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Midterm Review
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your transmitter.
Sirius, the brightest star in the sky, has a
trigonometric parallax of p = 0.385 arc
seconds. What is its distance from Earth?
1.
2.
3.
4.
5.
0.385 pc
0.80 light years
1.255 pc
2.60 light years
8.47 light years
Distances of Stars
d in parsec (pc)
p in arc seconds
1
d = __
p
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.
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?
1.
2.
3.
4.
5.
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.
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.
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.
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.
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
Absolute Magnitude = Magnitude
that a star would have if it were at
a distance of 10 pc.
The absolute magnitude measures a star’s
intrinsic brightness (= luminosity).
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?
1.
2.
3.
4.
5.
O3V
F9V
B2Ia
K5III
G2V
Temperature
Spectral Classification of Stars
Spectral Classification of Stars
Mnemonics to remember the spectral sequence:
Oh
Oh
Only
Be
Boy,
Bad
A
An
Astronomers
Fine
F
Forget
Girl/Guy
Grade
Generally
Kiss
Kills
Known
Me
Me
Mnemonics
Ia Bright Supergiants
Ia
Luminosity
Classes
Ib
Ib Supergiants
II
II Bright Giants
III Giants
III
IV
IV Subgiants
V
V Main-Sequence
Stars
Masses of Stars
in the
HertzsprungRussell Diagram
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
Masses in units
of solar masses
40
18
6
3
1.7
> 0.08 solar
masses
1.0
0.8
0.5
In a binary star system …
1.
2.
3.
4.
5.
The less massive stars orbits around the
more massive one.
The more massive star orbits around the
less massive one.
Both stars orbit on identical orbits around
the mid-point between them.
Both stars orbit around their center of mass,
which is closer to the less massive star.
Both stars orbit around their center of mass,
which is closer to the more massive star.
The Center of Mass
center 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?
1.
2.
3.
4.
5.
Newton’s first law
Kepler’s third law
Einsteins theory of general relativity
Newton’s third law
Kepler’s second law
Estimating Stellar Masses
Rewrite Kepler’s 3. Law as
1 = aAU3 / Py2
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:
3
a
____
AU
MA + MB =
Py2
(MA and MB in units of solar masses)
Which is the most common
type of binary star systems?
1.
2.
3.
4.
5.
Spectroscopic binaries
Eclipsing binaries
X-ray binaries
Visual binaries (where both stars and
their motion can be resolved)
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?
1.
2.
3.
Proton-proton chain
CNO Cycle
Triple-Alpha Process
The CNO Cycle
In the sun, energy
production is
dominated by direct
fusion of H into He
(PP chain).
In stars slightly more
massive than the
sun, a more powerful
energy generation
mechanism than the
PP chain takes over:
The CNO Cycle.
Energy Transport Structure
Inner convective,
outer radiative
zone
Inner radiative,
outer convective
zone
CNO cycle dominant
PP chain dominant
Summary:
Stellar Structure
Convective Core,
radiative envelope;
Energy generation
through CNO Cycle
Radiative Core,
convective envelope;
Energy generation
through PP Cycle
Sun
What are “globules”?
1.
2.
3.
4.
5.
Small planetary bodies, still in the process of growing
into planets (“globes”)
Large, cold, uncompressed molecular clouds that may
eventually form thousands of stars.
Small, compressed pockets of dense gas that may form
stars.
The remnants of the explosions of sun-like stars.
The remnants of the explosions of high-mass stars.
(Bok) Globules
Compact,
dense pockets
of gas which
may contract to
form stars.
~ 10 – 1000
solar masses;
Contracting to
form protostars
Jets of gas ejected from
protostellar disks are called …
1.
2.
3.
4.
5.
Globules
Planetary Nebulae
Novae
Herbig-Haro Objects
Pulsars
Herbig-Haro Objects
What happens in the TripleAlpha Process?
1.
2.
3.
4.
5.
Fusion of Hydrogen to Helium
Fusion of Helium to Carbon
Fusion of Carbon to Neon
Fusion of Silicon to Iron
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”?
1.
2.
3.
4.
5.
A failed star that does not become hot
enough to ignite nuclear fusion.
The burned-out remnant of a very low-mass
star that never ignites Helium fusion.
The collapsed Carbon/Oxygen core of a sunlike star.
The collapsed iron core of a high-mass star.
The collapsed iron core of a sun-like star.
White Dwarfs
Degenerate stellar remnant (C,O core)
Extremely dense:
1 teaspoon of WD material: mass ≈ 16 tons!!!
Chunk of WD material the size of a beach ball
would outweigh an ocean liner!
White Dwarfs:
Mass ~ Msun
Temp. ~ 25,000 K
Luminosity ~ 0.01 Lsun
Summary of Post-Main-Sequence
Evolution of Stars
Fusion proceeds to
formation of Fe core.
M > 8 Msun
Fusion
stops at
formation
of C,O
core.
M < 4 Msun
M < 0.4 Msun
Evolution of
4 - 8 Msun
stars is still
uncertain.
Red dwarfs:
He burning
never
ignites
Which was the first method that
allowed astronomers to measure
the distances to other galaxies?
1.
2.
3.
4.
5.
Light-travel time measurements
Gravitational-lensing measurements
Trigonometric parallax
Using Cepheid Variables
Warp-Drive travel
Cepheid Variables:
The Period-Luminosity Relation
The variability period of a
Cepheid variable is correlated
with its luminosity.
The more luminous it is, the
more slowly it pulsates.
=> Measuring a
Cepheid’s period, we
can determine its
absolute magnitude!
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?
1.
2.
3.
4.
5.
The brightness of red giants.
The number of white dwarfs.
The average surface temperature of neutron
stars.
The turn-off point from the Main Sequence.
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
Turn-off point
Low-mass stars
still on the main
sequence
The lower
on the
MS the
turn-off
point, the
older the
cluster.