3D motions of SFRs in MWG based on radio astrometry

Toshihiro HandaKagoshima Univ.

Gaia-JASMINE symposium2016/12/8 @ NAOJ mtk

VERA array

Introduction

▶ (Radio) astrometry

■ Annual parallax motion distance

■ Secular proper motion kinematics

Systemic motion of a source

Internal motion in a source

Burns+2015 MNRAS

Note: observed 3D velocity of source

▶ astrometry: motion on the sky

■ reference frame = Sun

■ vel. across LoS :ml cos b d = vl, mb d = vb,

▶ radio spectroscopy: vel. along LoS

■ reference frame = LSR

■ assumed solar motion

(U☉, V☉, W☉)=(+10.3, +15.5, +7.7) km/s

(a, d)1900=(18h, +30o), v=20 km/s

► See Kerr & Lynden-Bell 1986, Ando+2011

▶ Caution: Rest frames are different!

Disentanglement of proper motion

▶ Proper motion

■ Systemic motion of a source

■ = average of maser spots

assume that spot motion is symmetric/random.

Chibueze+2016 PASJ

Disentanglement of 3D proper motion

▶ 3D proper motion (systemic motion)

■ galactic rotation of LSR

■ peculiar motion of LSR (?) / correction of vsun

■ galactic rotation of source

■ peculiar motion of source

▶ assume to disentangle above comp.

1. “nominal LSR” rotates circularly.

2. galactic rotation model

■ Galactic const. R0=8.5kpc, Q0=220km/s OK?

■ conventional (flat?) rotation curve OK?

Use 1st order approximation model as 1st step

Angular rotation velocity of LSRstart from Ando+2011, Nagayama+2011

Part 1

Galactic constants: Watch ourselves!

▶ measure the galactic constants R0, Q0

■ Direct measurement of R0 is still difficult. L

■ Ratio W0 =Q0 /R0 can be measured! J

Sources on tangent point & sol. circle

▶ Model assumption

■ Pure circular rot. (non peculiar motion)

random pec. motion. can remove by statistics

▶ advantage of this method

■ Independent of the “rotation curve”

System proper motion & galactic rotation

▶ geometry

■ vl=Q sinq －Q0 cosl

■ vLSR=Q cosq －Q0 sinl

■ Ro sinl =R cosq

■ d=Ro cosl ± Ro sinl tanq

▶ after vanishing of q …

■ vLSR=(Q/R-Q0/Ro) Ro sinl

■ vl=(Q/R-Q0/Ro) Ro cosl -Q d/R

Special location #1 : tangent point

▶ at the tangent point

■ Source shows vLSR=max, v⊥=0, then

■ d=Ro cosl ± Ro sinl √Q 2/(vLSR+Q0 sinl)2-1

=Ro cosl

■ vl=－Q0 cosl

■ W0=Q0/R0=vl/d =ml

Special location #2: solar circle

▶ On the solar circle

■ Source shows vLSR=0, Q=Q0, then

■ d=Ro cosl ± Ro sinl √Q 2/(vLSR+Q0sinl)2-1

=2Ro cosl

■ vl=Q sinq －Q0 cosl

= －2 Q0 cosl

■ W0=Q0/R0=vl/d =ml

Wo=Ro/vo can be estimated near these points

▶ Exact values of two velocities are

■ vl=(Q /R-Q0 /Ro) Ro cosl -Q0 d/R

■ vobs=(Q /R-Q0 /Ro) Ro sinl

∴Wo= Q0 /Ro = -vl /d +vLSR(1/(d tanl)- 1/(Ro sinl ))

for solar circle for tangent point

Ando+2011

Nagayama+2011

historical estimation of W0

▶ Oort constants

■ A=-1/2 R d(Q/R)/dR =1/2 [Q0/Ro -(dQ/dR)R=Ro]

■ B=-1/2 R-1 d(QR)/dR=1/2 [Q0/Ro +(dQ/dR)R=Ro]

■ A:shear velocity, 2B：vorticity

▶ then, traditionally we get

■ W0=Q0/Ro =A-B

▶ difference of our method

■ using sources over the whole Gal. disk

W0 : angl. vel. of LSR from radio astrometry

▶ Solar circle, tangent points

■ W0 = 27.6±0.7 km s-1 kpc-1

W49N; large peculiar vel?

■ Sgr A*

with VLA

13Burns+ 2014a

Solar circle, tangents

Hipparcos (Cep, OB; Miyamoto & Zhu 1998)

Sgr A* (Reid & Brunthaler 2004)

global fit (Honma+2012)

IAU1985

W49N

Statistics of pec. mot. of SFRsHateruma, Handa+ in prep

part2

Peculiar motion＝deviation from circ. rot.

▶ obs. with VERA, VLBA, EVN, LBA

■ massive SF regions

■ H2O & methanol maser

▶ total : 111 objects

■ Reid+ 2014 103 objects

■ add 8 sources

Burns+ 2014a, 2014b, 2015

Chibueze+ 2014a, 2014b

Sakai+ 2015, Nakanishi+ 2015, Krishnan+ 2015

G168.06+00.82 G182.67-03.26 correctedby Hachisuka et al. 2015

Histogram of peculiar velocity

▶ Histogram of 111 SFRs obs. with VERA, VLBA, EVN, LBA

This time we use R0=8.5kpc, Q0=220km/s

160

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-100-90-80-70-60-50-40-30-20-10 010203040506070

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Vs

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Ws

with large peculiar motion

▶ peculiar motion along z-axis

■ set |w|>18km/s; independent of Gal. rot. model

17

Source Us[km/s] Vs[km/s] Ws[km/s]

G010.47+00.02 +9.05 -109.85 +18.74

G078.12+03.63 -38.46 -10.46 +23.86

G016.58-00.05 +22.58 -14.33 +26.81

NGC6334I(N) +21.03 +26.30 +32.06

G028.86+00.06 +27.05 -18.51 +63.09

G000.67-00.03 +30.89 -118.88 -48.93

G078.88+00.70 -16.05 -8.11 -21.73

G045.45+00.05 -18.50 +2.86 -20.77

ws[km/s]

Sun

G.C.

U

VW

[kpc]

[kpc]

100km/s

5kpc

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Ws[km/s]

8 sources

radial peculiar motion (Us)

■ with very large negative (infall)

near GC

■ Us(peak)≅0 km/s

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Us(103天体)

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Us(111天体)

[km/s]

rotational peculiar motion (Vs)

■ Non-gaussian like

■ negative (slower rotating) tail

inconsistent to Gaia results? diff. b/w star & gas?

[km/s]

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Vs(103天体)

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Vs(111天体)

Kinematical center of MWGHateruma, Handa+ in prep

part3

Kinematical center of the Galaxy

▶ Concept & model

■ Using 3D peculiar motion

■ Circular rotation + random motion

■ statistically estimate the rotation center

to minimize peculiar motion

▶ advantage of this method

■ Independent of the “rotation curve”

Basic calculation

▶ Source at (l, q)

■ u=(vLSR+R0W0 sinl) sinq – (vl+R0W0 cosl) cosq

■ v=(vLSR+R0W0 sinl) cosq – (vl+R0W0 cosl) sinq

■ use q = q (d, l, R0)

▶ Model constraint

■ circular rotation <u> should be zero.

■ W0 is given from obs. (SolCir/Tan source, Sgr A*)

▶ Estimate R0 to minimize <u>

Data for calculation

▶ total : 111 objects

■ Reid+ 2014 103 objects

■ add 8 sources

Burns+ 2014a, 2014b, 2015

Chibueze+ 2014a, 2014b

Sakai+ 2015, Nakanishi+ 2015, Krishnan+ 2015

■ No rejection in this trial

(Large pec. vel. sources should be removed.)

Distance to the kinematic center

▶ with 3 different W0

IAU1985 Burns+2015 Reid+2014

Model value of

W0 [km/s/kpc]25.9 29.45 29.75

Estimated distanceR0 [kpc]

6.76 7.87 7.87

rms of u2[km/s] 25.0 25.2 25.0

Corresponding Q0

[km/s]175 234 232

summery

1. Angular velocity of LSR

■ well estimated by TP & SC sources

■ circular rot. model is valid as 1st order model

■ The value should be revised.

comparison of Oort constants with Gaia data

2. Peculiar velocity

■ Us, Ws: peak 0 km/s, Vs : negative tail

3. Kinematical center of MWG

■ as 1st trial with fixed W0

■ R0= 7.5 – 8.0 kpc

improved by Gaia data?