Masers as Probes of Galactic Structure Mark J. Reid Harvard-Smithsonian Center for Astrophysics Collaborators: K. Menten, A. Brunthaler, K. Immer , Y. Choi, A. Sanna, B. Zhang (MPIfR) X-W Zheng, Y. Xu, Y. Wu (Nanjing) L. Moscadelli (Arcetri) G. Moellenbrock (NRAO) M. Honma, T. Hirota, M. Sato (NAOJ) T. Dame (CfA) A. Bartkiewicz (Torun) K. Rygl (INAF, Rome) K. Hachisuka (Shanghai) Here to present preliminary results from a major effort, world-wide, to measure distances to SFRs using gold-standard method: trigonometric parallax Goals to give solid distances to MSFRs….allowing accurate measures of mass, size and luminosity of constituents of SFRs and to study the structure and dynamics of the Galaxy

What does the Milky Way look like? Hipparcos range Distances to stars long solved…even distances to galaxies solved using “standard candles” eg, Cepheids But still we don’t even know what the Milky Way looks like…perhaps a mix of these two spirals. (Spirals traced by newly formed, massive stars that are very hot 10’s of thousands K, ionize surrounding clouds of Hydrogen which glow blue) Why? Distances are very great (Hipparcos surveyed just a very small volume: Solar Neighborhood)…cannot give Galactic structure …Significant progress optically (even with future $1B space mission like GAIA) will be limited by dust extinction in the plane of the Galaxy. 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

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 Relative positions (to QSOs): DQ ~ 1 deg (0.02 rad) cancel systematics: DQ*2qf ~ 10 mas Key is not optical light (absorbed by dust throughout M.W.), but other wave bands, eg, Radio Explains why we can achieve ~0.01 mas accuracy Radio waves “see” through galaxy Can “synthesize” telescope the size of the Earth

Parallax Signatures What do parallax data look like? Earth moves in near circular orbit; viewed from source, projects to ellipse on sky Relative motion of Sun & Target gives proper motion Combination of Pi and P.M. gives curliques on sky Can separate E and N vs time; Can plot with remove p.m. If well designed expt; pi and p.m. uncorrelated For Galactic sources, EW amplitude > NS amplitude…often pays to only go after the EW signature.

Orion Nebular Cluster Parallax Orion is archetypal MSFR…extensively studied from radio – x-rays T Tauri –like stars exhibit compact, non-thermal, radio continuum (from magnetic field activity from inner accretion disk) 3 stars vs 1 QSO overplotted…one star is distant companion of Theta-1A Orionis (Trapezium) 2% parallax measured; slightly better than Bowers measure of 1 star, and recently equalled by VERA…all agree well within joint errors Orion 10% closer than had been assumed…changes young stellar luminosities by 20%, and hence YSO ages and masses VLBA: P = 2.42 ± 0.04 mas D = 414 ± 7 pc VERA: D = 419 ± 6 pc Menten, Reid, Forbrich & Brunthaler (2007)

Mapping the Milky Way 6.7/12.2 GHz CH3OH masers 22 GHz H2O masers Key Project to map spiral structure of Milky Way 6.7/12.2 GHz CH3OH masers 22 GHz H2O masers VLBA Key Science Project: 5000 hours over 5 years to measure hundreds of parallaxes/proper motions Observations for ~70 masers started 2010/2011 recently completed

Parallax for Sgr B2(Middle) H2O masers P = 129 ± 12 mas (D=7.8 ± 0.8 kpc)

Parallax for W 49N H2O masers P = 82 ± 6 mas (D=12.2 ± 0.9 kpc)

Mapping Spiral Structure Preliminary results of parallaxes from VLBA, EVN & VERA: Arms assigned by CO l-v plot Tracing most spiral arms Inner, bar-region is complicated Background: artist conception by Robert Hurt (NASA: SSC)

Spiral Arm Pitch Angles For a log-periodic spiral: log( R / Rref ) = -( b – bref) tan y Outer spiral arms: ~13˚ pitch angles Inner arms may have smaller pitch angels (need more observations) Sun Sources with uncertainty in log(R/kpc) < 0.1 and beta < 10 deg Dashed lines correspond to perfect log-spirals with 16 degree pitch angles (no attempt to adjust pitch angle to optimize) Undoubtedly more complicated than single, global pitch angle, but fairly clear that MW has 4 arms, not 2

Convert observations from Heliocentric to Galactocentric coordinates Galactic Dynamics Qo ~ 220 km/s Vsun ~ 20 km/s Vsun Convert observations from Heliocentric to Galactocentric coordinates Qo l d Ro VGC R VHelio Qo+Vsun Why? … Measure in Heliocentric frame Vhelio (ie, Vsource – Sun’s full motion) To obtain VGC (in Galactocentric frame) , must add back To+Vsun: Vsun directly measurable in Solar Neighborhood…but has held surprises recently Theta_o more difficult but of great astrophysical interest

The Milky Way’s Rotation Curve Q0 = 245 km/s Blue points moved up 25 km/s Q0 = 220 km/s Theta_o not easy to measure since all observables are Heliocentric and have removed Theta_o from measurements When one adds back a Theta_o one “basically gets one one puts back”…see two examples of RC for two Theta_o values. In right panel, move the blue points up by the difference in Theta_o used (25 km/s). .. Mostly line up! But, there are differences which give a handle on To (also, for parallax/p.m.’s can compare D vs To to help fit for To); It takes the entire data set to solve for Theta_o! Remember we have all phase space info…imagine how tricky if only have radial velocity and less reliable distances! Controversial!

Modeling Parallax & Proper Motion Data Data: have complete 3-D position and velocity information for each source: Independent variables: a, d Data to fit: p, ma, md, V Data uncertainties include: measurement errors source “noise” of 7 km/s per component (Virial motions in MSFR) Model: Galaxy with axially symmetric rotation: R0 Distance of Sun from G. C. Q0 Rotation speed of Galaxy at R0 ¶Q/¶R Derivative of Q with R: Q(R) º Q0 + ¶Q/¶R ( R – R0 ) Usun Solar motion toward G. C. Vsun “ “ in direction of Galactic rotation Wsun “ “ toward N. G. P. <Usrc> Average source peculiar motion toward G. C. <Vsrc> “ “ “ “ in direction of Galactic rotation How we fit the data to a model of the Galaxy: Every sources gives us 4 measurements to fit: parallax, 2 pm’s, Vlsr In interest of keeping simple now, only use two parameters for Rotation Curve: Theta_o and dTheta/dR or other 2-param formulations

“Outlier-tolerant” Bayesian fitting Prob(Di|M,si) µ exp(- Ri2 /2) Ri = (Di – Mi) / si Prob(Di|M,si) µ (1 – exp(- Ri2 /2) ) / Ri2 Since we expect departures from simple model (eg, near bar or from supernova induced shells), using outlier-tolerant Bayesian fitting…not sensitive to outliers (but will return larger uncertainties…very conservative) Sivia “A Bayesian Tutorial”

Model Fitting Results for 93 Sources Method / R0 Q0 dQ/dR <Vsrc> <Usrc> Q0/R0 Rotation Curve used (kpc) (km/s) (km/s/kpc) (km/s) (km/s) (km/s/kpc) “Outlier-tolerant” Bayesian fitting Flat Rotation Curve 8.39 ± 0.18 245 ± 7 [0.0] -8 ± 2 5 ± 3 (28.2) Sloped “ “ 8.38 ± 0.18 243 ± 7 -0.4 ± 0.7 -8 ± 2 6 ± 2 (29.0) Least-Squares fitting: removing 13 outliers (>3s): Sloped “ “ 8.30 ± 0.09 244 ± 4 -0.3 ± 0.4 -8 ± 2 5 ± 2 (29.4) Notes: Assuming Solar Motion V-component = 12 km/s (Schœnrich et al 2010) <Vsrc> = average deviation from circular rotation of maser stars <Usrc> = average motion toward Galactic Center Q0/R0 = 28.8 ± 0.2 km/s/kpc from proper motion of Sgr A* (Reid & Brunthaler 2004) Using 62 sources with parallax/pm measurements from VLBA, VERA and EVN. Expect simple model will not characterize all data (eg, doesn’t account for local effects of Bar or super-bubbles). Therefore, adopt an “error tolerant” Bayesian approach…maximize the Prob(D|M) with function that falls as 1/R^2 instead of exponentially for a Gaussian prob This handles outliers very well…doesn’t let them dominate the fit as it would for least squares. Get Ro~8.5 kpc and Theta_o~245 km/s…close to Paper VI results with only 18 sources. Can remove 11 outliers (>3sigma residuals) based on Bayesian fit and perform a (more accurate) Least Squares fit. Get Ro=8.6 kpc and Theta_o=248…almost same but with reduced uncertainties (one loses accuracy with the error-tolerant Bayesian fit as the price for not being sensitive to outliers) Other info: average counter-rotation (C.R.) 6 km/s; average toward G. C. 5 km/s Angular rotation Theta_o/Ro = 28.8 +/- 0.8 km/s/kpc (matches value inferred from Sgr A*’s proper motion of 28.8 +/- 0.2 km/s when using Vsun=12 km/s)

The Milky Way’s Rotation Curve For R0 = 8.4 kpc, Q0 = 243 km/s Assumes Schoenrich Solar Motion Corrected for maser counter-rotation New and direct result based on 3-D motions “gold standard” distances Examples of Rotation Curves over plotted on our data (for Theta_o=245) Blue points have >3sigma residuals, probably owing to 1) near bar, 2) near super-bubbles

Conclusions VLBA, VERA & EVN parallaxes tracing spiral structure of Milky Way Milky Way has 4 major gas arms (and minor ones near the bar) Outer arm spiral pitch angles ~13o Star forming regions “counter-rotate” by ~8 km/s (for Vsun=12 km/s) Parallax/proper motions: Ro ~ 8.38 ± 0.18 kpc; Qo ~ 243 ± 7 km/s/kpc VLBI can achieve <10 uas parallax uncertainty in 1 year…adding ~60 measures per year Spiral arms are being traced and it appears that a “global” average pitch angle is ~13 deg (~ for Sbc galaxy) 3) On average, MSFRs counter rotate (ie, are near apocenter in slightly elliptical orbits) 4) Ro, To being tightly constrained using full 3D info; compares well to only other truly DIRECT measurements

Conclusions VLBA, VERA & EVN parallaxes to massive young stars (via masers) tracing spiral structure of Milky Way Milky Way has 4 major gas arms (and minor ones near the bar) Outer arm spiral pitch angles ~13o Star forming regions “counter-rotate” by ~8 km/s (for Vsun=12 km/s) Parallax/proper motions: Ro ~ 8.38 ± 0.18 kpc; Qo ~ 243 ± 7 km/s/kpc G.C. stellar orbits + Sgr A* p.m.: Ro ~ 8.2 ± 0.3 kpc; Qo ~ 236 ± 10 km/s/kpc VLBI can achieve <10 uas parallax uncertainty in 1 year…adding ~60 measures per year Spiral arms are being traced and it appears that a “global” average pitch angle is ~13 deg (~ for Sbc galaxy) 3) On average, MSFRs counter rotate (ie, are near apocenter in slightly elliptical orbits) 4) Ro, To being tightly constrained using full 3D info; compares well to only other truly DIRECT measurements

Is Q0 really >220km/s ? Parallax/Proper Motions of Star Forming Regions R0 = 8.4 ± 0.2 kpc & Q0 = 243 ± 7 km/s Q0 / R0 = 29.0 ± 0.9 km/s/kpc (assuming Schoenrich, Binney & Dehnen 2010 Solar Motion) Sgr A*’s proper motion (caused by Sun’s Galactic orbit) Q0 / R0 = 28.62 ± 0.15 km/s/kpc (Reid & Brunthaler 2004) IR stellar orbits R0 = 8.3 ± 0.3 kpc (Ghez et al 2008; Gillessen et al 2009) Hence, Q0 = 238 ± 9 km/s Now back to our question…can we confirm large To value? Yes…totally independent and direct measurements consistent result. Combined result: Q0 = 241 ± 6 km/s

Carbon Monoxide (CO) Longitude-Velocity Plot Doppler Velocity Dame, Hartmann & Thaddeus (2001) Galactic Longitude

Counter-Rotation of Star Forming Regions Compute Galacto-centric V Transform to frame rotating at Qo = 250 km/s (yellow) See peculiar (non-circular) motions …clear counter-rotation Transform to frame rotating at Qo = 235 km/s (red) Still counter-rotating Now on to dynamics…remember not only have parallax, but also proper motion and Vlsr (3-D velocity vector in km/s) Transform to frame rotating with the Galaxy (flat rotation curve) and plot peculiar (non-circular) velocities Clearly see an average counter rotation. First thought might be that this indicates To too large…but value of To largely cancels. Dropping To by 15 km/s makes very little difference

Sensitivity to Rotation Curve Method / R0 Q0 dQ/dR C.R. G.C. Q0/R0 Rotation Curve used (kpc) (km/s) (km/s/kpc) (km/s) (km/s) (km/s/kpc) “Error-tolerant” Bayesian fitting: Prob(Di|M) µ (1 – exp(- Ri2 /2) ) / Ri2 where Ri = (Di – Mi) / si Flat Rotation Curve 8.51 ± 0.25 244 ± 9 [0] 5 ± 2 5 ± 3 (28.6) Sloped “ “ 8.53 ± 0.27 246 ± 9 1.1 ± 0.9 6 ± 2 5 ± 3 (28.9) R.C. params a1 a2 Brand-Blitz formulation 8.64 ± 0.28 250 ± 9 .06±.03 [0] 6 ± 2 5 ± 3 (29.0) Polynomial formulation 8.77 ± 0.32 253 ±10 -1.0±1 -1.5±.5 5 ± 2 5 ± 3 (28.8) “Universal” formulation 8.80 ± 0.30 250 ±11 1.1±.2 1.6±.7 5 ± 2 5 ± 3 (28.4) Brand-Blitz Q = Q0 ra1 + a2 where r = R/R0 Polynomial Q = Q0 + a1 (r - 1) + a2 (r - 1)2 Universal Q = f( Q0, Ropt = a1 R0, L = a2 L* ) Checking sensitivity to various rotation curves (RC) Not much change in Ro, Theta_o ; if anything favors slightly larger Ro, To values (keeping ratio constant near 28.8 km/s/kpc)

Sgr A*’s Proper Motion m = ( Q0 + V ) / R0 220 km/s 8.4 kpc Apparent motion of Sgr A* (Galactic Center compact radio source) traces Galactic orbit directly gives (To+Vsun)/Ro Here’s how we measure it…

Reid & Brunthaler (2004) + new data Proper Motion of Sgr A* Parallel to Galactic Plane: 6.379 ± 0.026 mas/yr  Qo/Ro = 28.62 ± 0.15 km/s/kpc (after removing V=12 km/s) Remove Qo/Ro = 29.4 ± 0.9 km/s/kpc Sgr A*’s motion || to Gal. Plane -7.2 ± 8.5 km/s (Ro/8 kpc) Perpendicular to Gal. Plane: -7.6 ± 0.7 km/s Remove 7.2 km/s motion of Sun Sgr A*’s motion ^ to Gal. Plane -0.4 ± 0.9 km/s ! Galactic Plane What do we see… Plotted is small piece of sky; major tics at 10 mas; position of Sgr A* plotted from 1995 (top) to 2003 (bottom) Value is 6 mas/yr measure to 0.3% accuracy as expected from Sun’s orbit Implies Rot Speed/Distance = 29.5 (for a flat rotation curve -> A=14.75) Fit is red dashes; Gal Plane is blue line…difference is Vsun out of G.P. Could use to help redefine G.P. Sgr A* intrinsic motion extremely small…less than military aircraft! …must be extremely massive fit to data Reid & Brunthaler (2004) + new data

Effects of Increasing Q0 Reduces kinematic distances: Dk by 15%, hence… Molecular cloud sizes (R µ jD) by 15% Young star luminosities: L µ R2 by 30% (increasing YSO ages) Cloud masses (from column density & size): M µ R2 by 30% Milky Way’s dark matter halo mass: M µ (Vmax) 2 RVir Vmax µ Q0 & RVir µ Q0 M µ Q03 or up by 50% Increasing Q0, increases expected dark matter annihilation signals Largest uncertainty for modeling Hulse-Taylor binary pulsar timing is accounting for the acceleration of the Sun in its Galactic Orbit: Q2/R0

Effects of Increasing Q0 1) Increases mass and overall size of Galaxy 2) Decreases velocity of LMC with respect to M.W. Both help bind LMC to M.W. (Shattow & Loeb 2009) Increases likelihood of an Andromeda-Milky Way collision MW LMC Measurement so accurate, need to consider some pretty exotic possibilities for apparent motion of Sgr A* This effect comparable to our measurement accuracy