Exam 2, Astro 1220 UVA

2026 --> bradely johnson

Chapter 14

• learning about our sun and how it was created.

what process causes the sun to shine?

nuclear fusion

how did the sun’s core grow hot enough to allow nuclear fusion to start?

gravitational contraction raised the internal temperature and pressure of sun’s core.

how was the sun formed?

formed by a collapsing cloud of interstellar gas

how long ago was the sun formed

4.5 billion years ago

how does the sun continue to shine steadily?

2 balances:

1. gravitational equilibrium

2. energy balance

what is gravitational equilibrium?

it is the inward pull of gravity balances outward push of internal gas pressure at every point within the sun

• basically meaning — gravity wants to crush the sun and pull all the gas inward but the gas wants to explode/expand because of its hotness but because both of these forces are equally matched the sun stays stable.

Pressure increases with depth?

true

does pressure make gas hot and dense enough to sustain nuclear fusion?

true

energy released by nuclear fusion in turn heats up gas and maintains the pressure needed for equilibrium

true (this is called energy balance)

what is the rate of energy balance?

rate of energy released in sun’s core is = to rate at which the sun’s surface radiates energy into space

what if fusion did not replace energy radiated from the surface?

the gravitational contraction wouldcause the sun to shrink and its core temp to rise.

what does the sun look like?

has solar flares/sunspots/swirls with radiating gas.

• sunspots/flares are caused by loop of hot gas extending into the sun’s corona. — created by magnetic fields

Basic properties of the sun

• radius = 696,000

• mass = 2 X 10³⁰ kg — about 300,00 times the mass of earth

• luminosity = 3.8 X 10²⁶ watts

• composition — 70% hydrogen, 28% helium, 2% heavier elements

• rotation rate = 25 days equator and 30 days poles

• surface temp = 5800K and sunspots = 4000K

• core temp = 15 million K

5 seconds of the sun’s luminosity is enough to meet human energy demands for 500,000 years?

false, it is 1 second

what is the sun’s structure?

the sun is made of a ball of plasma that has different temps and densities at different depths.

what is solar wind?

stream of charged particles.

• forms a comet tail ( 2 — dust tail and plasma tail )

what is the corona?

• the outermost layer of the sun’s atmosphere.

• several million km from the surface of the sun.

• low density

• temperature = 10⁶ K —- hotter than sun’s surface

• strong magnetic fields carry energy upward from chromosphere and coronas

• emits most of sun’s X-rays

what is the chromosphere

• middle layer of solar atmosphere

• temperature = 10⁴ K

• emits most of sun’s ultra violet light

what is the convection zone?

• energy from core transported to surface from hot gas

• cool gas moves downward

• causes churning/swirls appearance on Sun’s surface.

what is the radiation zone?

• 1/3 of the way down to the core

• hot gas turns into plasma

• energy flows outward in the form of photons/x-rays

• temperature = 10⁷ K

what is the core?

• nuclear fusion transforms hydrogen into helium

• density is 100 times of water.

• pressure is 200 billion times greater than earth’s surface.

• temperature = 1.5 X 10⁷ K

What is nuclear fusion in the sun?

• uses quantum tunneling

• to proton need to get hot enough to come together — once they come together one proton looses charge and turns into neutron (need 4 protons to give us 1 he+ energy)

• The sun uses hydrogen fusion

• emits gamma rays and neutrino and positron

nuclear fission vs nuclear fusion

• fission = splits a large nucleus into smaller nuclei

• fusion = combines smaller nuclei into large nucleus

equation for mass difference

E = mc²

when the core temp rises what happens?

leads to large increase in fusion rate, which raises the core pressure which causes the core to expand and cool down leading to equilibrium stability.

when core temp lowers, what happens?

leads to decrease in fusion rate, lowers pressure in core, causes core to contract and heat up, which then leads to stability.

how long does it take for energy to travel from the core to the photosphere?

hundreds of thousands of years, electrons redirect photons when they travel through suns plasma. — called radiative diffusion

how do we know what is happening inside the sun?

we learn through…

• observations of solar vibrations — mainly through Doppler shifts

• mathematical models of the sun — helioseismology

• observations of solar neutrinos — detected using the Super kamiokande neutrino observatory in Japan.

example problem #1 —

• how much hydrogen is converted to helim each second in the sun?

• how much helium nuclei are created by fusion each second in the sun?

1. we need to understand we need to use the equation E = mc².

2. we have to understand that E = L x 1 sec — they give us luminosity. so we plug that into L —> will equal , We also have to understand that m = ( 4m_p - m_he) N. , c is just the speed of light.

3. so we do not know m fully (we need to find N) , but we know E, c, and some of m, we just need to find N. so then the equation turns into N = (L x sec 1)/ ( 4m_p - m_he)c²

4. if we plug the stuff we know we get — (3.8 × 10²⁶ w x 1 sec) / (4 × 1.6726 × 10^-27kg - 6.643 × 10^-29kg) c² ———-if we calculate this it will give use 8.91 ×10³⁷ which is the # of helium nuclei produced

5. to get total mass of hydrogen we nee to time N to 4m_p —→ 4 (1.6726 × 10^-27kg)(8.91 ×10³⁷) —> this then turns into 5.96 × 10¹¹ kg

to answer the next part we need to use what we learned from question 1.

1. the M of sun is 2 × 10³⁰ kg — then we divide this by our answer from question 1 and get 3 × 10 ^-17%

example problem #2

• The sun core contains about 10²⁶ particles per cubic centimeter at a temp of 15 million K. Compare the sun’s core pressure to that of earth’s atmosphere at sea level, where the density is about 2.4 X 10¹⁹ particles per cubic centimeter and the temp is about 300 K

1. we need to use P = nkT —> P = pressure, N = # of density, K = boltzman constant, T = Temp. —- you wouldn’t end with any units. — the answer will get 2.1 × 10¹¹

Unit 15

surveying the stars

IceCube Neutrino Observatory

• used to detect neutrinos using thousands of optical sensors in antarctic.

• when neutrinos interact with an atom in ice it can produce a charged particle that travels faster than the speed of light in ice, emitting a flash of blue light

• particles direction is determined by measuring the timing and intensity of this light at multiple sensors.

how do we measure stellar luminosities?

what does apparent brightness depend on?

• luminosity and distance

what is luminosity?

• amount of power a star radiates — energy per second = watts (energy/light that comes out of the sun)

• passes through each sphere at the same time

• can determine this by 4π x (distance)² x (apparent brightness)

what is apparent brightness?

• amount of starlight that reaches Earth (energy per second per square meter)

• divide the luminosity by area of sphere(4π(radius)²) to get brightness.

what is the apparent brightness of the sun in our sky?

1,340 W/m²

what is stellar parallax?

• parallax is the apparent shift in position of a nearby object against a background of more distant objects

• angle depends on distance

• apparent positions of nearest stars shift by an arcsecond as earth orbits sun.

• measured by comparing snapshots that are taken at different time and then measuring them

what is Gaia spacecraft?

• measures the parallax and proper motion between stars.

• will survey about 1 billion stars in the milky way

Parallax example

steps to solve

1. we must first understand the equation and the variables in the equation. — p= parallax angle, in this case it is 0.379, arcsec is the unit it is already in. d = distance. 3.36 is a constant for light-years

2. if we want to do it the simply way to find parsecs we can just plug in the information into the question. but lets say our professor want meters or something else we must do it the long way.

3. the long way = 1st change p[arcsec] into sin(1 arcsec), and then change 1 into 1 au. 2nd understand that 1 au = 1.5 × 10¹¹ meters and sin = 0.379 x deg/3600 arcsec x π rad/ 180 deg. 3rd is canceling out the variables that they are 2 of. ex: arcsec, deg. 4th times everything together and use rad as you units giving you (1.837 × 10^-6 rad). 5th then put the answer into the arcsec place in sin and then divide 1.5 × 10¹¹ by your answer (1.837 × 10^-6 rad). ex: 1.5 × 10¹¹m/ sin(1.837 × 10^-6 rad). 6th then you get 8.116 × 10¹⁶m. 7th then we need to multiply this by parsec/ 3.09 × 10¹⁶m. we finally get the answer.

for lightyear we would do the same thing but instead of using parsec/ 3.09 × 10¹⁶m in step 7 we would use lightyear/ 9.46 × 10¹⁵m

what are some stellar temps?

• 5800K = sun temp

• 50,000 = hottest star temp

• 3,000k = coolest star temp

Can stars be different colors?

yes

what is thermal radiation?

• every object emits thermal radiation with a spectrum that depends on temp. —- ex’s: planets, you, stars

• an object with a fixed size grows more luminous as its temperature rises

• depends only on temp

• hotter objects emit photons with higher average energy

how do we measure stellar temps?

we use absorption lines in star spectrum to tell us its ionization level

• lines in a star’s spectrum corresponds to a spectral type that reveals its temperature.

what are the types of binary star systems?

• visual binary —>we can see with a telescope as the star orbit each other.

• spectroscopic binary —> used when we cannot determine stare with telescope due to diffraction limit. (we use Doppler shifts in spectral lines to determine this)

• eclipsing binary —> pair of stars orbit in the plane of our line of sight. ex: the ellipse

ex: Sirius A and Sirius B

about 3/8 of all stars are in binary systems?

false — ½

what happens to the spectral lines when a n object is away from us?

• the lines will shift towards the right/ blueshifted

• if close to use it will be redshifted

is Mizar a visual binary or spectroscopic binary?

its both!

how do we measure stellar mass and Radii?

• p = period, g(m₁+M₂) = mass of stars, a³= average separation

• direct mass measurements are only porrible for stars in binary star systems.

we need any 2 of these 3 observable:

1. orbital period

2. orbital separation (a or r {radius})

3. orbital velocity (v) — for circular orbits (v = 2πr/p)

center of mass

• if 2 stars are equal mass then the center of mass will lie halfway between them

• if 2 stars with different masses — the center will be closer to the one with more mass.

• if the star has much more mass than the planet the center of mass is in the star.

1 AU = what?

150 million km

measuring stellar mass example

steps:

1st we must understand the question

• both stars are traveling at a orbital speed/v of 80,000 m/s or 8.0 ×10 ⁴ m/s.

• total time it takes to complete 1 full orbit is 6 months

2nd we must convert our variable P into secs.

• p = 6 months x 30/1 × 24/1 × 3600 sec/ 1

• gives use 1.555 × 10⁷ sec

3rd - we do not know (m₁+m₂)/ the distance between the stars

• we must first rearrange the equation —- 4π²/ G x a³/p². — but we still do not know a³. luckily we can change it to (vp/π)³

• resulting in 4π²/ G x (vp/π)³/p² then this turns into — 4π²/ G x v³p³/p² π³ — but then we can just do — (4 x π² x v³ x p³)/ (G x π³ x p²)

• then cancel out things —> leading to (4 x v³ x p)/ Gπ

• then we solve by plugging in v and p and g giving us —> 1.521 × 10³² kg. (total mass of both star)

4th - we must divide our answer by 2

• 1.521 × 10³² kg / 2 = 0.7605

• then we convert into scientific notation — 7.605 × 10³¹

note we must get rid of 1 space to make up for dividing.

stellar mass range?

• sun’s mass= 2.0 × 10³⁰kg

• most massive star = 100 M_sun

• least massive stars = 0.08 M_sun

How do we classify stars?

we use the Hertzsprung- Russell (H-R) diagram

• Most stars fall somewhere along the main sequence. — our sun is on this

• the stars in the upper right are called super-giants — meaning they are very large and very bright

• below super giants are giants

• stars near the lower left are called white dwarfs— have really high temps

there are 5 classes in the HR sequence, what are they?

1. super-giant

2. bright giant

3. giants

4. subgiant

5. main sequence stars

what is each main sequence star fused with?

fuse with hydrogen into helium in their cores

mass increases going down the main sequence (left - right)

false — decreases

what is the most important feature of hydrogen fusing stars?

mass

small increase in mass produces a large increase in luminosity?

true

what must a very luminous star have?

• large mass or high surface temp

they could have both.

are stars born with a limited supply of core hydrogen?

yes

more massive stars = lifetime decrease

true

what do stellar properties depend on?

age and mass

all stars become larger and redder when they have exhausted their hydrogen core

true

when fusion ends most stars will end up as what?

white dwarfs

a star that varies significantly in brightness with time is called?

variable star

why do some stars vary in brightness?

• because they cannot achieve balance between power from the core and power from the surface

• star might expand and contract

where do they fall on the HR diagram — variable stars?

• within the instability strip

• called — cepheid variables

• pulsation period is closely related to their luminosity

• used to determine galaxy distances

what are the 2 types of star clusters?

1. open cluster —> loosely packed stars, always found in galactic disk, young, 30 light years across.

2. globular cluster —> up to a million or more stars, dense ball, found in galactic halo, 60-150 light years across, oldest stars —> ex: M4

UNIT 16

star formation

is the space between stars empty

no - it contains small amounts of Hydrogen, helium, and other heavy elements

what is the gas between stars called

interstellar medium (ISM) — also can have huge temp and density differences.

what type of area does new stars from?

cold and dense regions of dusty gas. —> this is called molecular clouds

what are molecular clouds?

• cold

• dense —→ 300 molecules per cubic centimeter

• allows atoms to form into molecules

• have a temp of 10-30K

composition of star-forming clouds

• we can observe composition of forming stars through absorption lines or emission lines of carbon monoxide

• measures show similar to sun

what can block our view of stars in a gas cloud?

interstellar dust

• if we view stars toward the edge of clouds they look redder because of dust blocks.

• infrared light can pass through cloud easier and show us the other side

what does false color images combine?

infrared light over a range of wavelengths

• color corresponds to different temps

• blue = 40K

• green = 10K

how does star form?

• molecular clouds — because gravity causes molecular clouds to contract which then gets the core hot enough for fusion.

• gravity must overcome thermal pressure in a cloud

before fusion starts what is the star called?

protostar

what does emission lines from molecular clouds do?

• can prevent pressure buildup by converting thermal energy into infrared and radio protons that escape the cloud

what does molecular cloud evolution look like?

rotation in star birth

• speed of rotation increases as the cloud contracts — conservation of angular momentum — also cause jets of matter to shoot out along rotation axis

• collision between particles in the rotating cloud causes disk to flatten

how do planets form?

• starts out as globs of gas and dust that orbits a central star even if star is just forming

• gravity and other forces cause material within disk to collide

• if collision is gentle the material fuses like rolling snow balls

• dust particles turn into pebbles — then into mile size rocks

• then they clear material from their path, leaving tracks of largely empty space

• stars gobble up nearby gas and push more material further away.

illustration of star formation

• sun required about 30 million years to go from a protostar to a main sequence star.

• higher mass = forms faster

• lower mass = slower

what does degeneracy pressure due for mass of stars?

• do not let it get below 0.08

• if dp fails then star will turn into a failed star/brown dwarf

there are 3 types of brown dwarfs

1. L dwarfs = temp between 1400 K — 2200 K

2. T dwarfs = 500K —1400K

3. Y dwarfs = below 500K

demographic of newborn stars

refer to pic.

UNIT 17

star stuff

when pressure overcomes dense molecular cloud what forms?

protostar

what is life as a low-mass star?

• after star ends main sequence life — helium core contracts while a hydrogen shell begins to spread along the surface — shell starts to expand outward — outer layers start to shrink. due to helium mass is added to core which increases temp and helium fusion rate —increase radius weakens gravity at the surface which allows stellar winds to escape —- Degeneracy pressure balances out gravity in helium core.

what does helium fusion require?

• high temp — 100 million K because helium has 2 protons

degeneracy pressure increases with temp

false - doesn’t do anything

what is a helium flash?

• when temp rises drastically

• causes enormous amounts of energy in the core

• thermal pressure dominates degeneracy pressure

what happens after helium fusion stops?

helium fuses into carbon shell around the carbon core.

• never reaches equilibrium —

• thermal pulses makes convection drap carbon up from the core to the surface

what is earths fate?

hydrogen fusion in high mass stars

• start with hydrogen fusion — but they fuse it with carbon, nitrogen, and oxygen (elements that were in the molecular cloud) — this speeds up fusion rate because it causes more energy and higher radiation pressure.

• higher radiation pressure= strong stellar wind that can blow away mass

• same process (no helium flash) but turns into super giants

what element is not possible to generate nuclear energy?

• iron

• iron reverses fusion and fission.

how are super novas created?

• DP supports iron core

• Gravity overcomes DP and electrons and protons combine to form neutrons

• electrons and DP disappears

• iron core collapses into a ball of neutrons — halted by neutron degeneracy.

• outer layer of star is blown out into space

• neutron star is left

• if ND is overcame by gravity then black hole forms

what image is this

crab nebula