5 53 Ari, $\xi$ Per, $\zeta$ Pup, and $\lambda$ Cep

The previous sections gave a specific example of each formation mechanism for runaway stars, and described our orbit retracing methods in detail. We now consider the three other classical runaways, as well as $\zeta$ Pup, and we discuss the likely formation mechanisms. The results are summarized in Table 5.

5.1 53 Arietis & Orion OB1 (star 2)

Blaauw (1956) classified 53 Arietis (HIP 14514) as a runaway star based on its proper motion which is directed away from the Orion association. He deduced that 53 Ari left the Orion association $\sim$4.8 Myr ago and predicted the radial velocity of the star (at that time unknown) to be $\sim$18 km s^-1. The discrepancy in kinematic ages of AE Aur and $\mu$ Col (Sect. 4) and that of 53 Ari indicates that it is not related to the same event that created AE Aur and $\mu$ Col (Sect. 4) but is another runaway from the Orion star-forming region. Table 3 lists the observables of 53 Ari.

Figure 12: Predicted distance ( left) and kinematic age ( right) of 53 Arietis as a function of the distance of the parent association: Ori OB1 subgroup a ( top), Ori OB1 subgroup b ( middle), and Ori OB1 subgroup c ( bottom). The Hipparcos distance and its 1$\sigma$ error are indicated in the left panels. Distance estimated by Warren & Hesser (1977a, 1977b, WH77), Brown et al. (1994, B94), and de Zeeuw et al. (1999, Z99) are indicated in the middle panels

The Ori OB1 association has four subgroups: a, b, c, and d (Blaauw 1964; Brown et al. 1994). We do not consider subgroup d (the Trapezium) as a possible parent group of 53 Ari, since this subgroup is younger than the runaway (Sect. 4). The ages of the other subgroups are: 8-12 Myr for subgroup a, 2-5 Myr for subgroup b, and $\sim$4 Myr for subgroup c (Warren & Hesser 1977a, 1977b; Brown et al. 1994).

Simulations

We performed a set of simulations as in Sect. 2, retracing orbits for each subgroup (a, b, c). The kinematic age of 53 Ari from subgroup a is $\sim$4.3 Myr (Fig. 12). This means that the subgroup was $\sim$6 Myr old when 53 Ari became a runaway star. This very likely rules out the DES as the formation mechanism (see Sect. 1). However, there is little direct evidence in favor of the BSS. The helium abundance of 53 Ari is unknown and its observed rotational velocity is small ( $v_{\rm rot} \sin i = 10$ km s^-1), but this could be caused by a near pole-on orientation. We did not find a neutron star associated with 53 Ari, but our sampling of the nearby compact objects is severely limited (Sect. 2.1).

If subgroup b is the parent association the kinematic age for 53 Ari is $\sim$4.8 Myr. This is comparable to the canonical age of the subgroup, and excludes the BSS as a production mechanism for 53 Ari (see Sect. 1). If Ori OB1 b is the parent group of 53 Ari then the kinematic age is $\sim$4.8 Myr and the formation mechanism is most likely the DES. However, the most recent age determination (Brown et al. 1994) gives $1.7\pm1.1$ Myr. If Ori OB1 b is indeed this young then the subgroup is younger than 53 Ari and cannot be the parent group.

For subgroup c we find that the minimum separation between the subgroup centre and the runaway was never smaller than 15 pc, while the simulations for the other two subgroups a and b yield minimum separations as small as 1 pc. The space motion of Ori OB1 is mostly directed radially away from the Sun, and the proper motion component is relatively small. The Hipparcos data did not allow de Zeeuw et al. (1999) to discriminate between the different subgroups in their selection procedure; they only give one proper motion and radial velocity for the whole Orion complex. It is possible that subgroup c has a motion that differs slightly from that of the other two subgroups, so that it cannot be ruled out as a candidate parent group. The age of subgroup c, $\sim$5 Myr, is similar to the kinematic age of 53 Ari. By the argument given above this suggests that if Ori OB1 c is the parent association of 53 Ari, then the formation mechanism is most likely the DES.

In order to decide which of the Ori OB1 subgroups is the parent group of 53 Ari, we need to know the distances and velocities of the subgroups and the runaway star with a better accuracy than is now available. Figure 12 could then be used to pin down the parent group, and the mechanism which is responsible for the runaway nature of 53 Ari. Since subgroup a is the only one for which the BSS is indicated, finding a pulsar originating from subgroup aat the same time as 53 Ari would also clinch the issue.

5.2 $\xi$ Persei & Perseus OB2 (star 3)

The O7.5III star $\xi$ Persei (HIP 18614) lies within the boundary of the Per OB2 association on the sky. This positional coincidence, and the low density of early-type stars near Per OB2, led Blaauw (1944) to propose $\xi$ Per as a member of the association. At that time it was thought that the large radial-velocity difference between $\xi$ Per and Per OB2 ($\sim$40 km s^-1) was due to uncertainties in the measurement of $v_{\rm rad}$ for $\xi$ Per. However, when the radial velocity of $\xi$ Per was confirmed, its membership of the Per OB2 association became doubtful (Blaauw 1952a). In Paper I, Blaauw classified $\xi$ Per as a runaway star from the Per OB2 association, which naturally explains the discrepancy of the radial velocity of the star and the association. $\xi$ Per was the first star to be classified as runaway based on its $v_{\rm rad}$ alone. Most other runaways were recognized because their proper motions were directed away from an association. The parent group, Per OB2, has an age of $\sim$7 Myr (e.g., Seyfert et al. 1960; de Zeeuw & Brand 1985).

Data

We adopt $v_{\rm rad}=58.8$ km s^-1 for $\xi$ Per (Bohannan & Garmany 1978; Garmany et al. 1980; Stone 1982; Gies & Bolton 1986). This value differs by 10 km s^-1 from those quoted in the Hipparcos Input Catalogue (67.1 km s^-1, Turon et al. 1992) and the WEB catalogue (70.1 km s^-1, Duflot et al. 1995), which derive from the value listed in the General Catalogue of Radial Velocities (70.1 km s^-1, Wilson 1953). We take the radial-velocity error to be 5 km s^-1; this is equal to the amplitude of the velocity variations induced by the non-radial pulsations of $\xi$ Per (de Jong et al. 1999). The rotational velocity and helium abundance are $v_{\rm rot} \sin i = 200$ km s^-1 and $\epsilon = 0.18$, respectively (see also Table 3).

Figure 13: Predicted distance ( left) and kinematic age ( right) of $\xi$ Per as a function of the distance of Per OB2. The Hipparcos distance and its 1$\sigma$ error are indicated in the left panel. Distance estimates for Per OB2 by Klochkova & Kopylov (1985, KK85), Cernis (1993, C93), and de Zeeuw et al. (1999, Z99) are indicated in the middle panel

Simulations

Our orbit calculations (Sect. 2) show that the kinematic age of $\xi$ Per is $\sim$1 Myr (Fig. 13). At that time the star was located $\sim$5 pc from the center of Per OB2, well inside the association. Figure 13 also shows that the present distance of the runaway is 360 pc, assuming 318 pc as the distance of Per OB2 (de Zeeuw et al. 1999). This distance for $\xi$ Per is consistent with the Hipparcos parallax at the 2$\sigma$ level.

We infer that the BSS is responsible for the runaway nature of $\xi$ Per based on (i) the 6 Myr age of Per OB2 at the time that $\xi$ Per was ejected, (ii) the high helium abundance of $\xi$ Per, (iii) its blue straggler nature (Sect. 9), and (iv) the large rotational velocity (see Sect. 1). Further evidence of a supernova explosion in the Per OB2 association is provided by a shell structure containing HI, dust, OH, CH, and other molecules (Sancisi 1970; Sancisi et al. 1974). This feature has been interpreted as a supernova shell which is physically connected to the Per OB2 association. We have not found a pulsar counterpart.

$\xi$ Per presently illuminates the California Nebula (NGC 1499), resulting in an HII emission region. The distance of this nebula is hard to determine (350-525 pc; Bohnenstengel & Wendker 1976; Sargent 1979; Klochkova & Kopylov 1985; Shull & van Steenberg 1985), but must be similar to that of $\xi$ Per, i.e., $\sim$360 pc.

5.3 $\zeta$ Puppis, Vela R2, Vela OB2 & Trumpler 10 (star 10)

The O4I star $\zeta$ Puppis (HIP 39429) is the brightest and nearest single O star to the Sun. Its location outside any known association and its large space velocity ($\sim$60 km s^-1) led Upton (1971) to propose $\zeta$ Pup as a runaway star. In spite of the many groups of young, massive stars in the direction of $\zeta$ Pup, Upton could not make a unique identification of the parent association. He proposed Vel OB2 as the most likely candidate. In a recent study of the stars and ISM in the direction of Vela, Sahu (1992) proposed the R association Vel R2 as a possible parent for $\zeta$ Pup, based on the retraced path of the runaway on the sky. For our simulations we considered Vel OB2, Vel R2, the open cluster NGC 2391, and the cluster/association Tr 10 (de Zeeuw et al. 1999) which also lies in the same direction as Vel R2.

Data

Table 3 summarizes the data for $\zeta$ Pup. The position and velocity for the associations Vel OB2 and Tr 10 are adopted from de Zeeuw et al. (1999). Only two of the Vel R2 members are contained in the Hipparcos Catalogue. Their distances, 411_-143⁺⁴⁷³ (HIP 43792) and 294_-61⁺¹⁰⁷ (HIP 43955), have large uncertainties or do not agree well with the canonical distance of Vel R2, $\sim$870 pc (Herbst 1975). We are therefore unable to obtain meaningful phase-space coordinates of Vel R2.

Simulations

Although we are unable to run our simulations for Vel R2, we conclude that it is not a likely candidate parent association for $\zeta$ Pup. The distance difference between Vel R2 ($\sim$870 pc) and $\zeta$ Pup $(\sim$400 pc, its canonical distance) is too large. The relative radial velocity between the star and association is $\sim$40 km s^-1 ( $v_{\rm rad, \zeta~Pup} = -23.9$ km s^-1 and $v_{\rm rad, Vel~R2} \sim 20$ km s^-1). The differences in distance, $\sim$400 pc, and velocity, $\sim$40 km s^-1, between $\zeta$ Pup and Vel R2 yield a kinematic age of $\sim$10 Myr. This is older than the expected life time of $\zeta$ Pup (van Rensbergen et al. 1996). Hence Vel R2 is not likely to be the parent group.

Our simulations also show that Vel OB2 is not the parent association. The minimum separation between the association and the runaway star is never smaller than 40 pc for reasonable association distances. Since the association radius is, at maximum, 30 pc, we conclude that $\zeta$ Pup has never been inside the boundaries of Vel OB2. We similarly rule out NGC 2391 as parent group.

Figure 14: Predicted distance ( left) and kinematic age ( right) of $\zeta$ Pup as a function of the distance of Tr 10. The Hipparcos distance and its 1$\sigma$ error are indicated in the left panel. The distance estimate by de Zeeuw et al. (1999, Z99) is indicated in the middle panel

The simulations for the Trumpler 10 group result in minimum separations of $\ge$10 pc. The inferred kinematic age is $\sim$2 Myr (Fig. 14). Ten parsec is comparable to the radius of Tr 10, so we cannot unambiguously identify or exclude it as the parent association. Furthermore, if $\zeta$ Pup was in or near Tr 10, then its current distance must be 250-350 pc (Fig. 14), which is smaller than the canonical distance of 400 pc.

The Vela region contains many young stellar clusters, and suffers from a fair amount of extinction (although $\zeta$ Pup itself is almost unreddened). It is therefore reasonable to assume that we have not yet identified the parent group of $\zeta$ Pup. Similar conclusions were obtained by Vanbeveren et al. (1998), and Vanbeveren, De Loore & Van Rensbergen (1998).

Figure 15: Predicted distance ( left) and kinematic age ( right) of $\lambda$ Cep as a function of the distance of Cep OB3. The Hipparcos distance and its 1$\sigma$ error are indicated in the left panel. The distance estimate by Crawford & Barnes (1970, CB70) is indicated in the middle panel

5.4 $\lambda$ Cephei, Cepheus OB2 & Cepheus OB3 (star 22)

$\lambda$ Cep (HIP 109556) was first classified as a runaway star by Blaauw (Paper I). He noted that its position on the sky, the direction of the proper motion, and the radial velocity were consistent with an origin in the association Cep OB2 (see, e.g., Fig. 22 in de Zeeuw et al. 1999). This luminous supergiant (O6I(n)f) is located below Cep OB2 (in Galactic coordinates) and is traveling away from the Galactic plane and Cep OB2. Several other stellar groups are located near Cep OB2, and of these, Cep OB3 may also be a possible parent of $\lambda$ Cep. We consider both associations.

Data

The data for $\lambda$ Cep are given in Table 3. The phase-space coordinates of Cep OB2 are adopted from de Zeeuw et al. (1999). Unfortunately, the Hipparcos data did not allow these authors to obtain meaningful results for Cep OB3 which is at a distance of $\sim$730 pc (Crawford & Barnes 1970). To estimate the phase-space coordinates of Cep OB3 we used the mean position, proper motion, and radial velocity for the Cep OB3 members of Blaauw et al. (1959): $(\ell,b) = (110\hbox{$.\!\!^\circ$ }50,2\hbox{$.\!\!^\circ$ }91)$; $(\mu_{\ell\ast},\mu_b) = (-2.72 \pm 0.28,-1.78\pm 0.30)$ mas yr^-1; $v_{\rm rad} = -17.4 \pm 3.0$ km s^-1.

Simulations

The orbit calculations show that Cep OB2 cannot be the parent group of $\lambda$ Cep. The simulations do result in small minimum separations between the two, but only for $D_{\lambda~{\rm Cep}} \sim 250$ pc and a kinematic age of $\sim$9 Myr. These values do not agree with the observed photometric (860 pc, Gies 1987) and trigonometric distances ( 505_-95⁺¹⁵³ pc, Hipparcos) of $\lambda$ Cep, nor with the age of the association (5-7 Myr, de Zeeuw et al. 1999). Moreover, $\lambda$ Cep is a massive O supergiant, and its lifetime cannot be more than a few million years.

When we run the simulations using Cep OB3 as the parent group we also obtain minimum separations <10 pc. Figure 15 shows that the expected distance of the runaway is now $\sim$450 pc and that the kinematic age is $\sim$4.5 Myr. This is a little on the large side for the nominal lifetime of a 40 $M_\odot$ star, but might not be impossible. Cep OB3 consists of two subgroups with ages of 5.5 (subgroup b) and 7.5 Myr (subgroup a) (e.g., Jordi et al. 1996). Considering the high helium abundance and large rotational velocity of $\lambda$ Cep, subgroup a is a likelier parent of the runaway than subgroup b, since the age difference between the subgroup and the runaway is 3 Myr for a. For subgroup b this is only 1 Myr, leaving little time for binary evolution. We conclude that $\lambda$ Cep is likely to have become a runaway star as the result of a supernova explosion in a binary system in subgroup a of Cep OB3 $\sim$4.5 Myr ago.