Astronomy 21 – Test 2 – Answers
Section I – Short Answers - 2 pts per question
1.
What is self-propagating star formation? Why is it important?
Hot, young massive stars with strong stellar winds produce shock fronts, which in turn
compress the ISM and thus trigger new star formation.
2.
Why is the sky blue? And is the sun red at sunset? Explain the astrophysical processes.
Rayleigh scattering is happening in the atmosphere due to dust particles which have roughly
comparable sizes as visible wavelengths. Blue light thus gets scattered preferentially causing
a blue looking sky. Longer wavelength light can penetrate without being scattered. During
sun set light from the sun has to pass through more dust in the atmosphere scattering more
and thus causing the Sun to look relatively redder.
3.
What is a Pulsar? What type of light does it radiate? Explain.
A pulsar is a rapidly spinning neutron star that has a strong magnetic field. Electrons get
accelerated and emit synchrotron emission that is beamed out in the form of jets. Each time
the jets point towards us we see a pulse of radiation similarly to how a light house functions.
4.
What is thermal and hydrostatic equilibrium and what role does it play in Cepheid
Variables?
When in thermal equilibrium, the star maintains a constant temperature and luminosity.
When in hydrostatic equilibrium, the gravitational pressure is balanced by the pressure of the
hot gases of the inner regions of the star. Cepheid Variables are not in hydrostatic equilibrium
– their envelope expands and contracts.
5.
How does the energy from the core of the star get to its surface? (List and explain 3
mechanisms)
Conduction (collisions between particles), Convection (rising of hotter blobs and sinking of
colder ones giving rise to motion), & Radiative Diffusion (radiation traveling and carrying
energy away).
6.
You see (a) a red star (b) a red galaxy that reveals strong Balmer Lines. What is going
on?
Red stars with Balmer lines do not exist so we are dealing with a Binary star. A red galaxy
with Balmer lines has had recent episodes of star formation.
7.
Draw the rotation curves of (a) a solid body, (b) a planetary system, (c) a typical galaxy.
Why is the rotation curve of galaxies different from (a) & (b)?
The rotation curve increase steeper than that of a solid body (more mass in the inner regions)
and then levels off and does not fall off like in the case of a planetary system, proving that
there is dark matter in the halos of galaxies.
8.
What type of radiation do you see when observing a supernova remnant at radio
wavelengths? Explain the nature of this radiation.
You observe synchrotron emission from super nova remnants. Electrons in the magnetic field
get accelerated and then loose their energy again by emitting a photon. This is non-thermal
radiation.
9.
Which elements form inside stars? How? Which cannot be formed inside stars – why?
Where and how do those elements form?
H, He, Be & Li are formed in the big bang. Elements heavier than He form inside stars (Li &
Be get destroyed). Only elements up to iron can form in stars by fusion. Heavier elements
form though fission which requires high energies that are only obtained during supernova
explosions.
10. How would you determine the spiral structure of the Milky Way? Also – what is 21-cm
emission (explain the astrophysical mechanism)?
You have to look through dust so you have to use longer wavelength observations. The 21cm line is useful for that (it is radiation emitted during the spin flip of the electron of atomic
hydrogen). Redshifts of that line can be measured and velocities can be mapped out. The
Spiral structure of the HI clouds then becomes apparent.
11. How would you determine the age of a globular cluster? What types of observations
would you need? How can the same observations be used to determine the distance of
that cluster?
You need to measure colors and magnitudes, draw a HRD, and then determine the turnoff
point of in the main sequence. This is related to the age of the cluster. You get the distance
also from the HRD by determining m-M for the whole cluster.
12. Give several reasons of why the evolution of massive stars is faster than that of low mass
stars.
More massive stars have more gravitational potential energy so the cores of those stars can
achieve relatively higher temperatures. This gives rise to faster reaction rates. Also, nuclear
reactions are progress via the CNO-cycle as opposed to the pp-chain. Energy transport in the
core is via convection.
13. Given that there is an empirical relationship between the mass and the luminosity of
main sequence stars (where L  M3.5), derive an expression for the main sequence
lifetime (in solar units) of stars of any mass M.
t = M/L; since L is the total energy produced assume E=fMc2 (where f is some fraction);
since t = M/L and L  M3.5  t  M/M3.5  t  M-2.5
14. What are the radiation mechanisms (list several!) of active galaxies? Explain the concept
of non-thermal activity).
Active galaxies emit non-thermal radiation from their centers. This is synchrotron emission
where electrons get accelerated in a magnetic field. AGN’s often have jets that propagate
through the ISM/IGM. X-ray emission is often observed from the accretion disk surrounding
the black hole.
15. What is the winding dilemma? What are spiral density waves and what role to they play
in star formation?
The winding dilemma is that the spiral structure of spirals is not caused by their rotation. If
that was the case the spiral arms would have been wound up by something like a factor of
100. Spiral density waves are density waves that propagate through the spiral galaxy and
trigger star formation.
16. Comment on how the Unified Picture of Active Galaxies can explain the characteristics
of the many different types of Active Galaxies.
The idea is that the type of active galaxy that you observe depends on the orientation and
viewing angle of the galaxy. If you look straight down the torus you’ll observe a BL Lac
object, at some angle Seyfert galaxy and at a larger angle a radio galaxy.
17. Some astronomers believe all galaxies have a black hole in their centers. What do you
think? Support your arguments. How could you test this picture?
Really any logical argument goes including: Two pictures – short lived scenario where many
galaxies go though an active phase versus fewer longer lived episodes. Do a statistical
analysis to find out.
Section II: The Interstellar Medium and Stellar Evolution
10 pts per question
1) Stellar Evolution
a) Why are low temperatures necessary for proto-stars to form inside dark nebulae?
For stars to form inside a cloud, the cloud has to be dense and cool. Collapse will occur only when
the gravitational potential energy of the fragment exceeds the thermal energy of the gas inside the
fragment.
b) Why do disks form around contracting proto-stars? Why do those stars have jets?
As rotating objects collapse they spin up to conserve angular momentum. Collapse will be much
radical at the poles because the centrifugal force will counterbalance the collapse of material in the
disk. The material collapsing onto the central objects will want to escape and the only place it can go
is to the poles – so jets will form.
c) What is the energy source of a main sequence star like our sun? What is the energy
source of main sequence star like Vega? What are the energy production
mechanisms? How and why are they different in the Sun and in Vega? Explain.
The main energy source of stars like the sun is nuclear fusion of H to He. Gravity (particularly in the
core of the star) also plays a role, but it is minor compared to the nuclear energy generation. Vega has
the same energy sources as the sun. The energy production mechanisms, however, are different. In
the Sun the pp-chain (a 3-step process) will happen where protons fuse with protons to form He-4. In
Vega the CNO-chain will happen where C, N, O are used at catalysts. This reaction requires higher
temperatures because the repulsion between a proton and the positively charged C, N, and O nuclei
are much larger.
d) What is Hydrostatic Equilibrium? Are main sequence stars in Thermal Equilibrium?
See part 1 question 4.
e) Why do stars “evolve off the main sequence”? Why do these stars expand? Why do
their temperatures become cooler?
Stars evolve off the main sequence as they use up their fuel in their cores. As 4 protons get turned
into alpha particles the core can contract, thus transforming some gravitational energy into heat. A
higher central temperature will give rise to faster reaction rates, thus producing more energy per unit
time. This energy will travel outward to the surface of the star (first via radiation and later via
convection). The larger central energy supply will cause the envelope to take up a larger volume (the
gas law applies) and thus expand. Since the surface of the star is not farther away from the core and
since there is a decreasing temperature gradient, the surface temperature of the star will actually be
lower than what it was when the star was physically smaller.
f) What is a Helium Flash? What is “degeneracy” and what role does it play in the
Helium Flash? Which types of stars have a Helium flash and which do not? Explain
why some stars do not have a Helium Flash?
A helium flash is the explosive onset of He-to-C fusion (it is a core explosion that is actually damped
by the rest of the envelope – because of that, it has never been observed). It is also called the triple
alpha reaction. A gas only turns degenerate only under extreme situation of very high pressures.
Simply put, degeneracy happens when you cannot pack electrons any closer. All of the possible
electron levels are filled up. It is determined by the Pauli Exclusion Principle that states that you
cannot have more than two electrons (with opposite spins) in one quantum state. When a gas turns
degenerate, the normal gas law on longer applies and the temperature increase can no longer be
compensated by an increase in volume. Thus, as the temperature increases, reaction rated will speed
sup leading to yet higher temperatures. This gives rise to a run-away process that results in a core
explosion and a very sudden onset of He burning. Only low mass stars will experience a He-flash –
more massive stars have a convective core, so mixing can happen. This means that the depletion of
He is more gradual and degeneracy never occurs.
g) What are the three main end-states of stars and what does that depend on?
The three end states are (a) White Dwarf that is initially surrounded by a Planetary Nebula, (b)
Neutron Star or Pulsar (depending on our viewing angle of it) surrounded by a supernova remnant,
and (c) Black Hole also surrounded by a SNR. The fate of the star depends on the mass of the
progenitor star. Stars up to 3Mo will turn into WD (that have masses up to 1.4Mo), stars up to about
8Mo will turn into neutron stars and even more massive stars will become stellar black holes.
h) Which elements can form inside stars? What does that depend on?
See part I, question 9, but also mention that all elements up to Iron can form inside stars in an onionshell structure. In each shell a progressively heavier element is fusing. Whether heavier metals are
formed critically depends on the mass of the star. Stars of lower mass then the Sun can only form up
to carbon, the Sun can fuse some Oxygen, and more massive stars burn accordingly heavier elements.
2) The Interstellar Medium
a) Pink clouds.
i) Is this light from gas or dust? Explain!
Gas – it is emission from ionized hydrogen gas.
ii) What is the approximate temperature of that gas/dust?
A few x 1,000K. It is hot because this light is only seen when hydrogen is ionized.
iii) What is the astrophysical process that gives rise to that light? Why is this light
red, why not blue or green?
Emission lines are produced by the ionized gases. In hot gases the electrons occupy higher
energy orbits, and as the gas cools, the electrons drop down to lower levels. During that process
energy is liberated, which is emitted in the form of a photon. All gases have characteristic
emission line spectra. In star forming regions, hydrogen is the most abundant element. In the
visible part of the spectrum Hydrogen emits the Balmer lines (H, H, H and H). The brightest
line is H, which is in the red part of the spectrum. This line dominates the light giving the gas a
reddish tint. [For extra credit: If Oxygen is mixed in with the Hydrogen, then the Oxygen gas
may add a greenish/yellowish shimmer (and if Carbon was present you’d see purple). But in star
forming regions there are only small traces of these elements.]
iv) How do the properties of light depend on the luminosity and color of nearby stars?
If the nearby stars are hot and blue, they will produce many high energy photons (UV radiation)
that will heat and ionize the gas. Low luminosity red stars do not have enough high energy
photons to ionize the gas, unless there is an unrealistically high proportion of low mass stars.
b) Blue clouds.
i. Is this light from gas or dust? Explain!
Dust – it is reflected star light. (Aside: It could be emission line gas from another element, but
since most gas in star forming regions is hydrogen, a reddish tint would dominate).
ii. What is the approximate temperature of that gas/dust?
Between 100K to ~300K.
iii. What is the astrophysical process that gives rise to that light? Why is this light
blue, why not red or green?
Red light can pass through dust clouds, because the wavelength of red light is longer than the
size of the grains. Blue light, on the other hand, has a shorter wavelength and therefore gets
reflected off the dust grains. Since the reflected light is blue light, the dust grains will have a blue
shimmer. [For extra credit: The color of the light depends on the size of the grains. If the grains
were smaller, only the UV (purple light) would get scattered, and if the grains were larger, longer
wavelength light (such as green, yellow or red) would get scattered.]
iv. How do the properties of light depend on the luminosity and color of nearby stars?
If the stars were too hot and luminous (O and B type stars), they would produce many UV
photons that would dissociate the dust and ionize the dust. This would then result in HII regions,
i.e., pink clouds. Cooler stars clearly produce less UV photons. [For extra credit: If however the
proportion of the cooler stars is very high, and the dust clouds are very near (i.e. a high flux),
there may be enough photons to ionize the gas. Very cool stars like for example red giants and
supergiants do not produce enough UV photons. However, they do not have much blue light
either, so blue light will not get scattered. Since some of the longer wavelength light also gets
scattered, dust regions surrounding red supergiants may look yellowish.]
c) Dark clouds.
i. Why is this stuff dark? Explain!
Dark stuff must be dense, because otherwise you could see through. It is dark because it does not
emit light in the visible region.
ii. What is the approximate temperature of that stuff?
Temperature is cold, even colder than in the case of “blue scattered light”. If they were warmer
the clouds would not be dense. Approx temperature is 10-40K; 100K max.
iii. Everything emits light as long as its temperature is above absolute zero – you
cannot see this light with your eyes (unless it is silhouetted against brighter
background regions) – how could you “observe” dark clouds nevertheless? What
is the astrophysical process that gives rise to that “invisible” light?
There are at least two options, you only need to mention one for full credit (and repeating
silhouettes does not earn points). (a) Dust will get heated by proto-stars that are inside those dark
clouds. The temperatures of the dust may rise to a few hundred degrees Kelvin. Warm dust
grains then emit the same radiation as any solid or dense bodies do – they emit black body
radiation that peaks at infra-red wavelengths. So you’d see the dust in dark clouds with infra-red
telescopes (actually you’d see it in far-IR; near IR radiation is emitted from yet hotter objects –
actually with near-IR observations you can look through the dust and study proto-stars).
b) You can also use radio telescopes – you will be able to look through the dust and observe the
cool gases that are always mixed with the dust-grains. You’ll be able to detect molecular clouds
at 6cm, and atomic clods at 21 cm. Neither of these radiations are black body radiation. You’ll
detect emission lines from CO molecules (due to changes in vibrational energy levels), or you’ll
detect emission lines from the H-atom when the electron undergoes a spin slip and drops to a
lower energy level.
d) Planetary Nebulae
i. Is this light from gas or dust? Explain!
Temperature is very hot – ionized gases. Several thousand degrees.
ii. What is the astrophysical process that gives rise to that light? Why is this light
colorful (blue, red, green, yellow)?
Hydrogen light is pink as explained above. Other gases have other signatures – different
emission lines (emission at other wavelengths), and can thus have different colors. Oxygen is
green; Nitrogen blue, etc.
e) Supernova Remnants
iii. Is this light from gas or dust? Explain
Temp is very hot – ionized gasses, mostly H.
iv. What is the astrophysical process that gives rise to that light? Why is this light
colorful (blue, red, green, yellow)?
Same as above.
3) Dark Matter
a) How can we derive the mass of a galaxy from its rotation curve? Explain how to do this
conceptually – if you derive this quantitatively you’ll receive extra credit.
b) What other theoretical and/or observational evidence do we have for the existence of
Dark Matter?
c) What form can Dark Matter take? Distinguish between baryonic and non-baryonic Dark
Matter.
d) Describe a few experiments that did/did not detect some of that Dark Matter.
e) Where in the universe would you find what type of Dark Matter? Also comment on
possible distributions of Dark Matter.
f) Describe an alternate theory to explain the concept of Missing Dark Matter.
4) The Formation and the Evolution of Galaxies
a) Explain how our Galaxy could have formed. In what sense is the formation of ellipticals
galaxies different from that of spirals?
b) Hubble proposed that ellipticals could evolve into spirals. What evidence is there to
support this picture? What evidence is there to object to this picture?
c) What are the dominant morphologies of galaxies in rich clusters, in poor clusters and in
the field? In what sense does the evolution of galaxies depend on the environment?
d) The Merger Mechanism is the most popular mechanism, but it does NOT explain the
whole picture. Why not? List and explain other physical mechanisms that transform
galaxies. What evidence do we have for each picture?
e) Comment on differences between very distant and close galaxies. (Comment on the
morphologies of galaxies, their colors, their luminosities, and their spectra.)