Midterm Review

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Sirius, the brightest star in the sky, has a trigonometric parallax of p = 0.385 arc

seconds. What is its distance from Earth?

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1. 0.385 pc2. 0.80 light years3. 1.255 pc4. 2.60 light years5. 8.47 light years

Distances of Stars

Trigonometric Parallax:Star appears slightly shifted from different

positions of the Earth on its orbit

The further away the star is (larger d), the smaller the parallax angle p.

d = __ p 1

d in parsec (pc) p in arc seconds

1 pc = 3.26 LY

Star A has an apparent magnitude of mA = 5.6 and an absolute magnitude of MA = 2.3. Star B has an apparent magnitude of mB = 0.6 and an

absolute magnitude of MB = 2.3.Which of the following statements is true?

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1. The flux received from both stars is the same, but star B is 5 times more luminous than star A, so star B must be further away.

2. The flux received from both stars is the same, but star B is 100 times more luminous than star A, so star B must be further away.

3. Both stars are equally luminous, but the flux received from star A is 5 times less than from star B, so star A must be further away.

4. Both stars are equally luminous, but the flux received from star A is 100 times less than from star B, so star A must be further away.

5. Both stars are equally luminous, but the flux received from star A is 5 times more than from star B, so star B must be further away.

Absolute Magnitude

The absolute magnitude measures a star’s intrinsic brightness (= luminosity).

Absolute Magnitude = Magnitude that a star would have if it were at

a distance of 10 pc.

If we know a star’s absolute magnitude, we can infer its distance by comparing

absolute and apparent magnitudes.

Which of these spectral types describes a Red Giant?

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1. O3V2. F9V3. B2Ia4. K5III5. G2V

Spectral Classification of Stars

Tem

pera

ture

Spectral Classification of Stars

Mnemonics to remember the spectral sequence:

Oh Oh OnlyBe Boy, BadA An AstronomersFine F ForgetGirl/Guy Grade GenerallyKiss Kills KnownMe Me Mnemonics

Luminosity ClassesIa Bright Supergiants

Ib Supergiants

II Bright Giants III Giants

IV Subgiants

V Main-Sequence Stars

IaIb

IIIII

IVV

Masses of Stars in the

Hertzsprung-Russell Diagram

0.5

18

6

31.7

1.00.8

40

Masses in units of solar masses

Low m

asses

High masses

Mass

The higher a star’s mass, the more luminous it is.

High-mass stars have much shorter lives

than low-mass stars

Sun: ~ 10 billion yr.10 Msun: ~ 30 million yr.0.1 Msun: ~ 3 trillion yr.

< 100 solar masses

> 0.08 solar masses

In a binary star system …

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1. The less massive stars orbits around the more massive one.

2. The more massive star orbits around the less massive one.

3. Both stars orbit on identical orbits around the mid-point between them.

4. Both stars orbit around their center of mass, which is closer to the less massive star.

5. Both stars orbit around their center of mass, which is closer to the more massive star.

The Center of Masscenter of mass =

balance point of the system.

Both masses equal => center of mass is in the middle, rA = rB.

The more unequal the masses are, the more

it shifts toward the more massive star.

Which law allows astronomers to calculate the masses of stars in binary systems?

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1. Newton’s first law2. Kepler’s third law3. Einsteins theory of general relativity4. Newton’s third law5. Kepler’s second law

Estimating Stellar MassesRewrite Kepler’s 3. Law as

1 = aAU3 / Py

2

Valid for the Solar system: star with 1 solar mass in the center.

We find almost the same law for binary stars with masses MA and MB different from 1 solar mass:

MA + MB = aAU

3 ____ Py

2

(MA and MB in units of solar masses)

Which is the most common type of binary star systems?

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1. Spectroscopic binaries2. Eclipsing binaries3. X-ray binaries4. Visual binaries (where both stars and

their motion can be resolved)5. Binary neutron stars

Spectroscopic Binaries

The approaching star produces blue shifted lines; the receding star produces red shifted lines

in the spectrum.

Doppler shift → Measurement of radial velocities

→ Estimate of separation a

→ Estimate of masses

Which of these fusion mechanisms does NOT fuse

Hydrogen to Helium?

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1. Proton-proton chain2. CNO Cycle3. Triple-Alpha Process

The CNO Cycle

In stars slightly more massive than the

sun, a more powerful energy generation

mechanism than the PP chain takes over:

The CNO Cycle.

In the sun, energy production is

dominated by direct fusion of H into He

(PP chain).

Energy Transport Structure

Inner radiative, outer convective

zone

Inner convective, outer radiative

zone

CNO cycle dominant PP chain dominant

MassSun

Radiative Core, convective envelope;

Energy generation through PP Cycle

Convective Core, radiative envelope;

Energy generation through CNO Cycle

Summary:

Stellar Structure

What are “globules”?

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1. Small planetary bodies, still in the process of growing into planets (“globes”)

2. Large, cold, uncompressed molecular clouds that may eventually form thousands of stars.

3. Small, compressed pockets of dense gas that may form stars.

4. The remnants of the explosions of sun-like stars.5. The remnants of the explosions of high-mass stars.

(Bok) Globules

~ 10 – 1000 solar masses;

Contracting to form protostars

Compact, dense pockets of gas which

may contract to form stars.

Jets of gas ejected from protostellar disks are called …

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1. Globules2. Planetary Nebulae3. Novae4. Herbig-Haro Objects5. Pulsars

Herbig-Haro Objects

What happens in the Triple-Alpha Process?

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1. Fusion of Hydrogen to Helium2. Fusion of Helium to Carbon3. Fusion of Carbon to Neon4. Fusion of Silicon to Iron5. Nuclear fission of Uranium

Red Giant Evolution

4 H → He

He

He-core gets denser and hotter

until the next stage of nuclear burning can begin in the

core:

He fusion:

3 4He → 12C

“Triple-Alpha Process”

Fusion of Helium into Carbon

What is a “white dwarf”?

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1. A failed star that does not become hot enough to ignite nuclear fusion.

2. The burned-out remnant of a very low-mass star that never ignites Helium fusion.

3. The collapsed Carbon/Oxygen core of a sun-like star.

4. The collapsed iron core of a high-mass star.5. The collapsed iron core of a sun-like star.

White DwarfsDegenerate stellar remnant (C,O core)

Extremely dense:

1 teaspoon of WD material: mass ≈ 16 tons!!!

White Dwarfs:

Mass ~ Msun

Temp. ~ 25,000 K

Luminosity ~ 0.01 Lsun

Chunk of WD material the size of a beach ball would outweigh an ocean liner!

Summary of Post-Main-Sequence Evolution of Stars

M > 8 Msun

M < 4 Msun

Evolution of 4 - 8 Msun

stars is still uncertain.Fusion

stops at formation

of C,O core.

Fusion proceeds to formation of Fe core.

Red dwarfs: He burning

never ignitesM < 0.4 Msun

Which was the first method that allowed astronomers to measure the distances to other galaxies?

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1. Light-travel time measurements2. Gravitational-lensing measurements3. Trigonometric parallax4. Using Cepheid Variables5. Warp-Drive travel

Cepheid Variables:The Period-Luminosity Relation

The variability period of a Cepheid variable is correlated

with its luminosity.

=> Measuring a Cepheid’s period, we

can determine its absolute magnitude!

The more luminous it is, the more slowly it pulsates.

If you plot all stars of a star cluster on a Hertzsprung-Russell diagram:

Which feature will allow you to determine the cluster’s age?

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1. The brightness of red giants.2. The number of white dwarfs.3. The average surface temperature of neutron

stars.4. The turn-off point from the Main Sequence.5. The minimum mass of stars at the lower end

of the main sequence.

Example:HR diagram of the star cluster M 55

High-mass stars evolved onto the

giant branch

Low-mass stars still on the main

sequence

Turn-off point

The lower on the MS the turn-off

point, the older the cluster.