E5 stellar processes and stellar evolution (HL only)

Star formation

Star formation

Interstellar space consists of gas (74% H, 25% He by mass) and dust at a density of about 10-21 kg.m-3. This is about one hydrogen atom to every cm3 of space.

Star formation

When the gravitational energy of a given mass of gas exceeds the average kinetic energy of the molescules the gas cloud becomes unstable and starts to collapse.

GM2/R > (3/2)NkT

“Jeans criterion”

Star formation

As the cloud collapses, the particles get faster and eventually clumps form that are hot enough to emit light. Protostars are formed.

Star formation

If the star is big enough the collapse will continue until the star is hot enough for nuclear fusion to occur. The radiation pressure produced by the fusion balances the pull of gravity and equilibrium is reached. The star is a main sequence star (like our sun).

Main sequence

41H → 4He + 2e+ + 2γ + 2νe (26.7 MeV)

Mass v luminosity relation

L α Mα

where 3 < α > 4

Mass v luminosity relation

Since the luminosity could be the total energy given out by the star (E) divided by the lifetime of the star T we get

E/T α Mα

Since E = Mc2 from Einstein’s formulaMc2/T α Mα T α M1-α

Taking α = 4 we get T α M-3

Lifetime of a star

T α M-3

The bigger the mass of a star, the shorter its life

(it “burns” out quicker)

A star with a mass 10x greater than the sun will have a life time a factor 10-3 (1/1000) less than

the sun

When the hydrogen runs out?

Schönberg – Chandrasekhar limit

• After the star has used up about 12% of its hydrogen, its core will contract but the outer layers will expand substantially ()fusion continues there). The star leaves the main sequence and moves over to the Red Giant branch

Mstar < 0.25Msun

• No further nuclear reactions• Core stays as Helium• After a Red giant it becomes a White Dwarf

0.25Msun < Mstar < 4Msun

• Core temperature reaches 108 K enabling Helium fusion (higher temperature is needed because Helium nuclei have 2 positive charges)

• Helium fuses to form oxygen and carbon• After a Red gaint a White Dwarf with a

carbon/oxygen core is formed

4Msun < Mstar < 8Msun

• Core temperature rises further enabling the fusion of carbon and oxygen to take place producing a core of oxygen, neon and magnesium

• After a Red giant a White Dwarf with an oxygen/neon/magnesium core is formed

8Msun < Mstar

• Core temperature rises further so heavier elements fuse. Helium in the outer layers continues to fuse too. Eventually iron is produced (which does not fuse – see topic 7)

• This is a RED SUPERGIANT• Will eventually become a NEUTRON STAR

Anatomy of a RED SUPERGIANT

and neon

Evolution of stars < 8Msun

• Core contracts under its own weight• It stops when electrons have to be forced into the

same quantum state. This is not allowed so this “electron degeneracy pressure” stops the star collapsing further

• The outer layers are released to form a planetary nebula

• The resultant White dwarf has no energy source so is doomed to cool down to become a Black dwarf.

Evolution of stars > 8Msun

• If the core is above 1.4 solar masses (the Chandrasekhar limit) Electrons are forced into protons producing neutrons.

• The core is only made of neutrons and contracting rapidly.

Evolution of stars > 8Msun

• The neutrons get too close to each other (this time it is “neutron degeneracy pressure” caused by neutrons not being allowed to occupy the same quantum state) and the entire core rebounds to a larger equilibrium size.

• The causes a catastophic shock wave which explodes the star in a SUPERNOVA

Evolution of stars > 8Msun

• The neutron star left over after the supernova remains stable provided its has a mass of no more than 3 solar masses (the Oppenheimer-Volkoff limit)

Evolution of stars > 8Msun

• Neutron stars with masses substantially more than the Oppenheimer-Volkoff limit continue to collapse as the neutron pressure is insufficient. They become Black holes

• At the centre of the black hole is a singularity• The boundary around the singularity where

even light does not have sufficient escape velocity to escape is called the event horizon or gravitational radius.

Stellar evolution

Evolution of stars on the HR diagram

Evolution of stars on the HR diagram

Pulsars• Another very important property of neutron star is

its strong magnetic field. When electrons move in spirals around magnetic lines of force, radio waves are produced and radiated out along the two magnetic poles of the star.

Pulsars• Usually, the rotational axis of the neutron star does

not align with the magnetic axis. The radiation beams will sweep around and create the light house effect. What we observe on Earth will be pulses of radio wave with very stable period. This is a pulsar.