VLBA Parallaxes Across the Milky Way
and the Distance to NGC 4258
Mark J. Reid
Harvard-Smithsonian
Center for Astrophysics
Trigonometric Parallax
D(parsecs) = 1 / A(arcseconds)
1 parsec = 3.26 light years = 205,000 A.U.
p
d(kpc) = 1 / p(mas)
Nearest stars:
d = 1 pc
p = 1”
d
Center of Milky Way:
d ~ 10 kpc
p ~ 0.1 mas
Other galaxies
d ~ 1 Mpc
p ~ 1 mas
1 A.U.
Friedrich Wilhelm Bessel
• Used Fraunhofer’s last telescope
p = 0.37” ± 0.03”
measured first stellar parallax:
61 Cygni: p = 0.314” in 1838
(p = 0.287”)
p = 0.25” ± 0.03”
Friedrich Wilhelm Bessel (1838)
HIPPARCOS
(HIgh Precision PARallax COllecting Satellite)
118,000 stellar parallaxes
sp ~ 0.001 arcseconds
10% accuracy at 100 pc…
mapped solar neighborhood
(Perryman et al 1997 A&A 323 49)
Pleiades Distance Problem
• Hipparcos:
D = 120.2 ± 1.9 pc
• Ground based
• HST (3 parallaxes):
D = 131  135 pc
D = 134.6 ± 3.1 pc
• VLBA (4 parallaxes): D = 136.2 ± 1.2 pc
Carl Melis et al (in prep)
uncertainty dominated by cluster depth (2.3pc),
not measurement accuracy
Very Long Baseline Interferometry:
VLBA, VERA & EVN
Fringe spacing (eg, VLBA):
qf~l/D ~ 1 cm / 8000 km = 250 mas
Centroid Precision:
0.5 qf / SNR ~ 10 mas
Systematics:
path length errors ~ 2 cm (~2 l)
shift position by ~ 2qf ~ 500 mas
• Radio waves “see” through
galaxy
• Can “synthesize” telescope
the size of the Earth
Relative positions (to QSOs):
DQ ~ 1 deg (0.02 rad)
cancel systematics: DQ*2qf ~ 10 mas
What does the Milky Way look like?
Hipparcos range
Gaia range (± 10 to 20 mas); but cannot
see through dust in Galactic plane
VLBI range (± 5 to 20 mas): can “see” through plane to massive star forming
regions that trace spiral structure
The BeSSeL Survey Team
M. Reid, T. Dame (CfA)
K. Menten, A. Brunthaler, B. Zhang,
Y. Wu, M. Sato, Y. Choi, A. Sanna
(MPIfR)
X-W Zheng, Y. Xu (Nanjing)
L. Moscadelli (Arcetri)
A. Bartkiewicz (Torun)
K. Hachisuka (Shanghai)
K. Rygl (Netherlands)
Parallax for W 49N H2O masers
p = 90 ± 7 mas (D=11.1 ± 0.9 kpc)
Zhang+ (2013)
Mapping Spiral Structure
• Parallaxes: VLBA, EVN & VERA
>100 parallaxes for massive
young stars
• Tracing most spiral arms, eg…
Outer arm traced
Perseus arm “gap”
Local arm significant
• Model entire data set:
R0 = 8.34 ± 0.16 kpc
Q0 = 240 ± 8 km/s
QR ~ 0
Reid et al 2014
Local Group Proper Motions
• 1920s van Maanen claimed to see
M33 spin!
• mas/yr motions  Spiral nebulae
nearby (Galactic)
• Hubble argued more distant
(extra-galactic)
• van Maanen’s error not found
M33
Extragalactic Proper Motions
• van Maanen experiment:
M33
M33/19 – M33/IC133 masers
VLBA: Dmx = 30 +/- 2, Dmy = 10 +/- 5 mas/yr
HI:
Dvx = 106 +/-20, Dvy = 35 +/- 20 km/s
D = 750 +/- 50 +/- 140 kpc
sm
sv
• Next: M31 (Andromeda)
5 masers
higher rotation speed
Brunthaler+ 2006
NGC 4258
• Seyfert 2 galaxy
• H2O masers in edge-on warped disk
Radius 0.15 -> 0.30 pc
Rotation speed ~ 1000 km/s
Period ~ 1000 years
M ~ 4 x 107 Msun
• Decade of VLBA and GBT observation
• Geometric model  Distance
• With HST observations,
recalibrate Cepheid PL relation
Herrnstein, Greenhill, Moran, Miyoshi…
NGC 4258: Accretion Disk (r ~ 0.1 pc)
Parameter
Valuea
Modeling Disk Dynamics
Distance, D (Mpc)
7.60 ± 0.17
A = V2 / r & r = D q
Black hole mass, M bh (× 107 M )
4.00 ± 0.09
M ~ r V2
Galaxy systemic velocity, vsys (km s− 1 )
474.25 ± 0.49
Dynamical center x-position, X 0 b (mas)
− 0.204 ± 0.005
Dynamical center y-position, Y0b (mas)
0.560 ± 0.006
Inclination, i 0 (deg)
71.74 ± 0.48
Inclination warp, di / dr (deg/ mas)
2.49 ± 0.11
Position angle, Ω0 (deg)
65.46 ± 0.98
Position angle warp, dΩ/ dr (deg/ mas)
5.23 ± 0.30
Position angle warp, d2Ω/ 2dr 2 (deg/ mas2 )
− 0.24 ± 0.02
Eccentricity, e
0.006 ± 0.001
Periapsis angle, ω0 (deg)
293.5 ± 64.4
Periapsis angle warp change, dω/ dr (deg/ mas)
59.5 ± 10.2
a
√
et al (2013)
Uncertainties have been scaledHumphreys
by χ 2 / N , i.e.,
1.403.
b
Positions are measured relative to that of maser emission at
Center of P-V diagram
VLBA map
Very small
Base Model
7.596
± 0.167
2.20
Modeling Disk Dynamics
S y st e m a t ic U n ce r t a in t ie s
Value in
Dist ance
Base Model
∆ D from
r Base Model
or rm s est im at e
(Mp c)
(Mp c)
(%)
1.0 km s− 1
7.624
0.028
0.37
30 µas
7.639
0.043r
0.57
0.3 km s − 1 yr − 1
7.564
-0.032
0.42
Different init ial condit ionsa
—
—
± 0.114
1.50
Assum ing eccent ricity is zero
—
7.619
0.023
0.30
Inclusion of d2 i / dr 2 t erm (solves t o -0.112± 0.034 deg m as− 2 )
—
7.562
-0.034
0.45
Unm odeled spiral st ruct ure
—
—
± 0.076
1.00
Diffe ent hv-feat ure velocity uncert aint ies (0.7 & 1.3 km s − 1 )
Different y-error floor (20 µas)
Diffe ent accelerat ion error floor (0.5 km s − 1 yr − 1 )
S y st e m a t ic U n ce r t a in t ie s A d d e d in Q u a d r a t u r e
0.15
2.0 %
U n c e r t a in t y in t h e M a s e r D is t a n c e t o N G C 4 2 5 8 b
0.23
3.0 %
Estimating H0
• DNGC4258 = 7.60 ± 0.17 ± 0.20 Mpc
(total ±3%)
Extremely accurate, direct distance to a galaxy.
• H0 = Vrec/ D very uncertain (Vrec = Vobs – Vpec)
But, very useful for re-calibrating Cepheids…
H0,NGC4258 = 72.0 ± 3.0 km/s/Mpc
H0,NGC4258 = 70.6 ± 3.3 km/s/Mpc
(see Riess+ 2011,12)
(see Efstathiou 2014)
• Established H2O megamaser method for distances.
Observe similar AGN disks in galaxies where Vpec << Vrec
and estimate H0 directly without standard candels.