Rotation Curve of the Milky Way What does

Rotation Curve of the Milky Way • What does our Galaxy’s rotation curve V(R) look like? • From local stellar kinematics (Oort constants A, B) : d. V/d. R = -( A + B ) = -3. 4 km/s/kpc V V 0 w 0 = V 0 / R 0 = A – B = 27. 2 km/s/kpc R 0 R P = 2 p / w 0 = 2 p / ( A - B ) = 2. 3 x 108 yr • How do we extend this? • Radio Emission lines : • radio waves go through dust • can probe whole galaxy • Doppler shift gives radial velocity distance • Use HI at 21 cm and CO at 2. 6 mm AS 2001 Galactic Astronomy

Line Emission from Gas Clouds • Single cloud : • Multiple clouds : Flux Vr • • AS 2001 Spectrum resolves clouds due to radial velocity Observed widths of lines from clouds > 5 km/s Thermal width ~ 1 km/s ( T ~ 100 K ) Clouds are turbulent or have velocity gradients Galactic Astronomy

Radio Emission-line Map Radial velocity Brightness Temperature TB ( l , Vr , b ) for b = 0 How to interpret this huge data cube ? l = +180 o AS 2001 l = -180 o Galactic Astronomy

Rotation Curve of the Galactic Disc • Assume : (1) Circular orbits with rotation curve V(R). • (2) Angular velocity ω = V / R decreases outwards. • True for any “reasonable” model of the Galaxy : • If density decreases outwards, • enclosed mass with a <3 • Radial velocity Vr depends on angular velocity w and Galactic longitude l of emitting cloud : • Measure emission from clouds vs longitude l and Vr. • Determine rotation curve V( R ). AS 2001 Galactic Astronomy

Radial Velocities in the Galactic Disc • For 3 lines of sight, what range of radial velocity seen? (1) (2) A V B r C (2) V 0 r (1) V A r R C l V 0 -V 0 B R 0 G. C. • A (1) : Tangent point : r = R 0 cos l , R = R 0 sin l max radial velocity : Vr = Vmax = V( R ) – V 0 sin l (2): Solar circle : r = 2 R 0 cos l , R = R 0 constant separation : Vr = 0 • B, C : Vmax = 0 at r = 0 , R = R 0. • A, B, C : Vmin = –V 0 sin l at r = ∞, R = ∞. AS 2001 Galactic Astronomy

Velocity Range vs Galactic Longitude • Looking in : 0 o < l < 900 : Tangent point • Max Vr at the tangent point along line of sight. Vmax( l ) = V( R ) - V 0 sin l at R = R 0 sin l Vmin( l ) = - V 0 sin l at R = ∞ • Vmax( l ) determines rotation curve V( R ) for R < R 0 • Looking out: 90 o < l < 180 o No tangent point Vmax( l ) = 0 at R = R 0 Vmin( l ) = - V 0 sin l AS 2001 at R => ∞ Galactic Astronomy

Flat Rotation Curve : V( R ) = V 0 Vr =V(R) -V 0 sin l +V 0 Vr = -V 0 sin l tangent points Vr B Vr C -V 0 180 AS 2001 A C -V 0 A 90 r 0 -90 -180 l Galactic Astronomy B

Data ! CO emission vs ( l, Vr ) for b = 0 • Use tangent points to find V( R ) = Vmax -V 0 sin l +V 0 tangent points Vr -V 0 AS 2001 180 90 0 l -90 -180 Galactic Astronomy

MW Rotation Curve V( R ) From tangent-points : V( R ) = Vmax -V 0 sin l at R = R 0 sin l +V 0 Vr -V 0 AS 2001 180 90 0 l -90 Galactic Astronomy -180

Outer edge of cool gas disc • At l = 90 o, Vr range should be 0 to -V 0 ~ -200 km/s. • Observed emission covers Vr from 0 to -150 km/s. • Thus HI gas disc extends to only ~4 R 0 ~ 34 kpc +V 0 Vr -V 0 AS 2001 180 90 0 -90 l Galactic Astronomy -180

Warning: Ambiguity of Vr • Can use radial velocities to map Galactic structure • e. g. spiral arms ( e. g. in the Galactic Astronomy Lab ) • However : Vr for | l| < 90 o not unique to one distance (2) V 0 Vr (1) l G. C. (1) (2) r r 1 r 2 • Inward lines of sight ( | l | < 90 o ) intersect circular orbits at two different distances for the same radial velocity ! • Ambiguity sometimes resolvable: larger d, smaller range in latitude b for fixed size of a gas cloud AS 2001 Galactic Astronomy

Oort’s 1958 Map of HI gas • Reconstructed from 21 cm emission from HI gas Why not here ? AS 2001 Galactic Astronomy

Milky Way Spiral Structure in Cool Gas Oort 1958 http: //www. ioa. s. u-tokyo. ac. jp/~sofue/h-mw. htm AS 2001 Galactic Astronomy

Gas distribution inside Solar circle • • 3 rings: R > R 0 R << R 0 vr 0 solar circle sun 180 l 0 -180 tangent point Trace gas structures. Less gas inside 3 kpc. Inner Bar (non-circular) Spiral arm patterns. AS 2001 Galactic Astronomy

Milky Way’s Cool Gas Disc in 3 D http: //www. ioa. s. u-tokyo. ac. jp/~sofue/h-mw. htm As viewed from Andromeda: HI (red) AS 2001 + CO (green) Galactic Astronomy

Mapping Cool Gas in External Galaxies Cool gas (HI, CO emission lines) extends well beyond the starlight distribution. Detailed rotation curves and internal structure AS 2001 Galactic Astronomy

Thanks for Listening AS 2001 Galactic Astronomy

HI map of Cool Dust AS 2001 Galactic Astronomy