Astronomy Exam 3

Sun’s surface temperature

6000 Kelvins

Core temperature of the sun

15 million Kelvins

Stefan Boltzmann Law

Luminosity of any object is directly proportional to surface area and surface temperature to the 4th power

L = (sigma)4(pi^2)(surface temperature^4)

How are wavelengths and temperatures related

Hotter temp - shorter wavelength

Cooler temp - longer wavelength

Four forces in the universe from strongest to weakest

Strong nuclear force

Electromagnetic force

Weak nuclear force

Gravitational force

Range of strong nuclear force

Size of a nucleus of an atom

Fission reaction

Heavy nucleus splits into lighter nuclei to generate energy

Fusion reaction

light nuclei merge to form a heavier nucleus to generate even more energy

How does nuclear fission work

Fire a neutron to split the nucleus

Manhattan project

US built 3 nuclear fission bombs dropped one in New Mexico as a test and the other two on Hiroshima and Nagasaki

How does nuclear fusion work

Make the nuclei move so fast and at such hot temperatures that they approach within range of strong nuclear force which overpowers electromagnetic force

Quantum mechanical tunneling

electrons can overcome energy barriers even when they do not have enough energy to overcome the barrier

Nuclear fusion bombs

US creates the hydrogen bomb/H bomb

Nuclear reactions in the sun’s core

Hydrogen 1 + Hydrogen 1 -→ Deuteron + entielectron (positron) + neutrino

What is a positron

Antimatter and it annihilates and contributes to high energy photons

Annihilation

Putting matter and antimatter together

4 reactions

Chemical

Fission

Fusion

Matter-Antimatter annihilation

Random walk

Sun is a hot plasma so photons execute a strange trajectory from the many collisions

Photons do this is the radiation zone of the sun and it takes 100,000 years to exit the radiation zone

Layers of the sun

Radiation zone

Convection zone

Photosphere (layer we see)

Granulation of the sun

Grainy appearance from the convection zone under the photosphere

Rigid body rotation and differential rotation

rigid body - every part rotates at the same rate (solids)

differential - different parts rotate at different rates (fluids)

Sunspots

Due to sun’s differential rotation, the magnetic field of the sun gets dragged and stretched and it breaks

After breaking, it reconnects in complicated ways

Sometimes they anchor on two places on the sun and sometimes only one and when anchored, the magnetic field is very high so for balance, the thermal pressure decreases so these spots are cooler than the rest and appear black

Flare

Eruption follows magnetic field outward and our satellites are often destroyed by flares

Sun’s atmosphere layers

Chromosphere (hundreds of thousands of Kelvins)

Corona (millions of Kelvins)

Solar wind

Since sun’s atmosphere is so hot, most hydrogen and helium atoms are ionized and escape from gravity so there is a stream of charged particles leaving the sun

Neutrino

weakly interacting particle that refuses to participate in every force in the universe except weak nuclear force (but barely)

New units of angle

One arcminute - one 60th of a degree

One arcsecond - one 60th of an arcminute

1 parsec (pc) - how far a star of one arcsecond parallax is from us (31 trillion km/3.26 light years)

If a star is 5 parsecs away, then the parallax angle is

1/5 of an arcsecond

If a star is 10 parsecs away, then the parallax angle is

1/10 of an arcsecond

Star A looks brighter than star B does this mean that A is more luminous than B?

No because its possible for B to be further away

Intrinsic brightness

Luminosity

Apparent brightness

How bright the star appears to be based on distance

Color indices

Astronomers put blue and red filters over stars and subtract blue magnitude and red magnitude to get the color index and from this we can determine the peak of the spectrum

What color index means star is hotter than our sun

The blue magnitude number < red magnitude number

What color index means the star is cooler than ours

Blue magnitude number > red magnitude number

Temperature sequence in order of hottest to coolest

OBAFGKM

and 0-9 for each letter

(oh be a fine girl kiss me)

What is our sun on the temperature spectrum

G2

Luminosity type for our sun

V (roman numeral 5)

Hertzsprung Russell Diagram

y-axis is luminosity/absolute magnitude/intrinsic brightness

x-axis is surface temperature (also tells us the color)

Luminosity type of main sequence stars

V

In the Stefan Boltsmann Law what variables affect luminosity

radius and more severely temperature

Red giant stars

Stars that are cool and luminous which means that they are gigantic

White dwarfs

Stars that are hot and dim which means they are incredibly small

Which star is more luminous K3 or K9

Which star is more luminous K3 main sequence or K9 main sequence

Not enough info provided

K3 main sequence

Which is larger G4V or G7V

G4V

What other types of sequences is the main sequence

Mass, temperature, radius/size, luminosity, population abundance (early stars are less common and late are more common), lifetime

What are stars born from

a nebula (giant cloud of gas of varying density due to forces acting and most dense parts have gravity dominating all other forces to collapse on itself so it gets hotter until a protostar is born)

All stars are born as

main sequence stars (fusing hydrogen into helium in the core)

How does mass affect star birth

High mass -→ hot and luminous

Low mass -→ cool and dim

Edington limit

roughly 100 solar masses and is the max mass of a born star

Min allowed mass

0\.08 of our sun

Brown dwarf stars

Tiny, dim stars at the right end of the main sequence like gas giant planets only difference though is stars are born from a collapsing nebula and planets from protoplanetary disk

Fragmentation

Protostars collapse so much that centrifugal force rips the star into smaller masses so most star systems are binary

Closest star system to ours

alpha centauri (trinary star system)

Lifetime of high mass vs low mass stars

High mass live shorter on the main sequence and low mass live longer because reactions happen slower in low mass stars

Which star lives longer B3V or B8V

B8V

Cut off between low and high mass stars

7-9 solar masses

Low mass death

Nuclear reactions end when hydrogen runs out so the core collapses and gets hotter causing an outward pressure that expands the rest of the star until it becomes cooler and hotter (a red giant)

The core then reaches the threshold temperature for helium flash to fuse helium into carbon and the star stabilizes

When the star runs out of helium, it becomes a red giant again and low mass stars cannot reach the threshold temperature for carbon flash so electron degeneracy pressure halts the collapse of the core but the outer layers keep fusing until they completely divorce from the core and the gas expels to become a planetary nebula

The core is then naked and very hot from the twice collapse but also so small that its dim (a white dwarf)

The planetary nebula expands into the interstellar medium (where new stars are born)

The white dwarf slowly cools to become a black dwarf

Pauli-exclusion principle

certain particles are excluded from occupying the same quantum state at the same time which causes a repulsion (degeneracy pressure)

electrons obey this

Very low mass death (under half a solar mass)

Helium flash does not occur because the star is too small so it only becomes a red giant once and the planetary nebula surrounds a helium white dwarf instead of a carbon white dwarf

High mass death (7-9 solar masses greater than our sun O or B)

Big enough for carbon flash to occur and carbon fuses into oxygen and then neon and then magnesium and then silicon and the nuclear chain reaction goes on until around the middle of the periodic table (because those atoms are too stable to participate in nuclear reactions)

Iron and nickel are too stable to participate in the reactions and because of the pauli-exclusion principle the core stops collapsing and we get an iron-nickel white dwarf surrounded by many fusion layers

The rest of the star is not hot enough to participate in fusion and the core has collapsed so many times and the outer layers expanded so much that they become red supergiants

The core of a red supergiant is under so much pressure that exotic reactions occur

Electron capture occurs and electron degeneracy can no longer support the star and the pressure vanishes leaving the star at gravity’s mercy

Neutrons are left which obey pauli exclusion so they can provide neutron degeneracy pressure (a repulsion) which creates a neutron star roughly the radius of 10 km

The collapse from a white dwarf (size of earth) to neutron star (10 km) in one millisecond causes billions of solar luminosities to be liberated (energy equal to the size of an entire galaxy of stars) and this explosion is a Type II supernova

The neutron star is left behind and the outer layers (rapidly expanding) are called a supernova remnant

Very high mass star death (O stars)

So much mass that neutron degeneracy pressure cannot halt the collapse so it collapses all the way down to a black hole

Supernova and neutron star are analogous to what

A nebula and white dwarf

Electron capture

a proton eats an electron transmitting itself into a neutron and a neutrino flies out

Generations of stars

Stars explode into supernovas that release other elements into the universe polluting the new stars that are born

Our sun is a gen 3 star

What star in Orion is a red supergiant

Betelgeuse

Also Antares in Scorpius

One star in a galaxy explodes per

century

Naked eye supernovae that have occurred in the past

the crab, the tycho, the kepler

On Feb 23, 1987, neutrino detectors detected over 20 in 30 seconds because a supernova occurred called SN1987A

Chandrasekhar limit

max mass electron degeneracy can support (cutoff between high and low mass stars) in terms of the CORE

1\.4 solar masses corresponds with total solar mass of 7-9

less than 1.4 solar masses → electron degeneracy pressure supports and we get a white dwarf

greater than 1.4 solar masses → neutron star triggering supernova because electron degeneracy pressure does not support

Tolman Oppenheimer Volkoff limit

cutoff between ordinary high mass and high mass stars (depends on neutron degeneracy pressure) in the CORE

Around 2.4 solar masses (corresponds with total solar mass 20-25)

under 2.4 is supernova

over 2.4 is black hole

You have a star with total mass of 5 solar masses how does it die

white dwarf

Star with core mass of 5 solar masses how does it die

black hole

Star death and what we get

Very low mass death: planetary nebula surrounding helium white dwarf

Low mass death: planetary nebula surrounding carbon white dwarf

Ordinary high mass death: supernova

Very high mass death: black hole

Main sequence turn off

early part of main sequence always missing when studying star clusters so high mass stars live shorter on main sequence than low mass

reveals the age of the cluster (must be old enough for A and B types to already die)

no main sequence turnoff later than G

Asymptotic giant branch

stars swell to be red giants

Horizontal branch

stars settle after the helium flash to become helium burning stars which is what the clump after this branch is

How to determine the distance to a star cluster

Construct Hertzsprung Russell diagram using apparent magnitude if the stars are close enough to each other, they are roughly the same distance to one another which means that the apparent and absolute magnitude are proportional

This is main sequence fitting and it works slightly beyond the solar neighborhood

Detached binaries and close binaries

stars orbiting far enough away that they do not affect each other

Stars orbiting close enough that they do affect each other

What is the fourth dimension

temporal

Time dilation

time slows down when you move

Length contraction

space contracts when you move so objects contract in the direction they are moving

How does the theory of relativity affect mass

an object gains mass when it moves

Mass and energy are

the same thing

e equals mc squared

(when you are moving you have more energy so you have more mass)

general theory of relativity says

spacetime is curved and gravity is the curvature of spacetime

Gravity does what to time

slows it down

Length contraction for general theory

stronger gravity causes more severe length contraction

The orbit is not a perfect ellipse, it is a

precessing ellipse

What is the precession

574 arcseconds per century

According to Einstein, light

is affected by gravity and is displaced by it

Deflection of a star around the sun

1\.75 arcseconds

Gravitational lens

gravity of galactic superclusters is called this because it bends light

Einstein ring

sometimes things line up and you see light in a ring around the cluster

Einstein arcs

when Einstein rings are slightly misaligned

Einstein’s cross

four duplicate images of the same galaxy in shape of a cross

The number of sun spots goes through a

11 year cycle

Vries cycle

the 11 year sunspot cycle goes through a 200 year cycle

sun gradually increases in activity - solar maximum (100 years)

sun gradually decreases in activity - solar minimum (100 years)

luminosity of any object can be calculated using

 *I* = ℒ / 4π*r^*2 where r is the distance from us

lower magnitude number stars are

brighter

both *m*Blue–*m*Visual and *m*Visual–*m*Rred will be negative numbers for

hot, blue stars

both *m*Blue–*m*Visual and *m*Visual–*m*Rred will be positive numbers for

cool, red stars