# Massive stars in the hinterland of the young cluster, Westerlund 2

J. E. Drew,1, A. Herrero2,3, M. Mohr-Smith1, M. Monguió1, N. J. Wright4, T.
Kupfer5,6, R. Napiwotzki1

1School of Physics, Astronomy & Mathematics, University of Hertfordshire,
Hatfield AL10 9AB, UK
2Instituto de Astrofisíca de Canarias, 38200, La Laguna, Tenerife, Spain
3Departamento de Astrofísica, Universidad de La Laguna, 38205, La Laguna,
Tenerife, Spain
4Astrophysics Group, Keele University, Keele, ST5 5BG, UK
5Kavli Institute for Theoretical Physics, University of California, Santa
Barbara, CA 93106, USA
6Cahill Center for Astronomy & Astrophysics, California Institute of
Technology, Pasadena, CA 91125, USA
E-mail<EMAIL_ADDRESS>
###### Abstract

An unsettled question concerning the formation and distribution of massive
stars is whether they must be born in massive clusters and, if found in less
dense environments, whether they must have migrated there. With the advent of
wide-area digital photometric surveys, it is now possible to identify massive
stars away from prominent Galactic clusters without bias. In this study we
consider 40 candidate OB stars found in the field around the young massive
cluster, Westerlund 2, by Mohr-Smith et al (2017): these are located inside a
box of 1.5$\times$1.5 square degrees and are selected on the basis of their
extinctions and $K$ magnitudes. We present VLT/X-shooter spectra of two of the
hottest O stars, respectively 11 and 22 arcmin from the centre of Westerlund
2. They are confirmed as O4V stars, with stellar masses likely to be in excess
of 40 M⊙. Their radial velocities relative to the non-binary reference object,
MSP 182, in Westerlund 2 are $-$29.4$\pm$1.7 and $-$14.4$\pm$2.2 km s-1,
respectively. Using Gaia DR2 proper motions we find that between 8 and 11
early O/WR stars in the studied region (including the two VLT targets, plus WR
20c and WR 20aa) could have been ejected from Westerlund 2 in the last one
million years. This represents an efficiency of massive-star ejection of up to
$\sim$ 25%. On sky, the positions of these stars and their proper motions show
a near N–S alignment. We discuss the possibility that these results are a
consequence of prior sub-cluster merging combining with dynamical ejection.

###### keywords:

stars: early-type, (Galaxy:) open clusters and associations: Westerlund 2,
Galaxy: structure, surveys

##  1 Introduction

Massive OB stars are critically important objects in shaping the evolution of
galactic environments: it has long been recognised that the UV radiation,
supernovae and winds they produce play leading roles in shaping the
interstellar medium (ISM). But because of their relative rarity at formation
and their short lives, their properties have proved difficult to nail down.
Indeed, their mode or modes of formation are still unclear (Tan et al., 2014).
The debate is fuelled by questions concerning the impact of binarity on both
evolution and dynamics (Sana et al., 2012) and the implications of the stark
environmental contrast between dense young clusters and looser OB associations
as formation sites (e.g. Wright et al., 2014). To add to this, there remains a
lack of clarity over the possibility that some fraction of massive stars could
even form in relative isolation (de Wit et al., 2005; Bressert et al., 2012;
Gvaramadze et al., 2012). In this last case, the vagaries of random sampling
of the initial mass function (IMF) may be relevant (Parker & Goodwin, 2007).

It is a common perception that the centre of more massive clusters is the
preferred birthplace for most O stars ($T_{eff}>30kK$ on the main sequence,
our working definition of an O star). In this context the phenomenon of
runaway O stars (Blaauw, 1961) slots into place as the explanation for massive
objects found in the field (Portegies Zwart et al., 2010). To begin with,
Blaauw (1961) placed a minimum threshold on space velocity at 40 km s-1, but
over time this has moderated to 30 or 25 km s-1 (Hoogerwerf et al., 2001;
Portegies Zwart, 2000). The favoured mechanisms for ejection are kicks within
binaries arising from supernova explosions or dynamical intra-cluster
interactions (see discussion in Hoogerwerf et al., 2001). Both mechanisms can
produce space velocities of up to 200 km s-1. The binary frequency among
runaway stars is still uncertain: based on examination of a bright sample
dominated by O stars, Mason et al. (2009) concluded that the frequency is
lower among confirmed runaways than in clusters, although this is contradicted
by Chini et al. (2012).

To better understand the constraints on how and where the most massive stars
can form, it is helpful to properly characterize the field population and
establish the relative numbers of runaway objects and stars likely to have
formed in situ. We are in a better position to do this if we remove current
biases in the on-sky two-dimensional distribution of known O stars – existing
Galactic compilations are dominated by the local volume (to $\sim$ 2 kpc) and,
on longer scales, by the contents of recognised open clusters (e.g. Sota et
al., 2014). Now, we can link up what we already know on the few-arcminutes
scale around massive Galactic clusters, with the wider field on the scale of
degrees, thanks to recent wide-area digital photometric surveys.

We begin to explore this here via a worked example of the massive star content
in the wider environment around Westerlund 2, a compact cluster near the
tangent of the Carina Arm. We present follow up spectroscopy and radial
velocity measurements of two confirmed very hot O stars, clearly exterior to
the main clustering. For these, we clarify their basic stellar parameters and
ask whether they are potentially recent ejections. Westerlund 2 is one of a
limited number of dense clusters in the Milky Way estimated to be more massive
than $10^{4}$ M⊙ – recently, Zeidler et al. (2017) have obtained $(3.6\pm
0.3)\times 10^{4}$ M⊙. About the oldest age estimated for it is 2.5 Myrs (Rauw
et al., 2007): this cluster is young enough that the first supernova explosion
is probably yet to happen. If so, the mechanism for creating runaway stars is
limited to dynamical interaction.

In two previous papers (Mohr-Smith et al., 2015, 2017, hereafter MS-I and MS-
II), we presented validated blue selections of OB stars from the VST
Photometric H$\alpha$ Survey of the Southern Galactic Plane and Bulge (VPHAS+,
Drew et al., 2014) across the Carina region. Our method of selection
incorporated fits to merged VPHAS+ optical and 2MASS NIR photometry that
provided a high-quality characterisation of the extinction towards the
selected objects. The typical precisions achieved were $\sim$0.1 in each of
$A_{0}$, the monochromatic extinction in magnitudes at 5495 Å, and $R_{V}$,
the ratio of total to selective extinction. This extra information provides a
start on teasing out the relationship between a young cluster and its wider
environment. The fits also gave a rough constraint on effective temperature
that permits the efficient selection of likely O stars. For Westerlund 2 and
its hinterland, we have all these data.

In a certain respect the methods applied here and the questions addressed
parallel the work of Lamb et al. (2016), with the difference that the ’stellar
field’ here is a sky region around one massive Galactic cluster, while Lamb et
al. (2016) investigated the Small Magellanic Cloud OB population, selecting
objects at least 28 pc distant from any other OB candidates. They found
evidence from their sample of 399 stars that around a third are runaways and
up to half may have formed in extreme isolation. Here we consider stars that
are at least $\sim$15 pc from Westerlund 2, and consider in detail a projected
on-sky region of 130$\times$130 pc2. The new feature is that we focus on the
relation between a specific dense massive cluster, just a few kiloparsecs
away, and the scatter of massive stars near it. We also deploy extinction as a
first, crude distance proxy to limit depth in the third dimension.

This paper is organised as follows. First, we extract from the larger
catalogues presented by MS-I and MS-II a set of high-confidence O stars within
a region of 1.5$\times$1.5 sq.deg region centred on Westerlund 2 (hereafter
Wd2, (section 2). We then introduce additional spectroscopy obtained of two of
the hottest O stars in the set (section 3), and describe an analysis that
yields improved stellar parameters including an estimate of mass (section
4.1). The results of radial velocity measurements for these stars are then
presented (section 4.2). The results are considered together in section 5 with
optical and near-infrared survey photometry in an initial appraisal of the
links between the dispersed O stars in the region and Wd2. We then collect and
analyse the newly-released Gaia DR2 proper motions for the whole sample
(Section 6): this confirms the two stars with spectroscopy as ejections from
Wd2, along with up to 9 more. The paper ends with a discussion of the results
in the context of relevant models for O-star dispersal into the field (Fujii &
Portegies Zwart, 2011; Fujii et al., 2012; Lucas et al., 2018).

##  2 Westerlund 2 and the O stars around it

Figure 1:  Top: the distribution of extinction, $A_{0}$ (magnitudes) for 43 of
the 46 MS-II catalogue OB stars located on the sky within 6 arcmin of the
centre of Wd2. The plotted range is restricted to $5<A_{0}<8$ to bring out the
main grouping. The remaining 3 stars are at greater extinction ($8<A_{0}<9$).
Bottom: the distribution of $K$ magnitudes, for all 46 stars within 6 arcmin
of Wd2 centre.

###  2.1 The centre of Wd2 and the cluster distance

Expressed in Galactic co-ordinates, the approximate centre of Wd2 was given by
Moffat & Vogt (1975) as $\ell=284.3^{\circ}$, $b=-0.3^{\circ}$. We shall use
$\ell=284^{\circ}.27$, $b=-0^{\circ}.334$ as our central reference position -
it is located in the main cluster about 0.3 arcmin from the very massive WR
20a binary system. The box we place around this captures the ranges,
$283.5^{\circ}<\ell<285.0^{\circ}$, and $-1.0^{\circ}<b<0.5^{\circ}$.

Studies that have focused on the stellar content of Wd2 have typically
examined the inner few arcminutes, or few parsecs [Moffat et al. (1991) and
Zeidler et al. (2017) represent bookends in time to the several papers that
have been published]. The X-ray data collected by Tsujimoto et al. (2007) were
exceptional in spanning a region of 17$\times$17 sq.arcmin (backed up by NIR
photometry over the inner 8.3$\times$8.3 sq.arcmin). This permitted these
authors to argue that the stellar over-density associated with Wd2 may have a
radius of 6–7 arcmin (or $\sim$10 pc), and they identified 14 candidate early-
type stars more than 3 arcmin away from the cluster centre. In the more recent
catalogue created by MS-II, 46 objects, fitting successfully as OB stars, fall
within a circle of radius 6 arcmin around the cluster centre: most are already
known in the literature to be OB stars. The list of 46 is not complete as some
objects cannot be extracted in the brilliant cluster core (as imaged in the
VPHAS$+$ survey) due to source crowding. But, for present purpose, it is large
enough subset to portray typical Wd2 cluster-member properties reliably.
Specifically, in figure 1, the extinction and 2MASS K magnitude distributions
near cluster centre are shown.

Estimates of the distance to Wd2, have ranged from 2.8 kpc (Ascenso et al.,
2007) up to around 8 kpc (Rauw et al., 2011). But there has been some
convergence recently on 4–6 kpc among optical stellar photometric studies that
have paid attention to the significant variation of the extinction law away
from the typical $R_{V}=3.1$ version (Vargas Álvarez et al., 2013; Hur et al.,
2015; Zeidler et al., 2015, and MS-I). Studies of the molecular and ionized
interstellar medium have favoured a somewhat longer sightline of 5–7 kpc
(Dame, 2007; Furukawa et al., 2009; Benaglia et al., 2013).

The recent availability of Gaia DR2 does not help us here since the current
global astrometric solution has been reported by Lindegren et al. (2018) as
carrying a systematic uncertainty of up to 0.1 mas: given that parallaxes for
objects in Wd2 are mostly under 0.25 mas, it is clear that the data are not
yet good enough to provide reliable and precise distance estimates either to
individual objects or Wd2 as a whole. The alternative of deriving a kinematic
distance from the proper motions (see Section 6) is also hindered by the
uncertain peculiar motions of young clusters relative to mean rotation (Reid
et al., 2014), and the still uncertain knowledge of the mean disc rotation as
a function of Galactocentric radius (see e.g. Huang et al., 2016; Harris et
al., 2018; Kawata et al., 2018).

In order to place the results of this study onto an absolute physical scale we
need a working distance. For this purpose we adopt 5 kpc, roughly in the mid
range of the recent optical photometric work – and at the bottom end of the
ISM estimates. To keep in mind how distance affects derived quantities, we
adopt error bounds of $\pm$1 kpc. Given the accumulation of work on Wd2, a
distance of less than 4 kpc appears relatively unlikely – see e.g. Vargas
Álvarez et al. (2013) on the likely problems with the Ascenso et al. (2007)
result. This will be important when, in Section 6, use is made of Gaia DR2
proper motions: a minimum of 4 kpc puts a useful lower limit on transverse
speeds deduced from them. Similarly, with $D\geq 4$ kpc, the 1.5$\times$1.5
sq.deg sky region we consider corresponds to a projected area of at least
100$\times$100 pc2. The 6 kpc upper bound is of less significance, but if it
is exceeded, it puts some strain on the stellar atmospheric analysis of
Section 4.1.

###  2.2 The cluster hinterland

Table 1: Properties of candidate OB stars within the region of study, more than 10 arcminutes away from the core of Wd2. Part (a) of the table contains objects with extinctions overlapping those typical of the cluster, while part (b) lists the higher-extinction candidates ($A_{0}>7.5$). The estimated extinction parameters, $A_{0}$ and $R_{V}$, and effective temperatures, $T_{\rm eff}$, given in columns 5 – 7, are drawn from the MS-II catalogue. Effective temperatures estimated from photometry with typical errors in the region of 5000 K, are printed in italic type, while those derived from spectroscopy are in normal type and are accompanied by their formal errors. No $T_{\rm eff}$ estimate is given for either WR 20aa or WR 20c, as the fitting method is, in these cases, unreliable, and only delivers approximate extinction data. Column 8, $\theta_{r}$, specifies the angular separation of each object from the Wd2 reference position at $\ell=284^{\circ}.27$, $b=-0^{\circ}.334$. The remark, ”$A_{0}\sim 8$ BG?”, in the comments column identifies candidate members of a more reddened, background association (see section 5.3). Columns 2 and 3 give positions in Galactic coordinates – alternative RA and Dec (J2000) positions are given in the Appendix, along with the names of cross-matched Gaia DR2 sources.  MS-II # | Galactic Coordinates | 2MASS K | A0 | RV | Teff | $\theta_{r}$ | comment
---|---|---|---|---|---|---|---
| $\ell^{\circ}$ | $b^{\circ}$ | (mag) | (mag) |  | (kK) | (arcmin) |
(a) $5.5<A_{0}<7.5$ |  |  |  |
0673 | 283.505754 |  $-$0.538484 | 11.75$\pm$0.02 | $5.73_{-0.10}^{+0.09}$ | $3.72_{-0.07}^{+0.07}$ | 29 | 47.47 |
0693 | 283.536501 |  $-$0.426998 | 10.57$\pm$0.02 | $6.73_{-0.10}^{+0.09}$ | $4.34_{-0.08}^{+0.09}$ | 30 | 44.36 | emission line star
0708 | 283.561722 |  $-$0.979383 | 7.94$\pm$0.03 | $6.84_{-0.09}^{+0.08}$ | $3.77_{-0.06}^{+0.06}$ | 31 | 57.49 | NGC 3199/foreground
0893 | 283.842822 |  $-$0.705926 | 10.87$\pm$0.03 | $6.81_{-0.06}^{+0.05}$ | $3.80_{-0.05}^{+0.05}$ | 41 | 33.98 |
0986 | 283.937827 |  $-$0.830267 | 11.56$\pm$0.05 | $7.40_{-0.10}^{+0.10}$ | $4.07_{-0.07}^{+0.07}$ | 28 | 35.83 |  $A_{0}\sim 8$ BG?
0987 | 283.939130 |  $-$0.910605 | 11.93$\pm$0.02 | $7.33_{-0.10}^{+0.09}$ | $3.99_{-0.06}^{+0.06}$ | 29 | 39.89 |  $A_{0}\sim 8$ BG?
0994 | 283.947686 |  $-$0.489082 | 10.29$\pm$0.02 | $5.58_{-0.09}^{+0.08}$ | $3.79_{-0.07}^{+0.08}$ | 31 | 21.46 |
1046 | 284.046887 |  $+$0.425467 | 9.14$\pm$0.02 | $6.20_{-0.08}^{+0.06}$ | $3.57_{-0.05}^{+0.06}$ | 35 | 47.49 |
1102 | 284.142129 |  $-$0.188894 | 9.62$\pm$0.02 | $6.28_{-0.07}^{+0.05}$ | $3.64_{-0.05}^{+0.05}$ | 38 | 11.60 |
1133 | 284.193343 |  $-$0.132585 | 9.93$\pm$0.02 | $7.01_{-0.07}^{+0.05}$ | $3.72_{-0.05}^{+0.05}$ | 38 | 12.93 |
1164 | 284.227820 |  $-$0.687882 | 9.65$\pm$0.02 | $6.40_{-0.08}^{+0.06}$ | $3.91_{-0.06}^{+0.07}$ | $34.3_{-0.6}^{+0.5}$ | 21.38 |
1236 | 284.276442 |  $-$0.163506 | 10.04$\pm$0.02 | $7.29_{-0.10}^{+0.09}$ | $3.53_{-0.05}^{+0.05}$ | $41.8_{-3.2}^{+6.2}$ | 10.24 |
1273 | 284.298853 |  $-$0.519768 | 9.52$\pm$0.02 | $6.67_{-0.09}^{+0.06}$ | $3.87_{-0.06}^{+0.06}$ | $40.6_{-0.8}^{+2.5}$ | 11.28 | X-shooter target
1308 | 284.331634 |  $-$0.583555 | 8.39$\pm$0.03 | 5.6 | 4.3 | – | 15.42 | WR 20aa
1338 | 284.378387 |  $+$0.009138 | 9.41$\pm$0.02 | $6.17_{-0.07}^{+0.05}$ | $3.58_{-0.05}^{+0.05}$ | $42.5_{-0.8}^{+0.7}$ | 21.59 | X-shooter target
1356 | 284.402022 |  $-$0.548087 | 10.34$\pm$0.02 | $5.68_{-0.06}^{+0.05}$ | $4.05_{-0.07}^{+0.07}$ | $39.0_{-0.4}^{+0.3}$ | 15.09 |
1374 | 284.418116 |  $-$0.927350 | 10.54$\pm$0.02 | $5.61_{-0.09}^{+0.08}$ | $3.75_{-0.07}^{+0.07}$ | $38.6_{0.4}^{+0.5}$ | 36.69 |
1550 | 284.638801 |  $-$0.499403 | 10.43$\pm$0.04 | $6.87_{-0.10}^{+0.10}$ | $3.98_{-0.07}^{+0.07}$ | $36.4_{1.1}^{+1.5}$ | 24.25 |
1567 | 284.657774 |  $-$0.775554 | 9.89$\pm$0.02 | $5.55_{-0.09}^{+0.08}$ | $3.71_{-0.07}^{+0.07}$ | $34.3_{-0.3}^{+0.2}$ | 35.26 | in own cluster
(b) $A_{0}>7.5$ |  |  |  |
0685 | 283.527633 |  $-$0.860257 | 11.54$\pm$0.03 | $8.33_{-0.14}^{+0.08}$ | $3.70_{-0.05}^{+0.05}$ | 32 | 54.60 |
0785 | 283.684167 |  $+$0.417875 | 12.36$\pm$0.03 | $7.81_{-0.15}^{+0.09}$ | $3.64_{-0.05}^{+0.06}$ | 31 | 57.19 |
0826 | 283.744780 |  $-$0.630411 | 10.34$\pm$0.02 | $9.84_{-0.13}^{+0.06}$ | $4.05_{-0.05}^{+0.05}$ | 35 | 36.19 |
0879 | 283.828965 |  $-$0.736854 | 10.71$\pm$0.02 | $7.77_{-0.08}^{+0.06}$ | $3.89_{-0.05}^{+0.05}$ | 36 | 35.84 |  $A_{0}\sim 8$ BG?
0881 | 283.829449 |  $-$0.595493 | 10.83$\pm$0.03 | $8.28_{-0.12}^{+0.11}$ | $3.91_{-0.05}^{+0.05}$ | 28 | 30.74 |  $A_{0}\sim 8$ BG?
0896 | 283.848489 |  $-$0.848510 | 9.60$\pm$0.02 | $8.03_{-0.08}^{+0.06}$ | $4.07_{-0.05}^{+0.06}$ | 35 | 39.91 |  $A_{0}\sim 8$ BG?
0904 | 283.858744 |  $-$0.932254 | 12.39$\pm$0.03 | $7.72_{-0.07}^{+0.05}$ | $3.88_{-0.05}^{+0.05}$ | 39 | 43.56 |  $A_{0}\sim 8$ BG?
0918 | 283.873029 |  $-$0.917056 | 10.86$\pm$0.02 | $8.15_{-0.05}^{+0.05}$ | $3.93_{-0.05}^{+0.05}$ | 40 | 42.32 |  $A_{0}\sim 8$ BG?
0919 | 283.873213 |  $-$0.910814 | 11.25$\pm$0.03 | $7.76_{-0.10}^{+0.09}$ | $3.88_{-0.05}^{+0.06}$ | 30 | 42.01 |  $A_{0}\sim 8$ BG?
0921 | 283.875873 |  $-$0.910293 | 10.14$\pm$0.03 | $8.35_{-0.10}^{+0.08}$ | $3.95_{-0.06}^{+0.06}$ | 31 | 41.89 |  $A_{0}\sim 8$ BG?
0925 | 283.879042 |  $-$0.917201 | 10.44$\pm$0.04 | $8.37_{-0.06}^{+0.06}$ | $3.95_{-0.05}^{+0.05}$ | 41 | 42.13 |  $A_{0}\sim 8$ BG?
0930 | 283.885189 |  $-$0.907088 | 11.77$\pm$0.05 | $8.33_{-0.08}^{+0.06}$ | $3.91_{-0.06}^{+0.06}$ | 39 | 41.42 |  $A_{0}\sim 8$ BG?
0931 | 283.885209 |  $-$0.912074 | 9.96$\pm$0.03 | $9.34_{-0.09}^{+0.06}$ | $3.75_{-0.04}^{+0.04}$ | 37 | 41.67 |
0934 | 283.885885 |  $-$0.960334 | 12.69$\pm$0.04 | $7.56_{-0.13}^{+0.11}$ | $4.08_{-0.07}^{+0.07}$ | 29 | 44.08 |  $A_{0}\sim 8$ BG?
0938 | 283.889741 |  $-$0.563901 | 11.95$\pm$0.03 | $8.59_{-0.19}^{+0.12}$ | $4.09_{-0.06}^{+0.06}$ | 30 | 26.66 |  $A_{0}\sim 8$ BG?
0953 | 283.903648 |  $+$0.372327 | 11.73$\pm$0.04 | $8.26_{-0.19}^{+0.13}$ | $3.70_{-0.06}^{+0.06}$ | 29 | 47.74 |
0958 | 283.908449 |  $-$0.903378 | 11.63$\pm$0.02 | $7.60_{-0.10}^{+0.08}$ | $3.88_{-0.06}^{+0.06}$ | 31 | 40.47 |  $A_{0}\sim 8$ BG?
0965 | 283.917002 |  $-$0.804651 | 12.43$\pm$0.04 | $7.79_{-0.10}^{+0.08}$ | $4.04_{-0.07}^{+0.07}$ | 34 | 35.30 |  $A_{0}\sim 8$ BG?
0968 | 283.917749 |  $-$0.964225 | 11.59$\pm$0.03 | $8.44_{-0.14}^{+0.08}$ | $3.86_{-0.05}^{+0.05}$ | 33 | 43.32 |  $A_{0}\sim 8$ BG?
1086 | 284.119503 |  $-$0.071365 | 9.65$\pm$0.02 | $9.67_{-0.14}^{+0.07}$ | $3.54_{-0.04}^{+0.04}$ | 35 | 18.16 |
1119 | 284.175755 |  $+$0.077817 | 9.04$\pm$0.02 | 10.3 | 3.7 | – | 25.35 | WR 20c
Figure 2:  The region around Westerlund 2. The blue-selected O stars from the
catalogue of MS-II, listed in Table 1, are superposed on an image of the field
constructed from VPHAS+ data (Drew et al., 2014). All the named objects,
including the nebula NGC 3199, are discussed later in the text. For emphasis,
the two X-shooter targets, stars #1273 and #1338, are diamonds enclosed in
boxes. Stars appearing in the lower-extinction/upper half of table 1 are drawn
as circles and coloured blue, while the red triangles pick out the higher-
extinction objects in the lower half of the same table. The black dashed
circle is centred on the reference position, $\ell=284^{\circ}.27$,
$b=-0^{\circ}.334$, and has a radius of 10 arcmin. The radial velocity
comparison stars, MSP 182, MSP 183 and MSP 199 (not marked) are all located in
the cluster centre, within an arcminute of the reference position.

As a first step to identifying candidate O stars in the immediate field around
Wd2, we apply the following criteria. First, we restrict attention to objects
at an angular separation from the cluster reference position that exceeds 10
arcmin: this minimum angular scale maps onto a plane-of-sky distance at 5 kpc
of 15 pc – or the distance travelled in 1 Myr at a projected speed of 15 km
s-1. The majority of cluster escapes, with full three-dimensional space
velocities of $\sim$30 km s-1 or more should lie outside this circle.

Next, we take from the catalogue of MS-II as our primary sample those stars
hot enough to classify as O stars ($\log(T_{eff})>4.45$) for which the
estimated extinction lies within the range, $5.5<A_{0}<7.5$ (motivated by the
top panel of figure 1). This is aimed at cutting out objects likely to be well
into the foreground with respect to Wd2. We also limit ourselves to objects
whose OIR photometry fits with high-confidence to a reddened OB spectral
energy distribution ($\chi^{2}<8$, see MS-I). The one exception we make to
this last rule is for the Wolf-Rayet star, WR 20aa, for which $\chi^{2}\simeq
13$. Finally, we drop from consideration any relatively faint objects $K>12.5$
(cf. the bottom panel of figure 1).

The 19 objects satisfying all the above criteria are set out in the top half
of Table 1 along with their 2MASS $K$ magnitudes, and the extinction
parameters and effective temperatures reported by MS-II. In most cases, the
tabulated effective temperature estimate is based on the fit to VPHAS$+$ and
2MASS photometry. However, for some, we have more reliable spectroscopically-
based estimates (see MS-II for further discussion).

We retain, as a distinct group, candidate objects with extinctions exceeding
the $A_{0}=7.5$ limit imposed on the main sample: we view them as potentially
in the cluster’s background, and thus less likely to be associated with it.
This applies the broad principle that extinction rises with distance (see the
extensive discussion of this and how the region around Wd2 is challenging in
MS-II). The same minimum effective temperature, the same angular separation
from Wd2, and the same confidence cut are imposed, giving a group of objects
that is in the mean $\Delta K=0.7$ fainter (and no object is fainter than
$K=12.7$). The data on this set of 21 stars are presented in the lower half of
Table 1. The highest-extinction object in this group, is WR20c ($A_{0}\simeq
10.3$): this object has been claimed as one of a runaway pair from Wd2 by
Roman-Lopes et al. (2011). WR 20aa, in the upper half of the table, is the
other star making up the proposed pair.

How both groups of objects are distributed on the sky is shown in figure 2.
Our initial hypothesis is that the first candidate group are the best options
for physical proximity to Wd2: whatever the distance to Wd2 is, these stars
should be at essentially the same distance until the balance of evidence gives
reasonable doubt. This is not anticipated for the second group. We return to
this in the closing discussion (Section 7).

##  3 Observations

The multi-colour photometry and low resolution spectroscopy underpinning this
study was presented and described by MS-II. Here we complete the picture with
a description of higher-quality observations obtained since, of two of the
hottest O-stars in the circum-cluster environment of Wd2, using the X-shooter
instrument on ESO’s Very Large Telescope (VLT) in April/May 2015.

###  3.1 Choice of targets for higher resolution spectroscopy

Table 2: Positions and properties of the X-shooter targets. Target name | RA (J2000) | Dec (J2000) | $g$ | Spectral type and heliocentric
---|---|---|---|---
|  |  |  |  | RV from Rauw et al (2011)
|  |  | Vega mag. | source |
#1273 | 10 23 26.43 |  $-$57 56 03.68 | 15.56 | MS-II |
#1338 | 10 26 03.10 |  $-$57 31 43.06 | 14.99 | MS-II |
MSP 182 | 10 23 56.18 |  $-$57 45 30.00 | 15.33 | MS-II | O4V-III((f)), RV $=30.5$ km s-1
MSP 199 | 10 24 02.65 |  $-$57 45 34.33 | 14.79 | VPHAS$+$ DR2 | O3-4V, RV $=30.6$ km s-1
MSP 183 | 10 24 02.36 |  $-$57 45 30.59 | 15.41 | VPHAS$+$ DR2 | O3V((f)), RV $=23.9$ km s-1
Table 3: Journal of X-shooter observations. The given observation timings correspond to mid-observation times. Target name | Galactic Coordinates | Date (MJD) | UVB exposure time (secs)
---|---|---|---
|  $\ell$ (deg.) |  $b$ (deg.) |  |
#1338 | 284.29885 |  $-$0.51977 | 57132.002615 | 2 x 600
|  |  | 57135.108884 | 2 x 600
|  |  | 57142.049693 | 2 x 600
#1273 | 284.37839 |  $+$0.00914 | 57142.994510 | 2 x 900
|  |  | 57144.992392 | 2 x 900
|  |  | 57155.986232 | 2 x 900
|  |  | 57158.986483 | 1 x 900
MSP 182 | 284.26045 |  $-$0.33575 | 57132.032011 | 2 x 800
MSP 199 | 284.27326 |  $-$0.32911 | 57143.095241 | 2 x 800
MSP 183 | 284.27221 |  $-$0.32859 | 57156.013090 | 2 x 600

MS-I identified a number of potential O-star ejections from Wd2, based on
similarity of extinction to those measured in the cluster itself: 14 objects
were found at separations up to 80 arcmin within the extinction range
$5.8<A_{0}<7.2$ (i.e. to within $1\sigma$ of the measured mean for Wd2, see
Table 8 in MS-I). Some of these were included as targets in the low-resolution
spectroscopic follow-up programme reported by MS-II. Two objects, named #916
and #646 by MS-I, were confirmed as very hot O stars: fits to the low
resolution spectra obtained indicated effective temperatures of $\sim$42.5 kK
and $\sim$40.6 kK respectively, and surface gravities compatible with the main
sequence. Here, they are named according to the superseding MS-II catalogue as
VPHAS-OB1-01338 and VPHAS1-OB1-01273, or #1338 and #1273, for short.

Since these first spectra were not well enough resolved for radial velocity
measurement, we obtained X-shooter observations over a spread of dates in
April and May 2015 that were. To place the new spectra in the Wd2 context, we
also obtained observations of three O stars located in the heart of the
cluster, that have comparable effective temperatures and known radial
velocities. They were selected from the study by Rauw et al. (2011) as
suitable reference objects since they presented no obvious radial velocity
changes due to binary motions. They are MSP 182, 183 and 199 with mean
measured heliocentric radial velocities of 30.5, 23.9 and 30.6 km s-1 (as
obtained from Gaussian fits to the HeII 541.2 nm line). Some of the properties
of these stars are set down in Table 2.

###  3.2 X-shooter observations

The X-shooter spectrograph delivers a spectral resolution of $R=11000$ in the
blue/optical wavelength range where the strongest photospheric absorption
lines seen in O star spectra are located. The target stars #1338 and #1273
were observed in queue mode 3 and 4 times each, over time spans of 10 and 17
days respectively, with the reference objects interspersed. A journal of all
the blue/optical observations obtained per target is given as Table 3. The
seeing at the time of observation was generally not more than 1 arcsec, but
always exceeded the slit width of 0.5 arcsec. The data were extracted into
one-dimensional spectra using the REFLEX package (Freudling et al., 2013),
using default settings of the routines appropriate to the slit/stare mode. In
the case of MSP 183, the traces of two fainter stars are visible in the image
frames towards one end of the 11 arcsec slit: since the sky subtraction uses
median values sampled from $2\times 4$ arcsec along the slit, these will have
had minimal impact on the final spectrum.

##  4 Results

###  4.1 The stellar parameters of #1338, #1273 and the three comparison
objects

Here, we present the results of fitting NLTE model-atmosphere line profiles to
selected transitions in the blue X-shooter spectra. Fits have been applied to
the RV control stars (MSP 182, 199 and 183) as well as to #1338 and #1273 so
that we can place our results in the context of previous work.

The fitting methodology is as described in Sabín-Sanjulián et al. (2014) and
Holgado et al. (2017). Briefly, we first determine the rotational and so-
called macroturbulent velocities with the IACOB-BROAD tool (see Simón-Díaz &
Herrero, 2014), which uses both the Fourier transform and goodness-of-fit
methods. With these values, we then use the grid-based automatic tool IACOB-
GBAT (Simón-Díaz et al., 2011) to determine the stellar parameters. IACOB-GBAT
finds them using an extensive grid of model atmospheres calculated with the
code FASTWIND (Santolaya-Rey et al., 1997; Puls et al., 2005) covering a large
range of stellar model parameters. Six model parameters are varied in the
grid: the effective temperature $T_{\rm eff}$; stellar gravity $\log g$;
helium abundance by number relative to hydrogen $Y_{\rm He}$; the
microturbulence; the exponent of the wind velocity field – assumed to be a
$\beta$ law; the wind-strength parameter $Q={{\dot{M}}/(Rv_{\infty})^{1.5}}$,
where $\dot{M}$ is the mass-loss rate, $R$ the stellar radius and $v_{\infty}$
the wind terminal velocity. A $\chi^{2}$ analysis is carried out over a grid
of nearly 200 000 models (see the above references for more details). Final
fits can be seen in Fig. 3.

Figure 3:  Final fits to the observed target and control stars. We represent
in red the part of the observed spectra that has been used for the analysis,
in blue parts of the observed spectra not used for the analysis and in black
the theoretical spectra, convolved with the rotational and macroturbulent
velocities and the instrumental profile (assumed gaussian). The gray
horizontal and vertical lines give the axes scales

The results for effective temperature, surface gravity, helium abundance and
wind strength parameter are set down in table 4 together with their
uncertainties111the uncertainty in the surface gravity of star $\\#1338$ has
been increased to $\pm$0.10 instead of the formal one of $\pm 0.05$, following
the discussions in Sabín-Sanjulián et al. (2017) and Holgado et al. (2017).
The errors on microturbulence and the wind $\beta$ exponent are degenerate,
i.e., there is not enough information in the observed spectrum to determine
them, and so we do not specify them. At a first glance, all the derived
surface gravities are compatible with the dwarf main sequence status: Martins
et al. (2005) give $\log g=3.92$ (as compared with $<3.8$ for the hottest
giants and supergiants), and the recent work by Holgado et al. (2017) also
indicates that these gravities correspond to luminosity class V stars.
Compared to the fits to the lower spectral resolution AAOmega results reported
by MS-II, the effective temperatures of #1338 and #1273 are raised (to $\sim
45$ kK) but not by amounts incompatible with the uncertainties.

Because there is only one epoch of observation available, the determinations
for the control stars are less precise, reflecting the lower total observed
counts. However, it is striking that all the derived parameters for MSP 182
(O4V, Rauw et al., 2011) nearly match those for #1338 and #1273 (although the
fit to He I 447.1 nm is poorer). The absolute visual magnitudes of the three
objects are consistent with the value of -5.50 assigned to O4V by Martins et
al. (2005), given the likely uncertainty in this quantity of $\sim$0.15. The
effective temperatures are all a little high, by $\sim 1.5-2.0$ kK, relative
to the Martins et al. (2005) and Holgado et al. (2017) scales. However, the
number of stars with spectral type O4 and earlier considered by these authors
is very small and the dispersions relatively large. The derived helium
abundances, $Y_{\rm He}$, are expressed by number relative to hydrogen and
they too agree and are normal. The wind strength parameter log$Q$ is in the
upper range of the values given by Holgado et al. (2017) for dwarfs, as
corresponds to their early spectral types. Taken as a whole, these results
suggest that all three objects are plausibly normal abundance O4V stars at
much the same distance from us: in terms of relative error the $\sim$0.3 mag
dispersion in derived $M_{V}$ is inside the standard deviation of 0.4 mag
specified for dwarfs by Martins et al. (2005).

The other control stars, MSP 199 and MSP 183, lie in the more crowded heart of
Wd2 and are more at risk of contamination, both photometrically and
spectroscopically. In the tabulated results of the Hubble Space Telescope
(HST) analysis by Vargas Álvarez et al. (2013), respectively two and six close
companions to MSP 199 and MSP 183 are listed. The next brightest companion to
MSP 199 is $\sim$2.4 magnitudes fainter in $V$ and at an angular separation of
1.3 arcsec, while for MSP 183 these numbers become $\sim$2.0 magnitudes and
1.5 arcsec. Inspection of the X-shooter 2-D images indicates negligible
contamination (at worst, sky subtraction of MSP 183 is marginally affected).
But there are raised uncertainties in the photometric magnitudes extracted
from ground-based overlapping stellar images.

In recent dedicated photometric studies of Wd2, the cited $V$ magnitudes of
MSP 199 and MSP 183 each span a range of $\sim$0.3. Unfortunately it is not
quite as straightforward as adopting what ought to be cleaner HST $V$
magnitudes because of the evidence that the absolute scale applied by Vargas
Álvarez et al. (2013) is slightly faint (see discussion of this point in
MS-I). For both stars, and also MSP 182, we use the Rauw et al. (2007) visual
magnitudes since they sit in the midst of the published alternatives. For the
visual extinction of MSP 183, we provisionally adopt and adapt the Rauw et al.
(2007) result – replacing their assumed $R_{V}=3.1$ law, by the more suitable
$R_{V}=3.8$ law. This gives $A_{V}\simeq 6.8$. We caution this is much more
uncertain than the extinctions for the other stars since there is no direct
measurement of $R_{V}$.

Table 4: Apparent magnitudes and the absolute visual magnitudes derived from them are presented here, along with the fundamental astrophysical stellar parameters derived from fitting NLTE model-atmosphere line profiles to the observations. The sources consulted for the apparent magnitudes and visual extinctions are given, except for the more crowded and challenging case of MSP 183 (see discussion in text). The data for MSP 183 affected by the greater uncertainty in $A_{V}$ are shown in italic font. The absolute visual magnitudes have been computed for a distance of 5 kpc – note that these would be 0.5 magnitudes fainter if a distance of 4 kpc were adopted instead. Star | $V$ |  $V$ Ref | $A_{V}$ |  $A_{V}$ Ref | $M_{V}$ | $T_{\rm eff}$ | $\log g$ | $Y_{\rm He}$ | log$Q$
---|---|---|---|---|---|---|---|---|---
| (mag.) |  | (mag.) |  | (mag.) | (kK) |  |  |
#1338 | 13.95 | MS-II | 6.17 | MS-II | -5.71 | 45.2$\pm$0.9 | 3.90$\pm$0.10 | 0.10$\pm$0.01 |  $-$12.38$\pm$0.10
#1273 | 14.49 | MS-II | 6.67 | MS-II | -5.67 | 46.3$\pm$1.6 | 3.92$\pm$0.12 | 0.11$\pm$0.03 |  $-$12.70$\pm$0.26
MSP 182 | 14.45 | Rauw et al 2007 | 6.37 | Vargas et al 2013 | -5.41 | 45.5$\pm$3.5 | 3.98$\pm$0.23 | 0.12$\pm$0.05 |  $-$12.57$\pm$0.28
MSP 199 | 14.36 | Rauw et al 2007 | 6.40 | Vargas et al 2013 | -5.53 | 49.1$\pm$3.4 | 4.05$\pm$0.15 | 0.15$\pm$0.07 |  $-$12.78$\pm$0.34
MSP 183 | 13.57 | Rauw et al 2007 | 6.8 | see text | -6.7 | 49.0$\pm$3.0 | 3.88$\pm$0.12 | 0.16$\pm$0.05 |  $-$12.79$\pm$0.33
Table 5: Derived stellar radii, masses, luminosities and wind momenta at the working distance of 5 kpc. We have adopted an uncertainty of $\pm$0.3 mag for $M_{\rm V}$. As in table 4, the less certain data for MSP 183 are shown in italic font. A distance error of $\pm$1 kpc translates into uncertainties of $\pm$0.4 mag in $M_{V}$, and 20% in stellar radius.  Star | $M_{V}$ | $F_{m}$ | $R/R_{\odot}$ | $M/M_{\odot}$ | log$L/L_{\odot}$ | log$\dot{M}$ | log$D_{\rm mom}$
---|---|---|---|---|---|---|---
| (mag.) |  |  |  |  |  |
#1338 |  $-$5.71 |  $-$29.653 | 13.4${}^{+2.0}_{-1.7}$ | 53${}^{+23}_{-16}$ | 5.83$\pm$0.13 |  $-$5.56$\pm$0.14 | 29.22$\pm$0.16
#1273 |  $-$5.67 |  $-$29.685 | 12.9${}^{+1.9}_{-1.7}$ | 51${}^{+24}_{-17}$ | 5.84$\pm$0.14 |  $-$5.91$\pm$0.28 | 28.87$\pm$0.29
MSP 182 |  $-$5.41 |  $-$29.658 | 11.6${}^{+1.8}_{-1.6}$ | 48${}^{+38}_{-21}$ | 5.72$\pm$0.19 |  $-$5.80$\pm$0.30 | 28.97$\pm$0.32
MSP 199 |  $-$5.53 |  $-$29.767 | 11.7${}^{+1.8}_{-1.6}$ | 56${}^{+32}_{-20}$ | 5.86$\pm$0.18 |  $-$5.97$\pm$0.36 | 28.83$\pm$0.37
MSP 183 |  $-$6.7 |  $-$29.758 | 20 | 115 | 5.86 |  $-$5.66 | 29.25

The collected results for MSP 199 and MSP 183 in table 4 indicate these stars
are, at $\sim$49 kK, even hotter than MSP 182. The sense of this difference is
certainly consistent with the earlier O3 spectral types attributed to them by
Rauw et al. (2011). For types earlier than O4, the extremely weak or absent He
I lines drive the effective temperatures towards higher values, producing a
change in the slope that is still controversial (see Sabín-Sanjulián et al.,
2017, and references therein). In this respect, the outcome of the model fits
is satisfactory. But the estimate of $M_{V}$ for MSP 199 is fainter than the
-5.85 expected on the main sequence for O3, while for MSP 183 the estimate is
appreciably brighter and even too bright for supergiant status (whilst more
than 5 kK hotter than viewed as representative for O3I, see Martins et al.,
2005; Holgado et al., 2017). However, their wind strength parameters look
normal for early dwarfs. The results for these two objects are thus less
convincing than for MSP 182, and oppose each other in terms of the distance
that would best suit them – indeed, our 5 kpc working distance emerges as a
rough compromise. The helium abundances for both MSP 199 and 183 are somewhat
elevated, which may imply both are moving away from the zero age main
sequence. This would not be surprising.

Table 6: Radial velocity determinations. All are expressed in a frame that places MSP 182 at 0 km s-1. The errors, $\epsilon$, on the individual measurements are the Gaussian fit uncertainties, while the epoch means have been computed weighting each measure by $1/\epsilon^{2}$. The errors on the means have been computed from the observed scatter of the data contributing to each mean. | Cross-correlation RV shifts (km s-1) | Epoch mean | Overall mean
---|---|---|---
| wrt MSP 182 | via MSP 199 | via MSP 183 |  |
#1338: epoch 1 |  $-$32.2$\pm$2.0 |  $-$30.1$\pm$2.5 |  $-$28.9$\pm$2.0 |  $-$30.4$\pm$2.0 |
2 |  $-$30.2$\pm$2.0 |  $-$26.2$\pm$2.0 |  $-$26.5$\pm$2.0 |  $-$27.6$\pm$2.4 |
3 |  $-$31.5$\pm$2.0 |  $-$28.6$\pm$2.2 |  $-$28.3$\pm$1.9 |  $-$29.5$\pm$1.4 |  $-$29.4$\pm$1.7
#1273: epoch 1 |  $-$18.2$\pm$2.1 |  $-$15.9$\pm$2.0 |  $-$15.3$\pm$1.8 |  $-$16.3$\pm$1.7 |
2 |  $-$17.4$\pm$1.8 |  $-$14.3$\pm$2.0 |  $-$14.1$\pm$1.9 |  $-$15.4$\pm$2.1 |
3 |  $-$13.8$\pm$1.7 |  $-$10.8$\pm$1.8 |  $-$10.9$\pm$1.7 |  $-$11.9$\pm$1.9 |
4 |  $-$16.1$\pm$2.1 |  $-$12.5$\pm$2.0 |  $-$11.8$\pm$1.9 |  $-$13.3$\pm$2.6 |  $-$14.4$\pm$2.2

Now we use the derived parameters to estimate stellar radii for all 5 objects.
Following the same practice as Herrero et al. (1992), the radius $R$ is
defined by

$5\log\frac{R}{R_{\odot}}=29.57-(M_{V}-F_{m})$ (1)

where $F_{m}$ is the logarithm of the integral of the model stellar flux
within the $V$ passband. Finally, the stellar mass, luminosity, mass loss rate
$\dot{M}$ and modifed wind momentum ($D_{\rm mom}$) follow from the values
derived for surface gravity and $R$ (table 5). $D_{\rm mom}$ is obtained from
the modified wind-momentum luminosity relationship (WLR, see Puls et al.,
1996):

$\log D_{\rm mom}=\log(\dot{M}v_{\infty}R^{0.5})=x\log L/L_{\odot}+D_{\rm 0}$
(2)

where values for $x$ and $D_{\rm 0}$ can be found for example in Mokiem et al.
(2007). For the wind terminal velocity ($v_{\infty}$), that we cannot derive
from our spectra, we adopt the canonical relationship between escape velocity
$v_{\rm esc}$ and $v_{\infty}$, that $v_{\rm esc}/v_{\infty}$= 2.65, Kudritzki
& Puls (2000), (but see Garcia et al. (2014) for the limitations of this
assumption). On this basis we find all targets are consistent with the
expectations from the WLR, indicating normal stellar winds for the spectral
types.

The derived masses for #1338, #1273, MSP 182 and MSP 199 are broadly
consistent with the 40–60 M⊙ evolutionary tracks computed by Ekström et al.
(2012), taking stellar rotation into account. For the error propagation we
have considered a somewhat large error for $M_{\rm V}$ ($\sim$ 0.3 mag) but do
not take into account an error in the adopted distance. The high mass
estimated for MSP 183 is subject to the greatest uncertainty, thanks
especially to the less well-validated visual extinction (a change of 0.1 in
$A_{V}$ alone propagates directly to a 10% change in stellar mass – the error
could easily be twice this).

###  4.2 Radial velocity analysis

Our approach to measuring the radial velocities of the two O stars, relative
to the reference objects, has been to use cross-correlation in the blue
spectrum from 360 nm to 510 nm. Tapering to eliminate end effects reduces the
effective wavelength range to 367 – 503 nm. Routines from two independent
astronomical packages (DIPSO and IRAF) have been applied to this task, thereby
testing for differences in numerical handling, such as in the method of
spectrum normalisation. In both cases, the parts of the spectrum containing
the stronger diffuse interstellar bands at $\lambda\lambda$s 442.7 nm and
488.2 nm were removed and replaced by linear interpolations. Each epoch of
observation has been cross-correlated with each reference object, yielding a
grid of $3\times 3$ and $4\times 3$ RV measurements for #1338 and #1273,
respectively. The best agreement, to well within the mutual errors, between
the two independent measures was achieved when the fits included only the top
half of the main cross-correlation function (CCF) peak. We give the results
based on the DIPSO routines as these are accompanied by explicit errors on the
individual CCF peak fits (see Table 6). They are specified in km s-1 on a
scale that sets the mean heliocentric velocity of MSP 182 (30.5 km s-1 Rauw et
al., 2011) to zero.

In extracting these results we need to assume that the mean RVs obtained by
Rauw et al. (2011) for the reference objects remain sound. It is reassuring
that there is no strong systematic effect apparent that undermines this – but
there is some sign in Table 6 of a $\sim$3 km s-1 offset between MSP 182 on
the one hand, and MSP 199 and 183 on the other. This contrast may have its
origin in the spectral type difference (section 4.1 and Rauw et al., 2011) and
could argue for weighting the epoch averages in favour of cross-correlations
with MSP 182 since this star most closely resembles #1273 and #1338. Rather
than introduce arbitrarily-chosen unequal weights in forming the means, we
just take note that the derived means potentially underestimate the blueshifts
by up to $\sim$3 km s-1.

We have also carried out fits of the HeII $\lambda$541.1 nm line profile alone
as a further comparison. The overall means obtained by this route for the two
targets are $-31.1\pm 1.7$ and $-17.5\pm 2.2$ km s-1. To within the errors,
these outcomes are consistent with the cross-correlation results but have the
disadvantage of a systematic dependence on the choice of continuum around the
one line, and of some wind effect on the profile. Accordingly, we prefer the
tabulated cross-correlation measures that capitalise on several spectral
features. These In Table measures are $-29.4\pm 1.7$ and $-14.4\pm 2.2$ for
#1338 and #1273 respectively (Table 6).

The epoch to epoch radial-velocity variation of each star is compatible with
measurement error, with a little more variation apparent in #1273. The
consistency and the pattern from the observations, spanning 10 and 17 days for
#1338 and #1273 respectively, indicate that binary motion is not prominent in
either target and that the measured radial velocities are likely to be a good
guide to the systemic motions of our two targets. We have set up Monte Carlo
simulations to quantify the probabilities involved, using the same method as
Rauw et al. (2011): the reader is referred to section 4, figure 14 and tables
7 and 8 of this previous study for the details. Like Rauw et al. (2011), we:
consider only periods up to 100 days; assume zero eccentricity at periods
shorter than 4 days; adopt flat distributions in both eccentricity ($0<e<0.9$)
and binary mass ratio ($0.1<q<1$). For #1338, the maximum radial velocity
change over the 3 epochs of data is under 5 km s-1. In this case, for a
plausible stellar mass of 50 M⊙, so small a variation all but rules out an
orbital period of under a month – our simulation indicates under 0.5% of
binaries could produce such a signature. The ’missed binary’ percentage rises
to $\sim$2% and $\sim$7% of binaries for periods of respectively 1-2 months,
and $>$2 months. The analogous probabilities for #1273, observed on 4 dates,
and yielding a maximum radial velocity change less than 7 km s-1, would be
very similar, i.e. no more than 0.2%, 1.5% and 6%.

It thus seems most likely that #1338 and #1273 can be regarded, for present
purposes, as single stars whose spectra provide reliable radial velocities.

##  5 Further considerations – a preliminary discussion

Before going onto the relative proper motion data for the entire sample, some
comment is appropriate on three issues: how the radial velocities of #1273 and
#1338 fit into what is already known about the Wd2 sightline kinematics; what
can be gleaned from the literature on potential ejections from Wd2 so that we
do not overlook them; other evidence regarding some sample members that
already implies no association with Wd2 or else that they are not ejections.

###  5.1 On the measured radial velocities of #1273 and #1338

Both of the O stars followed up with X-shooter observations have been shown to
have significantly blueshifted radial velocities relative to the previous
measurements of Wd2 by Rauw et al. (2011). This earlier study noted that most
of the cluster stars were compatible with systemic radial velocities in the
range 20–30 km s-1, in the heliocentric scale. In the Rauw et al. (2011)
sample, four O stars were found to show no or negligible binary motion, and
the mean radial velocity among these is close to $+$27 km s-1. Three of this
group of four are our reference objects, MSP 182, 199 and 183. Referred to MSP
182, the measured relative radial velocities of our two targets are $-29.4\pm
1.7$ and $-14.4\pm 2.2$ km s-1 (Table 6): accepting 30.5 km s-1 as the mean
heliocentric radial velocity of MSP 182 (Rauw et al., 2011), these convert to
absolute heliocentric values of $+1$ and $+16$ km s-1 (hereafter rounding to
the nearest km s-1). Expressed relative to the Wd2 cluster mean taken as $+$27
km s-1, the radial velocities of #1338 and #1273 become $v_{r}=-26$ and $-11$
km s-1, similarly rounded.

Already, the first of our targets, #1338, comes close to fitting the commonly-
understood definition of a runaway star, with a space velocity exceeding 25 or
30 km s-1 (depending on preferred definition). Later, account will be taken of
the transverse motion (see Section 6).

For object #1273, the circumstances are not so clear-cut. To expose this, it
is helpful to shift from the heliocentric frame to the Local Standard of Rest
(LSR). The correction from heliocentric to LSR is $-9.0$ km s-1 (using the
solar motion data from Schönrich et al., 2010). This places Wd2 at a
$v_{LSR}=18$ km s-1 and object #1273 at $v_{LSR}=7$ km s-1. CO observations of
the region have revealed molecular clouds at $v_{LSR}=16$, $4$ and $-4$ km s-1
(Furukawa et al., 2009), that all show elevated temperatures consistent with
heating by Wd2 and its HII region RCW 49 (Ohama et al., 2010). Dame (2007)
presented absorption measurements showing that the 4 and $-$4 km s-1 clouds
are in front of the 16 km s-1 cloud, and argued that Wd2 is in a cavity in
front of the latter, whilst behind the former. Given the uncertainty in the
measured stellar radial velocity, and the location of #1273 on the edge of the
$+$4 km s-1 cloud, the evidence may be read as a potential kinematic relation
between the two.

###  5.2 Candidate massive star ejections from Wd2 from prior literature

The work by Rauw et al. (2011) pointed to two more early O stars with, again,
significantly negative radial velocities relative to the other Wd2 members.
These were MSP 18 and 171, for which the mean heliocentric radial velocities
obtained were $(-1.1\pm 1.8)$ and $(-9.3\pm 6.9)$ km s-1. Relative to the mean
for the cluster these become $v_{r}=-28$ and $-36$ km s-1 – similar to, if a
little larger than, our result for #1338. Here, if these stars are ejections,
the transverse velocities should not contribute very much to the total space
velocity since both objects are only modestly displaced from the bright
cluster core. The repeat observations obtained by Rauw et al. (2011) did not
reveal obvious binary motion in either case.

We mentioned already in Section 2.2 the proposal by Roman-Lopes et al. (2011)
that the Wolf-Rayet (WR) stars WR20c and WR 20aa, both typed as O2If∗/WN6,
were ejected from Wd2. Their angular separations from Wd2 bracket that of
object #1338, in being $\sim$25 and $\sim$15 arcmin respectively. Roman-Lopes
et al. (2011) were particularly struck by the fact that the line on the sky
joining WR 20c and WR 20aa passes through the stellar-density centre of Wd2.
Whilst the arresting sky geometry might suggest ejection, there is no back up
from radial velocities since these are very hard to measure from spectra
dominated by strong and broad WR line emission.

A challenge presented by WR 20c, is that its extinction is appreciably higher
than prevails in and around Wd2 itself. Roman-Lopes et al. (2011) provide a
measurement of the colour excess, $E(B-V)=2.9$, which is close to the value of
2.8 consistent with the MS-II best fit values, $A_{0}\simeq 10.3$ and
$R_{V}\simeq 3.7$ (see table 1). The visual extinction to this object,
although approximate, lies well above and outside the range $5.5<A_{0}<7.5$ we
have used here to select O stars more likely to have a physical association
with Wd2. If this WR star is an ejection from Wd2, it has moved behind a very
substantial, localised column of gas and dust - representing around two-thirds
of the column, in addition, that accumulates towards Wd2 itself (assuming no
great change in dust grain properties). In this circumstance, the heating and
ionizing effect of WR 20c on a nearby dark cloud. might well be noticeable,
and yet there is no clear sign of heated dust in WISE data. This absence along
with the enormous additional dust column raises the suspicion WR 20c may be a
background object.

For WR 20aa, the extinction is not obviously problematic – the MS-II measures
are $A_{0}\simeq 5.6$ and $R_{V}\simeq 4.3$, implying $E(B-V)=1.3$ (cf. 1.5
from Roman-Lopes et al., 2011). This is less than for Wd2 itself, but by no
more than a magnitude.

At this point it is appropriate to also mention the brighter WR star, WR 21a,
located $\sim$16 arcmin away from the centre of Wd2. It is too bright to have
been included in the MS-II catalogue. This star is known to have an O star
companion and the binary orbit has been analysed (Tramper et al., 2016), but
there is no reported measurement of a systemic radial velocity. Roman-Lopes et
al. (2011) drew attention to it as lying on a vector almost perpendicular to
the line on the sky joining WR 20c and WR 20aa, and wondered if it too is an
ejection.

###  5.3 A distinct OB grouping and other ’unrelated’ objects

Figure 4:  Top panel: a $3\times 3$ arcmin2 cut-out VPHAS$+$ $i$-band image
around object #1338. The stellar density in the area is significant, but there
is no sign of an over-density of fainter stars around #1338. The green circle
has a radius of 10 arcsec. Lower: the 2MASS $K$ versus $J-K$ colour-magnitude
diagram, around #1338. All objects within a radius of 3 arcmin are included,
and they are coloured according to how far they are from #1338: bright pink
implies $<0.25$ arcmin separation; cyan $<0.5$ arcmin; grey (circles) $<1$
arcmin. Star #1338 itself is in pink, located at $K\simeq 9.4$.)

Figure 5:  The same as Figure 4 for #1567. In this case there is sign of a
rise in fainter-star stellar density around #1567, that is backed up by
evidence in the NIR CMD that there are the beginnings of a credible localised
cluster main sequence (the line of 7 bright pink points, with #1567 at the top
– two of the stars have almost identical $J-K$, $K$ magnitudes.)

We now pose the question as to which of the O star candidates in Table 1
exhibit properties that argue against a connection with Wd2. One such property
– already used against WR 20c – is appreciably higher extinction that could
point to greater distance. We deal with this first in considering the
candidate objects also included in the lower part of Table 1.

Above $A_{0}=7.5$, the MS-II catalogue lists only 4 good OB stars located
within 10 arcmin of the centre of Wd2 - to be compared with 36 in the range,
$5.5<A_{0}<7.5$. Just one of the four is close to the dividing line with its
extinction given as 7.74. It was this dramatic dropping away in the extinction
distribution that prompted the choice of $A_{0}=7.5$ as a selection boundary
and the division into two of Table 1. All the same, it is arbitrary, and we
now examine it in more detail.

A notable feature of the sky distribution of the $A_{0}>7.5$ objects, more
than 10-arcmin radius from Wd2, is that 14 (out of 21 altogether) appear
loosely grouped around $\ell=283.9^{\circ}$, $b=-0.9^{\circ}$ (see Figure 2).
The extinctions for these stars fall within the range $7.5<A_{0}<8.6$ (Table
1), hinting this is not necessarily an asterism. 8 of the 14 objects form a
dense inner cluster. Perhaps this is an association, independent of Wd2, at a
different, possibly greater, distance. These stars are identified in Table 1
by the comment ’$A_{0}\sim 8$ BG’ – BG is short for ’background group’. We add
to the group two stars, #0986 and #0987, with $A_{0}=7.33$ and 7.40 that
belong otherwise to the upper part of Table 1. Their location in the same part
of the region and their almost-as-high extinction indicate this could be
appropriate.

The $K$ magnitudes of the proposed grouping are fainter, ranging from 9.6 down
to 12.7. Presently, none of these stars has a spectrum, and so only the
photometric estimates of effective temperature are available: they run from
$\sim 30$ up to $\sim 40$ kK. Of the 6 remaining higher-extinction objects
(excluding WR 20c), 2 are in the same sky area as the $A_{0}\sim 8$ group,
while the other 5 are widely scattered (see Figure 2).

A separate question to ask of the candidate objects in the upper part of Table
1 is whether any of them seems likely to have an associated cluster of fainter
stars. Any that do cannot have formed in and have been ejected from Wd2 –
ejected stars do not take clusters with them. We have examined VPHAS+ $i$ band
images for relative stellar over-densities around these objects, and have
constructed 2MASS colour-magnitude diagrams (CMDs) to look for evidence of
coherent cluster sequences. VPHAS+ $i$ offers the higher dynamic range in that
most of the 19 stars have $i$ magnitudes between 12 and 13, easily permitting
a well-defined search for companion objects that are 6–7 magnitudes fainter,
reaching down into the later A spectral-type range (assuming $M_{i}\sim-4$ for
late O stars, and $M_{i}\sim 2.5$ for late A stars). From 2MASS, we have
constructed $K$ versus $J-K$ diagrams that optimise for minimum impact of
extinction on the vertical axis, and a better dynamic range in the colour
dimension on the horizontal axis.

The results of this exercise are illustrated in Figures 4 and 5, which include
an $i$-band cut-out and 2MASS CMD for respectively #1338 as an example of a
star without any evident clustering around it, along with the same for #1567
which emerges as the only object colocated with a potential cluster. The $i$
over-density in this second case within 0.5 arcmin of the star is 1.9$\sigma$
(assuming Poisson statistics), and it is the only example that indicates a
convergence onto a nearly vertical cluster main sequence as the area of 2MASS
selection around the star is shrunk down onto the star. The next best example
is #1102 for which the over-density significance is down to 1.4$\sigma$, and
yet the NIR CMD is unconvincing. Consequently, only #1567 is proposed with any
confidence as associated with its own cluster, thus becoming an unlikely
ejection.

Last of all, some words on object #0708 are appropriate. The photometric
estimate of this object’s effective temperature (in Table 1, part (a))
suggests it is a B1–O7 star. It can be seen in Figure 2 that this star is
positioned close to the bow-shaped nebulosity near $\ell=283.5^{\circ}$,
$b=-1.0^{\circ}$. The nebula here is NGC 3199, an HII region excited by WR 18,
a bright Wolf-Rayet star, likely to be $\sim$2 kpc away (van der Hucht, 2001).
The angular separation between #0708 and WR 18 is just 1.14 arcminutes, and
the 2MASS K magnitude of #0708, the brightest in our selection, is only 0.26
fainter than that for WR 18. Accordingly a physical association between WR 18,
NGC 3199 and #0708 at $\sim$2 kpc appears to be the better bet. In addition,
recent work by Toalá et al. (2017) challenges an older view that WR 18 is a
runaway from Wd2: they do this on grounds of proper motion data on the WR star
and stars near it, and also the far-infrared morphology of NGC 3199.

##  6 Relative proper motions from Gaia DR2

Whilst Gaia DR2 parallaxes are not yet good enough for estimating the distance
to Wd2 or the potentially associated O stars, the proper motion (PM) data are
already very useful. In and around Wd2 they are typically 5–7 mas yr-1 in
magnitude, and we can propagate the uncertainties in PMs relative to the
cluster mean from those stated in the released database. The first step in
measuring the relative PMs is to determine the Wd2 cluster mean.

The Gaia DR2 database was cross-matched with the objects in Figure 1, after
the stars lying outside the core $8<K<12$ range had been trimmed off. The
remaining objects were then checked for astrometric quality: one object was
removed for being flagged as ’duplicate’, while some were rejected on grounds
of high excess astrometric source noise (using $\epsilon_{i}$, see the
$G$-dependent thresholds in table B.1 of Lindegren et al., 2018). We also
excluded MSP 18 and MSP 171, since these are candidate runaway stars (see
Section 5.2). This left us with 25 objects. The median proper motion derived
from them is $\mu_{\alpha,*}=-5.172$ mas yr-1, $\mu_{\delta}=2.990$ mas yr-1.
Further reduction of the sample to limit it to 18 stars in the densest part of
the cluster, occupying a little over one square arcminute, only altered the
last decimal place in these measures. The sample standard deviations (for the
25 stars), created by a combination of astrometry error and velocity
dispersion with the cluster, are 0.204 and 0.164 mas yr-1 in RA$\ast$ and Dec
respectively.

Converting the median cluster PM into Galactic co-ordinates, we obtain
$\mu_{\ell,*}=-5.970$ mas yr-1, $\mu_{b}=-0.227$ mas yr-1. It is encouraging
and to be expected that the representative cluster PM emerges as almost
entirely in the longitude direction: a cluster as young as Wd2 should closely
follow Galactic disc rotation. These values have been subtracted from the
proper motions, in Galactic coordinates, of all the objects listed in Table 1
(see the Appendix for the names of Gaia DR2 sources cross-matched to them).
The resulting relative PMs, and their errors, are visualised in Figure 6.

Figure 6:  The relative proper motions derived for all objects in Table 1, excepting #1550 for which the Gaia DR2 data are problematic. MSP 18 and MSP 171, near the cluster centre are not included either since most of their space motion is in their radial velocities. The direction and amount of proper motion is represented by the black line drawn away from each object: the length of each vector corresponds to the angle each object would move through in 0.2 Myr. The red circles pick out the stars listed in Table 7 (excepting WR 21a – see text), whose relative PM vectors point outward from Wd2. The remaining objects and WR 21a, are shown as blue dots, and in many cases the relative proper motion is so small that the PM vector is hard to see. The white box at the end of each relative PM vector indicates the directional error zone propagated from the Gaia DR2 uncertainties.  Table 7: Proper motions and related quantities for stars potentially qualifying as runaways from Wd2. The Gaia DR2 proper motions appear in columns 2 and 3. Columns 4 and 5 give the proper motion relative to the WD2 cluster median, re-expressed in Galactic coordinates. Column 6 is the (distance-independent) travel time from the fiducial position, $\ell=284^{\circ}.27$, $b=-0^{\circ}.334$. Column 7 gives $v_{t}$ for the working distance of 5 kpc, accompanied by the range allowing for varying the distance from 4 to 6 kpc in brackets and taking into account random error in the total relative proper motion. The last column gives the full space velocity, $v_{s}$, where known – again giving the range for $4\leq D\leq 6$ kpc in brackets. The 3 objects below the horizontal line are additional to the MS-II sample of stars in Table 1. Object | Proper motion | Relative PM | Travel time | $v_{t}$ | $v_{s}$
---|---|---|---|---|---
|  $\mu_{\alpha,*}$, $\mu_{\delta}$ mas/yr |  $\Delta\mu_{\ell,*},\Delta\mu_{b}$ mas/yr | Myr | km/s | km/s
Wd2 centre | -5.173$\pm$0.041 | 2.995$\pm$0.033 | $-$ | $-$ |  |  |
#1046 |  $-$4.441$\pm$0.051 | 6.675$\pm$0.051 |  $-$1.344$\pm$0.062 | 3.494$\pm$0.064 | 0.76 | 89 (69–110) |
#1102 |  $-$5.489$\pm$0.051 | 3.722$\pm$0.054 |  $-$0.653$\pm$0.062 | 0.440$\pm$0.067 | 0.88 | 19 (15–23) |
#1133 |  $-$5.092$\pm$0.067 | 3.967$\pm$0.074 |  $-$0.449$\pm$0.071 | 0.859$\pm$0.088 | 0.80 | 23 (18–29) |
#1236 |  $-$4.707$\pm$0.075 | 3.781$\pm$0.079 |  $-$0.024$\pm$0.080 | 0.907$\pm$0.090 | 0.68 | 22 (17–27) |
#1273 |  $-$5.716$\pm$0.060 | 1.872$\pm$0.056 | 0.143$\pm$0.071 |  $-$1.244$\pm$0.066 | 0.54 | 30 (23–37) | 32 (26–38)
#1338 |  $-$3.856$\pm$0.064 | 3.949$\pm$0.058 | 0.605$\pm$0.068 | 1.504$\pm$0.075 | 0.80 | 39 (30–48) | 47 (40–54)
#1374 |  $-$5.973$\pm$0.037 | 1.126$\pm$0.033 | 0.324$\pm$0.053 |  $-$2.011$\pm$0.049 | 1.08 | 48 (38–60) |
WR20aa |  $-$5.876$\pm$0.055 | 1.186$\pm$0.054 | 0.374$\pm$0.065 |  $-$1.908$\pm$0.067 | 0.48 | 46 (36–57) |
WR20c |  $-$3.715$\pm$0.154 | 6.119$\pm$0.140 |  $-$0.434$\pm$0.136 | 3.412$\pm$0.165 | 0.44 | 82 (60–106) |
MSP 18 |  $-$5.295$\pm$0.085 | 3.292$\pm$0.085 |  $-$0.260$\pm$0.085 | 0.273$\pm$0.100 |  $\sim$0.1 | 9 (6–12) | 29 (28–31)
MSP 171 |  $-$4.761$\pm$0.063 | 2.898$\pm$0.059 | 0.402$\pm$0.072 | 0.133$\pm$0.070 |  $\sim$0.1 | 10 (7–13) | 37 (34–42)
WR 21a |  $-$4.025$\pm$0.051 | 2.518$\pm$0.045 | 1.226$\pm$0.062 | 0.205$\pm$0.059 | 0.65 | 30 (23–37) |

Data on the relative PMs of those stars revealed in Figure 6 as potential
ejections, are set out in Table 7 along with the main derived quantities: we
specify the relative PM and error, along with estimates for: the travel time
as given by ratio of the relative PM to the angular separation from Wd2 (this
assumes constant ejection speed); the transverse speed, $v_{t}$ in the plane
of the sky; finally, where we have it, $v_{s}=\sqrt{v_{t}^{2}+v_{r}^{2}}$, the
full space motion. The error budget does not include the $\sim$0.1 mas
basement error advised by Lindegren et al. (2018) since this is systematic and
unlikely to influence relative motions measured within $\sim$1 degree on the
sky. The PM errors from the individual-source random errors and correlations
are indicated in Figure 6. It is important and of course very useful that
these errors are mostly small. We did not compute the relative PM for one
object – #1550: this had to be left out because the Gaia DR2 catalogue flags
it as duplicated, and indeed the stated errors are very large. In all other
cases, the available astrometry is based on at least 15 distinct epochs and
all, bar WR 20c, have $u=\sqrt{\chi^{2}_{\nu}}$ safely below the cut
recommended by Lindegren et al. (2018) (see their equation C.1). For WR 20c –
by far the reddest object in the sample – $u$ is $\sim$9, rather than
$\lesssim 3$ as recommended by the $G$-sensitive cut.

The most striking features of the derived relative PMs are the number of
likely ejections (up to 12, at first sight) and their apparent on-sky
alignment with a direction almost perpendicular to the Galactic equatorial
plane. Both WR 20c and WR 20aa are included in this group, with WR 20c as the
only example from the lower half of Table 1. In general terms, the expectation
that stars with similar extinctions to the stars in Wd2 would more likely be
associated with the cluster has been borne out: seven objects from the upper
half of Table 1 have relative PMs compatible with ejection from Wd2. This
group includes both #1338 and #1273. The earliest ejection appears to be
#1374, for whom the travel-time estimate is a little over 1 million years.

There is one exception to the general alignment: the binary, WR 21a also has a
significant PM relative to Wd2, but it stands apart in being directed almost
at right angles to the main ejection axis (see Figure 6). As for WR 20c and
WR20aa, no systemic radial velocities are yet available (and will be
challenging to obtain). But there is an important point of difference in that
the raw PM in this case, $\mu_{\ell,*}=-4.744\pm 0.048$, $\mu_{b}=-0.022\pm
0.048$ mas yr-1, has a negligible Galactic latitude component. This offers an
alternative reason for the difference in its PM compared with Wd2: WR 21a may
simply be unrelated and at greater distance than the cluster.

We include in Table 7 the relative PMs of MSPs 18 and 171, the objects
measured by Rauw et al. (2011) to have significant blueshifted radial
velocities (see Section 5.2). At amounts corresponding to transverse
velocities of no more than $\sim$10 km s-1 at 5 kpc, in both cases, it is
clear that most of their motion is indeed radial (see section 5.2 and Table
7). Their relative PMs are directed away from the main clustering, although
defining this precisely is rendered impossible by both the greater
significance of the errors and proximity to the central region. However, the
existence of some proper motion and the positioning of both toward the
periphery of the main Wd2 cluster allows a very rough estimate of the elapsed
time since expulsion: it cannot be much more than 105 years in either case.

A further outcome is support for the presence of a distinct, potentially
background, OB-star grouping (discussed above in Section 5.3). There are
evidently small and disordered relative PMs within or near the rectangular
region picked out in Figure 6, no star in this region presents with $v_{t}$
approaching 20 km s-1 (at 5 kpc), that is also directed away from Wd2.

There is one prominent example of an object with a large relative proper
motion that does not trace back to the vicinity of Wd2: this is object #1356,
below Wd2 in Figure 6 moving at $\sim$60 km s-1 relative to Wd2 (if 5 kpc
away). It has a significant absolute proper motion away from the Galactic
Plane (of $-1.078\pm 0.047$ mas yr-1) suggesting it could be an escape, but
from where is as yet unidentified. Object #1086 above Wd2 in Figure 6 is a
more modest example: it is much more highly extinguished ($A_{0}=9.7$) and
perhaps well beyond Wd2.

Finally, we note that #1567, the star picked out as most likely to be in a
cluster of its own (Section 5.3), is seen in Figure 6 to show little relative
proper motion.

##  7 Discussion

Fujii & Portegies Zwart (2011); Fujii et al. (2012) carried out simulations of
massive young clusters, citing Wd2 as such a cluster, in order to quantify the
likely ejection yield from early-phase intra-cluster dynamical interactions.
Essentially, the simulated ejections are all the product of interaction with a
steadily hardening binary in the cluster core. (Fujii & Portegies Zwart, 2011)
predicted that clusters like Wd2 should eject $5.2\pm 1.6$ stars more massive
than 8 $M_{\odot}$ in their first Myr. Their results also showed that the
distribution of space velocities is skewed towards the low end, heavily
favouring the 20–30 km s-1 range (see Figure 6 in Fujii & Portegies Zwart,
2011). However the expectation for early O stars would be space velocities
more in the region of 40 km s-1. We can ask now whether this makes sense
compared with our results on the diaspora of O Stars around Westerlund 2.
Given that we now have, from Table 7:

  * •

Up to 7 O-star ejections in the neighbourhood, exhibiting extinctions and $K$
magnitudes compatible with those of O-type members of Wd2. Radial velocities
are presently unmeasured for 5 of them. Objects #1338 and #1273 are in this
group of 7, and have full space motions that fit in with ’runaway’
designation, even at a distance of 4 kpc, that we regard as at the low end of
the likely distance range to Wd2 and associated objects. The longest timescale
since ejection is just over 1 Myr (for object #1374). For #1374 and #1046 the
relative PMs are already so large, it goes against Occam’s Razor not to regard
them as most likely ejections from Wd2. There are thus 3 stars, #1102, #1133
and #1236, with more modest relative PMs for which the case for association
and ejection is not quite as complete. It is noteworthy that #1236 might be a
partner to #1273, lying directly on the opposite side of the cluster centre
(see Figure 6).

  * •

A demonstration that WR 20c and WR 20aa have proper motions consistent with
ejection from Wd2 also within the last million years.

  * •

MSP 18 and MSP 171, the $\sim$O5 stars studied by Rauw et al. (2011)
projecting onto the cluster core. Their space motions away from Wd2 are
respectively 29 and 37 km s-1 and are dominated by the distance-independent
radial velocities. In view of their sky positions close to the centre of Wd2
this is as expected.

This adds up to 8 convincing ejections, and 3 more that could be, within the
1.5$\times$1.5 sq.deg. box examined. In view of WR 21a’s PM and relative PM
being almost entirely in Galactic longitude and, so, potentially attributable
to being more distant than Wd2, we do not include it in the tally.

The prediction of Fujii & Portegies Zwart (2011) for ejected numbers has been
more than met. There is potential here for the ejected O-star population to be
a large fraction of the total remaining in the cluster. The cluster core only
contains $\sim$30 O stars altogether (Vargas Álvarez et al., 2013), implying
an ejection efficiency of between 21 and 27%. But the data in Figure 3 of
Fujii & Portegies Zwart (2011) would favour only 5 to 10% . There is a clear
candidate ’bully binary’ in this cluster in WR 20a, for which the estimated
total mass is $\sim$165 M$\odot$ (Bonanos et al., 2004), but can it have
promoted so many ejections, and why would there be a preferred plane for the
process?

A separate clue to what might be going on here comes from the structure of Wd2
itself: Zeidler et al. (2017) have commented on the presence of the ’northern
clump’ offset from the main cluster by almost an arcminute: they argue that
this would be consistent with late merging behaviour if Wd2 has built up from
sub-clusters. These authors, along with Furukawa et al. (2009) and others
studying the molecular gas, have also raised the possibility that a larger
scale molecular cloud collision was the ultimate trigger for Wd2’s formation.
If so, the modelling of Lucas et al. (2018) on the creation of an O-star halo,
as a product of earlier molecular cloud/proto-cluster merging history, becomes
directly relevant. A feature of these models is that lower space velocities
($<20$ km s-1) are expected, and the distribution of objects within the halo
should follow what would once have been tidal tails in the merging process.
Whilst this might explain the existence of the preferred proper motion plane –
which is roughly north-south – higher measured speeds are more in keeping with
dynamical ejection. Even at the near distance of $\sim 4$ kpc, the 4 complete
space velocities now in hand scatter from 26 up to 40 km s-1 (see Table 7).
Interestingly, the follow-up simulations by Fujii et al. (2012) did examine
the option of merging 4 sub-clusters as a model for Wd2: the key result
apparent in Figure 7 of their paper is that the runaway fraction would then
rise to 15 to 20% (depending on where the stellar mass cut is made). This is
more promising.

Ultimately, it is certainly credible that both dynamical ejection and sub-
cluster collision and merging can operate. In the case of #1273, it was
pointed out in Section 5.1 that its RV is similar to one of the molecular gas
components plausibly just in front of Wd2. This may not be a coincidence. What
is clear, and has no dependence on the still uncertain distance to Wd2, is
that the ejections identified so far have taken place over the last million
years. If this phase of activity was initiated by the merging of pre-existing
sub-clusters, it leaves open a longer timescale for the WR stars to evolve
within. Indeed a search over a wider area for more ejected objects might
provide evidence for a longer timescale.

A further point to make is that all the likely ejections are either earlier-
type O or WR stars. For 3 of them (#1046, #1102, #1133) we do not have
spectroscopic parameters to hand. Among these, #1046 has the coolest effective
temperature estimate ($\sim 35$ kK) of the set, based on its photometric
properties. On the Martins et al. (2005) scale, this corresponds to $\sim$O7
spectral type. The status of #1273 and #1338 is now very clear: these are
certainly O4 stars, with masses most likely $\sim$50 M⊙ or more (Section 4.1).
Better parameters from spectroscopy are clearly needed to e.g. tie down the
higher stellar mass favouritism of the ejection process and its efficiency.

In contrast, there remains a set of 5 mostly cooler O stars (#0673, #0693,
#0893, #0994 and #1164) from the upper half of Table 1 that show little
relative PM and no clear sign, so far, of associated clusters. Only for #1567
is there sign it has its own cluster. As found in other work there remains
scope for isolated formation and/or stochastic sampling of the IMF. How far
these stars are from Wd2 is another question awaiting follow up spectroscopy.

The object, WR 20c, remains a conundrum. Its kinematics, as revealed by its
proper motion, are clearly consistent with ejection from Wd2. But how then are
we to understand the huge differential extinction of around 4 visual
magnitudes with respect to Wd2 – combined with no sign in WISE mid-IR data of
local dust warming. This warrants further investigation, and we note that the
astrometry on this object – no doubt thanks to its high extinction – is the
least robust at the present time.

##  8 Conclusions

New observations presented here have enabled the measurement of stellar
parameters and radial velocities of two recently-identified massive stars
($M>40M_{\odot}$) at projected distances of $\sim$15 and $\sim$30 pc from Wd2.
At the working distance of 5 kpc, the absolute magnitudes of VPHAS-OB1-01273
and VPHAS-OB1-01338 (and their RV comparison stars in Wd2) fit comfortably
with the class V values for their spectral types set out by Martins et al.
(2005). The radial velocity and proper motion data now in hand for both
indicate they are moving away from this young massive cluster, and that they
meet the standard runaway criterion, of a space velocity exceeding $\sim$25 km
s-1 or more (at a distance of at least 4 kpc). Repeat observations indicate a
low risk that the measured radial velocity of either object is significantly
influenced by so-far undetected binarity.

The second main result, based on Gaia DR2 proper motions, concerns the
frequency and on-sky distribution of recent early O and WR star ejections from
Wd2 (located within a box of 1.5$\times$1.5 sq.deg.). The number of likely
ejections (between 8 and 11), their typical speeds, and their near N–S
alignment cannot be explained by either sub-cluster merging or dynamical
ejection alone. A combination of both might work.

Spectroscopic follow up of a quality sufficient to provide more radial
velocities to a precision of 2–3 km s-1, and stellar mass estimates, for more
of the recently uncovered O stars in the area is needed to work through what
is proving to be an interesting and informative example of a massive-cluster
O-star diaspora. In discussing the results now available, we can already see
that insights into the history of Wd2’s formation may be forthcoming. The work
so far has neatly distinguished ’runaway’ O stars ejected in the last million
years, from those exhibiting little relative motion that remain as isolated
field O stars, mostly with little sign of their own clusters. A search over a
wider sky area than here could be of interest to rule on whether Wd2 has been
ejecting massive stars for longer than a million years. Given the young age of
Wd2, more than $\sim$2 million years is very unlikely.

In this study of Wd2 we began with the hypothesis that extinction can provide
a first cut on identifying a cluster’s more immediate associated population.
It is an easy cut to make, given the good quality extinction data available
from MS-II, and it has proved useful. Making this distinction helped draw
attention to a separate, more reddened physical grouping, made up of a tight
clustering of O stars at $\ell\simeq 283.88^{\circ}$, $b\simeq-0.91^{\circ}$,
embedded in a lower density $\sim$20 arcmin halo. This first impression is now
backed up by the relative proper motion data. All the new candidates for
ejection from Wd2 have come from an initial selection of stars with similar
reddening to Wd2.

Now that we can (i) find O and early B stars with ease across the Galactic
Plane to many kiloparsecs and behind up to $\sim$10 magnitudes of optical
extinction, (ii) combine these findings with Gaia proper motions, the path to
a much richer understanding of the sites of their formation and subsequent
kinematic histories is well and truly open.

## Acknowledgements

This paper is based on data products from observations made with ESO
Telescopes at the La Silla Paranal Observatory under programme ID 095.D-0843.
It also rests on results obtained directly from the VST Photometric Hα Survey
of the Southern Galactic Plane and Bulge (VPHAS+, www.vphas.eu; ESO programme
177.D-3023). Use is also made of data products from the Two Micron All Sky
Survey, which is a joint project of the University of Massachusetts and the
Infrared Processing and Analysis Center/California Institute of Technology,
funded by the National Aeronautics and Space Administration and the National
Science Foundation. WISE and AAT service programme acknowledgements. This work
has made use of data from the European Space Agency mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

This research made use of TopCat (Taylor, 2005).

JED and MM acknowledge the support of a research grant funded by the Science,
Technology and Facilities Council of the UK (STFC, ref. ST/M001008/1). AH
acknowledges support from Spanish MINECO under project grants
AYA2015-68012-C2-1 and SEV2015-0548 and from the Gobierno de Canarias under
project grant ProID2017010115. NJW acknowledges receipt of an STFC Ernest
Rutherford Fellowship (ref. ST/M005569/1).

We thank an anonymous referee for comments that have helped improve this
paper’s content.

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##  Appendix A Further positional information

The table below supplements Table 1 with celestial coordinates for every
object and identifies the cross-matched 19-digit Gaia DR2 source name. For
completeness, the additional objects discussed in connection with Table 7 are
also included. It can be seen that the typical cross-match distance is most
often between 0.1 and 0.15 arcsecs. In no case is there difficulty in
identifying the counterpart source.

Table 8: The columns contain: the full MS-II object name; object position as given by MS-II (RA, Dec J2000); the linked Gaia source identification number; cross-match distance in arcsec between the MS-II and Gaia DR2 positions, rounded to 2 significant figures. Note that the celestial coordinates are also rounded, rather than truncated, to two decimal places (in seconds of time and arc). The order of listing in the table is as in Table 1, with the 3 already known objects added on in section (c). Objects appearing in Table 7 are marked with an asterisk in the final column. MS-II name | RA,Dec J2000 | Gaia Source # | offset |
---|---|---|---|---
| (hh:mm:ss) | (dd:mm:ss) |  | (arcsec) |
(a) |  |  |  |  |
VPHAS-OB1-00673 | 10:18:22.62 | -57:31:08.63 | 5258689821862198272 | 0.08 |
VPHAS-OB1-00693 | 10:19:01.47 | -57:26:34.40 | 5258710854331053696 | 0.12 |
VPHAS-OB1-00708 | 10:16:53.91 | -57:55:02.11 | 5258584101263763200 | 0.09 |
VPHAS-OB1-00893 | 10:19:47.82 | -57:50:38.64 | 5258666800837002880 | 0.19 |
VPHAS-OB1-00986 | 10:19:53.04 | -58:00:00.42 | 5258659074204741760 | 0.16 |
VPHAS-OB1-00987 | 10:19:33.60 | -58:04:05.07 | 5258656909541094400 | 0.15 |
VPHAS-OB1-00994 | 10:21:20.56 | -57:43:09.40 | 5255690873859259904 | 0.14 |
VPHAS-OB1-01046 | 10:25:35.77 | -57:00:00.07 | 5351803514564210560 | 0.12 | *
VPHAS-OB1-01102 | 10:23:46.52 | -57:34:15.51 | 5351760152573602944 | 0.12 | *
VPHAS-OB1-01133 | 10:24:19.34 | -57:33:02.48 | 5351760908487879296 | 0.12 | *
VPHAS-OB1-01164 | 10:22:18.41 | -58:02:16.66 | 5255647507548038272 | 0.10 |
VPHAS-OB1-01236 | 10:24:43.47 | -57:37:15.94 | 5351757438154160000 | 0.13 | *
VPHAS-OB1-01273 | 10:23:26.43 | -57:56:03.67 | 5255669399023171456 | 0.16 | *
VPHAS-OB1-01308 | 10:23:23.50 | -58:00:20.80 | 5255667681036173568 | 0.13 | *
VPHAS-OB1-01338 | 10:26:03.10 | -57:31:43.06 | 5351717851422618496 | 0.06 | *
VPHAS-OB1-01356 | 10:23:59.03 | -58:00:48.44 | 5255668024633629824 | 0.12 |
VPHAS-OB1-01374 | 10:22:32.65 | -58:20:31.99 | 5255633871052073728 | 0.14 | *
VPHAS-OB1-01550 | 10:25:41.75 | -58:05:52.80 | 5255622016940658304 | 0.18 |
VPHAS-OB1-01567 | 10:24:42.37 | -58:20:31.94 | 5255590264223148032 | 0.11 |
(b) |  |  |  |  |
VPHAS-OB1-00685 | 10:17:10.97 | -57:47:57.31 | 5258678689306546304 | 0.11 |
VPHAS-OB1-00785 | 10:23:19.04 | -56:48:47.93 | 5354818130613185792 | 0.12 |
VPHAS-OB1-00826 | 10:19:29.49 | -57:43:37.95 | 5258671959106226432 | 0.13 |
VPHAS-OB1-00879 | 10:19:34.95 | -57:51:44.54 | 5258666564627442304 | 0.17 |
VPHAS-OB1-00881 | 10:20:09.94 | -57:44:39.35 | 5258669038528673920 | 0.16 |
VPHAS-OB1-00896 | 10:19:14.68 | -57:57:59.27 | 5258659864478620800 | 0.13 |
VPHAS-OB1-00904 | 10:18:57.74 | -58:02:31.51 | 5258657837254006400 | 0.12 |
VPHAS-OB1-00918 | 10:19:06.93 | -58:02:14.03 | 5258658180851400320 | 0.13 |
VPHAS-OB1-00919 | 10:19:08.56 | -58:01:55.61 | 5258658176542224256 | 0.13 |
VPHAS-OB1-00921 | 10:19:09.69 | -58:01:59.30 | 5258657974692975744 | 0.12 |
VPHAS-OB1-00925 | 10:19:09.18 | -58:02:26.35 | 5258657974680705024 | 0.09 |
VPHAS-OB1-00930 | 10:19:14.02 | -58:02:08.06 | 5258658009052717568 | 0.15 |
VPHAS-OB1-00931 | 10:19:12.79 | -58:02:23.10 | 5258657974692975872 | 0.15 |
VPHAS-OB1-00934 | 10:19:01.03 | -58:04:49.65 | 5258657424937135232 | 0.14 |
VPHAS-OB1-00938 | 10:20:40.41 | -57:45:02.26 | 5258691475439095424 | 0.15 |
VPHAS-OB1-00953 | 10:24:29.87 | -56:58:08.61 | 5351810901907785088 | 0.09 |
VPHAS-OB1-00958 | 10:19:23.76 | -58:02:42.80 | 5258657184419001472 | 0.15 |
VPHAS-OB1-00965 | 10:19:51.48 | -57:58:02.22 | 5258659417802053888 | 0.15 |
VPHAS-OB1-00968 | 10:19:12.15 | -58:06:04.33 | 5258656634663154048 | 0.11 |
VPHAS-OB1-01086 | 10:24:06.02 | -57:27:34.29 | 5351762489035515904 | 0.10 |
VPHAS-OB1-01119 | 10:25:02.61 | -57:21:47.33 | 5351766715283439104 | 0.08 | *
(c) |  |  |  |  |
MSP 18 | 10:24:02.44 | -57:44:36.05 | 5255678500030907904 | 0.11 | *
MSP 171 | 10:24:04.90 | -57:45:28:35 | 5255678126396953344 | 0.11 | *
WR 21a | – | – | 5351703390282380800 | – | *