Astronomy Exam 3

Equation for transit depth

(Rplanet/Rstar)^2

What is the smallest mass required to start nuclear fusion in the core? Why are smaller mass objects not able to keep contracting to get dense enough to start fusion?

-0.75 masses of the sun -Degeneracy pressure keeps objects like brown dwarfs from collapsing any further.

What is the largest mass a star can have, and what stops clouds from forming larger stars?

-100-200 masses of the sun -Radiation coming from the massive star pushes away any more material trying to fall into it.

Describe the characteristics of the various kinds of interstellar gas (HII regions, neutral hydrogen clouds, ultra-hot gas clouds, and molecular clouds).

-H II regions consist of ionized hydrogen and other elements. They have temperatures close to 10,000 K, and glow brightly in visible light due to fluorescence. H II regions are produced by the ultraviolet light of hot, young stars. -Neutral hydrogen clouds are regions where the hydrogen is neutral, that is, not ionized. They can have a wide range of temperatures and densities. Temperatures range from about 100-8000 K, and densities from about 0.1-100 atoms per cm3. This is the dominant phase of the interstellar medium. -Ultra-hot gas is gas at temperatures of millions of degrees. It is produced by supernova shockwaves that heat up gas as they propagate through the interstellar medium. It emits X-ray and ultraviolet light. -Molecular clouds are regions where the ultraviolet light of stars has been blocked out, allowing the hydrogen atoms to combine to form H2. They are cold, with temperatures around 10 K, and dense (in comparison to other phases of the interstellar medium), with densities of hundreds to thousands of atoms per cm3. Within them, atoms can form complex chemical compounds.

What happens when a star runs out of hydrogen in its core? How does what happens to the core of the star differ from what happens to the surface?

-The core begins to contract and heat up. -As the core contracts, heat from gravitational contraction raises the temperature in the surrounding hydrogen layers and fusion begins. This causes the layers around the core to begin expanding, causing the radius of the star to increase to a giant size.

What do astronomers believe exists in the center of nearly every galaxy?

A black hole

What does an object with a mass 10 times that of Jupiter form in a molecular cloud?

A brown dwarf

What is a gravitational wave and why was it so hard to detect?

A gravitational wave is a disturbance in spacetime caused by a rearrangement of matter. It was hard to detect because even from rearrangements of really large masses it is very weak compared to electromagnetic radiation.

The nuclear process for fusing helium into carbon is often called the "triple-alpha process." Why is it called as such, and why must it occur at a much higher temperature than the nuclear process for fusing hydrogen into helium?

A helium nucleus (two protons and two neutrons) is called an alpha particle by physicists, and it takes three (triple) helium nuclei to simultaneously come together to ultimately form a carbon nucleus. Since each helium nucleus has two positive protons, the six protons repel each other, and it takes a lot of kinetic energy and temperature to get the three helium nuclei to stick together.

​How does the equivalence principle lead us to suspect that spacetime might be curved?

A light beam emitted in an orbiting spacecraft must strike the wall at the same height at which it was emitted. This can happen only if the light curves down along with the ship's motion. This suggests that the light, traveling in spacetime, follows a curved path.

How is a nova different from a type Ia supernova? How does it differ from a type II supernova?

A nova is a smaller energy explosion on the surface of a white dwarf in a close binary system, where fresh material from a donor star is deposited on the surface of the white dwarf until it ignites. A type Ia supernova has a similar configuration, but in this case, the material deposited on the surface of the white dwarf is sufficient to push the white dwarf past the Chandresekhar limit. Once that happens, the white dwarf will collapse and then explode into a type Ia supernova. A type II supernova does not involve a white dwarf but instead requires a massive star to reach the end of its ability to generate energy in its core. This results in a collapse of the core and an explosion into a type II supernova.

What is a T-Tauri star?

A protostar that produces X-Ray flares.

Astronomers believe there are something like 100 million neutron stars in the Galaxy, yet we have only found about 2000 pulsars in the Milky Way. Give several reasons these numbers are so different. Explain each reason.

A pulsar radiates detectable amounts of radio energy for only about 10 million years, with its rotation gradually slowing throughout that time. Ultimately, the rotation becomes so slow that the pulsar no longer produces significant beams of particles and energy. However, a dead pulsar is still a neutron star; it is just difficult to observe from afar. Furthermore, even active pulsars are observable only if their beams of energy happen to be directed toward us.

How to determine if the red glow around a star is an H II region or dust.

A spectrum of the reddish glow can distinguish dust clouds from H II regions. If the reddish glow is produced by dust that is reflecting light from the star, then the spectrum of the dust cloud will look like the spectrum of the star. If the reddish glow is produced by ionized hydrogen around the star, then there will be emission lines from hydrogen in the spectrum.

How would the spectra of a type II supernova be different from a type Ia supernova? Hint: Consider the characteristics of the objects that are their source.

A type II supernova is formed from the collapse of a massive star, which, although it has made heavier elements in its core, is still mainly composed of hydrogen and helium. These should be visible in the spectrum, along with the other elements produced in the supernova. However, the amount of hydrogen and helium is still significantly larger than the other elements. A type Ia supernova is formed from a white dwarf star, which contains elements other than hydrogen, such as carbon, oxygen, neon, and magnesium. The spectrum of a type Ia supernova would show spectral features associated with elements other than hydrogen. (Even if the other star is dumping hydrogen onto the white dwarf, the tremendous compression and heating, and then the explosion, will convert that hydrogen to heavier elements.)

Suppose an astronomer known for joking around told you she had found a type-O main-sequence star in our Milky Way Galaxy that contained no elements heavier than helium. Would you believe her? Why?

A type-O main-sequence star must have formed in just the past few million years because its main-sequence lifetime is no more than a few million years. Since many generations of stars must have completed their evolution and spewed heavy elements out into space before this star formed, it is very unlikely that the star would have formed of pure hydrogen and helium. Today, it is improbable that there is any pristine cloud of material left in the Milky Way dating back to the Big Bang, from which new stars can form.

What stellar endpoint has not ever been observed?

A white dwarf from a star 0.8 masses of the sun

How does a white dwarf differ from a neutron star? How does each form? What keeps each from collapsing under its own weight?

A white dwarf is an electron degenerate object, while a neutron star is a neutron degenerate object. A white dwarf has a larger radius and is much less dense than a neutron star. All white dwarfs are less than 1.4 MSun while neutron stars are between 1.4 and 3 MSun. A white dwarf forms after a star with an initial mass less than 10 MSun ends its core energy generation, while a neutron star forms from a star with an initial mass between 10 and 40 MSun. A white dwarf would form after the planetary nebula phase of a star, while a neutron star forms just before the rest of the star experiences a type II supernova detonation.

Describe the spectrum of each of the following: A. starlight reflected by dust, B. a star behind invisible interstellar gas, and C. an emission nebula.

A. The overall shape of the spectrum is the similar to that of the star: a continuum with some emission or absorption lines superimposed, depending on the star. The spectrum will be slightly altered in that it will contain more blue and less red light than the original stellar spectrum, due to the preferential scattering of blue light. B. The spectrum will look the same as for an unobscured star, except that there will be narrow absorption lines at certain wavelengths, corresponding to colors that can be absorbed by atoms such as calcium and sodium in the interstellar gas. C. The spectrum of an emission nebula is dominated by emission lines, most prominently the Balmer line of hydrogen, along with helium and other light elements. The continuum will be very faint or entirely undetected.

Describe the evolution of a pulsar over time, in particular how the rotation and pulse signal changes over time.

As beams of particles and their associated energy are given off, the pulsar will lose energy slowly, which will decrease the rate of its rotation. The frequency of pulses would therefore decrease, so that fewer pulses are observed in a given time span. The strength of the pulse signal will also decrease so the pulses will become fainter. Eventually, the pulsar should rotate so slowly and have such a low emission of radiation that it would no longer be observable.

Why have we learned a lot about star formation since the invention of detectors sensitive to infrared radiation?

As stars form (during the proto-star stage) they are collapsing and heating up. For much of the formation process they give off a considerable part of their emission in the infra-red. Star formation happens best in great (molecular) clouds of gas and dust, which have a lot of dust particles. Infrared radiation can penetrate the dust but visible light cannot. Thus, the ability to use infrared detectors lets us see through the dust deep into the clouds where the star formation is happening.

Suppose that, instead of being inside the Local Bubble, the Sun were deep inside a giant molecular cloud. What would the night sky look like as seen from Earth at various wavelengths?

At visible, ultraviolet, and X-ray wavelengths, the night sky would be completely black. The dust in the cloud would block out all starlight. At infrared wavelengths, we would be able to see other stars, and farther into the infrared, we would see a glow from the dust all around us. At radio wavelengths, the sky would be filled with very bright molecular line emission.

What kind of remnant will a 100 M Sun star leave?

Black hole

Why do disks form around young stars?

Collisions between rotating gas particles flatten the gas cloud along its axis of rotation.

Which of the following sets of measurements CANNOT be used to determine a main sequence star's eventual fate?

Color and composition

Why is it difficult to determine where cosmic rays come from?

Cosmic rays are charged particles, which means that they can be deflected by magnetic fields. As a result, they do not travel in straight lines. They curve due to the magnetic fields of Earth and those found in interstellar space. Because they travel in curved paths, we cannot easily trace them back to their point of origin.

Why do molecules, including H and more complex organic molecules, only form inside dark clouds? Why don't they fill all interstellar space?

Dark clouds are vulnerable to dissociation by ultraviolet light. Most of interstellar space is filled with ultraviolet light from stars, so any molecules that form there are quickly disrupted. Significant numbers of molecules can build up only in places where the ultraviolet light is blocked, and the only places in interstellar space that meet that requirement are inside dark clouds.

Suppose someone told you that she had discovered H II around the star Aldebaran. Would you believe her? Why or why not?

Don't believe it. Aldebaran is a red supergiant star with a surface temperature of about 4000 K. That is not hot enough to emit much light at the extreme ultraviolet wavelengths capable of ionizing hydrogen atoms and producing H II. Only much hotter stars can make H II regions.

Where does interstellar dust come from? How does it form?

Dust forms in the winds coming off stars as they lose mass at the end of their lives, or from condensing in the material from supernova explosions. Dust grains can also grow when they find themselves in dense environments like molecular clouds.

New stars form in regions where the density of gas and dust is relatively high. Suppose you wanted to search for some recently formed stars. Would you more likely be successful if you observed at visible wavelengths or at infrared wavelengths? Why?

Dust is an efficient absorber of visible radiation, and so star-forming regions often cannot be observed at visible light wavelengths. Infrared radiation does penetrate the dust, and so infrared observations are an essential tool for studying regions of star formation.

What is meant by "dust" in astronomy, and how does dust affect our ability to observe objects?

Dust is interstellar material that is not gas but solid material, like silicates or water, methane, and ammonia ice. Dust affects out ability to observe objects by blocking the light from distant stars, emitting energy in the infrared part of the spectrum, reflecting the light from nearby stars, and by making distant stars look redder than they really are.

Apart from the masses, how are binary systems with a neutron star different from binary systems with a white dwarf?

Each can produce different events that can be observed. A white dwarf binary can lead to a nova or a type Ia supernova. A neutron star can cause an X-ray burst. Or if two neutron stars merge, it can cause a gamma-ray burst.

One way to calculate the size and shape of the Galaxy is to estimate the distances to faint stars just from their observed apparent brightnesses and to note the distance at which stars are no longer observable. The first astronomers to try this experiment did not know that starlight is dimmed by interstellar dust. Their estimates of the size of the Galaxy were much too small. Explain why.

Extinction by interstellar dust makes stars appear fainter than they would if there were no dust. Suppose an RR Lyrae variable could just barely be seen at a distance of 10,000 light-years in the absence of interstellar extinction. Now consider the case that there is enough interstellar extinction to dim the light from distant RR Lyrae stars by a factor of 10. The RR Lyrae stars at a distance of 10,000 light-years will become too faint to be detected. Only those RR Lyrae stars closer than (10)^0.5 x 10, light-years = 3200 light-years will still be bright enough to be detected. Therefore, if no allowance is made for dimming by interstellar dust, astronomers will conclude that the Galaxy is only about one-third its true size. These arguments can be generalized to apply to any type of star and any amount of extinction.

Describe what happens when a star forms. Begin with a dense core of material in a molecular cloud and trace the evolution up to the time the newly formed star reaches the main sequence.

Generally, collapse leads to central heating, which eventually leads to hydrogen ignition temperatures. Specifically, when gravity exceeds pressure in the molecular cloud, material from the outer reaches of the cloud transfers gravitational potential energy into kinetic energy as it falls in towards the center of the cloud. When it reaches the center of the cloud, the kinetic energy is converted to thermal energy as the material is either added to the central Protostar or spun out into the protoplanetary disk. The protostar increases in temperature and luminosity as more material is added. Its central pressure and temperature also increase until temperatures of 10-15 million K are achieved and nuclear fusion begins. In the meantime, other processes related to conservation of angular momentum shape the material surrounding the collapsing core and limit the amount of material involved in the collapse.

In which of these star groups would you mostly likely find the least heavy-element abundance for the stars within them: open clusters, globular clusters, or associations?

Globular clusters: they have very low heavy-element abundances because they contain very old, first-generation stars that are composed of only hydrogen, helium, and traces of lithium.

What is the source of energy which heats up the gas and provides the energy it emits as light?

Gravitational contraction

The terms H II and H2 are both pronounced "H two." What is the difference in meaning of those two terms? Can there be such a thing as H III?

H II means hydrogen that has been stripped of its electron (ionized). The Roman numeral I indicates an atom with all its electrons, II means one electron removed, III means two electrons removed, and so on. There is no such thing as H IIII because that would mean hydrogen with two electrons removed. However, hydrogen only has one electron to start with. In contrast, H2 means a hydrogen molecule: two hydrogen atoms held together by a bond.

What molecule is the most abundant in giant molecular clouds in the Milky Way?

H2

Even though neutral hydrogen is the most abundant element in interstellar matter, it was detected first with a radio telescope, not a visible light telescope. Explain why.

Hydrogen in interstellar space outside H II regions is so cool that all of its atoms are in the lowest-energy state. At such low temperatures, the most likely transition for a neutral hydrogen atom is merely to change the orientation of the spin of its electron relative to the spin of the proton, and this does not produce any spectral lines in the visible region of the spectrum. This could not be detected until astronomers began to build radio telescopes that can detect such lower-energy radiation.

If the Sun were a member of the cluster NGC 2264, would it be on the main sequence yet? Why or why not?

If the Sun were a member of NGC 2264, it would probably not have reached the main sequence yet. This cluster is so young (only a few million years old) that, as the NGC 2264 H-R Diagram shows, stars with luminosities similar to that of the Sun are still contracting to the main sequence. For reference, the Sun is estimated to have taken between 30 million to 50 million years to reach the main sequence.

Dust was originally discovered because the stars in certain clusters seemed to be fainter than expected. Suppose a star is behind a cloud of dust that dims its brightness by a factor of 100. Suppose you do not realize the dust is there. How much in error will your distance estimate be? Can you think of any measurement you might make to detect the dust?

If the brightness decreases by a factor of 100 because of dust, and we cannot detect the dust, then we will estimate that the star is 10 times farther away than it actually is; brightness decreases as the square of the distance. The dust should also redden the star, and so if its color is redder than we would expect from the spectral type that we observe, then we can tell that dust is affecting the brightness of the star.

How are planetary nebulae comparable to a fluorescent light bulb in your classroom?

Illumination for both is due to the glow produced when ultraviolet light (from the dying star in the nebula and from mercury vapor inside a fluorescent tube) ionizes various gases and causes them to glow with visible light.

Where do high-mass stars form?

In massive clumps

Why do stars tend to form in large clouds of gas, and what causes the clouds to collapse and form stars?

In molecular clouds, dust particles are cold enough and dense enough to start forming together. Inside of molecular clouds there are clumps or areas where the molecular cloud is denser and inside these clumps are interstellar cores which are where dust particles have been gathering to form stars. When these interstellar cores shrink and increase in density by a factor of 10^20, they collapse and form a star.

List three ways in which the exoplanets we have detected have been found to be different from planets in our solar system.

In other planetary systems, gas giant planets can reside close to the star (hot Jupiters) or in highly elliptical orbits around the star. Super-Earths and mini-Neptunes have been found around other stars, but we don't have any in our solar system. In other solar systems, small rocky planets are commonly found inside of Mercury's orbit. Some exoplanets have been discovered to orbit binary stars.

The Large Magellanic Cloud has about one-tenth the number of stars found in our own Galaxy. Suppose the mix of high- and low-mass stars is exactly the same in both galaxies. Approximately how often does a supernova occur in the Large Magellanic Cloud?

In our own Galaxy, we estimate that a supernova occurs once every 25-100 years. If the Large Magellanic Cloud has about one-tenth the number of stars as our own Galaxy but the same mix of masses, then we would expect a supernova to occur only about 1/10 as often or once every 250-1000 years. We were very lucky that supernova 1987A happened to occur in this century!

The evolutionary track for a star of 1 solar mass remains nearly vertical in the H-R diagram for a while. How is its luminosity changing during this time? Its temperature? Its radius?

In this vertical region on the diagram, luminosity is dropping while the surface temperature remains constant. This is a stage where the material of the star is falling inward without any hindrance and since the star has less and less surface area with which to give off radiation, its luminosity is decreasing together with its radius.

Explain how an H-R diagram of the stars in a cluster can be used to determine the age of the cluster.

Initially, most of the stars in a cluster will be distributed all along the main sequence of the H-R diagram. Eventually, the more massive stars will end the hydrogen fusion in the core and move off the main sequence, creating a "turn" in the distribution of the stars in the cluster on the H-R diagram. As more time goes by, stars of even lower mass (and lower on the main sequence) will move toward the giant branch of the diagram, leaving the top of the main sequence without stars on it. The location of the turn thus indicates the age of the cluster.

Describe the properties of the dust grains found in the space between stars.

Interstellar dust grains are typically hundredths to tenths of a micron size. They are composed of either carbon-rich (sooty) or silicate (sandy) material. When found inside dark clouds, they also have mantles of ice, composed of water, ammonia, methane, and similar materials around them. Dust grains can have temperatures from around 10-500 K.

Why is the Schwarzschild radius significant?

It is the distance within which nothing can escape a black hole.

Suppose a star cluster were at such a large distance that it appeared as an unresolved spot of light through the telescope. What would you expect the overall color of the spot to be if it were the image of the cluster immediately after it was formed? How would the color differ after 1010years? Why?

Just after the cluster formed, it would look blue since the light from the cluster would be dominated by the O and B stars. After 1010 years, the O and B stars would have died and other main-sequence stars (of about 1 solar mass) would be evolving to red giants. These red giants would be the most luminous stars, so the cluster would appear noticeably red.

What do astronomers think are the causes of longer-duration gamma-ray bursts and shorter-duration gamma-ray bursts?

Long-duration bursts (lasting more than a few seconds) come from massive stars with their outer hydrogen layers missing that explode as supernovae. Short duration bursts are believed to be mergers of stellar corpses (neutron stars or black holes).

Why is a massive protostar more luminous than a low-mass protostar?

Massive protostars have more gravitational potential energy before they collapse.

Why can't we use visible light telescopes to study molecular clouds where stars and planets form? Why do infrared or radio telescopes work better?

Molecules can only exist in dark clouds where ultraviolet starlight is blocked out. However, these same regions are also very cold because the same photons that destroy molecules are also responsible for heating up the gas. Regions that are dark enough to have molecules are therefore also too cold to emit much at visible light wavelengths. Furthermore, the dust that is responsible for protecting the molecules would also block any visible light from escaping to our telescopes. Both of these problems are diminished or go absent at infrared and radio wavelengths. Colder material does emit infrared and radio light, and the wavelengths are much less subject to extinction by dust.

If general relativity offers the best description of what happens in the presence of gravity, why do physicists still make use of Newton's equations in describing gravitational forces on Earth (when building a bridge, for example)?

Newton's equations are simpler to use than the equations of general relativity and are accurate enough for most daily activities, such as building a bridge on Earth. That's because the gravity on our planet is sufficiently weak that the predictions of Newtonian theory don't differ very significantly for everyday activities from the predictions of general relativity.

Would you expect to be able to detect an H II region in X-ray emission? Why or why not?

No. The gas in an H II region is at around 10,000 K, so Wien's law tells us that the emission will peak at λmax = b/T = 0.29 micron, where b = 2900 micron K. (Note that this expresses Wien's law in units useful for infrared astronomy.) This is in the near UV part of the spectrum. While Wien's law isn't strictly true for an H II region, since it's not a blackbody, this calculation still shows that H II regions are too cool to emit X-rays.

What characteristics must a binary star have to be a good candidate for a black hole? Why is each of these characteristics important?

One member of the binary system must be invisible, since no radiation can leave a black hole. One member of the binary system must have very high mass yet be small in size (collapsed), since those are characteristics of a black hole. The pair must radiate energetic X-rays, since such X-rays arise from accretion disks in which matter is being pulled into a black hole.

Would you expect to observe every supernova in our own Galaxy? Why or why not?

Only some of the supernovae that occur in our Galaxy are observable. Type II supernovae (the explosions of massive stars) tend to occur in the disk of the Milky Way, and they may be hidden by intervening dust if they are located in more distant parts of the Galaxy. Type Ia supernovae, which require a white dwarf star in a binary star system, are brighter than type II supernovae, but some of them could also happen in older parts of the Galaxy that are hidden by the buildup of gas and dust in the disk.

List any similarities between discovered exoplanets and planets in our solar system.

Over 500 planetary systems are similar to our solar system in having more than one planet orbiting the same star; we find a range of planetary masses among the planets in the same system. Kepler is sensitive to co-planar planetary systems, so many systems that have been discovered appear to be co-planar like our solar system.

Why is it so hard to see planets around other stars and so easy to see them around our own?

Planets only reflect light and so are much fainter than their host stars when viewed at large distances. Therefore, glare from the host stars often completely washes out the planetary light.

If the formation of a neutron star leads to a supernova explosion, explain why only three of the hundreds of known pulsars are found in supernova remnants.

Pulsars can remain visible through their radio emission much longer than the material from a supernova explosion stays visible. Also pulsars can be "kicked" from the site of the supernova through a process that causes them to move away from the remnant at very high velocities.

In which wavelength regime are the periodic signals from pulsars typically seen?

Radio

What are black holes?

Region of spacetime from which gravity prevents anything, including light, from escaping.

Muons created by cosmic rays in Earth's atmosphere survive much longer than those created in the laboratory. This is because of:

Relativistic time dilation

If a star's temperature were to double, by what factor would its rate of fusion increase?

Since the rate of fusion (like temperature) goes up to the fourth power, it would increase by a factor of 24, or 16 times.

What causes reddening of starlight? Explain how the reddish color of the Sun's disk at sunset is caused by the same process.

Small particles, either dust grains in interstellar space or molecules in Earth's atmosphere, can absorb and scatter light. Both absorption and scattering are more efficient for blue light than for red light. As a result, they cause more extinction of blue light than of red light, so starlight that passes through a region filled with small particles will emerge redder than it was when it entered. In the case of Earth's atmosphere, the sun appears redder at sunset than midday. Since it is lower in the sky, its light must travel a longer path through the atmosphere, with a greater chance that sunlight will be scattered. Since red light is more likely to be scattered than blue light, the Sun appears increasingly red as it approaches the horizon.

Why is star formation more likely to occur in cold molecular clouds than in regions where the temperature of the interstellar medium is several hundred thousand degrees?

Stars can form when gravity (which pulls things together) exceeds the local pressure (which tends to push atoms apart.) Pressure is higher in hot material and lower in cold material, so colder clouds put up less resistance to gravity and can collapse more readily. Also, at lower temperatures, molecules form. Because molecules are heavier than individual atoms, they move around more slowly and can congregate in a small volume of space, increasing the local matter density and thereby the local gravity.

Describe how the T Tauri star stage in the life of a low-mass star can lead to the formation of a Herbig-Haro (H-H) object?

Tauri stars show a stellar wind, a flow of atomic particles away from the star. While the star is still surrounded by an accretion disk around its equator, the wind is stopped in that direction, and it emerges far more effectively in two cones or jets, perpendicular to the accretion disk. As these jets plow into the surrounding material, they can occasionally collide with a somewhat-denser lump of gas nearby, transferring energy and exciting its atoms, causing them to emit light. These glowing regions are called Herbig-Haro (HH) objects, after the two astronomers who discovered them. There are often two such objects, one on each side of the star where the jets emerge.

Describe how the 21-cm line of hydrogen is formed. Why is this line such an important tool for understanding the interstellar medium?

The 21-cm line is formed when hydrogen atoms in which the proton and electron are aligned "flip" so that the proton and electron are anti-aligned. Hydrogen atoms that are in the anti-aligned state will be excited into the aligned state by collisions, and will subsequently emit a photon with a wavelength of 21 cm, giving rise to the line. The line is important because it is produced by neutral hydrogen everywhere. Since cold hydrogen atoms make up the largest part of the interstellar medium, the 21-cm line allows us to study the most common component of interstellar gas.

Which types of planets are most easily detected by Doppler measurements? By transits?

The Doppler technique measures the motion of the star caused by the pull of one or more planets around it. The gravitational force is proportional to the mass of the planet and inversely proportional to the square of the separation. So the easiest planets to detect with this method are massive and close to the star. That's why the hot Jupiters were found first. The transit probability (the chance that the orbit will bring the planet in front of the star for a transit) is greatest for close-in planets. The size of the planet must be big enough to give a measureable decrease in the brightness of the star. Since astronomers need to wait for three transits before they feel comfortable confirming their observation, that means that the longer the planet takes to orbit its star, the longer it will take to confirm the existence of a transiting planet. So this method works best for planets of larger size, orbiting close to their stars.

Give several reasons the Orion molecular cloud is such a useful "laboratory" for studying the stages of star formation.

The Orion cloud is nearby (astronomically speaking) so we have a close-up view of star formation processes. We know the distance to Orion's star-forming regions, so we know how luminous objects are from simply measuring the brightness of the sources. We can see a number of stages in the formation process of stars and protoplanetary disks in the region. Orion is also close to the celestial equator so it can be observed from all the large observatories in the Northern and Southern Hemispheres.

Suppose the amount of mass in a black hole doubles. Does the event horizon change? If so, how does it change?

The Schwarzschild radius (radius of the event horizon) is proportional to the mass in the black hole. If the mass doubles, the Schwarzschild radius, and thus the event horizon, also doubles.

Would the Sun more likely have been a member of a globular cluster or open cluster in the past?

The Sun more likely would have been a member of an open cluster with other stars that would have formed from the same cloud of gas and dust. Stars in an open cluster can have a range of ages, whereas stars in a globular cluster are all very old—much older than the current age of the Sun. Also, if we had been born in a crowded (dense) globular cluster, all the stars in the cluster would still be around us and with us. In contrast, stars in a loose open cluster can disperse with time, leaving a star like the Sun alone later in its life (just as we now are).

We can detect 21-cm emission from other galaxies as well as from our own Galaxy. However, 21-cm emission from our own Galaxy fills most of the sky, so we usually see both at once. How can we distinguish the extragalactic 21-cm emission from that arising in our own Galaxy?

The answer is by using the Doppler effect. External galaxies are moving relative to ours, and thus, their emission is shifted to a slightly different wavelength. In a spectrum, this makes the 21-cm emission from other galaxies distinguishable from the 21-cm emission from ours.

Why does the duration over which a massive star fuses elements decrease from hydrogen to iron?

The core temperature increases, it produces less energy per fusion reaction, and the density of the core increases as well.

Compare the scale (size) of a typical dusty disk around a forming star with the scale of our solar system.

The dusty disks range in size from 10 to 1000 AU. Jupiter's orbit is about 10 AU wide. The orbit of Pluto has a diameter of 80 AU. The outer diameter of the Kuiper belt of smaller icy bodies is about 100 AU. Eris' orbit has an average diameter of about 136 AU.

Why did it take astronomers until 1995 to discover the first exoplanet orbiting another star like the Sun?

The first discovery of an exoplanet took place by finding the changing Doppler shift in the spectrum of the star as the planet moved in orbit around it. To measure the really small variations in the spectra of stars in a stable way over long periods of time, astronomers had to build very precise spectrometers.

Would you expect to find an earthlike planet (with a solid surface) around a very low-mass star that formed right at the beginning of a globular cluster's life? Explain.

The first generation of stars contained only hydrogen and helium and no heavy elements, since there had not been time to fuse them. Globular clusters are very old, so any stars that formed right at the beginning of their lives would be very close to the first generation of stars in the Galaxy. Since earthlike planets require the presence of heavier elements, we would not expect to find them around such a star.

What is the helium flash of a low mass star, and what happens to the star after the helium flash? Why does the star shrink in size even though the core is now supplying energy through fusion again?

The helium flash occurs when a low mass star reaches a high enough temperature in it's core to begin fusing helium into carbon. As the core is no longer contracting, the layers around the core can no longer be heated to temperatures high enough to continue hydrogen fusion, hence why the star shrinks back to a regular size.

Why would we not expect to detect X-rays from a disk of matter about an ordinary star?

The intense gravitational field near a neutron star or black hole can accelerate the matter in the accretion disk to such high speeds that the temperature becomes high enough to produce X-rays as they whirl around and jostle each other. Ordinary stars (meaning main-sequence stars, for example, and not collapsed star remnants) have lower density and do not have intense enough gravitational fields to produce such a hot vortex.

Stars form in the Milky Way at a rate of about 1 solar mass per year. At this rate, how long would it take for all the interstellar gas in the Milky Way to be turned into stars if there were no fresh gas coming in from outside? How does this compare to the estimated age of the universe, 14 billion years? What do you conclude from this?

The interstellar medium contains about 7 billion solar masses of gas, so at a rate of 1 solar mass per year of consumption, it would take about 7 billion years to turn all the gas into stars if there were no fresh gas supplies. This is less than the age of the universe, which suggests that either there must be fresh gas supplies, or that we are living at a special time when the supply of gas in the Milky Way is just about to run out, or that the rate of star formation is not constant.

What is the interstellar medium, what is it made of?

The interstellar medium is the entire collection of interstellar matter, or all of the matter between stars such as nebula and clouds of dust.

The 21-cm line can be used not just to find out where hydrogen is located in the sky, but also to determine how fast it is moving toward or away from us. Describe how this might work.

The key here is to use the Doppler effect. The 21-cm line can be redshifted or blueshifted just like any other radiation, and this shift can be used to measure the velocity of the hydrogen that is emitting. If the line is shifted slightly redward of 21 cm, the hydrogen is moving away from us. If it is shifted blueward, the hydrogen is moving toward us. The amount of shift indicates the speed.

Astronomers recently detected light emitted by a supernova that was originally observed in 1572, just reaching Earth now. This light was reflected off a dust cloud; astronomers call such a reflected light a "light echo" (just like reflected sound is called an echo). How would you expect the spectrum of the light echo to compare to that of the original supernova?

The light echo spectrum should look similar to that of the original supernova, with the exception that it will be bluer than the original. That is because the blue light is be scattered more efficiently than the red light in the dust cloud.

What observations from SN 1987A helped confirm theories about supernovae?

The light variation from the supernova changed due to the influence of radioactive elements decaying. This included the decay of nickel-56 and cobalt-56. As these elements decayed, their gamma rays interacted with the material from the explosion, causing the energy output to change. Since these elements decay very quickly, they must have been created by the supernova explosion itself; they would not have survived if they had been created during earlier stages of the star's life. Neutrinos were also observed from the supernova on the day before the light from the supernova was observed. If enough neutrinos were created so that a good number reached Earth, 160,000 light-years away, and a few could interact with our detectors, this shows that a lot of neutrinos must have been made by the events connected with the supernova. This confirms our idea that in the formation of the neutron star, before the explosion, a large number of neutrinos were created in the process of joining electrons and protons to make neutrons.

How would a white dwarf that formed from a star that had an initial mass of 1 MSun be different from a white dwarf that formed from a star that had an initial mass of 9 MSun?

The lower initial mass white dwarf would be composed primarily of carbon and oxygen, while the higher initial mass star would form a white dwarf with higher mass elements, such as oxygen, neon, and magnesium.

According to the text, a star must be hotter than about 25,000 K to produce an H II region. Both the hottest white dwarfs and main-sequence O stars have temperatures hotter than 25,000 K. Which type of star can ionize more hydrogen? Why?

The main-sequence O star is much more luminous than the white dwarf and produces more ultraviolet photons capable of ionizing hydrogen. Therefore, the O main-sequence star can ionize more hydrogen than the white dwarf even though both have the same temperature.

In the H-R diagrams for some young clusters, stars of both very low and very high luminosity are off to the right of the main sequence, whereas those of intermediate luminosity are on the main sequence. Can you offer an explanation for that?

The most massive stars go through each stage of their lives most quickly, while the lowest-mass stars do everything more slowly. In a cluster in which both the most and least luminous stars lie to the right of the main sequence, the most massive stars have already converted the hydrogen in the core to helium and are beginning to evolve to the supergiant stage. The lowest-mass stars have yet to arrive on the main sequence and begin hydrogen fusion; they are still contracting (and moving toward the main sequence as a consequence).

What observations or types of telescopes would you use to distinguish a binary system that includes a main-sequence star and a white dwarf star from one containing a main-sequence star and a neutron star?

The motion of the stars in the binary system can be used to determine the size of the orbit and the orbital period. This information, along with the mass of the main-sequence star, allows us to use the version of Kepler's third law for stars to obtain a value for the mass of the degenerate star. This information can be found using visible-light telescopes (obtaining a spectrum). If there is mass going from the main-sequence star to the other star, then outbursts may occur: either a nova (from the white dwarf) or X-ray bursts (from the neutron star). For the former, a visible-light telescope is fine; for the latter case, an X-ray telescope is required.

Suppose you wanted to observe a planet around another star with direct imaging. Would you try to observe in visible light or in the infrared? Why? Would the planet be easier to see if it were at 1 AU or 5 AU from its star?

The planet will be easier to see if it is farther away from its parent star; closer planets would be even more likely to be lost in the glare of the parent star. The ratio of the brightness of the planet to the brightness of the star is very small at all wavelengths, but will be larger in the infrared than in visible light so observations should be made in the infrared.

How did astronomers finally solve the mystery of what gamma-ray bursts were? What instruments were required to find the solution?

The problem was that early gamma-ray telescopes did not allow astronomers to pinpoint the location of the bursts very precisely—only within a box on the sky that could include a lot of different objects. What it took was finding the "afterglow" of bursts in other wavelengths (X-rays, visible light, radio). For those other wavelengths, telescopes could measure the location of the afterglow much more precisely and find what the objects were in which the bursts happened. Satellites like Swift have telescopes in several bands of the electromagnetic spectrum; once a gamma-ray burst location is identified, the satellite swivels automatically to point X-ray and other telescopes at the location.

How can the Crab Nebula shine with the energy of something like 100,000 Suns when the star that formed the nebula exploded almost 1000 years ago? Who "pays the bills" for much of the radiation we see coming from the nebula?

The pulsar is providing the energy through the emission particles from its magnetic poles. These high velocity particles emit a range of energy, and they interact with and energize the material that was expelled during the supernova explosion. This energy source is ultimately powered by the rotation of the pulsar in the center of the Crab Nebula. As it emits particles, the pulsar loses energy and spins slower.

Why do nebulae near hot stars look red? Why do dust clouds near stars usually look blue?

The red color of nebulae comes from the Balmer line produced when ionized hydrogen captures an electron and becomes neutral again. Nebulae are filled with ionized hydrogen that combine with an electron to produce this line. Dust clouds are blue because the light we see from them is scattered starlight. Blue light scatters more than red light, so the light we see coming off the clouds is bluer than the light from the stars.

Suppose that, instead of being inside the Local Bubble, the Sun were inside an H II region. What would the night sky look like at various wavelengths?

The sky would look much the same as it does now at X-ray and most other wavelengths, but it would also be filled with bright light at particular visible wavelengths, particularly the red color corresponding to the Balmer line. The sky would glow red.

What did Einstein's work determine to be a constant of nature?

The speed of a photon

What happens when a massive star's core becomes iron?

The star can no longer support itself against gravity.

If the rate of fusion of a star increased 256 times, by what factor would the temperature increase?

The temperature would increase by a factor of 256^0.25 (that is, the 4th root of 256), or 4 times.

Einstein's general theory of relativity made or allowed us to make predictions about the outcome of several experiments that had not yet been carried out at the time the theory was first published. Describe three experiments that verified the predictions of the theory after Einstein proposed it.

There are a number of possible answers. Observations of the eclipse of 1919 verified the bending of light by the Sun's mass (or gravity). Experiments in 1959 with twin atomic clocks operating at different heights in a physics building verified the slowing of time in a stronger gravitational field. In 1976 radio signals from the Viking landers on Mars passing near the Sun were used to show the slowing of time in a gravitational field. In the mid-1970s, a hydrogen maser, carried by a rocket to an altitude of 10,000 km was compare to the frequency of the signal emitted from a similar maser on Earth, again to show that the pace of time depends on the strength of gravity. And you could say that the accuracy of GPS devices demonstrates that general relativity works, since corrections for the effects of general relativity are included in the software of all such devices, and the devices help us pinpoint our location on Earth with remarkable accuracy.

Pictures of various planetary nebulae show a variety of shapes, but astronomers believe a majority of planetary nebulae have the same basic shape. How can this paradox be explained?

There is a variety of planetary nebula shapes because astronomers are looking at the same basic shape (a thicker torus right around the star or stars and outflows through the hole in the torus in opposite directions) from different points of view.

What helps support molecular clouds against gravitational collapse?

Thermal pressure, turbulence, and magnetic fields.

If the speed of light were infinite, how would black holes change?

They would not exist.

Stars that have masses approximately 0.8 times the mass of the Sun take about 18 billion years to turn into red giants. How does this compare to the current age of the universe? Would you expect to find a globular cluster with a main-sequence turnoff for stars of 0.8 solar mass or less? Why or why not?

This is older than the age of the universe, which is approximately 14 billion years old. Thus, we would not expect to find globular clusters with main-sequence turnoffs for stars of this solar mass (at least not yet).

Equation for total interstellar mass

Total mass=volume x density of atoms x mass per atom

Which of the following can most efficiently be used to measure the distance to a galaxy?

Type 1a supernovas

How do the two types of supernovae discussed in this chapter differ? What kind of star gives rise to each type?

Type Ia supernovae are produced by white dwarf stars in a binary star system that have exceeded their Chandrasekhar limit when the companion star dumps a lot of material onto them. Type II supernovae are produced by massive stars whose cores collapse following the exhaustion of their fusion processes. Type Ia supernovae are more luminous than type II supernovae and have a more consistent value for maximum brightness. Type Ia supernova are also visible in all types of galaxies, while type II are not observed in all galaxies.

What revisions to the theory of planet formation have astronomers had to make as a result of the discovery of exoplanets?

We now understand that planets can migrate in the protoplanetary disk through gravitational friction or drag. For example, Jupiters can migrate inward and be quite close to their stars (hot Jupiters). We now understand that planet formation is more chaotic and less orderly than we imagined. Instead of all the planets orbiting in one plane and in the same direction, we now see some planets orbiting at right angles to the plane of the other planets or even moving backward. We also learned that it is possible to have stable planets orbiting a system of two stars.

At what point does a protostar become a star?

When the center reaches the temperature of 10 million kelvin, nuclear fusion begins.

What is required for nuclear fusion to start in the core of a protostar?

When the core temperature reaches 10 million kelvin.

What slows down the contraction of a cloud into a star, forming a protostar?

When the mass begins to heat up, rotate, and produce a magnetic field.

Why are young Jupiters easier to see with direct imaging than old Jupiters?

Young Jupiters have more internal heat from the process of accretion and formation. This energy is radiated as infrared, and so young Jupiters will be brighter infrared sources. Since the planet cools with time, younger Jupiters are more luminous and easier to see with direct imaging techniques.

How are molecular clouds structured?

hierarchical, with structure on a wide range of length scales.

A set of stars all initially have the same mass of 20 M Sun, but their other properties differ. Which is LEAST likely to form a black hole at the end of its life?

the star that transfers most of its mass to a binary companion