Star Birth and Death

Lecture 18: Star Birth and Death

In the Milky Way we observe stars as old as the Universe (13 billion years), stars like the sun with 4.5 billion years, star clusters a few million years old, and stars which are just forming.

Stars burn fuel to produce energy and shine --> they must evolve.

Any model of stellar formation and evolution must explain the H-R diagram (main-sequence, red giants, supergiants, white dwarfs).

I. Star formation and pre-main-sequence evolution

Molecular clouds (raw material for star formation)

Very thin, low-density cloud (10,000 atoms per cm³) (almost a perfect vacuum compared with room air: 2x10¹⁹ molecules per cm³).

Very cold, T~10-20 K, so molecules can form --> molecular cloud.

Made mostly of H (75%) and He (23-25%) gas and a bit of heavier atoms (<2%).

Most abundant molecules are H₂, CO, H₂O, and other complex forms such as C₂H₅OH (ethyl alcohol), amino acids (building blocks of life), and dust grains.
The Orion Nebula, an interstellar cloud in which star systems and possibly planets are forming.

Initially the cloud was about several light years across with several thousand solar masses.

A small overdensity in the cloud causes a gravitational pull on the surrounding low-density gas. Contraction begins and the overdensity grows, thus producing a faster contraction.

As collapse proceeds, the cloud subdivides into concentrations containing enough mass for hundreds of stars.

The material is not uniform so new fragments form that lead to the formations of a star cluster (stars are not born in isolation).

The rotation speed of each cloud gradually increases due to conservation of angular momentum.

The rotating ball collapses into thin disk with most of the mass concentrated near the center (a protostar).

Close-up of the Orion Nebula obtained with HST, revealing what seem to be disks of dust and gas surrounding newly formed stars. These protoplanetary disks span about 0.14 light years and are probably similar to the Solar Nebula.

During contraction, gravitational potential energy is converted into kinetic energy of the individual gas particles. Collisions between particles convert this energy into heat (random motions). The protostar releases its gravitational energy in the form of light. A star like the sun can reach a surface temperature of a few thousand degrees and a luminosity of 100x the Sun's present luminosity. Newly forming stars are located above and to the right of the main-sequence.

The star becomes hottest near the center where much of the mass is collected. At some point the central temperature rises to 10 million K. The collisions among the atoms are so violent that nuclear reactions begin (H --> He), at which point the star is born. A Sun-like star takes ~10 million years to reach the main-sequence.

What prevents further collapse? As temperature and density increase toward the center, so does the pressure causing a net force pointing outward. The star reaches a balance between the gravitational force and the internal pressure, aka hydrostatic equilibrium.

What range of stellar masses are possible?

A cloud with less than ~0.08 solar masses contracts, but never reaches the temperature for nuclear fusion. They glow in the infrared due to the gravitational energy, and then fade before nuclear reaction can begin. These are substellar objects, aka "brown dwarfs".

A cloud with more than 100 solar masses produces so much energy that the object blows apart.

II. Evolution on the main-sequence

Main-sequence: The diagonal band that runs from hot-luminous-blue stars to cool-faint-red stars.

It is the location of the stars that get their energy by fusing H into He in their cores.

Nuclear reactions provide a stable heat source that creates outward pressure that counterbalances gravity: hydrostatic equilibrium.

What's the reason for the spread along the main-sequence? Observations and theoretical calculations show that mass is the key parameter that determines the properties (luminosity, temperature) of a star. (How can we measure stellar masses?)

As mass increases, pressure and temperature must increase in the core to compensate the greater gravity.

Higher temperatures increase the rate of collisions and nuclear reactions.

More energy production leads to higher luminosities.

Greater pressure pushes the outer layers outward --> bigger radius.

Massive main-sequence stars are larger, more luminous and hotter than lower mass main-sequence stars.

Nuclear burning:

If M<1.5 solar masses, T < 15x10⁶ K, and the star gets its energy from the proton-proton chain.

¹H + ¹H --> ²H + e⁺ + neutrino

²H + ¹H --> ³He + photon

³He + ³He --> ⁴He + ¹H + ¹H + photon

If M>1.5 solar masses, T > 15x10⁶ K, the carbon cycle is the dominant reaction:

¹²C + ¹H --> ¹³N + photon

¹³N --> ¹³C + e⁺ + neutrino

¹³C + ¹H --> ¹⁴N + photon

¹⁴N + ¹H --> ¹⁵O + photon

¹⁵O --> ¹⁵N + e⁺ + neutrino

¹⁵N +¹H --> ¹²C + ⁴He

Stars must evolve because they are gradually using their fuel. As a star evolves, it changes its chemical composition and must reach a new equilibrium.

Main-sequence lifetimes: The more massive a star, the higher its core temperature and the faster it consumes the nuclear fuel.

The Sun will stay ~10 billion years on the MS (click here).

At the top of the MS, a 100 solar mass star has a luminosity of 10⁶L_o and will stay there only 1 million years.

At the bottom of the MS, a star with only 0.1 M_o has a luminosity of 10^-3L_o and has a MS lifetime of 10¹² years.

The largest fraction of a star's life is spent on or near the MS because there is a lot of H for burning --> 90% of the stars fall in the MS.

Dating star clusters: in a cluster of stars that formed at the same time more massive stars leave the MS earlier.

After 1 million years, stars larger than 100 solar masses will have disappeared from the MS.

After 100 million years, stars larger than 4 solar masses will have evolved off the MS.

After 10 billion years, stars larger than 1 solar mass will leave the MS.

The H-R diagram is a powerful tool to date star clusters:

(Source: http://www.astronomy.ohio-state.edu/~ryden/ast162_4/notes17.html)

Left: Old stellar cluster. Right: Young cluster displaying luminous hot stars.

III. Post main-sequence evolution and star death

Evolution of a low-mass (1 solar mass) star (what happens to a star as it evolves?)

Eventually the star runs out of H at the center --> pressure decreases --> inert He core starts contracting and getting hotter.

Hydrogen nuclear burning moves to shells around the core.

Higher temperatures around the core increase energy production causing great expansion of outer layers.

The star becomes a red giant in 1 billion years.

The star is up to 1000x Sun's radius (the size of Jupiter's orbit)!!

Meanwhile, He core continues contracting until reaching 200 million degrees --> He ignition (helium flash)

⁴He + ⁴He --> ⁸Be + photon

⁸Be + ⁴He --> ¹²C + photon

This reaction produces C in the star's core (basis of life on Earth).

When He depletion occurs at the center, the inert C core contracts and gets hotter.

He burning migrates to a shell around the inert C core, which causes expansion of the outer layers.

Low escape velocity from giant and supergiant stars causes the gas of the outer layers to blow out in a stellar wind.

The light from the central star causes the wind to glow in a planetary nebula.
heavy elements are ejected out to space to be reused

What happens to the C core?

If the star has a mass < 8 solar masses the core cannot get hot enough for C ignition.

Without pressure generated by nuclear reactions, the core contracts up to the point where electrons resist further packing.

This process creates a very dense star about the size of the Earth called a white dwarf.

Densities of 10⁸ to 10¹¹ kg/m³ (a teaspoon of white dwarf matter on Earth would weight as much as an elephant).

Initially the white dwarf is very hot at 100,000 K and cools slowly. The coolest WD has 4,000 K.

Without nuclear reactions, white dwarfs have low luminosities (down to 10^-4 solar luminosities).

white dwarfs are unstable if M > 1.4 solar masses (gravity too strong for "electron pressure")

the Sun will become a red giant, then lose about 40% of its mass and finally become a white dwarf of 0.6 solar masses.

A white dwarf is the end product for low and intermediate mass stars (0.08 < M < 8 solar masses).

Evolution of a high-mass star

stars more massive than 8 solar masses are able to reach higher temperatures and fuse heavier elements:

¹²C + ⁴He --> ¹⁶O + photon (for 500 million degrees)

¹⁶O + ⁴He --> ²⁰Ne + photon (for 500 million degrees)

¹²C + ¹²C --> ²⁴Mg + photon (for 1 billion degrees)

¹⁶O + ¹⁶O --> ³²S + photon (for 1 billion degrees)

iron is the heaviest element from which you get energy out in fusion

Reactions to heavier elements go faster and faster : creating C, O, Ne, Mg takes 1000 years --- production of S takes few days.

In the H-R diagram the star leaves the main-sequence and migrates to the region of supergiants.

Fusion reactions lead an onion skin structure with more heavy elements concentrated toward the center.
Onion-skin structure with iron at the center (not to scale)

Iron has the most stable configuration of all elements --> energy is consumed as iron fuses: bad news for the star.

The iron core will not ignite even though it is extremely dense and hot.

A star with > 8 solar masses initially, will form a core with mass > 1.4 solar masses - too big for a white dwarf!

Not even the electrons can support the pressure to balance gravity --> the core collapses in a fraction of a second to a radius of 50 km.

Protons and electrons collide to produce neutrons and lots of neutrinos.

At such high densities neutrinos interact with the matter and push the envelope outward at 5% the speed of light.

The result is a big explosion called supernova that momentarily outshines the Sun by 10 billion times! As bright as an entire galaxy (movie).

During the explosion atoms heavier than iron are formed and thrown into space (Silver=47 protons, Gold=79 protons) --> the star is dead.

Supernova are rare events: once every 50 years in a galaxy like ours. The last one was observed by Kepler in 1604. If a nearby SN explodes, we might be able to observe it during daytime. If it is too close (<15pc)...

SN 1987A in the LMC has been the brightest event in the past 4 centuries. It allowed us to observe the neutrinos produced in the core (for the first time) and the inner onion skin layers of the star.

SN 1987A in the Large Magellanic Cloud
The Crab nebula: the remnant of a SN recorded in A.D. 1054

What happens to the core? It depends on its mass.

If the core has less than 3 solar masses, gravity can be balanced by the pressure of the tightly packed neutrons (almost touching each other). Neutrons stop the collapse and form a stable system called a neutron star.

This is the densest form of matter in the observable universe: 10¹⁷ kg/m³ (a teaspoon of neutron star matter on Earth would weight 100 million tons).

Mass ranges between 1.4-3 solar masses

Typical radius ~ 10 to 20 km!

Conservation of angular momentum should lead to a fast spinning object with strong magnetic field.

In 1967 a radio telescope detected a new type of object that emitted radio pulses every 1.33733 seconds. These objects are now called pulsars.

Pulsars are the fast spinning neutron stars which act like lighthouses. They emit strongly beamed radiation along the poles of the neutron star which is periodically directed toward the Earth as the pulsar spins. The radio pulses arrive with the frequency corresponding to the spinning frequency of the pulsar (animation).

typical "beep" period few seconds, some are milliseconds

If the core has more than 3 solar masses, neutrons cannot stop the collapse, gravity wins, and the result is a black hole.

In theory, all the mass falls into a point.

If you get closer to the BH the escape velocity increases. At some distance the distance required to escape the BH would be the speed of light. This is an imaginary sphere around the BH called the event horizon. Nothing (not even light) can escape this region --> BHs are black.

The radius corresponding to the event horizon is called the Schwarzschild radius and can be computed from the mass of the BH: R_s = 2GM/c²

For an object like the Sun, R_s = 3 km --> Squeeze the Sun down to the size of a small town and you get a BH.

For the Earth, R_s = 1 cm.

Any object can be a black hole, if you can squeeze it small enough. Even the Earth could be a BH but there is no way to overcome the pressure unless we have a big mass.

Gravity alone can make BHs if there is more than 3 solar masses, in which case R_s = 9 km.

Light passing near a BH will be deflected because space is curved by gravity.

Eintein's cross (multiple images of one quasar)

If you were falling into a BH, you would be stretched by the tidal forces well before reaching the event horizon.

Time dilation: If you could survive, you would cross the event horizon in a finite time. However, as seen from outside your clock would appear to slow down as you took an infinite amount of time to reach the event horizon (you appear to never get there).

Nobody knows what happens inside the event horizon. Even though we cannot get any information from a BH, in principle we can detect them by their strong gravity (a star orbiting a BH, for example). There is indirect evidence of stars orbiting an unseen object, as well as massive BHs in the center of galaxies.

IV. Cosmic abundances of chemical elements

The Universe was born with 75% of H and 25% of He.

Stars are the fusion factories for the production of heavier chemical elements.

Life-giving elements are produced deep inside stars and are expelled into space during the late stages of a star's life.

The ejected gas is rich in heavy elements. Chemically enriched interstellar material becomes the raw material for a new generation of stars and the cycle of stellar birth and death begins again.

The Sun is a second-generation star. Each of the heavy atoms of your body was once part of another star. The iron of our bodies once flew in a supernova explosion!
(Note: Several images come from http://zebu.uoregon.edu/~js/ast122/)