arXiv:1011.1188v1 [astro-ph.GA] 4 Nov 2010 o.Nt .Ato.Soc. Astron. R. Not. Mon. .Co¸skuno˘gluB. Rest of Standard Data RAVE Local from I. Kinematics Stellar Local .Bienaym´eO. .Siviero A. .K Grebel K. E. ⋆ (LSR), Rest of Standard Local not the be to is to need which accordingly obtain corrected Sun, we the parameters kinematical to the relative stationary, Galaxy are the observations of informa- the evolution vital the Since provide and structure Sun the the regarding near tion stars of kinematics The INTRODUCTION 1 c 1 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 sablUiest,SineFcly eateto Astro of Department Faculty, Science University, Istanbul SA utainNtoa nvriy abra Australi Canberra, University, USA National Kentucky, Australian Green, Univers RSAA, Bowling Physics, University, of Kentucky School Western Astronomy, for Institute Sydney France Strasbourg, Lond Strasbourg, College de Scie Space Observatoire University Laboratory, and Science Planetary Space Imaging, OHA Mullard Electronic CB3 for Cambridge, Centre Road, Departe2v Madingley Letters, Astronomy, and of Science Institute of Faculty University, Beykent -al [email protected] E-mail: etro xelneSAES,Lulaa Slovenia. Ljubljana, Physic SPACE-SI, and Excellence Mathematics of of Center Faculty Ljubljana, USA of Maryland, University Baltimore, University, Hopkins Australia John Sydney, Observatory, Astronomical Germany Australian Potsdam, Potsdam, Institut Victori Astrophysikalisches Australia of Sydney, University University, Astronomy, (VI) Macquarie and Asiago Physics 36012 of Padova, Department of Observatory Astronomical INAF f¨ur Astronomie Zentrum UK Rechen-Institut, Preston, Astronomisches Lancashire, Central of University RAS 12 , 15 11 6 .Steinmetz M. , .Bland-Hawthorn J. , .Munari U. , 1 ⋆ 000 .Ak S. , 1– , ?? oinw eiei necletareeti radial in agreement excellent Res of s in Standard these is Local for the well-d derive motions to space we with respect derive survey, with We motion velocity RAVE Sun. space the the solar of high-p the 18026 from pc of 600 sample stars a within isolate 82850 dwarfs to parameters, of stellar and sample velocities a analyze We ABSTRACT oin ihohrrcn eemntos u eie tangential derived Our determinations. recent V other with motions oa tnado et tla content stellar rest, of standard local ntecmaio apecoe,o ntemto faayi.The analysis. of potential. symmetric method near words: the a Key in on relaxed, or dynamically signiﬁc chosen, well not very sample are seems values comparison derived the The on studies. earlier with disagreement ⊙ )Pitd2 coe 08(NL (MN 2018 October 29 Printed () 1 geswt eyrcn eemntos hc aorvle near values favour which determinations, recent very with agrees .Bilir S. , 12 .F Navarro F. J. , 15 .G Watson G. F. , aay ieaisaddnmc,slrnihorod oa motion solar neighbourhood, solar dynamics, and kinematics Galaxy: 1 .Karaali S. , 7 .Campbell R. , oyadSaeSine,319 nvriyItnu,Turk University-Istanbul, 34119, Sciences, Space and nomy a eto ahmtc n optr ekn,338 Istanbul 34398, Beykent, Computer, and Mathematics of ment n obr tMr,Drig H N,UK 6NT, RH5 Dorking, Mary, St Hombury on, e nvri¨tHiebr,Hiebr,Germany Heidelberg, Universit¨at Heidelberg, der t fSde,NW20,Australia 2006, NSW Sydney, of ity ,Lulaa Slovenia Ljubljana, s, csRsac nttt,TeOe nvriy itnKeyne Milton University, Open The Institute, Research nces . ,Vcoi,B,Cnd 8 5C2 V8P Canada BC, Victoria, a, UK , Italy , aatcptnila ucino,freape eoiyd local velocity the example, of for symmetry of, the com- function a of the as test potential a of Galactic is properties sample stellar kinematic parison of and function a distribution as spatial determination their as interest, intrinsic h oa euirvlct opnnsrltv ota sta that of to determination relative components dard, the velocity implies peculiar gravitational This solar of the Galaxy. the location in orbit the the circular at of a star on potential a be of would frame that Sun rest the the as deﬁned is which 13 .A Parker A. Q. , 2 16 .Yaz E. , U .F .Wyse G. F. R. , ⊙ A , T 8 V E .C Freeman C. K. , ⊙ tl l v2.2) ﬁle style X and 1 W .Gilmore G. , ⊙ hs ausaeas fconsiderable of also are values These . 14 U , 16 ⊙ .Siebert A. , 17 n vertical and .Zwitter T. , 9 .Gibson B. , .Tepcla solar peculiar The t. 3 oaiiythin-disc robability .M Seabroke M. G. , euirvelocity, peculiar as n deduce and tars, nl dependent antly 3k s km 13 ey W oa galaxy local 6 ⊙ etermined , ,UK s, Turkey , peculiar 18 − , 1 19 10 in , the is- n- , , 4 , 5 , 2 Co¸skuno˘glu et al. persion. One can test if thin disk slowly moving stars are, or ues of V⊙ than that of DB98. Piskunov et al. (2006) de- are not, aﬀected by a Galactic bar, among many other con- termined a value diﬀerent from that of DB98 by about 7 siderations. Uncertainty in the solar kinematic parameters km s−1 in the V component of the solar motion, when de- can have profound implications for Galactic structural anal- termined with respect to open clusters in the solar neigh- yses (cf. e.g. McMillan & Binney 2010) and may be aﬀected bourhood. Binney (2010) ﬁtted distribution function models systematically in turn by presumptions about larger scale to two sets of velocity distributions and obtained a diﬀer- Galactic stellar populations (cf. e.g. Sch¨onrich et al. 2010). ence of about 6 km s−1 compared to the value of DB98. There have been several very recent determinations of the This higher value of V⊙ has been conﬁrmed by Reid et al. solar peculiar velocity, including some using RAVE (RAdial (2009) and Rygl et al. (2010) in their works related to ra- Velocity Experiment, Steinmetz et al., 2006, see also Section dio frequency astrometry of masers in regions of massive 2) data as we use here (e.g. Pasetto et al. 2010). A summa- star formation (though see McMillan & Binney (2010) for rized list of recent determinations of the space velocity com- a diﬀerent analysis). Sch¨onrich et al. (2010) applied a par- ponents of the Sun appearing in the literature is given in ticular chemodynamical model of the Galaxy to DB98’s data Table 1, while Francis & Anderson (2009) provide an even and determined a value for the V⊙ solar velocity component longer list of references. Given the astrophysical signiﬁcance consistent with recent high values. The key factor in the of systematic sample- and method-dependent eﬀects in the Sch¨onrich et al. (2010) analysis, and of others, is the rele- 2 determination, we consider here a further determination of vant range of radial velocity dispersions σR which is used the solar space velocity, using a complementary technique. in the Jeans’ analysis. Sch¨onrich et al. (2010) showed that 2 −1 2 The determination of the solar space motion relative for σR>600 (km s ) the Hipparcos data deﬁne a straight 2 −1 2 to a Local Standard of Rest (LSR) is a long-standing chal- line, whereas for σR6400 (km s ) they deviate from such lenge. The robust determination of the systematic motion of a simple ﬁt. If one omits stars with low dispersions, and ex- some stellar population relative to some agreed LSR would trapolates the linear ﬁt for stars with high dispersion to zero, itself be of considerable interest. Hence many studies have the linear ﬁt for stars with high dispersions, one conﬁrms the been carried out since that of Homann (1886) to estimate low value of DB98. Actually, this is the procedure used by these parameters. However, there is still uncertainty about DB98, who also ignored stars with low velocity dispersion the numerical values of the solar velocity components, rela- due to their probable lack of dynamical equilibrium. While tive to local thin disc stars, especially for the V⊙ component, it is true that low velocity dispersion stars are likely to be due to the complexity involved in compensating for the ve- most aﬀected by the eﬀects of dissolving star clusters and locity “lag” of sample stars. The diﬀerence between the re- the non-axisymmetric gravitational potential of spiral arms, sults of diﬀerent researchers originates from diﬀerent data as one does need to consider carefully the oﬀset character of 2 well as diﬀerent procedures used. The very diﬀerent results the relation between Va and σR at low velocity dispersions derived by Dehnen & Binney (1998) and Sch¨onrich et al. to avoid bias. (2010), both of whom who used the Hipparcos data, are Here we use a new sample of stars and a diﬀerent an illustration of the continuing model-dependence of the methodology to re-estimate the U⊙, V⊙ and W⊙ solar veloc- result. ity components. 1) We use RAVE data extending to larger The radial (U⊙) and vertical (W⊙) components of the distances than the Hipparcos sample. 2) We applied the fol- solar motion, as a function of the relevant stellar popula- lowing constraints to obtain a sample of main sequence stars: tion, can be obtained in principle by direct analysis of the i) we selected stars with surface gravity 4
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Table 1. Space velocity components of the Sun with respect to the LSR as given in the literature.
Reference Source U⊙ V⊙ W⊙ (km s−1) (km s−1) (km s−1)
This study (2010) RAVE DR3 8.50±0.29 13.38±0.43 6.49±0.26 Bobylev & Bajkova (2010) Masers 5.5±2.2 11.0±1.7 8.5±1.2 Breddels et al. (2010) RAVE DR2 12.0±0.6 20.4±0.5 7.8±0.3 Sch¨onrich et al. (2010) Hipparcos 11.10±0.72 12.24±0.47 7.25±0.36 Francis & Anderson (2009) Hipparcos 7.5±1.0 13.5±0.3 6.8±0.1 Veltz et al. (2008) RAVE DR1 8.5±0.3 – 11.1±1.0 Bobylev & Bajkova (2007) F & G dwarfs 8.7±0.5 6.2±2.2 7.2±0.8 Piskunov et al. (2006) Open clusters 9.44±1.14 11.90±0.72 7.20±0.42 Mignard (2000) K0-K5 9.88 14.19 7.76 Dehnen & Binney (1998) Hipparcos, dmax=100 pc 10.00±0.36 5.25±0.62 7.17±0.38 Binney et al. (1997) Stars near South Celestial Pole 11±0.6 5.3±1.7 7.0±0.6 Mihalas & Binney (1981) Galactic Astronomy 2nd Ed. 9.2±0.3 12.0 6.9±0.2 Homann (1886) Solar neighbourhood stars 17.4±11.2 16.9±10.9 3.6±2.3 metallicity, surface gravity, of up to one million stars using stars were obtained by matching RAVE DR3 with Tycho-2, the 6 degree Field (6dF) multi-object spectrograph on the USNO-B, DENIS and 2MASS catalogues. The analysis here 1.2 m UK Schmidt Telescope of the Australian Astronomi- uses stars in RAVE DR3 with 2MASS catalogue photome- cal Observatory. The RAVE programme started in 2003, ob- try. taining medium resolution spectra in the Ca-triplet region (8410-8795 A)˚ for southern hemisphere stars in the mag- nitude range 9
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Figure 2. E(B − V ) reddening map in the solar neighbourhood for our RAVE main sequence sample. (a) stars with |b| 6 30◦, (b) stars with 30◦ < |b| 6 60◦ and (c) stars with |b| > 60◦.
excess at the distance of the star, Ed(B − V ), can be evalu- ated using a speciﬁc form of Eq. 1:
Ad(b) = 3.1Ed(B − V ) (3)
That value was used in Fiorucci & Munari’s (2003) equations to obtain the total absorptions for the J, H and Ks bands, i.e. AJ = 0.887 × E(B − V ), AH = 0.565 × E(B − V ) and AKs = 0.382 × E(B − V ), which were used in Pogson’s equation (mi − Mi = 5 log d − 5+ Ai; i denotes a speciﬁc band) to evaluate distances. Contrary to the assumption above, the original (J − H) and (H − Ks) colour indices are not de-reddened. Hence, the application of the equations (1) to (3) is iterated until the distance d and colour index Ed(B − V ) approach constant values. Our resulting distribution of E(B − V ) reddening for our 21310 RAVE main sequence stars in the X-Y Galactic plane is given in Fig. 2. To analyze the reddening in the solar neighbourhood more accurately, we divided the stars into three subsamples according to their Galactic latitude: Fig. 2a shows the stars with |b| 6 30◦, in Fig. 2b the stars with 30◦ < |b| 6 60◦ are shown, whereas Fig. 2c gives the stars with |b| > 60◦. The ﬁrst feature of the reddening distri- bution is the complex structure of the reddening in the ﬁrst Figure 1. Two colour diagrams for two samples of RAVE DR3 two panels. The local bubble, i.e. the region within 0.1 kpc stars. (a) for the original sample (main sequence stars and giants), distance from the Sun, is not aﬀected by the reddening eﬀect (b) for main sequence stars only. of the interstellar dust, whereas E(B − V ) can be as high as 0.35 mag at larger distances. As expected high latitude stars (Fig. 2c) have smaller reddening values. The second star. The relation between the total and selective absorp- feature is that one can not ignore the interstellar reddening tions in the UBV system, i.e. even when using NIR bands. The distribution of distances (Fig. 3) shows that 80% of A∞(b) = 3.1E∞(B − V ) (1) the sample stars have almost a normal distribution within gives A∞(b) which can be used in evaluating Ad(b) using the distance interval 06d60.4 kpc, whereas the overall dis- Bahcall & Soneira’s (1980) procedure: tribution which extends up to 1 kpc is skewed, with a median of 0.276 kpc. However, 97% of the sample stars are within − | d sin(b) | d=0.6 kpc. Ad(b)= A∞(b) 1 − exp (2) " H !# The position of the sample stars in the rectangular co- ordinate system relative to the Sun is given in Fig. 4. The where b and d are the Galactic latitude and distance of the projected shapes both on the Galactic (X, Y ) plane, and star, respectively. H is the scaleheight for the interstellar on the vertical (X, Z) plane of the sample show asymmetri- dust which is adopted as 125 pc (Marshall et al. 2006) and cal distributions. The median coordinates (X=60, Y =-107, A∞(b) and Ad(b) are the total absorptions for the model and Z=-108 pc) of the sample stars conﬁrm this appearance. The for the distance to the star, respectively. Then, the colour inhomogeneous structure is due to the incomplete observa-
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U, V and W are the components of a velocity vector of a star with respect to the Sun, where U is positive towards the Galactic centre (l=0◦, b=0◦), V is positive in the direc- tion of Galactic rotation (l=90◦, b=0◦) and W is positive towards the North Galactic Pole (b=90◦). Correction for diﬀerential Galactic rotation is necessary for accurate determination of U, V and W velocity compo- nents. The eﬀect is proportional to the projection of the distance to the stars onto the Galactic plane, i.e. the W velocity component is not aﬀected by Galactic diﬀerential rotation (Mihalas & Binney 1981). We applied the proce- dure of Mihalas & Binney (1981) to the distribution of the sample stars in the X-Y plane and estimated the ﬁrst order Galactic diﬀerential rotation corrections for U and V veloc- ity components of the sample stars. The range of these cor- −1 Figure 3. Cumulative (a) and frequency (b) distributions of dis- rections is -25.13
4 KINEMATICS 5 POPULATION ANALYSIS We combined the distances estimated in Section 3 with We now wish to consider the population kinematics as RAVE kinematics and the available proper motions, apply- a function of stellar population, using space motion as a ing the (standard) algorithms and the transformation matri- statistical process to label stars as (probabilistic) “mem- ces of Johnson & Soderblom (1987) to obtain their Galactic bers” of a stellar population. We used the procedure space velocity components (U, V , W ). In the calculations, of Bensby, Feltzing & Lundstr¨om (2003) and Bensby et al. the epoch of J2000 was adopted as described in the Interna- (2005) to allocate the main sequence sample (20453 stars) tional Celestial Reference System (ICRS) of the Hipparcos into populations and derived the solar space velocity compo- and Tycho-2 Catalogues (ESA 1997). The transformation nents for the thin disc population to check the dependence of matrices use the notation of a right handed system. Hence, LSR parameters on population. Bensby et al. (2003, 2005)
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Table 2. The space velocity component ranges for population types of RAVE main sequence stars.
Parameters UVW (km s−1) (km s−1) (km s−1)
TD/D 6 0.1 (-85, 75) (-80, 40) (-55, 40) 0.1 < TD/D 6 1 (-105, 100) (-100, 50) (-70, 50) TD/D > 1 (-165, 155) (-175, 60) (-115, 90)
where 1 k = 3/2 (6) (2π) σULSR σV LSR σW LSR normalizes the expression. For consistency with other anal-
yses, we adopt σULSR , σV LSR and σW LSR as the character- istic velocity dispersions: 35, 20 and 16 km s−1 for thin disc (D); 67, 38 and 35 km s−1 for thick disc (T D); 160, 90 and 90 km s−1 for halo (H), respectively (Bensby et al. 2003). −1 Vasym is the asymmetric drift: -15, -46 and -220 km s for thin disc, thick disc and halo, respectively. ULSR, VLSR and WLSR are LSR velocities. The space velocity components of the sample stars relative to the LSR were estimated by adding the values for the space velocity components evalu- ated by Dehnen & Binney (1998) to the corresponding solar ones. The probability of a star of being “a member” of a given population is deﬁned as the ratio of the f(U, V , W ) distri- bution functions times the ratio of the local space densities for two populations. Thus, X f X f T D/D = TD . TD TD/H = TD . TD (7) Figure 5. Error histograms for space velocity (a) and its compo- XD fD XH fH nents (b-d) for RAVE main sequence stars. The arrow in panel (a) are the probabilities for a star of it being classiﬁed as indicates the upper limit of the total error adopted in this work. a thick disc star relative to being a thin disc star, and The shaded part of the histogram indicates the error for diﬀerent relative to being a halo star, respectively. XD, XTD and velocity components of stars after removing the stars with large XH are the local space densities for thin disc, thick space velocity errors. disc and halo, i.e. 0.94, 0.06, and 0.0015, respectively (Robin et al. 1996; Buser et al. 1999). We followed the ar- gument of Bensby et al. (2005) and separated the sam- ple stars into four categories: T D/D60.1 (high probability thin disc stars), 0.1
Figure 6. The distribution of velocity components of RAVE main 6 RESULTS sequence stars in two projections onto the Galactic Plane: (a) U- V and (b) W -V . We analysed the U, V and W space velocity components for the main sequence sample (20453 stars) as well as for four subsamples, i.e. high probability thin disc stars of dif- assumed that the Galactic space velocities of stellar popu- ferent spectral types a) F, G and K (N=17889 stars), b) F lations with respect to the LSR have Gaussian distributions (N=9654 stars), c) G (N=5910 stars), d) K (N=2325 stars) as follows: and estimated the modes of the Gaussian distributions for
2 each category and each space velocity component. Spectral U 2 (V − V ) W 2 f(U, V, W )= k . exp − LSR − LSR asym − LSR ,types(5) were determined according to the 2MASS colours of 2σ2 2σ2 2σ2 ULSR V LSR W LSR !the stars (Bilir et al. 2008, see Table 3). The colour range is
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rium state of stellar populations by comparing their deduced solar peculiar motion, or equivalently their mean motion rel- ative to a LSR. One may wonder if the kinematically cold thin disc stars feel a large asymmetric gravitational poten- tial from, perhaps, an inner Galactic bar. Do spiral arms have systematic kinematic eﬀects visible in young stars? Is the LSR deﬁned by the high velocity halo stars, which feel largely extended dark matter potentials, the same as that of thick disc stars, and thin disc stars? These questions es- sentially repeat a query on the closeness of the higher-order Oort Constants to zero, for all Galactic components. The signiﬁcance is such one wishes to determine the “solar peculiar velocity” for many samples, using several Figure 7. Distribution of main sequence stars of diﬀerent popu- lation types on two Galactic space velocity planes: (a) U-V and techniques. Doing this (see Table 1 above for a list) has (b) W -V . The contours indicate (outwards from the centre) high led, in general to determinations of the peculiar motion ra- probability thin disc (TD/D 6 0.1), low probability thin disc (0.1 dially outwards from the Galactic centre U⊙ which are con- < TD/D 6 1) and low and high probability thick disc and halo sistent and small, independent of the comparison sample stars (TD/D > 1). chosen. Every stellar sub-population in the Galaxy seems remarkably radially stable and circularly symmetric, with no evidence for bar-like perturbations. Similarly, doing this 0.08
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Table 3. Space velocity components of the Sun with respect to the LSR for ﬁve population subsamples, as described in the text.
Parameters Colour Range U V W N (km s−1) (km s−1) (km s−1)
All sample 0.056(J − H)060.55 8.83 ± 0.24 14.19 ± 0.34 6.57 ± 0.21 20 453 TD/D 6 0.1 0.056(J − H)060.55 8.50 ± 0.29 13.38 ± 0.43 6.49 ± 0.26 18 026 F Spectral Type 0.08<(J − H)060.30 8.35 ± 0.36 13.14 ± 0.43 6.24 ± 0.27 9 654 G Spectral Type 0.30<(J − H)060.42 9.25 ± 0.50 14.42 ± 0.57 6.67 ± 0.38 5 910 K Spectral Type 0.42<(J − H)060.55 7.01 ± 0.67 11.96 ± 0.66 7.03 ± 0.38 2 325
Figure 8. The distribution functions of Galactic space velocities for the 20453 main sequence stars, with overlaid best-ﬁt Gaussian distributions. as a preferred sample in our work. We estimated solar space the Science & Technology Facilities Council of the UK, Opti- velocity components for ﬁve samples: for all our RAVE main con, Strasbourg Observatory, and the Universities of Gronin- sequence stars; for the sub-sample of high-probability thin gen, Heidelberg, and Sydney. disc main sequence stars; and separately for the thin disc This work has been supported in part by the Scientiﬁc main sequence stars of F, G and K spectral types. The re- and Technological Research Council (TUB¨ ITAK)˙ 108T613. sults (see Table 3 above) are consistent, within sampling er- Salih Karaali is grateful to the Beykent University for ﬁnan- rors, across all sub-samples. They are also in agreement with cial support. This publication makes use of data products recent determinations using other population subsamples, from the Two Micron All Sky Survey, which is a joint project and over very diﬀerent ranges. There is increasing agreement of the University of Massachusetts and the Infrared Process- that the solar peculiar velocity in the rotation direction has ing and Analysis Center/California Institute of Technology, been underestimated in older studies. The internal agree- funded by the National Aeronautics and Space Administra- ment between our diﬀerent samples, and between this study tion and the National Science Foundation. and others, provides evidence that the Galactic potential This research has made use of the SIMBAD, NASA’s near the Sun is symmetric, with no evident time dependent Astrophysics Data System Bibliographic Services and the variation. NASA/IPAC ExtraGalactic Database (NED) which is oper- ated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics 8 ACKNOWLEDGMENTS and Space Administration. We thank the anonymous referee for his/her comments. Funding for RAVE has been provided by: the Australian Astronomical Observatory, the Astrophysical Institute Pots- REFERENCES dam, the Australian National University, the Australian Re- search Council, the French National Research Agency, the Bahcall J. N., Soneira R. M., 1980, ApJS, 44, 73 German Research Foundation, the Istituto Nazionale di As- Bensby T., Feltzing S., Lundstr¨om I., 2003, A&A 410, 527 troﬁsica at Padova, The Johns Hopkins University, the W.M. Bensby T., Feltzing S., Lundstr¨om I., Ilyin I., 2005, A&A, Keck Foundation, the Macquarie University, the Nether- 433, 185 lands Research School for Astronomy, the Natural Sciences Bilir S., Karaali S., Gilmore G., 2006, MNRAS, 366, 1295 and Engineering Research Council of Canada, the Slovenian Bilir S., Karaali S., Ak S., Yaz E., Cabrera-Lavers A., Research Agency, the Swiss National Science Foundation, Co¸skuno˘glu K. B., 2008, MNRAS, 390, 1569
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Figure 9. The distribution functions of Galactic space velocities for the high probability thin disc stars, with overlaid best-ﬁt Gaussian distributions.
Binney J. J., Tremaine S., 1987, Galactic Dynamics, Piskunov A. E., Kharchenko N. V., R¨oser S., Schilbach E., Princeton Univ. Press, Princeton Scholz R.-D., 2006, A&A, 445, 545 Binney J. J., Dehnen W., Houk N., Murray C. A., Penston Reid M. J., et al., 2009, ApJ, 700, 137 M. J., 1997, ESASP, 402, 473 Robin A. C., Haywood M., Cr´eze M., Ojha D. K., Bienaym´e Binney J. J., 2010, MNRAS, 401, 2318 O., 1996, A&A, 305, 125 Bobylev V. V., Bajkova A. T., 2007, ARep, 51, 372 Rygl K. L. J., Brunthaler A., Reid M. J., Menten K. M., Bobylev V. V., Bajkova A. T., 2010, MNRAS, 408, 1788 van Langevelde H. J., Xu, Y., 2010, A&A, 511A, 2 Breddels M. A., et al., 2010, A&A, 511, 90 Schlegel D. J., Finkbeiner D. P., Davis M., 1998, ApJ, 500, Buser R., Rong J., Karaali S., 1999, A&A, 348, 98 525 Cutri R. M., et al., 2003, 2MASS All-Sky Catalogue of Sch¨onrich R., Binney J., Dehnen W., 2010, MNRAS, 403, Point Sources, CDS/ADC Electronic Catalogues, 2246 1829 Dehnen W., Binney J. J., 1998, MNRAS, 298, 387 Seabroke G. M., Gilmore G., and the RAVE Collaboration, Dinescu D. I., Girard T. M., van Altena W. F., 1999, AJ, 2008, MNRAS, 384, 11 117, 1792 Skrutskie M. F., et al., 2006, AJ, 131, 1163 ESA, 1997, The Hipparcos and Tycho Catalogues, ESA Steinmetz M., et al., 2006, AJ, 132, 1645 SP-1200. ESA, Noordwijk Str¨omberg G., 1946, ApJ, 104, 12 Fellhauer M., Wilkinson M. I., Evans N. W., Belokurov V., van Leeuwen F., 2007, A&A, 474, 653 Irwin M. J., Gilmore G., Zucker D. B., Kleyna J. T., 2008, Vidojevic S., Ninkovic S., 2009, AN, 330, 46 MNRAS, 385, 1095 Wilkinson M. I., et al., 2005, MNRAS, 359, 1306 Zwitter T., et al., 2008, AJ, 136, 421 Fiorucci M., Munari U., 2003, A&A, 401, 781 Francis C., Anderson E., 2009, NewA, 14, 615 Gilmore G., Wyse R. F. G. & Kuijken K., 1989, ARAA, 27, 555 Hernquist L., 1990, ApJ, 356, 359 Homann H., 1886, AN, 114, 25 Jenkins A., 1992, MNRAS, 257, 620 Johnson D. R. H., Soderblom D. R., 1987, AJ, 93, 864 Johnston K. V., Spergel D. N., Hernquist L., 1995, ApJ, 451, 598 Katz D., et al., 2004, MNRAS, 354, 1223 Marshall D. J., Robin A. C., Reyl´eC., Schultheis M., Pi- caud S., 2006, A&A, 453, 635 McMillan P., Binney J., 2010, MNRAS, 402, 934 Mignard F., 2000, A&A, 354, 522 Mihalas D., Binney J., 1981, Galactic Astronomy: Struc- ture and Kinematics, 2nd edition Munari U., 2003, ASPC, 298 Pasetto S., Grebel E., Bienaym´eO., and the RAVE Col- laboration, 2010, A&A (submitted) Pickles A. J., 1998, PASP, 110, 863
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