Exam 3

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Chapter 15

The theory of relativity

Albert Einstein surprised the world in 1905 when:

He theorized that time and distance cannot be measured absolutely

Only have meaning when measured relative to something

Einstein published his theory in two steps

Special theory of relativity (1905) – space and time are interwoven

General theory of relativity (1915) – effects of gravity on space and time

What is relative in relativity?

All motion is relative

Measurements of motion make no sense unless we are told what they are being measured relative to

What is absolute in relativity?

Laws of nature are the same for everyone

Speed of light, c, is the same for all

What is relative?

A plane flies from Nairobi to Quito at 1650 km/hr; the earth rotates at 1650 km/hr

An observer:

On earth’s surface sees the plane fly westward overhead

At a far distance sees the plane stand still and the earth rotates underneath it

The "Up" Paradox

In childhood, we regard up as a single direction above our heads

Up is relative to the center of the earth

Is the speed of light absolute?

The speed of light was first measured by Olaus Roemer in 1675

Experimental evidence for the absoluteness of c came in 1887

Michelson-Morley experiment

AA Michelson and EW Morley used an interferometer to show the speed of light is unaffected by the earth's motion around the sun

Speed of light also unaffected by the motion of binary stars

Light travels straight up and down

Warping of Time by Gravity

In the vicinity of the black hole, time slows down.

If we launched a probe to it, as it approached the event horizon

From the mother ship’s view, it takes forever to reach event horizon

Light from the probe is red-shifted

Probe would eventually disappear

From the probe’s view:

Head straight into the black hole

Light from the mother ship is blue-shifted

Regions of the Milky Way Galaxy

Diameter of disk = 100,000 ly

Thickness of disk = 1000 ly

Number of stars = 200 billion

Sun is in the disk, 28000 ly away from center

Disk

Younger generation of stars

Contains gas and dust

Location of the open clusters

Bulge

Mixture of both young and old stars

Halo

Older generation of stars

Contains no gas or dust

Location of the globular clusters

Halo vs. Disk

Stars in the disk are relatively young

Fraction of heavy elements same as or greater than the sun

Plenty of high and low mass stars, blue and red

Stars in the halo are old

Fraction of heavy elements much less than the sun

Mostly low-mass, red stars

Stars in the halo must have formed early in the Galaxy’s history

Formed at a time when few heavy elements existed

No ISM in the halo

Star formation stopped long ago in the halo when all gas flattened into the disk

The Interstellar Medium (ISM)

The stuff between the stars

Mostly a vacuum

Composed of 90% gas and 10% dust

Gas: individual atoms and molecules

Dust: large grains made of heavier elements

The ISM effectively absorbs or scatters visible light

Masks most of the milky way galaxy from us

Radio and infrared light does not pass through the ISM

We can study and map the milky way galaxy by masking observations at these wavelengths

Stellar Orbits in the Galaxy

Stars in the disk all orbit the galactic center

Same direction

Same plane

“bobble” up and down

Due to gravitational pull from the disk

Gives the disk its thickness

Stars in the bulge and halo all orbit the galactic center

Different directions

Various inclinations to the disk

Higher velocities

Not slowed by disk as they plunge through it

Mass of the galaxy

We can use Kepler’s third law to estimate the mass

Sun’s distance from center: 28000 ly

Suns orbital period: 230 million years

Total mass of MW galaxy: 10^12 M

Total number of stars in MW galaxy: ~ 2 x 10^11

Center of the Galaxy

Measure the orbits of fast-moving stars near the galactic center

Measurements must be made in the infrared

What can be so small, yet so massive?

Xray Flare from Sgr A

Emission region is 20 times the size of the event horizon of the 4 million M black hole

Observations consistent with existence of supermassive black hole at center of our galaxy

Energy from flare likely came from a comet sized lump of matter, torn apart before falling beneath event horizon

Classification of galaxies

Using a system invented by Edwin hubble, astronomers classify galaxies into 3 major types

Spiral

Elliptical

Irregular

Sizes of 3 types span wide range

Dwarf galaxies

Contain 100 million stars

giant galaxies

Contain 1 trillion stars

Quasars

In the early 1960s, Maarten Schmidt identified the radio source, 3C 273, with a faint blue star

The stars spectrum displayed emission lines

Wavelengths of these lines matched no known element

Schmidt realized that the emission lines belonged to Hydrogen, but were highly redshifted

Object is very far away

Other such objects were subsequently discovered

Were called quasi-stellar radio sources or quasars for short

Quasars exist only in the early universe

The farther away we look out in distance, the farther back we look in time – lookback time

Extremely luminous

10^40 watts

1000 times brighter than the entire milky way galaxy

Extremely variable

Luminosity changes <1 hour

Implies they have a very small size

Redshifted emission lines

Greatest is 6.8 times the lower redshifts

Have absorption lines at lower redshifts

From gas clouds and galaxies between us and the quasar

Quasar spectra

Star-like objects which:

Have spectra that look nothing like a star

Highly redshifted

Can be strong radio source

90% are not

Emit light at all wavelengths

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Chapter 16/17

What is Cosmology?

Cosmology is understanding the nature of the universe and its size, shape, age, genesis, and fate

The hubble deep field telescope has an open camera shutter for days or weeks

Allows it to see the "empty" part of space

Galaxies are in the "empty" space

Henrietta Swan Levitt

Used radar to measure distance (only works with close things)

USed parallax method to find the distance of nearby stars

Cepheid variables - measure size and distance of object by measuring brightness, which is found by how fast it pulses

Distance indicators can overlap, causes error

Error is greater for further distances

Edwin Hubble (1889-1953)

Discovered Cepheid Variable in the Andromeda galaxy

Calculated distance to Andromeda galaxy

2 million light years

Not in the milky way

Developed a classification scheme for galaxies

Has a space telescope named after him

Milton Humanson (1891-1972)

Former mule-team driver, dropped out of 8th grade

Helped build observatories by hauling supplies by mule

Got interested in astronomy and started working with Hubble

took spectra and measured redshifts of many galaxies

Worked with Hubble, who measured distances to the same galaxies

didn't get credit for helping Hubble

Plotted distance vs. velocity and formulated Hubble's Law

v=Hd

Hubble's Law

Hubble supplies the distance to a galaxy

Using Cepheid or "brightest star" standard candles

Humanson measured the shift to longer wavelengths of absorption lines in galaxy's spectrum

used doppler formula to calculate velocity

Plot resulted in a straight line

Farther away a galaxy was, faster it was moving away from us

Velocity increased linearly with distance

H, the slope of the line, is called Hubble's constant

Hubble's law does not apply to nearest galaxies

An Expanding Universe

The consequence of Hubble's law is:

Most galaxies are moving away from us

If all galaxies swarm out through a void, then is the Milky Way at the center of the Universe?

The universe itself is expanding

Galaxies expand with it

No center or edge to the universe

Imagine a balloon with dots on it, blow it up and dots expand and spread apart

From a galaxy's pov, other galaxies are all moving away from it

The age of the universe

In the context of the expanding universe:

H tells us the rate at which galaxies are moving apart from one another

If we run the clock backward to when the galaxies were all at one point

1/tells use how long it took the universe to expand to its current size

If the expansion rate was constant, 1/H would only estimate the age of the universe

Best measurement was of the Hubble constant

comes from the Wilkinson Microwave Anisotropy Probe

Results announced by NASA in February 2003

H ~ 70 km/s per Mpc

The age of the universe, 1/H ~13.8 billion years

Size of the Observable Universe

Universe has no edge, but it does have a horizon

The cosmological horizon is the place where lookback time equals the age of the universe

Cannot see beyond this horizon, because we would be looking at a time before the Universe existed

Our observable Universe grows 1 light year in size every year

Fritz Zwicky

assume galaxies orbit about the cluster center

measure orbital velocities of galaxies

measure each galaxy's distance from the center

apply Kepler's law to calculate mass of cluster

Mass we can't see is Dark Matter

It took ~40 years for people to take him seriously

What is dark matter made of?

Could be "ordinary" particles (protons, neutrons, electrons)

Same matter we are made up of

If this is so, then the only unusual thing about dark matter is that its dim

However, some or all of dark matter could be made of particles that have not yet been discovered

This would be "extraordinary" matter

Baryonic matter - physicist title for ordinary matter

Protons and neutrons called baryons

Call extraordinary matter nonbaryonic matter

An ordinary matter candidate

Our galactic halo should contains baryonic matter, which is dark

Low mass dwarfs, brown dwarfs, and jovian sized planets

Too faint to be seen at large distances

Have been called "Massive compact halo objects" or MACHOs

Stars that never got big enough - too faint

We detect them if they pass in front of a star where they:

gravitationally lens the star's light - bend star's light

star gets much brighter for a few days to weeks

Can measure MACHO's mass

Happens to only 1 in a million stars per year

Must moniter huge numbers of stars

# of MACHOs detected so far does not account for the Milky Way's dark matter

Another nonbaryonic form of matter:

The neutrino, detected from the sun

neutrinos interact with other particles through only 2 of the natural forces

gravity

weak force

Masses are so low d speeds are so high, they will escape the gravitational pull of a galaxy, they cannot account for the dark matter observed

The 4 forces

Strong - holds nuclei together

electromagnetic - chemistry and biology

weak - nuclear reactions

gravity - large-scale structure

What if there were a massive weakly interacting particle?

physicists call them Weakly interacting Massive Particles (WIMPs)

Have not yet been discovered

Massive enough to exert gravitational influence

emit no electromagnetic radiation or be bound to any charged matter that could emit light

would not collapse with a galaxy's disk

remain gravitationally bound in galaxy's halo

Critical density

Gravitational attraction between galaxies can overcome expansion of the universe in localized regions

How much gravity would stop the entire universe from expanding?

it depends on the total mass density of the universe

Refer to mass density required for this gravitational pull to = the kinetic energy of the universe as the critical density

if mass < critical density, universe will expand forever

if mass > critical density, the universe will stop expanding and then contract

The value of H tells us the current kinetic energy of the Universe

critical density is 10^-29 g/cm^3

All the luminous matter that we observe accounts for ~ 4% of critical density

For dark matter to stop universal expansion, the average M/L of the universe would have to be 1000 M/L, a few times greater that clusters

Research suggests the universe will expand forever

4 Models for the Future of the Universe

Recollapsing universe - expansion will someday halt and reverse (mass > critical density)

Critical universe - will not collapse, but will expand more slowly with time (mass=critical density)

Coasting universe - will expand forever with little slowdown (mass < critical density)

Accelerating universe - expansion will accelerate with time (currently favored)

Does gravity alone influence the expansion?

recent observations of white dwarf supernovae have yeilded unexpected results

remember, white dwarf supernovae make very good standard candles, supernovae are apparently fainter than predicted for their redshifts

Implies that universal expansion is accelerating

be an as yet unknown force which repels galaxies

DARK ENERGY

Hubble's Law

Hubble's law shows the universe expanding linearly, this is not accurate

Hubble supplied the distance to a galaxy

using Cepheid or "brightest star" standard candles

Humanson measured shift to longer wavelengths of absorption lines in the galaxy's spectrum

Used doppler formula to calculate velocity

Plot resulted in a straight line

the farther away a galaxy was, the faster it was moving away from us

velocity increased linearly with distance

v = Hd

H, the slope of the line, is called Hubble's constant (km/s per Mpc)

Condition in the early universe

the most distant galaxies we observe come from a time when the Universe was a few billion years old

The cosmic microwave background prevents us viewing light from before the universe was 380,000 years old

How do we know what conditions were like at the beginning of time?

We know the conditions and expansion rate of the universe today

By running expansion time backwards:

we can predict the temperature and density of the universe at anytime in history using basic physics

We study how matter behaves at high temperatures and densities in lab experiments

current experimental evidence provides info on conditions as early as 10^-10 seconds after the big bang

The creation of matter

The early universe was filled with radiation and subatomic particles

We've seen matter converted to energy

Einstein's famous equation

Photons come together to create matter and antimatter

matter and antimatter annihilate each other to create photons

Olber's paradox

f the universe is infinite and filled with stars, then why is the night sky black?

there is a finite number of stars, because the universe had a beginning

Starlight is redshifted out of the visible range