Download PS 224, Fall 2014 HW 4

PS 224, Fall 2014
HW 4
1. True or False? Explain in one or two short sentences. (2x10 points)
a. The fact that we have not yet discovered an Earth-size extrasolar planet in an Earth-like
orbit tells us that such planets must be very rare.
False. Our observational techniques are not yet very sensitive to planets of such low
mass, so the lack of such discoveries says more about our technology than about small
planets. b. Some extrasolar planets are likely to be made mostly of water.
True. Some planets with water have been discovered.
c. Some extrasolar planets are likely to be made mostly of gold.
False. We know of no process that enriches gold over other metals. d. Current evidence suggests that there could be 100 billion or more planets in the Milky Way.
True. In fact, results from Doppler and transit studies already hint that planets are at
least as common as stars in our galaxy. e. Planets like Earth probably didn’t form around the first stars because there were so few
heavy elements back then.
True. Earth formed through the accretion of smaller, rocky objects made from heavy
elements. f.
The Sun’s velocity around the Milky Way tells us that most of our galaxy’s dark matter lies
near the center of the galactic disk.
False. The Milky Way’s rotation curve remains flat well beyond the orbit of the Sun,
indicating that the majority of the Milky Way’s mass lies beyond the Sun’s orbit. g. We know that a black hole lies at our galaxy’s center because numerous stars near it have
vanished over the past several years, telling us that they’ve been sucked in.
False. The orbital velocities of stars at the galactic center are what indicate a black hole.
None of these stars has vanished from sight.
h. If we could watch a time-lapse movie of a spiral galaxy over millions of years, we’d see
many stars being born and dying within the spiral arms.
True. Spiral arms are bright because they contain many short-lived blue stars that shine
for only a few million years. i.
The star–gas–star cycle will keep the Milky Way looking just as bright in 100 billion years as
it looks now.
False. The star-gas-star cycle will only last for 100 million years or so. In 100 billion
years, all the gas in the Milky Way will have been exhausted.
PS 224, Fall 2014
HW 4
2. What are the strengths and limitations of the Doppler and transit techniques? What kinds of
planets are easiest to detect with each method? Are there certain planets that each method
cannot detect, even if the planets are very large? Explain. What advantages are gained if a
planet can be detected by both methods? (10 pts)
Doppler technique: Good at finding massive planets at small distances from the host stars.
This cannot detect (1) small planet at large distances as the radial velocity “wiggle” is too small
and (2) planets that have a radial velocity of zero.
Transit technique: Good at finding large planets at small distances from the host star. As this
technique depends on measuring how much light is blocked, planets around smaller host stars
are easier to find (as long as you get enough light from the smaller host stars). This cannot
detect (1) small planet at large distances as the blocked light is too small of a fraction and (2)
planets that are not in the line of sight of the observer.
By detecting a planet with both the doppler and transit techniques, we can (1) verify that the
different methods work and (2) combine information to understand the planet better. For e.g.,
mass from Doppler technique and radius from transit technique gives us the density of the
planet and help us understand what the planet is made up of.
3. Discuss why our current understanding of the exoplanet population is incomplete. How can
we get a more complete picture? (5 pts)
Our current census of the exoplanet population is incomplete and biased toward large planets at
small distances. This limitation is due to our observational techniques. Plus, we have only been
finding planets for about a decade, with the vast majority of planets discovered by the Kepler
mission. Therefore, our current sample of exoplanets has significant biases and probably not
representative of the entire population. To get a complete picture, we need future surveys that
will detect other types of planets. Ideally, we would search for planets with multiple techniques
that are complementary and be able to find exoplanets of all masses, sizes, and at all distances
from the hist star.
4. Draw simple sketches of our galaxy as it would appear face-on and edge-on. Identify the disk,
bulge, halo, and spiral arms, and indicate the galaxy’s approximate dimensions. (5 pts)
PS 224, Fall 2014
HW 4
5. Describe and contrast (a) open clusters and globular clusters and (b) stars in the disk and
halo of the Milky Way. (5+5 pts, 5 pts for three or more differences.)
(a) open clusters and globular clusters
Open clusters are found near the disk of the Galaxy whereas globular clusters are in the halo.
Open clusters are young (~1 Gyr) whereas globular clusters are old (>12 Gyr).
Open clusters have a lot of gas and dust whereas globular clusters have no gas and dust.
Open clusters are relatively small with hundreds of stars while globular clusters are massive
with 100,000 stars.
Open clusters are generally metal-rich whereas globular clusters are some of the most metalpoor parts of the Galaxy.
(b) disk vs. halo stars
Disk stars are younger (few Gys) than halo stars (>10 Gyr).
Disk stars are generally near the Galactic disk whereas the halo stars are scattered all ove the
halo of the Galaxy.
Disk stars rotate around the Galactic center in an organized way whereas the halo stars have
random orbits.
Disk stars are more metal-rich than the halo stars.
6. Summarize the stages of the star–gas–star cycle in Figure 15.3. (5 pts)
Atomic Hydrogen Gas: The Galactic disk is mostly made up of atomic gas.
Molecular Clouds: This gas cools down to about 10 K and forms molecular hydrogen. This
precipitates a collapse and star formation.
Star Formation: The molecular gas collapses due to gravity and becomes denser. Stars are
formed if the density gets high enough.
Nuclear Fusion in Stars: At the core of the stars, the hydrogen is under high temperature and
pressure, causing nuclear fusion. This produces helium, carbon, and other heavier elements.
When a massive star goes supernova, even heavier elements are formed.
Returning Gas: Stellar winds and supernova returns most of a star’s hydrogen and other
elements into the neighboring environment. The recycling is faster when more massive stars are
formed.
Hot bubbles: The returning gas is initially separated from its surroundings by its hotter
temperature. Over time, these clouds cool down and mix with the atomic gas nearby.
PS 224, Fall 2014
HW 4
7. Formation of the Milky Way. Figure 15.18 outlines a basic model that accounts for some but
not all of the features of the Milky Way. What observational evidence indicates that the Milky
Way’s protogalactic cloud contained virtually no elements other than hydrogen and helium?
What evidence suggests that the halo stars formed first and disk stars formed later? What
features of the Milky Way are not explained by this basic model? (5 pts)
Some observational evidence for the model in Figure 15.18 comes from the structure of our
own galaxy. The halo is full of old stars and is spherical in shape, which suggests that star
formation ceased there many billions of years ago. In contrast, the galactic disk hosts both
old and young stars, so star formation is continuing there. So the order of formation,
spherical cloud followed by disk, is primarily motivated by the study of our galaxy.
The idea that the original protogalactic cloud was made of pure hydrogen and helium
comes from two sources: the discovery that stars create heavy elements during their lives
and while they die. Thus, multiple generations of stars make ever more elements.
Extrapolating back into time, earlier generations of stars had to have fewer heavy elements.
Astronomers have known since the mid-1950s that the conditions in the hot and dense
early universe could create hydrogen and helium but only trace amounts of any heavier
elements. So, those two ideas converge on the idea of a protogalactic cloud that begins as
pure hydrogen and helium.