Rotation Curve of the Galaxy

Mareki Honma and Yoshiaki Sofue

The University of Tokyo,Received 1996 October 25; accepted 19971997 April 10

Journal review, 05/21(Fri.), 2010Journal review, 05/28(Fri.), 2010@Kagoshima University, M2:Nobuyuki, Sakai

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

i. Analyzing the HI data with two methods for exploring ofthe outer rotation curve.

ii. We present the overall rotation curve (from 0.3R0 to 2.5R0).

iii. This rotation curve shape depends on the galactic constants.

R0=8.5kpc, Θ0=220[km/s] 〃 , Θ0<200[km/s]

Abstract

Following describes details.

But,,

Rotation Curve

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

1. Introductioniii:Inner Rotation

Assumptions of axisymmetryaxisymmetry and circular orbit.circular orbit.

So, D, Vt, and Vr are described by below equations.

s]mvelocity[krotation

l)RR

Θ

R

Θ(=V

lR

DlR

R

Θ

R

Θ=V

r

t

/：Θ

sin

coscos

00

0

00

0

( Ⅱ現代の天文学：銀河 )

The radial velocity along a line of sight becomes maximum at the tangential point.

lRR sin0

There have been some observations (CO, HI, etc.) for Inner Rotation.

lRRlRD 220

20 sincos

1. Introductioniii:Outer Rotation

There is no tangential point.

Distance measuring (e.g., photmetric distance) is necessary.

HII regionsObservations

(photmetric distance).(e.g., Brand, Blitz (1993))

Planetary nebulaeobservations.

(e.g., Schneider, Terzian (1983))

but,,

There is large uncertainty.

∵ i)An error in the estimate of the distance.

1. Introductioniii:Another 2 methods for Outer Rotation

Petrovskaya, Terrikorpi (1986)Merriefield (1992)

Assumption:

Constant thickness(Z0) along each HI ring

D

Sun Z0

b

)sincos

arctan(

)arctan(

20

20

0

0

lRRlR

zD

zb

Δ

Observed Δb(l) can determine R/R0.

Assumption:

・ HI gas density is constant along a HI ring・ Optical depth at specific frequency

|)(|

)(),(

'

'

RRr

r

dr

dVRkN

lV

τ

k=N(R) ： HI density=constant

:continued

2. Derivation of Outer Rotation Curve

2-1. Data

・ We reanalyzed the galactic HI survey data with two methods.

Reffer of HI data l range

[deg.]

b range

[deg.]

Angular

Resolution

Note

Weaver & Williams (1974)

10~350 |b|≦10 35’.5 Nothern

hemisphere

Kerr et al., (1986) 〃 〃 48’ Sourthern

hemisphere

2-2. Analysis

2. Derivation of Outer Rotation Curve

Merriefield (1992) Petrovskaya, Terrikorpi (1986)

Considering:

HI density ∝ Tb

when optical depth is small.

4

4202 )(

i

ii

T

Tbbb

Σ

ΣΔ

b0: centroid= ∂Δb / ∂b0 =0

24ii TofinsteadT

Effect of diffuse gas is removed.

Considering:

I will use

for convenience of fitting.

)sin*/(1 22 lTbξ

Q1: What is the HI density?

(My) Answer 1: HI density is HI column density↓∵

2-2. Analysis

2. Derivation of Outer Rotation Curve

Merriefield (1992) Petrovskaya, Terrikorpi (1986)

Considering:

HI density ∝ Tb

when optical depth is small.

4

4202 )(

i

ii

T

Tbbb

Σ

ΣΔ

b0: centroid= ∂Δb / ∂b0 =0

24ii TofinsteadT

Effect of diffuse gas is removed.

Considering:

I will use

for convenience of fitting.

)sin*/(1 22 lTbξ

2-3. Effect of Warp

2. Derivation of Outer Rotation Curve

R/R0=1.68 R/R0=2.22

lRWl)RR

Θ

R

Θ(=Vr sin*)(sin0

0

0

b0

l [deg.]

Sin curve

i)Circular orbit.ii)Orbit plane is rotated

with respect to thegalactic plane around

the line of sight to the G.C.Two method can apply!Two method can apply!

Orbit plane

Galactic plane

Q2: What is the sin curve?

(My) Answer 2: There are same suggestions.But…

↓∵

2-3. Effect of Warp

2. Derivation of Outer Rotation Curve

R/R0=1.68 R/R0=2.22

lRWl)RR

Θ

R

Θ(=Vr sin*)(sin0

0

0

b0

l [deg.]

Sin curve

i)Circular orbit.ii)Orbit plane is rotated

with respect to thegalactic plane around

the line of sight to the G.C.Two method can apply!Two method can apply!

Orbit plane

Galactic plane

Circular orbit may be correct.

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/R0=1.68(outer region) R/R0=0.85 (inner region)

flat

Observation

The difference between flat and observation indicates that R of observation is larger than that of flat.

If: Θ0=220km/s

The result is in agreement with the tangential method.

Θ=221km/s

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/R0=1.14

There are large uncertainties.

R/R0=1.63

2-4. Fitting and Uncertainty Estimate

2. Derivation of Outer Rotation Curve

Results both (Merriefiled, 1992) and (Petrovskaya &Teerikorpi, 1986)

SummaryMerrifield’s method is better.

These results are consistent with

each other within

the errors.

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.

4. Discussion

Inner:

(Fich et al. 1989)

Outer:

Merriefield’s

method

Overall rotation curves of the Galaxy

R0=8.5kpc, Θ0=220[km/s] 〃 , Θ0<200[km/s]

Outer rotation depends strongly

on the galactic constants.

Something extraMy ORC research with VERA would result in

most precisely Outer Rotation Curve. (??) (laugh)

There are uncertainties in outer rotation even Merrifield’s.

Fin.