Astronomy Exam

Life Stages of a Low-Mass Star

1. protostar: gravitational contraction

2. nuclear fusion begins: gravity balances pressure

3. main sequence: H → fusion in core

4. end of main sequence: hydrogen runs out in core

5. red giant: H → He fusion in shell around contracting core (leading to He flash)

6. He fusion in core

7. double shell fusion: He → C; H → He

8. ejection of H and He in a planetary nebula

9. leaving behind an inert white dwarf (made of carbon just radiating remnant heat)

death of a low mass star

planetary nebula and white dwarf

are white dwarfs always left alone?

• sometimes they can have a companion star

• the white dwarf can steal mass from it

• the stolen matter forms an external layer which can quickly ignite and shine brightly creating a nova

• the small star sirius B is a white-dwarf companion of the much larger and brighter sirius A

whats a nova

• a nova occurs in binary systems where a white dwarf is pulling mass from its companion

• a nova is a relatively gentle explosion of hydrogen gas on the surface of a white dwarf in a binary star system

• this process does not damage the white dwarf and it can repeat

supernova - type Ia

• sometimes the mass transfer can be excessive, so excessive that the white dwarf will not be able to support the mass it gains

• so, what would have been a nova becomes a supernova (Type Ia)

• this results in the white dwarf star exploding and leaving no remnant

massive stars (>8M)

• greater than 8 solar masses

• begins life on main sequence as a blue star

• follows the same path as a low-mass star but everything occurs faster

• end stage is different than a low mass star

• when hydrogen fusion in the core ends, the star leaves the main sequence

• fusion in the core continues through many more stages than for low mass stars

• heavier elements (and burning shells in the star) are produced (carbon, oxygen, neon, silicon, and so on up to iron)

super giants on the H-R diagram

as the shells of fusion around the core increase in number:

→ thermal pressure overbalances the lower gravity in the outer layers

→ the surface of the star expands

→ the surface of the star cools

• the star moves toward the upper right of the H-R diagram

• it becomes a red supergiant (example is beteleguese)

the iron (Fe) problem

the red supergiant has an inert iron (Fe) core

• fusing iron does not release energy

• so you keep making iron

• it marks the end-point of nuclear fusion to give energy (i.e., iron needs energy to fuse)

supernova - type II

if fusion stops at the core, then:

• gravity overcomes pressure

• gravity even pulls electrons which are smashed into protons and form neutrons

• no more atoms…

• the neutron core collapses and inward falling material rebounds off the core

• this only takes seconds

• the core recoils and sends the rest of the star flying into space

• this results in one of the biggest explosions in the entire universe

• the light given off from supernova explosion can be brighter than the entire galaxy

many supernova type II occurred before we did

• the amount of energy released was so great, that most of the elements heavier than iron are instantly created (like lead, copper, and gold)

• the atoms that created our world and solar system came from nuclear fusion in stars and from supernova events

• we are all made of star stuff

• big bang gave is 70% H, 30% He, everything else is from stars

what happens to the core after a type II supernova

the whole story depends on mass

1. neutron star: the really big ones: remaining core mass of ~1.4M to 3M

2. black hole: the really really big one: remaining core mass greater than 3<

the end states of stars

1. white dwarf: remnants of low mass stars (<1.4M) - typical size 10 000km (size of earth)

2. neutron stars: core remnants of high mass stars - typical size 10 km (size of big city

3. black holes: core remnants of high mass stars - small size less then 10 km (about the size of a few city blocks)

white dwarfs

• are remnants of low-mass main sequence stars, supported against gravity by electron degenerate pressure (electron-electron repulsion of carbon atoms)

• the composition of the core is carbon

• not hot enough to fuse carbon any further

small mass stars end life as white dwarfs

• core becomes so dense can not contract and heat any more

• star supported by pressure of degenerate

• size about size of earth

• star slowly cools

neutron stars

• these are leftover cores from high mass star supernova (type II) explosions

• pressure becomes so high that electrons and protons combine to form neutrons throughout the object

• protons combine with electrons to make neutrons and neutrinos (really small particles)

properties of neutron stars

• very dense and small

• it will stop collapsing and be held up by neutron degeneracy pressure

• they spin very rapidly: 0.03 to 4 sec

• typical size: R= 3M

• mass: 1.4M - 3M

• density: 10^11 kg/cm³

• piece of neutron star matter of the size of a sugar cube has a mass of ~100 billion pounds

why do neutron stars spin so fast

conversation of angular momentum: before collapsing, the stars core probably rotates once every few hours

• collapse to a smaller radius, the rotation rate increases exponentially

• consider figure skater performing a spin: to rotate faster, they pull their arms in

pulsars

• in 1967, graduate student Jocelyn bell accidentally discovered a sharp pulse of light which recurred every 1.3 sec

• she called it a pulsar

• the pulsars observed were originally though to be a signal from extraterrestrials

• this was later shown to be unlikely after many other pulsars were found all over the sky

• the mystery was solved when another pulsar was discovered in the heart of the Crab Nebula

• the crab pulsar pulses in visual light as well as radio

pulsars and neutron stars

• all pulsars are neutron stars (but all neutron stars are not pulsars)

• pulsars are rotating, magnetized neutron stars

• emission (mostly radio) is concentrated at the magnetic poles and focused into a beam

pulsars - light house model

• beams of radiation emanate from the magnetic poles

• as the pulsar rotates, the beams sweep across the sky

• if the earth happens to lie in the path of the beams, we see the pulsar

• pulsars are the lighthouses of galaxies

the fates of neutron stars

• like the white dwarfs, a neutron star slowly irradiate the thermal energy into surrounding space… and eventually come into thermal equilibrium with the cold universe

• similar to an isolated white dwarf, the neutron star will eventually stop rotating, cool to the temperature of the surrounding universe, and becomes inert

• similar to a white dwarf, in a close binary system, a neutron star in a close binary system would still have a life after death

black holes

if a type II supernova explosion leaves behind a core that is greater than 3M:

• collapsing core passes though a neutron star stage

• neutron star not stable

• core shrinks even more and becomes a black hole

• “black” because it neither emits nor reflects light

• “hole” because nothing entering can ever escape

what did einstien say about gravity

mass distorts space - “curving it”

• objects and light moving near the massive objects are forced to take a curved path around the object, just like the moon orbiting the earth

what is a black hole?

• an unimaginably dense region of space where space is curved around it so completely and gravity becomes so strong that nothing, not even light, can escape

• mass is so great in such a small volume that the velocity needed to escape is greater than the speed light travels

a black hole has only a “center” and a “surface”

• the black hole is surrounded by an event horizon which is the sphere from which light cannot escape

• the distance between the black hole and its even horizon is the Schwarzchild radius

• the center of the black hole is a point of infinite density and zero volume, called a singularity (smaller than the size of an atom)

• a black hole is 3-dimensional

the schwarzchild radius

the larger the mass of a black hole, the larger the schwarzchild radius

• once light or any object has crossed the schwarzchild radius (or event radius), it can never escape the force of gravity of the black

• this is the point of no return

the center of the milky way

• the galactic center lies in the constellation of Sagittarius

• a supermassive black hole exists in the center

• probably a black hole 3 million times the mass of the sun → named Sagittarius A*

• not much matter appears to be accreted by a black hole

falling into a black hole: tidal forces

• falling toward a black hole wouldn’t be a pleasant experience

• falling feet first, your body would be scrunched sideways and stretched along the length of your body by the tidal forces (spaghetti noodle)

• stretching happens because your feet would be pulled much more strongly than your head

falling into a black hole: time dilation

• a friend watching you as you enter a black hole, would see your clock run slower and slower than theirs as you approach the event horizon

• your friend would see you brake an infinite amount of time to cross the event horizon → time would appear to stand still

• however, in your time frame your clock would run forward normally and you would read the center very soon

falling into a black hole: redshifted

• any light falling in will have its wavelength stretched

• the light would be extremely red-shifted

more on astronaut falling into black hole

• suppose he sends us a signal every second, according to his watch as he falls in space-time gets stretched more and more

• the time between signals get stretched also

• his signals appear to get further and further apart in time

• his signals are red-shifted

• any light reflected off him is red-shifted also, so he looks redder and redder

falling into a black hole - summary

1. object is stretched by tidal forces

2. time slows down as seen by outside observers

3. light gets extremely redshifted

wormholes and time machines

• Einstein discovered that general relativity predicts the possibility that black holes could connect our universe to another ‘parallel’ universe via a bridge

• such a bridge is called a wormhole

• however theories suggest that these wormholes collapse as soon as they are formed

• also, since traversing a wormhole means that you are emerging at a different space domain than the one you started with, you could star at present time and emerge at a time in the past (or future) - time travel!

intro to solar system

the solar system formed from a rotating cloud of cold gas and dust called the solar nebula about 4.6 billion years ago

birth of the solar system

1. collapse of a slow rotating cloud of interstellar gas and dust

2. cloud flattens and central region condenses

3. young sun shines with disk of gas and dust in which the planets are forming - random collision and sticking of particles

collisions dominated the early solar system

• clump collapses

• forms protoplanetary disk (planets form from the disk)

• center collapses, heats up, forms sun

• disk fragments forms planets

• “debris” gets cleared

• within the disk that surrounds the protosun, solid grains collide and clump together into planetesimals

our own solar system

• nearly circular orbits

• all going the same way around

• all in nearly the same plane

8 planets in the solar system

planets are categorized according to composition and size, there are two main categories of planets

1. small rocky planets (terrestrial) → mercury, venus, earth, mars

2. gas giants → jupiter, saturn, uranus, and neptume

inner (terrestrial) planets

• they are made mostly of rock and metal

• they are relatively heavy

• they are relatively small

• they have no rings and few moons (if any)

mercury

• a small, hot, rocky planet

• 1/3 of earths radius

• no atmosphere → heavily cratered

• temp: 430 degrees C to 180 degrees C

• no moons

• can be seen transiting the sun, it happened recently

venus

• earths twin in size

• brightest object in the sky … look west at sunset

• no moons

• carbon dioxide atmosphere (greenhouse effect)

• very hot → 480 degrees C

• venus transits the sun

• most recent: 2012, next is 2117

• the surface of venus is completely hidden beneath permanent cloud cover

our living earth and the atmosphere

• earth is the only planet known to support living organisms

• earths surface is composed of 71% water

• water is necessary for life on earth and the oceans help maintain earths stable temperatyres

• earth has one moon

• conditions of life is not too hot not too cold

the greenhouse effect

• visible light enters though glass

• warms the ground and air

• ground and air give off IR

• IR cant exit through a glass

• greenhouse gets warmer than outside

the greenhouse effect and earth

• sunlight energy comes in mostly as visible light

• warms atmosphere and ground which emit IR

• IR light is absorbed by greenhouse gases (CO2) in the atmosphere

• “recycles” some of the energy → warms earth

asteroids belt and ceres

• asteroids are composed of carbon or iron and other rocky material

• the asteroid belt is a group of ricks that appear to have never joined to make a planet

• most asteroids remain in the asteroid belt between mars and jupiter but a few have orbits that cross earths path

• many asteroids enter earths atmosphere

• on average, 3 large asteroids hit the earth every 1 million years

shooting star

• when a small asteroid enters earths atmosphere, it burns up as it encounters air friction at tremendous speeds

• a shooting star is just a tiny grain/rock that has entered the earths atmosphere

• air friction causes the rock to heat up so much it begins to burn across the sky

craters

• hole in the ground caused by an asteroid hitting earth

• daniel barringer purchased this land in 1904 to look for iron, there was no iron found in the depot was 174 meters

why are mercury and the moon heavily cratered

no atmosphere to cause asteroids to burn up, they always reach the surface

earths moon

• it takes the moon approximately 29 days to complete one rotation around earth

• the same side of the moon always faces us

• the moons surface is covered in dust and rocky debris from meteor impacts

• it has no water or atmosphere

• the moon reflects light from sun onto the earths surface

how did we get our moon

according to one theory, 4.5 billion years ago a mars sized asteroid rock hit the earth at such a high speed that both liquified, debris created another large rock close to earth

phases of the moon

• moon appears different over the course of one month due to its orbit around the earth

• we (from earth) only see certain parts of the moon lit up by the sun at different times

why do we have seasons

• look at the earth-sun distance in july and january

• when we are closest to sun, were 3% closer than the farthest point

• the tilt of the earth causes seasons

• since the earth is tilted, the sun strikes earth differently in various parts

• the angle of sunlight affects heating

• sunlight is spread over a larger area when the suns altitude is low, thus does not penetrate the ground as much

mars

• smaller in size than earth

• rusty red soil

• temperature: -10 degrees to -120 degrees

• atmosphere is mostly carbon dioxide

• gravity is ~1/3 that of earth

• 2 moons (phobos and deimos)

• contains water - both liquid and frozen

• enormous volcanoes (valles marineris is as big as the entire united states)

• olympus mons: the largest volcano in the solar system has a base larger than the state of arizona and is 25 km high

liquid water on mars?

• today the surface temperature and pressure seem too low for liquid, but there is some debatable evidence that it happens

• other sources of H2O, polar caps, under ground

outer (jovian) gas planets

jupiter, saturn, uranus, neptune

characteristics:

• enormous

• made mostly of hydrogen and helium

• far from sun

• separated by large distances

• have ring systems

• have many moons

jupiter

• is the largest of the gas giant planets

• 79 moons

• has faint rings

• gravity is 2.5 times that of earths

• great red spot → giant hurricane

four of jupiters biggest moons

• Io

• Europa

• Ganeymede

• Callisto

Saturn

• saturn has the most extensive ring system in the solar system

• rings are just ice/rocks orbiting saturn

• less dense than water → would float in a bathtub big enough

• 82 moons

uranus

• is tipped on its side about 98 degrees

• 27 moons

• narrow faint rings

neptune

• is the smallest of the gas giants

• faint rings

• great dark split is an occasional giant storm like the one on jupiter

• 13 moons

frost line

• is the dividing line between where hydrogen compounds can and cannot condense out (forms ice)

• the formation of jovian planets occurred outside the frost line, where ices could also form small particles

dwarf planets

orbits in a zone that has other objects in it

newtons law of gravity

• newtons saw an apple falling

• he though: if it is gravity that causes the apple to fall to earth, then it is probably gravity that holds the moon in orbit around the earth

gravity and acceleration

• falling objects accelerate (due to gravity)

• earth: g=10m/s²

mass is not weight

• mass = the amount of matter in an object

• measured in gram or kg

• weight = a measure of force

weightlessness

• gravity always still there

• whats missing is a contact force (nothing is holding you up)

• apparent weight is the strength of that contact force

• so you fall with 10m/s² and feel weightless

newtons law of gravitation

says the strength of the force depends on the:

1. masses of the objects

2. distance between them

masses of the objects

• gravitational force is small between objects that have small massive

• it is large between objects that have large masses

• If one object doubles in mass, then the gravitational force doubles

• If both objects double in mass, then the force doubles twice, becoming four times as strong

distance between objects

• gravitational force is strong when the distance between objects is small

• if the distance between object increases, then gravity decreases

inverse square law

• Gravitational force is inversely proportional to the square of the distance between objects

• Doubling the separation distance produces one-fourth of the force

• If the distance is reduced by one-half, force is four times as great

planets orbiting other stars

• An extrasolar planet, or exoplanet is a planet beyond our solar system, orbiting a star other than our sun

Overview of Extrasolar Planets

• First extrasolar planet found around a sun-like star: 1995

• Number to date: over 4000 planets

• Closest to parent star: 0.006 AU (compared with mercury 0.4 AU)

• Furthest from parent star: 650 AU (compared with pluto 40 AU)

• Detention methods: numerous, mostly indirect

Detecting Extrasolar Planets

1. Method 1: Direct Observation

• The most obvious method of detecting a planet around another star is to directly image the planet, just as we image stars

• Unlike stars, planets are both much smaller and observable only in reflected light, and so far fainter

• The glare of their parent star makes it incredibly difficult to see them

2. Method 2: Transits

• Planets observed at inclinations near 90 degrees will transit their host stars (pass in front of their stars relative to us)

• We can determine orbital period and size of planet

• Advantages: easy, can be done with small cheap telescopes, possible to detect low mass planets such as earths

• Disadvantages: probability of seeing a transit is low, easy to confuse with star spots, binary systems, needs other measurements for confirmation and masses

3. Method 3: Doppler Planet Detection

• In a stellar system with a planet, both the star and the planet revolve around the center-of-mass

• Even if the planet is not directly visible (as is usual), the star can be observed to rotate around the center-of-mass of the combined system

Radial Velocity Technique (Doppler “Wobble”)

• Star + planet orbit common centre of mass

• As stars move towards observer, wavelength of light shortens (is blue-shifted)

• Starlight red-shifted as stars moves away

• Lets us determine mass of planet