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###### Abstract

We discuss the origin of the runaway early B-type star HD 271791 and show that its extremely high velocity () cannot be explained within the framework of the binary-supernova ejection scenario. Instead, we suggest that HD 271791 attained its peculiar velocity in the course of a strong dynamical encounter between two hard massive binaries or via an exchange encounter between a hard massive binary and a very massive star, formed through runaway mergers of ordinary massive stars in the dense core of a young massive star cluster.

Keywords. Binaries: close – stars: individual: HD 271791 – stars: kinematics – galaxies: star clusters.

On the origin of the hypervelocity runaway star HD 271791] On the origin of the hypervelocity runaway star HD 271791 V.V.Gvaramadze] V.V.Gvaramadze

## 1 Introduction

HD 271791 is a massive (; Przibilla et al. ?) extremely high-velocity runaway star with a Galactic rest-frame velocity of (Heber et al. ?), typical of the so-called hypervelocity stars (HVVs) – the ordinary stars moving with peculiar velocities exceeding the escape velocity of our Galaxy (Brown et al. ?; Edelmann et al. ?; Hirsch et al. ?). The existence of the HVSs was predicted by Hills (?), who showed that close encounter between a tight binary system and the supermassive black hole (BH) in the Galactic Centre could be responsible for ejection of one of the binary components with a velocity of up to several . Yu & Tremaine (?) proposed and additional possible mechanism for production of HVSs based on the interaction between a single star and a putative binary BH in the Galactic Centre. It is therefore plausible that some HVSs were produced in that way (Gualandris, Portegies Zwart & Sipior ?; Baumgardt, Gualandris & Portegies Zwart ?; Levin ?; Sesana, Haardt & Madau ?; Ginsburg & Loeb ?; Lu, Yu & Lin ?; Löckmann & Baumgardt ?). At present, however, proper motion measurements are not available for all but one of the known HVSs so that it is impossible to unambiguously associate their birthplace with the Galactic Centre. HD 271791 is the only HVS with measured proper motion and all measurements show that this star was ejected from the periphery of the Galactic disc (at a galactocentric distance of kpc; Heber et al. ?).

There are two possible alternative explanations of the origin of HVSs. The first one is that the HVSs attain their high peculiar velocities in the course of strong dynamical three- or four-body encounters in young and dense star clusters located in the Galactic disc (Gvaramadze ?, ?; Gvaramadze, Gualandris & Portegies Zwart ?, ?) or in the Large Magellanic Cloud (Gualandris & Portegies Zwart ?). The second one was proposed by Abadi, Navarro & Steinmetz (?). According to these authors, some HVSs could originate from tidal disruption of dwarf galaxies during their close passage near the Milky Way. The young age of HD 271791 of Myr (Przybilla et al. ?) is inconsistent with the second possibility since there are no indications of a recent encounter between a dwarf satellite with the Milky Way. So, we are left with the first one. Before discussing it in Section 4, we consider a proposal by Przybilla et al. (?) that HD 271791 attained its peculiar velocity in the course of disintegration of a close massive binary system following the supernova (SN) explosion.

## 2 HD 271791: former secondary in a massive binary system

The spectral analysis of HD 271791 by Przybilla et al. (?) revealed that the Fe abundance in its atmosphere is subsolar and that the -process elements are enhanced. The first finding is consistent with the origin of HD 271791 in the metal-poor outskirts of the Galactic disc, while the second one suggests that this star was a secondary component of a massive tight binary and that its surface was polluted by the nucleosynthetic products after the primary star exploded in a SN. Przybilla et al. (?) believe that the binary-SN explosion could be responsible not only for the -enhancement in HD 271791 but also for the extremely high space velocity of HD 271791. Below, we outline their scenario.

The large separation of HD 271791 from the Galactic plane ( kpc) along with the proper motion measurements (Heber et al. ?) implies that the time-of-flight of this B2III star is comparable to its evolutionary age, which in turn implies that the star was ejected within several Myr after its birth in the Galactic disc. The ejection event was connected with disruption of a massive tight binary following the SN explosion. The original binary was composed of a primary star of mass of and an early B-type secondary (HD 271791), so that the SN explosion and the binary disruption occurred early in the lifetime of HD 271791. The system was close enough to go through the common-envelope phase before the primary exploded in a SN. During the common-envelope phase, the primary star lost most of its hydrogen envelope and the binary became a tight system composing of a Wolf-Rayet star and an early B-type main-sequence star. At the moment of SN explosion, the mass of the primary star was and the binary semimajor axis was (that corresponds to the orbital velocity of the secondary of ). The exploded star expelled of its mass while the remaining mass collapsed to a BH. The SN explosion was asymmetric enough to disrupt the system. Przybilla et al. (?) assumed that HD 271791 was released at its orbital velocity and that at the time of binary disruption the vector of the orbital velocity was directed by chance along the Galactic rotation direction. The first assumption is based on the wide-spread erroneous belief that runaways produced from a SN in a binary system have peculiar velocities comparable to their pre-SN orbital velocities. The second assumption is required to explain the difference between the assumed space velocity from the binary disruption and the Galactic rest-frame velocity of HD 271791 (provided that the latter is on the low end of the observed range ).

In the next section, we discuss the conditions under which the secondary star could be launched into free flight at a velocity equal to its pre-SN orbital one.

## 3 Binary-supernova ejection scenario

One of two basic mechanisms producing runaway stars is based on a SN explosion in a massive tight binary system (Blaauw ?). After the primary star exploded in a SN, the binary system could be disintegrated if the system lost more than half of its pre-SN mass (Boersma ?) and/or the SN explosion was asymmetric (so that the stellar remnant, either a neutron star (NS) or a BH, received at birth a kick velocity exceeding the escape velocity from the system; Stone ?; Tauris & Takens ?).

In the case of binary disruption following the symmetric SN explosion, the stellar remnant is released at its orbital velocity, while the space velocity of the secondary star, , is given by (Boersma ?; Radhakrishnan & Shukre ?; Tauris & Takens ?)

 Vsec=√1−2m1+m2m21Vorb, (3.0)

where , and are the pre-SN masses of the primary and the secondary stars, is the mass of the compact object formed in the SN explosion, is the orbital velocity of the secondary star, is the gravitational constant and is the binary semimajor axis. It follows from equation (2.1) that if .

The above consideration shows that the secondary star could achieve a high peculiar speed if one adopts a large pre-SN mass of the primary (i.e. ). But, the stellar evolutionary models suggest that the pre-SN masses of stars with initial masses, from 12 to do not exceed (Vanbeveren, De Loore & Van Rensbergen ?; Meynet & Maeder ?). Using these figures and assuming that the pre-SN binary is as tight as possible (i.e. the secondary main-sequence star is close to filling its Roche lobe), one can estimate the maximum possible velocity achieved by a runaway star in the process of binary disruption following the symmetric SN explosion. Assuming that the SN explosion left behind a NS (i.e. ) and adopting , one has that a secondary star could attain a peculiar velocity of , while a star could be ejected with a speed of .

Note that the pre-SN mass is maximum for stars with initial mass and [see Fig. 6 of Meynet & Maeder (?)]. In the first case, the SN explosion leave behind a NS, while in the second one the stellar SN remnant is a BH of mass (e.g. Woosley et al. ?). The large separation of HD 271791 from the Galactic plane implies that this massive star was ejected very soon after its birth in the Galactic disc. From this, it follows that to explain the space velocity of HD 271791 within the framework of the binary-SN scenario one should assume that the primary was a short-lived very massive star (Przybilla et al. ?). In this case, the stellar SN remnant is a BH and the SN ejecta is not massive enough to cause the disruption of the binary system.

According to Przybilla et al. (?), the pre-SN mass of the primary star was (i.e. somewhat larger than the maximum mass predicted by the stellar evolutionary models; see above) and the SN explosion left behind a BH of mass (comparable to the mass of the secondary star, HD 271791), i.e. the system lost less than a half of its mass. Thus, to disrupt the binary, the SN explosion should be asymmetric. In this case, the space velocities of the BH and HD 271791 depend on the magnitude and the direction of the kick imparted to the BH at birth (Tauris & Takens ?). To estimate , one can use equations (44)-(47) and (54)-(56) given in Tauris & Takens (?). It follows from these equations that is maximum if the vector of the kick velocity does not strongly deviate from the orbital plane of the binary and is directed nearly towards the secondary, i.e. the angle, , between the kick vector and the direction of motion of the exploding star is , where is the relative orbital velocity and is the kick velocity (see Gvaramadze ?).

Fig. 1 shows how the direction and the magnitude of the kick affect . The three solid lines represent calculated for the binary parameters suggested by Przybilla et al. (?) and three kick magnitudes of (short-dashed), (solid line) and (long-dashed line). One can see that to launch HD 271791 at its pre-SN orbital velocity the kick imparted to the BH should be at least as large as . In fact, the kick magnitude should be much larger since for kicks the kick direction must be carefully tuned (see Fig 1), i.e. should be either or (note that for the binary system remains bound). The even larger kicks of and are required to explain the Galactic rest-frame velocities of HD 271791 of and [corresponding, respectively, to the ”best” and the maximum proper motions given in Heber et al. (?); see also Przybilla et al. (?)]. Although one cannot exclude a possibility that BHs attain a kick at birth, we note that there is no evidence that the kick magnitude could be as large as required by the above considerations (e.g. Nelemans et al. ?).

Thus, we found that to explain the peculiar velocity of HD 271791 the magnitude of the kick attained by the BH should be unrealistically large (), that makes the binary-SN ejection scenario highly unlikely (cf. Gvaramadze ?; Gvaramadze & Bomans ?). Nevertheless, some authors still believe that “HD 271791 is a plausible runaway star produced by a supernova explosion in a massive binary system” (Bromley et al. ?).

## 4 Dynamical ejection scenario

The second basic mechanism responsible for the origin of runaway stars is based on dynamical three- or four-body interactions in dense stellar systems (Poveda et al. ?; Aarseth ?; Gies & Bolton ?). Below, we discuss two possible channels for producing high-velocity runaways within the framework of the dynamical ejection scenario (cf. Gvaramadze ?).

The first possibility is that the high-velocity runaways originate through the interaction between two massive hard binaries (Mikkola ?; Leonard & Duncan ?). The runaways produced in binary-binary encounters are frequently ejected at velocities comparable to the orbital velocities of the binary components (Leonard & Duncan ?) and occasionally they can attain a velocity as high as the escape velocity, , from the surface of the most massive star in the binaries (Leonard ?). For the upper main-sequence stars with the mass-radius relationship (Habets & Heintze ?), , where and are the stellar radius and the mass, one has , so that the ejection velocity could in principle be as large as if the binaries contain at least one star of mass of .

To reconcile this ejection scenario with the presence of nucleosynthetic products in the atmosphere of HD 271791, one should assume that (i) HD 271791 was a secondary component of one of the binaries involved in the encounter, and (ii) by the moment of the encounter, the binary containing HD 271791 has experienced supernova explosion and remained bound [i.e. the stellar supernova remnant (BH) received a small or no kick at birth]. The requirement that HD 271791 was a member of a post-supernova binary should also be fulfilled in the second dynamical process discussed below.

The second possibility is that the high-velocity runaway stars attain their peculiar velocities in the course of close encounters between massive hard binaries and a very massive star (Gvaramadze ?; Gvaramadze et al. ?), formed through runaway collisions of ordinary massive stars in dense star clusters (e.g. Portegies Zwart et al. ?). A close encounter with the very massive star results in a tidal breakup of the binary, after which one of the binary components becomes bound to the very massive star while the second one recoils with a high velocity, given by (Hills ?):

 V∞≃500kms−1(MVMS/100M⊙)1/6(a′/30R⊙)−1/2(M1/10M⊙)1/3, (4.0)

where is the mass of the very massive star and is the post-SN binary semimajor axis. It follows from equation (4.1) that, to explain the peculiar velocity of HD 271791 of , the mass of the very massive star should be [the first figure corresponds to the mass of the most massive star formed in a ‘normal’ way in a cluster with a mass (Weidner, Kroupa & Bonnell ?)]Simple estimates show that our Galaxy can currently host about 100 star clusters with a mass (Gvaramadze et al. ?).. The above estimates can be supported by the results of three-body scattering experiments which showed that per cent of encounters between hard massive binaries and a very massive star of mass of produce runaways with (Gvaramadze et al. ?).

Note that the requirement that HD 271791 was a member of a post-SN binary does not contradict to our proposal that this star can attain its high speed via a three-body encounter with a very massive star (i.e. with the star more massive than the primary star in the original binary). The merging of ordinary stars results in effective rejuvenation of the collision product (e.g. Meurs & van den Heuvel ?) so that the very massive star could still be on the main sequence when the most massive ordinary stars start to explode as SNe (e.g. Portegiez Zwart et al. ?).

## 5 Acknowledgements

I am grateful to L.R.Yungelson for useful discussions, to the Russian Foundation for Basic Research and the International Astronomical Union for travel grants and to the Deutsche Forschungsgemeinschaft for partial financial support.

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