Tracing the runaway orbits back in time provides, for the first time, direct evidence that both scenarios produce single runaway stars (Hoogerwerf et al. 2000). The orbit calculations demonstrate that the runaway $\zeta$ Oph and the progenitor of PSR J1932+1059 once formed a binary system in the Upper Scorpius association, and that the neutron star acquired a kick velocity of $\sim$ 350 km s^-1 in the supernova explosion. The runaways AE Aur and $\mu$ Col, and the binary $\iota$ Ori were involved in a dynamical interaction (a binary-binary collision) $\sim$ 2.5 Myr ago, which took place in the Trapezium cluster.

**Table 5:** Parent associations, kinematic ages ( $\tau_0$ ) and formation mechanisms of the runaways and neutron stars discussed in this paper. For runaway stars which have more than one possible parent we give the results for the individual parent associations/clusters. The last column indicates the number of the runaway/pulsar in Fig. 2. Abbreviations: US: Upper Scorpius; UCL: Upper Centaurus Lupus; LCC: Lower Centaurus Crux; BSS: binary supernova scenario; DES: dynamical ejection scenario
HIP	Name	Parent	$\tau_0$	Origin	Fig. 2
			[Myr]
3881	$\nu$ And	Lacerta OB1 b	9.0	DES	1
14514	53 Ari	Orion OB1 a	4.3	BSS	2
		Orion OB1 b	4.8	DES	2
		Orion OB1 c	5.0	DES	2
18614	$\xi$ Per	Perseus OB2	1.0	BSS	3
22061		$\lambda$ Ori SFR	1.1	DES	4
24575	AE Aur	Trapezium	2.5	DES	5
27204	$\mu$ Col	Trapezium	2.5	DES	6
29678		$\lambda$ Ori SFR	1.1	DES	7
38455		Collinder 135	3.0	BSS	8
38518		Vela OB2	6.0	BSS	9
39429	$\zeta$ Pup	?			10
42038		UCL	8.0	BSS	11
		IC 2391	6.0	BSS	11
46950		IC 2602	2-10	BSS	12
48943		LCC	4.0	BSS	13
49934		IC 2391	3.0	BSS	14
		IC 2602	6.0	BSS	14
57669		IC 2602	3.0	BSS	15
69491		UCL(?)	3.0	?	16
		Cepheus OB6(?)	10.0	?	16
76013	$\kappa^1$ Aps	LCC	2.5	BSS	17
81377	$\zeta$ Oph	US	1.0	BSS	18
82868		IC 2602	6.0	BSS	19
91599		Perseus OB2	8.0	DES	20
		Perseus OB3	6.0	BSS	20
102274		Cepheus OB2	2.5	BSS	21
109556	$\lambda$ Cep	Cepheus OB3	4.5	BSS	22

	J0826+2637	Perseus OB3	1.0	?	1
	J0835-4510	Vela OB2	0.01	?	2
	J1115+5030	Perseus OB3	1.5	?	4
	J1932+1059	US	1.0	BSS	8
	Geminga	$\lambda$ Orionis	0.35	?	9

The current investigation is biased towards finding BSS runaways. This is mainly due to the fact that the accuracy of the available data, and our knowledge of the location and motions of star-forming regions, restrict the study to $\sim$ 700 pc. The small volume implies that we are only able to identify runaway stars with small kinematic ages of 0-10 Myr (i.e., runaways which recently left their parent association). Runaways which were created at an earlier time have most likely traveled outside our sample limits. Since associations and open clusters can create BSS runaways during $\sim$ 50 Myr (approximately the lifetime of a $8~M_\odot$ star) and DES runaways only in the inital stages when the group still has a high density, we expect to find more BSS than DES runaways because there are relatively many more old parents than young parents in the Solar neighbourhood. This bias is somewhat weakened by the fact that most dynamical interactions produce two runaway stars while the binary-supernova mechanism produces only one.

The creation of runaway stars modifies the mass function of the parent group at the high-mass end, where the total number of stars is small. For example, the encounter in Orion described in Sect. 4 removed four stars with a total mass of order 70 $M_\odot$ from the Trapezium cluster, while only six stars more massive than 10 $M_\odot$ remain. Derivation of the initial mass function of young stellar groups from the present-day mass function without accounting for the associated runaway stars leads to erroneous results.

Our Hipparcos-based study has identified 56 runaway stars within 700 pc from the Sun, and tripled the subset of these for which a parent group is known (from 6 to 21). As mentioned in Sect. 2, less than a third of the O-B5 stars in the Hipparcos Catalog have a measured radial velocity. Obtaining these is likely to result in another factor of three increase in the size of the sample, so that statistical studies become possible.

The next major step in our understanding of the origin of runaway stars will come when large datasets of micro-arcsecond ( $\mu$ as) astrometry and accurate radial velocities (1-2 km s^-1) become available. Distances accurate to a few parsec will allow for a final confirmation or rejection of the genetic link between runaways and their parents (e.g., Fig. 12). These data will become available over the next two decades with the launches of several astrometric satellites (FAME, SIM, GAIA). These aim to obtain $\mu$ as astrometry for a large number of stars, from $10\,000$ stars with SIM to 1 billion stars with GAIA. Besides astrometry, accurate radial velocities are also required; unfortunately, there is no dedicated effort to obtain these for a large number of O and B stars.

The BSS and DES can produce runaway stars with spectral types beyond B5 (e.g., Kroupa 2000b; Portegies Zwart 2000). These will be harder to find, as the velocity distribution of the later-type stars in the Galactic disk is broader than for the O-B5 stars, and the fractional production of low-mass runaways is small. Identifying their parent groups is also harder, because these stars may have traveled for much longer times. However, $\mu$ as accuracy astrometry complemented with accurate radial velocities will undoubtedly reveal such objects, and will provide further constraints on the binary fraction and the binary mass-ratios in open clusters and associations.

$\begin{figure}\includegraphics[angle=0.0, width=14cm, clip=true, keepaspectratio=true]{10198_figa1.eps} \end{figure}$

Figure A1: Left to right: The distribution of absolute differences between two observable quantities, $\Delta$ , in one ( $F_{\rm 1D}$ ), two ( $F_{\rm 2D}$ ), and three ( $F_{\rm 3D}$ ) dimensions, taking into account the measurement errors. Top: $\mu = 0$ , 1, 2, and 3 are represented by the solid, dotted, dashed, and dot-dashed lines, $\sigma$ is indicated in the top right of each panel. Bottom: $\sigma = 1$ , 2, 3, and 4 are represented by the solid, dotted, dashed, and dot-dashed lines, $\mu$ is indicated in the top right of each panel

Figure 1b shows that there are 19 additional pulsars within one kpc for which an accurate proper motion is not available. A systematic program to measure these might allow the detection of more examples of pairs such as $\zeta$ Oph and PSR J1932+1059. It would also improve the characterisation of the pulsar population as a whole. VLBI techniques hold the promise of achieving sub-mas astrometry (positions, proper motions, and parallaxes) in the near future.

10 Concluding remarks