1 Introduction

About 10-30% of the O stars and 5-10% of the B stars (Gies 1987; Stone 1991) have large peculiar velocities (up to 200 km s^-1), and are often found in isolated locations; these are the so-called "runaway stars'' (Blaauw 1961, hereafter Paper I). The velocity dispersion of the population of runaway stars, $\sigma_{\rm v} \sim 30$ km s^-1 (e.g., Stone 1991), is much larger than that of the "normal'' early-type stars, $\sigma_{\rm v} \sim 10$ km s^-1. Besides their peculiar kinematics, runaway stars are also distinguished from the normal early-type stars by an almost complete absence of multiplicity (cf. the binary fraction of normal early-type stars is >50% [e.g., Mason et al. 1998]). Furthermore, over 50% of the (massive) runaways have large rotational velocities and enhanced surface helium abundances (Blaauw 1993).

Several mechanisms have been suggested for the origin of runaway stars (Zwicky 1957; Paper I; Poveda et al. 1967; Carrasco et al. 1980; Gies & Bolton 1986), two of which are still viable: the binary-supernova scenario (Paper I) and the dynamical ejection scenario (Poveda et al. 1967). We summarize them in turn.

Binary-supernova scenario (BSS)

In this scenario a runaway star receives its velocity when the primary component of a massive binary system explodes as a supernova. When the supernova shell passes the secondary the gravitational attraction of the primary reduces considerably, and the secondary starts to move through space with a velocity comparable to its original orbital velocity (30-150 km s^-1). What remains of the primary after the explosion is a compact object, either a neutron star or a black hole. Depending on the details of the preceding binary evolution, the eccentricity of the orbit, and the kick velocity $\vec{v}_{\rm kick}$ due to the asymmetry of the supernova explosion (e.g., Burrows et al. 1995), the compact object may or may not remain bound to the runaway star (e.g., Hills 1983). In most cases less than half of the total mass of the binary is expelled in the explosion. As this is insufficient to break up the binary (Paper I), most BSS runaways are expected to remain double. Examples of such systems are provided by the high-mass-X-ray binaries (e.g., van den Heuvel et al. 2000). Their typical velocities of $\sim$50 km s^-1(Kaper et al. 1997; Chevalier & Ilovaisky 1998) are the natural result of the recoil velocity acquired when the supernova shell leaves the binary system.

Several searches failed to find compact companions of classical runaway stars (Gies & Bolton 1986; Philp et al. 1996; Sayer et al. 1996), suggesting that for these systems $\vec{v}_{\rm kick}$ of the neutron star was large enough (several 100 km s^-1) to unbind the binary (e.g., Frail & Kulkarni 1991; Cordes et al. 1993; Lai 1999). The typical magnitude of this "threshold'' kick velocity is uncertain (e.g., Hills 1983; Lorimer et al. 1997; Hansen & Phinney 1997; Hartman 1997).

Single BSS runaways must originate in close binaries because these systems have the largest orbital velocities, and therefore they have experienced close binary evolution before being ejected as a runaway. This leads to the following observable characteristics:

1:

BSS runaways are expected to have increased helium abundance and large rotational velocity: when the primary fills its Roche lobe, mass and angular momentum is transferred to the star that will become the runaway. The mass transfer stops when the "primary'' has become a helium star (i.e., only the helium core remains). This process enriches the runaway with helium, and spins it up (e.g., Packet 1981; van den Heuvel 1985; Blaauw 1993);

2:

A BSS runaway can become a blue straggler, because it is rejuvenated during the mass-transfer period through the fresh fuel it receives from the primary;

3:

The kinematic age of a BSS runaway star (defined as the time since the runaway left its parent group) should be smaller than the age of the parent group. The primary of the original binary system first evolves for several Myr before it explodes and the runaway is ejected.

Dynamical ejection scenario (DES)

In this scenario runaway stars are formed through gravitational interactions between stars in dense, compact clusters. Although binary-single star encounters produce runaways (e.g., Hut & Bahcall 1983), the most efficient interaction is the encounter of two hard binary systems (Hoffer 1983). Detailed simulations show that these collisions produce runaways with velocities up to 200 km s^-1(Mikkola 1983a, 1983b; Leonard & Duncan 1988, 1990; Leonard 1991). The outcome of a binary-binary collision can be (i) two binaries, (ii) one single star and a hierarchical triple system, (iii) two single stars and one binary, and (iv) four single stars (Leonard 1989). In most cases the collision will result in the ejection of two single stars and one hard binary with an eccentric orbit (Hoffer 1983; Mikkola 1983a). Since the resulting binary is the most massive end product of the collision it is unlikely to gain a lot of speed; it might even remain within the parent cluster. This process naturally leads to a low (0-33%) runaway binary fraction which is in qualitative agreement with the observations (e.g, Gies & Bolton 1986). For the DES to be efficient the initial binary fraction in clusters needs to be large. Recent observations show that the binary fraction for massive stars in young clusters is >50% (Abt 1983; Kroupa et al. 1999; Preibisch et al. 1999 [approaching 100%]).

DES runaways have the following characteristics:

1:

DES runaways are formed most efficiently in a high-density environment, e.g., in young open clusters. They may also originate in OB associations. These birth sites of massive stars are unbound stellar groups and therefore expand (e.g., Blaauw 1952a,1978; Elmegreen 1983; Kroupa 2000a), so DES runaways must have been ejected very soon after their formation. The kinematic age and the age of the parent association are thus nearly equal;

2:

DES runaways are not expected to show signs of binary evolution such as large rotational velocities and increased helium abundance. However, Leonard (1995) suggested that some binary-binary encounters produce runaways consisting of two stars that merged during the interaction. These would have enhanced helium abundances and large rotational velocities (Benz & Hills 1987, but see Lombardi et al. 1995);

3:

DES runaways are expected to be mostly single stars.

   

Table 1: The nearby runaway stars and pulsars with accurate astrometry. HIP indicates the number of the runaway star in the Hipparcos Catalogue, $v_{\rm space}$ indicates the space motion of the runaway star relative to Galactic rotation (in km s^-1), and PSR indicates the pulsar identifications

HIP	$v_{\rm space}$	HIP	$v_{\rm space}$	HIP	$v_{\rm space}$	HIP	$v_{\rm space}$	HIP	$v_{\rm space}$	HIP	$v_{\rm space}$	PSR
3478	80.4	28756	196.6	43158	57.2	61602	30.2	91599	44.7	101350	36.4	J0826+2637
3881	32.1	29678	63.0	45563	125.9	62322	43.9	92609	31.0	102274	46.1	J0835-4510
9549	107.9	30143	55.5	46928	45.3	66524	112.7	94899	162.8	103206	32.3	J0953+0755
10849	50.0	35951	34.9	46950	32.1	69491	77.2	94934	94.0	105811	38.3	J1115+5030
14514	39.4	36246	32.1	48715	34.5	70574	205.3	95818	34.7	106620	45.2	J1136+1551
18614	64.9	38455	41.4	48943	35.2	76013	69.0	96115	165.6	109556	74.0	J1239+2453
20330	34.7	38518	31.1	49934	31.2	81377	23.5	97774	35.0			J1456-6843
22061	86.5	39429	62.4	52161	34.8	82171	62.9	97845	70.3			J1932+1059
24575	113.3	40341	61.7	57669	31.1	82868	30.3	99435	39.4			Geminga
27204	107.8	42038	31.3	59607	78.8	86768	30.1	99580	55.6

Which of the two formation processes is responsible for runaway stars has been debated vigorously. Both mechanisms create stars with large peculiar velocities which enable them to travel far from their parent group: a velocity of 100 km s^-1 corresponds to $\sim$100 pc in only 1 Myr. The relative importance of the two scenarios can be established by (i) studying the statistical properties of the ensemble of runaway stars, or by (ii) investigating individual runaways in detail. The former approach is based on differences in the general runaway characteristics predicted by each scenario. This requires a large, complete database of runaway stars, which is, to date, unavailable (e.g., Moffat et al. 1998). Here we therefore follow the latter, individual approach by retracing the orbits of runaway stars back in time. The objects encountered by a runaway along its path (e.g., an open cluster, an association, other runaways, or a neutron star), and the times at which these encounters occurred, provide information about its formation. Evidence for the BSS as the formation mechanism for single runaway stars is to find a runaway and a neutron star (pulsar) which occupied the same region of space at the same time in the past. Evidence for the DES is to find a common site of origin for the individual components of the encounter, e.g., a pair of runaways and a binary, in a dense star cluster.

The individual approach requires highly accurate positions ($\alpha$, $\delta$, $\pi$) and velocities ( $\mu _{\alpha \ast }$, $\mu _\delta$, $v_{\rm rad}$). Here $\alpha$ denotes right ascension, $\delta$ declination, $\pi$parallax, $\mu_{\alpha\ast} = \mu_\alpha \cos \delta$ proper motion in right ascension, $\mu _\delta$ proper motion in declination, and $v_{\rm rad}$ the radial velocity. The milli-arcsecond (mas) accuracy of Hipparcos astrometry (ESA 1997) allows specific investigations of the runaway stars within $\sim$700 pc. Positions and proper motions of similar accuracy are now available as well for some pulsars through timing measurements and VLBI observations (e.g., Taylor et al. 1993; Campbell 1995). The Hipparcos data also significantly improved and extended the membership lists of the nearby OB associations (de Zeeuw et al. 1999), and of some nearby young open clusters. The resulting improved distances and space velocities of these stellar aggregates make it possible to connect the runaways and pulsars to their parent group, and, in some cases, to identify the specific formation scenario (Hoogerwerf et al. 2000; de Zeeuw et al. 2000). Pre-Hipparcos data (e.g., Blaauw & Morgan 1954; Paper I; Blaauw 1993; van Rensbergen et al. 1996) allowed identification of the parent groups for some runaways, but generally lacked the accuracy to study the orbits of the runaways in detail (but see Blaauw & Morgan 1954; Gies & Bolton 1986).

We define a sample of nearby runaways and pulsars with good astrometry in Sect. 2, and then analyse two cases in depth: $\zeta$ Oph and PSR J1932+1059 in Sect. 3 and AE Aur, $\mu$ Col and $\iota$ Ori in Sect. 4. We apply the method developed in these sections to the entire sample of runaways and pulsars in Sects. 5, 6, and 7. We discuss helium abundances, rotational velocities and the blue straggler nature of runaways in Sects. 8 and  9, and summarize our conclusions in Sect. 10.