the family of stars chapter 8:. organizing the family of stars: the hertzsprung-russell diagram we...
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The Family of Stars
Chapter 8:
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Organizing the Family of Stars: The Hertzsprung-Russell Diagram
We know:
Stars have different temperatures, different luminosities, and different sizes.
To bring some order into that zoo of different types of stars: organize them in a diagram of:
Luminosity versus Temperature (or spectral type)
Lum
inos
ity
Temperature
Spectral type: O B A F G K M
Hertzsprung-Russell Diagram
orA
bsol
ute
mag
.
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The Hertzsprung Russell Diagram
Most stars are found along the
Main Sequence
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The Hertzsprung-Russell Diagram
Stars spend most of their active
life time on the M
ain Sequence.
Same temperature,
but much brighter than
MS stars
→ Must be much larger
→ Giant Stars
Same temp., but
fainter → Dwarfs
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Radii of Stars in the Hertzsprung-Russell Diagram
10,000 times the
sun’s radius
100 times the
sun’s radius
As large as the sun100 times smaller than the sun
Rigel Betelgeuze
Sun
Polaris
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Luminosity ClassesIa Bright Supergiants
Ib: Supergiants
II: Bright Giants
III: Giants
IV: Subgiants
V: Main-Sequence Stars
IaIb
II
III
IVV
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Luminosity effects on the width of spectral lines
Same spectral type, but different luminosity
Lower gravity near the surfaces of giants
smaller pressure
smaller effect of pressure broadening
narrower lines
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Binary StarsMore than 50 % of all stars in our Milky Way
are not single stars, but belong to binaries:
Pairs or multiple systems of stars which
orbit their common center of mass
If we can measure and understand their orbital
motion, we can
estimate the stellar masses.
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The Center of Masscenter of mass =
balance point of the system
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.
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Estimating Stellar MassesRecall Kepler’s 3. Law:
Py2 = aAU
3
Valid for the Solar system: star with 1 solar mass in the center
We find almost the same law for binary stars with masses MA and MB different from 1 solar mass:
MA + MB = aAU
3 ____ Py
2
(MA and MB in units of solar masses)
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Visual Binaries
The ideal case:
Both stars can be seen directly, and
their separation and relative motion can be followed directly.
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Spectroscopic Binaries
Usually, the binary separation a can not be measured
directly because the stars are too close to each other.
A limit on the separation and thus the masses can
be inferred in the most common case:
Spectroscopic Binaries
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Spectroscopic Binaries
The approaching star produces blue shifted lines;
the receding star produces red shifted lines in the spectrum.
Doppler shift → Measurement of radial velocities
→ Estimate of separation a
→ Estimate of masses
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Spectroscopic Binaries
Tim
e
Typical sequence of spectra from a spectroscopic binary system
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Eclipsing BinariesUsually, the inclination
angle of binary systems is unknown →
uncertainty in mass estimates.
Special case:
Eclipsing Binaries
Here, we know that we are looking at the
system edge-on!
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Eclipsing Binaries
Peculiar “double-dip” light curve
Example: VW Cephei
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Eclipsing Binaries
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.
Example:
Algol in the constellation of Perseus
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The Mass-Luminosity Relation
More massive stars are more
luminous.
L ~ M3.5
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Masses of Stars in the Hertzsprung-Russell Diagram
Masses in units of solar masses
Low m
asses
High masses
Mass
The higher a star’s mass, the more
luminous (brighter) it is:
High-mass stars have much shorter lives than
low-mass stars:
Sun: ~ 10 billion yr.
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.
L ~ M3.5
tlife ~ M-2.5
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Surveys of Stars
Ideal situation:
Determine properties of all stars within a
certain volume
Problem:
Fainter stars are hard to observe; we
might be biased towards the more luminous stars.
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A Census of the StarsFaint, red
dwarfs (low mass) are the most common
stars.
Giants and supergiants
are extremely rare.
Bright, hot, blue main-sequence
stars (high-mass) are very rare.