The kinematic properties of BHB and RR Lyrae stars towards the Anticentre and the North Galactic Pole: the transition between the inner and the outer halo

Abstract

We identify 51 blue horizontal branch (BHB) stars, 12 possible BHB stars and 58 RR Lyrae stars in Anticentre fields. Their selection does not depend on their kinematics. Light curves and ephemerides are given for seven previously unknown RR Lyrae stars. All but four of the RR Lyrae stars are of Oosterhoff type I.

Our selection criteria for BHB stars give results that agree with those used by Smith et al. and Ruhland et al. We use five methods to determine distances for the BHB stars and three methods for the RR Lyrae stars to get distances on a uniform scale. Absolute proper motions [largely derived from the Second Guide Star Catalogue (GSCII) and Sloan Digital Sky Survey (Seventh Data Release) data bases] are given for these stars; radial velocities are given for 31 of the BHB stars and 37 of the RR Lyrae stars.

Combining these data for BHB and RR Lyrae stars with those previously found in fields at the North Galactic Pole, we find that retrograde orbits dominate for galactocentric distances greater than 12.5 kpc. The majority of metal-poor stars in the solar neighbourhood are known to be concentrated in a L_⊥ versus L_z angular momentum plot. We show that the ratio of the number of outliers to the number in the main concentration increases with galactocentric distance. The location of these outliers with L_⊥ and L_z shows that the halo BHB and RR Lyrae stars have more retrograde orbits and a more spherical distribution with increasing galactocentric distance. Six RR Lyrae stars are identified in the H99 group of outliers; the small spread in their [Fe/H] suggests that they could have come from a single globular cluster. Another group of outliers contains two pairs of RR Lyrae stars; the stars in each pair have similar properties.

1 INTRODUCTION

The blue horizontal branch (BHB) and RR Lyrae stars are well-established tracers of the oldest stars in the Galactic halo although their galactic distribution may not coincide with other halo tracers such as the turn-off stars (Bell et al. 2010). This paper continues those on other surveys for BHB and RR Lyrae stars (Kinman et al. 2007b; Kinman & Brown 2011) and extends previous work in the Anticentre direction (Kinman, Suntzeff & Kraft 1994). Our BHB and RR Lyrae stars are in the range 10 < V < 17 and so range in distance from those in the solar neighbourhood to those distant enough to be included in the Sloan Digital Sky Survey (SDSS) DR7 survey (Abazajian et al. 2009). This allows our selection methods for BHB stars to be compared with other methods for identifying halo SDSS stars (Smith et al. 2010; Ruhland et al. 2011).

The globular-cluster halo is thought to consist of an old halo and a young halo in which the clusters have different horizontal branch (HB) morphologies that can be interpreted as an age difference (Zinn 1993). The shape of the field star halo changes with galactocentric distance (Schmidt 1956; Kinman, Wirtanen & Janes 1966) which suggests that it may not be homogeneous. It is now usual to postulate that the field stars belong to an ‘inner halo’ that was formed in situ and an ‘outer halo’ that has largely been accreted. Earlier work on the field star halo has been summarized by Helmi (2008). Since then, there have been several more investigations of halo structure using various tracers. Surveys using BHB stars have been made by Smith et al. (2010), Xue et al. (2011), Ruhland et al. (2011) and Deason, Belokurov & Evans (2011). Surveys using RR Lyrae stars have been made by Watkins et al. (2009) and Sesar et al. (2010). The stars in these surveys are mostly too distant to have good proper motions from which space motions could be derived. They do, however, allow space densities to be determined as a function of galactocentric distance. The surveys of Deason et al. (2011) for BHB stars and of Sesar, Jurić & Ivezić (2011) for turn-off stars both show breaks in the slopes of their density distributions at 28 kpc from the galactic centre; this suggests that the halo may have two components.

Recent surveys for stars that are close enough for existing proper motions to allow a kinematic analysis include the survey for subdwarfs by Smith et al. (2009), but this survey does not extend far enough in galactocentric distance to sample the outer halo. Carollo et al. (2007, 2010) have analysed the space motions of a large number of stars within 4 kpc and find that a two-component halo is needed to account for the galactic rotation of these stars. They find that there is an outer halo that is more metal-poor and that has a more retrograde rotation than the inner halo. It should be noted that two haloes overlap spatially and the outer halo is less centrally concentrated than the inner. The difference in metallicity between the two haloes has been confirmed by De Jong et al. (2010). Recently, Carollo et al. (2012) have shown that the fraction of carbon-enhanced metal-poor stars is twice as great in the outer halo as in the inner halo. Schönrich, Asplund & Casagrande (2011) re-analysed the Carollo et al. (2010) data and failed to find any reliable evidence for an outer counter-rotating halo. Inter alia, they criticized the luminosity classification of the turn-off stars. In a rebuttal, Beers et al. (2012) re-analysed their data (re-classifying the turn-off stars and criticizing the main-sequence luminosity relation used by Schönrich et al.); they substantiate their original conclusion that the inner halo is nearly non-rotating while the outer halo has ‘a retrograde signature’ with a transition at 15 to 20 kpc from the Sun.

Recent simulations of galaxy formation support the idea that the haloes of galaxies like the Milky Way have a dual origin and have been formed both in situ and by accretion (Zolotov et al. 2009, 2010, 2011; Oser et al. 2010; Font et al. 2011; McCarthy et al. 2012). Zolotov (2011) discusses a dual halo in which the role of accretion increases outwards from the Galactic Centre and the halo is formed solely by accretion if R_gal > 20 kpc. In these simulations, the fraction of the halo that is accreted depends upon the mass of the galaxy. The average of the 400 simulations given by Font et al. has the inner ‘in situ’ component dropping to 20 per cent and the accreted component rising to 80 per cent at a galactocentric distance of 20 kpc. McCarthy et al. (2012) find that the ‘in situ’ component has a flattened distribution and a rotation that is intermediate between that of the disc and the ‘outer halo’.

In this paper we examine halo stars in the Anticentre direction because this is the best direction in which to study the transition from the ‘in situ’ to the accreted halo and the kinematic properties of the outer halo. We do not have sufficient data to discuss the abundance differences between the two haloes. Section 2 identifies the sources and their galactic distributions from which our BHB candidates and our RR Lyrae stars are taken. In Section 3 we give the photometric data for the BHB stars, and in Appendix A we describe the techniques used to identify these stars and the methods used to estimate their distances. Section 4 gives the photometric data and periods for the RR Lyrae stars and shows that they mostly belong to Oosterhoff type 1; in Appendix B we give the ephemerides for the new RR Lyrae stars and the methods used to estimate their distances. Section 5 gives the adopted distances, proper motions and radial velocities of our programme stars together with their galactic space motions (Table 1). It is shown in Section 5 that the galactic rotation velocity (V) becomes more retrograde with increasing galactocentric distance. Appendix C gives details of the sources of the proper motions. Section 6 introduces the angular momenta L_z and L_⊥ and their relation to the galactic rotation (V) and the maximum height above the plane of the star’s orbit (z_max). It is shown that the halo becomes more spherical with increasing galactocentric distance (Table 2). Appendix D discusses the location of thick disc in the L_z and L_⊥ plot. Appendix E gives the angular momenta of the RR Lyrae and BHB stars near the North Galactic Pole (NGP), those of the local BHB stars and those of the galactic globular clusters within 10 kpc. Appendix F discusses the properties of the kinematic groups H99 and K07. The candidates for membership of the K07 group are given in Table 3 in the main part of the paper. The results of the paper are summarized in Section 7.

2 TARGET SELECTION

Our study of the Anticentre halo began with a search for RR Lyrae stars in the fields RR VI (l= 180°, b=+26°) and RR VII (l= 183°, b=+37°); each field covers an area of 30 deg² (Kinman, Mahaffey & Wirtanen 1982). Later Sanduleak provided BHB star candidates for the RR VII field and these were discussed by Kinman et al. (1994). These samples of BHB and RR Lyrae stars have been enlarged for the present paper. New BHB candidates were taken from the objective prism surveys of Pesch & Sanduleak (1989; Case A–F stars) and of Beers et al. (1996; BPS BS stars). We are indebted to Dr Peter Pesch (private communication) for sending us unpublished candidate stars from the Case survey. These are given the prefix ‘P’ in Column 2 of Table 4 unless there is a previous identification in the literature.

Our methods of selecting BHB stars from these candidates and the calculation of their distances are described in Appendix A. Apart from the RR Lyrae stars in fields RR VI and RR VII, the additional RR Lyrae stars have mostly been found among BHB candidates that were found to be variable. Seven of these RR Lyrae stars have not been previously identified and their light curves and ephemerides are given in Appendix B. All our program stars are listed in Tables 4 and 5 for the BHB and RR Lyrae stars, respectively. These tables give positions and photometric data for the BHB stars and, also, metallicities and periods for the RR Lyrae stars; sources of these data are given in notes to these tables.

The galactic distributions of our program stars are shown separately for the BHB and RR Lyrae stars in Fig. 1. Not only do our BHB and RR Lyrae stars cover somewhat different areas of the Anticentre sky, but they also cover different magnitude ranges so that the volumes of space that they occupy only partially overlap. Also, our selection of RR Lyrae stars favours the bluer (Bailey type c) and may miss some of the redder (Bailey type ab) RR Lyrae variables and so our sample may not be complete. This must be taken into account in comparing the properties of our two samples.

The period–amplitude distribution of our RR Lyrae sample is shown in Fig. 2 for the variables with galactic latitudes less than 50°. The solid and dotted curves show the loci of the Oosterhoff type I and II variables, respectively (these were taken from Cacciari, Corwin & Carney 2005). Most of our RR Lyrae stars lie close and to the left of the Oo I curve; this suggests that the majority are Oo I variables. The four stars that are most likely to be Oo II variables are indicated by their numbers in Fig. 2. This preponderance of Oo I variables in the Anticentre is compatible with the discovery by Miceli et al. (2008) that the Oo II variables are more concentrated towards the Galactic Centre than the Oo I variables. The ratio of Oo I to Oo II variables should therefore increase with galactocentric distance and so the Oo I variables should predominate towards the Anticentre.

3 THE BHB STARS

Our BHB stars were chosen from candidates in the sources given in Section 2. Table 4 gives the equatorial and galactic coordinates of these stars, together with photometric data (using the system used in Kinman et al. 1994). Details of the photometric observing are given in Kinman et al. (1994) for photoelectric observations and in Kinman & Brown (2011) for CCD observations. Table 4 also gives the GALEXNUV magnitude (effective wavelength 2267 Å) that was taken from MAST.1 We assumed that stars with V < 12.5 had saturated GALEXNUV magnitudes and should not be used. We also give the Two Micron All-Sky Survey (2MASS) K magnitude that was taken from the 2MASS Point Source Catalogue using the Vizier access tool.

The selection of BHB stars from the candidates is described in Appendix A. We show there how a weight W (Table 4, Column 13) was assigned to each star that depends on the probability that it is a BHB star. The stars were given a type (Table 4, Column 15) that depended on this weight. Stars with a high probability of being BHB stars were classified as BHB, those with a high probability of not being BHB were classified as A while intermediate types were classified as bhb. A comparison of our classifications with those obtained by methods based on SDSS photometry suggests that stars with both BHB and bhb classifications have a high probability of being BHB stars.

Appendix A also contains a discussion of five different methods of getting the absolute magnitudes (and hence distances) of BHB stars. These distances and the adopted distances are given in Table A1. The reddenings of both BHB and RR Lyrae stars were taken from Schlegel, Finkbeiner & Davis (1998).

4 THE RR LYRAE STARS

Most of the RR Lyrae stars in Table 5 are listed in the General Catalogue of Variable Stars (GCVS; Kholopov et al. 1985) and subsequent Name Lists and have the traditional identification by constellation; those without GCVS names are taken from Pier, Saha & Kinman (2003), Kinman, Saha & Pier (2004) and Kinman & Brown (2010). Seven of the stars in Table 5 have not been previously identified as RR Lyrae stars; their light curves and ephemerides are given in Appendix B. The mean K magnitudes (〈K〉) in Table 5 were derived from the 2MASS K magnitudes using the method given in Feast et al. (2008). We follow the methods given in Kinman et al. (2007b) to derive distances for the RR Lyraes. These are briefly restated in Appendix B where we give distances by three separate methods together with adopted distances (D) that are adjusted to be on the same scale as those adopted for the BHB stars (Appendix A).

4.1 Oosterhoff types of the RR Lyrae stars

The globular clusters with Oosterhoff type I RR Lyrae stars are known to have different kinematics (more retrograde orbits) than those containing Oosterhoff type II RR Lyrae stars (van den Bergh 1993; Lee & Carney 1999).2 The Oosterhoff type is determined from the period–amplitude diagram and this is shown in Fig. 2 for our RR Lyrae sample with b≤ 50°. In this figure, the loci for the Oosterhoff type I and II variables are shown by solid and dotted curves, respectively (these curves were taken from Cacciari et al. 2005). Most of our RR Lyrae stars lie close and to the left of the Oo I curve. Type ab stars that lie to the left of the Oo I curve may either be metal-rich or have smaller mean amplitudes because of the Blazhko effect. This suggests that the majority of our stars are Oo I variables. Four stars that are most likely to be Oo II variables are indicated by their numbers in Fig. 2. Stars 29, 30 and 46 are type c variables while 28 is type ab. These four stars have 〈Z〉= 3.9 kpc and 〈R_gal〉= 14.3 kpc compared with 〈Z〉= 6.6 kpc and 〈R_gal〉= 19.6 kpc for the whole sample. The preponderance of Oo I variables in our Anticentre fields and the smaller 〈R_gal〉 of our Oo II variables is to be expected if the Oo II variables are more concentrated towards the Galactic Centre than the Oo I variables (Miceli et al. 2008). The smaller 〈Z〉 of our Oo II variables also agrees with the preponderance of Oo I variables at high Z that was found by De Lee (2008). This suggests that the Oo II variables are not only more concentrated to the Galactic Centre but also form a more flattened system than the Oo I variables.

5 THE GALACTIC SPACE MOTIONS OF THE PROGRAM STARS

Tables 6 and 7 give the parallaxes, proper motions, radial velocities and the Galactic Space Motions (U,V,W) with respect to the local standard of rest (LSR) for the BHB and bhb stars and the RR Lyrae stars, respectively. The parallaxes are derived from the adopted distances (D) given in Tables A1 and B2 in Appendices A and B, respectively. The error in the parallax is derived from the rms scatter given in the last columns of Tables A1 and B2 and does not include any systematic error in the case of the BHB stars. In the case of the RR Lyrae stars, a small distance-dependent error has been added in quadrature to the rms scatter to derive the error of the parallax as explained in the Section B2. Heliocentric space–velocity components U, VandW were derived from the data listed in these tables. We used the program by Johnson & Soderblom (1987) (updated for the J2000 reference frame and further updated with the transformation matrix derived from the Vol. 1 of the Hipparcos data catalogue). This program gives a right-handed system for U, V and W in which these vectors are positive towards the directions of the Galactic Centre, but we here use the left-handed system so as to be comparable with most other recent work. These heliocentric velocities were then corrected to velocities relative to the LSR using the solar motion relative to the LSR km s⁻¹ (Dehnen & Binney 1998).

5.1 Radial velocities and proper motions

The sources of our radial velocities are given in Column 8 (S_RV) of Tables 6 and 7. The Bologna velocities were derived from spectra taken with the 3.5-m LRS [Telescopio Nazionale Galileo (TNG)] spectrograph. The Kitt Peak velocities were derived from spectra taken with RC spectrograph on the 4-m Kitt Peak telescope and kindly made available to us by Nick Suntzeff (private communication). The remaining velocities were taken from the literature as given in the notes to Tables 6 and 7.

The absolute proper motions given in this paper come primarily from astrometric data assembled from the Second Guide Star Catalogue (GSC-II; Lasker et al. 2008), and the Seventh Data Release of the SDSS (DR7; Abazajian et al. 2009; Yanny et al. 2009). Details are given in Appendix C. In the case of a few of the brighter stars (V < 12.3) we have chosen the proper motions given in the NOMAD Catalogue (Zacharias et al. 2004). In the case of the BHB star P 30-38, we chose the proper motion given by the SDSS DR7 because the GSC-II-SDSS proper motion has unusually large errors. The SDSS DR7 proper motions have also been used for the stars (mostly BHB stars) for which GSC-II–SDSS proper motions were not available.

We have only used stars that have radial velocities to compute U, V and W, and since only four of the BHB stars that only have SDSS DR7 proper motions also have radial velocities, possible systematic differences between the SDSS DR7 and the GSC-II–SDSS proper motions should have little effect on our overall results.3 A comparison of the SDSS DR7 and the GSC-II–SDSS proper motions (Appendix C) shows good agreement at the 1 mas yr⁻¹ level; this corresponds to a tangential velocity of 40 km s⁻¹ at a distance of 8.5 kpc.

5.2 Discussion of the space motions U, V and W

Table 1 gives the space motions for various subgroups of our program stars; all velocities are with respect to the LSR. The possible BHB stars (type bhb) have a V motion and velocity dispersions (σ_u, σ_v and σ_w) that are similar to those of the local BHB stars. This suggests that the majority are BHB stars but, conservatively, we have not included them in any of the other samples.

We have used the angular momenta (L_⊥) and (L_z) to distinguish between disc and halo stars. These quantities are defined in the appendix of Kepley et al. (2007) and are given for our program stars in Columns 15 and 16 of Tables 6 and 7. Following the discussion given in our Appendix D2, we identify the BHB star RR7 064 and the RR Lyrae stars TW Lyn and P 82 06 as probable disc stars and have excluded them from further discussion.

Figs 3(a), (b) and (c) are plots of the galactic velocity components 〈V_lsr〉, 〈U_lsr〉 and 〈W_lsr〉, respectively, against galactocentric distance (R_gal) for both our Anticentre stars and those at the NGP (Kinman et al. 2007b). Although there is considerable scatter between the different samples, there is clearly a trend in 〈V_lsr〉 from zero galactic rotation in the solar neighbourhood to a strong retrograde rotation for R_gal greater than 12.5 kpc. On the other hand, both 〈U_lsr〉 and 〈W_lsr〉 are essentially zero at all Galactocentric distances. This supports our conclusion that the trend of 〈V_lsr〉 with galactocentric distance is real and not produced by systematic errors in the proper motions. If the outer halo has a significantly retrograde rotation, as originally found by Carollo et. al (2007, 2010), and confirmed by Beers et al. (2012), this suggests that the outer halo dominates beyond R_gal= 12.5 kpc.

6 STRUCTURE IN THE MOTIONS OF OUR HALO STARS

Plots of the angular momenta L_⊥ and L_z can be used to demonstrate kinematic structure among halo stars (e.g. Helmi et al. 1999). We give a L_⊥ versus L_z plot for our Anticentre BHB and RR Lyrae stars in Figs 4(a) and in (b) for our NGP sample of these stars (Kinman et al. 2007b). Similar plots are shown in Fig. 5 for local RR Lyrae and BHB stars and in Fig. 6 for the globular clusters within 10 kpc. Definitions of L_⊥ and L_z are given by Kepley et al. (2007). We calculated these quantities and their errors with a program that was kindly made available by Heather Morrison and modified for our use by Carla Cacciari. The values of L_⊥ and L_z for the NGP RR Lyrae stars and BHB stars, the local BHB stars and the globular clusters within 10 kpc are tabulated in Appendix E, where we also compare our L_⊥ and L_z with those calculated by Re Fiorentin et al. (2005) and Morrison et al. (2009) for a small sample of halo stars.5

L_z correlates with galactic rotation: in the left-handed system of coordinates, objects with positive L_z are prograde (the Sun has L_z∼1760 kpc km s⁻¹) and those with negative L_z are retrograde. L_⊥ correlates with the maximum height of the orbit above the plane (Fig. 7).

Morrison et al. (2009) investigated the L_⊥ versus L_z plot for 246 local metal-poor stars. The majority (∼90 per cent) of their sample, which we will call the main concentration, are in the location bounded by the black dotted line in Figs 4, 5 and 6. This is taken from the outer contour of their fig. 3. They also discovered a flattened component whose location is shown by the full black contour in our Figs 4, 5 and 6. The remaining 10 per cent of their sample lie outside the black dotted contour and, following Kepley et al. (2007) and Smith et al. (2009), we call them outliers. About a third of these outliers in the Morrison et al. (2009) sample belong to the prograde group (H99) discovered by Helmi et al. (1999) and further investigated by Re Fiorentin et al. (2005); the location of the majority of stars in this group is shown by the black rectangle in Figs 4, 5 and 6. The green rectangle shows the location of another group suggested by Kepley et al. (2007). The magenta box in Figs 4, 5 and 6 shows the location of stars in the main concentration that have a high probability of belonging to the thick disc; this is discussed in Appendix D.

The review by Klement (2010) lists 16 halo ‘streams’ that have been identified among stars in the solar neighbourhood. All except the H99 and the Kapteyn Group lie within the main concentration in the L_⊥ versus L_z plot. An example of structure within the main concentration is shown by the RR Lyrae stars at distances between 1 and 2 kpc (Fig. 5b) which are less evenly distributed than those at distances less than 1 kpc (Fig. 5a). In general, the identification of structure in this main concentration is only possible for stars with relatively large proper motions and well-determined distances. In discussing our program stars, we shall therefore largely confine ourselves to discussing the outliers and the ratio of the number of outliers to the number in the main concentration.

6.1 Ratio of the number of outliers to the number in the main concentration

The ratio of the number of outliers to the number in the main concentration is a simple measure of the spread of halo stars in the L_⊥ versus L_z plot. Our sample of globular clusters within 10 kpc contains five (with [Fe/H] > −1.0) that belong to the disc or bulge. Among the remainder, 24 belong to the main concentration and two (or 8 per cent) are outliers. The two outliers are NGC 3201 and NGC 6205 (M13). Although these two clusters are listed as ‘young’ by Marín-Franch et al. (2009), Dotter et al. (2010) give ages of 12.00 ± 0.75 and 13.0 ± 0.50 Gyr for NGC 3201 and NGC 6205, respectively, which do not support this description. NGC 6205 (together with NGC 5466, NGC 6934 and NGC 7089) is one of a group of four globular clusters with similar L_⊥ and L_z that are discussed by Smith et al. (2009) in connection with an overdensity in the subdwarfs that they studied. Smith et al. list the properties of 12 outlier subdwarfs that lie at heliocentric distances of up to 5 kpc. They are shown by yellow open circles in Figs 4(a) and (b). They show some tendency to occur in groups among themselves in their L_⊥ versus L_z plot (as discussed by Smith et al.) but their locations in our plot [Figs 4(a) and (b)] show little in common with those of our RR Lyrae and BHB outliers.

The local BHB stars within 1 kpc all belong to the main concentration and have no outliers. The RR Lyrae stars within 1 kpc have four outliers that belong to the H99 group (RZ CEP, XZ CYG, CS ERI and TT LYN); MT TEL is a possible retrograde outlier that lies just outside the main concentration. The RR Lyrae stars at distances between 1 and 2 kpc have two outliers that belong to the H99 group (TT CNC and AR SER), two that belong to the Kepley retrograde group (AT VIR and RV CAP) and one prograde outlier (U CAE) besides several that are on the edge of the main concentration. Kepley et (2007) found that XZ CYG belongs to the H99 group and CS ERI is also likely to be a member of this group. The H99 and K07 outlier groups are discussed further in Appendix F.

Of the 188 RR Lyrae stars within 2 kpc for which we have data, 41 are likely to belong to the thick disc. Of the remaining 147 halo stars, there are five in Fig. 5(a) and 10 in Fig. 5(b) that formally lie outside the main concentration and so would formally be considered outliers. Five of those in Fig. 5(b), however, lie so close the boundary of the main concentration that (with reasonable assumptions as to their error bars) it seems likely that most belong to the main concentration. The 10 certain outliers comprise 7 ± 2 per cent of the total. If we include the five that lie close to the main concentration boundary, there are 15 outliers or 10 ± 3 per cent of the total. These percentages are comparable with those found (10 per cent) by both Helmi et al. (1999) and Morrison et al. (2009) among their local samples of metal-poor halo stars.

Table 2 gives the number of stars in the main concentration and the number of outliers for the BHB and RR Lyrae stars within 8.5 kpc in both the Anticentre and NGP (Kinman et al. 2007b) fields. The percentage of outliers and the L_⊥ of the stars in these fields is shown plotted against galactocentric distance in Figs 8(a) and (b), respectively. It can be seen from Figs 4 and 8(b) that the majority of outliers have greater L_⊥ and more negative L_z than the stars in the main concentration. This shows, according to the correlations shown in Fig. 7, that the orbits of the outliers tend to be more retrograde and reach larger ∣z_max∣ than the stars in the main concentration. The increase in the percentage of outliers with galactocentric distance shown in Fig. 8(a) therefore implies that as the galactocentric distance increases, the halo has an increasing contribution from stars that have more retrograde orbits and a more spherical distribution than the stars in the main concentration that predominate in the solar neighbourhood. This result is in general agreement with the observational results of Carollo et al. (2007, 2010) and Beers et al. (2012) and the simulations of Oser et al. (2010), Font et al. (2011) and McCarthy et al. (2012). Our observational support for the duality of the halo is important because (as the simulations have shown) dual haloes are a general property of the stellar spheroids of disc galaxies whose masses are comparable with that of the Milky Way. We are grateful to the referee for asking us to emphasize this point.

We note that a simulation of a ‘smooth halo’ with a Gaussian distribution of velocities (e.g. the right-handed L_⊥ versus L_z plot of fig. 5 in Smith et al. 2009) gives a main concentration that is similar in shape but smoother than that shown by the observations. In this connection we note that Hattori & Yoshii (2011) conclude that violent relaxation has been effective for stars within a scale radius of 10 kpc from the Galactic Centre. We suggest that the stars of the main concentration are those where this relaxation has been most effective.

7 SUMMARY AND CONCLUSIONS

Fifty-one BHB stars and 12 possible BHB stars are identified in the Anticentre. Our selection criteria for these stars give results that agree with those used by Smith et al. (2010) and Ruhland et al. (2011). 58 RR Lyrae stars are identified in the Anticentre; seven of these are new and their light curves are given in Appendix B. Photometric data for the BHB and RR Lyrae stars are given in Tables 4 and 5, respectively. Five methods are used to get distances for the BHB stars and three methods for the RR Lyrae stars; these are compared and combined to give distances on a uniform scale. Absolute proper motions (largely derived from the GSCII and SDSS DR7 data bases) are given for all these stars and also radial velocities for 31 of the BHB and 37 of the RR Lyrae stars (Tables 6 and 7). Our conclusions are itemized below.

• All but four of the 58 RR Lyrae stars in the Anticentre fields are of Oosterhoff type I; this agrees with the Oo II stars being more centrally concentrated in the Galaxy than those of Oo type I (Miceli et al. 2008). Oo I globular clusters tend to have retrograde orbits (van den Bergh 1993; Lee & Carney 1999); the field RR Lyrae stars in the Anticentre tend to have retrograde orbits.

• We combined the kinematic data of our Anticentre stars with those of the stars in the NGP fields (Kinman et al. 2007b). In the combined data, the Galactic V motion (Fig. 3) is significantly retrograde for both BHB and RR Lyrae stars with R_gal > 10 kpc. This agrees with the findings of Carollo et al. (2007), Carollo et al. (2010) and Beers et al. (2012) that the outer halo shows retrograde rotation compared with the rotation of the stars in the solar neighbourhood where the inner halo predominates. The lack of any similar trend in the Galactic U and W motions makes it unlikely that the trend in the V motion is caused by a systematic error in the proper motions.

• Angular momenta plots (L_⊥ versus L_z) for the BHB and RR Lyrae stars in the Anticentre fields and the NGP fields are compared with similar plots for these stars in the solar neighbourhood and for the globular clusters nearer than 10 kpc. We suggest that halo stars belong to either of two groups – either the main concentration or the outliers– according to whether they lie inside or outside a contour in this plot which encloses the majority of metal-poor stars in the solar neighbourhood (as defined by Morrison et al. 2009). We suggest that the stars in the main concentration are those for which violent relaxation has been most effective (Hattori & Yoshii 2011). The ratio of outliers to main concentration stars increases with galactocentric distance (Fig. 8). The outliers primarily have retrograde orbits. Since L_⊥ correlates with z_max (the orbit’s maximum height above the Galactic plane), this also implies that the halo becomes more spherical with increasing galactocentric distance (cf. Schmidt 1956; Kinman et al. 1966; Miceli et al. 2008, Table 2). It also agrees with the simulations (McCarthy et al. 2012) that predict that the inner halo should be more flattened than the outer halo.

• A review of the RR Lyrae stars in the H99 group of outliers (Helmi et al. 1999) shows that there are six RR Lyrae stars that are likely members (all probably of Oo type I) and that their mean [Fe/H] is −1.59. Their mean rms scatter in [Fe/H] is 0.16 which is comparable with the likely errors in these metallicities. These RR Lyrae stars therefore form a more homogeneous set than the later-type stars in H99 (Roederer et al. 2010) and they could have originated from a single globular cluster. Another grouping with similar L_⊥ and L_z (which we call K07) contains 15 BHB and RR Lyrae stars at distances in the range 1.1 to 8.5 kpc. K07 contains two pairs of RR Lyrae stars (AT VIR & RV CAP and IP COM & EO COM); the stars in each pair have similar properties. Better data are needed to verify membership of the other stars in K07.

We thank D.R. Soderblom for kindly making available the program to calculate the UVW space motions and Heather Morrison for allowing us to use her program for computing L_⊥ and L_z and the referee for comments which helped improve the paper. This research has made use of 2MASS data provided by the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

The GSCII is a joint project of the STScI and the INAF-Osservatorio Astronomico di Torino (INAF-OATo).

This work is partly based on observations made with the Italian TNG operated on the island of La Palma by the Fundacion Galileo Galilei of the Istituto Nazionale di Astrofisica (INAF) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias.

This work has been partly supported by the Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) under PRIN-2001-1028897 and PRIN-2005-1060802.

Footnotes

REFERENCES

Appendices

APPENDIX A: THE BHB STARS

A1 Our selection methods

Kinman et al. (1994) used both photometric and spectroscopic criteria to identify 15 BHB stars in the Anticentre field RR VII (l= 183°, b=+37°) which Kinman et al. (1982) had previously searched for RR Lyrae stars. Brown et al. (2003) independently confirmed these classifications for nine stars in this field (six BHB and three non-BHB stars). The classification of these 15 stars (RR 7-02, -08, -15, -21, -23, -36, -43, -53, -58, -60, -64, -66, -84, -90, -91)6 is therefore considered to be secure.

Additional BHB star candidates with (170° < l < 207°) were taken from BHB candidates discovered in the objective prism surveys of Pesch & Sanduleak (1989) (AF-nnn) and Beers et al. (1996) (BS nnnnn-nnn). We also included unpublished BHB candidates from the Case Survey that were kindly made available to us by Dr Peter Pesch; we call these P nn.nn stars. All these stars are included in Table 4 (main section of this paper) with a running number which is also used as a means of identification in the figures.

Following Kinman & Brown (2011), BHB stars were selected from these candidates by three methods.

• The (u−B)_K0 versus (B−V)₀ plot where u is a Strömgren magnitude and B and V are Johnson magnitudes. The plot is shown in Fig. A1 where the dotted lines enclose an area in which (B−V)₀≤ 0.18 and (u−B)_K0 is within ±0.075 mag of a curve defined by nearby BHB stars whose classification rests on high-resolution spectroscopy (Kinman et al. 2000; Behr 2003).

• The (NUV−V)₀ versus (B−V)₀ plot where NUV is the near-UVGALEX magnitude (effective wavelength 2267Å) taken from the MAST (http://archive.stsci.edu/). The plot is shown in Fig. A2 where the dotted parallelogram (taken from Kinman, Salim & Clewley 2007a) shows the expected location of BHB stars. This method can only be used for stars fainter than about V= 12 because the GALEX magnitudes of brighter stars are affected by saturation.

• The Strömgren β versus (B−V)₀ plot is shown in Fig. A3 which is taken from fig. 9(a) of Kinman & Brown (2011). The full curve shows the expected location of BHB stars and dashed curve shows the lower limit of β for non-BHB stars. This method was only used for eight of the brighter stars.

In these figures, a running number (from Table 1) is given against each star in Fig. A3 and for those stars whose error bars lie outside the defining boxes in Figs A1 and A2. For stars in (a) Fig. A1 and (b) Fig. A2, those whose colours fall within the defining box were given weight +4; those whose error bars intersected the defining box were given weight +2 and the rest were given weights of 0 or −3 according to their distance from the defining box. For the stars in (c) Fig. A3, those whose error bars intersect the full curve are given weight 3, those whose error bars lie above this line but below the dashed line are given weight 1 and those with larger β are given weight −3. The weights from the three methods were added to give a total weight (W) that is given in Column 14 of Table 1. Stars with W≥ 6 are taken to have a high probability of being BHB stars; those with zero or negative weights are taken to have a high probability of not being a BHB star (class A) while those with intermediate W are considered to be an intermediate class which we call ‘bhb’. The distribution of these three classes as a function of the weight (W) is shown in Fig. A4(a).

A2 Comparison with other selection methods

Smith et al. (2010) have used machine-learning methods to estimate the probability that a star is a BHB star from its SDSS photometry. Their preferred probability (P_svm) is derived from the support vector machine method and is available for those of our program stars whose SDSS magnitudes are unsaturated (roughly those with V > 14.5). The distribution of P_svm for the stars that we classify as BHB and bhb is shown in Figs A4(b) and A4(c), respectively. Most of the stars that we classify as BHB and bhb have a high probability of being BHB stars on the Smith et al. criterion. The only exception is our program star 47 (BS 16468-00260) which is missing from the Smith et al. (2010) catalogue although its (u−g)₀ and (g−r)₀ are similar to those of stars that are given a high value of P_svm. The stars that we classify as bhb all have P_svm greater than 0.6; this suggests that most are likely to be BHB stars.

Ruhland et al. (2011) have shown that the BHB stars lie in a relatively well-defined locus in the (u−g)₀ versus (g−r)₀ diagram; this is enclosed by the full magenta line in Fig. A5. All the stars with unsaturated SDSS magnitudes that we classify as BHB or bhb (shown by filled blue circles and blue open circles, respectively) lie within this line except for stars 56 and 61 for which we assigned weights +11 and +8, respectively. There are two discrepant u magnitudes for the object in the position of star 56 and this presumably explains the location of this star in Fig. A5. Star 61 has V= 14.57 which is close to the saturation limit of SDSS magnitudes. For these reasons we think that the anomalous locations of stars 56 and 61 are caused by errors in the SDSS magnitudes and that the high weights that we have assigned to these stars are trustworthy. Overall, there is satisfactory agreement between our selection criteria and the most recent selection criteria based on SDSS magnitudes.

A2.1 Reddenings

The reddenings E(B−V) in this paper were taken from the total reddenings of Schlegel et al. (1998). All but five of our BHB and RR Lyrae stars are more than 1 kpc above the Galactic plane and so the reddenings to these stars will be close to the total reddenings in these sight-lines. The reddening corrections for other colours are derived from the relations E(V−K) = 2.75E(B−V), A_V= 3.1E(B−V) and A_K= 0.35E(B−V) (Cardelli, Clayton & Mathis 1989).

A3 Distances of the BHB stars

We have used five methods to determine absolute magnitudes (and hence distances) for our BHB stars.

1. Sirko et al. (2004) gave absolute SDSS g magnitudes based on models by Dorman, Rood & O’Connell (1993) for various BHB properties including SDSS colours. Smith et al. (2010) used these data to derive distances for their sample of BHB stars which includes 40 of our BHB and bhb stars; these are given as D1 in Table A1.

2. Deason et al. (2011) derived the absolute magnitudes of BHB stars using the SDSS photometry of 11 globular clusters by An et al. (2008). They expressed the absolute magnitude (M_g) in their equation (7) as a quartic in (g−r)₀. We used this expression to derive distances (D2 in Table A1) for the 43 stars for which unsaturated SDSS colours were available from SDSS DR7.7

3. Preston et al. (1991) used the Johnson photometry of 15 globular clusters to derive the absolute V magnitude of BHB stars in terms of a cubic in (B−V)₀. A slightly adjusted version of this expression is given as their equation (5) by Kinman et al. (2007b). We used this expression to derive the distances (D3) in Table A1.

4. Kinman et al. (2007b) attempted to improve on the cubic equation in (c) by deriving another cubic based on the photometry of the intermediate-metallicity globular clusters M3 (Ferraro et al. 1997) and M13 (Paltrinieri et al. 1998). This cubic is given as their equation (6) in Kinman et al. (2007b). The corresponding distances are given as (D4) in Table A1.

5. Kinman et al. (2007b) gave a cubic expression for the infrared absolute magnitude M_K in terms of the (V−K)₀ colours. The calibration was derived from the colour–magnitude diagrams of the globular clusters M3 and M13 given by Valenti et al. (2004). This cubic is given as their equation (3) by Kinman et al. (2007b). The corresponding distances are given as (D5) in Table A1.

We assume that the random error in these distances is given by the rms scatter among the distances d1, d2, d3 and d5. This is given (in kpc) in Column 15 in Table A1. We have used these errors in computing the error bars of the velocities and angular momenta (L_⊥, L_z) that are distant-dependent. It remains to consider the effect of possible systematic errors. The question is whether these systematic errors depend on distance. If they do, there would be systematic errors in our velocities and angular momenta that would produce errors in these quantities as a function of galactocentric distance. The most likely source of a distance-dependent error is in the absolute magnitudes and proper motions since neither the radial velocity, apparent magnitude nor extinction are likely to have distance-dependent errors. Such an error could arise if the mean colours of our BHB stars varied with distance. Using only the stars that we used in our velocity and angular momentum analyses, we find a mean (B−V)₀ of +0.61 ± 0.018, +0.075 ± 0.012 and +0.081 ± 0.012 mag at mean galactocentric distances of 10.6, 13.4 and 15.9 kpc, respectively. These data would be compatible with a difference of say 0.02 mag in the mean (B−V)₀ between galactocentric distances of 10.6 and 13.4 kpc. This corresponds to a difference in 0.05 mag in the absolute magnitude or 2.3 per cent in the distance. This error is far too small to account for the change in galactic rotation (V) of about 100 km s⁻¹ between these two distances. Likewise, it would require a systematic difference of –1.6 mas yr⁻¹ between the proper motions of the stars at V= 13.0 and those at V= 15.0 to produce the differences in galactic rotation (V) that we observe (Section 5.2). This seems unlikely since the galactic U and W velocities show no dependence on distance.

APPENDIX B: RR LYRAE STARS

B1 The new RR Lyrae stars

Seven of the stars listed in Table 4 (identified by the number 7 in the Notes column) have not previously bee identified as RR Lyrae stars. All are of low amplitude and all but one are of Bailey type c. Their V and B−V light curves are given in Figs B1 and B2. The ephemerides and photometric data for these variables are given in Table B1. The observations were made in the same way as those described by Kinman & Brown (2010) but in general there are fewer observations than for the stars observed in that paper. This is particularly true of AF-194, AF-197, AF-400 and AF-430. Consequently, the periods of these stars are less reliable than we would wish. In assigning periods and Bailey types, however, we took into account the mean (B−V) colours which are well determined and which can be used to distinguish between Bailey type c and Bailey type ab. These Bailey types are therefore more certain than would be inferred from the V light curves alone.

B2 The distances of the RR Lyrae stars

We use three methods to estimate the distances of our RR Lyrae stars; details of these methods are given in Kinman et al. (2007b).

1. The absolute visual magnitude M_V is derived in terms of the metallicity [Fe/H] using coefficients given by Clementini et al. (2003):

   

   If [Fe/H] is not known, it is assumed to be −1.6. An error of ±0.5 dex in [Fe/H] leads to an error of ±0.1 mag in the distance modulus and about 5 per cent in the parallax.
2. The infrared absolute magnitude (M_K) is derived from [Fe/H] and the period (P) (in days) in the form given by Nemec, Nemec & Lutz (1994):

   

   The periods of the Bailey type c stars must be ‘fundamentalized’. For this purpose, we assumed that the ratio of the period of the first overtone (c type) to that of the fundamental (ab type) is 0.745 (Clement et al. 2001).
3. The infrared magnitude (M_K) can be derived from (V−K)₀ and the metallicity [Fe/H]:

   

   If [Fe/H] is not known, it is assumed to be −1.6. In this case the relation is the same as that used in method (5) for the BHB stars.

In a recent review, Feast (2011) has shown that the current calibration of RR Lyrae absolute magnitudes is not satisfactory: there is a significant spread in the coefficients and zero-points derived from trigonometric parallaxes, statistical parallaxes and pulsation parallaxes. It is hoped that, in the future, new trigonometric parallaxes such as those recently given by Benedict et al. (2011) will eventually improve this situation. The expressions for the RR Lyrae absolute magnitudes given above are the best that we have available now but may well require some correction in the future.

Distances D_a, D_b and D_c were derived for our RR Lyrae stars using methods (1), (2) and (3), respectively, and are given in Table B2. There are 31 of these RR Lyrae stars that have both radial velocities and proper motions and that are closer than 17 kpc (the limit that we have taken for the proper motions to yield meaningful velocities). Of these 31 stars, 19 have known [Fe/H] and 26 have K magnitudes. As noted above, distances can be derived even if [Fe/H] is not known by assuming that it is −1.6, although this involves a loss of accuracy. We need the distances of the RR Lyrae stars to be as closely as possible on the same scale as that of the BHB stars. Now method (3) for the RR Lyraes (with [Fe/H] =−1.6) is the same as method (5) for the BHB stars [with (B−V)₀=+0.18]. We have therefore converted the distances D_a and D_b to the scale of the distances D_c by dividing them by the factors R_a and R_b, respectively. R_a is the mean value of D_a/D_c and equals 1.0228 ± 0.0005. R_b is the mean value of D_b/D_c and equals 1.0468 ± 0.0017. After we have divided the distances D_a by 1.0228 and the distances D_b by 1.0468, they will be on the scale of D_c which is the same as the BHB scale D5. Now the BHB stars were all adjusted to be on the scale of BHB distance D2. To get the RR Lyrae star’s distances on this scale, they must further be divided by the factor F5 (see Section A3). This factor (F5) must be evaluated at the blue edge of the instability gap [(B−V)₀=+0.18] where it has the value 0.953. We call the final values of these RR Lyrae distances d_a, d_b and d_c. All these distances and our adopted distance (D) which is the unweighted mean of d_a, d_b and d_c are given in Table B2.

For the 35 RR Lyrae stars where all three distances are available, our adopted distance is the arithmetic mean of the three distances and σ is the rms scatter of a single distance. In Fig. B3 we have plotted σ/D against D for (a) the nine stars for which [Fe/H] and 〈K〉 are best determined and (b) for the remaining 26 stars for which σ is available. We see that σ/D is roughly independent of distance and less than 0.06 except for the seven numbered stars in Fig. B3(b). It seems likely that the larger σ/D of these stars is produced by larger errors in 〈K〉. In the cases where only d_a is available we therefore conservatively adopted σ= 0.05 D for its error. Some allowance must be made for systematic errors in our distance scale and this can only be a rough estimate based on the spread amongst the various distance estimates that we have used. In calculating the space motions we have included a systematic error of 0.015 D in quadrature with the random errors given in Tables A1 and B2.

Our distances for TT Lyn, TW Lyn and X LMi (0.71 ± 0.01; 1.69 ± 0.02; 2.20 ± 0.01 kpc) are in satisfactory agreement with those given in the recent compilation of bright RR Lyrae stars by Maintz (2005) (0.71; 1.65; 2.20 kpc).

APPENDIX C: PROPER MOTIONS

The proper motions used in this paper come from astrometric data that were assembled from the GSC-II (Lasker et al. 2008) and the SDSS DR7 (Abazajian et al. 2009; Yanny et al. 2009). Absolute proper motions were obtained by correcting the relative proper motions to a reference frame provided by a Large Quasar Reference Frame assembled by Andrei et al. (2009). Proper motions were computed for 77 million sources by combining SDSS second-epoch positions with multi-epoch positions derived from the GSC-II data base and spanning a time baseline of 40 to 50 years. As described in Spagna et al. (2010a,b), proper motion formal errors are typically in the range 2 to 3 mas yr⁻¹ at intermediate magnitudes (16 < r < 18.5). Comparisons against a sample of 80 000 quasars indicate that the random errors of the two catalogues are, on average, comparable but that the reference system of the SDSS proper motions is affected by a global systematic rotation Δμ≃−− 0.40 mas yr⁻¹, which is not present in the GSC-II frame. Further details concerning the data base from which our proper motions were obtained may be found in Spagna et al. (2010a,b).

Overall, we consider these proper motions to be the most accurate available for the magnitude range, ⁠, covered by the bulk of our objects. It is important, however, to compare our proper motions with those from other catalogues because their proper motions may be preferable for the brightest stars or for a rare case where the GSC-II + SDSS DR7 error is unusually large.

C1 Proper motions for the brighter or anomalous stars

Table C1 gives the GSC-II–SDSS proper motions for our brighter program stars together with those given by the NOMAD catalogue (Zacharias et al. 2004), the UCAC3 catalogue (Zacharias et al. 2009) and the SDSS DR7 catalogue (Abazajian et al. 2009). Following this comparison, we have chosen to use the NOMAD proper motions for the brighter BHB stars RR7-15, RR7-64, BS 16473-09 and BS 16927-22 and for the brighter RR Lyrae stars TT Lyn, X LMi and DQ LYN.8 These are all stars whose V magnitudes are brighter than 12.3.

Fig. C1 gives separate plots for the proper motions in RA and declination for the GSC-II–SDSS against those given by the SDSS DR7. Both catalogues are based on quite similar material [i.e. first epochs from the Palomar Schmidt Sky Survey (POSS) photographic plates and second epochs from the SDSS measurements], but they were processed and calibrated in different and independent ways. The plot shows good agreement in general at the milliarcsec per year level except for the proper motion in RA for the BHB star P 30-38. We have preferred the SDSS DR7 proper motion because it roughly agrees with that given by the NOMAD catalogue and because the errors in the GSC-II–SDSS catalogue for this star are unusually large.

APPENDIX D: THICK DISC

Fig. D1 shows the L_⊥ versus L_z plot for the thick disc stars within 2 kpc from Bensby et al. (2011) (crosses) and the thick disc stars within 0.5 kpc (ages 8 to 11 Gyr and −0.4 < [Fe/H] < −0.5) from the Geneva–Copenhagen Survey of the Solar Neighbourhood III (Holmberg, Nordström & Andersen 2009)(small black open circles); Most of these stars have L_⊥ < 650 kpc km s⁻¹ and 1100 < L_z < 2000 kpc km s⁻¹; we have used these limits to define the location of stars that belong to the thick disc.9 There is a strong concentration of local RR Lyrae stars (red circles) in this location but rather few local BHB stars (Fig. D1); these stars are listed in Table D1. Table D2 gives the mean properties of the 46 RR Lyrae stars in this thick disc location: five stars (11 per cent) have [Fe/H] ≤−1.50 and have a high probability of being halo stars; 19 (41 per cent) have [Fe/H] > −0.5 and can definitely be called disc stars. The remaining 22 (48 per cent) have intermediate [Fe/H] (−0.5 > [Fe/H] > −1.5) and mean values of their orbital eccentricity and maximum orbital height above the Galactic plane (z_max) and angular momentum L_⊥ that lie between those of the stars with [Fe/H] > −0.5 and those with [Fe/H] < −1.5. All of the 19 RR Lyrae stars with [Fe/H] > −0.7 and 73 per cent of the 22 with −0.7 > [Fe/H] > −1.5 have L_⊥ < 325 kpc km s⁻¹; consequently ∼82 per cent of the likely thick disc stars, those with [Fe/H] > −1.5, should have L_⊥ < 325 kpc km s⁻¹ and 1100 < L_z < 2000 kpc km s⁻¹. The isolation of a purer sample of disc stars requires additional chemical or kinematic information. Only three local BHB stars (within 1 kpc) have L_⊥ < 650 kpc km s⁻¹ and 1100 < L_z < 2000 kpc km s⁻¹ and two of these have [Fe/H] < −2.0 and so are almost certainly halo stars. Thus, unlike RR Lyrae stars, BHB stars do not have a strong disc component in the solar neighbourhood as was found by Kinman, Morrison & Brown (2009).

APPENDIX E: THE ANGLUAR MOMENTA L_⊥ AND L_z FOR OBJECTS IN FIGS 4, 5 and 6

Tables E1, E2, E3 and E4 give the Angular Momenta L_⊥ and L_z for the RR Lyrae stars at the NGP (table 2 in Kinman et al. 2007b), the BHB stars at the NGP (table 1 in Kinman et al. 2007b), Local BHB stars within 1 kpc (Kinman et al. 2000) using proper motions taken from the NOMAD catalogue (Zacharias et al. 2009) and globular clusters within 10 kpc. We have only included RR Lyrae and BHB stars at the NGP whose distances are less than 10 kpc.

Definitions of L_⊥ and L_z are given in the appendix of Kepley et al. (2007). The calculations of these quantities and their errors were made using a program kindly made available by Heather Morrison and modified for our use by Carla Cacciari. Table E5 compares the values of L_⊥ and L_z that we calculated with this program for a number of halo objects with those given by Re Fiorentin et al. (2005) and Morrison et al. (2009). The differences are generally less than the quoted errors and are probably largely produced by differences in the proper motions that were used. An exception is HD 128279, where our values of L_⊥ and L_z agree with those of Re Fiorentin et al. (2005) but not with those of Morrison et al. (2009).

APPENDIX F: GROUPS OF OUTLIERS

This section summarizes additional data about the two groups of outliers called H99 and K07.

F1 The H99 group

This group was discovered by Helmi et al. (1999) and further investigated by Re Fiorentin et al. (2005). Roederer et al. (2010) made a detailed chemical analysis of these stars (excluding the RR Lyrae stars) and showed that they had a metallicity range of −3.4 < [Fe/H] < −1.5 but were otherwise chemically homogeneous. They concluded that the wide metallicity range precluded the progenitor being a single globular cluster. We note that the globular cluster NGC 6205 (M13) ([Fe/H] =–1.57) has a rather similar L_⊥ to that of this group but a different L_z. The 4 RR Lyrae stars that belong to the H99 group RZ CEP, TT CNC, AR SER and TT LYN have [Fe/H] =−1.77, −1.57, −1.78 and −1.56, respectively (Re Fiorentin et al. 2005), and XZ CYG and CS ERI have [Fe/H] =−1.44 and −1.41, respectively. The mean [Fe/H] of these six RR Lyrae stars is −1.59 and the rms scatter in their [Fe/H] about this mean is 0.16 which is comparable with the likely error in their metallicity. The period distribution of the six RR Lyrae stars corresponds to Oosterhoff type I; NGC 6205 has too few RR Lyrae stars to have a reliable Oosterhoff type. The RR Lyrae members of H99 therefore are more homogeneous than the later-type stars in the group and could possibly have originated from a single globular cluster.

F2 The K07 group

Kepley et al. (2007) identified six low-metallicity outliers in their table 5. Two of these outliers (RV CAP and HD 214925) that have similar location on the L_⊥ versus L_z plot and 13 other outliers are also close to this location. The assumed boundaries of what we call the K07 group are −2300 < L_z < −1500 and +1300 < L_⊥ < +2200 and are shown by the green rectangle in Figs 4, 5 and 6. The 15 low-metallicity stars within these boundaries are listed in Table 3. These stars cover a wide range of distances and it seems unlikely that they all belong to the same group. It is more likely that they belong to several groups that have similar L_⊥ and L_z. Thus, AT VIR and RV CAP (at ∼1 kpc) have similar properties and IP COM and EO COM (at ∼7 kpc) also have similar properties. Further analysis requires more accurate data and is beyond the scope of this paper.