systems where a is between R ⊙ and R ⊙ . For simplicity, we assume e = ,i.e. circular outer orbits. We further simplify the system byomitting tidal effects, allowing for all three stars to be ap-proximated as point masses.We then proceed to use a Monte Carlo method to gener-ate a sample of such close hierarchical triple systems as fol-lows. We generate each of the three masses, m , m , and m ,by drawing them randomly from a Salpeter IMF (Salpeter1955), the low-mass cutoff of which is set at . M ⊙ . We alsogenerate inner and outer orbital periods P and P , such MNRAS , 1–6 (2019) igh Velocity Runaway Binaries from Tertiary Supernovae in Triple Stellar Systems that log P follows a flat distribution in both cases. It shouldbe noted that this is directly analogous to distributionsthat other authors have used (e.g. Rebassa-Mansergas et al.2019). The ranges of log P from which the orbital periodsare generated are log [ P /( )] = − to -2 (hence generatingan outer orbital period between 0.3 days and 3 days for theinner orbit) and log [ P /( )] = − to 2 (hence generatingan outer orbital period between 0.3 days and 100 years forthe outer orbit). The rationale behind the former is that allvalues of a derived from this range lies within the R ⊙ to R ⊙ range that we study. The inclination angle i is assumedto follow a flat distribution from to π , for want of a bet-ter approximation. All systems are required to match thefollowing criteria: • M ⊙ < m < M ⊙ . We need m to evolve into a core-collapse supernova, for which this mass range is ideal. • The zero age main sequence (ZAMS) and terminal agemain sequence (TAMS) radii of both m and m must besmaller than their Roche Lobes within the inner binary. Ifthis criterion is violated, it is possible that the inner binarycomponents may fill their Roche Lobes during the MS phase,leading to complications. The stellar radii were calculatedvia Demircan & Kahraman (1991), while the Roche Lobesizes were calculated via Eggleton (1983). • R ⊙ < a < R ⊙ , because this is the range we study, asnoted above. • The value of a , calculated via m , m , m , P and P ,must be larger than or equal to the critical value a , crit givenby Eq. 1.Also implicit in these requirements is that m must be muchlarger than m + m , so that it will explode as a supernovalong before either m or m can evolve. This is ascertainedby the first two criteria. If any of these criteria are violated,the system is discarded and regenerated.Thus, we generate hierarchical triple systems. Sincewe have already assumed that e = , calculation of theorbital velocity distribution of the inner binary centres ofmass is trivial: v = (cid:18) m m + m + m (cid:19) r µ a , (2)where µ = G ( m + m + m ) .The distribution of these initial orbital velocities is plot-ted in Fig. 1, where it can be seen that the velocity undergoesa sharp cutoff at around v = km/s. As the components of the stellar triple evolve, m undergoescore-collapse long before m or m leave the MS. The super-nova event dissipates most of the mass of m , leaving only aneutron star in its wake. The sudden mass loss may or maynot unbind the outer orbit of the triple system - if it does,and if the resulting velocity of the inner binary after escap-ing the gravitational potential of the remnant neutron starof m is significant, a HVRB composed of the inner doubleMS binary is born.To simulate the effects of a core-collapse supernova in m , we set its mass to exactly one tenth of its initial amount( m NS = m / ), while retaining its original orbital velocity C oun t v Figure 1.
Initial orbtial velocity distribution of inner binaries inour Monte Carlo sample. The masses of these systems are drawnfrom a Salpeter IMF, while the orbital separations are determinedby assuming a flat log P distribution for the orbital periods. Allsystems satisfy the selection criteria that the tertiary has an ap-propriate mass, the inner binary does not undergo Roche Lobeoverflow, the inner binary separation is between R ⊙ and R ⊙ ,and the triple system is dynamically stable when the componentsare at initial masses. The final orbital velocities are calculatedusing Eq. 2. The velocity distribution undergoes a sharp cutoffat around v = km/s. It should be noted that this distributioncan be used as a proxy for the HVRB velocity once neutron starkicks are considered (see discussion for details). (no kick). The mass loss removes from the system a quantityof momentum equal to ( m − m NS ) (cid:18) m + m m + m + m (cid:19) r µ a , (3)and the remnant system’s centre of mass consequently at-tains a velocity of v COM = (cid:18) m − m NS m + m + m NS (cid:19) (cid:18) m + m m + m + m (cid:19) r µ a (4)relative to the centre of mass of the original progenitor sys-tem (prior to the supernova explosion).In the reference frame where the remnant system’s cen-tre of mass is stationary, the velocity of the inner binary is v inner = (cid:18) m NS m + m + m NS (cid:19) v rel , (5)where v rel is the relative velocity between the inner binaryand the remnant neutron star (Jacobian coordinates). Afterthe remnant binary escapes to infinity, v rel can be calculatedvia v = v − G ( m + m + m NS ) a , (6)where v init = p µ / a is the original relative velocity at thetime of the explosion, which is equal to the relative velocityprior to the explosion. Needless to say, if the right-hand side MNRAS , 1–6 (2019)
Y. Gao et al. C oun t v HVRB (km/s)
Figure 2.
Projected ejection velocity distribution of a popula-tion of HVRBs generated from our Monte Carlo sample of triplesystems, the initial orbital velocities of which are plotted in Fig.1. The velocity values are calculated via Eqs. 4 to 7. The ve-locity distribution undergoes a sharp cutoff at around v = km/s. This velocity is usually insufficient to escape the Galac-tic potential, but once combined with Galactic rotation or LargeMagellanic Cloud effects, could lead to enhanced velocities whichcan. of Eq. 6 is smaller than zero, the system remains bound,the inner binary cannot escape to infinity from the remnantneutron star, and no HVRB is born. However, this is not thecase for any of our systems.The final velocity of the inner binary after it has escapedthe remnant neutron star in the reference frame of the centreof mass of the original progenitor system is taken to be thefinal HVRB velocity, which is equal to: v HVRB = v inner + v COM . (7)This is calculated for all the triple systems in our Monte-Carlo sample, and the distribution of the final HVRB veloc-ities is plotted in Fig. 2, where a velocity cutoff at around v = km/s can be seen. In this paper, we have studied the production of runawaybinaries originating from supernova explosions in the ter-tiaries of close hierarchical triple systems. Throughout ourinvestigation, we made several implicit assumptions, whichwe bring to the attention of the reader here.Before the tertiary ( m ) becomes a supernova, it willunavoidably become a giant first, and fill its Roche Lobe.Throughout our simulations, we disregard this process. How-ever, it should be noted that previous work on binary super-nova HVSs have allowed the Roche Lobe overflow of theexploding star, opting instead to avoid the formation of acommon envelope (e.g. Tauris 2015). Unless the overflowmaterial can cause the inner binary to merge in the sys-tems we simulate (which is intuitively unlikely), disregarding such Roche Lobe overflow becomes indistinguishable fromthe protocols hitherto adopted.Perhaps more relevant are the issues of Lidov-Kozai res-onance (Kozai 1962, see also Naoz 2016) and tertiary tides(Gao et al. 2018, see also Fuller et al. 2013), which can al-ter the dynamical evolution of the inner binary. Lidov-Kozairesonance, acting on triple systems with high relative orbitalinclination, would inject eccentricity into the inner binary,causing it to undergo Roche Lobe overflow more easily. Asfor the latter, since it is inevitable that the tertiary willfill its Roche Lobe prior to its supernova explosion, tertiarytides will serve to harden the inner binary before the HVRBreceives its velocity. This can affect the evolution of the in-ner binary, leading to complications. All these effects willpresumably be more of a problem for inner binaries thatare more massive (and hence have components with largerradii), which will have lower final velocities, and as such willbe less relevant to the high-velocity end of our results.The two aspects of supernova explosions which we choseto leave out of our calculations, namely the neutron starkicks and shock waves from supernovae, also deserve at-tention. After all, judging by the results of Tauris (2015),these factors can result in a final ejection velocity twicethat of the initial orbital velocity for HVSs. However, thisis only the case for extreme neutron star kicks of ∼ log P distri-bution. This practice is common in studies of low-mass bina-ries, since the orbital period distributions of such binaries donot deviate far from a flat distribution in the local universe(e.g. Duquennoy & Mayor 1991). However, The orbital pe-riod distribution of hierarchical triples has not been studiedso extensively, especially for hierarchical triples with massivetertiaries, and this assumption may consequently under- oroverestimate the amount of orbits at a certain orbital period,resulting in a bias. To demonstrate the extent of such a po-tential bias, we repeat our simulations, this time assuming afixed value for a of R ⊙ , thereby eliminating all the highest-velocity HVRBs emanating from systems with inner orbitalseparations in between 3 and R ⊙ and their correspondingshort orbital periods. The results are almost indentical toour original results, except that the high-velocity cutoff oc-curs at roughly 350km/s and 300km/s in the counterpartsof Figs. 1 and 2, respectively. We also try a lognormal dis-tribution for logP with a mean of log(P/days)=5.03 and astandard deviation of 2.28 (Raghavan et al. 2010), which isan alternative logP distribution adopted by many authors inrecent years (e.g. Toonen et al. 2017). Substituting the flatlogP distribution with this more complicated distribution,while keeping our other methods intact (including demand-ing that log [ P /( )] = − to -2 and log [ P /( )] = − to2), yields similar results to our original analysis, with the MNRAS , 1–6 (2019) igh Velocity Runaway Binaries from Tertiary Supernovae in Triple Stellar Systems cutoff velocities undergoing only a 20 km/s shift towardsthe low velocity end.With these issues in mind, what are the implicationsof this work? First of all, it should be pointed out that thesystems herein studied, namely, HVRBs generated by core-collapse explosions of massive tertiaries in close hierarchicaltriples, are likely to form the bulk of the high-velocity HVRBpopulation generated far from the Galactic centre. As pre-viously mentioned, HVRBs generated by inner binary su-pernova explosions require SMBH tertiaries to form HVRBs(Lu & Naoz 2019), and even in that case are incapable offorming MS-MS binaries like our model could, while dynam-ical ejection from globular clusters result in HVRBs of farlower velocities (Perets & ˇSubr 2012). Tertiaries explodingas Type Ia supernovae are infeasible, since there is no ev-idence of CO white dwarf tertiaries being able to accretematter from an inner binary. Triple systems in central config-urations are highly unstable for triple systems of comparablemass, and thus cannot exist long enough to form a HVRB.Finally, while it cannot be ruled out that chaotic triples cansurvive long enough for a stellar component to evolve beyondthe MS phase (Szebehely & Peters 1967), such occurrencesare rare, and we do not expect these formation scenarios toaffect the real-world HVRB velocity distribution to a highdegree of significance.Next would be the issue of how well our sample re-flects real-world HVRB progenitors. The fraction of stellarsystems in the real world that can be represented by thesample we generated using our Monte Carlo simulations canbe shown to be f = × − (cid:18) f tr (cid:19) (cid:18) f i . (cid:19) (cid:18) f M . (cid:19) (8)where f tr is the fraction of stellar systems that are hierarchi-cal triples, f i is the fraction of hierarchical triples with in-ner binary separations within the range of our simulations,and f M is the fraction of hierarchical triples that have ter-tiaries in the mass range 14 to 20 M ⊙ , allowing them to un-dergo core collapse. f tr has been shown to be on the order of by many authors in the field (e.g. Raghavan et al. 2010;Michaely & Perets 2014), whereas f M is roughly . ac-cording to most mainstream IMFs. It should be noted herethat tertiaries in hierarchical triples tend to be statisticallyless massive than the inner binary components in general,but we do not expect this to affect our conclusions below.As for f i , a brief glance at the contents of the Multiple StarCatalogue (Tokovinin 1997, 2010, see also Tokovinin 2018)reveals that roughly 0.3% of all hierarchical multiple systemsin that sample have inner binary separations between R ⊙ and R ⊙ , which is the range we study. However, we cautionthe reader that the MSC is prone to certain selection effects,the correction of which is beyond the scope of our work. Ifit can be assumed that f = × − , then the Galaxy, withits stars, ought to yield roughly × triple systemsanalogous to those in our sample. This is roughly 1/30 thesample size of our simulated triple systems.In other words, we conclude that it should be possi-ble that a HVRB of roughly 350 km/s can be found inthe Milky Way which was generated in the manner herestudied, with greater velocities of up to about 400 km/spossible with neutron star kicks and supernova shocks, butthat greater velocities relative to the centre of mass of the original triple are unlikely. These velocities are generallynot high enough to be unbound from the Galaxy. How-ever, once the Galactic rotational velocity of roughly 240km/s (Bland-Hawthorn & Gerhard 2016) or HVRBs hail-ing from the LMC (378km/s relative to the Milky Way, seeBoubert et al. 2017) are considered, velocities capable of es-caping the Galaxy could potentially be achieved. As such,the production channel studied in this paper ought to beconsidered, alongside other possibilities such as triple sys-tems in which one component undergoes absorption by asupermassive black hole (Perets 2009), if one is ever found.Lastly, we consider the effect that this conclusion mayhave on the velocity distribution of classical HVSs. If in-ner binaries in hierarchical triples could indeed be accel-erated to velocities in excess of 300 km/s, one would ex-pect that much faster HVSs would be produced if and whenthe more massive star of the HVRB evolves into a super-nova, assuming that the velocity of the HVRB and that ofthe resultant HVS are aligned. No evidence of such a two-stage HVS exists. Yet while we have no concrete evidenceof the existence of such objects, it should be noted thatseveral abnormally fast B-type HVSs have been noted byIrrgang, Kreuzer, & Heber (2018). These objects, being ofspectral type B, could not have attained velocities muchfaster than 500km/s, which they actually possess, from bi-nary supernova kicks (Tauris 2015), and could not have beenaccelerated by the Galactic central black hole, since theirreversed trajectories point nowhere near the Galactic cen-tre. But before we get carried away and declare that theseobjects evolved from HVRBs, it should be noted that othermore viable explanations also exist for these objects, as men-tioned in Irrgang, Kreuzer, & Heber (2018), such as dynam-ical ejection from unstable multiple stellar sytems in whichmost of the other components are far more massive than theejected component. ACKNOWLEDGEMENTS
This work was jointly supported by the Natural ScienceFoundation of China (Grant No. 11521303), and the Scienceand Technology Innovation Talent Programme of YunnanProvince (Grant No. 2017HC018).
REFERENCES
Beniamini P., Piran T., 2016, MNRAS, 456, 4089Blaauw A., 1961, BAN, 15, 265Bland-Hawthorn J., Gerhard O., 2016, ARA&A, 54, 529Boubert D., Erkal D., Evans N. W., Izzard R. G., 2017, MNRAS,469, 2151Boubert D., et al., 2019, MNRAS,Bromley B. C., Kenyon S. J., Brown W. R., Geller M. J., 2018,ApJ, 868, 25Demircan O., Kahraman G., 1991, Ap&SS, 181, 313Duquennoy A., Mayor M., 1991, A&A, 248, 485Eggleton P. P., 1983, ApJ, 268, 368Eggleton P., Kiseleva L., 1995, ApJ, 455, 640Fuller J., Derekas A., Borkovits T., Huber D., Bedding T. R.,Kiss L. L., 2013, MNRAS, 429, 2425Gaia Collaboration, et al., 2018, A&A, 616, A1Gao Y., Correia A. C. M., Eggleton P. P., Han Z., 2018, MNRAS,479, 3604MNRAS , 1–6 (2019)
Y. Gao et al.
Gvaramadze V. V., Gualandris A., Portegies Zwart S., 2009, MN-RAS, 396, 570Hattori K., Valluri M., Bell E. F., Roederer I. U., 2018, ApJ, 866,121He M. Y., Petrovich C., 2018, MNRAS, 474, 20Heger A., Fryer C. L., Woosley S. E., Langer N., Hartmann D. H.,2003, ApJ, 591, 288Hills J. G., 1988, Natur, 331, 687Irrgang A., Kreuzer S., Heber U., 2018, A&A, 620, A48Kozai Y., 1962, AJ, 67, 591Lu C. X., Naoz S., 2019, MNRAS, 484, 1506Marchetti T., Rossi E. M., Brown A. G. A., 2018, MNRAS,Mardling R. A., Aarseth S. J., 2001, MNRAS, 321, 398Margalit B., Metzger B. D., 2017, ApJ, 850, L19Michaely E., Perets H. B., 2014, ApJ, 794, 122Naoz S., 2016, ARA&A, 54, 441Perets H. B., 2009, ApJ, 698, 1330Perets H. B., ˇSubr L., 2012, ApJ, 751, 133Raghavan D., et al., 2010, ApJS, 190, 1Rebassa-Mansergas A., Toonen S., Korol V., Torres S., 2019, MN-RAS, 482, 3656Salpeter E. E., 1955, ApJ, 121, 161Shen K. J., et al., 2018, ApJ, 865, 15Szebehely V., Peters C. F., 1967, AJ, 72, 1187Tauris T. M., Takens R. J., 1998, A&A, 330, 1047Tauris T. M., 2015, MNRAS, 448, L6Tokovinin A. A., 1997, A&AS, 124, 75Tokovinin A., 2010, yCat, 73890925Tokovinin A., 2018, ApJS, 235, 6Toonen S., Hollands M., G¨ansicke B. T., Boekholt T., 2017, A&A,602, A16Wang B., Han Z., 2009, A&A, 508, L27Widmark A., Leistedt B., Hogg D. W., 2018, ApJ, 857, 114Yu Q., Tremaine S., 2003, ApJ, 599, 1129This paper has been typeset from a TEX/L A TEX file prepared bythe author. MNRAS000