6 Identification of new parent groups

The orbit retracing technique allows us to identify the (likely) parent group for thirteen "new'' single runaways, one new pair, two more pulsars, and Geminga from the samples defined in Sect. 2. Little is known about most of these objects, so our discussion is relatively brief. The results are summarized in Table 5.

6.1 HIP 3881 & Lacerta OB1 (star 1)

The orbit of the spectroscopic binary $\nu$ Andromedae (B5V+F8V) intersected the Lac OB1 association 8-10 Myr ago. If this is the parent group, then the kinematic age is comparable to the (uncertain) age of the association ($\sim$10 Myr). This, together with a normal rotational velocity for the primary (80 km s^-1) and the binary nature (two main-sequence stars) of this runaway, suggests that it was formed by dynamical ejection.

6.2 HIP 22061, HIP 29678, Geminga & the $\lambda$ Ori region (stars 4 and 7 and neutron star 9)

The two stars form an analog of the runaway pair AE Aur and $\mu$ Col (Sect. 4). They also move in opposite directions and with similar space motions: 86.5 km s^-1 for HIP 22061 (B2.5V) and 63.0 km s^-1 for HIP 29678 (B1V) (velocities are with respect to their own standard of rest). Retracing the orbits of HIP 22061 and HIP 29678, we find that the two stars were close together $\sim$1.1 Myr ago, suggesting that these two runaways were also formed by the DES. We did not find a possible third party (i.e., another runaway in the neighbourhood or a massive binary).

Applying the principle of conservation of linear momentum at the time of the encounter, as we did in Sect. 4, we can predict the properties of the parent cluster. We can only use these two stars and not three as in Sect. 4.5. We find that the parent cluster should be located around $(\ell,b) \sim (196\hbox{$.\!\!^\circ$ }5,-12\hbox{$.\!\!^\circ$ }0)$. This coincides with the $\lambda$ Orionis star-forming region (e.g., Gomez & Lada 1998; Dolan & Mathieu 1999), which contains at least three young stellar clusters (the $\lambda$ Ori cluster and the clusters associated with the dark clouds B30 and B35) and is surrounded by the $\lambda$ Orionis ring. Several authors have suggested that this expanding ring of molecular clouds is the result of a supernova explosion $\sim$0.35 Myr ago (e.g., Cunha & Smith 1996). The predicted cluster position does not coincide with one of the three star clusters. Furthermore, the predicted radial velocity of the cluster, $\sim$10 km s^-1, differs significantly from that of the $\lambda$ Ori clusters, $\sim$24 km s^-1. However, these differences might be erased if a third body (either a single star or a binary) was involved (cf. Sect. 4).

The conclusion that the DES is the acting mechanism for these runaways is supported by (i) the youth of the clusters in the $\lambda$ Ori star-forming region, 2-6 Myr (Dolan & Mathieu 1999), (ii) the density of these clusters (Dolan & Mathieu), and (iii) the small rotational velocity of HIP 29678, <25 km s^-1 (Morse et al. 1991).

It is worth mentioning that HIP 22061 and HIP 29678 are not the only objects running away from the $\lambda$ Orionis region. Frisch (1993) and Smith et al. (1994) suggested that the neutron star Geminga also originated from this star-forming region (Fig. 2; but see Bignami & Caraveo 1996). Moreover, the age of Geminga ($\sim$$350\,000$ yr) agrees well with the time of the supernova explosion which created the $\lambda$ Orionis ring.

6.3 HIP 38455 & Collinder 135 (star 8)

The ellipsoidal variable star HIP 38455 (B2V) moves away from the open cluster Collinder 135 with a velocity of almost 40 km s^-1, mostly in the radial direction. The orbits of the runaway and cluster intersected each other about 3 Myr ago; this is significantly smaller than the age of the open cluster: $\sim$35 Myr. This difference, and the large rotational velocity ( $v_{\rm rot} \sin i = 212$ km s^-1), suggest that the runaway originated via the BSS. Ellipsoidal variable stars show brightness variation because of their non-spherical shapes. The deformation of the star is thought to be due to tidal interactions with a companion star (Beech 1985). The fact that HIP 38455 is double (cf. Häfner & Drechsel 1986) suggests that the kick velocity of the compact object created in the supernova explosion was small and that the binary remained bound. This system might in the future become a high-mass X-ray binary (Sect. 1).

6.4 HIP 38518 & Vela OB2 (star 9)

This B0.5Iab supergiant is located behind the Vel OB2 association and is currently moving away from it. Retracing the orbit shows that $\sim$6 Myr ago the star was located inside the Vel OB2 association. This kinematic age is smaller than the association age (10-15 Myr). Adding to this the large rotational velocity ( $v_{\rm rot} \sin i = 220$ km s^-1) and the blue straggler character of HIP 38518 (see Sect. 9 for a further discussion), we infer that the BSS is the preferred scenario.

6.5 HIP 42038 & Upper Centaurus Lupus or IC 2391 (star 11)

The path of the B3V runaway star HIP 42038 traversed the open cluster IC 2391 $\sim$6 Myr ago and the Upper Centaurus Lupus association $\sim$8 Myr ago. Little is known about HIP 42038, making it difficult to determine its origin. The only available criterion is that the kinematic age is smaller than both the age of IC 2391 (45 Myr) and the age of Upper Centaurus Lupus (13 Myr) favoring the BSS.

6.6 HIP 46950 & IC 2602 (star 12)

Somewhere between 2 Myr and 10 Myr ago the B1.5IV star occupied the same space as the open cluster IC 2602. The only bit of information available for the identification of the runaway's origin is the difference between the kinematic age and the age of the open cluster ($\sim$25 Myr). This would suggest that the BSS is the origin.

6.7 HIP 48943 & Lower Centaurus Crux (star 13)

HIP 48943 is a runaway from the Lower Centaurus Crux association. The orbit of the B5Ve star intersected the association center $\sim$4 Myr ago. The runaway has a rotational velocity of 230 km s^-1 and its kinematic age is significantly smaller than the age of Lower Centaurus Crux, $\sim$10 Myr. The BSS is thus the most likely formation mechanism.

6.8 HIP 49934 & IC 2391 or IC 2602 (star 14)

The retraced orbit of the emission-line star HIP 49934 (B2IVnpe) intersects two open clusters: IC 2391 $\sim$3 Myr ago and IC 2602 $\sim$6 Myr ago. The large difference between the nuclear ages of both clusters (45 Myr and 25 Myr, respectively) and the kinematic age indicates that the BSS is the most likely origin of HIP 49934. This assumption is supported by the large rotational velocity ( $v_{\rm rot} \sin i = 280$ km s^-1).

6.9 HIP 57669 & IC 2602 (star 15)

About 3 Myr ago the emission-line star HIP 57669 left the open cluster IC 2602. This B3Ve star has a large rotational velocity ( $v_{\rm rot} \sin i = 251$ km s^-1) and its kinematic age differs significantly from the age of IC 2602. Both these points suggest the BSS as the origin of HIP 57669.

6.10 HIP 69491 & Upper Centaurus Lupus or Cepheus OB6 (star 16)

This candidate runaway is an eclipsing binary (B5V). Its path traverses the Upper Centaurus Lupus association and the Cep OB6 association. The respective kinematic ages are 3 and 10 Myr. Both these kinematic ages are smaller than the association ages of 13 Myr for Upper Centaurus Lupus and $\sim$50 Myr for Cep OB6. This discrepancy in ages combined with the binary nature of the candidate runaway excludes both the standard BSS and the DES and might suggest that neither Upper Centaurus Lupus nor Cep OB6 is the parent of HIP 69491. The BSS is highly unlikely because the eclipses imply two objects of similar size and not, for example, a main-sequence star and a compact object. The DES is excluded because both associations were no longer compact/dense enough for dynamical encounters to be efficient at the time of ejection.

What other mechanisms do exist to create a fast moving ( $v_{\rm space} = 77$ km s^-1) binary system? One possibility is a supernova explosion in a triple system consisting of a hard binary and a third star with a larger semi-major axis (i.e., a stable triple system). This would result in either (i) a hard binary moving at moderate speed (<30 km s^-1) or (ii) a fast runaway and a normal field star. In the latter case one of the stars in the binary explodes and creates a fast runaway. The third star, being weakly bound to the system would hardly be affected by the explosion. In the former case the single star explodes causing the binary to start moving at the orbital speed it had within the triple system. This velocity should be small since the binary is much more massive than the third star. However, neither case would create a runaway binary-system like HIP 69491. Whereas it is likely that the star originated in either Upper Centaurus Lupus or Cep OB6, the mechanism that formed this runaway remains unknown.

6.11 HIP 76013 & Lower Centaurus Crux (star 17)

$\kappa^1$ Apodis is a B1npe emission-line star, and is the brightest component of a visual double system. This star has a radial velocity of 62 km s^-1 and is moving away from the Galactic plane. Its orbit intersects the Lower Centaurus Crux subgroup of Sco OB2 2-3 Myr ago. Because of the large difference in kinematic age and association age ($\sim$10 Myr) the BSS is the most likely explanation for the runaway nature of $\kappa^1$ Aps.

6.12 HIP 82868 & IC 2602 (star 19)

Little is known about the B3Vnpe star HIP 82868 whose orbit intersects that of the IC 2602 open cluster some 6 Myr ago. A firm identification of the formation mechanism is difficult, since we only know that the kinematic age differs from the age of IC 2602 (25 Myr). This suggests that HIP 82686 is a BSS runaway.

6.13 HIP 91599 & Perseus OB2 or Perseus OB3 (star 20)

HIP 91599 is a known runaway star (B0.5V; Vitrichenko et al. 1965); however, its parent association/cluster has never been identified. The simulations show that HIP 91599 originates from Per OB2 or Per OB3. The two associations have very different ages ($\sim$7 Myr for Per OB2 and $\sim$50 Myr for Per OB3). The kinematic age of HIP 91599 is $\sim$8 Myr and $\sim$6 Myr for Per OB2 and Per OB3, respectively. Since we lack information on the rotational velocity and the helium abundance, we are unable to conclude whether HIP 91599 is a DES runaway from Per OB2 or a BSS runaway from Per OB3.

6.14 HIP 102274 & Cepheus OB2 (star 21)

The B5 star HIP 102274 was located at the center of the Cep OB2 association between two and three Myr ago, when the association was 3-4 Myr old. This kinematic age coincides with the time of the supernova explosion proposed by Kun et al. (1987) to explain the characteristics of the Cepheus bubble, a ring-like structure of infrared emission. Taken together, this is strong circumstantial evidence for HIP 102274 being a BSS runaway.

6.15 PSR J0826+2637, PSR J1115+5030 & Perseus OB3 (pulsars 1 and 4)

The orbits of the pulsars J0826+2637 and J1115+5030 intersect that of the Per OB3 association. This group contains the $\alpha$ Persei open cluster, and is often referred to as the Cassiopeia-Taurus association (de Zeeuw et al. 1999). The simulations show that if Per OB3 is the parent of PSR J0826+2637, its kinematic age is $\sim$1 Myr and its radial velocity is $\sim$100 km s^-1. For PSR J1115+5030 we predict a kinematic age of $\sim$1.5 Myr and a radial velocity of $\sim$150 km s^-1. The characteristic ages ( $P/(2\dot{P})$) of the pulsars are 4.9 Myr and 10 Myr for PSR J0826+2637 and PSR J1115+5030, respectively. The unknown radial velocity of these pulsars makes it difficult to prove beyond doubt that these pulsars were born in the Per OB3 association. Although Fig. 2 shows that the orbits projected on the sky do not differ much for different radial velocities, and that they cross Per OB3, they may also cross the paths of other, more distant, associations or clusters not shown in the figure.

If the two pulsars orginated in Per OB3, then the initial periods would be 0.47 s for J0826+2637 and 1.53 s for J1115+5030, assuming no glitches occurred. The latter value is large, which might indicate that this pulsar travelled longer, from another site of origin.

It is not unlikely to find many pulsars associated with Per OB3 since its age, $\sim$50 Myr, is comparable to the main-sequence life-time of an 8 $M_\odot$ star. These are the least massive stars to explode as a supernova. Since the moment at which a star explodes, $\tau_{\rm SN}$, depends on its mass, ( $\tau_{\rm SN} \sim M^{-\alpha}$, where $\alpha > 0$ and $M > 8~M_\odot$) and the number of stars of mass M, N(M), also depends on the mass ( $N(M) \sim M^{-\beta}$, where $\beta > 0$), the number of supernovae increases with time ( $N_{\rm SM} \sim \tau^{\beta/\alpha}$, for $M > 8~M_\odot$). The number of supernovae, and thus the number of pulsars, will thus increase with time until the stars of $8~M_\odot$ have exploded as supernovae. Afterwards the pulsar production rate will drop to almost zero.

6.16 The Vela pulsar (pulsar 2)

PSR J0835-4510 is only $10\,000$ yr old, and therefore has not travelled far from its birth place ($\sim$9' on the sky), the Vela star-forming region at $\sim$450 pc. It lies within the boundaries of the $\sim$10 Myr old Vel OB2 association (de Zeeuw et al. 1999), which is the likely parent group.

Figure 16: Helium abundance ($\epsilon$: # relative to Hydrogen) versus rotational velocity for O stars. Left: open circles: stars with $\vert v\vert \le 30$ km s-1, filled circles: stars with |v| > 30 km s-1, stars: stars with $\pi - \sigma_\pi < 0$ mas, and asterisks: stars without Hipparcos data. Right: open circles: non-runaway stars, filled circles: runaway stars, and stars: doubtful runaways. The right of each panel display the helium abundances of stars with an unknown rotational velocity. See text for details