Download Star Formation

Star Formation
Classifying Stars
• The surface temperature of a star T
is compared to a black body.
– Luminosity L
– Radius R
L  4R 2T 4
• The absolute magnitude calculates
the brightness as if the stars were
10 pc away.
– Related to luminosity
M  2.5 log( L / Lsun )  4.72
• Type
O
B
A
F
G
K
M
•
Temperature
35,000 K
20,000 K
10,000 K
7,000 K
6,000 K
4,000 K
3,000 K
Stellar Relations
• Some bright stars
– Sun
– Sirius
– Alpha Centauri
– Capella
– Rigel
– Betelgeuse
– Aldebaran
(class)
G2
A1
G2
G8
B8
M1
K5
(absolute magnitude)
4.8
1.4
4.1
0.4
-7.1
-5.6
-0.3
Luminosity vs. Temperature
-20
-15
Abs. Magnitude
-10
-5
0
Sun
5
10
15
20
O B A F G K M
Spectral Type
• Most stars show a relationship
between temperature and
luminosity.
– Absolute magnitude can
replace luminosity.
– Spectral type/class can
replace temperature.
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
-20
• Most stars are on a line called
the main sequence.
-15
Abs. Magnitude
-10
-5
0
Sirius
5
1 solar
radius
10
15
20
O B A F G K M
Spectral Type
• The size is related to
temperature and luminosity:
– hot = large radius
– medium = medium radius
– cool = small radius
Giants
-20
-15
Abs. Magnitude
-10 Rigel
-5
0
5
supergiants Betelgeuse
giants
Aldebaran
Capella
10
15
20
O B A F G K M
Spectral Type
• 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.
Dwarves
-20
• Stars on the main sequence that
dim and cool are red dwarves.
-15
Abs. Magnitude
-10
-5
• Small, hot stars that are dim are
not on the main sequence and
are called white dwarves.
0
5
10
15
20
white
dwarves
O B A F G K M
Spectral Type
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.
r
m(r )    (r)4r 2 dr 
0
• 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
g (r ) 
Gm(r )
r2
2
1  dr  Gm0 Gm0

  
2  dt 
r
r0
0  2Gm
2Gm0 
dt
0

 
dr    

r0 dr
r0
r
r
0


0

3
32G 0
1 2
dr
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
dP
Gm(r )  (r )

dr
r2

R

R
0
0
R Gm( r )
dP
4r
 
dm
2
0
dr
r
3
4r 3
dP
 3 P V
dr
 3 P V  Egrav
P 
E grav
3V
• 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.
Adiabatic Index
• Adiabatic compression is not
linear in pressure and volume.
– Parameter g is adiabatic
index
– Relate to internal energy
• The gravitational energy was
also related to the pressure.
– Energy condition for
equilibrium
g
dV dP

0
V
P
1
dEint   PdV 
d ( PV )
g 1
E
P  (g  1) int
V

E grav
3V
 (g  1)
Eint
V
E grav  3(g  1) Eint  0
Formation Conditions
E grav  Eint
• Contraction requires
gravitational energy to exceed
internal energy.
– Thermal kinetic energy
3kT/2
GM 2
E grav   f
R
M min
3kT

R
2Gm
3  3kT 
J 


4M 2  2Gm 
3
• The conditions for cloud
collapse follow from mass or
density.
– Jeans mass, density MJ, J
Fusion Begins
• Initial energy is absorbed by
hydrogen ionization.
– eD = 4.5 eV
– eI = 13.6 eV
• Apply this to hydrostatic
equilibrium.
• Continued contraction results in
quantum electron gas.
– When degenerate it resists
compression
– Sets temperature at core
EI 
M
M
eD 
eI
2 mH
mH
kT 
1
e D  2e I   2.6 eV
12
(me kT )3 2
 m
h3
 G 2 m 8 3me  4 3
M
kT  
2
h


Birth of the Sun
-20
• Gravity continues to pull the
gas together.
– Temperature and density
increases
-15
Abs. Magnitude
-10
-5
0
1 M
• If the temperature at the center
becomes 5 million degrees then
hydrogen fusion begins.
5
10
15
20
O B A F G K M
Spectral Type
• At this point the star has
reached the main sequence.
Birth of Other Stars
-20
-15
Abs. Magnitude
-10
-5
10 M
0
3 M
0.5 M
5
10
0.02 M
15
20
O B A F G K M
Spectral Type
• 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.