Astronomy Notes

The Hertzsprung-Russell Diagram

• The H-R diagram is a plot of the luminosity of stars (vertical) versus their spectral class or temperature (horizontal).
• Thus, the cooler, red stars are to the right, the hotter blue stars to the left.
• Stars only found in certain areas of the H-R diagram.
• Because L = kR²T⁴, the largest stars are found in the upper right hand corner.
• Similarly, the smallest stars are in the lower left area.
• The position of a star on the H-R diagram is determined only by the surface brightness and temperature. The interior conditions are not shown at all.

Main Sequence

• Most stars fall in a band from upper left to lower right called the Main Sequence.
• The sun is the brighter and more massive than 90% of the nearest 100 stars.
• It is believed that the nearby stars are representative of all stars, so the sun is a far better than average star.
• Most stars are too dim to be seen if they are distant.
• Most stars which we can see are the very rare brightest beacons, which have far brighter luminosity than the sun.

Giants

• Above the main sequence in the yellow, orange and red area are found the giants.
• They are called giants because they 10 - 80 times the radius of the sun.
• Although they are cooler than the sun, they are about 100 times as luminous as the sun because they are so big.

Supergiants

• Another group of even much larger stars are called supergiants.
• They are located along the top of the H-R diagram, extending all the way from blue over to red.
• They are over 100 times the radius of the sun, with the red supergiants being the largest, nearly 1,000 solar radii.
• That means that if our sun were a red supergiant, the orbit of Jupiter would be inside of it.

White Dwarfs

• Another group of stars, the white dwarfs, are found below and left of the main sequence.
• They are white, having a temperature of about 10,000 K.
• They are only about the size of the earth, but have as much mass in them as the sun.
• Thus, a spoonful of a white dwarf would weigh as much as an elephant.
• Sirius is a binary star with a white dwarf companion, the first white dwarf discovered (called Sirius B).

The Mass-Luminosity Relation

• Eddington showed that stars of similar composition and energy source would having increasing luminosity with increasing mass, called the mass-luminosity relation.
• That explains the main sequence: the more massive stars are more luminous.
• That also implies that stars not on the main sequence have either different composition or energy generation.
• The Russell-Vogt Theorem is that the equilibrium structure (position on the main sequence) of a star is determined only by its mass and composition.
• These two relations explain why most stars lie on the main sequence--they differ mostly in mass, and slightly in composition.

The Energy Source of Stars: Nuclear Energy

• It is believed that stars must be very old because the earth appears to be billions of years old, and it is believed that earth formed with the sun and hence the sun (and hence other stars) must be very old.
• If stars are so old, then there must be some energy source capable of sustaining them for billions of years.
• Nuclear energy is a possible source, in which simple elements, like hydrogen, combine to form complex elements.
• Because nuclear reactions change the composition of the star, it can move around on the H-R diagram.
• The change in the appearance of one star with time is called stellar evolution. "Aging" would be a better word.

Pre-Main Sequence Evolution

• It is believed that stars contract from large interstellar clouds of gas and dust, called molecular clouds.
• As the protostar contracts, it increases in temperature and luminosity, until it enters the H-R diagram from the lower right-hand and proceeds upward and to the left until it reaches the giant region.
• It does not spend a long time in the giant region, so this phase is not believed to explain most giants.
• It then contracts as a pre-main sequence star to arrive at its birth place on the main sequence.

Molecular Clouds

• Not all clouds of matter will contract gravitationally because gravitation is counteracted by increasing pressure.
• For a given density of matter, one can calculate the size cloud that could gravitationally contract.
• For the density of interstellar space, the cloud must be large enough to form huge star clusters or galaxies.
• Certain regions of high density, called molecular clouds, could form into clusters of hundreds of stars.
• These clouds are believed to condense into star clusters rather than one huge star, because there is no one center.
• These are believed to be the only areas of star formation in our galaxy.
• The Orion Nebula and that entire region are believed to be areas of star formation.
• No such large scale contraction has been observed; rotation and magnetic fields are thought to inhibit it.

Protostars

• Once a molecular cloud reaches the point that it can contract, it can do so very quickly, in a hundred thousand yrs.
• The sun could have contracted from a huge cloud to R = 20, L = 100 (looking similar to a red giant) in only 1,000 years.
• That would mark the end of the protostar stage.

Pre-main-sequence Stars

• The energy in the pre-main-sequence stars comes from gravitational contraction, not nuclear energy.
• The pre-main-sequence star moves from the giant/supergiant region to the main sequence.
• Massive stars move much more quickly: 100 thousand yrs for M=15, whereas 10 million for M = 1.
• A cocoon nebula of dark dust might surround and hide the star, making it an infrared star.
• Stars too small to ignite hydrogen burning have been called brown dwarfs, down to twice the mass of Jupiter.
• Stars bigger than M = 100 have such a violent contraction that they blow apart again and hence are not stable.
• T Tauri stars are thought to be examples of pre-main-sequence stars losing their cocoons.

Main Sequence Evolution

• It is believed that most stars spend most of their life on the main sequence, hence most stars are found there.
• On the main sequence, stars begin "burning" hydrogen to form helium, which halts their motion on H-R.
• Because higher mass stars are much more luminous, it is believed that they are very short-lived.
• It is believed that the sun will be on main sequence for 10 billion years, but a M=10 star for only 20 million yrs.
• Low mass stars like the sun are believed to change hydrogen to helium using the proton-proton reaction.
• Higher mass stars are thought to use the CNO (carbon-oxygen-nitrogen) cycle.

The Red Giant Stage

• After the core hydrogen is exhausted, a shell of hydrogen around the core continues burning.
• This heats up the outer layers and the star expands to become a red giant (some are really yellow or orange).
• At some point, the shell is too cool for nuclear fusion and the helium core contracts, while outer layers expand.
• Soon the core has heated enough to begin burning Helium to Carbon with the triple-alpha process.
• This process burns the helium extremely quickly, called the helium flash, occurring in the giant region.
• This added heat apparently is enough to blow of the outer layers, causing mass loss.
• The star FG Sagittae has brightened by 4-6 magnitude since 1894, and cooled from B4 to G and tripled in size since 1960.

Variable Stage

• After the giant phase, the evolution is less well understood. The star apparently moves left.
• Here it crosses the nearly vertical instability strip on the H-R diagram.
• In that strip stars become Cepheid variables, named for the star Delta in the constellation Cepheus.
• These stars pulsate with a period directly related to their luminosity, useful for determining distances.
• They then move extremely quickly across the Hertzsprung Gap back toward the main sequence.

Planetary Nebulae

• Often the outer layers of the star are blown off in a spherical bubble.
• It can form a planetary nebula, which often looks like a doughnut or smoke ring, as in the Ring Nebula.
• A planetary nebula has nothing to do with planets; it just looked a little like a planet when discovered.
• A planetary nebula often leaves a white dwarf.

White Dwarfs

• When the star has run out of fuel, it can become a white dwarf if its mass is less than M = 1.4 (called the Chandrasekhar limit).
• A white dwarf is held up by electron pressure, that is, the electrons pressing against each other.
• These electrons are no longer associated with any one atom, but are free to move through it like a crystal.
• The stars are often made up of carbon, so they are truly "like a diamond in the sky."
• They are often called degenerate stars, because the electron pressure is from a effect in physics called degeneracy.
• White dwarfs are among some of the oldest stars, having lived 10 billion years, and cooled another 5-10 billion years.

Supernovae

• Stars that are larger than about M = 8 have a core larger than M = 1.4.
• The cores of such stars can burn all the way to form Iron, after which no more energy is available.
• Thus, a point can come where the core rapidly contracts and no more energy is available to stop it.
• The core contracts extremely rapidly (collapses), in a few seconds, creating enough heat to explode the entire star in a supernova.
• When a supernova is seen in a distance galaxy of billions of stars, it can be as bright as the entire galaxy!
• It is believed that elements heavier than iron are created in such an explosion, as they require energy to form.
• Supernovae are observed in our own galaxy about every 300 years, the last one being in the 1600's.
• In 1987 a supernovae was observed in our satellite galaxy called the Large Magellanic Cloud.

Neutron Stars

• A stellar core larger than M = 1.4 has so much gravity that it overcomes the electron degenercy pressure.
• The electrons are crammed onto the protons to form a star made entirely of neutrons.
• Hence, it is called a neutron star, and was predicted in 1934 as a remnant of a supernova.
• It is a dense as an atomic neucleus: a spoonful would weigh as much a 70,000 ships the size of the Queen Mary.
• They are only about 10 miles in diameter, and yet contain more mass than the entire sun!

Pulsars

• Neutron stars were discovered in the form of pulsars.
• Pulsars are neutron stars which have very rapidly pulsing brightness.
• It is believed they are pulsing because they are rotating and have a bright spot causing the pulses.
• The pulsar at the center of the Crab Nebula super novae remnant (of 1054 explosion) rotates every 1.3 seconds!

Black Holes

• Stars with cores too massive even to form neutron stars can collapse into black holes.
• A black hole is so-called because it is so massive that even light cannot escape from it.
• The neutrons are all crushed onto each other, and no one knows of anything that could stop the contraction.
• Hence, it is believed that the matter all collapses down into a point, perhaps going into another universe, from which it would be observed as a "white hole" with matter apparently being created from nowhere.
• The radius around a black hole within which no light can escape is called the Schwarzschild radius, and the sphere of that radius is called the event horizon.

Detecting a Black Hole

• Whereas white dwarfs and neutron stars are known to exist, it is hard to detect an invisible black hole.
• The best evidence for one is the source Cygnus X-1.
• It is an X-ray source, which fits a black hole because matter falling in would be heated enough to give off X-rays before falling over the event horizon, where it would become invisible.
• It is a double star, and hence its mass can be measured to be over M = 5, with is right for a black hole.
• Finally the X-ray emission varies on a short time period, implying that it is very small.
• Thus, it smells, tastes, and feels like a black hole, even though it cannot be seen.