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Our Galaxy
The Milky Way
Credit & Copyright Barney Magrath
History of Understanding: The
Milky Way
• Milky Way – bright band of light across sky
• Galileo
– First to use telescope to study MW
– Found it was made of millions of faint stars
• What is the Milky Way?
– Thomas Wright (1750) suggested that solar system was embedded
in enormous shell of stars…
– Emmanuel Kant (1755) realized that the MW is a giant disk of
stars
– Kant also hypothesized that space was full of other, similar disks
of stars.
• Nebulae
– Fussy blobs in the sky
– First systematically catalogued by Messier
– Messier was mainly interested in comets…
Credit : A. Dimai
• What were Messier’s objects?
• Possibilities…
– Glowing clouds of gas in between the stars
– Large collections of stars in our own Galaxy
– Whole other galaxies
• Turns out that all of these possibilities are
represented…
The Orion Nebula (M42)
Glowing gas
cloud
Andromeda “Nebula” (M31)
Another galaxy…
The Nature of Fuzzy Objects
• But, this was vigorously debated in early 1900s…
• The Great Debate (1920)
– NAS – downtown DC
– Debate between Harlow Shapley and Heber Curtis
– Shapley argued for nebula all being local (i.e. within the Milky
Way)
– Curtis argued for “island universe” hypothesis (i.e., there are many
islands of stars like the Milky Way in the universe)
• Really need a good distance indicator to solve the
problem…
Coordinate Systems
Regions of the Milky Way Galaxy
radius of disk = 50,000 l.y. (20 kpc)
thickness of disk = 1,000 l.y. (300 pc)
number of stars = 200 billion
Sun is in disk,
8kpc out from
center
Spherical Galactic Coordinates, l, b
• Coordinate system centered on
Sun
• Galactic Plane is plane in which
most of material lies
• Galactic coords, l, b are angular
coords on sphere
• b is Galactic latitude, angular
dist of source from Gal plane
• b=0 defines a circle on the
Galactic disk
Spherical Galactic Coordinates, l, b
• l is Galactic longitude 0360o
• b=0 defines a circle on the
Galactic disk
• l,b only define where
something appears on the
sky, to define actual
position we also need
distance from Sun
Cylindrical Galactic Coordinates, R,,z
• 3-D system with Gal
center at origin
• R dist from Gal center
• z height above disk
•  is angle from the SunGal Center line
• Dist of object from Gal
center is
R2  z 2
Distance Determination within
Milky Way
• Need distances of objects to:
• Map out galaxy in 3-D
• Understand physics of some sources
Measuring Distances to Stars
Trigonometric parallax – apparent wobble of a star
due to the Earth’s orbiting of the Sun
p
D
r
Measuring Distances to Stars
From math on the triangle we can get
r/D = tan p  p
If parallax angle p is in radians
Parallax also used to define the parsec (pc) as the
distance of a hypothetical source for which p=1”
D = (p/1”)-1 pc
Measuring Distances to Stars
From math on the triangle we can get
r/D = p
If parallax angle p is in arcsec and distance D is in
parsecs
A star with a parallax of 1 arcsec is 1 parsec distant
1 parsec  206,265 A.U.
= 3.26 light years
Measuring Distances to Stars
Practical limit on how small an angle can be
measured - ground based obs can measure
distances out to 30 pc
Using the HIPPARCOS satellite got past some
limitations extending use of method to 300 pc
GAIA will extend the range of the method by
another factor of ~5
Proper Motion
• Star velocities can be handled component
by component

• Radial
v>0 motion away
v
c
from us

• ‘Proper motion’ is denoted  and measures
angular velocity, a tangential vector, ie
change in position of star against backdrop
(separate from parallax) typically mas/yr
• Earth/Sun is a moving frame of reference
that needs to be corrected for - heliocentric
velocity
Main Sequence Fitting
•
The further a star is from you, the dimmer it appears.
Bright stars are close, and faint stars are farther away. This
simple idea would work perfectly if all stars had the same
intrinsic brightness. They don't.
Main Sequence Fitting
•
Studying stars en masse has taught us hot stars
are very luminous and cool stars are relatively
dim, so star temperature/color tell us something
about luminosity…and hence distance
• So measure stellar temperature-get intrinsic lum,
use inverse square law and apparent luminosity to
get distance
Flux = L / 4d
2
Star Clusters
• What are the two major types of star cluster?
• Why are star clusters useful for studying stellar
evolution?
• How do we measure the age of a star cluster?
Open Clusters
•
•
•
•
100’s of stars
106 - 109 years old
irregular shapes
gas or nebulosity is
sometimes seen
Pleaides (8 x 107 yrs)
Globular Clusters
• 105 stars
• 8 to 15 billion years
old (1010 yrs)
• spherical shape
• NO gas or nebulosity
M 80 (1.2 x 1010 yrs)
Clusters are useful for studying
stellar evolution!
• all stars are the same distance
• use apparent magnitudes
• all stars formed at about the same time
• they are the same age
Plot an H-R Diagram!
Pleiades H-R Diagram
Globular Cluster
H-R Diagram
Palomar 3
Cluster H-R Diagrams Indicate Age
• All stars arrived on the MS at about
the same time.
• The cluster is as old as the most
luminous (massive) star left on the
MS.
• All MS stars to the left have already
used up their H fuel and are gone.
• The position of the hottest, brightest
star on a cluster’s main sequence is
called the
main sequence
turnoff point.
Older Clusters have Shorter Main Sequences
Main Sequence Fitting
• In reality the stars age affects luminosity too, so want to
take account of that
• Plot HR diagram for the cluster
• Determine age from main sequence cut-off point
• Correct stellar luminosities to be as though they were in
zero-age stars
• Then slide cluster main sequence until it overlays
calibrated “zero-age main sequence” -the amount of
luminosity shift gives the distance
(App. Brightness) Flux = L / 4d
2
Recap: Magnitude System
apparent magnitude
= -2.5 log (app bright)
• brightness of a star as it appears from Earth
• each step in magnitude is 2.5 times in
brightness
absolute magnitude
• the apparent magnitude a star would have
if it were 10 pc away
Main Sequence Fitting
• Often magnitudes are used instead of flux/luminosity
m-M = 5 log (D/pc) - 5
m is the apparent magnitude
M is the absolute magnitude
Astronomical Dust
dust grains:
Not the dust one finds around the house, which is typically
fine bits of fabric, dirt, or dead skin cells!!
Interstellar dust grains are much smaller clumps, on the
order of a fraction of a micron across, irregularly shaped,
and composed of carbon and/or silicates. Dust is most
evident by its absorption, causing large dark patches in
regions of our Milky Way Galaxy and dark bands across
other galaxies.
The exact nature and origin of interstellar dust grains is
unknown, but they are clearly associated with young stars
Extinction & Reddening
• So extinction by dust gives a color change in the stellar
spectrum, consider specific intensity I at freq v for
material with abs coefficient  (absn coeff has unit of
1/length)
dI v
  v I  jv
ds
Over distance ds a fraction v ds
of photons of freq v are
scattered/absorbed
d I
d ln I 
  v ds
I
Integrate from 0 to s
s
ln I v (s)  ln I v (0)    ds ' v (s ')   v (s)
0
s
ln I v (s)  ln I v (0)    ds ' v (s ')   v (s)
0
• where tv is the optical depth, that depends on
frequency
  v (s)
• This reduces to
I v (s)  I v (0)e
specific intensity is reduced by factor e
compared to the case of no absorption
 v
Exactly the same for flux (ie integrated over
all directions for isotropic source)
Flux
I (s)  I (0)e
  v (s )
S (s)  S (0)e
  v (s)
m  2.5 log S  constant
Recall the relation between flux and magnitude
m  2.5 log S  constant
S 10
-0.4m
Sv
m m
m )
-0.4(m
0
 10
 e v  10 log(e) v
Sv,o
0
m
the apparent magnitude
m0
the apparent magnitude without absorption
Sv
-0.4(m m0 )
 v
 log(e) v
 10
 e  10
Sv,o
Thus can also define an extinction coefficient that describes
change of apparent magnitude due to absorption
Sv
Av  m  m0  2.5 log
Sv0
 2.5 log(e) v  1.086 v
Frequency dependence of extinction means it changes spectral
color, and thus often described in terms of the ratio of amounts of
flux in different frequency ranges
Av is the extinction coefficient that describes change of
apparent magnitude due to absorption
Sv
Av  m  m0  2.5 log
Sv0
Absorption always linked to a color change in the stars spectrum,
this is described by the color excess (CE)
So color excess defined as:
E(X  Y )  AX  AY  (X  X0 )  (Y  Y0 )  (X  Y )  (X  Y )0
AX
AY
Ratio depends on physical properties of dust
AY
E(X  Y )  AX  AY  AX (1 
)  AX RX 1
AX
Nicely separated out a factor of proportionality between extinction
coefficient and the color excess -depends on ‘colors’ considered
and the composition of the dust in the system
Blue (B) and visual (V) common colors used in astronomy so
commonly see Av = Rv E(B - V)
Av = (3.1+/-0.1) E(B - V)
D
Av  1mag
1kpc
for the dust in the Milky Way
in the neighborhood of the Sun
Color-Color Diagram
• Sometimes color ‘differentials’
are plotted, like (U-B) v (B-V)
• The relative suppression of the
two bands depends on dust
composition (assume known)
• Then we see how big the shift is
to estimate extinction
• m-M = 5 log (D/pc) - 5 + A
Distance determination
• Another way to get distance (or mass)
…..track a binary star system
Reminder: Newton’s version Kepler’s 3rd Law
• Consider isolated system of 2 bodies mass m1, m2
orbiting at distances r1, r2 from mutual center of gravity
• Bodies complete one orbit in same period, P
• Centripetal force F = mv2/r
Reminder: Centripetal Force
• The centripetal force is the external force required
to make a body follow a circular path at constant
speed
• The force is directed inward, oriented toward the
axis of rotation (force which is directed outward is
centrifugal force)
• Centripetal force is a force requirement, not a
particular kind of force. Any force (gravitational,
electromagnetic, etc.) can act as a centripetal force
Reminder: Newtonian physics
• Consider isolated system of 2 bodies mass m1, m2 orbiting at distances
r1, r2 from mutual center of gravity
• Bodies complete one orbit in same period, P, vel in orbit=2r/P
• Centripetal forces of the orbits are:
F1=m1v12/r1=42m1r1/P2 (1)
F2=m2v22/r2=42m2r2/P2
Reminder: Newtonian physics
F1=m1v12/r1=42m1r1/P2
(1)
F2=m2v22/r2=42m2r2/P2
• Newton’s 3rd Law has F1= F2 giving
r1/ r2=m2 /m1 more massive body orbits closer to center of mass
separation of two bodies a= r1+ r2 which gives us
r1=m2 a/(m1 + m2)
(2)
Mutual gravitational force F=G m1 m2 / a2
(3)
Combine 1,2,3 ->
P2=42 a3 /G(m1 + m2)
Distances of Visual Binary Stars
2
4

P2 
a3
G(m1  m2 )
Keplers 3rd law
• Period, p, and apparent orbit
diameter (a is semi-major axis)
are direct observables
• orbit may be inclined to sightline
• If know masses can get true
separation, a
• True versus apparent
separation gives distance
Cepheid Variables
She studied the
light curves of
variable stars in
the Magellenic
clouds.
Same distance
Henrietta Leavitt
(1868-1921)
Cepheid Variables
The brightness of the stars varied
in a regular pattern.
Cepheid Variables
prototype:  Cephei
F - G Bright Giants (II) whose
pulsation periods (1-100 days) get
longer with increased luminosity
Distance Indicator!!
Cepheid Variables
Recap: Luminosity of Stars
Luminosity – the total amount of power radiated by a star into space.
Flux = L / 4d
2
The Instability Strip
There appears to be an
almost vertical region on
the H-R Diagram where
all stars within it (except
on the Main Sequence)
are pulsating and
variable.
Distances of pulsating stars
Pulsations -radial density waves propagating with speed of
sound, cs
Period comparable to sound-crossing time P~ R/ cs
Speed of sound ~ thermal vel of gas particles so
kBT~mp
cs2 (mp is the mass of a proton, ie characteristic mass of
particles in the stellar plasma; kB is Boltmann’s constant)
Virial Theorem - gravitational binding energy of the star is
twice the kinetic (thermal) energy ->
Distances of pulsating stars
Virial Theorem - gravitational binding energy of the star is
twice the kinetic (thermal) energy -> k.e.=1/2 m v2 twice
k.e. is thus mp cs2
GMm p
R
Use kBT~mp cs2
: kBT
R R mp
P:
:
:
cs
K BT
3
2
1

R
 2
GM
Pulsation period depends only on mean density

Distances of pulsating stars
R R mp
P:
:
:
cs
K BT
3
2
1

R
 2
GM
Pulsation period depends only on mean density
Also know L M3 and L  R2T4 so
3
2
7
12
R
P
L
M

Metallicity
In astrophysics all elements heavier than H, He are called
metals
These elements, with the exception of traces of Li, were not
formed in the big bang, but rather in stellar interiors
Often the abundance of an element is defined scaled to
abundances in the Sun and one can use a metallicity index
that compares the log of the ratio of element X to Hydrogen
in the star, and in the Sun, ie:
Metallicity Index
X
n(X)
n(X)
[ ]  log(
)*  log(
)
H
n(H )
n(H )
Metallicity
X
n(X)
n(X)
[ ]  log(
)*  log(
)
H
n(H )
n(H )
where n is the number density of the species
[Fe/H]=-1 means Fe is at 1/10 solar abundance
Metallicity, Z defines the mass fraction of ALL elements
heavier than helium
The Sun has Z  0.02 - means 98% of mass of Sun is H plus
He