Download PS 224, Fall 2014 HW 4

PS 224, Fall 2014
HW 4
1. True or False? Explain in one or two short sentences.
a. Scientists are currently building an infrared telescope designed to observe fusion reactions
in the Sun’s core.
False. Infrared telescopes cannot see through the Sun.
b. Two stars that look very different must be made of different kinds of elements.
False. What a star looks like depends on many different properties like mass, age, and
size.
c. Two stars that have the same apparent brightness in the sky must also have the same
luminosity.
False. How bright a star appears depends on the luminosity of a stars and its distance
away from us.
d. Some of the stars on the main sequence of the H-R diagram are not converting hydrogen
into helium.
False. The main-seuqence is defined as the phase of a star’s life when it burns hydrogen
into helium.
e. Stars that begin their lives with the most mass live longer than less massive stars because
they have so much more hydrogen fuel.
False. Massive stars live have shorter lifetimes as they burn through their fuel faster.
f.
All giants, supergiants, and white dwarfs were once main-sequence stars.
True. Main-sequence stars evolve to become giants and supergiants based on their
mass and eventually end up as white dwarfs.
g. The iron in my blood came from a star that blew up more than 4 billion years ago.
True. All elements except hydrogen and helium were produced in stars.
h. If the Sun had been born 4½ billion years ago as a high-mass star rather than as a lowmass star, Jupiter would have Earth-like conditions today, while Earth would be hot like
Venus.
False. If the Sun had been born 4-1/2 billion years ago as a high-mass stars, it would
have blown up as a supernova long ago.
i.
j.
I just discovered a 3.5 MSun main-sequence star orbiting a 2.5 MSun red giant. I’ll bet that red
giant was more massive than 3 MSun when it was a main-sequence star.
True. The red giant had to be more massive than its companion for it to have evolved off
the main-sequence.
If you could look inside the Sun today, you’d find that its core contains a much higher
proportion of helium and a lower proportion of hydrogen than it did when the Sun was born.
True. The Sun has been hydrogen into helium for 4.5 billion years. (The core now
contains about 70% helium.)
PS 224, Fall 2014
HW 4
2. Explain briefly how you would differentiate between the two classes of objects. Note that
dwarf is generally used for stars in the main-sequence.
a. A dwarf vs. M dwarf
Observe them at different wavelengths. An A dwarf is hotter and its spectrum peaks in
the blue/UV while a red dwarf is cooler and its spectrum peaks in the red end of the
visible spectrum.
b. pre main-sequence star vs. red giant (both of which are about 3600 K)
Pre-main-sequence stars have disks which can be easily observed in the mm and radio
wavelengths. So I would get hold of a radio telescope and see which one has a disk.
c. red dwarf vs. red giant
Since their temperatures are similar, we need find out which one is brighter. But
brightness depends on distance as well. So I would find a way to measure the distance
to these stars. The further away one is the red giant.
3. Future Skies. As a red giant, the Sun will have an angular size in Earth’s sky of about 30°.
What will sunset and sunrise be like? Do you think the color of the sky will be different from what
it is today? Explain.
The Sun will have an angular size of 30°. The setting position moves through the sky—360°—once every 24 hours. So at 30°, or 1 of 360°, the 12 Sun will take 1 of 24 hours = 2 hours to set, from the moment the limb 12 touches the horizon to the time it vanishes below the horizon. (Compare that to the
approximately 2 minutes it takes the 0.5° Sun to set now.) The color of the sky should be
substantially different, because the light emitted by the Sun will be much redder than it is
today. There will be much less blue light to scatter around any surviving atmosphere,
and therefore the sky will be less blue than it is and will probably be redder. There will be
plenty of light. Of course, the perception of the color may change over time. If the
atmosphere does not survive the onslaught of the red giant Sun, the color of the sky will
be black, as it is on the Moon. PS 224, Fall 2014
HW 4
4. Homes to Civilization? We do not yet know how many stars have Earth-like planets, nor do
we know the likelihood that such planets might harbor advanced civilizations like our own.
However, some stars can probably be ruled out as candidates for advanced civilizations. For
example, given that it took a few billion years for humans to evolve on Earth, it seems unlikely
that advanced life would have had time to evolve around a star that is only a few million years
old. For each of the following stars, decide whether you think it is possible that it could harbor an
advanced civilization. Explain your reasoning in one or two sentences each.
a. 10 MSun main-sequence star
A 10-solar-mass star has a very short lifetime. It also produces copious
amounts of ultraviolet radiation that may discourage living organisms.
b. 1.5 MSun main-sequence star
A 1.5-solar-mass star has a lifetime of a few billion years and produces light of similar character to that of our Sun. It seems reasonable to imagine it being orbited by a planet with a civilization. c. 1.5 MSun red giant
A 1.5-solar-mass red giant is a temporary stage of life for a low-mass star. If an advanced civilization had already developed around this star, which is
possible, then it may have had the resources to respond to its expanding, reddened sun. d. 1 MSun helium core-fusion star
A 1-solar-mass horizontal branch star is a late-stage low-mass-star, burning helium. Life
had time to develop, but it would have had to be very clever and have sufficient natural
resources as well as a lot of cooperation to persist. e. Red supergiant
A red supergiant is a late-stage high-mass star in the advanced state of nuclear burning
—that is, burning elements heavier than helium in its core. Its envelope is gigantic. Its
age at this point is rather young because massive stars live short lives. With our stated
assumptions, an advanced civilization probably does not have enough time to develop. 5. Scientists estimate the life span of a star by dividing the total amount of energy available for
fusion by the rate at which the star radiates energy into space. Such calculations predict that the
life spans of high-mass stars are shorter than those of low-mass stars. Describe one type of
observation that can test this prediction and verify that it is correct.
If high-mass star lifespans are shorter than low-mass star lifespans, and if stars are
always born with a range of masses, then there should be star clusters or galaxies with
all old low-mass stars or star clusters and galaxies with a mix of low and high-mass stars,
but no star clusters or galaxies with only massive stars (and no low-mass protostars). PS 224, Fall 2014
HW 4
6. For the six stages of star formation shown below, briefly describe in 2–3 sentences what is
happening. (after you you do that, feel free to describe in as much gory detail as you want).
a: Dark cloud: Large molecular clouds develop dense regions that appear darker than
surrounding regions. This can be precipitated by external pressure or forces or random
fluctuations present in the cloud. These regions are very large, typically around 200,000 AU.
b: Gravitational collapse: When the dark regions get sufficiently dense, they collapse under
their own gravity to form a roughly spherical shape. This is generally considered as the birth of
star. The cloud can be as big as 10,000 AU at this time.
c: Protostars: By about 100,000 years, a protostar has formed at the center and is still
contracting. The rest of the gas and dust in the cloud falls to form a disk around the protostar.
The disk can be as large as 500 AU. In addition, the protostar has bipolar jets that is ejecting
material from the magnetic poles.
d: T Tauri star: By 3 million years, the protostar has lost the envelope that surrounds it. It can
be clearly seen by an observer. The disk is about 100 AU and is about to form planets.
e: Pre-main-sequence star: Between 3–50 million years after birth, the star has formed
planets. It is still contracting.While most of the disk has dissipated, a small debris disk remains.
f: Young stellar systems: After 50 million years, the star is burning hydrogen and is settling into
its adult life. It has lost its disk and has a family of planets. Such planetary systems are about 50
AU wide, which is 4000 times smaller than the molecular clouds it formed from.
PS 224, Fall 2014
HW 4
7. Study Fig 12.10. Tell me 3–5 interesting things about the main-sequence, solar-type dwarfs,
red dwarfs, giants and supergiants, brown dwarfs, and white dwarfs.
Main-sequence:
• Stars are burning hydrogen.
• They spend 90% of their life in the main-sequence.
• They physical properties only change by 2-5% during this entire time.
red dwarfs,
• They make up about 70% of the stars in the Galaxy.
• They are small stars that have extremely long lifetimes.
• Any red dwarf ever formed is still alive.
giants and supergiants,
• These are evolved main-sequence stars that are burning helium, carbon, and other
elements.
• They have similar temperature as dwarfs but are very big and therefore very luminous.
brown dwarfs
• These are failed stars that were never massive enough to burn hydrogen
• They do not produce any energy and fade as they get older.
white dwarfs.
• These are remnants of 95% of the stars in the Galaxy.
• They cannot burn anything, so they slowly cool down over time until ultimately fading away.
• They are extremely dense. A 1 Msun white dwarf is the size of Earth.
PS 224, Fall 2014
HW 4