star formation. classifying stars the surface temperature of a star t is compared to a black body....
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Star Formation
Classifying Stars
• The surface temperature of a star T is compared to a black body.
– Luminosity L
– Radius R
• The absolute magnitude calculates the brightness as if the stars were 10 pc away.
– Related to luminosity
•
• Type Temperature
O 35,000 K
B20,000 K
A 10,000 K
F 7,000 K
G 6,000 K
K 4,000 K
M 3,000 K
424 TRL
72.4)/log(5.2 sunLLM
Stellar Relations
• Some bright stars (class) (absolute magnitude)
– Sun G2 4.8
– Sirius A1 1.4
– Alpha Centauri G2 4.1
– Capella G8 0.4
– Rigel B8 -7.1
– Betelgeuse M1 -5.6
– Aldebaran K5 -0.3
Luminosity vs. Temperature
• Most stars show a relationship between temperature and luminosity.
– Absolute magnitude can replace luminosity.
– Spectral type/class can replace temperature.
-20
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-5
0
5
10
15
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Abs. M
agnitude
O B A F G K MSpectral Type
Sun
Hertzsprung-Russell Diagram
• The chart of the stars’ luminosity vs. temperature is called the Hertzsprung-Russell diagram.
• This is the H-R diagram for hundreds of nearby stars.
– Temperature decreases to the right
Main Sequence
• Most stars are on a line called the main sequence.
• The size is related to temperature and luminosity:
– hot = large radius
– medium = medium radius
– cool = small radius
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-5
0
5
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Abs. M
agnitude
O B A F G K MSpectral Type
1 solar radius
Sirius
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-5
0
5
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Abs. M
agnitude
O B A F G K MSpectral Type
Giants
• Stars that are brighter than expected are large and are called giants or supergiants.
• Betelgeuse is a red supergiant with a radius hundreds of times larger than the sun.
AldebaranCapella
RigelBetelgeusesupergiants
giants
Dwarves
• Stars on the main sequence that dim and cool are red dwarves.
• Small, hot stars that are dim are not on the main sequence and are called white dwarves.
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-5
0
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Abs. M
agnitude
O B A F G K MSpectral Type
white dwarves
Interstellar Medium
• Interstellar space is filled with gas (99%) and dust (1%).
• Interstellar gas, like the sun, is 74% hydrogen and 25% helium.
• Interstellar dust, like clouds in the gas giants, are molecular carbon monoxide, ammonia, and water.
• Traces of all other elements are present.
• Atoms are widely spaced, about 1 atom per cm3, a nearly perfect vacuum.
• The temperature is cold, less than 100 K.
Molecular Clouds
• The small mass of atoms creates very weak gravity.
• Gravity can pull atoms and molecules together.
• Concentrations equal to 1 million solar masses can form giant molecular clouds over 100 ly across.
Catalysts for Star Formation
• A cool (10 K) nebula can be compressed by shock waves.
• These shock waves are from new stars and exploding supernovae.
exploding star shock waves nebula with areas of higher density
Gravitational Contraction
• Density fluctuations cause mass centers to appear.
• Mass at a distance will be accelerated by gravity.
• If there is no outward pressure there will be free fall.
– Mass m0 within radius r
– Conservation of energy
– Calculate free fall time
2
)()(
r
rGmrg
r
rdrrrm0
24)()(
0
00
2
2
1
r
Gm
r
Gm
dt
dr
021
0
000
00
22rr
drr
Gm
r
Gmdr
dr
dt
032
3
G
Protostars
• Local concentrations in a nebula can be compressed by gravity. With low temperature they don’t fly apart again.
– Contracting material forms one or more centers
– The contracting material begins to radiate
– These are protostars, called T Tauri stars (G, K, M).
Hydrostatic Equilibrium
• Gravity is balanced by pressure.
– Equilibrium condition
– True at all radii
• The left side is related to average pressure.
– Integrated by parts
• The right side is the gravitational potential energy.
2
)()(
r
rrGm
dr
dP
RR
dmr
rGm
dr
dPr
0 20
3 )(4
gravEVP 3
VPdr
dPr
R34
0
3
V
EP grav
3
Adiabatic Index
• Adiabatic compression is not linear in pressure and volume.
– Parameter is adiabatic index
– Relate to internal energy
• The gravitational energy was also related to the pressure.
– Energy condition for equilibrium
)(1
1PVdPdVdEint
0P
dP
V
dV
V
EP int)1(
V
E
V
Eintgrav )1(
3
0)1(3 intgrav EE
Formation Conditions
• Contraction requires gravitational energy to exceed internal energy.
– Thermal kinetic energy 3kT/2
• The conditions for cloud collapse follow from mass or density.
– Jeans mass, density MJ, J
RmG
kTM
2
3min
intgrav EE
3
2 2
3
4
3
mG
kT
MJ
R
GMfEgrav
2
Fusion Begins
• Initial energy is absorbed by hydrogen ionization.
– D = 4.5 eV
– I = 13.6 eV
• Apply this to hydrostatic equilibrium.
• Continued contraction results in quantum electron gas.
– When degenerate it resists compression
– Sets temperature at core
IH
DH
I m
M
m
ME
2
eV6.2212
1 IDkT
3
23)(
h
kTmm e
342
382
Mh
mmGkT e
Birth of the Sun
• Gravity continues to pull the gas together.
– Temperature and density increases
• If the temperature at the center becomes 5 million degrees then hydrogen fusion begins.
• At this point the star has reached the main sequence.
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Abs. M
agnitude
O B A F G K MSpectral Type
1 M
Birth of Other Stars
• Large masses become brighter, hotter stars.
• Gravity causes fusion to start sooner, about 100,000 years.
• Small masses become dimmer, cooler stars.
• Gravity takes longer to start fusion, up to 100 million years.
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Abs. M
agnitude
O B A F G K MSpectral Type
10 M
3 M
0.02 M
0.5 M