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 B

20,000 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.

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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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1 solar radius

Sirius

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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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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

002

21

rGm

rGm

dtdr

021

0

000

00

22rr

drr

Gmr

Gmdrdrdt

0323

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

rrGmdrdP

RR

dmr

rGmdrdPr

0 20

3 )(4

gravEVP 3

VPdrdPr

R34

0

3

VE

P 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

1 PVdPdVdEint

0P

dPVdV

VEP int)1(

VE

VE intgrav )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

kTM23

min

intgrav EE

3

2 23

43

mGkT

MJ

RGMfEgrav

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 mM

mME

2

eV6.22121

IDkT

3

23)(hkTmm 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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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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3 M

0.02 M

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