AST106 review 1 - University of Rochesterdmw/ast106/AST106_review_1.pdf · core of the star, a...

Astronomy 106 Review for Exam 1

Ryan Rubenzahl Undergraduate Teaching Assistant

Department of Physics and Astronomy September 30th 2015

A Review Of:Age Dating Techniques

The Drake EquationChemical Composition of Life

Structure of the AtomNuclear Fusion

Generations of StarsStar/Planet Formation

Temperature of PlanetsHabitable Zone

Detecting ExoplanetsTidal Forces

Astronomy 106, Fall 2015 Review Session, Exam 1

How do we know the age of things?

Age of the Universe? • Calculate from the expansion caused by the Big Bang • Observe galaxies moving apart, measure their velocities • “Run time backwards” until all galaxies are in same spot • 13,700,000,000 years old

Hubble Ultra-Deep FieldAge of the Milky Way? • Can’t be older than Universe, so at most 13.7Gyr • Look at oldest objects in Milky Way to find minimum age • White-dwarfs form from stars that live for about 4Gyr • Oldest White-dwarfs observable are ~9.5Gyr

9.5Gyr Now4GyrWhite-dwarf

Total time = 4Gyr + 9.5Gyr = 13.5Gyr, So the Milky Way is ~13.5Gyr

Star


How do we know the age of things (cont.)?

Living things contain radioactive Carbon-14, which doesn’t decay while the organism is alive. Once it dies, the C-14 decays into the rare (and stable) Nitrogen-14:

Rocks aren’t alive, but they do contain different radioactive elements…

C-14

C-14 N-14C-14

N-14

The time it takes for half the initial amount to decay is a known rate, called the half life. For Carbon, this is 5700 years. This value is unique to the element that is decaying.

5700yrs 5700yrs

n = no

e�t ln 2t1/2 (1)

n = no

1

2

tt1/2 (2)

1

amount remainingoriginal amount

half life

time thing has been decaying for


Rb-87

Rb-87 Sr-87half-life

Age of the Solar System? • C-14 doesn’t work well for dating rocks • For one, C-14 is only found in living or once-living things, and rocks were never alive • C-14’s half life is too short to date rocks effectively… luckily rocks contain a different element:

Sr-86

ReferenceRadionuclide Daughter

n(Radionuclide)n(Reference)

N =

n(Daughter)n(Reference)

D =

=n(Rb-87)n(Sr-86)

=n(Sr-87)n(Sr-86)

Given two minerals A, B 1 2 ln 1 .ln 2

A B

A B

t D DtN N

! "−= +$ %

−& '


49,900,000,000yrsDoes not participate in

radioactive decay process

The halflife of is measured to be

Example. Samples of two minerals from the same igneous rock from northern Ontario are analyzed in a mass spectrometer, with these results for the number ratios N and D:

How old is the rock?

87Rb

Mineral Plagioclase 0.0755 0.7037 Pyroxene 0.3280 0.7133

87 86Sr Sr87 86Rb Sr

101 2 4.99 10 years.t = ×

(B)

(A)

(N) (D)



1 2 ln 1 .ln 2

A B

A B

t D DtN N

! "−= +$ %

−& '

So we have these experimental facts: ❑ The Universe is 13.7 billion years old, give or take about 0.1 billion. ❑ The Milky Way Galaxy is about 13.5 billion years old; certainly it cannot

be younger than the oldest white dwarfs it contains, which are 10 billion years old.

❑ The Solar system – Sun, planets, asteroids, etc. – is 4.5677 billion years old, give or take about a million years.

❑ The Earth’s surface solidified about 3.8 billion years ago. These timespans are much longer than the age the world was thought to have in Darwin’s time. This has expanded dramatically the scope of the slow processes of evolution.


Age Summary

Drake Equation


Much of LAWKI is similarly composed, but differs from the Earth’s composition and is in fact more closely similar to the Solar System at large.

By atom, per hundred oxygen atoms,

Element Bacteria Human Interior Crust Ocean Air Earth Sun CometsHydrogen

217.2 234.6 4.8 200.1 0.002 147058.8 200

Carbon 22.1 40.4 < 0.1 0.1 0.004 0.1 < 0.1 44.1 44.1

Nitrogen 4.8 9.2 0.0 372.1 13.4 13.4

Oxygen 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0

Phosphorus 0.4 0.5 0.1 0.3 0.3

Sulfur 0.2 0.5 4.8 0.1 0.1 4.8 1.4 1.4

Calcium < 0.2 0.9 2.0 3.1 2.0 0.3 0.3

Chemical Composition of Life As We Know It


Atoms are composed of three particles, or “ingredients” • Proton, + electric charge • Neutron, 0 electric charge • Electron, - electric charge

Structure of the Atom


N P

E

Electrons are held “in orbit” around nucleus by the Electrostatic Force Protons + Neutrons are held together by the Strong Nuclear Force

- Strong force only acts on very short distances (radius of proton) - In order to “stick” protons together, they must be pushed extremely close

- This requires extremely high temperatures and pressures

A Hydrogen Atom

Atoms have fixed energies corresponding to specific Energy Levels - Electrons in the atoms can move between Energy Levels under right circumstances - If an electron gains energy, it can move up a level. If it loses energy, it will move down a level

Atomic Energy Levels


E1

E2E3

E

E

E1

E2E3

E

E

Incoming light with E = E2 - E1

Outgoing light with E = E2 - E1

Every atom has a unique set of energy levels, so by measuring the spectra, or set of energy lines, of an object emitting light, we can determine its composition.

- The relative brightness of lines can be used to determine density, temperature, and pressure of the emitting region.

If we squish two atoms together at very high temperature and pressure we can create a new atom. This process can release A LOT of energy. A simplified example:

Hydrogen + Hydrogen + Hydrogen + Hydrogen = Helium + Energy

But the amount of energy produced decreases as the mass of the elements being fused increases. After Iron-56, the fusion reaction no longer produces energy but instead requires energy.

There are two known places in which the conditions for fusion exist: 1. The centers of stars (stellar-core nucleosynthesis) 2. Blast waves from exploding stars or the Big Bang itself (explosive nucleosynthesis)

The Universe started with all its mass in light elements and worked its way up through these two methods.

Nuclear Fusion


Big Bang Nucleosynthesis


• Within 1 second the Universe had cooled to the point where protons, neutrons, and electrons could form without being destroyed instantly.

• These particles could combine to become the first Hydrogen atoms • After about 100 seconds these Hydrogens started fusing into Helium atoms

• Other than very small amounts of Lithium and Beryllium-7, no other elements were made during the Big Bang

• For heavier elements, we need prolonged, sustained fusion reactions

• Thankfully, stars provide just that

The First Stars


• Called Population III Stars, these first stars formed around 300 million years after the Big Bang, creating the Universe’s first galaxies (including ours, remember the age we found for the Milky Way before?)

• These first stars were HUGE, typically 300 - 1000 times as massive as the Sun • Modern stars are typically 0.5 - 2 times the mass of the Sun

• Despite having so much mass, these stars burned through their fuel extremely rapidly (within a few million years)

• These stars were able to fuse elements up to Nitrogen (A=7) before dying

• When these stars died, they collapsed on themselves and exploded in what is called a core-collapse supernova

• These explosions created conditions capable of producing elements beyond Nitrogen and spread these ingredients into interstellar space

The Crab Nebula, a supernova remnant (Hubble Space Telescope)

• These stars formed from the leftover “guts” of the dead Population III stars • The “guts” now contained heavier elements, including the Universe’s first

Carbon • Much smaller than previous stars = MUCH longer lived, dimmer stars • New elements produced from fusion in these stars’ cores, and additional

nucleosynthetic options • New ways to die, as seen from planetary nebulae and new “types” of supernova

• Most of these stars are no longer around, but some of the smaller ones still exist

The Second Stars


Globular cluster M13, in true color (UR/Mees Observatory). Contains about 500,000 stars.

• These Population II stars mostly now live in globular clusters, all ~13Gyr old

• Those larger than 10 solar masses still died in supernova

• Smaller ones lived at most a few billion years, but died in a much less spectacular way

• Stars can now begin to burn Helium, which is a mechanically unstable process • Over time, the outer layers of the star begin to swell up (making the star a giant

or supergiant) • Inner material starts to mix with the outer layers of the star • The star “sheds” its outer layers, releasing the heavy-element enriched material

into interstellar space • After a few million years all that is left is the dead

core of the star, a White Dwarf

A New Way to Die


The Helix Nebula, a planetary nebula, the outer layers shed by a deceased star

(NASA, ESA, Vanderbilt University)

• White Dwarfs can actually “re-die” if they are part of a multi-star system

• One star in system dies, becomes white dwarf, and begins accreting, or taking, matter from companion star

• If the amount of matter accreted pushes the white dwarf beyond 1.4 solar masses, rapid collapse occurs and the star explodes in a Type IA Supernova

Population I


• Higher abundances of heavier elements • Orbits confined more tightly to plane of Milky Way, not random like Pop II • Absent from globular clusters, but can form in open clusters • The Sun is one of these stars

• Many successive generations of stars have enriched the interstellar medium with wide ranges of light/heavy elements: • First via explosive nucleosynthesis • Later with stars’s internal fusion products

Our sun, a population I star (NASA)

• The interstellar medium is composed of 99% gas (by mass) and 1% dust • This mixture leads to the formation of

lots of molecules

Molecules in the Interstellar Medium


How do molecules form from atoms in the ISM? Three ways: • Dust grain catalysis: H atom colliding and sticking with dust grain, moving along

surface, binding with another “stuck” H atom, recoiling/kicking dust grain away • Ion-molecule reactions (zero threshold) • Neutral-neutral reactions in shocked material (high threshold) Why isn’t all the ISM in molecular form? • Ultraviolet starlight destroys molecules, when they’re unprotected by lots of gas

and dust

The ISM of the Milky Way has a mass of: • 90% diffuse clouds • 10% molecular cloud complexes These molecular clouds can collapse gravitationally to form new stars/solar systems

Eagle Nebula, starforming region

(NOAO)

Star Formation


As molecular clouds collapse, molecules within the cloud collide and heat up • These fragments are slowly tumbling to start with, and collisions cause them to

tumble more • As the cloud collapses, this rotational speed increases due to conservation of

angular momentum (think of figure skater pulling their arms inward)

• The material in the center of the cloud, where the collapse is heading, becomes very dense and hot

• The rotating cloud flattens around the dense core into an accretion disk, as particles collide and fall inwards, heating the core even more

• Once the core becomes hot enough to sustain fusion, it ignites into a newborn protostar

• Over time, the disk dissipates due to processes that use up or drive away the surrounding gas

• After ~3-5 million years almost all tiny dust particles have been removed from the disk

Protoplanetary Disks


HL Tau protoplanetary disk (Atacama Large Millimeter Array)

Not all of the debris makes it into the central star • Particles in the accretion disk can clump and form larger objects • Bigger clumps are more likely to bump into other particles, and also have stronger

gravity which sucks up nearby particles • The original gas cloud is not necessarily uniform

in density - gravitational instabilities may exist • Gravitational instabilities in the gas in the disk

help to create gas giant planets • Gravitational instabilities in the dust in the

disk help to create rocky terrestrial planets • As the planets grow in size, their gravity

sweeps up everything nearby in a runaway core-accretion • This cleans up the planet’s orbit of most

other debris nicely, leaving just the planet behind

Temperature of Dust Grains


Planets can be thought of as very large dust grains • All opaque objects emit light • The Flux (power per given area) emitted by a body with temperature T is given by

4

5 1 2 4where 5.67 10 erg sec cm K .

F Tσ

σ − − − −

=

= ×Stefan-Boltzmann constant

Stefan’s Law

So how to find the temperature of dust grain orbiting a star? • Using Stefan’s Law and the geometry of the orbit, we find that

n = no

e�t ln 2t1/2 (1)

n = no

1

2

tt1/2 (2)

t = no

1

2

tt1/2 (3)

T = 279K ⇥

0

@(1�A)L[LJ]

(r[AU ])2

1

A1/4

(4)

1

n = no

e�t ln 2t1/2 (1)

n = no

1

2

tt1/2 (2)

t = no

1

2

tt1/2 (3)

T = 394K ⇥

0

@(1�A)L[LJ]

(r[AU ])2

1

A1/4

(4)

1

Where A is the albedo of the dust grain, L is the luminosity of the star in solar luminosities, and r is the orbital radius of the grain in Astronomical Units

Slow Rotator:Fast Rotator:

n = no

e�t ln 2t1/2 (1)

n = no

1

2

tt1/2 (2)

t = no

1

2

tt1/2 (3)

T = 394K ⇥

0

@(1�A)L[LJ]

(r[AU ])2

1

A1/4

(4)

r[AU ] =

✓279K

T

◆2q(1�A)L[LJ] (5)

1

The Habitable Zone


Star

T=373K T=273K

Rearranging the temperature equation from the previous slides gives us an expression for the orbital radius:

Slow Rotator:Fast Rotator:

We can use this equation with the temperature at the inner and outer boundaries of the habitable zone to see where planets could have liquid water on their surface

Too Hot!Too Cold!

If water boils at 373K and freezes at 273K, where does a planet need to be to be in the range where water is in its liquid state?

n = no

e�t ln 2t1/2 (1)

n = no

1

2

tt1/2 (2)

t = no

1

2

tt1/2 (3)

T = 394K ⇥

0

@(1�A)L[LJ]

(r[AU ])2

1

A1/4

(4)

r[AU ] =

✓394K

T

◆2q(1�A)L[LJ] (5)

1

Just Right

Observing Exoplanets


Three main methods for detecting exoplanets: 1. Direct Imaging: Take pictures over a period of time and actually watch the planet

orbit its host star

2. Radial Velocity (RV): Measure tiny, periodic wobble

3. Transits: Periodic eclipsing of star by planet, or vice versa

Of today’s exoplanets, 62% have been detected by transits, 31% by RV, and 3% by imaging. The remaining 4% were identified by a variety of lesser-used means.

Exoplanets are difficult to find - imagine looking at our Solar System from far away. The Sun would appear 2 billion times brighter than Jupiter! So how do we find them?

in star’s motion along motion of Doppler shift

www.stellarplanet.co.uk

Observing Exoplanets (cont)


As of now, we have detected 1,958 different exoplanets • These planets live in 1241 planetary systems: there are 488 multiple-planet RV or

RV+T systems so far. • 249 have two; 82 have 3, 29 have four, 11 have five, 3 have six, 2 have seven. Seen so far, that is.

Combining the transit method with RV can provide even more information about an exoplanet: • Aquire radius from transit, mass from RV, from radius we can calculate the volume

of the planet and combined with the mass we can get a density • This allows us to determine whether a planet is gaseous like Jupiter or rocky like

Earth

Rocky planets located in the habitable zone of their host star pose potential for harboring life

Stretch and squish greatly exaggerated

Toward orbital partner (star, planet or moon)Gravitational forces Forces from the

planet’s viewpoint

Planet

Tidal Forces


Take a planet orbiting a star (or a moon orbiting a planet). Gravity gets weaker the further you move from the star. What does that mean for our orbiting planet?

PlanetStarR1

R2

The gravitational pull felt by the planet due to the star will be greater on its near side than on its far side.

The differences in these forces felt by the planet are called tides.

Tidal Forces (cont)


The stretching/compressing of the planet due to the tidal forces takes work • Not all of the energy is restored when the forces decrease due to friction and

viscosity within the planet • This drains rotational and orbital energy causing the planet (or moon) to rotate

more slowly AND to drift to a larger orbital distance (also circularizes the orbit)

After a while (millions of years), this results in a special relation (equilibrium) between the orbital and rotation period called tidal locking.

The Pluto-Charon System (Wikipedia)Orbital period = Rotational period

Tidally Locked Worlds


If a planet is tidally locked, one side will forever face the sun and the other face away

Artist’s conception of a tidally locked planet (space.com)

• This could create extreme desert conditions on the day side, and oppositely extreme icy conditions on the night side (with a potential “goldilocks zone” in between in which liquid water could exist)

• Tidal forces can also heat the interior of the planet (like squeezing a tennis ball) • This is particularly interesting when

considering moons of gas giant planets • Tidal heating could warm an icy moon’s

interior to the point where an entire subsurface ocean of liquid water could exist

• This is exactly the case with Jupiter’s moon Europa and Saturn’s moon Enceladus

… Thus allowing life to exist outside the “habitable zone”

http://space.com


Don’t forget!

Review the practice exam

Go over old homework problems

Look over the lecture slides

Start the exam when you’re ready, but give yourself time to finish (6:00pm is the cutoff, if you start at 5:55, you will have 5 minutes

to take your exam)

Good Luck!!!

AST106 review 1 - University of Rochesterdmw/ast106/AST106_review_1.pdf · core of the star, a...

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