Homework from Astronomy Today 9e Homework on stellar evolution [ Ch. 18 Q(How many figures...?), ] <- not used after spring 2019 Ch. 18 RD 2,7,13 Ch. 19 RD 1,2,3,11 Ch. 20 RD 1,2,8,9,11,13 ------------------------------------------- Ch. 18 [ Q: How many figures show all 3 types of nebula (emission, reflection, and dark) in the same picture? Definite examples: Figs. 4,6,7,8,13,19 (6) Possible others: Figs. 0(opening), 1,5,9,10,14,20 (7) Thus, 6-13 is acceptable ] 2. What is the composition of the interstellar gas? What about interstellar dust? The gas is about 90% H, 9% He, and <1% metals (by number). The dust grains are dominated by Al,Fe,Mg,C,and Si. In cold regions, they can also contain ices (H20, CO2, NH3, methanol, etc). 7. What is an emission nebula? An emission nebula is a region of hot glowing gas (mostly hydrogen) surrounding a newly formed star or group of stars. The atoms of the gas absorbUV light emitted by the bright young stars, and in return, they emit a variety of emission lines characteristic of the elements in the cloud. One of the brightest hydrogen emission lines is H-alpha, which has a red color. It is so strong that it often overwhelms all other emissions and colors that might be seen. 13. What is 21-cm radiation? With what element is it associated? Why is it useful to astronomers? 21-cm radiation is a kind of electromagnetic radiation in the radio part of the spectrum (1.4 GHz). It is produced by the "spin-flip" transition of hydrogen (the electron flips its spin from parallel to anti-parallel relative to the proton). This radiation is extremely important to astronomers because it is emitted by gas clouds making up galaxies (especially spirals) and doppler shifting of the line allows them to figure out the motions of the different parts of the galaxies. 21-cm radiation has given us the best mapping of our Milky Way galaxy. [15. How does a molecular cloud differ from other interstellar matter? Molecular clouds are colder and denser than other phases of the ISM, but mostly they are distinguished by the presence of molecules (especially molecular hydrogen, H_2).] --------------------------- Ch. 19 1. Briefly describe the basic chain of events leading to the formation of a star like the Sun. The Sun-like star begins as a large interstellar cloud containing cold molecular hydrogen. Gravity makes it start collapsing and overdensities within the big cloud make it fragment into smaller clouds. These clouds collapse fairly quickly (10^4 yrs) because the grav potential energy goes into breaking H_2 bonds instead of increasing the gas temperature and pressure. After those bonds are broken, collapse goes more slowly as it is accompanied by increased temperature and pressure. The protostar gets hot and produces winds which blow away the outer parts of the cloud. Gas and dust remain the longest in a protoplanetary disk but eventually gets cleared. The center of the protostar finally starts fusion when its temperature gets above about 10 million K. After that there is some more slow collapse and heating of the center as the star settles onto the main sequence. 2. What are the roles of heat, rotation, and magnetism in the process of stellar birth? Heat: heating during the collapse of gas clouds creates gas pressure which is the main factor resisting gravitational collapse. Rotation: As an interstellar cloud collapses, it must spin faster as it conserves angular momentum. This can actually hinder star formation, as the rotation tends to fling material out of the cloud, opposing gravity. Thus, a rotating cloud needs a stronger gravitational pull and more mass to collapse than a cloud that is spinning slowly or not at all. Rapid spin also causes the cloud to flatten into a disk. Although most of the mass is still concentrated in the center, the material in the disk could form into planets. Magnetism: As the collapsing cloud gets heated it gets progressively more ionized. Ionized gas is deflected by magnetic field lines so that gas can move more easily along field lines than across them. This means that collapse is slowed down except in the direction parallel to the field lines. This also influences the shape of the cloud. 3. What is an evolutionary track? It is a curve on the H-R diagram which shows the path that a star of a given main sequence mass will take as it evolves. It may take the form of a dashed line for stages (like planetary nebula) in which the star's surface is ill-defined. The track depends mostly on initial mass, but also on composition (e.g., He/H ration). 7. What are T-Tauri stars? A T-Tauri star is a protostar that has heated up to the point in which extreme activity on the surface generates a powerful "protostellar wind". These winds can drive away material in the outer portions of the cloud. [8. Stars live longer than we do, so how do astronomers test the accuracy of theories of star formation? They study many, many stars that are in different stages of evolution. They rely on star clusters to compare the evolutionary stages of stars which have the same age but have a range of masses. Another important part of checking theories is computer modeling and simulations.] [9. At what evolutionary stages must astronomers use radio and infrared radiation to study prestellar objects? Why can't they use visible light? Radio and infrared are most crucial for studying star formation for the early stages when the gas is in its cold and medium temperature stages. Cold H_2 does not produce or absorb much visible radiation. Neither does HI. H_2 is traced by molecules like CO which produce emission in radio, and HI produces 21 cm radio waves. The dust in the cold gas absorbs visible light and makes it impossible to see through, but IR and radio can see warm "clumps" inside of these clouds. 11. Explain the usefulness of the H-R diagram in studying the evolution of stars. Why can't evolutionary stages 1-3 be plotted on the diagram? H-R diagrams are ideal for studying stellar evolution because it has a logarithmic luminosity axis which is capable of showing a huge range in luminosities. Individual stars can change their L by over 100x as they evolve into giants and supergiants. Stars also change in surface temperature (generally cooling as the expand), and the horizontal axis allows temperature changes to be shown. Stages 1-3 can't be plotted because there is no clear surface to the star. That means that the surface temperature and color are not well-defined. It may not even be distinct from other fragments in the molecular cloud. [Old # Why has it been difficult until recently to demonstrate that stars and protostars actually exist within star-forming regions? The smallest objects, the proplyds, are just out of reach of ground-based resolution. But with Hubble, they can just barely be resolved. Also, IR observations are relatively new (1980's) compared to visible. ] [Old # Compare the times necessary for the various stages in the formation of a star like the Sun. Why are some so short and others so long? The times are very short for the first few stages of development, because during those stages, gravity essentially has free reign and the cloud is in free fall. This is largely due to the presence of molecular H (H_2): the energy of collapse goes into its dissociation rather than raising the temperature and pressure of the gas. As the protostar becomes hotter and denser, the internal pressure generated begins to fight the force of gravity. This slows down the evolution. ] [13. Compare and contrast the observed properties of open star clusters with globular star clusters. The open clusters are found in the plane of the galaxy, while globular clusters (GC's) are found in its halo. OC's have many fewer stars than GC's. OC's are usually less compact. OC's contain young, blue stars, while GC's generally do not. OC's are young, GC's are old. OC's are higher in metals than GC's. [19. How can we tell whether a star cluster is young or old? The age of a star cluster is determined by the type of star that is about to leave its main sequence. The more massive a star is, the faster it uses up hydrogen fuel on the main sequence, so as the star ages, the more massive stars leave the main sequence first. If we can identify the star with the largest mass still on the main sequence, the cluster's age will be the same as the main sequence lifetime of that star.] --------------------------- Ch. 20 1. Why don't stars live forever? Which types of stars live the longest? Stars eventually run out of "fuel" for the core fusion processes which keep them stable. The low mass stars live the longest, even though they have less fuel, because they burn their fuel at such a slow rate. The rate of fuel burning is proportional to their luminosity, which goes roughly as mass to the 4th power. The lifetime is then the mass (of fuel) / Lum (rate of fuel burning), so T_lifetime ~ M/M^4 = M^-3. 2. How long can a star like the Sun keep burning hydrogen in its core? About 10 billion years. [12. How do astronomers test the theory of stellar evolution? Star clusters provide important checks on our theory of stellar evolution. A given cluster contains a bunch of stars with different masses but the same age. By looking at many clusters with different ages, we can see that stars start out along the main sequence and then evolve off it, starting with the massive stars. Computer simulations can also be used to check the stability of stars with different masses and compositions.] [Old # Why is the depletion of hydrogen in a star such an important event? Because that signifies the end of the longest stage of a stars life - the main sequence. The depletion of H means that the core has lost its fuel supply for the main fusion process, the p-p chain. This leads to the collapse of the core and the onset of H shell burning on the sub-giant and giant branches.] [7. Describe an important way in which winds from red-giant stars are linked to the interstellar medium. The winds from red-giant stars contain some products of nuclear fusion (these are "dredged" up during the red-giant phase). So they are a means of enriching the ISM with dust and metals (elements higher than He on the periodic chart). Although supernovae can produce much higher elements, they are less commonplace than red-giants, so red giants make a big difference in the evolution of the ISM. ] 8. What is the internal structure of a star on the asymptotic giant branch? A star on the asymptotic giant branch has a carbon core and is fusing Helium into carbon in a shell. (Above that He shell would be the usual H and Helium.) 9. What is a planetary nebula? Why do so many P.N. appear as rings? A planetary nebula is the blown off outer atmosphere of an evolved star. The central remnant is a white dwarf. These usually appear as rings because the intrinsic shapes are either spherical shells, or double lobes. A translucent, glowing shell will appear like a ring because there is more gas along a sightline through the edge than through the center. Double lobes can also appear ring like when viewed along their symmetry axis. [10. Why are white dwarfs hard to observe? Because they have very low luminosities. Their luminosities are low, in turn, because of their small size. ] 11. How do the late evolutionary stages of high-mass stars differ from those of low-mass stars? Their tracks on the H-R diagram are more horizontal (zig-zagging to the right), while low mass stars move primarily upward. Also, the high-mass stars go through more types of fusion in their cores than low-mass stars, and many of those types of fusion can happen simultaneously because of the shell-burning that occurs. More specifically, low-mass stars fuse H to He, and He to Carbon, but cannot fuse carbon. High-mass stars can fuse carbon into oxygen and also create Neon, Silicon and iron. 13. How can astronomers measure the age of a star cluster? They can plot the stars on an H-R diagram and look for the turn-off point. This point marks the highest mass star which is still on the main sequence. Theory can tell us the age of a star of that mass, and that age will be the age of the entire cluster. [14. What are the Roche lobes of a binary system? They are tear-drop shaped regions of space that mark transition region between the gravitational attraction to one star and the other. In particular, the two lobes meet at a point between the two stars where the pulls are equal. If a star expands out of its Roche lobe, it's out atmosphere will be pulled down onto its companion. ] ---------------------------