1. Rotation Curve of the Galaxy Mareki Honma and Yoshiaki Sofue The University of Tokyo, 1997 Received 1996 October 25; accepted 1997 April 10 Journal review, 05/21(Fri.), 2010 Journal review, 05/28(Fri.), 2010 @Kagoshima University, M2:Nobuyuki, Sakai

2. Merrifield,1992

3. Overview Abstract 1. Introduction 2. Derivation of Outer Rotation Curve -2-1.Data -2-2. Analysis -2-3.Effect of Warp -2-4. Fitting and Uncertainty Estimate 3. Overall Rotation Curve of the Galaxy 4. Discussion

4. i. Analyzing the HI data with two methods for exploring of the outer rotation curve. ii. We present the overall rotation curve (from 0.3R 0 to 2.5R 0 ). iii. This rotation curve shape depends on the galactic constants. R 0 =8.5kpc, Θ 0 =220[km/s] 〃, Θ 0 <200[km/s] Abstract Following describes details. But,, Rotation Curve

6. 1. Introduction i. Rotation Curve (e.g., Bosma 1981, Rubin et al. 1985) →One of the most powerful tools for studying dynamics of galaxies! ∵ RC can reveal mass distribution. ii. Flat rotation in spiral galaxies →Indicating the existence of dark matter! iii. As for the Milky Way Galaxy →Inner and outer rotation curves are derived by different methods! APOD より M83 (NGC5236) Sofue, et al. (1999) RC

8. Θ=216km/s, if Θ0=200km/s 銀河の構造、進化、活動性などと密接に 関連する。

9. 1. Introduction iii:Inner Rotation axisymmetry circular orbit. Assumptions of axisymmetry and circular orbit. So, D, Vt, and Vr are described by below equations. ( 現代の天文学：銀河Ⅱ ) The radial velocity along a line of sight becomes maximum at the tangential point. There have been some observations (CO, HI, etc.) for Inner Rotation.

10. ガス分子雲などは特定の周波数の電磁波の みを吸収・放射する。 → 線スペクトル：

12. P-V diagram (Sofue, 1991)

13. 1. Introduction iii:Outer Rotation There is no tangential point. Distance measuring (e.g., photmetric distance) is necessary. HII regions Observations (photmetric distance). (e.g., Brand, Blitz (1993)) Planetary nebulae observations. (e.g., Schneider, Terzian (1983)) but,, There is large uncertainty. ∵ i)An error in the estimate of the distance.

14. ・ Shklovskii method mainly depend on the PN mass. (Schneider, Terzian 1983) ・ Shklovsky (1956) ・ Shklovsky (1957)→ ・ The metalicity gradient in the Outer Galaxy is not determined well.(Brand, Blitz, 1993)

15. Surface brightness (L/arcsec^-2) Surface brightness(mag/arcsec^-2)

16. 1. Introduction iii:Another 2 methods for Outer Rotation Petrovskaya, Terrikorpi (1986) Merriefield (1992) Assumption: Constant thickness(Z 0 ) along each HI ring D Sun Z0Z0 b Observed Δb(l) can determine R/R0. Assumption: ・ HI gas density is constant along a HI ring ・ Optical depth at specific frequency k=N(R) ： HI density=constant :continued

18. ( 現代の天文学, 銀河Ⅱ )

19. 2. Derivation of Outer Rotation Curve 2-1. Data ・ We reanalyzed the galactic HI survey data with two methods. Reffer of HI datal range [deg.] b range [deg.] Angular Resolution Note Weaver & Williams (1974) 10~350 |b| ≦ 10 35 ’.5Nothern hemisphere Kerr et al., (1986) 〃〃 48’Sourthern hemisphere

20. Dickey, 1990

21. Tb > 5K in outer region r.m.s. ≒ 0.3K Centroid of gas distribution

22. 2-2. Analysis 2. Derivation of Outer Rotation Curve Merriefield (1992) Petrovskaya, Terrikorpi (1986) Considering: HI density ∝ Tb when optical depth is small. b 0 : centroid= ∂Δb / ∂b0 =0 Effect of diffuse gas is removed. Considering: I will use for convenience of fitting. Q1: What is the HI density? (My) Answer 1: HI density is HI column density ↓ ∵

23. Q1: What is the HI density? (My) Answer 1: HI density is HI column density ↓ ∵

24. 2-2. Analysis 2. Derivation of Outer Rotation Curve Merriefield (1992) Petrovskaya, Terrikorpi (1986) Considering: HI density ∝ Tb when optical depth is small. b 0 : centroid= ∂Δb / ∂b0 =0 Effect of diffuse gas is removed. Considering: I will use for convenience of fitting.

25. 2-3. Effect of Warp 2. Derivation of Outer Rotation Curve R/R 0 = 1.68 R/R 0 = 2.22 b0b0 l [deg.] Sin curve i)Circular orbit. ii)Orbit plane is rotated with respect to the galactic plane around the line of sight to the G.C. Two method can apply! Orbit plane Galactic plane Q2: What is the sin curve? (My) Answer 2: There are same suggestions. But… ↓ ∵

26. centroid

27. 2-3. Effect of Warp 2. Derivation of Outer Rotation Curve R/R 0 = 1.68 R/R 0 = 2.22 b0b0 l [deg.] Sin curve i)Circular orbit. ii)Orbit plane is rotated with respect to the galactic plane around the line of sight to the G.C. Two method can apply! Orbit plane Galactic plane Circular orbit may be correct.

28. 2-4. Fitting and Uncertainty Estimate 2. Derivation of Outer Rotation Curve ・ Both Δb and Tb were averaged between the northern part and the southern part of the disk, and averaged every 2.5°longitude interval. Δb result (Merriefield, 1992) Δb l R/R 0 =1.68(outer region) R/R 0 =0.85 (inner region) flat Observation The difference between flat and observation indicates that R of observation is larger than that of flat. If: Θ 0 =220km/s The result is in agreement with the tangential method. Θ=221km/s

29. W でのデータを作る ↓R0/R can be determined. Θ also can be determined.

30. 2-4. Fitting and Uncertainty Estimate 2. Derivation of Outer Rotation Curve ・ Both Δb and Tb were averaged between the northern part and the southern part of the disk, and averaged every 2.5°longitude interval. Tb result (Petrovskaya &Teerikorpi, 1986) l Sin^2 (l) ξ R/R 0 =1.14 There are large uncertainties. R/R 0 =1.63

31. 2-4. Fitting and Uncertainty Estimate 2. Derivation of Outer Rotation Curve Results both (Merriefiled, 1992) and (Petrovskaya &Teerikorpi, 1986) Summary Merrifield’s method is better. These results are consistent with each other within the errors.

32. 3. Overall Rotation Curve of the Galaxy ・ We compare rotation curve obtained by Marrifield’s method with those obtained by various method. Marriefield’s method: Filled open circle ORC Brand & Blitz 1993: HII regions Schneider & Terzian (1983) Planetary nebulae Merrifield’s method has the smallest error and the largest coverage of the galacto-centric radius.

33. 4. Discussion Inner: (Fich et al. 1989) Outer: Merriefield’s method Overall rotation curves of the Galaxy R 0 =8.5kpc, Θ 0 =220[km/s] 〃, Θ 0 <200[km/s] Outer rotation depends strongly on the galactic constants. Something extra My ORC research with VERA would result in most precisely Outer Rotation Curve. (??) (laugh) There are uncertainties in outer rotation even Merrifield’s. Fin.