Lecture 18: The Milky Way Galaxy Simple Version of Milky Way Galaxy Disk (spiral arms) ~15 kpc Bulge Halo few hundred pc ~ 8 kpc Galactic Coordinate System optical IR Inventory 9 Disk : LB =19× 10 L! 9 Bulge : LB =2× 10 L! 9 Halo : LB =2× 10 L! 9 Total : LB =23× 10 L! Total number of stars ~ 2 × 1011 Galaxy rotates... −1 v0 =220kms −1 = 225 kpc Gyr R0 =8kpc 2πR0 P0 = =0.22 Gyr v0 sun has orbited ~20 times for stars & gas to be on stable circular orbits means v(R)2 GM(R) R = R2 so υ(R)2R M(R)= G connection between “rotation curve” and mass what’s going on here? M (R) ~ R stars near center have slower linear velocities, faster angular velocities υ(R)2R M(R)= G Local Stellar Motions radial velocity ∆λ v = c r λ correct for Earth’s motion around Sun (~ 30 km/sec) and for Earth’s rotation <~ 0.5 km/sec mostly even about zero one notable outlier (Kapteyn’s star, 3.9 pc, v_r ~ 250 km/s) without this star, rms v_r ~ 35 km/s what’s up with outlier? halo star, very close to us and high tangential velocity tangential velocity vt µ = d mu in radians per year, v_t in pc/yr, d in pc space velocity v v2 v2 1/2 =( r + t ) Local Standard of Rest actual (example) orbit of Sun need better reference frame for other stars’ motion imaginary star on circular orbit at Sun’s current position, LSR = mean motion of disk material in solar neighborhood Local Standard of Rest in Cylindrical Coordinates velocities vLSR =(Π0, Θ0,Z0) vLSR =(0, 220, 0) positions relative to LSR v! =(−10.4, 14.8, 7.3) what does this mean? Sun at position of LSR, but not at its speed Differential Rotation Oort analysis GM(R) 1/2 Θ(R)= orbital speed R ω(R)=Θ(R)/R angular velocity at Sun’s location, angular velocity = 220 km/s / 8 kpc 1) Keplerian rotation, 2) constant orbital speed, 3) rigid-body rotation: how do M, Theta, and w scale with radius? ◦ vr =Θcos α − Θ0 cos(90 − l)=Θcos α − Θ0 sin l eliminate alpha (which can’t be measured) using trig: Θ Θ0 vr =( − )R0 sin l or vr =(ω − ω0)R0 sin l R R0 vt =Θsin α − Θ0 cos l eliminate alpha using trig: vt =(ω − ω0)R0 cos l − ωd for d << R_0, simplify by Taylor expanding ω dω ω R ω R R R ( ) ≈ ( 0)+dR|R=R0 ( − 0) equations define Oort’s constants A & B dω v ≈ R R − R l r 0(dR)R=R0 ( 0) sin also R − R0 ≈−d cos l for d << R_0 local disk shear, or degree of non- rigid body rotation (from mean radial velocities) finally R dω v ≈ Ad sin 2l A ≡− 0 r where ( )R=R0 2 dR local rotation rate (or vorticity) from A and ratio of random motions along rotation and (larger) toward center vt ≈ d(A cos 2l + B) where B ≡ A − ω0 get local angular speed (A-B), therefore distance to Galaxy center, rotation period of nearby stars 1.5 kpc Cepheid radial velocities vs. l 3 kpc 0 180 Cepheid proper motions vs. l (R < 2 kpc) Period - Luminosity Relationship (Large Magellanic Cloud) early 1900’s 1960’s We can apply Oort’s equation to get rotation curve .... but there’s dust! use HI (neutral hydrogen) instead of stars 21 cm radiation (1420 MHz) ~ once every 10 million yrs. the electron flips its spin galactic center sun can also invert this to get distances 8 kpc Nucleus of Galaxy 8 kpc away 28 magnitudes of extinction in optical 2 magnitudes in near IR with adaptive optics n* ~ 10^7 pc^-3 locally, n* ~ 0.1 pc^-3 Sag A (20 cm observations) zoom in to Sag A West (6 cm) center of Sag A West is Sag A* (Sag A star) 6 AU size proper motion is Sun’s reflex motion X-ray source bolometric luminosity ~ 10^3 L_sun what is it? stellar orbits M_BH = 3.7 x 10^6 M_sun R_Sch = 0.07 AU The Halo globular clusters stars (distinguished by kinematics and/or chemical abundances) Satellite Galaxies Magellanic Clouds sagittarius dwarf draco.