Lecture 18: The Milky Way Galaxy

Simple Version of Milky Way Galaxy

Disk (spiral arms)

Bulge

Halo

~15 kpc

~ 8 kpc

few hundred pc

Galactic Coordinate System

optical

IR

Disk :

Inventory

LB = 19 × 109L!

Bulge :

Halo :

Total :

LB = 2 × 109L!

LB = 2 × 109L!

LB = 23 × 109L!

Total number of stars ~ 2 × 1011

Galaxy rotates...

R0 = 8 kpc

v0 = 220 km s−1

= 225 kpc Gyr−1

P0 =2πR0

v0

= 0.22 Gyr

sun has orbited ~20 times

for stars & gas to be on stable circular orbits means

v(R)2

R=

GM(R)

R2

so

connection between “rotation curve” and mass

M(R) =υ(R)2R

G

stars near center have slower linear velocities, faster angular velocities

what’s going on here?M (R) ~ R

M(R) =υ(R)2R

G

Local Stellar Motions

vr =∆λ

λc

correct for Earth’s motion around Sun (~ 30 km/sec)and for Earth’s rotation <~ 0.5 km/sec

radial velocity

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?

tangential velocity

µ =

vt

d

mu in radians per year, v_t in pc/yr, d in pc

v = (v2

r + v2

t )1/2

space velocity

halo star, very close to us and high tangential velocity

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 currentposition, LSR = mean motion of disk material in solar neighborhood

Local Standard of Rest in Cylindrical Coordinates velocities

positions

vLSR = (0, 220, 0)

v! = (−10.4, 14.8, 7.3)

vLSR = (Π0,Θ0, Z0)

relative to LSR

what does this mean?

Sun at position of LSR, but not at its speed

Differential Rotation

Oort analysis

orbital speed

angular velocity

Θ(R) =

�GM(R)

R

�1/2

ω(R) = Θ(R)/R

at Sun’s location, angular velocity = 220 km/s / 8 kpc

vr = Θ cos α − Θ0 cos(90◦ − l) = Θ cos α − Θ0 sin l

vr = (Θ

R−

Θ0

R0

)R0 sin l or vr = (ω − ω0)R0 sin l

eliminate alpha (which can’t be measured) using trig:

1) Keplerian rotation, 2) constant orbital speed, 3) rigid-body rotation: how do M, Theta, and w scale with radius?

vt = Θ sinα − Θ0 cos l

eliminate alpha using trig:

vt = (ω − ω0)R0 cos l − ωd

for d << R_0, simplify by Taylor expanding ω

ω(R) ≈ ω(R0) +dω

dR|R=R0

(R − R0)

equations define Oort’s constants A & B

vr ≈ R0(dω

dR)R=R0

(R − R0) sin l

R − R0 ≈ −d cos l

also

finally

vr ≈ Ad sin 2l where A ≡ −

R0

2(dω

dR)R=R0

local disk shear, or degree of non-rigid body rotation (from mean radial velocities)

vt ≈ d(A cos 2l + B) B ≡ A − ω0where

local rotation rate (or vorticity) from A and ratio of random motions along rotation and (larger) toward center

get local angular speed (A-B), therefore distance to Galaxy center, rotation period of nearby stars

for d << R_0

Cepheid radial velocities vs. l

Cepheid proper motions vs. l

1.5 kpc

3 kpc

(R < 2 kpc)

0 180

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

~ once every 10 million yrs. the electron flips its spin

(1420 MHz)

sun

galactic center

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

stars (distinguished by kinematics and/or chemical abundances)

globular clusters

Satellite Galaxies

Magellanic Clouds

sagittarius dwarf

draco