What should I know for Midterm 2?ugastro.berkeley.edu/~ghalevi/c10f15/mt2review.pdf · What should I know for Midterm 2? Astro C10 // Fall 2015 // GSI: Goni Halevi. Overview of Topics

What should I know for Midterm 2?

Astro C10 // Fall 2015 // GSI: Goni Halevi

Overview of Topics

- Exoplanets- The Sun- Properties of stars- HR Diagram- Clusters- Stellar evolution- Supernovae/Neutron stars

- Black holes- Galaxies- Dark Matter- General Relativity- Hubble’s Law- Active Galactic Nuclei- Quasars

Overview of Topics

- Exoplanets- The Sun- Properties of stars- HR Diagram- Clusters- Stellar evolution- Supernovae/Neutron stars


What do I need to know about Exoplanets?- What are they?

Exoplanets are planets that orbit stars that aren’t our Sun.

- How do we detect them?

There are several methods. The most useful are the Transit Method and the Doppler Wobble Method.

- What do we find?

We mostly detect large, massive planets (“Hot Jupiters”) but more and more “Earth-like” planets are being found as technology improves.

What do I need to know about Exoplanets?- How does the transit method work? What are its limitations?

When we view a system EDGE-ON, we can see the brightness of a star dip as a planet passes in front of it.

We look for PERIODIC dips that imply an orbiting body.

It is easier to detect LARGE planets because they block more light, causing a larger, more easily detected dip.

What do I need to know about Exoplanets?- How does the Doppler Wobble method work? What are its limitations?

Stars and planets orbit a shared “CENTER OF MASS”, so stars with planets orbiting them “wobble” back and forth. We measure the shift in wavelength of the light emitted by these stars due to their wobble along the LINE OF SIGHT.

The effect is larger for more MASSIVE, CLOSER planets because they “tug” their star more (larger radial velocity). We can only get a MINIMUM mass for the planet because we don’t know the inclination of its orbit.

(Make Poodle analogy)

Overview of Topics

- Exoplanets ✓- The Sun- Properties of stars- HR Diagram- Clusters- Stellar evolution- Supernovae/Neutron stars


What do I need to know about the Sun?- What are the layers of the sun and how do their temperatures compare?

The core: where fusion occurs, very hot.

The photosphere: the visible “surface”, relatively cool.

The chromosphere: a thin layer, hotter than the photosphere.

The corona: larger, low-density envelope, hotter than the chromosphere, but cooler than the core.

What do I need to know about the Sun?- What kind of activity occurs on the sun?

Solar winds: electrons and positive ions stream from the Sun, interacting with planet magnetic fields and with comets

Solar flares: Violent release of energy from the Sun, high temperatures.

Coronal mass ejections: Large outbursts from the corona.

Prominences: More gentle eruptions on the Sun’s surface, loops of gas above the chromosphere, glowing pinkish/red with lower temperatures than flares.

What do I need to know about the Sun?- What are sunspots?

Sunspots are dark blotches on the photosphere. They are cooler than their surroundings, which is why they appear darker. They have strong magnetic fields that prevent hot, luminous gas from rising to the photosphere from below. We can measure the ROTATION PERIOD of the Sun by watching long-duration sunspots “move across its surface” as it spins.

- What are the periods of activity?

Sunspots, prominences, flares, and coronal mass ejections occur most often during cycle peaks. Each cycle is 11 years if ignoring the magnetic pole reversal, 22 if including it.

Overview of Topics

- Exoplanets ✓- The Sun ✓- Properties of stars- HR Diagram- Clusters- Stellar evolution- Supernovae/Neutron stars


What do I need to know about stellar properties?- What do we directly observe?

Parallactic angle (parallax).

Brightness

The spectrum of the star.

What do I need to know about stellar properties?- What can we derive from observed quantities? How?

Distance (from parallax)

If we have the parallax in arcseconds (1 arcsec = 1/3600 of a degree), we can get the distance measured in parsecs with a simple formula,

d = 1/p


Luminosity (from distance AND brightness)

If we have the parallax, we can get distance (d). We measure the brightness (b) directly, and we can calculate luminosity (L) using:

Note that luminosity is an INTRINSIC property of a star, while brightness is something we can OBSERVE and depends on the distance. (For example, a 60 Watt lightbulb is always 60 Watts, but if you move very far from it, it is dimmer than a lightbulb with less power that is right in front of you.)

b = L/(4 d2) ⇒ L = 4 d2b


Mass (from luminosity)

If we know that a star is on the MAIN SEQUENCE, and we have its luminosity through some method of calculation, we can calculate its (proportional) mass:

For example, we can compare to our sun and get L/L☉

= (M/M☉

)4 to get the mass measured in solar masses.

L∝M4


Composition (from spectra)

If we have taken the spectrum of a star, we can search for absorption and emission lines and compare them to those of known elements to determine whether specific elements are present in a star.

What do I need to know about stellar properties?Here’s an example of a solar spectrum!


Surface Temperature (from spectra)

Stellar spectra have continuous “blackbody/thermal emitter” curves that describe their overall shape. The curve peaks at a specific wavelength ( peak). Using Wien’s law,

We can solve for the surface temperature.peakT = 0.29 cm ∙ K

What do I need to know about stellar properties?Wien’s Law, illustrated.


Radius (from luminosity AND temperature)

Once we have the luminosity (L) and surface temperature (T) of a star, we can calculate its radius (R) using

L = 4 R2 T4

Overview of Topics

- Exoplanets ✓- The Sun ✓- Properties of stars ✓- HR Diagram- Clusters- Stellar evolution- Supernovae/Neutron stars


What do I need to know about the HR diagram?- The Hertzprung-Russel (HR) diagram compares a star’s LUMINOSITY (y-

axis) to its TEMPERATURE (x-axis).

Temperature increases to the LEFT rather than the right.

- Most stars are on the MAIN SEQUENCE, a line that goes diagonally down from high luminosity, high temperature, to low luminosity, low temperature.

- Luminosity is roughly proportional to the 4th power of mass for MS stars.

This implies that MASSIVE stars have SHORTER lives, since we can think of luminosity as a measure of HOW FAST A STAR BURNS FUEL.

- Know the diagram on the next slide by heart.

What do I need to know about the HR diagram?

Overview of Topics

- Exoplanets ✓- The Sun ✓- Properties of stars ✓- HR Diagram ✓- Clusters- Stellar evolution- Supernovae/Neutron stars


What do I need to know about star clusters?- There are two types of star clusters: OPEN and CLOSED

OPEN clusters are rather sparse

Often young

Often in the spiral arms of a galaxy

- Star clusters reveal stellar ages

All stars in a cluster have the same distance, age, and initial chemical composition

CLOSED clusters are dense

All old stars

In the spherical “halo” of galaxies

What do I need to know about star clusters?- Types of stars: O, B, A, F, G, K, M

O-type stars live shortest lives (most massive), M-type stars live longest lives (least massive)

- The “turn-off” point on the HR diagram gives the AGE of a cluster

Overview of Topics

- Exoplanets ✓- The Sun ✓- Properties of stars ✓- HR Diagram ✓- Clusters ✓- Stellar evolution- Supernovae/Neutron stars


What do I need to know about stellar evolution?- Not yet a star… The very beginning

Clouds of gas and dust start to contract due to SELF-GRAVITY

Cloud breaks apart into smaller parts: PROTOSTARS

As the protostar collapses inward, density increases, so collisions increase, temperature increases, and pressure increases

Contraction slows down due to pressure

The protostar continues to release GRAVITATIONAL ENERGY as it contracts slowly

What do I need to know about stellar evolution?- And so it begins, a star is born

Once temperatures are high enough, the star stops contracting and settles on the MAIN SEQUENCE: its temperature and luminosity are pretty much constant for now

Nuclear reactions occur in the core, providing the stability needed to stop from collapsing or expanding

The star is in HYDROSTATIC EQUILIBRIUM

(If the star fails due to not being massive enough, it becomes a BROWN DWARF, held up by degeneracy pressure.)

What do I need to know about stellar evolution?- Living a happy life on the main sequence

Stars on the MS have high core temperatures

Hydrogen atoms are ionized and nuclear fusion creates Helium from hydrogen

Energy is emitted!

0.7% of the mass of the hydrogen is converted into light through Einstein’s E=mc2 (burning fuel)

The star is held up against gravity by THERMAL PRESSURE

What do I need to know about stellar evolution?- Every good thing must come to an end: Stellar Death for LOW MASS (<8M

☉)

stars

The hydrogen envelope heats up and expands, so it begins to cool and bloat, becoming a RED GIANT

Relatively cool (low T) but very large (big R, so high L)

Carbon and Oxygen (C and O) fused from Helium!

Fusion slows down as temperature drops, the envelope expands and the star is no longer stable

What do I need to know about stellar evolution?Outer layers ejected, PLANETARY NEBULA forms (expanding shell of ionized gas)

HAS NOTHING TO DO WITH PLANETS

Loses mass due to the planetary nebulae and winds, not mostly C, O, and He, very low mass

Does not collapse because of ELECTRON DEGENERACY PRESSURE

Central star becomes a WHITE DWARF

Shines due to the atomic nuclei (positive ions) losing energy, but NO NUCLEAR REACTIONS OCCUR

What do I need to know about stellar evolution?Think of WDs as RETIRED stars

Nuclei cool down, luminosity and temperature both low

“BLACK DWARF” also held up by electron degeneracy pressure, still the same size as the WD (roughly Earth-size)

Mass limit of WD: Chandrasekhar limit (1.4 solar masses)

- Death for stars in a BINARY system (most stars)

MASS TRANSFER occurs, recipient stars dies QUICKER than it would alone

Overview of Topics

- Exoplanets ✓- The Sun ✓- Properties of stars ✓- HR Diagram ✓- Clusters ✓- Stellar evolution ✓- Supernovae/Neutron stars


What do I need to know about supernovae?- There are two types of SN: Type I and Type II

Type I: no H lines in spectra, Type II: prominent H in spectra

Type I: in all galaxies, Type II: in spiral galaxies, usually in arms

- SN occur “suddenly”, extreme increases in luminosity

Can rival the brightness of an entire galaxy

Quickly expanding gasses in outer layers

- 1 SN per galaxy per 100 years, on average (pretty rare)

What do I need to know about supernovae?- Type I occurs from WD in binary that approaches the Chandrasekhar limit

Runaway chain of nuclear reactions, huge amount of energy is released

- Type II occurs in very HIGH MASS stars (>10 solar masses)

Also called a CORE-COLLAPSE supernova

Occur in spiral galaxy arms because this is where MASSIVE STARS form

Red supergiant, iron core reaches Chandrasekhar limit and collapses

Most energy is released in the form of NEUTRINOS

What do I need to know about supernovae?Nucleosynthesis occurs

Gamma rays are produced (i.e. SN 1987A, a type II SN that Alex likes)

When a SN explodes, the elements in it are dispersed into the cosmos and form new stars, planets, and life

WE are made of star stuff

Neutron stars form from Type II supernovae

Held up by neutron degeneracy pressure, small in size

What do I need to know about supernovae?PULSARS are spinning neutron stars

They burst at regular periods

Highly magnetized

Overview of Topics

- Exoplanets ✓- The Sun ✓- Properties of stars ✓- HR Diagram ✓- Clusters ✓- Stellar evolution ✓- Supernovae/Neutron stars ✓


What do I need to know about Black Holes?- Neutron stars have a mass limit

If the mass of an NS exceeds 2-3 solar masses, it COLLAPSES into a BH

- BHs are VERY dense: a lot of mass concentrated in a very small volume- Gravity is so strong that NOTHING (not even light) can escape

Matter INSIDE a BH collapses to a SINGULARITY

We can’t SEE black holes; we detect them due to their gravitational effect

- Tidal forces are STRONGER near LOW mass BHs because the difference in gravitational force on two ends of an object is GREATER

What do I need to know about Black Holes?- What if you fell into a BH?

A person watching you would seem to see time slowing down for you

A person watching you would think you never fall in at all

You would know you were falling in

If you escape BEFORE crossing the EVENT HORIZON, you will have aged LESS than if you had stayed

Light signals from the event horizon would be redshifted to infinite wavelength, so zero energy, and nobody would see your light

What do I need to know about Black Holes?- BHs can rotate!

The event horizon of a rotating BH of mass M is SMALLER than that of a non-rotating BH with the same mass M

Rotating BHs have “ergospheres” from which energy can be extracted

- Gamma Ray Bursts (GRBs) have to do with the birth or growth of a BH

Jets of radiation formed through merging neutron star & BH, merging BHs, SN collapse into BHs, etc.

What do I need to know about Black Holes?- BHs can create WORMHOLES!

Wormholes are theoretical tunnels created by warped spacetime

They can connect between “parallel universes” or create a tunnel from one place in the universe to another

What do I need to know about Black Holes?- BHs can evaporate!

Again, all good things must come to an end, including BHs

Virtual pairs created, possible for one to fall in before annihilation can happen, in which case the other one escapes as Hawking radiation.

Overview of Topics


- Black holes ✓- Galaxies - Dark Matter- General Relativity- Hubble’s Law- Active Galactic Nuclei- Quasars

What do I need to know about galaxies?- Ours is called the MILKY WAY

It’s a SPIRAL galaxy: a disk with arms in which new stars form

When we look at it, the dust in the disk of the galaxy absorbs and scatters light (extinction) so it LOOKS like we’re at the center of it

Harlow Shapley used globular clusters to find out that we AREN’T at the center of the Milky Way

What do I need to know about galaxies?- Edwin HUBBLE observed Cepheid Variable Stars in some other galaxies,

which were then called “spiral nebulae”

Cepheids are very luminous, evolved supergiant stars that brighten and fade regularly due to oscillations in size

Hubble deduced what galaxies actually ARE: large stellar systems

- Two main types of galaxies: SPIRAL and ELLIPTICAL

Spiral: have new stars forming in arms, old stars dominate the bulge and halo

Elliptical: no disk, no arms, very little gas and dust, OLD stars

Overview of Topics


- Black holes ✓- Galaxies ✓- Dark Matter- General Relativity- Hubble’s Law- Active Galactic Nuclei- Quasars

What do I need to know about dark matter?- The evidence for it:

Spiral galaxies have basically flat rotation curves that we didn’t expect.

This suggests that there is a bunch of mass far out from the galactic center that we can’t see

What do I need to know about dark matter?Gravitational lensing

Light from distant objects is bent by the gravity of an intervening galaxy or cluster, producing an Einstein ring or an arc depending on the alignment

But if we calculate the expected mass of the intervening galaxy/cluster, it’s not enough to explain what we see!

What do I need to know about dark matter?- The candidates:

WIMPs: Weakly Interacting Massive Particles

Suggests that DM is made up of various exotic subatomic particles

MACHOs: MAssive Compact Halo Objects

Suggests that DM is “normal” stuff like BHs, neutron stars, brown dwarfs, WDs, and random planets

NOT ENOUGH matter there to explain the evidence we have, at least 25% of the matter in the universe must be some sort of more “exotic” DM

Overview of Topics


- Black holes ✓- Galaxies ✓- Dark Matter ✓- General Relativity- Hubble’s Law- Active Galactic Nuclei- Quasars

What do I need to know about General Relativity?

- It’s a theory from Albert Einstein that suggests that space and time form a sort of “spacetime fabric” that is warped by matter and energy

Warping of spacetime causes the paths of objects (including LIGHT) to curve

- We have evidence

The precession “rotation” of Mercury’s orbit

Bending of starlight near the Sun

Light gets redshifted when it exits a strong gravitational field

Gravitational lensing (light is bent by the warping of spacetime)

What do I need to know about General Relativity?

- More evidence!

Black holes: light can’t escape outside the radius of 2GM/c2

BINARY PULSARS: their orbital period decreases, they get CLOSER together due to gravitational waves

Overview of Topics


- Black holes ✓- Galaxies ✓- Dark Matter ✓- General Relativity ✓- Hubble’s Law- Active Galactic Nuclei- Quasars

What do I need to know about Hubble’s Law?

- Slipher noticed that spectra of galaxies have large redshifts

- Hubble used observations of Cepheids to derive distances and found that REDSHIFT IS PROPORTIONAL TO DISTANCE

Galaxies move away from us

FARTHER galaxies move away from us FASTER

- Redshift is denoted by “z” and DEFINED by the Doppler shift,

- When things are moving relatively slow (~<0.2c), we can thus APPROXIMATE the redshift as

z ~ v/c

z = Δ / 0


- Hubble’s law says that a galaxy that is a distance d away from us is receding at a speed of

where H0 is called “Hubble’s constant” and has a value of ~71 km/s/Mpc (WEIRD UNITS)

i.e. a galaxy 10 Mpc away recedes at 710 km/s

v = H0d


- What is Lookback Time?

Lookback time is how far back in time we are seeing when we look at a distant object, and is sometimes just called “distance”

Lookback time tells us how long ago the light we are seeing left the place where it came from, and is not equal to physical distance because of the expansion of the universe

Overview of Topics


- Black holes ✓- Galaxies ✓- Dark Matter ✓- General Relativity ✓- Hubble’s Law ✓- Active Galactic Nuclei- Quasars

What do I need to know about Active Galactic Nuclei (AGN)?- Using Hubble’s law and apparent

brightness, we find that some galaxies have very luminous (ACTIVE) centers

- Jets of particles and radiation are shot out of the nucleus

Stars are probably NOT responsible for the activity we see

- Radiation from AGN is thought to be a result of mass accretion by a supermassive BH at the center of the galaxy

What do I need to know about Active Galactic Nuclei (AGN)?

- AGN are VERY EFFICIENT (~10%, compared to 0.7% for stellar fusion)

- AGN are VARIABLE, so we can put an upper limit on the physical size of their emitting region

They cannot be larger than the distance light travels on the time scale of their variation periods

- We see BROAD emission lines in AGN spectra

The emitting material is revolving around the center BH at high speeds, causing a range of Doppler shifts

Overview of Topics


- Black holes ✓- Galaxies ✓- Dark Matter ✓- General Relativity ✓- Hubble’s Law ✓- Active Galactic Nuclei ✓- Quasars

What do I need to know about Quasars?- Quasi-stellar radio sources (QUASARS) are a TYPE of AGN

Not all AGN are quasars; there are other types, but ALL quasars are AGN

- Quasars look like stars, but their spectra are weird because they are VERY redshifted (high z), which made them hard to interpret early on

From Hubble’s law, this means that quasars are VERY DISTANT

The largest known quasar redshift is z=7.1, but remember that we cannot find its speed using z~v/c because it is too FAST for the approximation to work

What do I need to know about Quasars?- Since quasars look very BRIGHT, but

we know they are very FAR, this means they are very LUMINOUS

- Like other AGN, quasars have VARIABILITY that allows us to measure their size

We find that their light-emitting region is TINY, no larger than a few light years (for comparison, the Milky Way is about 100,000 times as large)

Overview of Topics


- Black holes ✓- Galaxies ✓- Dark Matter ✓- General Relativity ✓- Hubble’s Law ✓- Active Galactic Nuclei ✓- Quasars ✓

that’s all,good luck on midterm 2!

Documents

What should I know for Midterm 2?ugastro.berkeley.edu/~ghalevi/c10f15/mt2review.pdf · What should I know for Midterm 2? Astro C10 // Fall 2015 // GSI: Goni Halevi. Overview of Topics