A catalogue of young runaway Hipparcos stars within 3 kpc from the Sun

Abstract

1 INTRODUCTION

Almost 50 years ago, Blaauw (1961) found that many O- and B-type stars show large peculiar space velocities (>40 km s⁻¹). For this reason, they were assigned the term ‘runaway’ stars. Many studies concerning O- and B-type runaway stars have been published since then, covering different selection methods (e.g. Vitrichenko, Gershberg & Metik 1965; Cruz-González et al. 1974; Gies & Bolton 1986; Stone 1991; Moffat et al. 1998).

The following two theories on the formation of runaway stars are accepted.

• The binary supernova (SN) scenario (BSS; Blaauw 1961) is related to the formation of high-velocity neutron stars. The runaway and the neutron star are the products of a SN within a binary system. The velocity of the former secondary (the runaway star) is comparable to its original orbital velocity. Runaway stars formed in the BSS share typical properties, such as enhanced helium abundance and a high rotational velocity as a result of mass and angular momentum transfer during binary evolution. The kinematic age of the runaway star is smaller than the age of its parent association.

• In the dynamical ejection scenario (DES; Poveda, Ruiz & Allen 1967) stars are ejected from young, dense clusters via gravitational interactions between the stars. The (kinematic) age of a DES runaway star should be comparable to the age of its parent association, as gravitational interactions occur most efficiently soon after formation.

Which scenario is dominating is still under debate; however, both are certainly taking place (one example for each identified by Hoogerwerf, de Bruijne & de Zeeuw 2001: BSS, PSR B1929+10/ζ Oph; DES, AE Aur/μ Col/ι Ori).

The selection criteria for runaway stars of previous studies were either based on spatial velocities (e.g. Blaauw 1961), tangential velocities (e.g. Moffat et al. 1998) or radial velocities (e.g. Cruz-González et al. 1974) alone. According to Stone (1979), the velocity distribution of early-type stars can be explained with the existence of two different velocity groups of stars: a low-velocity group containing normal Population I stars and a high-velocity group containing the runaway stars (see, for example, Fig. 1). Because both groups obey a Maxwellian velocity distribution, runaway stars with relatively low velocities also exist. We want to combine previous methods in order not to miss an important star because the radial velocity may be unknown (hence no spatial velocity) or its tangential or radial velocity component may be significantly larger than the other component (hence it would be missed in one direction). Moreover, we also want to identify lower-velocity runaway stars by searching for stars that were ejected slowly from their parent cluster. Furthermore, we want to use the term ‘runaway’ star not only for O- and B-type runaway stars but also for all young (up to ≈50 Myr) runaway stars, to account for the possibility of less massive companions of massive stars (which, soon after formation, explode in a SN) and low-mass stars in young dense clusters, which also may be ejected as a result of gravitational interactions.

Figure 1

Distribution of the peculiar 3D space velocity v_pec (shaded histogram). The dashed and dash-dotted curves show the distribution for the low-velocity and high-velocity groups, respectively. The two curves intersect at v_pec = 28 km s⁻¹. The total distribution as the sum of the two is represented by the solid line. Considering that different moving groups and associations of stars are present, and thus both the low-velocity and high-velocity groups of stars might actually be better represented by a superposition of many Maxwellians with slightly different parameters, the fit (χ²_red = 1.57) is satisfactory.

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In Section 2, we describe the selection procedure of our sample of young stars. In Section 3, we apply different identification methods for runaway stars and assign runaway probabilities to each star. A catalogue containing our results is available via VizieR. We give a summary and draw our conclusions in Section 4.

2 SAMPLE OF YOUNG STARS

We start with all stars from the Hipparcos catalogue (Perryman et al. 1997), 118 218 in total, and collect spectral types as well as V magnitudes and B−V colours from the catalogue. According to the errata file provided with the Hipparcos catalogue, we correct erroneous spectral types. From the new Hipparcos reduction (van Leeuwen 2007), we obtain parallaxes (π) and proper motions (μ*_α=μ_α cos δ, μ_δ). We restrict our star sample to lie within 3 kpc from the Sun (π−σ_π≥ 1/3 mas with σ_π being the 1σ error on π).1 Furthermore, we remove stars in the regions of the Large and Small Magellanic Clouds having accidentally π−σ_π≥ 1/3 mas (cf. Hohle, Neuhäuser & Schutz 2010). This gives us an initial set of 103 217 stars.

In the cases where the Hipparcos catalogue does not provide sufficient spectral types, we take the spectral type from either the Simbad or VizieR data bases (Garmany, Conti & Chiosi 1982; Buscombe & Foster 1999; Grenier et al. 1999; Wright et al. 2003; Bobylev, Goncharov & Bajkova 2006; Abrahamyan 2007; Kharchenko et al. 2007; Kharchenko & Roeser 2009; Skiff 2009). Missing B−V colours were amended from different sources (Simbad; available via VizieR: Egret et al. 1992; Wright et al. 2003; Kharchenko, Piskunov & Scholz 2004; Kharchenko et al. 2007; Zacharias et al. 2005; Bobylev, Goncharov & Bajkova 2006).

Having now collected parallaxes and spectral types as well as V magnitudes and B−V colours, we calculate luminosities (L) and obtain effective temperatures (T_eff) from spectral types according to Schmidt-Kaler (1982) and Kenyon & Hartmann (1995). The extinction A_V is determined from the apparent B−V colour and the spectral type.2 The initial sample contains 1721 stars also included in the list of Hohle et al. (2010), who used additional colours to determine L. Thus, for these stars, we adopt their luminosities (without the Smith–Eichhorn correction).

For having full kinematics, we obtain radial velocities from Simbad or the following VizieR catalogues: Zwitter et al. (2008), Kharchenko et al. (2007, 2004), Bobylev et al. (2006), Gontcharov (2006), Malaroda, Levato & Galliani (2006), Karatas et al. (2004), Barbier-Brossat & Figon (2000), Grenier et al. (1999), Reid, Hawley & Gizis (1995), Hawley, Gizis & Reid (1996) and Evans (1967).

2.1 Age and mass determination

Because we are looking for young stars, our first goal is to obtain star ages. For this reason, we have checked our star sample for pre-main-sequence stars and have found 236 of these either in catalogues (The, de Winter & Perez 1994; Kenyon & Hartmann 1995; Neuhäuser et al. 1995; van den Ancker et al. 1997; Bertout, Robichon & Arenou 1999; Köhler et al. 2000; Neuhäuser et al. 2000; Teixeira et al. 2000; Valenti, Fallon & Johns-Krull 2003; Ducourant et al. 2005; Hernández et al. 2005; Wichmann et al. 1997; Chauvin et al. 2010) and/or fulfilling the lithium criterion from Neuhäuser (1997) (for individual stars, see also White, Jackson & Kundu 1989; Jeffries 1995; Favata, Micela & Sciortino 1997; Micela, Favata & Sciortino 1997; Tagliaferri et al. 1997; Gaidos 1998; Neuhäuser & Brandner 1998; Soderblom, King & Henry 1998; Webb et al. 1999; De Medeiros et al. 2000; Gaidos, Henry & Henry 2000; Strassmeier et al. 2000; Teixeira et al. 2000; Torres et al. 2000; Zuckerman & Webb 2000; Lawson et al. 2001; Montes et al. 2001; Zuckerman et al. 2001; Cutispoto et al. 2002; Neuhäuser et al. 2002; Song, Bessell & Zuckerman 2002; König 2003).

For the 236 pre-main-sequence stars in the sample, we used pre-main-sequence evolutionary models from D'Antona & Mazzitelli (1994, 1997), Bernasconi (1996), Baraffe et al. (1998), Palla & Stahler (1999), Siess, Dufour & Forestini (2000), Maeder & Behrend (2002) and Marques, Monteiro & Fernandes (2008)3 to estimate their masses and ages.

For main-sequence and post-main-sequence stars, we used evolutionary models starting from the zero-age main sequence (ZAMS) from Schaller et al. (1992), Claret (2004), Pietrinferni et al. (2004),4Bertelli et al. (2008, 2009) and Marques et al. (2008). For stars on or above the ZAMS, all models yield masses and ages based on luminosity and effective temperature. Stars that lie below the model ZAMS (mainly as a result of large uncertainties in the parallax, and thus in the luminosity) are shifted towards the ZAMS, and hence will be treated as ZAMS stars. For early-type stars, this has no effect on the age selection (see equation 1) because they are younger than 50 Myr even if their actual positions in the Hertzsprung–Russel diagram (HRD) are above the ZAMS. For most mid-F to mid-G stars, age determination is difficult and the error on the age is larger than the age value itself (expressing the time the star would evolve without moving in the HRD). Thus, these do not enter our list of young stars because of our age criterion (see equation 1). Even later late-type stars (later than mid-G) are already older than 50 Myr on the ZAMS.

We have used solar metallicity for all 101 628 stars in our sample with known magnitudes and spectral types; we have obtained masses and ages from luminosities and temperatures. For stars with unknown luminosity class, we adopt luminosity class V.5 For some stars where the spectral type is also uncertain to ±5 subtypes, we calculate masses and ages for all spectral subtypes (e.g. for a G star, G0 to G9) to derive the mean and the standard deviation of mass and age. We define a star to be ‘young’ if its age is ≤50 Myr. This limit is set for the following reason arising from the BSS formation scenario of runaway stars (Section 1): it is desirable to identify the (now isolated) neutron star, which was formed in the SN that released the runaway star. This would also yield the runaway's origin. For neutron stars, the radial velocity is unknown, and thus must be treated with a probability distribution (Tetzlaff et al. 2010). For this reason, the error cone of the spatial motion is large and the position of a neutron star can be determined reliably only for a few million years, optimistically ≈5 Myr. This is the maximum runaway time (the kinematic age) of the runaway star (as well as the neutron star) such that the neutron star could be identified. The latest spectral type on the main sequence for stars to explode in a SN and eventually become a neutron star is B3. These stars live about 35 Myr before they end their lives in SNe. We allow for an uncertainty of 10 Myr and find the maximum star age (not the kinematic age) of the BSS runaway for which the associated neutron star should still be identifiable to be ≈50 Myr. Despite this, a larger age would mean a longer time-span to trace back the star to identify its origin (if it is a DES runaway). This would cause large error bars on the past position of the runaway star, which would make it less reliable to find the origin.

However, star ages often suffer from large uncertainties because of large errors in distances and strong uncertainties in evolutionary models. This is why we have chosen the following criterion on the star age τ_★ (the median from all evolutionary models applied) for a star to be young within our definition:

1

where σ_τ,★ is the median deviation of τ_★ for different models. With this criterion, we allow for an error of τ_★, which is of the order of τ_★ itself but also exclude stars with accurately known ages above our limit of 50 Myr. Unfortunately, ages of supergiants are uncertain and we miss many of them when applying the criterion. For this reason, we add all stars of luminosity classes I and II as well as stars of luminosity class III earlier than A0 because they could certainly be younger than 50 Myr. Moreover, the classical definition of runaway stars by Blaauw (1961) includes stars up to B5 of luminosity classes IV and V. These are added as well. Finally, our sample contains 7663 young stars. Their Hipparcos numbers and common names as well as ages, masses and spectral types are listed in Table 1 (the full table is given as Supporting Information, and is available via the VizieR data base). Since 2250 stars in the table enter our list only because of their spectral type and luminosity class, we list only their spectral type and luminosity class as given in the literature.

2.2 Kinematics

The solar motion with respect to a specific star sample, that is, the local standard of rest (LSR), depends upon the age of the stars in the sample (e.g. Mihalas & Binney 1981). For this reason, we derive the kinematic centre of the stars in our sample as follows. We calculate the spatial velocity components of the 4195 stars with complete kinematic data (in a right-handed coordinate system with the x-axis pointing towards the Galactic Centre and y positive in the direction of galactic rotation) corrected for Galactic differential rotation using Keplerian orbits:

2

Here, U, V and W are the heliocentric velocity components (in the x, y and z directions, respectively) and U_rot and V_rot are the components of the rotational velocity of the star moving around the Galactic Centre. V_⊙,rot = 225 km s⁻¹ is the rotational velocity of the Sun around the Galactic Centre. To avoid significant contamination of high-velocity stars, we exclude stars with (i.e. approximately two times the median of ⁠).

Fitting a Gaussian to each velocity component, we find

3

The agreement of our LSR with the classical value of Delhaye (1965) [(9, 11, 6) km s^-1] is remarkable. In comparison with the most recent value published by Aumer & Binney (2009) [(9.96 ± 0.33, 5.25 ± 0.54, 7.07 ± 0.34) km s^-1], the V component differs significantly. However, Aumer & Binney (2009) obtained their results by examining the correlation between LSR and colour B−V (i.e. star age), extrapolating the curves to zero velocity dispersion and also ignoring stars with B−V≤ 0 (see also Dehnen & Binney 1998) because these are probably not yet mixed. Such stars are overabundant in our sample of young stars. From fig. 3 in Dehnen & Binney (1998), we can easily see that our result agrees well with their findings.

In the following section, we use equation (3) to correct the velocities for solar motion. The peculiar velocity is the velocity of a star corrected for solar motion and Galactic rotation.

3 YOUNG RUNAWAY STARS

Classically, a star was assigned to be a runaway star if its peculiar space velocity v_pec exceeded 40 km s⁻¹ (Blaauw 1961). Since then, Vitrichenko et al. (1965) and Cruz-González et al. (1974) have used radial velocities v_r alone to investigate the population of runaway stars, defining a more general definition of |v_r,pec| > v_crit,1D with v_crit,1D = 3σ, where σ is the mean velocity dispersion in one dimension of low-velocity stars. Based on this definition, Moffat et al. (1998) have investigated tangential velocities v_t to identify runaway stars. We now want to combine and extend all these methods.

3.1 Runaway stars identified from their peculiar space velocity

Runaway stars were first described as stars responsible for the longer tail in the velocity distribution such that it is not sufficiently describable with one Maxwellian distribution (Blaauw 1961). Stone (1979) has generalized this definition such that runaway stars are members of the so-called high-velocity group. These are stars with large peculiar velocities that can be represented by an additional Maxwellian distribution. The other Maxwellian distribution incorporates stars with lower velocities, and thus the low-velocity group (normal Population I stars). He has pointed out that by applying a velocity cut-off to identify runaway stars, a certain fraction of these would be missed.

However, this issue can only be handled for the determination of space frequencies (see Stone 1991) and a velocity cut-off is still inevitable for the identification of runaway star candidates. To obtain a reasonable cut-off, we fit the distribution of the peculiar space velocities v_pec of the sample stars (4180 with full kinematics) with two Maxwellians (Fig. 1). We evaluate the velocity errors utilizing a Monte Carlo simulation varying π, μ*_α, μ_δ and v_r within their confidence intervals.6 We find that

4

where σ_L and σ_H are the average velocity dispersions of the low- and high-velocity groups, respectively, and f_H is the relative frequency of the high-velocity group. The derived dispersions are in agreement with those found by Stone (1979) (with σ_H being slightly smaller) whereas f_H is smaller; however published values for f_H vary from 34 ± 14 per cent (Blaauw 1961, corrected – see Stone 1991) to 55 ± 12 per cent (Stone 1979). Furthermore, the star sample of Stone contains a much smaller number of stars than ours. In addition, to make sure that the low-mass stars in our sample do not distort the results, we check whether the outcome differs from a subsample comprising only O- and B-type stars as well as Wolf–Rayet stars (2368 stars with full kinematics). As we do not find significant differences, we conclude that young stars, no matter whether of low or high mass, share the same kinematic properties. The Maxwellian functions of both groups intersect at 28 km s^-1. Following Stone (1979), a star is a probable member of the high-velocity group if

5

For this reason, this will be our velocity cut-off defining runaway stars. In theory, with this definition we are able to identify 73 per cent of the high-velocity group members while the contamination of low-velocity stars is 9 per cent.

We perform a Monte Carlo simulation varying the observables π, μ*_α, μ_δ and v_r within their uncertainty intervals and we evaluate the probability of a star being a runaway star (the probabilities are given in Section 3.2). For 972 stars, the probability is higher than 50 per cent. Allowing for a 9 per cent contamination of low-velocity stars, this means that a probability criterion of 50 per cent allows us to identify 78 per cent of the high-velocity members.

3.2 Runaway stars identified from U, V, W, their radial and tangential velocities or proper motions

In addition to the peculiar three-dimensional (3D) space velocities v_pec, we investigate their one-dimensional (1D) components U, V and W separately to identify potentially slower high-velocity group members, which may show an exceptionally high velocity in only one direction. For the same reason, we also investigate the peculiar radial velocities v_r,pec.

In our sample, 45 per cent of the stars do not have radial velocity measurements available. Among these cases, the only way to identify runaway candidates is to use their peculiar two-dimensional (2D) tangential Galactic velocities v_t,pec or their 1D components, which are the peculiar proper motion in Galactic longitude μ_l,pec and Galactic latitude μ_b,pec. To make the velocities comparable, we transfer the proper motions into 1D velocities v_l,pec = 4.74μ_l,pec/π and v_b,pec = 4.74μ_b,pec/π.

All velocity distributions contain the two velocity groups of stars (Section 3.1) and can be fitted with bimodal functions (Gaussians for the 1D cases U, V, W, v_r,pec, v_l,pec and v_b,pec, and 2D Maxwellians for the 2D case v_t,pec). Table 2 lists the fitting results adopting f_H = 27.7 ± 1.9 per cent (see Section 3.1 and Figs 2–5).

Figure 2

Distribution of U, V and W (shaded histograms), the 1D components of v_pec. The dashed and dash-dotted curves represent the low-velocity and high-velocity groups, respectively. The two curves intersect at U≈±23 km s^-1, V≈±23 km s⁻¹ and W≈±12 km s^-1, respectively. The total distribution as the sum of the two is represented by the solid line.

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Figure 3

Distribution of the peculiar 1D radial velocity v_r,pec (shaded histogram). The dashed and dash-dotted curves represent the low-velocity and high-velocity groups, respectively. The two curves intersect at v_r,pec≈± 25 km s⁻¹. The total distribution as the sum of the two is represented by the solid line (χ²_red = 0.33).

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Figure 4

Distribution of the peculiar 2D tangential Galactic velocity v_t,pec (shaded histogram). The dashed and dash-dotted curves represent the low-velocity and high-velocity groups, respectively. The two curves intersect at v_r,pec = 20 km s⁻¹. The total distribution as the sum of the two is represented by the solid line (χ²_red = 2.58; see caption of Fig. 1).

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Figure 5

Distribution of the 1D components of the peculiar 2D tangential Galactic velocity v_t,pec: v_l,pec and v_b,pec (shaded histograms). The dashed and dash-dotted curves represent the low-velocity and high-velocity groups, respectively. The two curves intersect at v_l,pec≈±19 km s⁻¹ and v_b,pec≈±11 km s⁻¹, respectively. The total distribution as the sum of the two is represented by the solid line.

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The velocity dispersions of the high-velocity group are consistent with an isotropic velocity distribution arising from the runaway producing mechanisms (see Appendix A). Moreover, the low-velocity group dispersions are in good agreement with those of young disc stars (e.g. Delhaye 1965; Mihalas & Binney 1981).

Because the velocity distribution of the low-velocity group is not isotropic, that of the high-velocity group cannot be isotropic either (see Appendix A). Thus, we cannot simply translate the criterion given by equation (5) into the 1D case (⁠⁠, where X=U, V, W, v_r,pec, v_l,pec or v_b,pec). In addition, such a 1D criterion would lead to a contamination of low-velocity group stars among the identifications of approximately 50 per cent, for example, in the U and V components.

For these reasons, as for the peculiar spatial velocity v_pec, we have chosen the intersection points of the curves also for the 1D cases as well as v_t,pec to define the runaway criteria. In Table 3, we specify the selection criteria and theoretical expectations concerning the possible identifications as well as the number of runaway star candidates identified (stars with a runaway probability higher than 50 per cent). Allowing for the specific contamination of low-velocity group members, the number of identifications is generally in agreement with our theoretical predictions (Table 3).

With 972 runaway star candidates found in Section 3.1 and 1381 identifications in Table 3 (N_new), we find a total of 2353 runaway star candidates with a runaway probability higher than 50 per cent regarding at least one velocity investigated (Table 4; the full table is available as Supporting Information with this article, and via VizieR).

Table 4

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Runaway probabilities for 2353 runaway star candidates as found in Sections 3.1 and 3.2. Columns 3–10 list the individual probabilities P for each velocity component. We regard stars with P≥ 0.50 in at least one velocity as runaways. The peculiar space velocities v_pec and peculiar tangential velocities v_t,pec are given in the last two columns. The first five entries are shown here; the full table is available via VizieR and as Supporting Information with this article.

HIP	Other name		PU	PV	PW					vpec (km s−1)	vt,pec (km s−1)
85	CD-25 16747	0.89	0.93	0.47	0.22	0.01	0.96	0.52	0.99	52.9+22.8−35.2	52.7+24.8−37.2
135	HD 224908	–	–	–	–	–	0.99	0.00	1.00	–	22.1+1.9−2.1
145	29 Psc	0.13	0.00	0.00	0.95	0.31	0.00	0.00	0.00	22.4+3.9−4.1	1.9+2.0−2.0
174	HD 240475	1.00	0.52	1.00	0.00	1.00	0.04	0.04	0.00	59.6+4.8−5.2	6.9+3.0−1.0
278	HD 225095	0.45	0.13	0.23	0.04	0.51	0.03	0.02	0.03	27.3+8.9−7.1	9.5+3.0−1.0

HIP	Other name		PU	PV	PW					vpec (km s−1)	vt,pec (km s−1)
85	CD-25 16747	0.89	0.93	0.47	0.22	0.01	0.96	0.52	0.99	52.9+22.8−35.2	52.7+24.8−37.2
135	HD 224908	–	–	–	–	–	0.99	0.00	1.00	–	22.1+1.9−2.1
145	29 Psc	0.13	0.00	0.00	0.95	0.31	0.00	0.00	0.00	22.4+3.9−4.1	1.9+2.0−2.0
174	HD 240475	1.00	0.52	1.00	0.00	1.00	0.04	0.04	0.00	59.6+4.8−5.2	6.9+3.0−1.0
278	HD 225095	0.45	0.13	0.23	0.04	0.51	0.03	0.02	0.03	27.3+8.9−7.1	9.5+3.0−1.0

Table 4

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Runaway probabilities for 2353 runaway star candidates as found in Sections 3.1 and 3.2. Columns 3–10 list the individual probabilities P for each velocity component. We regard stars with P≥ 0.50 in at least one velocity as runaways. The peculiar space velocities v_pec and peculiar tangential velocities v_t,pec are given in the last two columns. The first five entries are shown here; the full table is available via VizieR and as Supporting Information with this article.

HIP	Other name		PU	PV	PW					vpec (km s−1)	vt,pec (km s−1)
85	CD-25 16747	0.89	0.93	0.47	0.22	0.01	0.96	0.52	0.99	52.9+22.8−35.2	52.7+24.8−37.2
135	HD 224908	–	–	–	–	–	0.99	0.00	1.00	–	22.1+1.9−2.1
145	29 Psc	0.13	0.00	0.00	0.95	0.31	0.00	0.00	0.00	22.4+3.9−4.1	1.9+2.0−2.0
174	HD 240475	1.00	0.52	1.00	0.00	1.00	0.04	0.04	0.00	59.6+4.8−5.2	6.9+3.0−1.0
278	HD 225095	0.45	0.13	0.23	0.04	0.51	0.03	0.02	0.03	27.3+8.9−7.1	9.5+3.0−1.0

HIP	Other name		PU	PV	PW					vpec (km s−1)	vt,pec (km s−1)
85	CD-25 16747	0.89	0.93	0.47	0.22	0.01	0.96	0.52	0.99	52.9+22.8−35.2	52.7+24.8−37.2
135	HD 224908	–	–	–	–	–	0.99	0.00	1.00	–	22.1+1.9−2.1
145	29 Psc	0.13	0.00	0.00	0.95	0.31	0.00	0.00	0.00	22.4+3.9−4.1	1.9+2.0−2.0
174	HD 240475	1.00	0.52	1.00	0.00	1.00	0.04	0.04	0.00	59.6+4.8−5.2	6.9+3.0−1.0
278	HD 225095	0.45	0.13	0.23	0.04	0.51	0.03	0.02	0.03	27.3+8.9−7.1	9.5+3.0−1.0

3.3 Stars with higher peculiar velocities compared to their neighbourhood or surrounding OB association/cluster

Some high-velocity group stars may still not have been identified. For this reason, we look for additional stars that show a different motion compared to their neighbouring stars. Because stars in clusters and associations share a common motion, runaway stars (i.e. stars that have experienced some interaction; see Section 1) can be identified through deviations from the common motion, especially if the velocity vector points towards a different direction than the cluster mean motion. From previous investigations, we can be sure that we have identified all the runaway stars with high peculiar velocities. The most important criterion now is the direction of a star's velocity vector compared to its neighbouring stars.

We select a sphere with a diameter of 24 pc7 around each individual star to define its neighbourhood. All sample stars within this sphere are chosen as comparison stars. We calculate the vectors of the peculiar velocities v_pec = (U, V, W) and the peculiar tangential velocities v_t,pec = (v_l,pec, v_b,pec) varying the observables within their confidence intervals. The neighbourhood velocity v_neigh is defined as the median velocity of the comparison stars. We define the runaway criterion such that v_★ must not lie within the 3σ error cone of v_neigh (Fig. 6). Varying the observables within their confidence intervals, we obtain runaway probabilities for each star (10 000 Monte Carlo runs).

Figure 6

Definition for identifying runaway stars by comparing with neighbouring stars. The neighbourhood is defined as a sphere around an individual star with a diameter of 24 pc (see footnote 7) or as the OB association/cluster (assumed to be spherical) inside which the star currently lies. The neighbourhood velocity v_neigh is given by the median velocity of the stars within the sphere or the mean motion of the association/cluster member stars as listed in Tetzlaff et al. (2010). If the velocity vector v_★ points into the grey shaded region, the star clearly moves away from its neighbouring stars and is thus a runaway star. The grey shaded area lies outside the 3σ error cone of v_neigh (dotted lines mark 1σ). Note that the length of v_★ and v_neigh (v_pec or v_t,pec) is not important here.

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Examining v_pec and v_t,pec, we find no stars with a probability of at least 50 per cent for being a runaway star under the above definition.

In addition, we compare the velocity vectors of each OB association and cluster listed in Tetzlaff et al. (2010),8 with the velocity vectors of each individual star situated within the association boundaries as listed in Tetzlaff et al. (2010) (assuming the associations/clusters are spherical; see Fig. 7 for the Orion OB1 association as an example). From v_pec, we identify 126 additional runaway star candidates. Another 58 runaway star candidates are identified from their v_t,pec. All runaway star candidates (192 for v_pec, 221 for v_t,pec; 124 included in both) are listed in Table 5 (the full table is available via VizieR and as Supporting Information with this article).

Figure 7

Motion of Ori OB1 member stars. The red cross marks the centre of the association and the dotted ellipse its boundaries (assuming spherical shape). The red thick arrow shows the mean peculiar tangential motion of the whole association (Blaha & Humphreys 1989; Brown et al. 1999; Dambis, Mel'nik & Rastorguev 2001; see also Tetzlaff et al. 2010). The green squares are runaway star candidates satisfying the criterion defined by Fig. 6, whereas blue stars mark runaway star candidates already defined by their large peculiar velocity (Section 3). The length of the arrows is scaled with distance to indicate tangential velocities.

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3.4 Stars outside OB associations/clusters and the Galactic plane

As runaway stars were ejected from their birth site (i.e. its host OB association/cluster or the Galactic plane), they are supposed to be isolated (outside any OB association/cluster and the Galactic plane). Thus, we look for young stars that are clearly outside any OB association/cluster listed in Tetzlaff et al. (2010) (outside three times the association radius, which corresponds to approximately 3σ) and probably outside the Galactic plane (z > 500 pc9).

There are 72 stars situated well outside any OB association/cluster and the Galactic plane; six of these have not been identified as runaway star candidates in the previous sections. These six are listed in Table 6. If they did not form in isolation, they are runaway stars.

3.5 Comparison with other authors

We compare our sample of runaway star candidates with lists from other authors (the most important sources being Blaauw 1961; Bekenstein & Bowers 1974; Cruz-González et al. 1974; Stone 1979; Gies & Bolton 1986; Leonard & Duncan 1990; Conlon et al. 1990; Philp et al. 1996; Moffat et al. 1999; Hoogerwerf et al. 2001; Mdzinarishvili & Chargeishvili 2005; de Wit et al. 2005; Martin 2006). There are 24 proposed runaway candidates satisfying our initial sample criteria (HIP star, π−σ_π≤ 1/3 mas, equation 1; i.e. are contained in our young star sample) that we have not identified as runaway stars. These are listed in Table 7, along with the respective publication source.

We add three of the missing stars, HIP 3881 ( = 35 And), HIP 48943 ( = OY Hya) and HIP 102195 ( = V4568 Cyg), as well as HIP 26241 (=ι Ori) because of its DES origin (see individual discussion in Appendix B).

As indicated by the discussion in Appendix B, several problems may lead to misidentification or non-identification of runaway stars. The major issue here is certainly the distance of a star, which greatly affects the calculated velocities. Because we have used precise Hipparcos parallaxes (while previous studies have often used ground-based distances), our results are not significantly influenced by this. Moreover, we derive runaway probabilities accounting for the errors on all observables instead of evaluating only a single velocity.

Another problem arises from the multiplicity of stars (e.g. 390 stars in our young star sample are spectroscopic binaries; Pedoussaut et al. 1988; Pourbaix et al. 2004). We have obtained radial velocities from catalogues that typically list the systemic radial velocity.

4 SUMMARY AND CONCLUSIONS

We have analysed the distributions of the peculiar velocities of 7663 young Hipparcos stars (4180 with full kinematics) in three and two dimensions, as well as one dimension, to identify members of the high-velocity group (i.e. stars that show different kinematics than normal Population I objects and hence have experienced some interaction – BSS or DES – that provides them with an additional velocity). As expected, the velocity component as a result of runaway formation is isotropic.

Performing Monte Carlo simulations by varying the observables π, μ*_α, μ_δ and v_r within their uncertainty intervals, we have assigned each star a probability of being a member of the high-velocity group (i.e. a runaway star). We have done this for the 3D velocity v_pec, its 1D components U, V and W, the 1D radial velocity v_r,pec as well as for the 2D tangential velocity v_t,pec and its 1D components v_l,pec and v_b,pec in order to identify as many members of the high-velocity group as possible, and also those with a relatively low velocity. We have found 2353 runaway star candidates (i.e. stars for which the runaway probability is higher than 50 per cent in at least one velocity component examined). The contamination of low-velocity members is about 20 per cent at most.

However, the high-velocity group members with very small velocities (as inferred for a Maxwellian distribution they exist) could still not be identified because of the velocity thresholds set. Therefore, we have compared the velocity vector (in three dimensions, v_pec, and two dimensions, v_t,pec) of each individual star with that defined by the stars in its neighbourhood or its surrounding OB association/cluster (v_neigh). If the velocity of the star clearly pointed away from v_neigh (see Fig. 6), the star was labelled a runaway star. We have made 184 new identifications.

Additionally, we have found six additional young stars that are situated well outside any OB association/cluster and the Galactic plane.

Finally, we have compared our list of runaway star candidates with previously published lists and we have added four stars (see the discussion in Appendix B).

This gives us a total of 2547 runaway star candidates (with a contamination of low-velocity group members, i.e. normal Population I stars, of 20 per cent at most). Thus, the runaway frequency among young stars is approximately 27 per cent, in agreement with our theoretical expectations.

Fig. 8 shows the distribution of the peculiar space velocity v_pec and the peculiar tangential velocity v_t,pec (see Figs 1 and 4) with the subsample of runaway candidates in dark grey. The number of runaway star candidates is higher than the number of stars belonging to the high-velocity group, especially in the range of medium velocities where the two curves intersect, as expected. However, with this conservative selection, we can be sure that we have not missed the actual runaway stars. Using our combined selection, we have also identified runaway star candidates with relatively low velocities, which certainly exist but would have not been identified by investigating only one velocity component or the absolute velocity.

Figure 8

Distributions of v_t,pec and v_pec. Light grey histograms represent the whole star sample whereas dark grey histograms show the distributions of runaway star candidates. The velocity distributions of the high-velocity group are shown with dash-dotted lines (cf. Figs 1 and 4).

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We have provided Tables 1, 4, 5 and 6 within an electronic catalogue available via VizieR.

We would like to thank C. Dettbarn, B. Fuchs and H. Jahreiß for helping with the kinematical data. We thank J. Hernández and F. Palla for providing the evolutionary models, and we also thank M. Ammler-von Eiff for his assistance in this regard. We thank the referee, Philip Dufton, for valuable comments. NT acknowledges financial support from the German National Science Foundation (Deutsche Forschungsgemeinschaft, DFG) in grant SCHR 665/7-1 and Carl-Zeiss-Stiftung. We acknowledge partial support from the DFG in the SFB/TR-7 Gravitational Wave Astronomy. Our work has made extensive use of the Simbad and VizieR services (http://cds.u-strasbg.fr).

REFERENCES