astro midterm 3 - dark energy, universe & galaxy formation, dark matter, relativity, & the big bang

so how do we measure distances?

for very nearby (milky way, neighbors): parallax

nearby distances (at to z = 0.01): cepheid distances

• ubiquitous (existing or being everywhere at the same time), but faint (good, but not enough)

far out (out to z = 1): type 1a supernovae

• once per galaxy per 100 years

• more rare, but bright

the universe is accelerating

dark energy

• Ωλ is proportional to Ω°λ(a)^3(1+w)

  • λ is dark energy

• Ωλ = p_DE/p_crit

• if w = -1, Ωλ is proportional to Ω°λ(a)³⁽⁰⁾ is proportional to Ω°λ

  • DE is constant in density

dark energy

current best definition: the energy of empty space/vacuum

• would have a constant energy density

what causes the expansion of the universe to accelerate

• the universe is 73% made of dark energy

the fate of our universe

big chill – universe will become very spread out

in 100 billion years the only things left visible will be the objects that are not expanding away from us (bound by gravity)

dark energy doesn’t affect our daily lives

amount of vacuum energy in 1 cubic meter = 6.75×10⁻¹⁰ J

• needed to cause the accelerating expansion

60 W light bulb puts out 60 J of energy every second = 889 billion times amount of vacuum energy in 1 cubic meter of space

• requires vast regions of empty space for it to matter

cosmology problems

coincidence problem & cosmological constant problem

the cosmological constant problem

quantum mechanics: makes predictions of the cosmological constant - the energy of the vacuum

• 10¹²⁰ off of what we measure for universe w/ supernovae

the coincidence problem

the energy density of dark energy is in the same order of magnitude as that of the only matter in this period

best models of galaxy formation assume:

matter originally filled all of space almost uniformly

• CMB

gravity of denser regions pulled in surrounding matter

denser regions contracted, forming protogalactic clouds

hydrogen & helium gas in these clouds formed the first stars

supernovae explosions from the first stars kept much of the gas from forming stars

• suppress star formation

leftover gas settled into a spinning disk due to the conservation of angular momentum

protogalactic clouds

a cloud with mass equal to that of a galaxy, and whose collapse leads to the formation of the currently observed stars

star forming clouds

types of galaxies

spiral (early type) & elliptical (late type galaxies)

why do galaxies differ?

1. initial conditions

2. something happened (ie collision)

conditions in protogalactic cloud

spin: the initial angular momentum of the protogalactic cloud could determine the size of the resulting disk

density: elliptical galaxies could come from dense protogalactic clouds that were able to cool & form stars before gas settled into a disk

galaxies conservation of angular momentum

spiral:

• the cloud can cool

• gravity

• radiation pressure unimpeded

elliptical:

• this cloud has more radiation pressure

• spherically symmetric

collisions of galaxies

spirals merge to form ellipticals

were much more likely early in time because the density of the universe/separation btwn galaxies was more dense

• many of the galaxies we see at great distances (and early times) do look violently disturbed

explains why elliptical galaxies tend to be found where galaxies are closer together

the collisions we observe nearby trigger bursts of star formation

the most likely reason that clusters of galaxies have more elliptical than spiral galaxies is that in the high density cluster environment

spirals merge to form ellipticals

starburst galaxies

form stars so quickly that they would use up all their gas in less than a billion years

• 100-1000x the star formation seen in our milky way

active galactic nucleii

brightest objects in the universe – quasars

• directly tired to galaxy formation

• seen at extremely large redshifts/distances

• allow us to study the intervening material over nearly the entire history of the universe

highly redshifted spectra indicate large distances

from brightness & distance, we find that luminosities of some are greater than 10¹² L_sun

variability shows that all this energy comes from a region smaller than our solar system

• this is the implication for supermassive black holes

at high redshift, a larger fraction of galaxies are “active” (show signs of powerful luminous nuclei) than at low redshift. Therefore, we can safely say that

some galaxies go through an active phase & more galaxies in the past were active than now

quasars powerfully radiate energy over a wide range of wavelengths

this indicates that they contain matter w/ a wide range of temperatures

energy from a black hole

gravitational potential energy of matter falling into a black hole turns into kinetic energy

friction in an accretion disk turns kinetic energy into thermal energy (heat)

heat produces thermal radiation (photons)

this process can convert 10 to 40% of E = mc² into radiation

what can you conclude from the fact that quasars usually have very large redshifts?

they are generally very distant, were more common early in time, and galaxy collisions could activate them

black holes in galaxies

many nearby galaxies – perhaps all of them – have supermassive black holes at their centers

these black holes today seem to be dormant active galactic nuclei

many galaxies may have passed through a quasar-like stage earlier in time

galaxies & black holes

the mass of a galaxy’s central black hole is closely related to the mass of its bulge

• the supermassive black hole is connected to the development of the galaxy

how do quasars let us study gas btwn the galaxies?

gas clouds btwn a quasar & earth absorb some of the quasar’s light

we can learn about protogalactic (gas & dust) clouds by studying the absorption lines they produce in quasar spectra

lyman alpha forest

a specific atomic energy level

• one specific rest wavelength

light in the milky way: how does luminosity change with radius from the center?

based on light profile, expect velocity to fall off

• there must be some matter that we cannot see

luminosity is a proxy for mass

if all the mass in the milky way is associated with luminous material, what would you expect the rotation curve, v(r), to be?

• it should fall off but it doesn’t

what is the mass of the galaxy (within the sun’s orbit)?

(most of the stars are enclosed within the sun’s orbit)

rearrange the velocity equation to get mass

M = 200 billion M_sun

• that’s too many – we expect ~ the same number of stars

• there must be nonvisible matter

dark matter

nonvisible & nonluminous matter that surrounds galaxies (unsure if it exists elsewhere)

spiral galaxies all tend to have flat rotation curves, indicating large amounts of dark matter

dark matter halo

the visible portion of a galaxy lies deep in the heart of a large halo of dark matter

elliptical galaxy rotation curves

velocity dispersion

broadening of spectral lines in elliptical galaxies tells us how fast the stars are orbiting

these galaxies also have dark matter

ellipticals don’t have an ordered disk for us to easily calculate rotation

what is the evidence for dark matter in clusters of galaxies?

we can measure the velocities of galaxies in a cluster from their doppler shifts

we can also use gravitational lensing

gravitational lensing

the bending of light rays by gravity

• can also tell us a cluster’s mass

relativity explains this

how do we measure dark matter using gravitational lensing?

α = 4MG/Rc²

• α is in radians

what kind of measurements would tell us the mass of a cluster of galaxies?

measuring velocities of cluster galaxies & distorted images of background galaxies

would not: measuring the total mass of a cluster’s stars & the rotation curve of a galaxy in the cluster

does dark matter really exist?

2 options:

1. dark matter really exists, & we are observing the effects of its gravitational attraction

2. something is wrong with our understanding of gravity, causing us to mistakenly infer the existence of dark matter

bullet cluster (dark matter collision passing through cluster thing) & weak lensing mass map (the map that maps that out) is evidence that it exists

• luminous matter experiences “friction” from the collision & dark matter doesn’t

if this is true, dark matter makes up ~ 85% of the total matter (ordinary & dark) in the universe

galaxy formation

slight over densities of dark matter coalesce (join to form one mass/whole) without friction

what ultimately caused protogalactic clouds was the dark matter over density

more gravity causing contraction of gas clouds

dark matter is not

anti-matter – when anti-matter combines, it emits radiation (gamma rays)

black holes – black holes are compact objects, dark matter appears to be diffuse (spread out) & far reaching

summary of what we know about dark matter

1. it’s a thing (not a misunderstanding of gravity)

2. it interacts with gravity

3. it only interacts w/ light through its gravity (or it interacts w/ light very weakly)

4. it’s dispersed in a dark matter halo

5. there’s a lot of it

• also lensing did not match the hot gas

if the universe’s expansion was decelerating 12 billion years ago, what can we conclude about that time?

the average density of dark matter must have been larger than that of dark energy (and of radiation) at that time

measuring the relative densities of matter & dark matter

can be measured by measuring the expansion of the universe

• Ω = p/p_crit

special relativity vs. general relativity

special relativity applies to things moving at constant velocity (inertial reference frames)

general relativity applies to things that are accelerating (non-inertial) or in a gravitational field

newtonian relativity (particles)

if i am on a moving train and i throw a ball up, it will fall straight back down – i don’t detect my own motion

• it doesn’t fall behind me because it has inertia

• i get the same result as if i was stationary on the ground…

if i am on a car moving at speed v and i shoot a ball at velocity v forwards, i will still see the ball at speed v (2v relative to the ground)

newtonian relativity (waves)

if i am running at v & holding a rope, & i generate a wave, that wave doesn’t have inertia, so its speed relative to the ground is only v (not 2v)

• newtonian relativity is not broken though

• despite not having inertia, you still can’t use this experiment to prove you are moving

michelson morley experiment (light/aether)

since sound travels through air, light waves must also?

interferometer:

• same speed of light in orthogonal directions of motion relative to earth’s motion around sun

• constructive interference → no aether

is newtonian relativity broken if light doesn’t travel through a medium?

einstein says no:

• the speed of light is c in all reference frames (fundamental constant)

special relativity

michelson & morely experiment tells us that the speed of light is a constant from all reference frames

• a simple thought experiment results in a predicament of time dilation

everything travels through space-time at the speed of light

• you can either move through time at the speed of light (1 sec per sec) or have some component of your motion through space (then your clock will slow relative to others)

• length contraction as well

time dilation

perceives an object or person to only have moved a shorter amount of time than they actually have

t = t₀/√1-v²/c² = γt₀

if we want to measure supernova 1a light curves at a very high redshift, how should we design our observing program?

a few long exposures, in redder filters, separated by 1 week

length contraction

L = L₀√1-v²/c² = L₀/γ

figuring out general relativity

newton gave us the strength of gravity, but never told us why

special relativity works for constant speeds but not accelerating speeds

there’s no way to tell the difference between sitting in a gravitational field & being accelerated

• the equivalence principle

the equivalence principle

F = m_Ia & F = m_Gg

m_I = m_G & a = g

gravity is acceleration

the ground is accelerating up at 9.8 m/s²

• very simple explanation for reading a scale

general relativity

implies that if you are standing on the surface of the earth, YOU are accelerating

astronauts in space station orbiting earth are the ones that are at rest in spacetime

everything wants to flow through space & time in a freefall trajectory

• anytime you don’t allow it to do that, you are the one accelerating the object

• objects that are at rest are in freefall

curvature of space time

time curvature + spatial curvature (gravity)

big bang timeline leading up to the CMB

10⁻⁴³ seconds: plank time - 10³⁴ K - earliest time physics can explain

10⁻³² seconds: inflation ends - 10¹⁸ K - end of expansion

10⁻⁶ seconds: universe has cooled enough for protons to form - 100 billion K

1-4 minutes: primordial nucleosynthesis - 100 million K - nuclei form - H (75%), He (25%) form - fully ionized

380000 years: recombination - 3000 K - electrons become bound to atoms

photons that escaped after recombination are seen as the CMB

the oldest proton we have access to are those from the CMB (redshift = 1100)

• universe goes from ionized to not

• we didn’t have any access to light before this time (primordial light) - universe was opaque before

arno penzias & robert wilson

working on a microwave antenna to relay phone calls to satellites

detected faint background noise all over the sky

in their research they learned of the CMB prediction by the big bang theory

won nobel prize in 1978 - “for their discovery of the cosmic microwave background radiation”

can calculate temperature of the CMB

z = 1100 → z = Δλ/λ = ΔT/T

λ = b/T

CMB temperature (calculated) = 3 K

CMB temperature (actual) = 2.728 K

COBE (1989)

measured a CMB is a blackbody with T = 2.75 K

their detection was mostly isotropic but w/ slight variations

mather & smoot won nobel prize

variation in CMB

slightly warmer in the direction of Leo & cooler toward Aquarius (dT = 0.0033 K)

• due to Earth’s motion toward Leo (shorter wavelength = higher T)

we live in a matter dominated universe

we can think of radiation having an effective matter density (E = mc²) & that it is dominated by the CMB w/ a temperature (today) of T = 2.725 K

today, the density of matter is higher than the density of radiation

in the early universe, the radiation was more concentrated, but the radiation also had lower z & so had more energy

transition occurred ~2500 years after the big bang (z ~ 25000)

the CMB is not totally isotropic

it has slight T variations (~ 10⁴ K) & slight density variations

matter & radiation were not totally uniform at recombination

john matter & george smoot

won nobel prize in 2006 “for their discovery of the blackbody form and anisotropy of the cosmic microwave background”

anisotropy

having a physical property that has a different value when measured in different directions

WMAP

observed the CMB w/ high resolution

the combined average mass density (from all forms of matter & E) = p₀

this affects the curvature of space (general relativity)

the isotropy problem (aka horizon problem)

w/ uniform expansion, we don’t expect that point A would 'know’ about point B, but we would expect that they would have had to have been in contact in order to have the same T

they are outside of each other’s cosmic horizon

information hasn’t had time to travel from one to the othert

the flatness problem

CMB says that Ω = 1 (universe is flat)

it must have been 1 during the big bang

• both p’s were much higher in the past, they decline together in a flat universe so that Ω = 1 is constant

if the density of was lower than the critical density at early times, the expansion would have been so rapid that galaxies never would have formed

if the density was higher than the critical value, there would have quickly been a big crunch

inflation

the universe experienced a brief period of very rapid expansion shortly after the Planck time

during this inflationary epoch, the universe expanded by a factor of 10⁵⁰ in 10⁻³² seconds

this accounts for the isotropy of the CMB - material that was originally near our location was moved out to large distances

when we the CMB from different parts of the sky, we see radiation from parts of the universe that were in contact with each other

solves the flatness problem

density fluctuations

stars & galaxies formed out of density fluctuations seen in the CMB

predicted by heisenberg uncertainty principle as small, quantum fluctuations in density

stretched during inflation to become appreciable in size

four models for the future of the universe

1. recollapsing universe: the expansion will someday halt & reverse

2. critical universe: will not collapse, but will expand more slowly w/ time

3. coasting universe: will expand forever w/ little slowdown

4. accelerating universe*: the expansion will accelerate w/ time

*currently favored