3d motions of sfrs in mwg based on radio astrometry · 3d motions of sfrs in mwg based on radio...
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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
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
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
5
10
15
20
25
30
-130
-120
-110
-100-90-80-70-60-50-40-30-20-10 010203040506070
Us
0
5
10
15
20
25
30
-130
-120
-110
-100-90-80-70-60-50-40-30-20-10 010203040506070
Vs
0
5
10
15
20
25
30
-130
-120
-110
-100-90-80-70-60-50-40-30-20-10 010203040506070
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
0
5
10
15
20
25
30
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10 0
10
20
30
40
50
60
70
Ws[km/s]
8 sources
radial peculiar motion (Us)
■ with very large negative (infall)
near GC
■ Us(peak)≅0 km/s
0
5
10
15
20
25
30
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10 0
10
20
30
40
50
60
70
Us(103天体)
0
5
10
15
20
25
30
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10 0
10
20
30
40
50
60
70
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]
0
5
10
15
20
25
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10 0
10
20
30
40
50
60
70
Vs(103天体)
0
5
10
15
20
25
-130
-120
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10 0
10
20
30
40
50
60
70
Vs(111天体)
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?