( 東京 ) Nobuyuki Sakai, National Astronomical Observatory of Japan October 9, Symp in Italy Direct Comparison between Astrometry Results and an Analytic Dynamics Model

1. Cont. & Goals 2. Method & Results 3. Discussions 4. Conc. Context ： Theory 1/9 V [km/s] = χ * μ [mas/year] * d [kpc], where χ = … Density wave theory (Lin & Shu 1964) Recurrent and transient spiral (e.g., Miller+1970; many papers) ©Ingo BergFujii et al. 2011:N-body simulation ・ Spiral arm is the most prominent structure in a disk galaxy. ・ However, nature, origin and evolution are still unknown.

1. Cont. & Goals 2. Method & Results 3. Discussions 4. Conc. Context ： 1-D observation 2/9 Perseus arm(?) Sun G.C. (Burton 1973) ●Distribution of line-of-sight velocity is asymmetry in the MW. → Effect of spiral arm ? ●The observed velocity field might be explained by gravitational perturbation (i.e., spiral arm) based on the density-wave theory. Systematic non-circular motion might be explained by the density-wave theory !

1. Intro 2. Results 3. Future 4. Summary Motivation from 1-D observation 2/20 Ａｍｐｌｉｔｕｄｅ： Spiral amplitude ：

1. Cont. & Goals 2. Method & Results 3. Discussions 4. Conc. 3D non-circular motion (U, V, W) in Reid+09 G.C. V U Right-handed coordinate system Averaged non-circular motions with 8 sources in the Perseus arm (U_mean, V_mean) = (9.8+/-2.6, ー 17.8+/-2.5) km/s in Sakai et al. (2012) →Systematic inward motion and slower Gal. rotation V (toward Gal. rotation) [km/s] U (toward G.C.) [km/s] Inter (no) arm Outer arm Perseus arm Flat rotation assumed. Perseus arm Choi et al. (2014) found the same tendency with 25 sources ! 3-D Context ： 3-D observation 3/9

1. General Intro 2. Results 3. Future 4. Summary The dark matter content in the MWG 11/20 Rotation curve of the MWG (Reid et al. 2014a) ~100 sources Almost flat rotation curve (in the outer part) ! Exponential disk (no dark matter) Large amount of dark matter! Rotation velocity Θ (km/s) Distance from the center R (kpc) An oscillation can be seen ! > Effect of Spiral arm ? RC of the MWG (Reid et al. 2014a updated)

1. Cont. & Goals 2. Method & Results 3. Discussions 4. Conc. Goals of this research 4/9 Churchwell et al Perseus arm Sun G.C. ① We compare astrometry (3D) results for the Perseus arm with an analytic gas dynamics model for deriving physical parameters of the spiral arm. ② Using the results, we make a suggestion toward an incoming astrometry (e.g., Gaia). Ultimate Goal ・ We understand nature, origin and evolution of the spiral arm especially for the Milky Way Galaxy.

1. Cont. & Goals 2. Method & Results 3. Discussions 4. Conc. Least Squares Method 5/9 χ^2 was calculated. Observables (U, V) for 27 sources in the Perseus arm Spiral model (density wave) ・ Pinol-Ferrer+12 (analytic) ・ Equations of motion with gas friction term added. Search Range Ref. Ωp Pattern speed 10 – 30 km/s/kpc Gies & Helsel 05 i Pitch angle 11.1 °Sakai+14b in prep Φa Relative Amp %Grosbol+04 R ref Reference1 period m Mode2 or 4Vallee 14 λ Friction term 1-30 km/s/kpc ε Artificial term 1-30 km/s/kpc

1. Intro 2. IRAS IRAS Conclusion Pinor-Ferrer+12 チェックポイント： iILR=0.7 kpc での leading arm, oILR=2.2 kpc での trailing arm, CR=4.5 kpc での damp, OLR=6.1 kpc. T-U 密度マップ (Pinol- Ferrer+12).

（ U_solor, V_solor, W_solor ） =(11.1, 12.24, 7.25) km/s Schonrich, Binney & Dehnen (2010) ・ Θ_0—240 km/s Reid & Brunthaler(2004)---Sgr A* の固有運動測定. μ_sgr=(V_0+V_solor)/R_0 ・ R_0—8.33 kpc, Gillesen et al. (2009)— 赤外観測で Sgr A* 周りの星 の軌道を観測・解析

1. Cont. & Goals 2. Method & Results 3. Discussions 4. Conc. Preliminary Results 6/9 Search Range Solution Ωp Pattern speed 10 – 30 km/s/kpc i Pitch angle 11.1 ° Φa Relative Amp % R ref Reference1 period m Mode2 or 4 λ Friction term 1-30 km/s/kpc ε Artificial term 1-30 km/s/kpc Search Range Solution (error) Ωp Pattern speed 10 – 30 km/s/kpc 17.6(0.6) i Pitch angle 11.1 ° Φa Relative Amp % 50% R ref Reference1 period 9.4 kpc m Mode2 or 4 2 λ Friction term 1-30 km/s/kpc 16.8(2.2) ε Artificial term 1-30 km/s/kpc 4.0(0.7) R ref Χ^2 R ref = 9.4 +/- 0.1 (kpc)

1. Context 2. Goals 3. Method 4. Results 4. Summary Results 6/10 Grosbol+04

1. Cont. & Goals 2. Method & Results 3. Discussions 4. Conc. Discussions ： Offset bet. gas and star Gas orbits model 7/9 Spiral potential Perseus arm ? Sun Direct comparison between astrometry and a model ・ Suggestion ： Stellar distribution as the bottom of the spiral potential is deviated from the dense gas region > Incoming astrometry (e.g., Gaia+VLBI) is important ! G.C.

1. General Intro 2. Results 3. Future 4. Summary Before ＆ After Line-of-sight velocity V lsr (km/s) l (°) 190° 110° 240° 50° Before ＆ After IRAS (Sakai+14b in prep.) IRAS (Sakai+12) IRAS (Sakai+14a) 5 sources in Reid /20 Color ： CO(J=1-0) Dame et al. (2001)

1. Cont. & Goals 2. Method & Results 3. Disussions 4. Conc. Discussions ： Ice Age Epochs 8/9 ・ Ωp = /- 0.6 km/s/kpc ・ Ω_sun = 28.8 (Reid+14) ・ m = 2 for main arms and 4 for gas arms (Churchwell+09) > Period of an arm passage = 2π / m(Ω_sun – Ωp ) = 137 +/- 7 Myr Shaviv & Veizer 2003 ~140 Myr. 18O/16O Veizer 2000

Shaviv & Veizer 2003 Iron meteorite Frakes+1992 ： Icehouse epochs

Greenhouse ： 18O/16O ↓ Icehouse ： 18O / 16O ---> Glacier ↑ 18O/16O ↑ Veizer 2000

1. Cont. & Goals 2. Method & Results 3. Dis. & Future 4. Conc. Simulation study for the future 9/10 Honma, Nagayama, and Sakai 2014 in submitted Spiral potential (Pinol-Ferrer+12) Simulated rotation curve Axisymmetric potential Axisymmetric parameter Spiral parameter ・ For N_obs ~ 500, R 0, Ω 0 (= R 0 / Θ 0 ) at 2% Spiral parameters at 10% are expected ! ・ Various Galactic dynamics models can be judged with the future astrometry (VLBI + Gaia + etc.) !

1. Cont. & Goals 2. Method & Results 3. Discussions 4. Conc. Conclusions 9/9 Astrometry results vs Gas dynamics model We made two suggestions for the spiral arm based on the comparison betw. astrometry results and a dynamics model. ① Offset betw. Gas and Star ② Relation betw. Ice ege epochs and arm passages We can judge various Galactic dynamics models by incoming astrometry !

19 Thank you for your attention! (c)Miyaji-san This is not the end. It is not even the beginning of the end. But it is, perhaps,the end of the beginning. by Sir Winston Churchill