Astronomy Midterm #2

Primary Galactic Features (2)

• we see the Milky Way from edge-on

• Primary features: disk, bulge, halo, globular clusters

Our galaxy: Interstellar Medium (2)

• Our view is obscured by dusty gas clouds, as they absorb visible light

• these clouds make new star systems

Galileo

• didn’t know shape of our galaxy, but used his telescope to discover many new stars

Herschel

• counted how many stars lies in each direction, suggested that the width was larger than thickness

Kapteyn

• confirmed Herschel result, suggested that
  our Sun is at the center of the Milky Way (wrong)

Shapley

• found that globular clusters appeared to be
  centered far from the Sun, at the true center of our
  galaxy

Stellar Orbit: Disk

• all stars in the disk orbit in the same direction with a
  little up-and-down motion

Stellar Orbit: Bulge and halo

• stars here orbit with random orientations

Getting stellar orbits (3)

• found by measuring stellar motion relative to the sun

• doppler effect can only tell up radial velocity

• tangential velocity is harder to measure, changes apparent position

Star-gas-star cycle: Recycling old star’s gas (9)

• low mass stars return gas to space through stellar winds and planetary nebulae

• high mass stars have strong winds that blow bubbles of hot gas

• gas is then ionized around exploding stars, new heavy elements in supernova remnants 

• remnant cools and expands, emitting visible light

• new elements made by supernova mix into the interstellar medium 

• radio emission in remnants from particles accelerated to near light speed (could also be source of cosmic rays 

• Atomic Hydrogen Gas Atomic forms as hot gas cools, allowing electrons to join with protons. This gas emits a spectral line with wavelength
  at 21 cm (radio portion of the electromagnetic
  spectrum)

• molecular clouds forms after atomic hydrogen gas, after the gas cools enough for molecule formation

• Gravity forms stars out of the gas in molecular clouds, completing the star–gas–star cycle

Galactic Recycling Summary (5)

• Stars make new elements by fusion

• Dying stars expel gas and new elements, producing hot bubbles (~106 K).

• Hot gas cools, allowing atomic hydrogen clouds to form (~100–10,000 K).

• Further cooling permits molecules to form, making
  molecular clouds (~30 K).

• Gravity forms new stars (and planets) in molecular
  clouds.

Observing star-gas-cycle (5)

• observed using light wavelengths

• Radio waves: atomic hydrogen shows where gas has cooled and formed a disk, carbon monoxide shows the locations of molecular clouds

• Infrared: reveals where young stars are heating dust grains and stars who’s light is blocked by gas

• x-rays: produced by the hot gas found above and below the disk

• gamma rays: reveals where cosmic rays collide with atomic nuclei

Ionization nebulae (3)

• located around short-lived, high-mass stars, aka regions of active star formation

• none are found in the halo

• mostly in disk where star formation occurs (spiral arms)
  formation

Spiral Arm star formation (3)

1. Gas clouds get squeezed as they move into spiral arms.
2. Squeezing of clouds triggers star formation.
3. Young stars flow out of spiral arms.

Halo stars

old stars, roughly 0.2% heavy elements

Disk stars (2)

• all ages, 2% heavy elements

• continually form as galaxy grows older

Galactic center (2)

• stars appear to orbit a massive (4Mx mass of sun), invisible black hole

• shown by x-ray flares from tidal forces tearing apart matter

Mass of a main-sequence star determines:

its core pressure and temperature

Stars of higher mass have: (3)

• higher core temperature and
  more rapid fusion

• this makes those stars both more luminous and shorter-lived.

• High-Mass Stars : > 8M Sun

Stars of lower mass have: (3)

• cooler cores and slower fusion rates

• this gives them smaller luminosities and longer lifetimes

• Low-Mass Stars < 2M Sun

Life Track after Main Sequence: (3)

• depends on stars mass

• Low-mass: red giant → planetary nebula → white dwarf

• High-mass: red super giant → supernova → black hole/neutron star

Red Giants: Broken Thermostat (3)

• during contraction, H fuses into He in a shell around the core

• luminosity increases as the increasing fusion within the shell doesn’t stop contraction

• overall increases temperature

Helium fusion does not begin right away because: (2)

• helium fusion requires higher temperature, as a larger electric charge leads to greater repulsion

• two helium nuclei cannot fuse, rather three fuse to make carbon

The thermostat of a low-mass red giant is broken because:

• the core is supported by degeneracy pressure

Core temperature rises rapidly when: 

helium fusion begins.

Helium fusion rate skyrockets until thermal pressure takes over and expands the core again. (Helium Flash)

Helium-burning stars neither shrink nor grow because:

• core thermostat is temporarily fixed

Life Track after Helium Flash: (2)

• models show that a red giant should shrink and become less luminous after helium fusion begins

• Helium burning stars are found on a horizontal branch on the HR Diagram

After core helium fusion stops: (2)

• the helium fuses into carbon around the now carbon core

• hydrogen fuses into helium in a shell around the helium layer

Double-shell burning stage  (3)

• stage where a lower mass star has a carbon core and two active fusion shells, outer hydrogen and inner helium

• equilibrium is never reaches, fusion rate periodically spikes in a series of thermal pulses

• with each spike, convection transports carbon from the core to the surface

Double shell burning ends with: (2)

• a pulse that ejects the hydrogen and helium into space as a planetary nebula

• the core left behind becomes a white dwarf

Fusion progresses no further in a low-mass star
because: (2)

• core temp never gets hot enough for fusion of heavier elements

• degeneracy pressure supports the now white dwarf star

Life Track of a Sun-like Star:

sub giant/red giant core → helium burning core → double shell burning core

Fate of Earth: (2)

• eventually, the suns luminosity will rise to 1000x its current level, making it too hot to sustain life on Earth

• the sun’s radius will grow to be near the current radius of earth’s orbit

CNO Cycle (2)

• high mass, main sequence stars begin fusing hydrogen to helium at a faster rate using carbon, nitrogen, and oxygen as catalysts

• the higher core temp allows hydrogen nuclei to overcome repulsion

Life Stages of High-Mass Stars: (2)

• Late life stages of high-mass stars are similar to
  those of low-mass stars

• Hydrogen core fusion (main sequence)→ Hydrogen shell burning (supergiant)→ Helium core fusion (supergiant)

Helium Capture

• higher core temperatures allow helium to fuse with heavier elements

Advanced Nuclear Burning

• core temperatures in stars with > 8M Sun allow fusion of elements as heavy as iron.

Multiple Shell Burning (2)

• advanced nuclear burning proceeds in a series of nested shells.

• Iron is a dead end for fusion a nuclear reactions involving iron do not release energy (iron has lowest mass per nuclear particle)

End of High-Mass star: (2)

• Iron builds up in core until degeneracy pressure can no longer resist gravity

• The core then suddenly collapses, creating a supernova explosion

Supernova Explosion (2)

• Core degeneracy pressure ceases because electrons combine with protons, making neutrons and neutrinos

• Neutrons collapse to the center, causing a supernova a forming a neutron star

Supernova remnant (2)

• energy released by the collapse of the core drives the star’s outer layers into space

• Ex. The Crab Nebula

Supernova 1987A

• The closest supernova in the last four centuries was seen in 1987

Intermediate mass stars:

• can fuse elements heavier than carbon but end as white dwarf

Low-Mass star summary: (5)

• Main Sequence: H fuses to He in core

• Red giant: H fuses to He in shell around core 

• Helium core burning: H fuses to C in core, H fuses to He in shell around core 

• Double shell burning: H and He both fuse in shell

• Nebula leaves behind white dwarf 

High-Mass star Summary: (5)

1. Main sequence: H fuses to He in core.

2. Red supergiant: H fuses to He in shell around He core.

3. Helium core burning: He fuses to C in core while H fuses to He in shell.

4. Multiple shell burning: Many elements fuse in shells.

5. Supernova leaves neutron star behind.

Life stage reasons: (4)

• Core shrinks and heats until it’s hot enough for fusion.

• Nuclei with larger charge require higher temperature for fusion (ex. helium requires higher than hydrogen)

• Core thermostat is broken while core is not hot enough for fusion (shell burning).

• Core fusion can’t happen if degeneracy pressure prevents core from shrinking

Mass Exchange

• stars with close companions can exchange mass, altering the usual life tracks of stars

White dwarf (3)

• the remaining cores of dead stars.

• electron degeneracy pressure supports them against the crush of gravity

• they cool off and grow dimmer with time

White dwarf: Sizes (2)

• white dwarfs with same mass as Sun are
  about same size as Earth

• Higher-mass white dwarfs are smaller

The White Dwarf Limit (4)

• aka “Chandrasekhar limit”

• quantum mechanics say that electrons must move faster when condensed in a small space (degeneracy pressure)

• when a white dwarf’s mass approaches 1.4M Sun, it gets smaller and more dense, meaning its inner electrons move faster, approaching the speed of light

• since nothing can move faster than light, the Chandrasekhar limit is 1.4M sun

White dwarf in a close binary system:

• the smaller star in the system gains mass from its companion until the mass-losing star becomes a white dwarf

Accretion Disks (3)

• the mass falling towards a white dwarf from its binary companion has some angular momentum

• this matter therefore orbits the white dwarf in an accretion disk

• friction between the orbiting rings of matter in the disk transfers angular momentum outward, causing the disk to heat up and glow

Nova (3)

• when fusion begins suddenly and explosively, a nova forms

• the nova star system will temporarily appear much brighter, the explosion drives the accreted matter into space

• the temp of that matter eventually becomes hot enough for fusion

Massive star supernova

• when the iron core of a massive star reaches the white dwarf limit, it collapses into a neutron star and causes an explosion

White Dwarf Supernova

• carbon fusion suddenly begins when a white dwarf star in a close binary system reaches the limit, causing an explosion

Telling supernova apart: 

• using a light curve, showing how luminosity changes with time

Nova vs. Supernova (3)

• supernova are much more luminous

• Nova: hydrogen to helium fusion of the layer of accreted matter leaves a white dwarf behind

• Supernova: complete explosion of a white dwarf, leaving nothing behind
  

Massive star vs white dwarf (2)

• the light curves and spectra are different

• ex. exploding white dwarfs don’t have hydrogen absorption lines

Neutron star (4)

• ball of neutrons left over after a massive star supernova

• electron degeneracy pressure goes away as electrons combine with protons to form neutrons and neutrinos

• the newly formed neutrons collapse to the center, forming a neutron star

• neutron degeneracy pressure now supports the star from collapsing under gravity

Neutron star size (1)

roughly the size of small city

Discovery of Neutron stars (2)

• in 1967, Jocelyn Bell noticed regular radio emission pulses coming from a point in space

• they were emitted from a spinning neutron star, aka a pulsar

Pulsars (3)

• a neutron star that beams radiation along its magnetic axis

• this axis is not aligned with its axis of rotation

• these beams sweep through space as the star rotates

x-ray bursts (1)

• the sudden onset of fusion from the heated accreted matter on a neutron star produces these

Pulsars spin fast because (2):

• conservation of angular momentum

• the speed of the core’s rotation increases as the star collapses into a neutron star

Accretion Disks and Neutron stars (3)

• matter falling towards a neutron star forms an accretion disk

• this matter adds angular momentum, increasing rotation speed

• this is much like a white dwarf binary system

Spacetime (3)

• as per Special Relativity, space and time are not absolute

• rather, they are linked in a 4-D combination coined ‘Spacetime’

• gravity comes from the distortion of spacetime

Key Ideas of General Relativity (5)

• Gravity arises from distortions of spacetime.

• Time runs slowly in gravitational fields.

• Black holes can exist in spacetime.

• The universe may have no boundaries and no center but may still have finite volume.

• Rapid changes in the motion of large masses cause gravitational waves.

The Equivalence Principle (2)

• Einstein preserved the idea that all motion is relative

• he pointed out that the effects of acceleration are exactly equivalent to those of gravity

Dimensions of Spacetime (3)

• We can move through three dimensions in space (x, y, z).

• Our motion through time is in one direction (t).

• Spacetime, the combination of space and time, has four dimensions (x, y, x, t).

Rules of Geometry in Flat Space (4)

• A straight line is shortest distance
between two points.

• Parallel lines stay the same distance apart.

• Angles of a triangle add up to 180°.

• Circumference of a circle is 2πr.

Geometry on a Curved Surface (1)

• the great circle connecting two points is the shortest distance between them

Gravity: Newton vs. Einstein (2)

• Newton viewed gravity as a mysterious
  “action at a distance.”

• Einstein removed the mystery by showing that what we perceive as gravity arises from curvature of spacetime.

Curvature Near Sun

• Sun’s mass curves spacetime near its surface.

• If we could shrink the Sun without changing its mass, curvature of spacetime would become greater
  near its surface, as would strength of gravity.

Curvature Near Black Hole (3)

• if the sun continued to shrink, the curvature of spacetime would become so great that it would form a “bottomless pit,” aka a black hole

• the curvature of spacetime near a black hole is so great that nothing can escape its gravity

• Event Horizon: “point of no return,” a three dimensional surface

Time in an Gravitational Field (2)

• effects of gravity = effects of acceleration

• time moves faster at higher altitudes in a gravitational field

Black Hole (1)

an object whose gravity is so powerful that not even light can escape it

“Surface” of a Black Hole (2)

• spherical surface called the Event Horizon, the radius where the escape velocity equals the speed of light

• this radius is called the “Schwarzschild Radius”

“No escape from a black hole” (3)

• Nothing can escape from within the event horizon because nothing can go faster than light

• no escape refers to completely losing contact with something that falls in, the object loses its identity

• this increases the holes mass and can change its spin/charge

Singularity (2)

• beyond the neutron star limit (TOV), no force can resist the crush of gravity

• gravity crushed all matter into a single point called this

Neutron Star Limit (3)

• stated by quantum mechanics: neutrons cannot occupy the same state at the same time

• if the mass of a neutron star exceeds roughly 3M Sun, neutron degeneracy pressure can no longer support the star from collapse

• some massive star supernova can create a black hole if enough mass falls into the core

Black Hole Verification (3)

• Mass is measured by using orbital properties and measuring the velocity and distance of orbiting gas

• if the mass exceeds the neutron star limit, and its not a star, its a black hole

• some x-ray binaries contain objects of mass exceeding 3MSun, meaning they are likely to be black holes

Interstellar Medium

The gas between the stars

Star Forming Clouds

dark clouds of dusty gas in
interstellar space

Cloud Composition (2)

• determined by gas absorption lines
  

• Milky Way Region:
  70% H 28% He 2% heavier elements

Molecular Clouds (3)

• most of the matter is the form of molecules (H2, CO, etc)

• temp = 10-30k

• density = 300 molecules per cubic centimeter

Interstellar Dust (2)

• blocks our view of stars

• made of elements like C, O, Si, and Fe.

Interstellar reddening

when interstellar dust blocks shorter-wavelength light more effectively than longer-wavelength, so stars viewed through the edges of the dust appear redder

Observing Newborn Stars

using infrared light, as most of a newborn star’s visible light is trapped within the dark gas clouds (interstellar reddening)

Glowing Dust

dust grains that absorb visible light, causing the grains to heat up and emit infrared light

Gravity vs. Pressure (2)

• gravity creates stars when it can overcome thermal pressure

• pressure buildup can be prevented by the conversion of thermal energy into infrared/photons

Mass of Star forming cloud

• typical molecular cloud (T~ 30 K, n ~ 300 particles/ cm3) must be at least a few hundred solar masses in order for gravity to overcome pressure.

Gravitational resistance

• if a cloud has other forces (ex. magnetic fields, turbulent gas) opposing gravity, the cloud must be more massive to begin gravitational contraction

Cloud Fragmentation (3)

• denser gas within cloud → stronger gravity within cloud

• meaning, in smaller, denser sections of a cloud, gravity can overcome pressure

• this leads to the cloud breaking apart into fragments, which can each go on and form a star
  

Isolated star formation

• in a small cloud, gravity can easily overcome pressure, forming a single star (like fragmentation)

First stars (2)

• more massive than today’s stars, as gravity has to overcome pressure for formation

• there was no CO in the early universe, meaning the clouds were much warmer

Trapping of Thermal Energy (3)

• contraction packs molecules and dust closer together, therefore making it harder for infrared and radio photons to escape the cloud

• this leads to a buildup of thermal pressure

• therefore, contraction slows down, and a protostar can form

Protostar

early stage of a star

Protostar Growth

matter from the surrounding cloud continues to fall into the protostar until it’s blown away

Nebula Theory of solar system (2)

• says the solar system formed from a nebula that collapsed from its own gravity, forming a disk

• illustrates the importance of rotation

Conservation of angular momentum 

cloud contraction → increased rotation speed

(smaller radius = higher velocity)