arXiv:1011.4092v1 [astro-ph.GA] 17 Nov 2010 ⋆
o.Nt .Ato.Soc. Astron. R. Not. Mon. ..Navarro J.F. ..Fulbright J.P. ...Wyse R.F.G. .Siebert A. extended the RAVE in with gradient disc velocity local radial a of Detection ..Freeman K.C. cetd.Rcie noiia om2 uy2018 July 29 form original in ; Received . Accepted c 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 nttt fAtooy abig,UK Cambridge, Astronomy, UK of Preston, Institute Lancashire, Central USA of MD, Sydn University Baltimore, Sydney, University, of Hopkins University Johns Astronomy, for Germany Institute Potsdam, Sydney , Potsdam Institut Australia Astrophysikalishes UK Canberra, Oxford, University, Physics, National Theoretical Australian for Centre Lond Peierls College Rudolf University Laboratory, Science Space Mullard CN Strasbourg, Universit´e de Astronomique, Observatoire -al [email protected] E-mail: etro xelne PC-I jbjn,Slovenia Ljubljana, Physic SPACE-SI, and excellence, Mathematics of of Center Faculty Ljubljana, of University Australia Sydney, Observatory, Anglo-Australian Australia Sydney, University, Canada Ital Macquary Victoria, Asiago, Victoria, Asiago, of in University Padova of Netherland Observatory the Astronomical Groningen, Institut, Astronomical Kapteyn f¨ur Astronomie Zentrum Rechen-Institut, Astronomisches 00RAS 0000 1 ⋆ .Famaey B. , 13 7 7 .Zwitter T. , 4 ..Parker Q.A. , ..Gibson B.K. , .Williams M. , 000 0–0 00)Pitd2 uy21 M L (MN 2018 July 29 Printed (0000) 000–000 , aisaddynamics. and matics h xsec fti rdeti h AEdt.Ti eoiygradien velocity This data. RAVE param the Galactic w in of centre, gradient and Galactic this to motions the of proper of quadran existence direction stellar fourth the the of the in In independent stars centre. method disc Galactic of the gradient from velocity a of detection nldn h a,tesia rsadpsil h litct ftedar the of ellipticity the Gala possibly words: the and Key of arms spiral components f the with non-axisymmetric bar, together the the latitudes, including constrain low confir at help observational stars Further should of speed. velocities circular line-of-sight local with and Sun the of fpoe oin n htmti itne ae ihro isoch on either based distances photometric and Stan K Local motions us the maps proper of respectively velocity of velocity Galactocentric field, radial two-dimensional velocity zero the the a reconstruct assuming of effect, shear the radial trate and divergence local e,lmtdt itneo p rmteSnadto and Sun ( the Experiment from Velocity kpc Radial 2 the of from distance stars a 713 to 213 limited of vey, sample a Using ABSTRACT bn antds n osdrn w eso ausfrteGalac the for values of sets two considering and magnitudes, -band | K 1 .Minchev I. , + 16 , C 14 17 8 5 | .Gilmore G. , ∼ > .Bienaym´e O. , ..Reid W.A. , ms km 3 tr:knmtc aay udmna aaees–Glx:kin Galaxy: – parameters fundamental Galaxy: – kinematics Stars: − 1 S tabug France Strasbourg, RS, 1 n omuyS ay okn,R56T UK 6NT, RH5 Dorking, Mary, St Holmbury on, kpc e nvri¨tHiebr,Hiebr,Germany Heidelberg, Universit¨at Heidelberg, der s y Australia ey, ..Seabroke G.M. , ,Lulaa Slovenia Ljubljana, s, y − 1 where , 14 9 u ik a aayi nqelbrtr nwhich kine in stellar laboratory from evolution unique and a structure is galactic study Galaxy to Way Milky Our INTRODUCTION 1 ..Grebel E.K. , .Siviero A. , 1 .Bland-Hawthorn J. , K and A T E C tl l v2.2) file style X 2 r h otcntnsmauigthe measuring constants Oort the are 5 .Binney J. , , 12 10 .Steinmetz M. , .Helmi A. , | z | < 6 3 .Campbell R. , aino u finding our of mation p,w eotthe report we kpc, 1 .Burnett B. , ado etw then we Rest of dard n w ieetsets different two ing ,drce radially directed t, 11 nodrt illus- to order In . oefitn ron or fitting rone rhrmodelling, urther pl simple a apply e .Munari U. , oeti radius tocentric tr oassess to eters tcpotential, ctic corresponds t halo. k 5 AE sur- RAVE) .Watson F. , 3 , 5 e- , - 12 , 15 , 2 A. Siebert et al.
1 matics. The story of the efforts to obtain such kinematic Here, we use line-of-sight velocity data (vlos) from the data nicely illustrates how theoretical progress and data RAVE survey to investigate whether the mean radial motion acquisition have to go hand in hand if one wants to gain of disc stars remains zero in the extended solar neighbour- insight into the structure and history of the Galaxy. Un- hood as compared to the one in the solar neighbourhood, til recently, most studies have been limited to the so- or whether large-scale radial streaming motions are present lar neighbourhood. The zeroth order approximation for in the vicinity of the Sun, which would translate in a ra- modelling these kinematic data assumes an axisymmet- dial velocity gradient in one or the other direction. In Sec. 2 ric model, in which the Local Standard of Rest (LSR) we present the sample used for our analysis while in Sec. 3 is on a perfectly circular orbit. However, the local veloc- we present the detection of a radial velocity gradient using ity field in the solar neighbourhood already displays pos- RAVE vlos, as well as the associated Oort constants and 2- sible signatures of the non-axisymmetry of the Galactic dimensional velocity field. Finally in Sec. 4 we discuss the potential in the form of stellar moving groups contain- implications of our results and present our conclusions. ing stars of very different ages and chemical compositions (Dehnen 1998; Famaey et al. 2005; Quillen & Minchev 2005; Bensby et al. 2007; Minchev et al. 2010). 2 THE RAVE SAMPLE
In external galaxies, large-scale distortions of the (line- Our analysis is based on the RAVE catalogue (Steinmetz et al. 2006; Zwitter et al. 2008) which provides of-sight) isovelocity contours of the gas have long been recog- −1 nised in two-dimensional velocity maps (e.g. Bosma 1978), vlos to 2 kms and stellar atmospheric parameters and allowing a quantification of the strength of non-circular distances to 30% for a large number of bright stars in the streaming motions (e.g., Sellwood & Zanmar Sanchez southern hemisphere with 9 Milky Way and in which the radial similar to a magnitude limited survey. The RAVE cata- streaming motions of the gas reach maxima of the order logue is cross-matched with astrometric (PPMX, UCAC2, of 50 km s−1. However, the stellar kinematics often turn Tycho-2) and photometric catalogues (2MASS, DENIS) to out to be slightly more regular and symmetric than the provide additional proper motions and magnitudes making gas kinematics (e.g. Pizzella et al. 2008). For instance, RAVE a suitable tool to study the Milky Way. Rix & Zaritsky (1995) estimate from 18 face-on spiral We use the latest version of the Zwitter et al. (2010) galaxies that the azimuthally averaged radial streaming catalogue, which contains four sets of distances in addition motions of disk stars should typically amount to a maxi- to the standard RAVE data (line-of-sight velocities and stel- mum of 7 km s−1 due to lopsided distortions and 6 km s−1 lar parameters). These four sets of distances are (i) the dis- due to intrinsic ellipticity. tance moduli computed using three sets of isochrones (in- cluding the Padova isochrones), and (ii) the distances of Breddels et al. (2010). In this paper we will use the dis- tance moduli based on the Padova isochrones but our re- In the Milky Way, non-axisymmetric motions are sults do not strongly depend on the set of isochrones used clearly visible in radio-frequency observations of gas flow (see also Sect.3.2 where all distances are multiplied by an in the inner Galaxy, implying that the amplitude of spiral arbitrary factor). This catalogue is cleaned from potentially structure could be larger by a factor ∼1.5 than its amplitude problematic fields using a list kindly provided by G. Matije- in the near-infrared luminosity density (Bissantz et al. vic (private communication) and we further select stars with 2003; Famaey & Binney 2005). On the other hand, radio |z| < 1 kpc to minimise contamination by halo stars. This interferometry used to determine the parallax of star- leaves us with a sample of 213 713 stars with known dis- forming regions in the Perseus spiral arm, together with tances, atmospheric parameters (log g, Teff , [m/H]), proper the measurement of their line-of-sight (los) velocities, show motions as well as vlos measurements that can be used to that these star-forming regions have peculiar non-circular compute the 3D space velocities. −1 motions amounting to ∼20 km s , assuming standard To verify that our analysis does not depend on the IAU Galactic parameters and a nearly-flat rotation curve method used to determine the distances or on the source (Xu et al. 2006; Binney 2006; Reid et al. 2009). However, of proper motions, we also use stars for which distances the amplitude of such non-circular motions strongly depends and proper motions are obtained independently. To do so, on the Galactic parameters adopted (McMillan & Binney we select a sub-sample of red clump candidates for which 2010), namely the Galactocentric radius of the Sun R0, the distance can be estimated using the K–magnitude alone the local circular speed vc0, and the reflex solar motion, as because of the narrow, almost Gaussian, luminosity func- well as the model for the rotation curve. Another example tion of the red clump. Red clump candidates are selected of such non-circular motion is the 3 kpc arm which has in the (log g, J − K) plane, as illustrated in Fig. 1. We −1 vlos = −80km s towards the Galactic centre (GC) and select the over-density using 0.5 < J − K < 0.735 and is known to have a counterpart on the far side of the GC (Dame & Thaddeus 2008). Its origin is associated to the 1 Galactic bar showing that non-circular motion of the similar Throughout this paper we will use the notation vlos or line-of- amplitude can be caused by various types of perturbations sight velocity to refer to the heliocentric radial velocity measured and not necessarily by spiral arms. by RAVE while radial velocity or VR means galactocentric radial velocity
c 0000 RAS, MNRAS 000, 000–000
A radial velocity gradient in the Galactic disc 3
0 67.23 to bottom in each panel in Fig. 3). The curves are drawn using 5 000 Monte Carlo realisations of the samples, replac- ing the measured velocities by random realisations of a thin 49.30 disc ellipsoid. The model used is the same for both sam- ples, kinematic parameters for the thin disc ellipsoid being 2 taken from Binney & Merrifield (1998) table 10.4. Clearly, our data are not compatible with a disc in circular rotation 31.38 log g because the mean projected line-of-sight velocity is system- atically lower than the expected mean velocity. The offset between the two panels reflects the different distribution in 13.45 R of the two samples. 4 Because our samples are not perfectly oriented towards the GC, the rotation component could bias our measure- −4.48 ment. Therefore, we reproduce this by modelling a thick disc 0.5 0.6 0.7 0.8 population which lags the circular rotation by 36 km s−1.
J−K2MASS The result for a thick disc is presented as dashed curves and is computed only in the case of circular rotation. The Figure 1. Distribution of stars in the (log g, J K) plane near the − results do not differ significantly from the thin disc results red clump for the RAVE internal release. Colour coding follows indicating that the contribution from v 0 to our line-of-sight the number of stars per bin of 0.03 mag width in J K and c − 0.05 dex in log g. The distribution is smoothed over 3 pixels to velocities is marginal and hence that our result truly mea- reduce the noise. Stars in the white box are identified as red-clump sures a radial velocity gradient in the RAVE data. stars.
3.2 Oort constants 1.8 < log g < 2.8: the red limit helps reduce the contam- ination by the upper red-giant-branch stars. Distances are As first worked out by Oort (1927) for an axisymmet- obtained assuming all stars in the sample are red clump ric Galaxy, and later generalised to non-axisymmetry (e.g., stars using a Gaussian luminosity function for this popula- Chandrasekhar 1942), a practical way to study the global tion with MK = −1.6 and σK = 0.22. We apply the same cut streaming motion of field stars in the Galaxy is to con- in z as for the full sample. This results in a sample containing sider an arbitrary smooth velocity field and Taylor expand it 29 623 red clump candidates. More details on the contam- around the position of the Sun. Such a Taylor expansion of ination and distance errors can be found in Siebert et al. the Cartesian velocity components (U,V ) to first order yields (2008). We cross-match this sample with the UCAC3 cat- the four Oort constants A, B, C, and K, measuring the az- alogue to provide a different source for the proper motion imuthal (A) and radial (C) shear, the local divergence (K), – the RAVE catalogue contains predominantly Tycho-2 and and the vorticity (B) of the velocity field (see e.g. Kuijken & PPMX proper motions. Hence, for this sample, the distances Tremaine 1994, Olling & Dehnen 2003, hereafter KT94 and and proper motions are independent from the full RAVE OD03 respectively). sample. The mean height above/below the Galactic plane While we note that such a first order Taylor expan- for each sample is shown in Fig. 2. sion might not be a valid description of the velocity field for sample depths larger than 1 kpc (as already noted in Pont et al. 1994 and OD03), we also note that, at least in the direction of the GC, a constant linear velocity gradient 3 A RADIAL VELOCITY GRADIENT −1 −1 ∂VR/∂R = K +C between −3 and −10 km s kpc is suf- 3.1 Line-of-sight velocity detection ficient to reproduce the trend seen in Fig.3. In view of this, we compute the Oort constants in the classical way using Most of the RAVE stars lie in the fourth Galactic quadrant with the tails of the distribution in Galactic longitude ex-
tending in the first and third quadrants. For our analysis to hvrad/ri = K + A sin 2ℓ + C cos 2ℓ , remain independent of Galactic parameters and proper mo- hvt/ri = B + A cos 2ℓ − C sin 2ℓ , (1) tions, we first look in the GC (and anticentre) direction with ◦ ◦ ◦ |l| < 5 (and 175 c 0000 RAS, MNRAS 000, 000–000 4 A. Siebert et al. Full sample Red clump candidates 2 1.0 2 1.0 1 1 0.7 0.7 0 0 Y (kpc) 0.4 Y (kpc) 0.4 −1 −1 0.1 0.1 −2 −2 −2 −1 0 1 2 −2 −1 0 1 2 X (kpc) X (kpc) Figure 2. Mean z distance to the Galactic plane in kpc for the two samples studied: full sample (left), red clump sample (right). The | | two panels contain 60 60 pixels in a box 4 4 kpc in extent. Both samples have an upper limit on z , max( z ) = 1 kpc. The Sun is × × | | | | located at the centre of the map, X is increasing in the direction of the Galactic centre and Y towards the Galactic rotation. The solar circle is shown as a dashed line. The circle in the centre represents a sphere 125 pc in radius. Full sample Red clump candidates 20 20 10 10 0 0 .cos(b)> (km/s) .cos(b)> (km/s) los −10 los −10 −20 −20 0 1 0 1 d.cos(l).cos(b) (kpc) d.cos(l).cos(b) (kpc) Figure 3. Projection of the mean RAVE vlos on the Galactic plane in distance intervals of 200 pc in the direction of the Galactic centre ( l < 5◦) and anticentre (175◦ c 0000 RAS, MNRAS 000, 000–000 A radial velocity gradient in the Galactic disc 5 rd respectively. The fit to vrad alone (3 line of Table 1) is the direction of Galactic rotation respectively. This places more reliable as it mostly relies on the RAVE line-of-sight the GC either at (8,0) or (7.8,0) depending on the Galac- velocities and is of better quality than the one including lon- tic parameters used. The solar circle (R = R0) is drawn as gitudinal proper motions (the reduced χ2 values are 1.4 and a dashed line and the open circle delimits a zone 125 pc 2.6 respectively). in radius similar to the Hipparcos sphere. For orientation, This fitting procedure of the Oort con- the location of the local (Orion) and Perseus arms are indi- stants thus confirmed our finding of Sect.3.1 that cated based on the CO map of Englmaier et al. (2010). No > −1 −1 |∂VR/∂R| ∼ 3 kms kpc in the RAVE catalogue. strong kinematic signal is associated with them in hVRi, but Let us note that, as we rely on a priori known distances, our a strong decrease of hVφi is associated with the Orion arm result is not affected by mode-mixing. However, in order to (while little data are available on the Perseus arm). This check whether the qualitative conclusion of the existence could help place limits on the size of the potential pertur- of non-zero velocity gradient depends on our estimates of bations associated with these arms, but is beyond the scope the distances, we assumed that all distances were wrong of this paper. by a factor f, and re-applied the same procedure. Results Again, the global structure of the velocity field in figs. 4 for f = 0.8 and f = 1.2 are listed at the end of Table 1, and 5, comparing the top and bottom panels, is similar for confirming that K + C 6= 0 in both cases. both samples. Small differences exist on local scales, espe- cially around (X,Y)=(0.8,−0.4), but aside from this region the velocity trends are compatible. Isocontours in hVRi are 3.3 Two-dimensional velocity field orientated about 50◦ from the direction to the GC and do To further investigate the velocity gradient detected with not follow a particular symmetry axis of our procedure or RAVE, we now compute the full 2D velocity field for our sample. Within the local neighbourhood indicated by the samples (making use of both the line-of-sight velocities and open circle, no net motion is detected and our values are the proper motion vectors). compatible with previous measurements. The velocity gra- The velocity fields in the Galactocentric reference frame dient becomes noticeable only outside the Hipparcos sphere. are computed using Comparing left and right panels of figs. 4 and 5, we see that using updated Galactic parameters does influence the V V V V GSR = ∗/⊙ + ⊙/LSR + LSR/GSR, (2) measured mean motions. In particular, in Fig. 4 it dimin- ishes but does not eliminate the mean motions. Trying to where V⊙/LSR is the Sun’s velocity with respect to the lo- minimise the gradient while keeping the ratio v 0/R0 con- cal standard of rest (LSR) and V is the motion c LSR/GSR stant, leads to unrealistic values for the Galactic parameters of the LSR with respect to the GC. Obviously, a possible −1 with R0 < 4 kpc and v 0 < 126 km s . radial motion of the LSR itself can be a priori difficult to c disentangle from large-scale streaming motions. In order to circumvent this, we use hereafter the standard assumption 3 that the LSR is on a circular orbit . The velocity of stars 4 DISCUSSION AND CONCLUSIONS VGSR is hereafter decomposed into three components in the In this paper, making use of RAVE line-of-sight velocities axisymmetric galactocentric reference frame (VR,Vφ,Vz), Vz pointing towards the south Galactic pole. and distances alone, we report the discovery of a radial veloc- This projection depends on two parameters : R0, ity gradient in the Galactic disc amounting to at least 3 km s−1 kpc−1 observed in the direction of the GC for d< 2 kpc. the distance to the centre of the Galaxy and vc0, the local circular speed. Unfortunately, as pointed out by Making use of the full sample, we fitted the Oort constants in McMillan & Binney (2010), neither of these parameters are the classical way, and obtained values globally in agreement with those of OD03 for old red giants. But as their measure- well constrained. The ratio vc0/R0 is however better con- strained, lying in the range 29.9 − 31.6 km s−1 kpc−1 with ment was based on proper motions alone, they could not V constrain the value of the Oort constant K, which we esti- some impact on the measured ⊙/LSR as shown in table 1 −1 −1 and 2 of McMillan & Binney (2010). mate here to be roughly between 4 and 6 km s kpc (see Therefore, we compute the 2D velocity maps for two Table 1). Then, assuming a zero radial velocity of the Local sets of parameters. In both cases we fix V⊙/LSR to the values of Sch¨onrich et al. (2010). The first set of parameters uses Standard of Rest, we reconstructed the 2D velocity map, −1 and found that the Galactic parameters do play a role in the standard IAU values vc0 = 220 km s and R0 = 8 kpc while for the second set we use the model 2 from table 2 of the measured amplitude of the streaming motion. Adopting −1 standard IAU values, which are suspected to underestimate McMillan & Binney (2010), vc0 = 247 km s and R0 = 7.8 kpc, which has a solar motion vector close to the latest vc0/R0, yields a larger amplitude. On the other hand, us- determination by Sch¨onrich et al. (2010). ing more recent values for vc0 and R0 reduces the net radial motion but does not eliminate it. The latter result is inde- The results for the 2D hVRi and hVφi velocity maps in the Galactic plane for a 4 × 4 kpc box (60 × 60 bins) cen- pendent of the source of proper motions and distances used. tred on the Sun are presented in Figs. 4 and 5 for both sets We note that the confirmed existence of such a net outwards of parameters and for both samples (full sample and red motion for stars, amounting to 10% of the circular speed, clump selection). X and Y increase towards the GC and in would raise the question of the validity of determining the Galactic parameters based on the assumption of circular mo- tion (see for example Reid et al. 2009), and the error bars 3 Although this does not formally exist in a non-axisymmetric on the measured ratio vc0/R0 are likely underestimated. We potential. however also note that, in order to establish it more firmly, c 0000 RAS, MNRAS 000, 000–000 6 A. Siebert et al. Table 1. Oort constants A, B, C and K measured using the RAVE sample. The kinematic centre ψν = 0.5 arctan( C/A), the amplitude 2 2 − −1 −1 √A + C , and the velocity gradient ∂VR/∂R = K + C are also given. All numbers (apart from ψν ) are in km s kpc . The first two lines give the old values from KT94 and OD03. For the RAVE sample, errors bars are computed using a Monte-Carlo sampling, but they do not take into account the possible systematics listed in OD03. The last two lines show changes in the Oort constants if one considers a 20% bias in our distances. The two cases are obtained by multiplying the distances of the whole catalogue by 0.8 or 1.2, then recomputing the velocities and re-applying the same R, z selection as before. 2 2 Sample A B C Kψν (deg) √A + C K + C KT94 vlos, µ , and µ 14.4 1 12.0 3 0.6 1 0.35 0.5 -1.2 14.4 0.25 b l ± − ± ± − ± OD03 µ 15.9 2 16.9 2 9.8 2 - 15.5 18.7 - l ± − ± − ± RAVE vlos and µ 13.6 0.5 - 9.6 0.5 5.7 0.3 17.6 16.6 -3.9 b ± − ± ± RAVE vlos, µ and µ 9.2 0.5 17.4 0.5 12.7 0.5 4.6 0.5 27.0 15.7 -8.1 b l ± − ± − ± ± d 0.8 vlos and µ 15.0 - -9.2 6.3 15.8 17.6 -2.9 × b d 0.8 vlos, µ and µ 11.1 -11.8 -10.5 5.6 21.7 15.3 -4.9 × b l d 1.2 vlos and µ 12.5 - -10.1 5.3 19.5 16.1 -4.8 × b d 1.2 vlos, µ and µ 7.9 -21.3 -14.4 4.1 30.6 16.4 -10.3 × b l our result should imperatively be confirmed by further line- ACKNOWLEDGEMENTS of-sight velocity measurements at lower latitudes with future Funding for RAVE has been provided by the Anglo- spectroscopic surveys (see e.g. Minchev & Quillen 2008). It Australian Observatory, by the Astrophysical Institute Pots- is indeed very intriguing that a strong 21-cm absorption fea- dam, by the Australian Research Council, by the German ture along the line-of-sight to the GC is compatible with a Research foundation, by the National Institute for Astro- zero mean velocity relative to the LSR (Radhakrishnan & physics at Padova, by The Johns Hopkins University, by the Sarma 1980). Netherlands Research School for Astronomy, by the Natural The cause of such a large-scale streaming motion would Sciences and Engineering Research Council of Canada, by clearly be a non-axisymmetric component of the Galactic the Slovenian Research Agency, by the Swiss National Sci- potential. It could thus be due to: (i) the Galactic bar; ence Foundation, by the National Science Foundation of the (ii) spiral arms; (iii) the warp; (iv) a triaxial dark mat- USA (AST-0908326), by the Netherlands Organisation for ter halo; or (v) a combination of some or all of these com- Scientific Research, by the Particle Physics and Astronomy ponents. Indeed, Minchev & Quillen (2007) have simulated Research Council of the UK, by Opticon, by Strasbourg Ob- the effect of spiral density waves on the Oort constants and servatory, and by the Universities of Basel, Cambridge, and have showed that for spiral-only perturbations, the value of Groningen. The RAVE web site is at www.rave-survey.org. |C| is larger for lower stellar velocity dispersions, contrary to the findings of OD03. The observed trend in C could, however, be explained with the effect of the Galactic bar (Minchev et al. 2007), but not its exact magnitude. 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