Lecture 18: The Milky Way Galaxyatropos.as.arizona.edu/aiz/teaching/a250/Lecture18.pdfSimple Version...
Transcript of Lecture 18: The Milky Way Galaxyatropos.as.arizona.edu/aiz/teaching/a250/Lecture18.pdfSimple Version...
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Lecture 18: The Milky Way Galaxy
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Simple Version of Milky Way Galaxy
Disk (spiral arms)
Bulge
Halo
~15 kpc
~ 8 kpc
few hundred pc
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Galactic Coordinate System
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optical
IR
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Disk :
Inventory
LB = 19 × 109L!
Bulge :
Halo :
Total :
LB = 2 × 109L!
LB = 2 × 109L!
LB = 23 × 109L!
Total number of stars ~ 2 × 1011
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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
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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
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stars near center have slower linear velocities, faster angular velocities
what’s going on here?M (R) ~ R
M(R) =υ(R)2R
G
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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
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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?
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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
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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
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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
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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
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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?
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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)
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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
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Cepheid radial velocities vs. l
Cepheid proper motions vs. l
1.5 kpc
3 kpc
(R < 2 kpc)
0 180
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Period - Luminosity Relationship (Large Magellanic Cloud)
early 1900’s
1960’s
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We can apply Oort’s equation to get rotation curve.... but there’s dust!
use HI (neutral hydrogen)instead of stars
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21 cm radiation
~ once every 10 million yrs. the electron flips its spin
(1420 MHz)
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sun
galactic center
can also invert this to get distances
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8 kpc
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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
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Sag A (20 cm observations)
zoom in to Sag A West (6 cm)
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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?
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stellar orbits
M_BH = 3.7 x 10^6 M_sun
R_Sch = 0.07 AU
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The Halo
stars (distinguished by kinematics and/or chemical abundances)
globular clusters
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Satellite Galaxies
Magellanic Clouds
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sagittarius dwarf
draco