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Draftversion January12,2017 PreprinttypesetusingLATEXstyleAASTeX6v.1.0 THE LOCAL SPIRAL ARM IN THE LAMOST-GAIA COMMON STARS? Chao Liu1 KeyLaboratoryforOpticalAstronomy,National AstronomicalObservatories,ChineseAcademyofSciences,Beijing100012, China 7 You-Gang Wang 1 0 KeyLaboratoryofComputational Astrophysics,NationalAstronomicalObservatories,ChineseAcademyofSciences,Beijing,100012, 2 China n a J Juntai Shen, Zhao-Yu Li, Yu-Jing Qin 0 KeyLaboratoryforResearchinGalaxies andCosmology,ShanghaiAstronomicalObservatory,ChineseAcademyofSciences, Shanghai, 1 200030, China ] A G Yonghui Hou, Yuefei Wang, Yong Zhang NanjingInstitute ofAstronomicalOptics&Technology, NationalAstronomicalObservatories,ChineseAcademyofSciences,Nanjing . h 210042, China p - o r Zihuang Cao, Yue Wu t s KeyLaboratoryofOpticalAstronomy,NationalAstronomicalObservatories,ChineseAcademyofSciences, Beijing100012,China a [ 1 1 [email protected] v 3 ABSTRACT 5 7 UsingtheLAMOST-Gaia commonstars,wedemonstratethatthein-planevelocityfieldforthenearby 2 young stars are significantly different from that for the old ones. For the young stars, the probably 0 perturbed velocities similar to the old population are mostly removed from the velocity maps in the . 1 X–Y plane. The residual velocity field shows that the young stars consistently move along Y with 0 faster v at the trailing side of the local arm, while at the leading side, they move slower in azimuth 7 φ 1 direction. At both sides, the young stars averagely move inward with vR of −5 ∼ −3km s−1. The : divergence of the velocity in Y direction implies that the young stars are associated with a density v i wave nearby the local arm. We therefore suggest that the young stars may reflect the formation of X thelocalspiralarmbycorrelatingthemselveswithadensitywave. Therangeoftheagefortheyoung r stars is around 2Gyr, which is sensible since the transient spiral arm can sustain that long. We also a point out that alternative explanations of the peculiar velocity field for the young population cannot be ruled out only from this observed data. Keywords: Galaxy: disk — Galaxy: structure — Galaxy: kinematics and dynamics — stars: kine- matics and dynamics 1. INTRODUCTION this was challenged by observations for external galax- ies (Foyle et al. 2011). Toomre & Toomre (1972) found The spiral arms are very common features in disk thatdynamicaltidalinteractioncaninducespiralstruc- galaxies and also found in our Galaxy (Kerr 1957; tures in a galaxy. But this is hard to explain why Benjamin et al.2005). However,theoriginofthesecom- galaxies not experienced major mergers also show spi- plicated structures is not conclusively solved, although ral arms, such as the Milky Way. Sellwood & Carlberg many theories are proposed (see Binney & Tremaine (1984) argued that the spiral structures are short-lived 2008; Shu 2016). Lin & Shu (1964) suggested the spi- and formed from the instability. Sellwood & Carlberg ral structures are long-lived density wave. However, 2 (2014)furtherexplainedthatthenatureoftherecurrent In this letter, we study the in-plane peculiar motions spiralarmsaretheoverlappingofmultiplespiralmodes. for the young stars in the solar neighborhood using the Kawata et al. (2014), on the other hand, claimed that latest astrometric data from Gaia. The data selection the spiral arms are corotating, i.e. their pattern speeds and processing are described in Section 2. The result equal to the circular speeds. and discussions are illustrated in Section 3. And a brief Because the dynamical properties of the spiral struc- conclusion is drawn in the last section. tures in the Milky Way is hard to be directly detected, most of the observational works turn to understand 2. DATA the spiralstructure throughthe perturbedstellarveloc- itydistributions(Quillen et al.2011;Siebert et al.2012; −6 Faure et al. 2014). In recent years, many observations −5 revealedthatthenearbystarsdisplayquitecomplicated −4 peculiar motions, which may be the result of pertur- −3 bations, in radial and vertical directions (Siebert et al. −2 2011;Williams et al.2013;Carlin et al.2013; Sun et al. g) 2015, etc.). However, the perturbed velocities (also ma−1 ( called bulk motion, asymmetric motion, streaming ve- MKs 0 N=3692 1 locity, or peculiar velocity in different studies) may be 2 either induced by the spiral structures, or other non- N=2011 3 axisymmetric features, e.g. the Galactic bar or the 4 merging dwarf galaxies (Bovy et al. 2015; Grand et al. 5 2015; G´omez et al. 2013). There are also some works 9000 8000 7000 6000 5000 4000 constrainingtheformingmechanismsofthespiralstruc- Teff(K) tureswiththecomparisonofthelocationsofthegaseous Figure 1. Thisfigureillustrates thecolor coded logarithmic and stellar arms (Hou & Han 2015). stellar density in the MKs vs. Teff plane for the LAMOST- Gaia starswitherrorsofthedistancesmallerthan30%. The Recently, Tian et al. (2015) showed that the young leftwhitesolidrectangleindicatestheselectionoftheF-type stars have different asymmetric motions with the old stars as tracers of theyoungpopulation and theright white stars in U and W. Tian et al. (2016) further compared dashed rectangle marks the old K-type sub-giant branch stars as the control sample. The magenta lines indicate the the radial variation of v and v between the young R φ PARSEC isochrone tracks with ages of 1, 3, 6, and 10Gyr and relatively old red clump stars from the LAMOST from top tobottom, respectively,at thesolar metallicity. survey and found that the radial oscillations of the ve- locities for the two populations show similar long-wave The data used in this work are from two sur- mode but different short-wave mode. These observa- veys, the stellar parameters and the line-of-sight ve- tional facts hint that the young stars may contain dif- locities are from the LAMOST DR3 data (Cui et al. ferent types of peculiar velocities. They may either re- 2012; Zhao et al. 2012; Deng et al. 2012) and the tain some memory of the kinematical features of their parallaxes and proper motions are from the Gaia birthplace,ordirectlyreflectthekinematicsofthespiral DR1 (Gaia Collaboration et al. 2016a). We adopt arms, or more sensitive to the perturbations than older the distanceestimatedby Astraatmadja & Bailer-Jones populations due to their more circular stellar orbits. In (2016), who applied a Bayesianmodelto derivethe dis- order to investigate the role played by the spiral arms tance from the parallax taking into account the Milky in the peculiar velocities, two-dimensional in-plane ve- Way prior and systematic uncertainties in Gaia cata- locityfield,ratherthanone-dimensionalradialvariation log. There are totally more than 190000 common stars ofthe velocities,isrequired. Subsequently, the accurate in the two catalogs. From the LAMOST derived stel- astrometric data, combined with the line-of-sightveloc- lar parameters (Wu et al. 2014), we select about 15000 ity measured from the stellar spectra, are needed. young F-type stars with 6500 < T < 7500K, error As September 14, 2016, the Gaia sur- eff of distance from Astraatmadja & Bailer-Jones (2016) vey (Gaia Collaboration et al. 2016b) published its smaller than 30% (including the systematic error of the first data release (Gaia Collaboration et al. 2016a), Gaia parallax),andabsolutemagnitudeinK bandbe- includingnewpropermotionestimateswithaccuracyof s ∼1masyr−1 for2millionbrightstars(Lindegren et al. tween -1 and 3mag1. Because in this work we focus 2016). TheGaia DR1,combinedwiththespectroscopic data from the LAMOST DR3 data, allows us to map the three dimensional velocities of the stars within 1 The absolute magnitude inKs band isderived fromthe dis- tance provided by Astraatmadja&Bailer-Jones (2016), the ap- ∼1kpc around the Sun with high accuracy. parent Ks magnitude from 2MASS, and the derived interstellar 3 on the disk, we cut the range of vertical distance to the Galactic mid-plane with |Z| < 0.3kpc. Meanwhile, we cut the distance with D < 0.6kpc to ensure the completeness of the data. Then we obtain 6822 F-type starsasthe tracersofthe youngpopulation. Inorderto 0.8 0.8 0.6 2 0.6 2 characterize the velocities for the young population, we 0.4 0.4 c) 1.5c) 1.5 also select 5088 K-type sub-giant branch (SGB) stars p 0.2 p 0.2 k k with 3800 < T < 5700K and −0.5 < M < 3 as Y ( 0 1 Y ( 0 1 eff Ks −0.2 0.5 −0.2 0.5 the control sample. Figure 1 shows the HR diagram of −0.4 −0.4 the LAMOST-Gaia common stars overlapped with the 9 8.5 8 9 8.5 8 X (kpc) X (kpc) PARSECisochrones(Bressan et al.2012)withageof1, Young Old 3, 6, and 10Gyr at solar metallicity (magenta lines). It is seenthatmostofthe selectedF-type stars(left white solid box) are around 1–3Gyr, while the K-type SGB Figure 2. The spatial distributions for the young and old controlsample(the rightwhite dashedbox)areconcen- samplesinleftandrightpanels,respectively. Thecolorcodes trated in the age around 3–6Gyr. the logarithmic stellar density in X–Y plane. The location of the Sun, which is marked as large black cross, is at (X, There are some stars with supersolar metallicity in Y)=(8.34, 0)kpc, the Galactic center is at the origin in the both the young and old populations. According to rightsideoftheplots,andthedirectionofY isaligned with Kordopatis et al. (2015) and Liu et al. (2015), these thedirectionoftherotationofthedisk. Theblacksolidline and the two black dotted lines crossing from top to bottom very metal-rich stars are likely formed from the inner in each panel indicate the local spiral arm and its width, disk. In order to make sure that the sample are local, respectively. we remove the stars with [Fe/H]> −0.05dex. We also cutoutafewstarswith[Fe/H]<−0.6toexcludemostof the contaminations, e.g. the blue straggler stars, from ues are providedonly for the bins containing more than the thick disk and stellar halo populations. After the 20 stars to ensure the good statistics. The bin size is cut in metallicity, the number of the rest F-type young 0.125×0.125kpc. No smoothing technique is applied to stars is 3692 and the number of the rest K-type SGB these maps. The local spiral arm derived from the as- stars is 2011. trometryofthemasers(Reid et al.2014;Xu et al.2016) We adopt that the solar motion w.r.t. the local stan- is superposedtothe figure(the centerofthe armis rep- dardofrestis(U⊙,V⊙,W⊙)=(9.58,10.52,7.01)kms−1 resentedby the solidlines and the width of it by dotted (Tian et al. 2015), the distance from the Sun to the lines). Galactic center is R =8.34kpc (Reid et al. 2014), and Frompanel(a)itisseenthatthemapofthemedianv 0 φ the local circular speed is 238kms−1 (Scho¨nrich 2012). for the young population displays clear declining trend Figure2showsthespatialdistributionoftheyoung(left withincreasingX. Asacomparison,panel(b)showsthe panel)andold(rightpanel)starsinX–Y plane,inwhich mapofv fortheoldK-typeSGBstars. Itshowsaridge φ X points fromthe Galactic center to the outskirtof the located from (8.9,-0.2) to (8.2,+0.4)kpc with lower v φ disk through the Sun and Y points to the direction of of about 220kms−1. Outside the ridge, v increases to φ the rotation of the disk. Noted that this right-hand co- around 225kms−1. This is substantially different with ordinates does not fit the usual direction to look at the the velocity gradientfor the young starsshowninpanel Milky Way, i.e. looking it from north Galactic pole. (a). The patternofv forthe oldstarsseemscorrelated φ Hence, in all rest figures in this letter, we flip the direc- with the direction of the local arm. This hints that the tionofX-axissothatthe MilkyWayis lookedfromthe velocitypatternmayreflecttheperturbationinducedby north Galactic pole and the direction of the rotation is the spiral arm. upward. The samplesare locatedwithin 0.6kpc around We then look at the map of v for the young popula- R the Sun. Thus, Y is approximately equivalent with the tioninFigure3(d). Itshowsthattheyoungstarsmove azimuth angle. inward with v ∼−3kms−1 at R<8.5kpc, while their R v is at around zero at R > 8.5kpc. Looking at the R 3. RESULT & DISCUSSIONS map of v for the old population in panel (e), we find, R Figure3showsthemapsofthemedianazimuthal(vφ) roughly, vR is around +5kms−1 at R > 8.5kpc and and radial (vR) velocities in X–Y plane for the young about zero or even smaller than zero at R < 8.5kpc. and old stars, respectively. The median velocity val- The trend of the gradients of v for the young and old R populations are similar. However, the values of v are R different such that the old populations show larger v R extinctioninKs bandaccordingtoMajewskietal.(2011). than the young one by around 5kms−1. It is noted 4 0.8 250 0.8 250 0.8 30 (a) (b) (c) 0.6 0.6 0.6 240 240 0.4 0.4 0.4 20 c) c) c) kp 0.2 230 kp 0.2 230 kp 0.2 Y ( 0 Y ( 0 Y ( 0 10 −0.2 220 −0.2 220 −0.2 −0.4 Youngvφ −0.4 Oldvφ −0.4 Young-Old∆vφ 0 210 210 9 8.88.68.48.2 8 7.8 9 8.88.68.48.2 8 7.8 9 8.88.68.48.2 8 7.8 X (kpc) X (kpc) X (kpc) 0.8 0.8 0.8 (d) (e) (f) 0.6 5 0.6 5 0.6 5 0.4 0.4 0.4 c) c) c) kp 0.2 0 kp 0.2 0 kp 0.2 0 Y ( 0 Y ( 0 Y ( 0 −0.2 −0.2 −0.2 −0.4 YoungvR −5 −0.4 OldvR −5 −0.4 Young-Old∆vR −5 9 8.88.68.48.2 8 7.8 9 8.88.68.48.2 8 7.8 9 8.88.68.48.2 8 7.8 X (kpc) X (kpc) X (kpc) Figure 3. Thetop rowshows themapsof themedian vφ intheX–Y planefortheF-typestars (young)and K-typeSGBstars (old) in panels (a) and (b),respectively. Thelocation of theSunis at theblack crosses. Theblack solid line and thetwo black dottedlinescrossingfrom toptobottomineachpanelindicatethelocalspiralarm anditswidth,respectively. Panel(c)shows theresidualmapofthesubtractionofpanel(b)from panel(a). ThebottomrowshowsthemapsofthemedianvR intheX–Y plane for theF-typestars (young) and K-typeSGB stars (old) in panels (d) and (e),respectively. Panel (f) shows theresidual map of thepanel (d) subtracted by panel (e). that the error of v for our sample is about 5kms−1, and 2) a special mechanism plays nothing with the old R whichleads to the orderof ∼1kms−1 in eachX–Y bin populations, but only influences the young stars. Then since each bin contains at least 20 stars. Because the we can remove most of the perturbed velocities due to uncertaintyofv in eachbin is comparablewiththe lo- the first driver by subtracting the maps of velocities for R cal variations in the v map, these variations between the oldstars fromthose for the young starsin the X–Y R neighboring bins in panels (d) and (e) are likely domi- plane. natedbythestatisticalfluctuation. However,Theglobal The residual velocity maps are shown in Figure 3 (c) radial trend displayed in both the young and old popu- and(f). InmostpartsoftheX–Y plane,theresidualv φ lationsmaynotbeduetothevelocityuncertainties,but in panel(c) is positive fromabout10 to 30kms−1. The islikelyatruefeaturesincelotsofbinsdemonstratethis positive residual values can be naturally explained by trend together. the different asymmetric drift, which is smaller for the The old stars should be completely relaxed. Hence, young populations than for the old ones. The residual the peculiar velocity shown in the old stars is most v also displays a clear gradient from bottom-right to φ likely due to the perturbations induced by the spiral top-left. The direction of the gradient is approximately arm or the bar. In principle, if the kinematics for the parallel with the norm direction of the local arm. It oldstarssuffers fromthe perturbations,the youngpop- shows that the young stars move along the azimuthal ulationshouldbe affectedinsimilarwaywithsimilaror directionfasterinthetrailingsideofthelocalarm,while even more intensive amplitudes because that they are they moves slower by 20kms−1 in the leading side. morekinematicallycoldandthuseasiertobeperturbed. The residual v in panel (f) displays negative val- R Therefore,thesignificantdifferenceinthe mapofveloc- ues around −5 ∼ −3kms−1 with some local varia- ities between the young and old populations in panels tions. Consider the uncertainty of v in each bin is R (a), (d), (b), and (e) of Figure 3 implies that the young around 1kms−1, the local features with variation of starsmaybedrivenbytwodifferentmechanisms: 1)the 1 ∼ 2kms−1 may be owe to the arbitrary fluctuation. perturbations same as those also affecting the old stars However, even taking into account the uncertainties, 5 panel(f)stillshowsthat,averagely,thev oftheyoung ics, R population is about 3 ∼ 5kms−1 smaller than that of dρ ∂v ∂v ∂ρ ∂ρ the old one. =−ρ( X + Y )−(v +v ), (1) X Y dt ∂X dY ∂X ∂Y if the stellar density does not rapidly change with time, then the left hand side of Eq. (1) essentially equals to ∂vY/∂Y (kms−1kpc−1) zero. Because Figure. 4 shows that the divergence of 0.8 50 velocity is dominated by ∂v /∂Y and the divergence 40 Y 0.6 alongY (X)directionwouldonly affectthe variationof 30 the density along Y (X) direction, the variation of the 0.4 20 stellar density ρ should be also dominated by ∂ρ/∂Y. 10 kpc) 0.2 0 ∂vY/∂Y declines from +30kms−1 kpc−1 to about Y ( −15kms−1 kpc−1, passing through the zero point at 0 −10 the line from (X, Y)∼(8.2, +0.3) to ∼(8.7, -0.1)kpc. −20 −0.2 Hence,∂ρ/∂Y increasesfromnegativevaluesbehindthe −30 −0.4 −40 line (w.r.t. the rotation direction) to positive values in −50 frontofthe line accordingtoEq.(1). Consequently,the 9 8.8 8.6 8.4 8.2 8 7.8 X (kpc) stellar density ρ mustincreasewith Y starting fromthe line. In other word,the young stars are associatedwith a density wavenearthe gas-identifiedlocalarm. There- ∂vX/∂X(kms−1kpc−1) fore,wesuggestthatthemotionoftheyoungstarsprob- 0.8 50 ably reflects the local arm by kinematically associating 40 themselves with a density wave. 0.6 30 Thisscenarioisnotconflictwiththe meanageforthe 0.4 20 young tracers, which is only ∼2Gyr. Such a time scale pc) 0.2 10 is within the expected lifetime of the transient spiral Y (k 0 structures (Sellwood & Carlberg 2014). 0 −10 Moreover, the distributions of the in-plane veloci- −20 ties displayed in Figure 5 show that, for the young −0.2 −30 stars (panel a), the velocity distribution forms a tight −0.4 −40 arc shape. By contrast, the old stars (panel b) −50 9 8.5 8 show an extended and roughly featureless distribu- X (kpc) tion with a moderate bump at around v ∼ 30kms−1 R and v ∼ 180kms−1, which should be the Hercules φ Figure 4. Inthetoppanel,thecolorscodethedivergenceof stream(Dehnen2000;Xia et al.2015). Thevelocitydis- velocity in Y direction, ∂vY/∂Y. And in the bottom panel, tribution shown in panel (a) can be qualitatively com- the colors code the divergence of velocity in X direction, pared with the simulations from Quillen et al. (2011). ∂vX/∂X. We find that the orientation of the arc similar to our sample is located at the inter-arm regime (see the pan- els at the 3rdrowand the 2nd, 5th, and6th columns in their figure 8), not on the arm, which is consistent with To better quantify the kinematical features, we dis- the location of the majority of our samples. play the two components of the divergence of the in- It is noted that, other than the transient spi- plane velocity in Figure 4. The top panel shows the ral mode (Sellwood & Carlberg 2014), quite a few map of ∂v /∂Y and the bottom panel shows the map works have discussed about the alternative channels Y of ∂v /∂X. First, the largest values of the divergence of the formation of the spiral structures and some X occursin∂v /∂Y,whichvariesfrom+30kms−1 kpc−1 theoretical works have given observational predictions Y to-15kms−1 kpc−1 frombottom-righttotop-leftinthe in velocity distributions. Particularly about the lo- X–Y plane. Second, the direction of the variation of cal arm, Xu et al. (2016) thought that it may be ∂v /∂Y is roughly along the norm directionof the gas- formed from the perturbation of the giant molecular Y identified local arm. Finally, ∂v /∂X is quite flat at clouds (D’Onghia et al. 2013) according to their latest X around zero, implying that almost no gradientof veloc- maserobservations. And Li et al.(2016)foundthatthe ity occurs along X. localarm,whichcansustainovera shorttime, may not Nowconsiderthecontinuityequationoffluidmechan- be due to the density wave, but be naturally induced 6 350 350 (a)Young (b)Old 300 300 250 250 −1) −1) s s m200 m200 k k ( ( vφ vφ 150 150 100 100 50 50 −150 −120 −90 −60 −30 0 30 60 90 120 150 −150 −120 −90 −60 −30 0 30 60 90 120 150 vR(kms−1) vR(kms−1) Figure 5. Panels(a)and(b)showthedistributionoftheF-typeyoungandK-typeoldSGBstarsinvφvs. vRplane,respectively. in the scenario such that the disk contains two pairs of also note that a few alternative mechanisms to explain prominent spiral structures based on their SPH simula- such a peculiar velocity field are not simply ruled out. tions. We also notice that, recently, Hunt et al. (2016) In future, it is worthy to directly compare the pecu- claimed that the fast rotating stars found at the radii a liar velocity field unveiled by the young stars in this few hundreds parsecs beyondthe Sun may be driven by work with various simulations so that the observational the Perseus arm other than the local arm. evidence can help to distinguish the origin of the spiral The different spiral theories may give different expla- structures. nationstothepeculiarmotionoftheyoungstellarpopu- lations unveiled in this work. Simply from the observed We appreciate the helpful comments from the anony- data,wecannotruleoutotherexplanations. Furtherin- mous referee. We thank Wyn Evens, Lia Athanassoula, vestigations, including more observations in larger vol- and Ron Drimmel for their helpful discussions and umeandwelldefinedN-bodysimulations,areanxiously comments. This work is supported by the Strategic required to clarify the nature of the peculiar velocity Priority Research Program “The Emergence of Cosmo- field for the young stars. logicalStructures” ofthe Chinese Academy of Sciences, Grant No. XDB09000000 and the National Key Basic Research Program of China 2014CB845700. CL ac- 4. CONCLUSIONS knowledges the NationalNatural Science Foundation of In this letter, we study the in-plane peculiar motions China (NSFC) under grants 11373032 and 11333003. usingmorethan3000youngstarscombinedthe line-of- YGW acknowledges the NSFC grant 11390372. This sightvelocityfromtheLAMOSTDR3withtheparallax project was developed in part at the 2016 NYC Gaia andproper motion fromthe Gaia DR1. The latter pro- Sprint, hosted by the Center for Computational Astro- videsaccuratepropermotionswithuncertaintyofabout physics at the Simons Foundation in New York City. 1mas yr−1 upto 1kpc indistance,whichis the bestas- Guoshoujing Telescope (the Large Sky Area Multi- trometric measurement so far. Object Fiber Spectroscopic Telescope LAMOST) is a WeselecttheF-typestarsasthetracersfortheyoung National Major Scientific Project built by the Chinese populationandthe oldK-type SGB starsas the control Academy of Sciences. Funding for the project has been sample. Afterremovingthepeculiarmotionsowetothe provided by the National Development and Reform perturbations, the residual velocity field for the young Commission. LAMOST is operated and managed starsshowcorrelationwiththegas-identifiedlocalspiral by the National Astronomical Observatories, Chinese arm. The ∂v /∂Y mapforthe youngstarsimplies that Academy of Sciences. This work has made use of data Y the stellar density may increase with Y starting from from the European Space Agency (ESA) mission Gaia thelinefrom(X,Y)∼(8.2,+0.3)to(8.7,-0.1)kpc. This (http://www.cosmos.esa.int/gaia),processedbythe hints that the young stars are associatedwith a density GaiaDataProcessingandAnalysisConsortium(DPAC, wave located aroundthe localspiral arm. We then sug- http://www.cosmos.esa.int/web/gaia/dpac/consortium). gest that the young stars are involved in the formation Funding for the DPAC has been provided by national ofthelocalarmbyinducingthedensitywaveandhence institutions, in particular the institutions participating directlyreflectsthekinematicalfeaturesofthearm. We in the Gaia Multilateral Agreement. 7 REFERENCES Astraatmadja,T.L.,&Bailer-Jones,C.A.L.2016, Kordopatis,G.,Binney,J.,Gilmore,G.,etal.2015,MNRAS, arXiv:1609.07369 447,3526 Benjamin,R.A.,Churchwell,E.,Babler,B.L.,etal.2005, Li,Z.,Gerhard,O.,Shen,J.,Portail,M.,&Wegg, C.2016,ApJ, ApJL,630,L149 824,13 Binney,J.,&Tremaine,S.2008,GalacticDynamics:Second Lin,C.C.,&Shu,F.H.1964,ApJ,140,646 Edition,byJamesBinneyandScott Tremaine.ISBN Lindegren,L.,Lammers,U.,Bastian,U.,etal.2016, 978-0-691-13026-2 (HB).PublishedbyPrincetonUniversity arXiv:1609.04303 Press,Princeton,NJUSA,2008., Liu,C.,Chen,X.-Y.,Yin,J.,etal.2015,arXiv:1510.06123 Bovy,J.,Bird,J.C.,Garc´ıaP´erez,A.E.,etal.2015,ApJ,800, Majewski,S.R.,Zasowski,G.,&Nidever,D.L.2011, ApJ,739, 83 25 Bressan,A.,Marigo,P.,Girardi,L.,etal.2012, MNRAS,427, Quillen,A.C.,Dougherty,J.,Bagley,M.B.,Minchev,I.,& 127 Comparetta, J.2011,MNRAS,417,762 Carlin,J.L.,DeLaunay, J.,Newberg,H.J.,etal.2013,ApJL, Reid,M.J.,Menten, K.M.,Brunthaler,A.,etal.2014, ApJ, 777,L5 783,130 Cui,X.-Q.,Zhao,Y.-H.,Chu,Y.-Q.,etal.2012, Researchin Sch¨onrich, R.2012,MNRAS,427,274 AstronomyandAstrophysics,12,1197 Sellwood,J.A.,&Carlberg,R.G.1984,ApJ,282,61 Dehnen,W.2000,AJ,119,800 Sellwood,J.A.,&Carlberg,R.G.2014,ApJ,785,137 Deng,L.-C.,Newberg,H.J.,Liu,C.etal.2012,Researchin Shu,F.H.2016, ARA&A,54,667 AstronomyandAstrophysics,12,735 Siebert,A.,Famaey,B.,Minchev,I.,etal.2011,MNRAS,412, D’Onghia,E.,Vogelsberger,M.,&Hernquist,L.2013,ApJ,766, 2026 34 Siebert,A.,Famaey,B.,Binney,J.,etal.2012,MNRAS,425, Faure,C.,Siebert,A.,&Famaey,B.2014, MNRAS,440,2564 2335 Foyle,K.,Rix,H.-W.,Dobbs,C.L.,Leroy,A.K.,&Walter,F. 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