( 東京 )

Nobuyuki Sakai, National Astronomical Observatory of JapanOctober 9, 2014@EVN Symp. 2014 in Italy

Direct Comparison between Astrometry

Results and an Analytic Dynamics Model

Context ： Theory 1/9

Density wave theory Density wave theory (Lin & Shu 1964)(Lin & Shu 1964)

Recurrent and transient spiralRecurrent and transient spiral(e.g., Miller+1970; many papers)(e.g., Miller+1970; many papers)

©Ingo Berg Fujii 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.

Context ： 1-D observation 2/9

Perseus arm(?)Sun

G.C.

(Burton 1973)

(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 !

3D non-circular motion (U, V, W) in Reid+09

G.C.

VU

Right-handedcoordinate 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

(to

war

d G

al.

rota

tion

) [k

m/s

]

U (toward G.C.) [km/s]

Inter (no) armOuter arm

Perseusarm

Flat rotation assumed.

Perseus arm

Choi et al. (2014) found the same tendency with 25 sources !

Context ： 3-D3-D observation 3/9

Goals of this research 4/9

Churchwell et al. 2009

Perseus armSun

G.C.

①We compare astrometry (3D) results for the Perseus arm with an analytic gas dynamics model for deriving physical parameters of the spiral arm.

②Using 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.

Least Squares Method 5/9

χ^2χ^2 was calculated.was calculated.

ObservablesObservables(U, V) for 27 sources in the Perseus arm

Spiral model (density wave)Spiral model (density wave)・ Pinol-Ferrer+12 (analytic)

・ Equations of motion with gas friction term added.

Search Range

Ref.

Ωp Patternspeed

10 – 30km/s/kpc

Gies & Helsel 05

i Pitch angle

11.1 ° Sakai+14b in prep

Φa Relative Amp.

10-50 % Grosbol+04

Rref Reference 1 period

m Mode 2 or 4 Vallee 14

λ Frictionterm

1-30km/s/kpc

ε Artificialterm

1-30km/s/kpc

Preliminary Results 6/9

SearchRange

Solution

Ωp Patternspeed

10 – 30km/s/kpc

i Pitch angle

11.1 °

Φa Relative Amp.

10-50 %

Rref Reference 1 period

m Mode 2 or 4

λ Frictionterm

1-30km/s/kpc

ε Artificialterm

1-30km/s/kpc

SearchRange

Solution(error)

Ωp Patternspeed

10 – 30km/s/kpc

17.6(0.6)

i Pitch angle

11.1 ° 11.1°

Φa Relative Amp.

10-50 % 50%

Rref Reference 1 period 9.4 kpc

m Mode 2 or 4 2

λ Frictionterm

1-30km/s/kpc

16.8(2.2)

ε Artificialterm

1-30km/s/kpc

4.0(0.7)Rref

Χ^2

Rref = 9.4 +/- 0.1 (kpc)

Discussions ： Offset bet. gas and starGas orbitsmodel

7/9

Spiral potential

Perseus arm ?

SunDirect 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.

Discussions ： Ice Age Epochs

8/9

・ Ωp = 17.6 +/- 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. ~140 Myr. ~140 Myr.

18O/16O

Veizer 2000

　　　　 Conclusions 9/9

Astrometry results vs Gas dynamics model

We made two suggestions for the spiral arm based onthe comparison betw. astrometry results and a dynamics model.

①Offset betw. Gas and Star

②Relation betw. Ice ege epochs and arm passages

We can judge various Galactic dynamics models by incoming astrometry !

20

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