Astronomy 3600 Term Test 3
Star A and Star B have different apparent brightnesses but identical luminosity. If star A is 20 light years away from earth and star b is 40 light years away from earth, which star appears brighter and by what factor?
Because star A and B have identical luminosity, the difference in apparent brightness is due solely to distance. Star B is twice as far from earth as A. Star A is therefore 4 times brighter than star B.
The nuclear process for fusing helium into carbon is ofter 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 nucleas is called an alpha particle by physicists, and it takes three 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.
What is a planetary nebula? Will we have one around the sun?
A planetary nebula is the distended outer atmosphere of a giant star as it floats away and is made to glow by ultraviolet light from the hot star that is collapsing inside the nebula. This is a stage that low-mass stars go through. The sun, which is considered a lower-mass star, will eventually have a planetary nebula from around it billions years from now, after it has been a red giant.
What did Annie Cannon contribute to the understanding of stellar spectra?
Annie Cannon created the spectral classification system based on surface temperature that astronomers use today. She also classified the spectra of around 500,000 stars in her career.
Based on their colors, which of the following stars is hottest? Which is coolest? Archenar (blue), Betelgeuse (red), Capella (yellow)
Archenar is hootest (blue). Betelgeuse is coolest (red)
Describe how the mass, luminosity, surface temperature, and radius of main-sequence stars change in value going from the bottom to the top of the main sequence
At the bottom, the mass, luminosity, surface temperature and radius are all at their lowest values. As you head to the top of the main sequence, the values all increase and are at a max at the top. The values that change the most are luminosity and temperature. Radius has the least amount of change in value.
Astronomers find that 90% of the stars observed in the sky are on the main sequence of an H-R diagram; why does this make sense? Why are there far fewer stars in the giant and supergiant region?
Being on the main sequence means that the star is converting hydrogen to helium in the core. Since stars are made mostly of hydrogen, this process takes approximately 90% of a star's life. Thus it makes sense that the 90% of the stars observed at some particular time would be undergoing this process. Being a red giant star is a brief stage in the life of each star, when the star is readjusting to the loss of energy from the fusion of hydrogen. In a relatively short time, the core collapses until it is hot enough for the fusion of helium into carbon, restoring the star's equilibrium. Since this is only a brief stage in the life of the star, it makes sense that only a few percent of stars will be found in the giant stage at any given time.
Do stars that look brighter in the sky have larger or smaller magnitudes than fainter stars?
Brighter stars have smaller magnitudes than fainter stars.
Certain stars, like Betelgeuse, have a lower surface temperature than the Sun and yet are more luminous. How do these stars produce so much more energy than the Sun?
Certain stars, like Betelgeuse, have swelled up to be giant stars. They produce more overall energy because of their much larger size (while each piece of the star's surface is cool, there are so many pieces that overall the stars give out more energy).
Describe what a typical star in the Galaxy would be like compared to the sun.
Cool, faint, low-mass stars located on the lower part of the main sequence are the most common, and therefore the most typical stars.
Describe the evolution of a star with a mass similar to that of the sun, from the protostar stage to the time it first becomes a red giant. Give the description in words and then sketch the evolution on an H-R diagram.
During the protostar stage, gravity gathers gas and dust toward a central location, which increases in temperature and pressure. Eventually, the temperature and pressure at the center of the gas and dust will reach critical thresholds and the nuclear fusion of hydrogen into helium will begin in what is now called the core. When this happens, the protostar officially becomes a zero-age main sequence star. For the next 10 billion years or so, the star will stably undergo nuclear fusion as it remains on the main sequence. Once the hydrogen gas runs out in the core, gravity will begin to re-collapse the stellaar atmosphere above the core, which in turn increases the temperature and pressure within the core again. While this occurs, a hydrogen shell around the core will begin nuclear fusion, causing the star to swell and become more luminous as it enters the red giant phase. Eventually, the temperature and pressure in the core will reach another set of critical thresholds and the nuclear fusion of helium into carbon will commence in an explosive helium flash, officially beginning a more stable phase.
Describe the evolution of a star with a mass similar to that of the sun, from just after it first becomes a red giant to the time it exhausts the last type of fuel its core is capable of fusing.
During the red giant phase, the star is swelling up due to the fusion of hydrogen in a shell around the collapsing core. Eventually, the helium gets got enough to be fused to carbon in the core, and the star regains a temporary equilibrium. When all the helium hot enough to fuse carbon is exhausted in the core, the star swells again as the inert core of carbon tries to reach a temperature and pressure necessary for the next fusion stage. For stars like the sun, that is not possible after the fusion of helium into carbon, so this is the last fuel it is capable of using.
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.
Describe the two ways of determining the diameter of a star.
In one method, the time for an object like the moon to pass in front of a star can be measured to determine the diameter of a star. Since we know the speed of the moon in its orbit, we can calculate the size of the star. For an eclipsing binary star, the time for one star to pass in front of another is dependent upon the relative diameters of each star. When the eclipses are aligned in such a way that they eclipse each other, we can measure the time for each star to eclipse the other. We can measure the speed of the stars from the Doppler shift in the spectrum. From knowing the time of eclipse and the speed, the size of each star can be determined.
Explain how an H-R diagram of the stars in a cluster can be sued to determine the age of the cluster.
Initially, most of the stars in a cluster will be distributed all along with 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 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.
Why are star clusters so useful for astronomers who want to study the evolution of stars?
It is reasonable to assume that the individual stars in a cluster all formed at nearly the same time from the same cloud of gas and dust. As a result, the only initial difference between the stars is their mass (and not their composition or the time that they began). Therefore, as we put all the stars in a cluster on an H-R diagram, we can see how stars of different mass will change their positions in the diagram over time and build up a picture of how stars of different mass go through the stages of their lives. Also, because high-mass stars evolve much more quickly than low mass stars, we can estimate the age of a cluster of stars by observing where its stars are currently leaving the main sequence.
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 10^10 years? 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 10^10 years, the O and B stars would have died and other main-sequence stars would be evolving to red giants. These red giants would be the most luminous stars, so the cluster would appear noticeable red.
What are the largest and smallest known values of the mass, luminosity, surface temperature, and diameter of stars (roughly)?
Mass ranges from more than 100 times the sun's mass down to 1/12 the sun's mass. Luminosity ranges from a million times the sun's luminosity down to 1/10,000 of the sun's. Surface temperature ranges from nearly 40,000 k down to 2700 k. Diameter ranges from 1000 times the sun's diameter down to 1/10 the sun's diameter.
The spectrum of the Sun has hundreds of strong lines of nonionized iron but only a few, very weak lines of helium. A star of spectral type B has very strong lines of helium but very weak iron lines. Do these differences mean that the sun contains more iron and less helium than the B star? Explain.
No. The primary reason that stellar spectra look different is the stars have different temperatures. Most stars have compositions very similar to that of the sun.
Suppose hominids one million years ago had left behind maps of the night sky. Would these maps represent accurately the sky that we see today? Why or why not?
No. The proper motion of the stars would have significantly changed their location on the celestial sphere relative to each other over one million years.
Approximately 6000 stars are bright enough to be seen without a telescope. Are any of these white dwarfs?
None of the stars visible to the unaided eye are white dwarfs. White dwarfs are hot but not very luminous since their surface area is so small. Just as we need telescopes to see low-luminosity, main-sequence stars, we need telescopes to see white dwarfs.
Order the seven basic spectral types from the hottest to coldest.
OBAFGKM : Oh Big And Fat Goat Kill Me
Describe the two "recycling" mechanisms that are associated with stars?
One recycling mechanism is that stars can sometimes use the ash from one nuclear fusion process as the fuel for the next. Another recycling mechanism is how all stars eventually end their lives by sending back into the cosmos a considerable part of their mass and all the elements within; this material becomes part of the interstellar medium of gas and dust that can form fmore stars.
Gravity always tries to collapse the mass of a star toward its center. What mechanism can oppose this gravitational collapse for a star? During what stages of a star's life would there be a balance between them?
Outward radiation pressure from gamma rays created by fusion in the core of the star opposes the inward gravitational collapse when a star is in equilibrium. Balances are generally achieved when there is a fuel hot enough to fuse in the core, like during the main-sequence stage when hydrogen fusion occurs and during helium core fusion after the helium flash.
The star Antares has an apparent magnitude of 1, whereas the star Procyon has an apparent magnitude of 0.4. Which star appears brighter in the sky?
Procyon appears brighter in the sky.
An astronomer discovers a type M star with a large luminosity. How is this possible? What kind of star is it?
Since M stars are cool and emit very little energy per unit area, the only way that an M star can have a high luminosity is if it is very large. This star is either a giant or a super giant.
Name and describe the three types of binary systems.
Spectroscopic, visual and eclipsing. A spectroscopic binary star is a binary star in which the components are not seen separately, but whose binary nature is indicated by periodic variations in radial velocity (changes in the doppler shift of the spectral lines), indicating orbital motion. A visual binary is a binary star in which the two components are telescopically resolved (can be seen individually). An eclipsing binary star is a binary star in which the plane of revolution of the stars is nearly edge-on to our line of sight, so that periodically, one star blocks the light of the other by passing in front of it.
Two stars have proper motions of one arcsecond per year. Star A is 20 light years from earth, star B is 10 light years away. Which one has the faster velocity in space?
Star A, since its farther from earth, its velocity in space must be greater than star B's to produce the same proper motion as seen from earth.
Suppose there are 3 stars in space, each moving at 100 km/s. Star A is moving across in our light of sight, B is moving directly away from earth, and C is moving away from earth at an angle of 30 degrees to the line of sight. From which star will you observe the greatest Doppler shift? From which star will you observe the smallest doppler shift?
Star B's motion is directly away from earth, it will show the greatest doppler shift. Star A, with its motion neither toward nor away from earth, will show the least doppler shift - no shift at all.
Star X has lines of ionized helium in its spectrum, and star Y has bands of titanium oxide. Which is hotter? Why? The spectrum of star Z shows lines of ionized helium and also molecular bands of titanium oxide. What is strange about its spectrum? Can you suggest an explanation?
Star X is hotter. Ionized helium lines are strongest at high temperatures, whereas titanium oxide lines are strongest at lower temperatures. Therefore, Star X must be hotter than Star Y. Star Z's spectrum is strange because the presence of ionized helium and titanium oxide lines indicate both high and low temperatures at the same time. One explanation for this strange spectrum would be that star Z is a hot star, like Star X, which creates the ionized helium lines, and that there is a cooler cloud of intervening material along the liens of sight that creates the observed TiO lines. Another explanation might be that what appears to be a single star is actually two stars so close together we cannot separate them visually - a hot star with a cool companion.
What elements are stars mostly made of? How do we know this?
Stars are mostly made of hydrogen and helium. We know this by analyzing the relative strengths of absorption lines in their spectra.
What is the defining difference between a brown dwarf and a true star?
Stars have internal temperatures capable of sustaining hydrogen fusion. Brown dwarfs do not.
How do we distinguish stars from brown dwarfs?
Stars have mass greater than 1/12 of the sun's mass, brown dwarfs generally have between 1/100 and 1/12 the mass of our sun, planets have masses less than that.
Name five characteristics of a star that can be determined by measuring its spectrum. Explain how you would use a spectrum to determine these characteristics.
TEMPERATURE: Measure the relative strengths of spectral lines to determine a star's spectral class, for examples, obafgkm. Spectral class corresponds to temperature. COMPOSITION: Use computer models and temperature to determine elemental abundances from relative strengths of absorption lines in a star's spectrum. CLASSIFY A STAR AS A DWARF OR A GIANT: Measure the width of spectral lines. If the lines are narrow, the star's diameters is large. If the lines are wider, the star's diameter is smaller. RADIAL VELOCITY: Measure the wavelengths of the lines in the star's spectrum. Compare the observed wavelengths to the known "rest wavelengths" of the lines to determine the Doppler Shift. The Doppler shift of the star is determined by its radial velocity-its motion toward or away from earth. ROTATION: Measure the width of the star's spectral lines. The star's rotation creates a broadening of the spectral lines, which can be used to determine the star's rotation.
Why can only a lower limit to the rate of stellar rotation be determined from line broadening rather than the actual rotation rate?
The Doppler shift can only detect radial motion, that is, motion toward or away from the observer. If the axis of rotation is perpendicular to the line of sight, then the full rotational motion is radial. However, if the axis of rotation is parallel to the line of sight, then non of the rotation motion is radial. In most cases, the inclination of the rotational axis will be somewhere between these extremes, so part of the rotational motion will be radial, but not the full rotational motion. This means that the rotational motion detected by lines broadening will usually not be the full rotational motion.
Where did the carbon atoms in the trunk of a tree on your college campus come from originally? Where did the neon in the fabled neon lights of broadway come from originally?
The carbon could have come from the product of helium fusion in a high-mass star. Neon must have come from fusion inside of a high-mass star, as its atomic number is higher that that of carbon and therefore could not be produced in low-mass stars
Suppose you were handed two H-R diagrams for two different clusters: diagram A has a majority of its stars plotted on the upper left part of the main sequence with the rest of the stars off the main sequence, and diagram B has majority of its stars plotted on the lower right part of the main sequence with the rest of the stars off the main sequence. Which diagram would be for the older cluster? Why?
The crucial idea here is that the more massive the star, the more quickly it goes through each stage of its life. The older cluster would be represented by diagram B, which indicates that higher-mass stars have already evolved past the main-sequence stage of their lives, while the lower mass stars continue to be on the main sequence. Diagram A indicates a young cluster, as only the higher mass stars have reached the main-sequence stage and the lower mass stars are still protostars and have yet to reach zero-age main sequence.
Would you expect to find an earth-like planet around a very low-mass star that formed right at the beginning of a globular cluster's life?
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.
Explain why color is a measure of a star's temperature?
The light emitted by a star approximates a blackbody. The hotter a star's temperature, the shorter the peak wavelength of its spectral curve. Therefore, cool stars exhibit reddish colors, whereas hot stars exhibit bluish colors.
What two factors determine how bright a star appears in the sky?
The luminosity and distance of a star determine its apparent brightness in the sky.
If we were to compare three stars with the same surface temperature, with one star being a giant another a super giant, and the third a main-sequence star, how would their radii compare to one another?
The main sequence star would have the smallest radius, whereas the giant would have a larger radius, and the super giant would have the largest radius. This is based upon the relationship of radius, temperature and luminosity.
Which changes by the largest factor along the main sequence from spectral types O to M mass or luminosity?
The mass varies from only about 100 Msun to about 0.08 Msun, or by about a factor of 1000 along the main sequence, whereas the luminosity varies from 10^6 for th msot luminous stars to less tahn 0.001 or a factors of more than 10^9 for the least luminous. Only the radii of main sequence stars are fairly similar to that of the sun, which implies that the radii change by a smaller factor than the luminosity. The validity of the conclusion can be shown by noting that the luminosity of a star is proportional to R^2T^4, but this is beyond what is covered.
In the H-R diagrams for some young clusterse, 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 thatt? Sketch an H-R diagram for such a cluster.
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.
What is the main reason that the spectra of all stars are not identical? Explain
The primary reason that stellar spectra look different is that the stars have different temperatures. Each element (and ion) has a characteristic temperature at which the spectral lines it produces are strongest. Stars of different temperatures, therefore, exhibit different spectral lines.
How would two stars of equal luminosity -one blue and the other red - appear in an image taken through a filter that passes mainly blue light? How would their appearance change in an image taken through a filter that transmits mainly red light?
The stars have equal total luminosity, but the blue star emits most of its energy at shorter wavelengths, whereas the red star emits most of its energy at longer wavelengths. Since a blue filter transmits only blue (shorter wavelength) light, the blue star will look brighter through the blue filter which the red star will look brighter through the red.
If all the stars in a cluster have nearly the same age, why are clusters useful in studying evolutionary effects?
The stars in a cluster presumably have the same age and chemical composition, but they do have different masses. The timescale for the evolutionary process depends critically on a star's mass, with stars of larger mass going through each stage more quickly. In a cluster with many stars, there is likely to be a good distribution of masses and so we can see stars in a variety of life stages. Even clusters of stars with only slightly different masses can vary considerably in their evolutionary stages. Thus, even stars in a rather small mass range can still be at different points in an evolutionary track. These tracks can be compared with theoretical ones from our mathematical models of how stars age.
How does the mass of the sun comapre with that of other stars in our local neighborhood?
The sun is more massive than the majority of stars in our neighborhood. Only a few other stars are more massive, whereas the vast majority are lower-mass stars.
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 opern 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 globular cluster, all the stars in the cluster can disperse with time, leaving a star like the sun alone later in its life (just as we now are)
Why do you think astronomers have suggested three different spectral types (L,T,Y) for the brown dwarfs instead of M? Why was one not enough?
The surface temperatures of brown dwarfs range from under 700 k to around 2400 k. Brown dwarfs of different surface temperatures show distinct characteristic spectral lines. Class L dwarfs show lines for metal hybrids and alkali metals, T dwarfs show methane lines, and Y dwarfs show ammonia lines.
What would you say to a friend who made this statement: the visible light spectrum of the sun shows weak hydrogen lines and strong calcium lines. The sun must therefore contain more calcium than hydrogen.
The temperature of a star's photosphere determines the pattern of spectral lines that we see. At the sun's temperature, hydrogen lines are weaker in the visible light part of the spectrum. Most stars have compositions very similar to the sun and are made mostly of hydrogen and helium.
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 from different points of view.
Stars that have masses approximately 0.8 times the mass of the sun take baout 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 swhy 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.
Suppose you want to search for a brown dwarf using a space telescope. Will you design your telescope to detect light in UV or the infrared part of the spectrum? Why?
Very low-mass stars or brown dwarfs are relatively cool, with temperatures of only about 2000K. Such stars emit most of their light in the infrared and practically none in the UV.
Why do most known visual binaries have relatively long periods and most spectroscopic binaries have relatively short periods?
Visual binaries must be rather well separated to be detected as such. Thus, they generally have large semimajor axes, and by kepler's third law, long periods and low orbital speeds. Spectroscopic binaries must have rather high orbital velocities sot that the effect of this motion is clearly identifiable in the spectrum. Hence, they tend to have short periods. High orbital velocities occur with long periods and large major axes only if the stars are massive.
A star is often described as moving on the H-R diagram, why is this description used and what is actually happening with the star?
What is actually happening is that the star is progressing into different evolutionary stages, during which various properties of the star (mass, luminosity, radius,..) change. The H-R diagram plots a star's luminosity versus its surface temperature. As the star evolves, these characteristics change. When the star is plotted on an H-R diagram as it goes through these evolutionary stages, the star's dot on the diagram moves from one location to another.
