Download Chapter 11: Stars

Chapter 11: Stars
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Fundamental Properties of Stars
• Luminosity
• Surface Temperature
• Mass
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The brightness of a star depends on
both its distance and luminosity
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Luminosity:
Amount of power a
star radiates.
Expressed in units of
energy per second
(e.g. Watts)
Apparent
brightness:
Amount of starlight
that reaches Earth
Expressed in energy per
second per surface area
(e.g. Watts/sq. meter).
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Relationship between
luminosity and apparent brightness
• Luminosity passing
through each
imaginary sphere is
the same.
• Area of sphere =
4π (radius)2
• Divide luminosity by
area to get brightness.
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Relationship between
luminosity and apparent brightness
Brightness =
Luminosity
4π (distance)2
This is the inverse square law for light.
Can use this to determine a star’s luminosity:
Luminosity = 4π (distance)2 x (Brightness)
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QUESTION: How would the apparent
brightness of Alpha Centauri change if
it were three times farther away?
A.
B.
C.
D.
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It would be only 1/3 as bright
It would be only 1/6 as bright
It would be only 1/9 as bright
It would be three times brighter
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QUESTION: How would the apparent
brightness of Alpha Centauri change if
it were three times farther away?
A.
B.
C.
D.
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It would be only 1/3 as bright
It would be only 1/6 as bright
It would be only 1/9 as bright
It would be three times brighter
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• We observe the apparent brightness of stars.
• To determine the luminosities (total energy output per
second), we need to know the distances to stars.
• How do we measure the distances to stars?
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Parallax = apparent motion of an object relative to
the background due to change in viewing positions.
More distant stars have smaller parallaxes.
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Units of stellar distances
• d = 1/p (for very small angles p)
• 1 parsec is distance when parallax
angle (p) is measured in arcseconds
• 1 parsec = 3.26 light years
Example: a star with p = 1/10 arcsec, is d
= 10 parsecs away, or 32.6 light years
away.
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Parallax
Parallax
is the apparent
shift in position
of a nearby
object against a
background of
more distant
objects.
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Parallaxes of the nearest stars
Apparent
positions of the
nearest stars
shift by about
an arcsecond as
Earth orbits the
Sun.
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Parallax Angle as a Function of Distance
Parallax
angle is
directly
proportional
to distance.
More
distant stars
have
smaller
parallaxes.
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Measuring Parallax Angle
Parallax is
measured by
comparing
snapshots
taken at
different
times and
measuring
the shift in
angle to star.
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There is a large spread in
stellar luminosities.
Use the luminosity of the
Sun LSun as a reference
Most luminous stars:
~106
LSun
Least luminous stars:
~10-4
LSun
(Lsun = Sun’s luminosity)
Factor of 10 billion spread.
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How hot are the stars?
• Every object emits
thermal radiation:
Hotter objects emit
more light at shorter
wavelengths (bluer
colors).
• So by measuring the
colors of stars, we
can determine their
surface temperature.
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Measuring a star’s surface T
• Astronomers measure the surface
temperature because the interior
temperature can only be inferred from
models.
• Surface T is easier to measure than its
luminosity because it does not depend
on distance.
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Two Properties of Thermal Radiation
Hotter objects emit more light at all wavelengths per unit area.
Hotter objects emit photons with a higher average energy (bluer).
Relative intensity
per unit area
•
•
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Hottest stars:
50,000 K
Coolest stars:
3,000 K
The Sun:
5,800 K.
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(All these
temperatures
refer to the
star’s surface.)
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Luminosity of an object depends both
on its size and temperature
• An object of fixed size
grows more luminous
as temperature rises.
• An object of fixed
temperature grows
more luminous as it
gets bigger.
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The types of absorption lines in a star’s spectrum
also tell us about its temperature.
(Hot interior emits a continuous spectrum,
which is partly absorbed by the cool outer layers.)
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106 K
105 K
104 K
Ionized
Gas
(Plasma)
103 K
Neutral Gas
102 K
Molecules
10 K
Solid
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The level of
ionization
depends on a
star’s surface
temperature.
Therefore, stars
of different
temperatures will
show different
absorption lines
in their spectra.
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Spectral type = classification of stellar
spectra based on the absorption lines
(hence, another way of determining stellar temperature)
Examples
O
Rigel
B
Sirius
A
Polaris
F
Sun, Alpha Centauri
A
G
Arcturus
K
Betelgeuse, Proxima
M
Centauri
Stars of Orion’s Belt
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30,000 K
20,000 K
10,000 K
7,000 K
6,000 K
4,000 K
3,000 K
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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”
• Spectral classes are further broken down into sub-classes,
numbered from 0 to 9 (warmer to cooler). For example, the
Sun is a G2 star, meaning it is warmer than a G5 star.
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QUESTION: Which kind of star is hottest?
A.
B.
C.
D.
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M star
F star
A star
K star
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QUESTION: Which kind of star is hottest?
A.
B.
C.
D.
M star
F star
A star
K star
“Oh, Be A Fine Girl, Kiss Me”
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Pioneers of Stellar Classification
Annie Jump
Cannon and
the
“calculators” at
Harvard laid
the foundation
of modern
stellar
classification.
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Pioneers of Stellar Classification
Williamina Fleming (1857-1911) classified stellar spectra according to the
strength of their hydrogen lines: A strongest, B slightly weaker, and O for
the weakest. She classified more than 10,000 stars, which Pickering
published in 1890.
Annie Jump Cannon joined Pickering’s group in 1896. Building on the
work of Fleming and Antonia Maury, she realized that the spectral
classes fell into a natural order – but not the alphabetical order
determined by hydrogen lines alone.
She also found that some of the original classes overlapped others and
could be eliminated.
She discovered that the natural sequence was OBAFGKM. She added
subdivisions by number.
Jump Cannon personally classified 400,000 stars.
In 1925, Cecilia Payne-Gaposchkin showed that the differences in
spectral lines from star to star reflected changes in the ionization of the
emitting atom. She published her findings in her doctoral thesis.
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How do we
determine the
masses of stars?
Use binary stars
(pairs of stars held
together by gravity).
About ~1/2 of all stars
are binaries.
Relative sky positions of Sirius A & B over 70 years
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We measure mass using gravity
(Newton’s version of Kepler’s
Third Law).
Direct mass measurements are
possible only for stars in binary
star systems
3
a
p
p22=
=
a3
G (M(M
+ M+M
)
2)


2
 4π2 


 G 



 1
4π
Isaac Newton
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2
p = period
a = average separation
M1, M2 = mass of the 2 stars
We measure the binary’s period
and separation to get the sum of
the stellar masses.
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