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Milky Way Galaxy
Dr. Bill Pezzaglia
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Updated: Nov 25, 2012
Milky Way
A. Star counts
B. Core and Arms
C. Galaxy Rotation
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A1a. Milky Way
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A1b. Milky Way: Galactic Equator
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2a. Galileo
Galilei
(1564-1642)
Galileo was one of the
very first scientists to
do experiments to
understand Nature
He was the first
astronomer to use a
telescope (in 1610)
to study the sky.
Sees that the Milky
Way is made of stars
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A1c. 1750 Thomas Wright
Milky Way is thin shell of stars, which
explains why we see a band across the sky.
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A1c. 1784 Herschel’s Telescope
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20 year study of 2400 regions
of sky (maps over 90,000 stars)
A1c. The Galactic Equator
1784 Herschel’s Star Gauging
•Counts stars in 683 regions
•Estimates universe is disk shaped
•Diameter is 5 times thickness
•Sun appears to be at the center
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A1c. Kapteyn Universe
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1897 measured that stars
move (rotate around universe)
(Parsec=3.26 light years=200,000 x distance to sun)
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Magnitude Distance Relation
• Objects further away look fainter
• If the star is too far away, it will be
fainter than our limiting magnitude and we
won’t see it.
• Assume at 10 parsecs an average star
has (absolute) magnitude of M=+2.5
• Every factor of 10 in distance it gets 5
magnitude fainter
m  M  5Log D/10 
Distance
(parsecs)
magnitude
10
2.5
32
5
100
7.5
316
10
1000
12.5
3162
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Space Penetrating Power
Turn this idea around. From the
limiting magnitude of our telescope,
we can estimate how “deep” we are
penetrating into the galaxy.
We need to see deeper than 500
parsecs to be able to see the
thickness of the Milky Way.
Limiting
Magnitude
Distance
(parsecs)
2.5
10
5
32
7.5
100
10
316
12.5
1000
15
3162
m/5
D  10  10
m  m  M
Counting Stars
The number of stars “N” seen in a field of view
of “” as a function of the “depth” we see into
space (“space penetrating power) assuming
constant density :
N  V
Log ( N )  Log

1
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 2   3Log ( D )
If density is constant, expect plot of log of star
count vs log of distance to have a slope of 3
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Stars vs Magnitude
Since magnitude is proportional to 5 times log
of distance, expect plot of log count vs
magnitude to be a line with slope of 0.6 :
Log ( N )  b  Log ( D )
3
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This assumes density of stars is constant.
Assume we live in a BIG spherical ball of
stars. Count ALL the stars we can see for
entire sky,
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3a Number of Stars by Magnitude
•There are only about 15 bright (first magnitude and brighter) stars
•There are only about 8000 stars visible to naked eye
•There are much more stars with higher magnitude!
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3b Number of Stars by Magnitude
Stellar Counts
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y = 0.4914x + 0.9204
R² = 0.9958
Log(Cumulative count)
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4
3
2
1
0
-2
0
2
4
Limiting Magnitude
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All visible stars up to m=+8.5
If a ball of stars expect slope of 0.6
If a thin disk of stars expect slope of 0.4
Our data is smack dab in the middle of the two.
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Sample in Milky Way
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Samples in Milky Way
Log of Count (unknown field size)
3.5
y = 0.442x - 2.9778
R2 = 0.9935
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2.5
2
1.5
1
0.5
0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
-0.5
Limiting Magnitude
If we sample a region of the sky along the Milky Way, we get a slope close to what
we expect for living in a “disk” of stars.
Sample far from Milky Way
Star Counts Centered on Arcturus from Starry Night
Program
Log of Star Counts per 90' field
2.5
y = 0.2442x - 1.2763
R2 = 0.9647
2
1.5
1
0.5
0
0
2
4
6
8
10
12
14
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-0.5
Limiting Magnitude
If we sample a region of the sky perpendicular to the Milky Way, we get a much
lower slope (closer to ¼ ) which implies we are seeing “out of the disk”.
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Galactic Longitude
View looking
down on disk
of galaxy
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Galactic Latitude
Side view of galaxy
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Galactic Coordinate of Some Stars
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What we should see
• Space penetration power “D” is furthest distance can see
with our telescope
• As galactic latitude “” increases, we hit the border of
disk of stars, so see less stars.
• Least number of stars seen at galactic pole
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Observational Data: as a Bar Graph
Galactic Star Counts
Average Number of Stars per Field
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28
25
20
15
13
10
8
5
2.3
2.95
1
0
7.5
22.5
37.5
52.5
Galactic Latitude
67.5
82.5
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Data: Line Graph
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Galactic Star Counts
Average Number of Stars per Field
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y = 35.33e-0.04x
R2 = 0.94
25
20
15
10
5
0
0
20
40
60
Galactic Latitude
80
100
The data can
be fitted with a
nice
exponential
decaying
formula. In fact
it’s a very good
fit (perfect
would have an
Rsquared
value of 1).
Thickness of Galaxy
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Calculate it from the ratio of counts of stars at
pole and at equator (assume D=1000 pc)
Galactic Star Counts
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 2(1000)
N0
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 658 parsecs
1
28
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Average Number of Stars per Field
T  2D
Np
28
25
20
15
13
10
8
5
2.3
2.95
1
0
7.5
22.5
37.5
52.5
67.5
82.5
Galactic Latitude
N0
Np
2c. Interstellar Reddening
Note NGC3603 (left) is more red than NGC3576
(right) because it is twice as far away. Short
wavelength Blue light is absorbed more than Red
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Extinction of Light
•There is a lot of gas and dust in the galaxy
•This absorbs light (1 magnitude per 1000 parsecs)
•Makes stars look fainter
•Hence we think they are further away than they really
are. Causes us to overestimate distances
•First measurements of the Milky Way (1920s) was
hence 10x bigger than it really is due to this error!
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Corrected Space Penetration
Limiting Magnitude vs Space Penetration Power
24.0
22.0
20.0
18.0
14.0
12.0
10.0
8.0
absorption 1 mag/kpc
6.0
no absorption
4.0
2.0
Distance in Parsecs
6500
6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0.0
0
Magnitude
16.0
Globular Cluster of Stars
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A2a. Shapley Core (1914-17)
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•Postulates globular clusters orbit galactic core
•More in direction of Sagittarius
•Estimates core is 15kpc away from sun (error: its 9 kpc)
Overestimated
distances,
because did not
know about
absorption of light
by galactic dust
A1c. Robert Trumpler
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1930 (Lick Observatory)
shows that there is dust in
the galaxy which absorbs
light.
Hence, clusters appear
fainter, and more distant
than they actually are.
Shapley’s size of universe is
40% too big!
A2b. The Central Bulge
Central Bulge is 4kpc in size, with a small 5 pc bright radio
source “Sagittarius A”, also bright in the IR (see below)
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A2c. Black Hole?
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In the center of the 5 pc Nucleus is
an X-Ray source smaller than 100 AU
Recent measurements of orbits of
stars around this core imply that
there is a 2.6 million solar mass black
hole!
http://en.wikipedia.org/wiki/File:A_Black_Hole%E2%80
%99s_Dinner_is_Fast_Approaching_-_Part_2.ogv
A3a. Mapping Spiral Arms (1960)
• 1944, Hendrik van de Hulst predicted Neutral
Hydrogen gas will emit a 21 cm “spin flip”
spectral line
• 1951 First Observed with radio telescope
• 1960 Used to map spiral arms of our galaxy
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A3b. Our place in the Galaxy
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A3c. Rotations of Galaxies
•Spiral Galaxies Rotate Slowly
•Sun takes 226 million years to go around
(220 km/sec or 1 AU in 8 days)
•The rotation speed
can be measured by
the Doppler effect on
the 21 cm radio line
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A3d. The “Winding Dilemma”
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Outer stars move
slower.
Why haven’t the spiral
arms wound up and
disappeared a long
time ago?
A3e. The “Winding Dilemma”
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A3f. Density Wave Theory
Bertil Lindblad
1925 Shows stars further from center
of galaxy should move slower due
to weaker gravity
1927 Jan Oort proves this with
observations
1940 Lindblad Proposes “density
wave theory” to explain spiral arms
(resolve the winding paradox)
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A3f. Density Wave Theory
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A compression wave through the galaxy causes stellar birth;
the bright short-lived O,B stars show the crest of the wave.
A3f. Density Wave Theory
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A3f. Emission Neb in M51
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This shows stellar formation
In in the spiral arms (where
Density waves bunch up matter
A3f. Emission Nebulae
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Red is ionized hydrogen gas
Emission nebulae are where stars
have recently formed.
Addenda: Rotation of Galaxies
A. The way galaxies should rotate
B. Galaxies rotating too fast
C. Theory of “dark matter”
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A4a. Rotation Curves
•Assuming most of mass of galaxy is in the core
•Velocity of a Star predicted by Newton’s Gravity:
V2/R = GM/R2
•Or:
V  1/R
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A4b. Rotating Rong?
•1980 Vera Rubin shows rotation
curves of galaxies are nearly constant!
•Implies a lot of “missing” (dark) matter
surrounds galaxies.
Pivotal Paper:
Rotational Properties of 21 Sc Galaxies with
a Large Range of Luminosities and Radii
from NGC 4605 (R=4kpc) to UGC 2885
(R=122kpc)," Astrophys. J. 238: 471 (1980),
V.C. Rubin, W. K. Ford, Jr. and N. Thonnard.
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A4c. What IS Dark Matter?
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•MACHOs (Massive Compact
Halo Objects) were looked for:
•White Dwarfs
•Brown Dwarfs
•Black Holes
•But its not enough!
•WIMPs (Weakly Interacting Massive Particles):
Must propose exotic things like a neutrino, but
with BIG mass (10 to 10,000x that of proton).
Even though 96% of the universe is made of it,
not a single piece of it is in this room.
•Or maybe there is something wrong with our theory of gravity?
REFERENCES
B Carroll and D. Ostlie, “An Introduction to Modern Astrophysics” (Addison-Wesley,
1996), Chapter 22
http://en.wikipedia.org/wiki/Supermassive_black_hole
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