Download Lecture 18: The Milky Way Galaxy

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
L!
L
=
23
×
10
Total : B
Total number of stars ~ 2 × 10
11
Galaxy rotates...
v0 = 220 km s
−1
= 225 kpc Gyr
−1
R0 = 8 kpc
2πR0
= 0.22 Gyr
P0 =
v0
sun has orbited ~20 times
for stars & gas to be on stable circular orbits means
GM (R)
v(R)2
=
R
R2
so
2
υ(R) R
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)2 R
M (R) =
G
Local Stellar Motions
radial velocity
∆λ
c
vr =
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 = (vr2 + vt2 )1/2
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
Θ(R) =
�
GM (R)
R
ω(R) = Θ(R)/R
�1/2
orbital speed
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 = Θ cos α − Θ0 cos(90 − l) = Θ cos α − Θ0 sin l
◦
eliminate alpha (which can’t be measured) using trig:
Θ Θ0
)R0 sin l
vr = ( −
R R0
or
vr = (ω − ω0 )R0 sin l
vt = Θ sin α − Θ0 cos l
eliminate alpha using trig:
vt = (ω − ω0 )R0 cos l − ωd
for d << R_0, simplify by Taylor expanding
dω
|R=R0 (R − R0 )
ω( R) ≈ ω(R0 ) +
dR
ω
equations define Oort’s constants A & B
dω
)R=R0 (R − R0 ) sin l
vr ≈ R0 (
dR
also
R − R0 ≈ −d cos l for d << R_0
finally
vr ≈ Ad sin 2l
where
local disk shear, or degree of nonrigid body rotation (from mean
radial velocities)
R0 dω
)R=R0
A≡− (
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