Stars, Galaxies, Universe Final

equivalence principle

Being in free fall is equivalent to being in 0 gravity space

Being in accelerating frame feels like gravity and can't be distinguished

understanding free falling satellites

All satellites in orbit around Earth are in free fall

Combo of speed at given moment in time and acceleration makes them move in circle

SPACETIME and gravity

Space and time are part of spacetime

3 dimensions of space, 1 dimension of time

Motions of objects as function of time

Objects are moving through spacetime

light's path bends due to gravity

Einstein realized this should happen

Bending of light predicted by Einstein is twice that predicted by Newton

Gravity is curvature in spacetime, not force

motion of mercury

Mercury has eccentric orbit (0.21) and orientation of major axis changes slightly over time

Partly expected due to gravitational preturbations from jupiter and saturn

Offset of 40 arcseconds no one could explain, maybe planet close to Sun (vulcan)

Einstein predicted offset of 43 arcseconds per century

deflection of starlight

Eddington read paper by Einstein

Looked for effect during eclipse in South Africa and Brazil in 1919

Einstein's predictions were true to 20% precision

gravitational lensing

Can cause objects to appear in different position, look brighter, or both

spacetime and GRAVITY

Stronger gravity = slower pace of time

We live in low-gravity environment

surface gravity on surface of neutron stars

100 lbs on Earth is 300 trillion pounds on Neutron star

Escape velocity is half of speed of light

limits of fighting gravity

Earth held up by fact that it's hard to squeeze rocks

Sun held up by pressure from lots of nuclear explosions

White dwarfs held up by fact that it's hard to squeeze electrons

Neutron stars held up by fact that it's hard to squeeze neutrons

No known force can fight black holes

event horizon of black hole

Schwarzchild calculated radius from which light can't escape a point mass in general relativity (Schwarzchild radius/event horizon)

Radius proportional to mass of black hole

falling into black hole

Current physical theories allow us to calculate how things behave up to singularity

Observer falling into black hole sees rest of universe blueshift as he approaches event horizon

If he sends signals once per second, they appear to take longer and longer to outside observers

For massive black holes, spaghettification happens inside black hole as tidal forces are shallower at surface

surface gravity of black holes

More massive black holes have smaller surface gravity

Radius of event horizon grows with mass, but gravity grows with radius

Billion solar mass black hole has 1500 times more gravity than Earth

evidence for black holes

We see motion around black holes, accretion on black holes, and gravitational waves

accretion onto black holes

Gas that falls into black hole gets accelerated to very high speeds

If a little energy escapes as light, it's more efficient engine to make light than star

Luminosities of super massive black holes near centers of most large galaxies can reach 1 trillion solar luminosities

mapping milky way galaxy

Hard to map Milky Way Galaxy because we live inside it

milky way galaxy has disk

Herschels were first astronomers to state Milky Way is shaped as disk

Sun is never in middle because there was the same number of stars in every direction

That's not true, it's only because of interstellar dust dimming stars

harlow shapley and milky way cartography

Shapley estimated distances to 93 globular clusters using period-luminosity relations of variable stars

Spherical distribution with center not near Sun but within disk and toward constellation sagittarius

disks and haloes

Halo is said to contain almost entirely old, metal-poor stars that formed with galaxy

Disk contains every kind of star making it younger and more metal-rich

Milky Way's Disk contains bar in central regions

spiral structure

Found in radio observations

We see gas located in specific lines of sight

Sun located in Orion spur

spiral arms

Gas clouds have differential rotation

Parts furthest from center of galaxy move at different speeds than parts close to center

Arms form their own self-gravity

keplerian estimate for galaxy’s mass

• Sun takes 225 million years to go around Galaxy and semi-major axis is 27,000 light years

• We get 100 billion solar masses an estimate if we use Newton’s genralization of Kepler’s third law

• Not quite right as Sun’s orbit isn’t quite and ellipse and there’s isn’t one point mass at center of galaxy, but rather a disk of mass with distribution of mass

orbital speeds in galaxy vs. solar system

• Galactic orbital speeds constantly at large radii

• Solar system orbital speeds decline at large radii

missing mass

• Distant objects orbit galaxy really fast in spite of there being very few visible objects out there

• Either our theory is wrong or dark matter is out there

modified gravity vs dark matter

• Modified gravity models vary, but common model is that at very low accelerations, gravity is stronger than expected

• Dark matter models also vary but common model is that there’s another particle, undetected by current particle accelerates that doesn’t interact much with protons and electrons but accounts for most of universe matter mass

lots of stuff near center of galaxy

• We see a ton of old stars near black hole, a hundredish OB stars indicating recent star formation but no ongoing star formation

Sagittarius A*

• Lots of mass which we can infer from stars moving rapidly

• We can’t see the mass, stars orbit around nothing

• Supermassive black hole with mass of 4 million solar masses

• One star gets as close as 124 AU from black hole

how do supermassive black holes form

• Nearly every massive galaxy has one at center

• When massive stars dies, they form black holes of 20-30 solar masses

• Having these reach 4 million or 4 billion solar masses, either by accreting hydrogen or having merger trees doesn’t seem to work mathematically

thin disk vs halo orbits

• Stars in thin disk have circular orbits 

• Stars in halo have random and elliptical orbits

two kinds of stars

• Discovered by Walter Baade during WWII

• Blackout of Los Angeles during war to make it harder for enemy submarines made the skies darker (good for astronomy) 

• Population I for bright blue stars in spiral arms

• Population II for stars in Halos and globular clusters

Pop I and Pop II Stars

• Pop I stars found only in disk and in nearly circular orbits 

• Bright supergiants, bright main-sequence stars, stars in spiral arms, and stars of young open clusters 

• Pop II stars found everywhere in galaxy 

• Both circular and eccentric orbits

• RR lyrae stars and globular cluster stars

• Pop II stars formed first 

• Pop II stars are 10-14 billion years old and Pop I are less than 12 billion years old

• Pop I stars have have 1-4% of their mass in elements heavier than hydrogen and helium 

• Pop II stars have less, sometimes their 99.999% hydrogen and helium

• All stars in Milky Way are Pop I stars

Why Younger Stars Have More Metals

• Universe stars with 75% hydrogen, 25% helium, and tiny amount of other elements

• Overtime, more heavy elements (metals) are contributed to interstellar gas from supernovae

And other dying stars

• That’s why Sun has 1.5-2% heavy metals

• Stars form heavy elements in interiors through nuclear fusion 

• When stars die, heavy elements released to interstellar medium

• New stars form from enriched gas

• Older stars have fewer metals

protogalactic cloud and monolithic collapse model

galactic mergers occur over time

• Galaxies merge with random orientations which can add shape and structure to galaxy

• Sagittarius dwarf spheroidal is small galaxy accreted by Milky Way and makes big stream

• Globular cluster M54, probably its nuclear star cluster

expanding universe

• From general relativity, universe is expected to expand or contract

• Einstein added a cosmological constant to keep it static

• Hubble used observations of variable stars in other galaxies in combination of Leavitt law to measure distances and redshifts to measure speeds to show distant galaxies are moving away from us

hubble time

• Big Bang was when all galaxies were close together

• Hubble’s constant says that objects further away move faster

hubble time / age of the universe

• Hubble time is time when galaxy separation was 0

• H0 is rate of expansion and 1/H0 gives age of universe

• Universe is 13.8 billion years old

accelerating expansion

• In 1990s, astronomers used standard candles to measure universe expansion

• Want to measure deceleration of expansion of universe

• They measured acceleration, things were moving faster away from each other over time even though gravity should be pulling them back

• Dark energy is pulling the universe apart and astronomers parameterize it with cosmological constant

future pathways to studying universe

• European Extremely Large Telescope being built in Chile will have 39 m mirror, making it most powerful telescope in the world

• Will directly measure accelerating expansion of universe

expansion of universe

• Space itself is expanding

• Only expansion in voids between galaxy clusters because galaxies have enough gravity that they can be same size

• Wavelength of light in accelerating universe also expands

cosmic tug of war

• Gravity

  • From light, matter, and dark matter, pulls things together

  • With enough gravity, universe expansion will slow down and maybe reverse

• Dark energy

  • Mysterious force pushing things outward

  • Could cause acceleration to be faster and faster

eventual fate of universe

• We don’t know since we don’t understand dark energy

• We expect big chill where we only see the galaxy we’re in, all stars die, only black holes left

critical density of universe

• Density needed to bring universe’s expansion to stop at infinity, then universe will have fixed size

• Universe has density of 30% of this quantity, so universe will expand forever

• Combined density of matter and dark energy is equal to critical density

ages of distant galaxies

• Astronomers quote ages in terms of redshift 

• Redshift z =1 galaxies is seen from when universe was half its current size 

• Red shift z =2 is a third and so on