Review for Test #3 Nov 17Topics:• The Sun• Stars• The Interstellar medium• Stellar Evolution and Stellar Death• Neutron stars and pulsars

Methods • Conceptual Review and Practice Problems Chapters 9 - 13• Review lectures (on-line) and know answers to clicker questions• Try practice quizzes on-line• Review (time Sunday, Nov 15 starting at 3pm) mainly Q&A format

Bring:• Two Number 2 pencils• Simple calculator (no electronic notes)• UNM Student ID

Reminder: There are NO make-up tests for this class

Test #3 ReviewHow to take a multiple choice test1) Before the Test:• Study hard (~2 hours/day Friday through Monday)• Get plenty of rest the night before• Bring at least 2 pencils, UNM student ID, and a calculator2) During the Test:• Write out and bubble your last name, space, first name and Exam

color in the name space of the scantron form. Write out and bubble your Banner ID in the ID space.

• Draw simple sketches to help visualize problems• Solve numerical problems in the margin• Come up with your answer first, then look for it in the choices• If you can’t find the answer, try process of elimination• If you don’t know the answer, Go on to the next problem and

come back to this one later• TAKE YOUR TIME, don’t hurry• If you don’t understand something, ask me.

Test #3 Useful Equations

parallactic distance d = 1/p where p is parallax in arcsec and d is in parsecs

R = 2 GM

c2

Schwarschild Radius:

Equivalence of Matter and Energy:

E = mc2

Lifetimes of stars (on the main sequence):

L = 1010/M2 years where M is the Mass in solar masses and L is the Lifetime

The Sun

The Sun in X-rays over several years

The Sun is a star: a shining ball of gas powered by nuclear fusion.

Luminosity of Sun = 4 x 1033 erg/s = 1 LSun

(amount of energy put out each second in form of radiation, = 1025 40W light bulbs)

Mass of Sun = 2 x 1033 g = 330,000 MEarth

= 1 M

Sun

Radius of Sun = 7 x 105 km = 109 REarth

= 1 RSun

Temperature at surface = 5800 K => yellow (Wien’s Law)

Temperature at center = 15,000,000 K

Average density = 1.4 g/cm3

Density at center = 160 g/cm3

Composition: 74% of mass is H 25% He 1% the rest

Rotation period = 27 days at equator 31 days at poles

The Interior Structure of the Sun(not to scale)

Let's focus on the core, where the Sun's energy is generated.

Core of the Sun

Temperature : 15 million K (1.5 x 107 K)

Density: 160 gm/cm3, 160 times that of water, 10 times the density of lead

What Powers the Sun

Nuclear Fusion: An event where nuclei of two atoms join together.

Need high temperatures.

Energy is produced. Elements can be made.

nuc. 1 + nuc. 2 → nuc. 3 + energy (radiation)

Mass of nuc. 3 is slightly less than mass of (nuc. 1 + nuc. 2). Thelost mass is converted to energy. Why? Einstein's conservation ofmass and energy, E = mc2. Sum of mass and energy always conserved in reactions. Fusion reactions power stars.

Chain of nuclear reactions called "proton-proton chain" or p-p chainoccurs in Sun's core, and powers the Sun.

neutrino (weird particle)

deuteron (proton + neutron bound together)

positron (identical to electron but positively charged)

proton

proton

1) proton + proton → proton+neutron + neutrino + positron (deuteron)

+ energy (photon)

photon

{

In the Sun's Core...

2) deuteron + proton → 3He + energy

He nucleus, only 1 neutron

3) 3He + 3He → 4He + proton + proton + energy

Net result:

4 protons → 4He + 2 neutrinos + energy

Hydrostatic Equilibrium: pressure from fusion reactions balances gravity. Sun is stable.

Mass of end products is less than mass of 4 protons by 0.7%. Mass converted to energy.

600 millions of tons per second fused. Takes billions of years to convert p's to 4He in Sun's core. Process sets lifetime of stars.

The Solar Constant

If we placed a light detector (a.k.a. solar cell) above the Earth’s atmosphere and perpendicular to the sun’s rays, we can measure how much solar energy is received per square meter (Watts / m2)

This is the solar constant => 1400 Watts / m2

About 50-70% of this energy reaches earth

So assuming 50% of this energy reaches of this energy reaches earth Every square meter receives 700 Watts Solar cells - devices to convert light into electricity are about

20% efficient So a square meter of solar cells generates 140 Watts To power a 2,000 sq. ft. house in summer with energy to run

washer/dryer etc., need about 14, 000 Watts peak or 100 sq. meter of solar cells

In 1960s Ray Davis and John Bahcall measured the neutrino flux from the Sun and found it to be lower than expected (by 30-50%)

Confirmed in subsequent experimentsTheory of p-p fusion well understoodSolar interior well understood

Solar neutrino problem

Theoriticians like Bruno Pontecorvo realizedThere was more than one type of neutrinoNeutrinos could change from one type to another

Confirmed by Super-Kamiokande experiment in Japan in 1998

Answer to the Solar neutrino problem

50,000 gallon tank

Total number of neutrinos agrees with predictions

How does energy get from core to surface?

core

"radiative zone":

photons scatter off nuclei and electrons, slowly drift outwards:"diffusion".

"surface" or photosphere: gas density low enough so photons can escape into space.

photon path

"convection zone"

some electrons bound to nuclei => radiation can't get through => heats gas, hot gas rises, cool gas falls

Sunspots

Roughly Earth-sized

Last ~2 months

Usually in pairs

Follow solar rotation

Sunspots

They are darker because they are cooler (4500 K vs. 5800 K).

Related to loops of the Sun's magnetic field.

radiation from hot gas flowing along magnetic field loop at limb of Sun.

The Solar Wind

At top of corona, typical gas speeds are close to escape speed => Sun losing gas in a solar wind.

Wind escapes from "coronal holes", seen in X-ray images.

Wind speed 500 km/sec (takes a few days to reach Earth).

106 tons/s lost. But Sun has lost only 0.1% of its mass from solar wind.

Active Regions

Prominences: Loops of gas ejected from surface. Anchored in sunspot pairs. Last for hours to weeks.

Flares: A more energetic eruption. Lasts for minutes. Less well understood.

Prominences and flares occur most often at maximum of Solar Cycle.

Solar FlareVideo

Measuring the Stars

How big are stars?How far away are they?How bright are they?How hot?How old, and how long do they live?What is their chemical composition?How are they moving?Are they isolated or in clusters?

By answering these questions, we not only learn about stars, but about the structure and evolution of galaxies they live in, and the universe.

How Far Away are the Stars?Earth-baseline parallax - useful in Solar System

Earth-orbit parallax - useful for nearest stars

New distance unit: the parsec (pc).

Using Earth-orbit parallax, if a star has a parallactic angle of 1",it is 1 pc away.

Remember 1" (arcsecond) = 1/60 arcmin = 1/3600 degrees

Distance (pc) = 1Parallactic angle (arcsec)

1 pc = 3.3 light years = 3.1 x 10 18 cm = 206,000 AU

1 kiloparsec (kpc) = 1000 pc1 Megaparsec (Mpc) = 10 6 pc

Closest star to Sun is Proxima Centauri. Parallactic angle is 0.7”, so distance is 1.3 pc.

If the angle is 0.5", the distance is 2 pc.

Spectral Classes

Strange lettering scheme is a historical accident.

Spectral Class Surface Temperature Examples

OBAFGKM

30,000 K20,000 K10,000 K7000 K6000 K4000 K3000 K

RigelVega, Sirius

Sun

Betelgeuse

Further subdivision: BO - B9, GO - G9, etc. GO hotter than G9. Sun is a G2.

Stellar Sizes - Indirect Method

Almost all stars too far away to measure their radii directly. Need indirect method. For blackbodies, use Stefan's Law:

Luminosity (temperature) 4 x (surface area)

Energy radiated per cm2 of area on surface every second T 4

(T = temperature at surface)

Determine luminosity from apparent brightness and distance, determine temperature from spectrum (black-body curve or spectral lines), then find surface area, then find radius (sphere surface area is 4 R2)

And:

Luminosity = (energy radiated per cm2 per sec) x (area of surface in cm2)So:

The Wide Range of Stellar Sizes

H-R Diagram of Well-known StarsH-R Diagram of Nearby Stars

Note lines of constant radius!

Main Sequence

White Dwarfs

Red Giants

Red Supergiants

Increasing Mass, Radius on Main

Sequence

The Hertzsprung-Russell (H-R) Diagram

Sun

How Long do Stars Live (as Main Sequence Stars)?

A star on Main Sequence has fusion of H to He in its core. How fast depends on mass of H available and rate of fusion. Mass of H in core depends on mass of star. Fusion rate is related to luminosity (fusion reactions make the radiation energy).

lifetime

mass (mass) 3

Because luminosity (mass) 3,

lifetime

or 1 (mass) 2

So if the Sun's lifetime is 10 billion years, a 30 MSun star's lifetime is only 10 million years. Such massive stars live only "briefly".

mass of core fusion rate

mass of star luminosity

So,

Star Clusters

Two kinds:

1) Open Clusters

-Example: The Pleiades

-10's to 100's of stars

-Few pc across

-Loose grouping of stars

-Tend to be young (10's to 100's of millions of years, not billions, but there are exceptions)

2) Globular Clusters

- few x 10 5 or 10 6 stars

- size about 50 pc

- very tightly packed, roughly spherical shape

- billions of years old

Clusters are crucial for stellar evolution studies because:

1) All stars in a cluster formed at about same time (so all have same age)

2) All stars are at about the same distance

3) All stars have same chemical composition

The Interstellar Medium (ISM) of the Milky Way GalaxyOr: The Stuff (gas and dust) Between the Stars

Stars form out of it. Stars end their lives by returning gas to it.

The ISM has:

a wide range of structures a wide range of densities (10-3 - 107 atoms / cm3) a wide range of temperatures (10 K - 107 K)

Why study it?

Compare density of ISM with Sun or planets:

Sun and Planets: 1-5 g / cm3

ISM average: 1 atom / cm3

Mass of one H atom is 10-24 g!So ISM is about 1024 times as tenuous as a star or planet!

ISM consists of gas (mostly H, He) and dust. 98% of mass is in gas, but dust, only 2%, is also observable.

Effects of dust on light:

1) "Extinction" Blocks out light

2) "Reddening" Blocks out short wavelength light better than long wavelength light => makes objects appear redder.

Grain sizes typically 10-5 cm. Composition uncertain, but probably silicates, graphite and iron.

Gas Structures in the ISM

Emission Nebulae or H II Regions

Regions of gas and dust near stars just formed.

The Hydrogen is essentially fully ionized.

Temperatures near 10,000 K

Sizes about 1-20 pc.

Hot tenuous gas => emission lines (Kirchhoff's Laws)

Rosette Nebula

Tarantula NebulaLagoon Nebula

Red color comes from one emission line of H atoms (tiny fraction of H is atoms, not ionized).

Why is the gas ionized?

Remember, takes energetic UV photons to ionize H. Hot, massive stars produce huge amounts of these.

Why "H II Region?

H I: Hydrogen atom H II: Ionized Hydrogen . . . O III: Oxygen missing two electrons etc.

Such short-lived stars spend all their lives in the stellar nursery of their birth, so emission nebulae mark sites of ongoing star formation.

Many stars of lower mass are forming too, but make few UV photons.

H I Gas and 21-cm radiationGas in which H is atomic.

Fills much (most?) of interstellar space. Density ~1 atom / cm3.

Galaxy IC 342 in visible light

HI in IC 342from VLA

Too cold (~100 K) to give optical emission lines.Primarily observed through radiation of H at wavelength of 21 cm.

H I accounts for almost half the mass in the ISM: ~2 x 109 MSun !

Origin of 21-cm photon:

The proton and electron each have “spin”. A result from quantum mechanics: if both spinning the same way, atom's energy is slightly higher. Eventually will make transition to state of opposite spins. Energy difference is small -> radio photon emitted, wavelength 21-cm.

Molecular GasIt's in the form of cold (~10 K) dense (~103 - 107 molecules / cm3)clouds.

Molecular cloud masses: 103 - 106 MSun !

Sizes: a few to 100 pc.

1000 or so molecular clouds in ISM. Total mass about equal to H I mass.

Optically, seen as dark dust clouds.=> Molecular Clouds important because stars form out of them!

They tend to be associated with Emission Nebulae.

We can observe emission from molecules. Most abundant is H2 (don't

confuse with H II), but its emission is extremely weak, so other "trace" molecules observed:

CO (carbon monoxide) H

2O (water vapor)

HCN (hydrogen cyanide) NH

3 (ammonia)

etc. . .These emit photons with wavelengths near 1 mm when they make a rotational energy level transition. Observed with radio telescopes.

Star Formation

Stars form out of molecular gas clouds. Clouds must collapse to form stars (remember, stars are ~1020 x denser than a molecular cloud).

Gravity makes cloud want to collapse.

Outward gas pressure resists collapse, like air in a bike pump.

Probably new molecular clouds form continually out of less dense gas. Some collapse under their own gravity. Others may be more stable. Magnetic fields and rotation also have some influence.

When a cloud starts to collapse, it should fragment. Fragments then collapse on their own, fragmenting further. End product is 100’s or 1000’s of dense clumps each destined to form star, binary star, etc.Hence a cloud gives birth to a cluster of stars.

Protostar and proto-planetary disk in Orion

As a clump collapses, it heats up. Becomes very luminous.

Eventually hot and denseenough => spectrumapproximately black-body.Can place on HR diagram.Protostar follows “Hayashitracks”

1700 AU

Now a protostar. May form proto-planetary disk.

Finally, fusion starts, stopping collapse: a star!

Star reaches Main Sequence at end ofHayashi Track

One cloud (103 - 106 MSun)forms many stars, mainly in clusters,in different parts at different times.

Massive stars (50-100 MSun) take about 106 years to form, least massive (0.1 MSun) about 109 years. Lower mass stars more likely to form.In Milky Way, a few stars form every year.

Brown Dwarfs

Some protostars not massive (< 0.08 MSun

) enough to begin fusion.

These are Brown Dwarfs or failed stars. Very difficult to detect because so faint. First seen in 1994 with Hubble. How many are there?

Stellar Evolution:Evolution off the Main Sequence

Main Sequence Lifetimes

Most massive (O and B stars): millions of years

Stars like the Sun (G stars): billions of years

Low mass stars (K and M stars): a trillion years!

While on Main Sequence, stellar core has H -> He fusion, by p-p chain in stars like Sun or less massive. In more massive stars, “CNO cycle” becomes more important.

Evolution of a Low-Mass Star(< 8 M

sun , focus on 1 M

sun case)

- All H converted to He in core.

- Core too cool for He burning. Contracts. Heats up.

Red Giant

- Tremendous energy produced. Star must expand.

- Star now a "Red Giant". Diameter ~ 1 AU!

- Phase lasts ~ 109 years for 1 MSun star.

- Example: Arcturus

- H burns in shell around core: "H-shell burning phase".

Red Giant Star on H-R Diagram

Eventually: Core Helium Fusion

- Core shrinks and heats up to 108 K, helium can now burn into carbon.

"Triple-alpha process"

4He + 4He -> 8Be + energy8Be + 4He -> 12C + energy

- First occurs in a runaway process: "the helium flash". Energy from fusion goes into re-expanding and cooling the core. Takes only a few seconds! This slows fusion, so star gets dimmer again.

- Then stable He -> C burning. Still have H -> He shell burning surrounding it.

- Now star on "Horizontal Branch" of H-R diagram. Lasts ~108 years for 1 MSun star.

Core fusionHe -> C

Shell fusionH -> He

Horizontal branch star structure

More massive less massive

Helium Runs out in Core

-All He -> C. Not hot enough-for C fusion.

- Core shrinks and heats up.

- Get new helium burning shell (inside H burning shell).

Red Supergiant

- High rate of burning, star expands, luminosity way up.

- Called ''Red Supergiant'' (or Asymptotic Giant Branch) phase.

- Only ~106 years for 1 MSun star.

"Planetary Nebulae"

- Core continues to contract. Never gets hot enough for carbon fusion.

- Helium shell burning becomes unstable -> "helium shell flashes".

- Whole star pulsates more and more violently.

- Eventually, shells thrown off star altogether! 0.1 - 0.2 MSun

ejected.

- Shells appear as a nebula around star, called "Planetary Nebula" (awful, historical name, nothing to do with planets).

White Dwarfs

- Dead core of low-mass star after Planetary Nebula thrown off.

- Mass: few tenths of a MSun

.

-Radius: about REarth

.

- Density: 106 g/cm3! (a cubic cm of it would weigh a ton on Earth).

- White dwarfs slowly cool to oblivion. No fusion.

Evolution of Stars > 8 MSun

Higher mass stars evolve more rapidly and fuse heavier elements.

Example: 20 MSun

star lives

"only" ~107 years.

Result is "onion" structure with many shells of fusion-produced elements. Heaviest element made is iron.

Eventual state of > 8 MSun

star

Fusion Reactions and Stellar Mass

In stars like the Sun or less massive, H -> Hemost efficient through proton-proton chain.

In higher mass stars, "CNO cycle" more efficient. Same net result: 4 protons -> He nucleusCarbon just a catalyst.

Need Tcenter

> 16 million K for CNO cycle to be

more efficient.

(mass) ->

Sun

Following the evolution of a cluster on the H-R diagram

T

1. White Dwarf (WD) If initial star mass < 8 M

Sun or so

(Max WD mass is 1.4 MSun

, radius is about that of the Earth)

2. Neutron Star (NS) 8 M

Sun < initial star mass < 25 M

sun

(1.4 M

Sun < NS mass < 3? M

sun

radius is ~ 10 km - city sized)

3. Black Hole (BH) If initial mass > 25 M

Sun

(For BH with mass = 3 Msun

radius ~ 9 km)

Final States of a Star

No Explosive Event + Planetary Nebula (Possible Nova from Carbon Flash)

Supernova + ejecta

GRB + Hypernova + ejecta

Stellar Explosions

Novae

White dwarf inclose binary system

WD's tidal force stretches out companion, until parts of outer envelope spill onto WD. Surface gets hotter and denser. Eventually, a burst of fusion. Binary brightens by 10'000's! Some gas expelled into space. Whole cycle may repeat every few decades => recurrent novae.

Death of a High-Mass Star

M > 8 MSun

Iron core

Iron fusion doesn't produce energy (actually requires energy) => core collapses in < 1 sec.

Ejection speeds 1000's to 10,000's of km/sec!(see DEMO)

Remnant is a “neutron star” or “black hole”.

T ~ 1010 K, radiation disrupts nuclei, p + e => n + neutrinoCollapses until neutrons come into contact. Rebounds outward, violent shock ejects rest of star => A Core-collapse or Type II Supernova

Such supernovae occurroughly every 50 yearsin Milky Way.

Example Supernova: 1998bw

Remember, core collapse (Type II) and carbon-detonation (Type I) supernovae have very different origins

Making the Elements

Universe initially all H (p’s and e’s). Some He made soon after Big Bang before stars, galaxies formed. All the rest made in stars, and returned to ISM by supernovae.

Elements up to iron (56Fe, 26 p + 30 n in nucleus) produced by steady fusion (less abundant elements we didn’t discuss, like Cl, Na, made in reactions that aren’t important energy makers).

Solar System formed from such "enriched" gas 4.6 billion years ago. As Milky Way ages, the abundances of elements compared to H in gas and new stars are increasing due to fusion and supernovae.

Heavier elements (such as lead, gold, copper, silver, etc.) by "neutron capture" in core, even heavier ones (uranium, plutonium, etc.) in supernova itself.

Neutron Stars

Leftover core from Type II supernova - a tightly packed ball of neutrons.Diameter: 20 km only!

Mass: 1.4 - 3(?) MSun

Density: 1014 g / cm3 !

Surface gravity: 1012 higherEscape velocity: 0.6c

Rotation rate: few to many times per second!!!

Magnetic field: 1012 x Earth's!

A neutron star over the Sandias?

The Lighthouse model of a pulsar