2 Nearby runaway stars and pulsars

The parent group is known for about a dozen "classical'' runaway stars (Paper I; Blaauw 1993). The Hipparcos Catalogue contains these stars, as well as many additional O and B stars which were known in 1982 to have large radial velocities, including 153 of the 162 runaway candidates in Hipparcos Proposal 141 (de Zeeuw et al. 1999). Many of these objects are located beyond $\sim$700 pc, where the Hipparcos parallax measurement is of modest quality. For this reason we restricted ourselves to a sample of nearby runaway stars, and added to this the (few) nearby pulsars with measured proper motions.

Figure 1: a) Histogram of the space motions of the sample of runaway stars defined in Sect. 2.1. b) Distribution of pulsars from the Taylor et al. (1993) catalogue with measured proper motions. The light grey histogram shows all pulsars within 2 kpc and the dark grey histogram shows the pulsar with accurate proper motions ( $\sigma_\mu/\mu < 0.1$). The latter, for D < 1 kpc, is the pulsar sample defined in Sect. 2.1

  
2.1 Selection of the sample

We started with all 1118 O to B5 stars in the Hipparcos Catalogue which have radial velocities listed in the Hipparcos Input Catalogue (Turon et al. 1992). Next we only considered those stars which have significant parallaxes ( $\pi - 2 \sigma_\pi > 0$ mas) and proper motions ( $\sigma_\mu / \mu \le 0.1$), and space velocities larger than 30 km s^-1 with respect to the standard of rest of the runaway. For the last requirement we corrected the runaway velocity for Solar motion and Galactic rotation (Dehnen & Binney 1997). The somewhat arbitrary choice of the velocity limit of 30 km s^-1 minimizes the contamination of the sample by normal O and B stars (Sect. 1). These criteria yield 54 runaway candidates (five of which are classical runaways). This new sample does not contain the nearby runaways $\zeta$ Oph and $\xi$ Per. The former is not selected because its space velocity is smaller than 30 km s^-1(although its velocity relative to its parent group Sco OB2 is larger, cf. Sect. 3) and the latter is not selected because $\sigma_\mu / \mu > 0.1$. However, since the runaway nature of these two stars is well established (e.g., Paper I) we included them in our sample, bringing the total to 56. The Hipparcos numbers and space velocities of these 56 stars are listed in Table 1. Panel a of Fig. 1 shows the histogram of the derived space velocities.

We selected a sample of nearby pulsars from the Taylor, Manchester & Lyne (1993) catalogue, as updated on http://pulsar.princeton.edu/. It contains 94 pulsars with known proper motions and distances. Only seven of these meet our distance (  kpc) and proper motion ( $\sigma_\mu/\mu < 0.1$) constraints (see panel b of Fig. 1). Most pulsar distances are derived from the dispersion measure. These distances are unreliable, especially for nearby objects, since they depend on the local properties of the ISM. For one nearby pulsar, PSR J0953+0755, high precision VLBA measurements became available recently (Brisken et al. 2000). We added this pulsar to our sample. The eight pulsars are listed in Table 1, together with Geminga, a nearby neutron star which is not a pulsar, for which an accurate proper motion is known (Caraveo et al. 1996).

   

Table 2: The nearby (D < 700 pc), young ($\tau < 50$ Myr), open clusters listed in the WEBDA Catalogue. The table gives the designation of the open cluster (Name), its position on the sky $(\ell ,b)$, the number of member stars contained in the Hipparcos (HIP) and Hipparcos Input Catalogues (HIC), its distance, proper motion, and radial velocity as obtained from the Hipparcos data (D, $[\mu_{\ell\ast},\mu_b]$, $v_{\rm rad}$), and whether the cluster is a candidate parent group in this study (Cand.). The candidate status is denoted by ``Y'' for the clusters with well-determined positions and velocities, by ``N'' for clusters for which not all information is available (either astrometry or radial velocity), by ``N<sup>*</sup>'' if the astrometry does not show a clear signature of an open cluster (i.e., a clump in the proper-motion vs. proper-motion diagram), or by ``?'' if the measurements are not very reliable (either because of a small number of member stars or a large spread in the data)

Name	$\ell$	b	HIP	HIC	D	$\mu_{\ell\ast}$	$\mu_b$	$v_{\rm rad}$	Cand.
	[deg.]	[deg.]	[#]	[#]	[pc]	[mas yr-1]	[mas yr-1]	[km s-1]
Collinder 359	29.75	12.54	10	-					N*
IC 4665	30.61	17.08	13	5	$385\pm40$	$-7.2\pm0.3$	$-3.0\pm0.3$	$-13.5\pm3.0$	Y
Stephenson 1	66.85	15.51	0	-					N
Roslund 5	71.40	0.25	13	-					N*
Stock 7	134.68	0.04	3	-					N*
$\alpha$ Persei	Central part of the Per OB3 association, contained in the list of de Zeeuw et al.
IC 0348	Associated with Per OB2
Collinder 69	195.05	-12.00	6	-	$\lambda$ Ori cluster				N*
NGC 1976	Trapezium cluster: associated with Ori OB1
NGC 2232	214.36	-47.65	10	3	$365\pm40$	$0.7\pm0.5$	$-5.2\pm0.5$	$14.6\pm3.0$	?
Collinder 121	Contained in list of nearby associations of de Zeeuw et al.
Collinder 140	245.18	-7.87	14	4	$375\pm40$	$-7.4\pm0.5$	$-5.5\pm0.5$	$22.4\pm3.0$	Y
Collinder 135	248.76	-11.20	19	4	$300\pm30$	$-10.3\pm0.5$	$-6.8\pm0.5$	$16.4\pm3.0$	Y
Pismis 5	259.39	0.86	0	-					N
Pismis 4	262.74	-2.37	4	0					N
Trumpler 10	Contained in list of nearby associations of de Zeeuw et al.
IC 2391	270.36	-6.88	24	13	$150\pm30$	$-33.1\pm0.5$	$-6.0\pm0.5$	$15.0\pm3.0$	Y
vdB-Hagen 99	286.56	-0.63	7	2	$500\pm50$	$-13.1\pm0.5$	$-6.4\pm0.5$	$12.0\pm3.0$	?
IC 2602	289.60	-4.90	25	8	$140\pm10$	$-20.4\pm0.5$	$1.2\pm0.5$	$24.1\pm3.0$	Y

Our sample of nearby runaway stars and compact objects is severely incomplete. The Hipparcos Catalogue is complete to V = 7.3-9 mag, with the limit depending on Galactic latitude and spectral type (2163 of the 3622 O to B5 stars have V > 7.3 mag). The data available for the O and B stars is inhomogeneous and incomplete, e.g., less than a third of the O to B5 stars in the Catalog has a measured radial velocity. We have excluded those with large $v_{\rm rad}$ but insignificant proper motions, as their retraced orbits are uncertain. The beamed nature of the radio emission from pulsars hides many from observation, and not all of those that do radiate in our direction have been found. Of these, only a few have an accurately measured proper motion and a reliable distance.

  
2.2 Nearby OB associations and open clusters

We adopt the positions and mean space motions of the OB associations within 700 pc of the Sun as derived by de Zeeuw et al. (1999) from Hipparcos measurements. For the open clusters we compiled a list from the WEBDA catalogue (http://obswww.unige.ch/webda/), and consider only those which are young ($\tau < 50$ Myr) and with distances less than 700 pc as likely parent groups. The age requirement is comparable to the age of the oldest runaways we consider here (B5V). Typical pulsar ages are less than 50 Myr (e.g., Blaauw & Ramachandran 1998). This selection yields nineteen open clusters (see Table 2), of which five are already covered in the study of the nearby associations by de Zeeuw et al. (1999). To obtain the space motion of these clusters we use the WEBDA member stars listed in the Hipparcos Catalogue to obtain reliable astrometry, and those in the Hipparcos Input Catalogue to obtain the radial velocity. In this way we are able to construct a more or less reliable space motion for seven of the fourteen remaining open clusters (those labeled "Y'' or "?'' in Table 2 which summarizes the results).

  
2.3 Orbits

Traditionally, the orbits of runaway stars have been traced back in time using straight lines through space. This is sufficiently accurate for identification of the parent group for times up to a few Myr and distances less than a few hundred pc. To make sure we include the effect of the Galactic potential, we use a fourth-order Runge-Kutta numerical integration method, with a fixed time-step of $10\,000$ yr, to calculate the orbit. The Galactic potential we use consists of (i) a logarithmic potential for the halo, (ii) a Miyamoto-Nagai potential for the disk, and (iii) a Plummer potential for the bulge of the Galaxy. The potential predicts Oort constants A = 13.5 km s^-1 kpc^-1 and B = -12.4 km s^-1 kpc^-1and a circular velocity $v_{\rm circ} = 219.8$ km s^-1 at R₀ = 8.5 kpc. These values agree with those which Feast & Whitelock (1997) obtained using Hipparcos data: $A = 14.82\pm0.84$ km s^-1 kpc^-1, $B = -12.37\pm0.64$ km s^-1 kpc^-1, $v_{\rm circ} = 231.2\pm16.2$ km s^-1 at R₀ = 8.5 kpc. Since the volume covered in the orbit integration is typically a few hundred pc, and the time of the integration is typically less than 10 Myr, perturbations of the orbits caused by small-scale structure in the disk are negligible.

Before integrating the orbit, we correct the observed velocity $\vec{v}_\ast$ for (i) the Solar motion with respect to the Local Standard of Rest, $\vec{v}_{\rm lsr}$ (Dehnen & Binney 1997), and (ii) the Galactic rotational velocity of the Local Standard of Rest, $\vec{v}_{\rm gr}$ (Binney & Tremaine 1987, p. 14). The stellar velocity $\vec{v}_{\rm gal}$ relative to the Galactic reference frame is then given by

$$\vec{v}_{\rm gal} = \vec{v}_\ast + \vec{v}_{\rm lsr} + \vec{v}_{\rm gr}.$$ (1)

To retrace the orbit, we reverse the velocity and integrate forward in time. We calculate the distance of a star as $1/\pi$, where $\pi$ is the trigonometric parallax. Since we use the individual parallax, we cannot correct this distance for possible biases (e.g., Smith & Eichhorn 1996).

2.4 Identification of parent groups

We calculate the past orbit of each of the 56 runaway stars listed in Table 1 for 10 Myr. We do this $10\,000$ times for each star, in order to sample the error ellipsoid of the measured parameters, defined by the covariance matrix of the Hipparcos astrometry and the error in the radial velocity measurement. Retracing the orbit of a pulsar is more difficult, because the radial velocity is unknown. We therefore cover a range of radial velocities of $v_{\rm rad} = 0 \pm 500$ km s^-1 in the orbit integrations for the pulsars. Figure 2 shows the positions of the runaways and pulsars on the sky, together with their orbits, retraced back for only 2 Myr so as not to confuse the diagram. Three orbits are shown for each pulsar: for $v_{\rm rad} = 0$ km s^-1 (filled square), $v_{\rm rad} = 200$ km s^-1 (open square), and $v_{\rm rad} = -200$ km s^-1 (open star).

We also retrace the orbits of the set of nearby OB associations and open clusters defined in Sect. 2.2. These groups have typical linear dimensions of 10-30 pc. We consider a group to be a possible site of origin for a runaway or pulsar if the minimum separation between the runaway/pulsar and the group was less than 10 pc at some time in the past 10 Myr. With this definition, we find a parent group for 21 of the 56 runaways. These stars are indicated by the filled circles in Fig. 2, and include the seven classical runaways in the sample. We discuss them in detail in Sects. 3-6 below. Six of the nine neutron stars possibly traversed one of the nearby stellar groups; these are PSR J0826+2637, PSR J0835-4510, PSR J1115+5030, PSR J1239+2453, PSR J1932+1059, and Geminga (objects 1, 2, 4, 6, 8, and 9 in Fig. 2). We discuss them in Sects. 3 and 6, and identify the parent group for four of them. Table 3 summarizes the data for the 22 runaways, four pulsars, and Geminga. The pulsars and runaways for which we cannot identify a parent group are discussed further in Sect. 7.

Figure 2: Top: Sample of runaway stars defined in Sect. 2.1, in Galactic cordinates. The open circles denote the present positions of the runaways, and the arcs show their past orbits, calculated for 2 Myr. The filled circles are the runaways for which we can identify the parent association. The numbers refer to the entries in Table 3. The asterisks indicate two additional runaways (72 Col, HIP 94899 [left most of the two asterisks]) discussed in Sect. 7. The grey fields outline the nearby OB associations (de Zeeuw et al. 1999). From left to right and from top to bottom: Per OB3 ($\alpha$ Persei), Per OB2, Cep OB3, Cep OB2, Cep OB6, Lac OB1, Upper Scorpius, Upper Centaurus Lupus, Lower Centaurus Crux, Tr 10, Vel OB2, Col 121, and Ori OB1. The open clusters are identified by the filled light-grey circles for those with reliable positions and velocities, and by the open, crossed circles for the remaining clusters. The positions and designations of the clusters can be found in Table 2. Bottom: Pulsar sample defined in Sect. 2.1, in Galactic coordinates. The filled circles indicate the present positions of the pulsars. The past orbits of pulsars, calculated for 2 Myr, are shown for three different assumed radial velocities: 0 km s-1 (filled squares), 200 km s-1 (open squares), -200 km s-1 (open stars). The pulsars are labeled 1 through 8; 1: J0826+2637, 2: J0835-4510 (Vela pulsar), 3: J0953+0755, 4: J1115+5030, 5: J1136+1551, 6: J1239+2453, 7: J1456-6843, 8: J1932+1059. Number 9 is the neutron star Geminga. The associations and open clusters typically move comparatively little in 2 Myr