Download 1 How luminous are stars?

How luminous are stars?
Luminosity passing
through each sphere is
the same
Luminosity:
Amount of power a star
radiates
(energy per
second=Watts)
Area of sphere:
4π (radius)2
Apparent brightness:
Amount of starlight that
reaches Earth
Divide luminosity by area
to get brightness
(energy per second per
square meter)
The brightness of a star depends on both distance and luminosity
So how far are these stars?
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 x (Brightness)
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Parallax
is the apparent shift in position of a nearby object against
a background of more distant objects
Most luminous
stars:
106 LSun
Least luminous
stars:
p (arcsec) = 1/d(AU)
How hot are stars?
Every object emits thermal radiation with a
spectrum that depends on its temperature
10-4 LSun
Shift is
measurable
for nearest
stars only
(LSun is luminosity
of Sun)
Laws of Thermal Radiation
1) Hotter objects emit more light at all wavelengths
2) Hotter objects tend to emit light at shorter wavelengths and
higher frequencies
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Hottest stars:
50,000 K
106 K
105 K
Coolest stars:
3,000 K
(Sun’s surface is
5,800 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
Lines in a star’s spectrum correspond to a spectral type that reveals its
temperature
(Hottest)
O B A F G K M
(Coolest)
This is a high-resolution spectrum of one star.
Absorption lines in star’s spectrum tell us ionization level
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Remembering Spectral Types
(Hottest)
O B A F G K M
(Coolest)
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Meaningfully
Thought Question
Thought Question
Which kind of star is hottest?
A.
B.
C.
D.
M star
F star
A star
K star
How massive are stars?
Which kind of star is hottest?
A.
B.
C.
D.
M star
F star
A star
K star
The orbit of a binary star system depends on strength of gravity
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The Center of Mass
Binary Stars
More than 50% of all stars
in our Milky Way are not
single stars, but belong to
binaries:
center of mass =
balance point of the
system.
Pairs or multiple systems
of stars which orbit their
common center of mass.
Both masses equal =>
center of mass is in the
middle, rA = rB.
The more unequal the
masses are, the more it
shifts toward the more
massive star.
If we can measure and
understand their orbital
motion, we can estimate
the stellar masses.
Isaac Newton
We measure mass using gravity
Direct mass measurements are
possible only for stars in binary
star systems
p2 =
aAU3
____
MA + MB =
Py2
4π2
G (M1 + M2)
p = period
a3
a = average separation
Need 2 out of 3 observables to
measure mass:
v
1)  Orbital Period (p)
2)  Orbital Separation (a or r=radius)
3)  Orbital Velocity (v)
For circular orbits, v = 2πr / p
r
M
Usually we don’t know inclination, so mass estimate is
uncertain:
(M1 + M2) = (a’/sin i)3/P2
(MA and MB in units of solar masses)
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Types of Binary Star Systems
Visual Binary
•  Visual Binary
•  Eclipsing Binary
•  Spectroscopic Binary
About half of all stars are in binary systems
Visual Binaries
We can directly observe the
orbital motions of these stars
Eclipsing Binary
The ideal case:
Both stars can be seen
directly, and their
separation and relative
motion can be followed
directly.
We can measure periodic eclipses
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Eclipsing Binaries
Usually, inclination angle of
binary systems is unknown
Eclipsing Binaries
Peculiar “double-dip” light curve
→ uncertainty in mass
estimates.
Special case:
Eclipsing Binaries
Here, we know that we
are looking at the system
edge-on!
Example: VW Cephei
Eclipsing Binaries
Spectroscopic Binary
Example:
Algol in the
constellation of
Perseus
From the light curve
of Algol, we can infer
that the system
contains two stars of
very different surface
temperature, orbiting
in a slightly inclined
plane.
We determine the orbit by measuring Doppler shifts
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Spectroscopic
Binaries
Spectroscopic
Binaries
Typical sequence of spectra from a
spectroscopic binary system
Time
The approaching star produces
blueshifted lines; the receding star
produces redshifted lines in the
spectrum.
Doppler shift → Measurement of
radial velocities
→ Estimate of separation a
→ Estimate of masses
Most massive stars:
100 MSun
Least massive stars:
0.08 MSun
(MSun is the mass of
the Sun)
Stellar Properties Review
Luminosity: from brightness and distance
(0.08 MSun) 10-4 LSun - 106 LSun (100 MSun)
Temperature: from color and spectral type
(0.08 MSun) 3,000 K - 50,000 K (100 MSun)
Mass: from period (p) and average separation (a)
of binary-star orbit
0.08 MSun - 100 MSun
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Luminosity
What is a
HertzsprungRussell
Diagram?
The Mass-Luminosity Relation
More massive stars
are more luminous.
An H-R
diagram
plots the
luminosity
and
temperature
of stars
L ~ M3.5
Temperature
Why is a star’s mass its most important property?
Main-Sequence Star Summary
Core pressure and
temperature of a
higher-mass star
need to be larger in
order to balance
gravity
High Mass:
Higher core
temperature boosts
fusion rate, leading
to larger luminosity
Low Mass:
High Luminosity
Short-Lived
Large Radius
Blue
Low Luminosity
Long-Lived
Small Radius
Red
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High-Mass Stars
Mass & Lifetime
Most stars reside on
the Main Sequence.
Until core hydrogen
(10% of total) is
used up
These stars are
burning hydrogen
in their cores.
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 million years ~ 10 billion years x 10 / 104
Life expectancy of 0.1 MSun star:
Low-Mass Stars
0.1 times as much fuel, uses it 0.01 times as fast
100 billion years ~ 10 billion years x 0.1 / 0.01
Stars with low
temperature and
high luminosity
must have large
radius
Luminosity
H-R diagram
depicts:
Temperature
Color
The Size (Radius) of a Star
We already know: flux increases with surface
temperature (~ T4); hotter stars are brighter.
But brightness also increases with size:
A
B
Spectral Type
Star B will be
brighter than star
A.
Luminosity
Radius
*Mass
*Lifespan
Absolute brightness is proportional to radius squared, L ~ R2.
Quantitatively:
L = 4 π R2 σ T4
*Age
Temperature
Surface area of the star
Surface flux due to a
blackbody spectrum
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Ia Bright Supergiants
Ia
Luminosity
Classes
Luminosity effects on the width of
spectral lines
Ib
II
Ib Supergiants
II Bright Giants
III Giants
III
IV
Same spectral type,
but different
luminosity
IV Subgiants
V
Lower gravity near the surfaces of giants
V Main-Sequence
Stars
⇒  smaller pressure
⇒  smaller effect of pressure broadening
⇒  narrower lines
C
D
A
Temperature
C
B
Which star
is the
hottest?
Luminosity
Luminosity
B
Which star is
the most
luminous?
D
A
Temperature
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C
D
A
Which star has
the largest
radius?
D
A
Temperature
Temperature
A
A
Which star is
most like
our Sun?
D
Luminosity
D
Luminosity
C
B
Which star is a
main-sequence
star?
Luminosity
Luminosity
B
B
B
C
Temperature
Which of these
stars will have
changed the least
10 billion years
from now?
C
Temperature
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A
Luminosity
D
B
Which of these
stars can be no
more than 10
million years
old?
Surveys of Stars
Ideal situation:
Determine properties
of all stars within a
certain volume.
Problem:
C
Fainter stars are hard
to observe; we might
be biased towards the
more luminous stars.
Temperature
A Census of the Stars
Faint, red dwarfs
(low mass) are the
most common
stars.
Bright, hot, blue
main-sequence
stars (high-mass)
are very rare.
Giants and
supergiants are
extremely rare.
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What are the two types of star clusters?
Open cluster: A few thousand loosely packed stars
How do we measure the age of a star cluster?
Massive blue stars die
first, followed by
white, yellow, orange,
and red stars
Main-sequence
turnoff
Pleiades
Globular cluster: Up to a million or more stars in a dense ball bound
together by gravity
Main
-sequence
turnoff
point of a
cluster tells
us its age
Pleiades now has no
stars with life
expectancy less than
around 100 million
years
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Detailed
modeling of the
oldest globular
clusters reveals
that they are
about 13 billion
years old
Sets minimum
age for the
Universe!
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