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Surveying the Stars
Properties of Stars
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Our goals for learning
How do we measure stellar luminosities?
How do we measure stellar temperatures?
How do we measure stellar masses?
How do we measure stellar
luminosities?
The brightness of a star depends on both distance and luminosity
Light and Distance
• Light spreads with distance,
expanding outward in a sphere
• The number of photons passing
through each sphere is the same,
but get spread over a larger area
• Thus light gets fainter with
distance
To find the differenceArea of sphere:
4π ( r a d 2 i u s )
Divide luminosity by area to
get brightness
The “Inverse square” law
Luminosity:
Amount of power a star
radiates
(energy per second =
Watts)
Apparent brightness:
Amount of starlight that
reaches Earth
(energy per second per
square meter)
The relationship between apparent brightness and
luminosity depends on distance:
Brightness =
Luminosity
4π (distance)2
We can determine a star’s luminosity if we can measure
its distance and apparent brightness:
Luminosity = 4π (distance)2  (brightness)
Apparent Magnitude
(how bright does
an object seem?)
• Magnitude scale 1st developed
by Hipparchus to compare the
different brightness of stars
• Brightest stars = 1
• Dimmest stars = 6
(designed before invention of
telescopes, so only naked eye
observations initially possible)
So how far are these stars?
Distance Measuring by Parallax
Parallax is the apparent shift in position of a nearby
object against a background of more distant objects
Stellar Parallax: positions of nearest stars
appear to shift as Earth orbits Sun
The amount
of shift
detected,
depends on
the distance
to the stars
Parallax and Distance
Use right-angled
triangles to get
distance
p = parallax angle
1
d  in parsecs  =
sin p  in arcseconds 
The Sun’s
Neighborhood
The distance to
these stars was
measured by
parallax
The Magnitude Scale
m = apparent magnitude ,
M = absolute magnitude
apparent brightness of Star 1
apparent brightness of Star 2
luminosity of Star 1
luminosity of Star 2
= 100
= 100
1/5

1/5

m1 −m
M 1− M
2
2
Stellar Distances
• Once we know the distance to stars by parallax, we can
compensate for the drop in light levels caused by distance.
• We can then see the difference in light levels caused by
differing power output
Most luminous stars: 106 LSun
Least luminous stars: 10-4 LSun
(LSun= luminosity of Sun)
A star can be classified by 'luminosity class'
(line shapes, related to the size of the star)
More luminous stars = more surface area = larger star
I - supergiant
II - bright giant
III - giant
IV - subgiant
V - main sequence
How do we measure stellar
temperatures?
Every object emits thermal radiation with a
spectrum that depends on its temperature
Properties of Thermal Radiation
1. Hotter objects emit more light per unit area at all
frequencies.
2. Hotter objects emit photons with a higher average
energy.
Hottest stars:
50,000 K
Coolest stars:
3,000 K
(Sun’s surface
is 5,800 K)
106 K
105 K
104 K
Ionized
Gas
(Plasma)
103 K
Neutral Gas
102 K
Molecules
10 K
Solid
Level of ionization
also reveals a star’s
temperature
Absorption lines in star’s spectrum tell us ionization level
Lines in a star’s spectrum correspond to a spectral type that reveals its
temperature
(Hottest)
O B A F G K M
(Coolest)
Pioneers of Stellar Classification
• Annie Jump
Cannon and the
“calculators” at
Harvard laid the
foundation of
modern stellar
classification.
Remembering Spectral Types
(Hottest)
O B A F G K M
(Coolest)
• Oh, Be A Fine Girl, Kiss Me
• Only Boys Accepting Feminism Get Kissed
Meaningfully
Remembering Spectral Types
(Hottest)
O B A F G K M
(Coolest)
The letter types also get sub-divided further by numbers 0-9
0=hottest stars within the spectral type
9= coolest stars within the spectral type.
Our Sun, Capella A and Tau Ceti are all G type stars.
Capella A is a G0 , the Sun is a G2, and Tau Ceti is a G8
A star’s full classification includes spectral type
(line identities) AND luminosity class (line
shapes, related to the size of the star):
Examples: Sun - G2 V
Sirius - A1 V
Proxima Centauri - M5.5 V
Betelgeuse - M2 I
How do we measure stellar masses?
Two stars in orbit of each other is called a binary system
•The orbit of a binary star system depends on strength of
gravity
•The gravity between those stars depend on their masses
•This means we can use Newton’s and Kepler’s laws to
calculate the stars’ mass:
2
3
4p a
M 1 + M 2=
G p2
About half of all stars are in binary systems!
Most massive
stars:
100 MSun
Least massive
stars:
0.08 MSun
(MSun is the mass
of the Sun)
What have we learned?
• How do we measure stellar luminosities?
– If we measure a star’s apparent brightness and
distance, we can compute its luminosity with
the inverse square law for light
– Parallax tells us distances to the nearest stars
• How do we measure stellar temperatures?
– A star’s color and spectral type both reflect its
temperature
What have we learned?
• How do we measure stellar masses?
– Newton’s version of Kepler’s third law tells us
the total mass of a binary system, if we can
measure the orbital period (p) and average
orbital separation of the system (a)
Patterns among Stars
• Our goals for learning
• What is a Hertzsprung-Russell diagram?
• What is the significance of the main
sequence?
• What are giants, supergiants, and white
dwarfs?
• Why do the properties of some stars vary?
What is a Hertzsprung-Russell
diagram?
Enjar Hertzsprung (Danish)&
Henry Norris Russell(American)
The H-R Diagram
The H-R Diagram
The H-R Diagram
The H-R Diagram
Large radius
Stars with
higher
luminosity
than mainsequence stars
must have
larger radii:
giants and
supergiants
The H-R Diagram
Stars with
lower
luminosity
than mainsequence
stars must
have smaller
radii:
small radius
dwarfs
Luminosity Classes and H-R
Luminosity class has a clear correlation with the size of the star
H-R diagram
depicts:
Luminosity
Temperature
Color
Spectral
Type
Luminosity
Radius
Temperature
C
B
Which star
is the
hottest?
Luminosity
D
A
Temperature
C
B
Which star is
the most
luminous?
Luminosity
D
A
Temperature
C
B
Which star is a
main-sequence
star?
Luminosity
D
A
Temperature
What is the significance of the
main sequence?
Main-sequence stars
are fusing
hydrogen into
helium in their
cores like the Sun
Luminous mainsequence stars are
hot (blue)
Less luminous
ones are cooler
(yellow or red)
High-mass stars
Low-mass stars
Mass
measurements of
main-sequence
stars show that the
hot, blue stars are
much more
massive than the
cool, red ones
Core pressure and
temperature of a
higher-mass star
need to be larger
in order to balance
gravity
Higher core
temperature
boosts fusion rate,
leading to larger
luminosity
Stellar Properties Review
Luminosity: from brightness and distance
10-4 LSun - 106 LSun
Temperature: from color and spectral type
3,000 K - 50,000 K
Mass: from period (p) and average separation (a)
of binary-star orbit
0.08 MSun - 100 MSun
What have we learned?
• What is a Hertzsprung-Russell diagram?
– An H-R diagram plots stellar luminosity of stars
versus surface temperature (or color or spectral
type)
• What is the significance of the main
sequence?
– Normal stars that fuse H to He in their cores fall
on the main sequence of an H-R diagram
– A star’s mass determines its position along the
main sequence (high-mass: luminous and blue;
low-mass: faint and red)
Mass & Lifetime
Sun’s life expectancy: 10 billion years
Mass & Lifetime
Sun’s life expectancy: 10 billion years
Life expectancy of 10 MSun star:
10 times as much fuel, uses it 104 times as fast
10 billion years x 10 / 104 ~ 10 million years
Mass & Lifetime
Sun’s life expectancy: 10 billion years
Life expectancy of 10 MSun star:
10 times as much fuel, uses it 104 times as fast
10 billion years x 10 / 104 ~ 10 million years
Life expectancy of 0.1 MSun star:
0.1 times as much fuel, uses it 0.01 times as fast
10 billion years x 0.1 / 0.01 ~
100 billion years
Main-Sequence Star Summary
High Mass:
High Luminosity
Short-Lived
Large Radius
Blue
Low Mass:
Low Luminosity
Long-Lived
Small Radius
Red
How do we Measure Stellar Diatances?
Based on our knowledge of star behavior, we can observe
the spectra of stars then calculate their properties,
including luminosity.
We can take a star, calculate its
luminosity, then the difference
between this and the star's
observed brightness, must be
caused by distance.
Stellar Distances
We now know both luminosity and apparent brightness,
we can re-use the inverse square law
Distance =
Using the H-R diagram this
way is called Spectroscopic
Parallax.
Stellar Distances
Stellar Mass
Distribution
What are giants, supergiants, and
white dwarfs?
Off the Main Sequence
• Stellar properties depend on both mass and age: those
that have finished fusing H to He in their cores are no
longer on the main sequence
• All stars become larger and redder after exhausting
their core hydrogen: giants and supergiants
• Most stars end up small and white after fusion has
ceased: white dwarfs
A
Luminosity
D
B
C
Temperature
Which of these
stars will have
changed the least
10 billion years
from now?
A
Luminosity
D
B
C
Temperature
Which of these
stars can be no
more than 10
million years old?
What have we learned?
Why is a star’s mass so important?
– A star’s mass controls how fast it consumes fuel.
– High mass stars are short-lived, low mass stars are
long-lived
– Over 70% of stars are less than the mass of our Sun
How do we measure stellar distances?
– A star's luminosity can now be estimated by it's
spactral type and main-sequence postion.
– The luminosity and measured brightness can be
combined to calculate the star's distance.
– This technique is Spectroscopic parallax
What have we learned?
What are giants, supergiants, and white dwarfs?
– All stars become larger and redder after core hydrogen
burning is exhausted: giants and supergiants
– Most stars end up as tiny white dwarfs after fusion
has cease
Star Clusters and the HR Diagram
Our goals for learning:
• What is a star cluster?
• How do we find the distance to a star cluster?
• How do we measure the age of a star cluster?
What is a star cluster?
A group of stars
clustered together,
because they are formed
from the same initial gas
cloud.
The stars were formed at
about the same time, so
have about the same age
and distance from Earth.
How do we find the distance to a star
cluster?
The stars of the
cluster will have
different luminosities.
So they will fall on
the line of main
sequence.
The light falls off
with distance, so the
cluster has an
apparent brightness.
The apparent
brightness of a
star cluster’s
main sequence,
compared to the
true main
sequence line
tells us its
distance.
This technique is
called Main
Sequence Fitting
main sequence
fitting and
spectroscopic
parallax are both
'Standard Candles'
A standard candle is
an object whose
luminosity we can
determine without
needing to
measuring its
distance first.
How do we measure the age of a
star cluster?
Massive blue
stars die first,
followed by
white, yellow,
orange, and
red stars.
-The age of a
cluster can be
first recognized
by its color!
When stars
start to die,
they leave the
main
sequence.
The shortlived ones do
so first, the
longer-lived
stars remain on
the main
sequence.
This cluster
now has no
stars with life
expectancy
less than
around 100
million years.
Thus, the
cluster must
be over 100
million years
old.
The mainsequence
turnoff point
of a cluster
tells us its
age.
This cluster
has lost it's
yellow sunlike stars, so
it must be
about 12-13
billion years
old.
What have we learned?
• What is a star cluster?
A groups of stars with similar age and distance.
• How do we measure the distance to a star cluster?
‒A cluster’s main sequence line will fall below where it
should be, because it has dimmed with distance
• How do we measure the age of a star cluster?
A star cluster’s age roughly equals the life expectancy of its
most massive stars still on the main sequence