Note: The following are brief summaries of what was covered in each class. Do not view these as complete lecture notes or outlines, but rather guidance as to topical material that you may need to fill in from the textbook or someone's notes if you miss a class.
Bob Ergun, who dubbed himself my "evil twin," gave this class in my place, as I was attending the annual meeting of the American Astronomical Society. Most of you know Bob, as he was your instructor last semester in ASTR 1030. In this class Bob discussed the Sun, and covered virtually all of the material in Chapter 16 of your textbook. You should be familiar with that material, as some of it will come up again later, especially when we discuss the basic properties and the structure and evolution of other stars.
I arrived on the scene and spent most of the class going over various aspects of the course and what you should expect. We spend considerable time on the syllabus, but some comments on various policies (Honor Code, Disabilities services, etc.) were left out, so you should be sure to read the online version.
Other items from this class: I asked each of you to send me an e-mail with some background on yourselves and your interests, including such things as whether or not you are majoring in our department; what previous astronomy classes you have had; and what special topics your might suggest for class discussion. We finished this class with a half-hour slide show which was intended to give you an overview of the universe beyond the solar system, which is the area to be covered in this course.
In this class we finally got into some material on astronomy, starting with notes on mathematical and geometric tricks of the trade, which will be helpful to you in solving problems. The first of these was the small-angle approximation, which relates the physical diameter and the angular diameter to the distance of an object. In its simplest form the small angle approximation uses angles in units of radians, so you need to be familiar with these units and their conversion to standard angular units (degrees, minutes, and seconds). We also talked about how to streamline computations, especially when comparing two objects for which you have separate equations (such as the Stefan-Boltzmann law). It usually simplifies things to divide the equations so that all constant terms cancel out, before substituting values and solving.
We then turned our attention to a quick review of gravitation and orbits, starting with a summary of orbital properties as a function of kinetic and potential energy. We discussed Kepler's laws of planetary motion as derived by Newton, and we derived Kepler's third law (algebraically) for the simple case of circular orbits.
We then embarked on a discussion of light, starting with a historical overview of how the photon concept came to be, including a listing of properties of light that indicate a wave nature, and properties that suggest a particle nature. Basic relationships between wavelength, frequence, speed of light, and photon energy were derived and discussed.
Homework No. 1 was assigned, and is due next Thursday, January 27.
After some opening announcements (especially the scheduling of our February 1 class for Fiske Planetarium), we resumed our discussion of light, further elaborating on the nature of a photon and why the term "electrocmagnetic radiation" is applied to all forms from gamma rays to radio; and a description of polarization, which occurs naturally in many astronomical situations.
We then discussed the laws of continuous (thermal) radiation, such as the Planck function, Wien's law, Stefan's law, the Stefan-Boltzmann law, and the inverse square law. All of these are empirical relationships that were initially found from experiments but later derived from first principles, in the era of quantum mechanics.
Next came a discussion of spectral lines, beginning with a historical overview of the lab experiments that led to the identification of certain line patterns with specific chemical elements; then a description of electron energy levels and the formation of absorption and emission lines; and finally a presentation on the Rydberg formula for calculating wavelengths of hydrogen atoms and hydrogen-like ions (i.e., those with only one electron).
Today we started with announcements and reminders: (1) Homework No. 1 is due this Thursday (January 27); (2) our class will meet at Fiske Planetarium next Tuesday (February 1).
We then talked about astronomy news of the day, which led to a discussion of NASA's leaked plans to completely drop all servicing mission options for restoring and upgrading the Hubble Space Telescope. If true, this decision will have important ramifications for astronomy research here at CU, as our group (CASA) has built a new spectrograph for the Hubble that was to be installed by astrononauts. So we spent a few minutes of class time talking about the politics, the science, the engineering, and the rationale behind NASA's decision. We will probably talk about this again, as events develop in Washington.
Then we got back to our discussions of the properties of light and telescopes (reminder: read Chapters 3, 4, and 5 in your textbook). We began by wrapping up our talk about spectral lines, with a discussion of what we can learn from them, in determining the properties of distant stars, nebulae, and galaxies. From spectra we can determine the degree of ionization of a gas such as a stellar atmosphere or nebula; from the degree of ionization we can determine the gas temperature (if the ionization is due to collisions, which is not always the case); from spectra we can also determine the degree of excitation (i.e., the fraction of electrons in excited states) which is an indicator of gas density because excitation rates depend on the frequency of collisions. And from spectra, using the Doppler effect, we can determine the line-of-sight speeds (ie., the radial velocities) of planets, stars, galaxies and virtually any other object that has spectral lines.
We then began our discussion of telescopes, by first developing a list of the advantages of telescopes over the unaided human eye, and then exploring some of these factors, such as light-gathering power and angular resolving power. The diffraction limit was introduced, and we carried out example calculations of the resolving power of small and large telescopes.
In the next class we will continue the telescope discussion, with comments on telescope design trade-offs; telescope mounting systems; and instruments and detectors.
We started with the collection of Homework No. 1 and then a reminder that Tuesday's class will be at Fiske Planetarium, where we will have an update on the current nighttime sky as seen from Boulder, and a showing ot the special program on the Deep Impact Mission to Comet Tempel 1, which was launched earlier this month and will send a major heayweight mass to crash into the comet's nucleus on July 4.
Schedule reminder, not mentioned in class today: Your next evening observing session will be next Tuesday (February 1), at 7:00. This one is part of our required series of nighttime activities, so you should plan to attend, weather permitting. If in doubt (eg., partly cloudy conditions), you can call Sommers Bausch Observatory at 303 492-2020 within the half hour or so before observing is to begin. Quyen will be there (unless conditions are obviously hopeless) and will be able to advise you as to whether or not the observing session will take place.
Astronomy news: I offered further comments on the politics and cost considerations behind NASA's leaked decision to cancel all attempts to service the Hubble Space Telescope, as a follow-on to the discussion that we had had during the previous class. Another bit of unhappy news is that CU's proposal for the JMEX (Jupiter Magnetospheric Explorer) mission was turned down by NASA after a long series of successes in passing competitive reviews along the way. It appears that hard times are coming for basic research that has traditionally been supported by NASA.
The depressing news aside, we then returned to our discussion of telescopes and observatories, on the ground and in space. I started by reviewing focal arrangement options for optical reflecting telescopes (e.g., the concepts and trade-offs for prime focus, Newtonian focus, Cassegrain focus, coude focus, and Naysmith focus configurations). I then moved on to a description and discussion of mounting systems for telescopes, emphasizing the extraordinary engineering challenges involved in building a multi-ton instrument that can be pointed to an accuracy of less than an arcsecond and then hold that pointing accuracy as the Earth rotates under the telescope. The two chief options are the equatorial mount, which was used in all telescopes until quite recently; and the alt-az mount, which is far simpler and less massive, but which requires a sophisticated computer control system.
We spent much of today's class time on a slide show about telescopes and observatories. I will finish this discussion in next Thursday's lecture (following our Planetarium class on Tuesday), when I will describe space-based observatories and will also talk about some of the wild and crazy ideas astronomers are developing for newer and bigger ground-based instruments.
During today's slide presentation I made numerous comments worth remembering: I explained the techniques and the trade-offs for constructing large monolithic mirrors; I described adaptive optics, which is required for both segmented mirror designs and meniscus (thin and floppy) mirrors; and I talked about interferometry, in the context of radio observatories. I will review some of these things in the next lecture (a week from today), but you should be sure to read about them in the text and online.
Class was held in Fiske Planetarium today, instead of our regular classroom. At Fiske we had an update on current nighttime sky objects and a review of constellation and star identification, hosted by Tito Salas, education coordinator for Fiske; and then we saw the show "Deep Impact." This program, which is now offered at several other planetariums around the U.S. and in Europe, was produced at Fiske. It is about the NASA-sponsored mission of the same name, now on its way to Comet Tempel 1 where a probe will be sent crashing into the comet so that the debris can be analyzed to measure the composition of material from beneath the crust of the comet's nucleus. You can learn more about at the Deep Impact mission web site.
Homework No. 1 was returned today, at the end of class. Your score is based on a twenty-point scale. Most of the class did very well on this straightforward computational problem set, where only a few difficulties showed up in unit consistency and conversions, and in significant digit retention. The solutions to Homework 1 are now posted on this web site, so that you can compare your answers to mine.
We then had a short discussion of astronomy news events, which was dominated by recent developments with regard to the Hubble Space Telescope. At a hearing yesterday by the House Science Committee there was a general consensus that the HST should be serviced, but not without concerns about where the money would come from and which other NASA programs would suffer cuts. On Monday of next week NASA will release the President's budget request for FY 2006, which is rumored to contain no funds for Hubble servicing. If so, then the Congress may have to force the issue, either by inserting extra funds into NASA's budget or by giving direction as to which programs in NASA should be cut in order to provide funds for HST servicing. No one expects a final decision on this until the new NASA Administrator is in office, and he or she has not yet even been selected.
We then completed our discussions of telescopes, with some final comments about telescope design for non-visible wavelengths and plans for future optical telescopes on the ground, leading up to the most ambitious idea yet, the Overwhelmingly Large Telescope (OWL), a 100-m segmented telescope which is being considered by the European Southern Observatory.
Moving on to the next major section of this course, we then began our discussions of stars. I started with a galactic overview and stellar statistics description that is not in the textbook in the same form, so you will need to rely on your class notes. This involved such things as the total number of stars in a galaxy like ours, the relative numbers of stars by mass, the locations of stars within the galaxy's disk and halo, the general nature of stellar clusters, and an overview of the interstellar medium.
Having set the stage with these contextual remarks, I then began our first detailed discussion of individual stars by reviewing some salient points about the Sun. This material is in Chapter 16 of the textbook, and much of it was covered by Bob Ergun during the first class (see notes above for January 11), but I emphasized some aspects of the Sun that are not clearly included in the text. One is the elemental composition of the Sun, which is the same (with minor variations that we will discuss later) for other stars in our galaxy and for those in other galaxies as well, and is now considered to represent the "cosmic abundances" in the modern universe. One of the goals of this course will be to understand how the stars in the galaxy and the universe came to have this composition.
We finished by talking about interior conditions in the Sun and how we know them. I challenged the class to explain how we know that the temperature rises as you go inward toward the center of the Sun, and this led to an interesting compilaton of observational and theoretical arguments. That is where we left things for the day.
Announcements: Homework 2 will be assigned this Thursday (February 10) and will be due one week later (February 17). Our first in-class test will take place on Tuesday, February 22. I will spend some time in class before then (probably on February 17) discussing the test and what you should expect and how to prepare for it.
We then returned to our discussions of the Sun, with an eye toward stellar physics in general. Today we reviewed the process of creating and testing stellar models, introducing the four basic equations of stellar structure (well OK - not the equations in detail, but a description of what they say and what they mean). We then carried out a series of calculations aimed at showing how energy is produced in the Sun through nuclear fusion reactions, first by computing the energy released in a single proton-proton chain sequence (derived by assuming that the mass difference between four protons and a single helium 4 nucleus is entirely converted into energy according to E = mc^2); and then by assessing the total energy available to the Sun over its hydrogen-burning lifetime, assuming that 0.007 of the mass in the innermost ten percent of the Sun is hydrogen that can be converted into helium by the proton-proton chain. We found that enough energy can be produced to keep the Sun shining at its current luminosity for about 10 billion years.
Next we moved on to discussions of basic observations of stars and the derivation of their main properties. I started by describing the three main types of observations (astrometry, photometry, and spectroscopy), and then conducted a discussion of astrometry, or positional astronomy. The main application of this science today is the determination of stellar parallaxes, and we spent the last few minutes of class time defining the parsec and deriving the relationship between parallax angle and distance.
Announcement: John Marberger, who is the current science advisor to the President, will be in Boulder early next week and will give a public talk on the role of science in policy decision-making, on Monday evening (February 14), at 7:00 P.M., in Math 100. I don't know whether he will discuss the NASA budget.
Repeat of a comment made in class: Some students appear not to be taking the recitation section for this course seriously, as there have been unexplained absences, students dropping by only long enough to turn in an assignment, and students deciding to attend the section they are not assigned to. None of the above is OK. The recitation is an integral part of this class; it is required; and you must attend and do the assigned work. If these comments apply to you, please start taking recitation more seriously. Ask Quyen if you have any questions about assignments and expectations in the recitation.
Homework No. 2 was handed out, and is due next Thursday (February 17). Also, our first test will take place on February 22, the following Tuesday. I will spend some class timeduring the preceding class February 17) to help you prepare for the test.
We then spent most of the class talking about stellar observations, starting with a quick overview of methods for making astrometric measurements, followed by a discussion of stellar parallaxes and how accurate the distances are that we can derive from parallax measurements. We then moved on photometry, or brightness measures of stars, and spent the rest of the lecture defining and applying the stellar magnitude system. We defined the system in its rigorous logarithmic form; we worked out examples in which we converted between magnitude differences and intensity ratios; we analyzed the effect of distance on magnitudes (developing the concepts of absolute magnitude and distance modulus); and we reviewed a technique for determining star's luminosity when its distance and the apparent magnitude are known to begin with.
This Thursday and Friday evenings there will be a talk at Fiske Planetarium by CU researcher Nahum Arav, at 7:30 P.M. both nights. The Thursday talk is free for CU students. The topic is "The Paranormal Universe," and Nahum will discuss the roles of human psychology, sociology, and the media in the popularization of pseudoscientific beliefs. The talk will be followed by a discussion period.
On Friday afternoon there will be a ceremony celebrating the 75th anniversary of the discovery of Pluto. CU has strong connections to Pluto, especially through the upcoming New Horizons mission, as there is a student-built experiment on board and the Principal Investigator, Alan Stern, is a former graduate student in our department. The celebration will take place outdoors at 4:00 Friday, at the Pluto pedestal in our scale model solar system (i.e., just south of Colorado Blvd., on the wide walkway that leads all the way to Fiske Planetarium, where the Sun pedestal is located). Speakers will include Mihaly Horanyi, who oversaw the development of the Student Dust Counter experiment for New Horizons; Fron Bagenal of our faculty; and Alan Stern, PI of the New Horizons mission.
Other announcements and reminders:
Homework No. 2 is due this Thursday.
Test No. 1 will take place next Tuesday, February 22.
The rest of today's class was a continuation of our discussions of stellar observations and the measurement of basic stellar properties. Note that some of this is a bit tedious, but it is IMPORTANT. Those of you who are planning to be astronomers really need to get comfortable with this section of the course, as it is here where you get the real nuts and bolts of astronomy: the methodology; the lore and the jargon; and the fundamental astrophysics that underlies our field.
Today we spent most of the time talking about stellar spectroscopy, including the historical background, the techniques, spectral classification (which includes both the spectral type and the luminosity class), and modern spectral analysis to obtain physical conditions and chemical compositions of stellar atmospheres.
Key points made: Spectral types represent a sequence of temperatures - the differing patterns of spectral lines are the result of ionization and excitation differences, not composition differences; the H-R diagram shows that stellar luminosity and temperature are related quantities; and the general assumption by astronomers that the spectral class of a star can be used as an indicator of its other properties. We discussed the various types of binary stars and how they are used to determine basic stellar properties, and we finished by listing those basic properties (L, T, R, M, composition) and reviewing how they are measured. Note that you get nowhere in this list without first knowing the distance - this is the topic we will start with at the beginning of the next lecture.
Announcements and reminders:
Special talks at 7:30 tonight and tomorrow night at Fiske Planetarium, on "The Paranormal Universe." Tonight's talk is free to CU students; you will have to pay if you attend this tomorrow night. The discussion session at the end of the talk might be really interesting.
Celebration of the 75th anniversary of the discovery of Pluto and of the upcoming New Horizons mission to Pluto, tomorrow at 4:00, at the location of the Pluto plinth (pedestal) at the northern end of the campus scale model solar system (just south of Colorado Blvd., on the north-south walkway where it passes between the Math and Engineering buildings).
I then provided an overview of what to expect on the test, as follows: The test will consist of short discussion-style questions, with a few problems mixed in. Be sure to bring a calculator. You will not need to memorize any specific formulae or data values as I will provide you with a data sheet that you can use during the test. Use your lecture notes as your primary guide to studying; I will not ask questions about things I did not talk about in lecture (and be reminded that these online notes are not complete; if you missed a class it would be wise to borrow notes from someone who was there that day).
Quyen will hold a review session on Monday evening, at Sommers Bausch Observatory, just prior to your observing session. Quyen's review will start at 6:00; observing starts at 7:00. Quyen will hold the review even if the weather is poor, and will extend it beyond 7:00 (until about 8:00 at the latest) if the weather precludes observations. Quyen is not planning to present a prepared talk or outline; instead the review session will depend on student questions, which she will answer and explain.
We then completed our discussion of basic stellar properties with a reminder that distance information must be available in order to derive certain stellar properties such as luminosity, radius, and mass. So we quickly reviewed distance measurement methods, emphasizing that parallax can be used only for very nearby stars. The next step in going outward to greater distances is called spectroscopic parallax, in which a star's visual absolute magnitude is derived from its position on the H-R diagram, providing the information needed (along with the meaured visual apparent magnitude) to use the distance modulus relation to find the distance.
Then we reviewed stellar model calculations, which have already been discussed in connection with the Sun. There are four basic equations of stellar structure, of which the one describing hydrostatic equilibrium is the most useful because it helps us understand some basic properties of a stellar interior (such as the high temperature and pressure at the core) and because it also explains the relationship between mass and other stellar properties. The Russell-Vogt theorem summarizes this by stating that the mass of a star, along with its composition, determines all other properties. Given this, we realize that the main sequence is really just a sequence of masses (ranging from 0.08 solar masses at the lower end to 50 - 100 solar masses at the top of the main sequence).
A next step was to estimate stellar hydrogen-burning lifetimes, which are proportional to stellar mass (because that determines the amount of nuclear fuel available) and inversely proportional to luminosity (which determines the rate at which a star loses energy). We found that high-mass stars have much shorter lifetimes than the Sun, and that low-mass stars have very long lifetimes, in some cases exceeding the age of the universe. We noted that hydrogen burning (i.e., the fusion of hydrogen to create helium) occurs by the CNO cycle instead of the proton-proton chain in stars on the upper main sequence, starting just above the Sun in mass. The net result of the CNO cycle is the same as for the proton-proton chain: four hydrogen nuclei are fused to form a helium 4 nucleus, with released energy due to the conversion of a fraction (0.007) of the original mass to energy.
Next we returned to the question of what happens in the core of a star when all the hydrogen has been converted into helium. For reasons discussed at length in class, the only viable reaction is the triple-alpha process, which converts helium to carbon. Following the production of carbon, further reactions can occur by alpha-capture, where for example a carbon 12 nucleus adds a helium 4 nucleus (i.e., alpha particle) to form oxygen 16, and so on. In the next lecture (after the test) we will complete this discussion of nuclear reaction sequences before we move on to star formation and evolution.
Our first in-class test took place today, so there was no regular lecture.
After some commentary and discussion on the test (which we might have ready to return on Tuesday), and some astronomy news updates (most notably the recent humongous gamma-ray burst from a neutron star in our galaxy), we returned to our discussion of the formation of elements by stellar nuclear reactions. The only general type of reaction not previously talked about are the neutron-capture reactions, which occur when free neutrons combine with nuclei. In a slow neutron capture process (s-process), the added neutron has time to beta-decay to a proton (the resulting electron escaping), thus forming proton-rich nuclei. Massive stars can make elements heavier than iron this way, even if they don't blow up as supernovae. In rapid neutron capture reactions (r-process), which can occur only during an explosive event such as a supernova, the neutrons are added more rapidly than the beta decay time, so these reactions produce neutron-rich nuclei. Both s-process and r-process nuclear reactions produce heavy elements.
We then turned our attention to stellar evolution, starting with an overview of mass loss, chromospheres, and coronae in stars of various types. From the viewpoint of stellar evolution, the most important point is that very luminous stars, the ones across the uppermost region of the H-R diagram, all lose mass at such great rates that their masses can be significantly reduced during their lifetimes. The hot massive stars (O and B stars) lose mass through rapid radiatively-driven stellar winds; the cool luminous stars (red supergiants) lose mass through slow, dense winds.
Next we began our discussions of stellar evolution, which will be our main topic for the next few lectures.We started with observational studies of evolution, including sudden changes (such as supernova explosions), observations of star formation, and what we can learn from star clusters. Starting with star clusters first, we talked about how the assumptions of common age, common distance, and common initial composition help astronomers to figure out how stars of different mass (i.e., at different positions on the main sequence) evolve. This shows that the massive stars (top of the main sequence) evolve fastest (which we already suspected from our estimates of hydrogen-burning lifetimes), and that they become red giants when they are done with their hydrogen-to-helium reaction stage. The age of a cluster can be estimated from the hydrogen-burning lifetime of a star at the cut-off point of its main sequence, since stars of higher mass have evolved into red giants.
We finished today's class with comments on observations of star formation (emphasizing the need for radio and infrared observations) and then we began a step-by-step discussion of star formation, based on a combination of observation and theory. We will resume this story on Tuesday.
Test 1 is not yet graded, due to illness on the part of our grader. I expect to return both this test and our second homework assignment this Thursday. Homework No. 3 will be assigned on Thursday and will be due one week later, on March 10.
After discussing astronomy news and related topics, we then talked about stellar evolution. This material is covered in Chapter 20 of your textbook, though in a rather haphazard fashion with several topics out of logical sequence. Sigh. But it is what we have. I urge you to read Chapter 20, but to rely on your class notes as your primary information source regarding stellar evolution.
I started with a reminder about how we observe stellar evolution (or at least its outcomes), and then completed our story about the steps in the formation of a star like the Sun (i.e., a one solar mass star), as outlined in Chapter 19 of your book. Then we moved on to a discussion ot the life story of a Sun-like star, from main sequence beginnings to white dwarf endings. We saw this through from the formation of the Sun and its initial appearance on the main sequence, where its main energy source is the proton-proton chain; to the main sequence lifetime as the Sun gradually converts its core hydrogen into helium; to the formation of a dense core whose pressure is dictated by a quantum physics phenomenon called the Pauli Exclusion principle - at this point the core is said to be degenerate, and the electrons govern the pressure due to their quantum refusal to be squeezed together any closer than a certain limit. Once the H is gone in the star's core there is a prolonged period where the core is not reacting but a spherical shell outside the core continues to convert H to He - and in the process injects enough radiative energy into the outer layers to cause them to expand as the star becomes a red giant. At the peak of the red giant phase the star's core undergoes a helium flash due to its degenerate nature, and then the star begins stable He-burning (by the triple-alpha process) in its core. The star moves down and to the left in the H-R diagram at this time. In the end the star stops undergoing nuclear fusion reactions, probably at the point where most of the helium has been converted to carbon, and after the ejection of its outer layers the star ends up as a white dwarf.
We finished by talking briefly about the evolution of stars more massive than the Sun, but did not get far before the class ended. I will pick up at that point on Thursday.
We started with the return of graded papers from Test 1 and Homework No. 2, followed by fairly expansive comments on my part about Test 1. Homework No. 3 was also handed out. Regarding test 1, I printed and distributed answer sheets so that everyone could compare their answers with mine, and try to understand why points might have been taken off here and there. There is an appeal process for those who feel that we blew it in grading some particular question, which requires you to write a note and return your test to me.
After a brief discussion of current events in astronomy, we returned to the consideration of stellar evolution, this time focusing on stars of initial mass much greater than the Sun. These stars join the main sequence above the Sun's position, convert H to He while on the main sequence (but do so dominantly by the CNO cycle), and they use up all their hydrogen a lot faster than the Sun does. We discussed what happens to these stars when their core hydrogen is used up, which is complicated by mass loss during the lifetimes of these stars, which can dramatically alter their mass and allow them to end up with masses that fall below the 1.44 solar mass limit for white dwarfs. Model calculations suggest that stars with initial mass up to about 8 solar masses can lose enough mass through stellar winds to end up as white dwarfs. But some stars are more massive than that, and they have to do something else when their nuclear reactions are complete. This is where we will start in next Tuesday's class.
As usual, we started with a couple of announcements and reminders:
Homework No. 3 was assigned last Thursday and is due this Thursday (March 10).
Your next observing session is scheduled for this Thursday (Marh 10), starting at 7:00 P.M. Be sure you are in touch with Quyen about preparations for this. And, if it is clear, I strongly recommend that you plan to attend and get at least one nighttime lab assignment done, as we cannot guarantee that the remaining nights on our schedule will be clear.
The main astronomy news item of the day was a mostly historical item, as the nuclear physics pioneer Hans Bethe died over the past weekend, at age 98. Bethe played a central role in deducing the specific nuclear fusion reactions that power the Sun and other stars, and he then became a major player in the Manhatten Project, which developed the atomic bombs that ended World War II. (In class I added a personal note to this, as Bethe was a visiting professor at the university where I did my Ph.D. dissertation, and I got his advice on some quantum mechanical questions that arose in the very first paper I ever wrote for the Astrophysical Journal - so he is acknowledged in that paper. At the time I did not fully appreciate who he was, but I sure valued his comments.)
We then returned to our discussions of the evolution of massive stars, emphasizing what happens in the end to stars with initial masses above 8 solar masses (stars that start out at about 8 or fewer solar masses apparently lose enough mass through stellar winds that they can end up as white dwarfs that fall below the degenerate electron gas limit of 1.4 solar masses). The more massive stars cannot become white dwarfs, and have to end up some other way. Up to a certain mass limit (not well defined, but probably around 20 solar masses initially, before mass loss) stars can die spectacularly in supernova explosions, which occur once the core is converted to iron in fusion reactions. Further reactions are endothermic and cause the core to collapse in free fall, forming a neutron star as protons and electrons are converted into neutrons (by inverse beta decay). Once the core is made of a pure neutron gas, it becomes degenerate, supported by degenerate neutron gas pressure (akin to the degenerate electron gas pressure that supports a white dwarf). At this point the core becomes extremely rigid, so that further infalling gas rebounds from its surface, creating an outward shock wave (assisted by neutrinos formed by the inverse beta decay in the core) sufficient to blow off the outer layers of the star entirely. This is a supernova of Type II, as discussed in class when we described the operational definitions of Supernovae I and Supernovae II. The best-known supernova of Type II is SN 1987A, and we spent some time talking about is specific characteristics. We followed the generic description of supernova (of Type II) with comments about the most recent naked-eye supernova, Supernova 1987A, which occurred in the Large Megallanic Cloud (there were many unique aspects of SN 1987A that were discussed in class). The energetics of a Type II supernova are extremely surprising to most people at first, as 99 percent of the energy comes out in the form of neutrinos which sail by and through us with little detectable trace. Most of the rest of the energy (about one percent) is converted into kinetic energy of the outflowing gas, and a mere 0.0001 of the total energy is released as visible light - yet a single supernova can temporarily outshine a galaxy. The energy released in the few seconds of a supernova is comparable to the amount of energy our Sun will produce during its entire 10 billion year lifetime.
We then talked briefly about mass transfer in close binary systems, which can completely alter the evolutionary paths of the two stars as they alternately gain or lose mass. The eclipsing binary Algol (aka Beta Persei, aka the "Demon Star") shows evidence that mass has been transfered from one member of the binary to the other. Close binaries where mass transfer can take place are not very unusual, and we will be talking about such systems in our upcoming discussions of stellar remnants.
On Thursday we will make a few more comments about core collapse at the end of the productive nuclear burning lifetime of a massive star, and then we will take a more detailed look at the various types of stellar remnants and how they are observed.
Homework No. 3 was collected, and you were reminded that tonight is the next telescope session for our class, starting at 7:00 P.M. If in doubt about the weather, consult Quyen's web site (origins.colorado.edu/~hartq/astr1040), where she will post any decision about whether to do it or not by about 6:00 P.M. Note that the forecast calls for clearing during the evening, and that Quyen will be there awaiting the chance to get to work if it appears there is any likelihood of that happening. So you ought to go if that is the situation, and wait out the weather (something real astronomers have to do all the time!).
Two astronomy news items today:
A new study of a very dense star cluster near the galactic center, using the Hubble Space Telescope, has shown that there is a cut-off of stellar masses somewhere around 150 solar masses. Stars heavier than that apparently do not form. This is consistent with other observations (and with our class discussions!), but was not clear from model calculations. For more information, go to the HST public information web site.
The American Astronomical Society, the primary professional organization of astronomers in the U.S., has issued a new call to NASA to restore the servicing mission to the Hubble Space Telescope. this is part of a large-scale effort to reverse the decision to cancel all future servicing missions. We probably will not know if the decision will change until there is a new NASA Administrator, and that appointment has not yet been announced, even though the office is currently vacant.
Onwards to our discussions of stellar evolution, focusing today on the end points, the remnants left behind when stars complete all their nuclear reaction stages. We started with a quick summary of which mass of star turns into what kind of remnant, then we proceeded to talk about the remnants themselves; how they are observed, their structure, and their evolution if they have any life left in them.
For white dwarfs we discussed the fact that many are close enough to be observed optically, so that we can analyze their spectra and learn their properties in a direct observational way. We found that their spectral lines are very broad (pressure broadening) and redshifted (gravitational redshift) and that some lines are widely split by the Zeeman effect, which is due to a strong magnetic field. Their surface compositions reflect the final nuclear burning phase of the progenitor star, and we have helium white dwarfs, carbon white dwarfs, oxygen white dwarfs, etc. The internal structure is rather simple, consisting of nuclui and free electrons, whose degenerate gas pressure supports the star so that it does not contract. The internal temperature is uniform (isothermal) because the electrons transport heat by conduction, which is extremely efficient. A lone white dwarf does nothing but cool off, but very slowly (billions of years) due to the radiation-trapping effect of the thin layer of normal gas that surrounds the degenerate core.
But a white dwarf in a close binary system where mass transfer occurs can live again, or at least glow again, creating a general class of peculiar stars called cataclysmic variables. Classical novae are white dwarfs which accrete enough new matter on their surfaces to heat up to the point where the new gas ignites nuclear burning, so that the entire surface quickly reacts (due to the degenerate nature of the underlying core) and the star flares up in brightness by many orders of magnitude. Classical novae can re-occur, usually on time scales of several decades, as new matter builds up on the surface of the white dwarf after the previous outburst. A dwarf nova does the same thing, but on a much shorter time scale, flaring up (but not as dramatically as the classical nova) every few days or weeks. These novae-producing systems have accretion disks, as the inflowing matter from the companion star arrives with a lot of angular momentum, and cannot fall directly onto the white dwarf, instead swirling around in a disk from which gas can gradually trickle onto the white dwarf. In mass transfer binaries where the white dwarf has an extremely strong magnetic field, magnetic forces can dominate over gravitational ones, and normal orbital mechanics do not apply. In such systems, called polars, the incoming gas can fall directly (vertically) onto the white dwarf, causing more heating and more high-energy emission such as hard X rays. Finally, another class of white dwarf mass exchange binaries is represented by the super soft sources (SSS's), where the surface gravity is so high that the accreted matter is heated to the point of emitting thermal X rays (but low-energy ones, hence the "soft" in the name). These white dwarfs probably have high masses, close to the Chandrasekhar limit, so we might wonder what happens if they gain enough mass to go over that limit...
When a white dwarf exceeds the Chandrasekhar limit because of mass accretion, it can collapse to form a neutron star, or it can do something more spectacular: it can explode. Details are not known, but apparently a carbon white dwarf will undergo a "deflagration" reaction (which means it takes place throughout the entire interior, all at once) in which the total mass of the star undergoes nuclear reactions in a matter of seconds. This is a Type I supernova, which displays no hydrogen spectral lines (because it was a carbon white dwarf), and which leaves no stellar remnant behind. It just all blows up and is dispersed into the interstellar medium, mostly in the form of iron (Type I SN are the primary source of iron in the universe).
Finally, we had enough time to talk a bit about neutron stars. These are too dim to detect directly through their surface thermal emission, but as we will see, they can be observed in various other ways. Neutron stars were quite hypothetical until 1967, when the first pulsars were discovered. We will pick up from this point on Tuesday.
The second test in lecture will be on Thursday, April 7, and will focus primarily on material covered in lecture since Test 1. The general style of the test will be similar to Test 1, with a combination of discussion-style questions and a few quantitative problems. Quyen is planning to devote the recitation sections the previous day to a review, to help you with preparation for the test.
Astronomy news du jour:
The second of the two Mars Rovers has benefited from a scouring of the solar panels by a Martian dust storm, whuch has clear off the dirt and enhanced the electrical output of the panels. These two small robots just keep on ticking!
The President has announced that Michael Griffin has been nominated as the new Administrator for NASA, subject to Senate approval. Griffin, a Ph.D. physicist with several additional degrees, is currently director of the Applied Physics Laboratory, which is affiliated with Johns Hopkins University, and which has designed and built many science satellites including the upcoming New Horizons mission to Pluto and the Kuiper belt. Griffin's position regarding the possible re-institution of servicing missions to the Hubble Space Telescope is unknown, though there may be reason for hope that he favors this, given his ties to Maryland, where the HST Science Center is located. On a related matter, Barbara Mikulsky, the senior senator from Maryland, has been applying very strong pressure on NASA to keep open the option of allowing astronauts to service the Hubble, and she is on a couple of very powerful committees which have clout with NASA. Stay tuned...
We spent the rest of the class talking about stellar remnants, specifically neutron stars and black holes. I brought slides to introduce our next topic, the Milky Way galasy, but we never got there due to all the fun we were having talking about these bizarre stellar objects. We will start the Milky Way discussion first thing on Thursday.
Back to stellar remnants: Neutron stars, once thought to be purely a theoretical construct with no hope of their being detected, now are observed fairly routinely - but only under special circumstances. Pulsars were discovered in 1967 as rapidly-repeating radio sources (frequencies up to several pulses per second) and it was not long before astronomers recognized that the observations were consistent with beamed radiation from rapidly rotating neutron stars. Data on the pulsar found in the Crab nebula quickly added support to this picture, as the pulsar there is gradually slowing, and the amount of rotational energy it is losing (if indeed it is a rotating neutron star) is precisely what is needed to explain the luminosity of the nebula. You will do an exercise in tomorrow's recitation in which you get to calculate this for yourselves.
The second way in which neutron stars can be detected is when they are members of close, mass-transfer binary systems. Then matter spiraling in from the companion star can form an accretion disk around the neutron star, and gravitational and rotational forces combine to compress and heat this disk to temperatures so high (of order 100 million K) that the disk emits thermal X rays. Such systems are recognized as binaries due to the periodic eclipses of the X ray source as it orbits its giant companion.
Finally, we turned our attention to the ultimate stellar remnant, the black hole. When a massive star undergoes core collapse at the end of its nuclear burning lifetime it may turn into a neutron star, but only if the core mass is less than the limit that can be supported by degenerate neutron gas pressure. If the final core mass exceeds the neutron star limit (about 3 solar masses, depending on rotation), then there is no known pressure source that can halt the contraction. The result is a black hole, something easier to describe mathetically (using general relativity theory) than physically (because we have no way to observe what happens to the star once it contracts within its Schwarzschild radius or event horizon). The collapse continues indefinitely. As was the case with neutron stars, the concept of a black hole preceded any serious thoughts of detection - but events led to the detection of black holes as well as neutron stars (OK, we have to be fair and say indirect detection because we cannot actually see a black hole). Stellar black holes (as opposed to the supermassive ones found in the cores of galaxies) are best detected through observations of X-ray binary systems where the application of Kepler's third law demonstrates that the unseen companion to a normal star has too much mass to be either a white dwarf or a neutron star. Many such systems are known today, and astronomers have little doubt that black holes exist.
Reminder: We decided to have Test 2 on Thursday, April 7. There is no new homework assignment yet, but there probably will be, shortly after spring break.
You should be reading along in the textbook, which is quite good in many of the areas we are currently discussing. The material on stellar structure and evolution is in Chapters 20 - 23. Today we ventured off to the next topic, the Milky Way galaxy, which is described in Chapter 23 (but note that we will be discussing the interstellar medium in this context, and our text describes the ISM in Chapter 18 - so you should review that chapter as well).
Astronomy news: From the Cassini mission we learn that the Saturnian moon Enceladus has been found to have a tenuous atmosphere. This may not surprise planetary scientists, as it was already known that Enceladus is undergoing continual resurfacing with water ice which is probably outgassed from its interior (as a by-product of tidal stresses caused by other satelites).
Follow-up: The President's designated (but not yet approved) new Administrator for NASA, Michael Griffin, is known to be sympathetic to the Hubble Space Telescope and to Maryland politics, so many of us here at Colorado who are awaiting a reversal of the previous decision not to service the Hubble in the future are now optimistic that this decision may soon be reversed, and that we will get back on track toward installing our CU ultraviolet spectrograph aboard the HST. Stay tuned...
Then we spent the rest of the class talking about the Milky Way galaxy. I started with some slides, while posing the question of how astronomers figured out that our galaxy is a disk-like structure with spiral arms, since we have no way of directly observing that structure from our position within the disk. This led to a summary of historical observations and conjectures by the likes of Herschel and Kapteyn, and more modern observations by Shapley, and analyses of stellar motion by Oort and Lindblad. The upshot was that, by the early 1920s, astronomers were convinced that we live in the disk of a flattened galaxy, and that the center of rotation of this disk is far from Earth (more than 10,000 pc, or 10 kpc) in the distance scale known at the time.
The main complicating factors for astronomers, in addition to our inability to travel several thousand light years away and look back at our galaxy, were that one of the key distance determination methods used by Shapley and others in the 1920s is more complicated than realized at the time (Cepheid variables come in two types, with different period-luminosity relations) and the presence of ubiquitous interstellar dust, which dims the light of distant stars, was not yet recognized. Nevertheless, in the 1920s it was realized that we live in a large spiral galaxy, at a position far removed from its center.
The next step is to determine the overall properties of this ensemble, and today we finished by talking about how to weigh the Milky Way; how to find out its mass. Using simple Keplerian mechanics we find a mass for the visible disk of about 100 billion Suns; but examination of the galactic rotation curve indicates that the total mass, including matter outside of the Sun's position, might be as much as ten times greater. We will start the next class (after Spring Break, on March 29) by discussing what this unseen matter might be and how to detect it. Have a great break!
Spring Break - no class!
Announcements and reminders:
Homework No. 4 was handed out, and is due a week from today (April 5).
Test 2 will be a week from Thursday (i.e., April 7). This test will focus on material covered in lecture since the previous test. Quyen will devote part of the recitation next week (April 6) to a review, as an aid in preparing for the test.
Readings in the textbook: Recently we have covered material from Chapters 20 - 22 (stellar structure and evolution, and remnants), and today we got well into material from Chapter 23 (the Milky Way galaxy), with some additional information from Chapter 18 (the interstellar medium) as well. You should read all of these chapters, keeping in mind that the test will be based on material discussed in lecture. And very soon (this Thursday) we will begin discussion external galaxies, so you should be looking at Chapter 24 also.
A few items came up since our last class:
NASA has moved the Space Shuttle Discovery into the Vertical Assembly Building (VAB) at the Kennedy Space Flight Center, where the solid-fuel booster rockets and the external fuel tank will be installed in preparation for the upcoming return to manned space flight. This first flight since the Columbia disaster will be primarily a check-out of new safety procedures, but will also include a delivery of supplies to the Space Station. The launch window is from May 15 until June 3.
NASA has initiated a new study of the possible toxic and instrument-damaging effects of lunar dust, in anticipation of the new mission to send humans to the Moon (and then Mars). Some of us thought that these questions were all answered in the 1960s and 1970s, during the Apollo program.
The Deep Impact mission has undergone its first full review since its launch on January 12, as all is going well with the exception that the optical camera associated with the High Resolution Instrument has not focused properly. Measures are being taken to correct the focus, but given that all other instruments are performing beautifully, mission officials are saying that even if this focus of this camera cannot be improved, all mission science goals will be achieved. Deep Impact will encounter Comet Tempel 1 on July 4, 2005, when its impactor module will be released into the path of the comet's nucleus so that the results of the impact (crater size, composition of released gases and solids) can be analyzed.
And finally, some really cool new science results: The Spitzer Space Telescope has directly detected infrared emission from two extrasolar planets. Both planets were already known to be in orbital planes seen edge-on from the Earth, so that the planets periodically pass behind their parent stars. By subtracting the IR flux from each system when the planet was hidden behind the star from the total IR flux when the star and planet were both visible, Spitzer astronomers were able to measure the excess IR radiation from the planets. This allowed the derivation (using Wien's law) of the surface temperatures of both planets, each of which was found to be about 1100 K. This is far hotter than the gas giants in our solar system, but not surprising given how close these extrasolar gas giants are orbiting to their parent stars.
We then turned our attention back to the Milky Way galaxy. I started by reminding you of how the galaxy's general properties were discovered, including the application of new distance determination methods (primarily the Cepheid variable period-luminosity relation), and by reviewing the derivation of the galaxy's mass (internal to the Sun's orbit) by assuming Keplerian motion for stars in the outer disk. The flat rotation curve out to distances well beyond the Sun's position indicates that most of the mass of the galaxy lies beyond the visible disk, in an outer halo that is not visible. The term "dark matter" applies here for the first time in our class, but will be discussed again and again as we explore external galaxies and the mass content of the universe as a whole.
Possible components of the dark matter in our galaxy's halo include dim stars, either normal red dwarfs or compact stellar remnants, and elementary particles such as WIMPS (Weakly Interacting Massive Particles), or all three. Normal red dwarfs have been ruled out by sensitive Hubble Space Telescope searches, but compact stellar remnants (primarily white dwarfs) may contribute a significant fraction of the unseen mass, as indicated by MACHO observations (the use of gravitational lensing to infer the presence of unseen stellar objects in the halo).
We then turned our attention to the interstellar medium (ISM), and spent the rest of this class on it. The ISM, despite being so low in density as to almost be non-existent, is important as it is the source of raw material for star formation as well as the repository of material ejected by stars as they evolve (via stellar winds and nova and supernova outbursts). The ISM is not uniform, instead having a variety of physical conditions ranging from dark molecular clouds to diffuse (transparent) clouds to a very hot intercloud medium (heated by mechanical energy due to supernova explosions and rapid stellar winds; the ISM is a very violent place!).
At the end of today's class I began a discussion of the chemistry of interstellar clouds, with an explanation of molecular infrared and radio spectral lines as consequences of vibrational and rotational energy level transitions. I then began a brief talk about a very intriguing research problem, the unidentified diffuse interstellar bands (DIBs) that I have worked on for most of my professional career. We will begin Thusday's class by completing that discussion, then talking about the spiral structure of our galaxy, the weird things going on at the galactic center, and the formation and evolution of the Milky Way. Then we will start talking about galaxies beyond ours (for this, read Chapter 24).
Repeat of several announcements, and a new one as well:
Homework No. 4 was assigned in class on Tuesday, and is due next Tuesday (April 5). While it is now on the web site, you really need to have a printed copy of this assignment, as there are a couple of graphs that I have not taken the time and effort to convert into digital files and provide online. So, if you do not have a copy of this assignment, you need to see me very soon to get one.
Test 2 will be next Thursday (April 7). It will cover all material discussed in class since Test 1, which is essentially all of stellar structure and evolution (Chapters 19 - 21), stellar remnants (Chapter 22), and the Milky Way galaxy (Chapter 23 with some of Chapter 18 as well). In next Tuesday's class we will begin to discuss external galaxies (Chapter 24). Use your lectures note as your guide for studying. Quyen will spend part of next Wednesday's recitation section as a review to help you prepare.
The new announcement: Fiske Planetarium will host a special show on Saturn next week, on both Thursday and Friday evenings (April 7 and 8), called "Unveiling Saturn." The show will focus on results from the Cassini mission and will be presented by Josh Colwell of APS and LASP, who is a member of the ultraviolet spectrometer team for Cassini. Starting times are 7:30 both nights, and there is an admission fee ($5 for students). Check out the Fiske Planetarium web site for more details.
The lecture today started with an overview of a very intriguing interstellar medium problem that I have worked on for most of my career. There is a large number (now known to be over 700) of absorption bands that are formed in diffuse interstellar clouds - but not even one of them has been identified yet. Known as the diffuse interstellar bands (DIBs), these features are now thought to be formed by a family of large carbon-bearing (organic) molecules, perhaps the ions of polycyclic aromatic hydrocarbons (PAHs), which recently were found to be abundant in the ISM. Astronomers, chemists, and astrobiologist have all become interested in this problem, and I am involved in a laboratory study here at CU, with colleagues in the Chemistry department, aimed at a better understanding of the chemical reactions undergone by these molecular ions in space. At the same time I continue to conduct telescopic observations of the DIBs, in a continuing effort to help limit the possible species that could form them.
That aside, we then returned to our discussion of the structure of the Milky Way, with information on its spiral arms; how we know our galaxy is a spiral; how the arms were formed; and how they are maintained. Much of this dicussion assumed that you understood the information presented to you in yesterday's recitation sections, where Quyen explained the atomic hydorgen spin-flip transition and the emission of the 21-cm radio line.
We finished today's class with the story of the nucleus of the Milky Way, where energetic activity is seen associated with the point source Sagittarius A*, which has been identified as the true center of rotation of the galaxy. Studies of orbital motions close to Sgr A* indicate that an enormous mass (more than a million solar masses) exists there in a voilume far too small to be anything but a black hole. Thus the Milky Way is now recognized as belonging to the large class of galaxies with active nuclei dominated by supermassive black holes.
At the beginning of the next class we will follow up on preliminary remarks I made today about the history and evolution of the Milky Way, and then we will move on to a discussion of external galaxies.
The usual reminders:
Test 2 is this Thursday (April 7). Similar format as Test 1; data sheet will be provided again; bring calculators. Coverage is stellar structure and evolution, including life stories of stars of different masses; stellar remnants; the Milky Way galaxy; and the bare beginning of our discussion of galaxies external to the Milky Way (which we just started today).
In addition to the special Fiske Planetarium shows on Cassini results from Saturn this Thursday and Friday (see details in the class notes for March 31), another special event is coming up:
The NASA-sponsored National Astrobiology Institute, which includes a Colorado "node" (of which I am a member, owing to my work on interstellar organic materials) is having its bicentennial meeting here in Boulder next week. So there will be a lot of scientists in town who are serious about ET life and how to find it. Most of the meeting is closed to the public, but there will be a special presentation on "Astrobiology and Cosmology, Science, and Religion: Our Place in the Universe," on Wednesday evening. This is free to the public and will take place in Macky Auditorium starting at 7:00. Click here for information on the event and the four speakers for the evening.
There was an announcement from NASA a few days ago, about the Hubble Telescope servicing mission, that looked alarming at first - but was actually no surprise and does not affect chances that a manned servicing mission could be restored. The announcement formally canceled NASA's plan to develop a robotic mission to visit the Hubble and install new equipment and science instruments, which had been NASA's official goal - but which few ever believed could be done. So that idea is officially dead (except for the remaining possibility of developing a robotic mission only to install a rocket motor to safely de-orbit the Hubble at the end of its lifetime). In the meantime, reconsideration of a manned Shuttle mission to the Hubble may occur as soon as next week, when the nominee for NASA Administrator, Michael Griffen, has his Senate confirmation hearings. Stay tuned...
Today's lecture started with a series of slides showing external galaxies, with commentary on their properties such as galaxy type, size, and luminosity, and their distribution in groups and clusters. For spiral galaxies the distinctions between stellar populations were introduced as we looked at the images.
We then completed our discussion of the Milky Way galaxy, by applying the Population concept to it (including a table of which kinds of objects are Population I and which are Population II), and then by describing the standard model of a collapsing rotating spherical cloud where the first stars to form (Pop. II objects in the halo and bulge) have a spherical distribution while stars formed after collapse to a disk represent Pop. I and orbit in the plane of the disk. There are discrepancies in this simple picture, though, because there are no stars with zero heavy elements, suggesting that some star formation must have occurred even before the pre-galactic cloud had formed; and because the globular clusters, traditionally considered to be primordial and all formed at the same time, display a range of ages from 9 to 14 billion years. These facts demand a revision of the standard model for Milky Way formation, to include the mergers of smaller systems such as globular clusters and dwarf galaxies over time. The modern view of Milky Way formation, and that of large galaxies in general, is that these systems grow by ingesting small neighbor galaxies such as the many known to accompany both M31 and the Milky Way.
We finished today's lecture with initial comments on external galaxies, starting with historical anecdotes about how astronomers discovered that galaxies exist outside of our own. This issue was debated in 1920 by Shapley and Curtis, but was not settled until 1926, when Edwin Hubble found Cepheid variable stars in the M31 nebula and used the period-luminosity relation to find their distances from Earth. Hubble found that these stars, hence M31 itself, were far too distant to belong to the Milky Way.
Hubble went on to study and classify galaxies, introducing the terms "elliptical" and "spiral" to designate the two general types. He organized the galaxy types into a split sequence (shown schematically by the "tuning fork" diagram) that he thought might represent evolutionary stages, with the idea that a galaxy would evolve from one type to the next. We now know that this is not generally the case, as galaxies of all types and subtypes are found to have very old stars in them and are therefore roughly the same age. We will pick up from this point next Tuesday when my lecture will be about how to measure the basic properties of galaxies such as distances, masses, and luminosities.
Test 2 today; no lecture.
Test 2 was returned! A new record! Answer sheets were handed out also. Homework 4 did not fare quite as well, as we gave priority to grading the test, but we expect to have the homework back to you this Thursday.
Astronomy news: The Senate confirmation hearing for Michael Griffin as NASA Administrator took place this morning, and went quickly and smoothly. He will be in office within a few days. During the questioning Griffin said that once the Space Shuttle is back in operation (next month) he will reassess the decision about servicing the Hubble Space Telescope with a manned Shuttle mission. Astronomers are optimistic that this means a positive decision, and if so this has huge implications for CU astronomy because it would mean that our new UV spectrograph would be installed aboard the Hubble after all. We are all keeping our fingers crossed...
Then we talked about galaxies. The material for this lecture and the next one or two is in Chapter 24 of your textbook, so please read it. Today I talked about the Hubble classification system and the relative populations of galaxies of different types (dwarf spheroidal systems being apparently the most common in the universe), and then I summarized distance determination methods for galaxies, starting with Cepheid variables for relatively nearby galaxies, then to other kinds of standard candles up to the ultimate one, Type I supernovae. Next I introduced the Hubble expansion law, with a little historical background on how it was discovered, but with emphasis on how it can be used to find the distance to any object whose spectrum, hence redshift, can be measured. We will talk about the cosmological implications of the expanding universe later.
We then turned our attention to measuring the other properties of galaxies, such as the mass and luminosity, and this included a discussion of the mass-to-light ratio, an indicator of the stellar content of a galaxy.
Finally, we began a discussion of the distribution of galaxies (and visible matter in general) in the universe. The subject of galaxy groups and clusters started with an introduction to the Local Group and then moved on to the distinction between groups like this one and the much larger rich clusters of galaxies. Rich clusters are dynamically relaxed systems whereas small groups are not. We will pick up from this point on Thursday.
Announcements and reminders:
Homework 4 was returned, along with an answer sheet (necessitated by the fact that you need to see the graphs, and I have not taken the time to scan them and put them on the web site - so if you were not in class today, be sure to get an answer sheet when you pick up your homework).
We then turned our attention to groups and clusters of galaxies, starting with more commentary from me on the importance of dynamical relaxation in rich clusters, which allows their masses to be determined from the velocity diseprsion of galaxies. Evidence that these clusters have undergone extensive gravitational interaction comes from the predominance of elliptical galaxies in the central regions, which is thought to be the result of frequent gravtational encounters and tidal interactions and stripping of interstellar material from spiral galaxies; from the existence of intracluster gas which is very hot (so it emits themal X rays) and which is enriched chemically, suggesting that this gas has been stripped out of galaxies where stellar processing had occurred; and the presence of giant elliptical galaxies at the centers of many rich clusters, presumably as the result of galactic mergers.
We then talked about the hierarchy of clustering in the universe, leading up to the realization that superclusters of galaxies exist and that they are organized into a vast network of walls and voids (nowadays referred to as the "cosmic web"). The size scale and the form of this structure cannot be the result of random gravitational encounters, and must therefore represent intrinsic structure that the universe was born with. We will return to the question of how this structure arose a bit later.
Before moving on to our discussions of cosmology, we then returned to galaxies for an interlude about active galaxies and quasars. These objects have a lot to tell us about the origin and evolution of galaxies and also about the universe itself, since some of them (the quasars specifically) act as signposts to the farthest observational reaches. We started with a few slides showing some active galaxies, and then began a systematic description of them, beginning with radio galaxies and Seyfert galaxies. We will move on from there in the next lecture.
Homework 5 assigned today; be sure to get a copy from me or download it if you were not in class. It is due next Tuesday, April 26.
Here are some important comments about this homework:
You will have to use the relativistic Doppler shift formula for many of the galaxies in the list. If the fractional shift (delta lambda/lambda) is as large as 0.1, then it becomes important to use this version of the Doppler shift. The equation for the relativistic Doppler shift is in your textbook and also on the data sheet that I have provided during our tests in this class.
Also, in part (b) of the problem, where you are asked to calculate the age of the universe using the value of the Hubble constant that you determine in part (a), the correction factors of 2/3 and 0.9 take into account the fact that the expansion rate has not been constant since the beginning of the expansion. The 2/3 factor comes from standard big bang models, in which it is assumed that the expansion has simply slowed since the beginning. The 0.9 factor comes from the more recent realization that the expansion is accelerating, which compensates for the initial slowing. So multiply these factors times the age you get from the simple 1/H calculation.
On Monday, April 25, there will be several celebrations around the country of the fifteenth anniversary of the launch of the Hubble Space Telescope. One of those celebrations, accompanied by the release of two new HST images, will occur at our very own Fiske Planetarium. Another will take place Monday evening at the Denver Museum of Nature and Science, in their IMAX theature, at 7:00 P.M. As luck would have it, I will be one of a small group of speakers at both events, as I have a long history with the HST.
Then it was on to our discussion of active galaxies and quasars. I completed the summary of properties of the various identified classes of active galaxies (radio galaxies, Seyfert galaxies, BL Lac objects). Quasars were introduced, and the case made that these are active nuclei of galaxies seen at high redshift, thus at very great distances and at times very long ago. Quasar spectra provide a wealth of information on intervening gas clouds,, such as primoridal clouds where no star formation has occurred (which are revealed by Lyman-alpha absorption systems) and galactic halos (which show up as metal-rich absorption line systems).
Announcements and reminders:
The press conference on Monday (April 25) to celebrate the 15th anniversary of the Hubble Space Telescope will be at 11:00, at the Fiske Planetarium. You are welcome to drop by.
Homework No. 5 is due Tuesday (April 26).
Our last class will be next Thusday (April 28), and our final exam will be just two days later, on Saturday, April 30 (10:30 A.M. to 1:00 P.M.).
I will hold a review session in preparation for the exam, on Friday (April 29), at 2:00 in room G2B-60 (basement level of Duane Physics). I will not have a prepared presentation, and will conduct the review by anwering youyr questions. So this will work best if you start studying before the review, so you will know which areas you want to ask me about.
Today's lecture ended about 10 minutes early, as I left so that you could fill in the Faculty Course Questionnaires.
Local astronomer Andrew Hamilton, of our department, has released a new study of galactic black holes in which he and graduate student Scott Pollack showed that the large size of a supermassive black hole event horizon means that tidal forces outside the horizon are not as great as they are outside of a stellar black hole - so if you happen to fall into a black hole, you are better off making it a supermassive one, where you will not be torn apart by the tidal force, instead getting in closer where you will be burned up by superheated plasma instead. You can learn more about this at Andrew's web site (which is a cool site anyway, with lots of stuff on black holes).
NASA announced that the sample collector panels from the Genesis mission, which crashed to Earth last fall, have been successfully retrieved from the wreckage and that they appear to be in perfect condition - thus ensuring that the original science goals of this mission, to capture and analyze solar wind particles to learn about the Sun's isotopic composition, will be achieved.
The Spitzer Space Telescope team held a press conference yesterday in Washington, to announce the discovery of an asteroid belt around a distant star (HD 69830), which is about 13 pc from Earth. This was the only case in a sample of 85 sun-like stars that showed evidence for an asteroid belt - and this belt is quite different from ours, in that it is much more massive and much closer to its star.
We turned our attention back to quasars as probes of the universe, and then we initiated our discussions of cosmology, the science of the universe as a whole, the Big Picture, the Whole Enchilada, etc. This is where we get to consider the grandest questions of all, about the cosmos, its origin, its future, and our place in it.
We started by considering the basic assumptions needed in order to characterize the universe. It's the only one we know, so we can't do comparative studies. Basic assumptions usually adopted include the postulates that the universe us both homogeneous and isotropic, meaning that it is generally similar everywhere, and that it looks the same in all directions. This is consistent with the general philosophy that we do not occupy a special place in the universe, and it is consistent with the basis of general relativity, which says that there is no special place, or reference frame, in the universe. General relativity led Einstein to develop a set of field equations describing the role of matter and energy in the universe, and from then until now the development of cosmological models has been done in this context. Solutions to the field equations led early theorists such as Einstein and de Sitter and LeMaitre to consider models in whcich the universe could expand or contract Le Maitre, as early as 1922, hypothesized an expanding universe that began in a highly compressed, hot state - note that this was before the expansion was discovered, and it was the predecessor to the big bang models to come later.
In the next class we will talk about the observational consequences of the various solutions to the field equations, and what the observations tell us.
Announcements and reminders:
Homework No. 5 was collected today.
Our last class is this Thursday, and the final exam is Saturday (April 30), 10:30 - 1:00, in our regular classroom. The test will be in the same format as our two mid-semester tests, and it will be comprehensive, covering the entire course. Use your lecture notes (and these online summaries) as your guide, as I hae done some thing very differently from the text. But the text is useful back-up, so you should be looking over all the chapters in Parts 3 and 4 of the book. There will be a few math problems on the final, so bring a calculator. I will provide the usual data sheet with all formulas and numerical values needed.
I will host a review session for the exam, on Friday at 2:00, in room G2B60 (basement level of Duane, two floors down from our classroom). I will not bring a prepared presentation; my plan is simply to be there to answer questions as long as some of you are there to ask them. I have the room for up to an hour and a half.
The only item today was a CU press release from our MCDB Department, about the discovery of microorganisms living inside of rocks in thermal pools at Yellowstone. The existence of these foolhardy critters is being taken as supporting evidence that life could have formed under similar conditions on Mars.
So, on to cosmology. Today I started with a brief review of the "standard" big bang model, in which there are three possible outcomes to the expansion: the open universe (negative curvature; expands forever though it may slow); the closed universe (positive curvature; expansion stops eventually and turns into a contraction); and the flat universe (expansion slows to a halt in infinite time). I commented that there was no a priori reason to expect any particular one of these three possibilities, and that initially most would have thought the flat universe very unlikely as it requires a precise balance between outward momentum and inward gravity - but, for reasons to be explained, a flat universe is apparently what we got.
I then discussed observational tests aimed at determining which outcome is the actual one. There are three general categories of tests: measuring the mass content of the universe to see whether gravity will overcome the outward momentum of the expansion; see what the expansion rate was long ago, to find out how much slowing (deceleration) has occurred; and determine the properties of the cosmic background radiation that is a natural consequence of the big bang model.
The first of these tests is posed in terms of whether the observed mass density of the universe exceeds the critical density for closure. Visible matter in the form of galaxies falls far short of the critical density, but adding in the dark matter in roughly the quantities inferred from galaxy rotation curves and galaxy cluster mass estimates, there is enough dark matter to bring the total mass density close to the critical value; i.e., the universe is close to being flat.
The second test, measuring changes in the Hubble constant over time, in principle should allow the expansion rate to be determined throughout past time, so that the presumed deceleration could be measured and used to determine whether the expansion will stop or not. But things went off the rails here, as astsronomers found to their surprise that the expansion is accelerating, and has been for about half the age of the universe. This implies a dark energy that began to overpower gravity when the universe was a few billion years old. This dark energy must be included in the calculation of omega nought, the ratio of actual density to critical density. Now we think of flatness as referring only to the geometry of the universe, which can be flat even though the expansion is going to continue speeding up instead of slowing to a halt.
The third observational constraint on the cosmological models is perhaps the most informative one. The cosmic background radiation, discovered in the 1960s, verifies the big bang model in general, and in specific it provides detailed information on the structure of the early universe, which is reflected in anisotropies (subtle temperature variations) in the modern background radiation. By interpreting these anisopropies in terms of acoustic oscillations in the early universe (at the time of decoupling, when electrons and protons combined and the universe became transparent) it is possible to determine very accurately the density and temperature of the universe at that time. The results are consistent with a flat universe.
In the next (last!) class we will wrap it all up, with a continuation of the big bang story, including an overarching model called the inflationary universe.
This is our last class (!). The final exam will be Saturday morning, at 10:30, in our regular classroom. See the notes from Tuesday's lecture (above) for a desctiption of the final and how to get ready for it
I will host a review session tomorrow afternoon, at 2:00, in Duane room G2B60, which is in the basement of Duane Physics (i.e., two floors below our classroom level). I will not make a prepared presentation, but will be there only to answer your questions.
The Deep Impact mission spacecraft has obtained its first images of Comet Temple 2, which will be its target for sending a massive chunk of copper into the comet's nucleus to see what comes out. The encounter will occur on July 4, and images will be obtained regularly until then, providing the best ones ever of a cometary nucleus in the last days before impact.
On to the universe. We completed our discussion of observational tests of the state of the universe, which included studies of the mass content, of the expansion and how its rate has varied, and of the cosmic background radiation. All three of these observational approaches are consistent with a flat universe (omega nought = 1), where the components of omega nought are normal (baryonic) matter 0.04; dark matter 0.21; and dark energy 0.75, for a total omega nought of 1.0.
We then considered how the universe started; what triggered the big bang expansion. Quantum mechanics tells us that a vacuum can have random energy fluctuations, and that if one of these fluctuations had sufficient energy density, a state called false vacuum is created, in which matter repels other matter, triggering an expansion. Because the density remains constant in a false vacuum, this expansion required the formation of new matter, thus leading to the universe. Note the interesting possibility that other random energy density peaks could cause the origin of other universes.
In considering how the universe came to be flat, Alan Guth in the 1980s posited that the universe must have once been small enough to be in full equilibrium so that it could be homogenous. This could only have happened if the universe was smaller than the distance light could travel over a time less than its age, which is not true today. So Guth postulated an early epoch (before about 10^-36 seconds) when the universe was this small, followed by a sudden expansion (called inflation) during which, within 10^-30 seconds, the size of the universe increased by a factor of 10^25 and it became larger than the distance light can cross over its own age. The inflationary model leads directly to a flat universe, and the fact that we seem to have such a universe was part of what inspired Guth to develop the model.
Next we discussed the origin and evolution of matter in the universe, starting with matter-antimatter particle pair formation during the early stages of the expansion, when photons had sufficient energy to equal the mass-energy equivalence of particle pairs such as proton-antiproton, neutron-neutron, and electron-positron. As the expansion cooled, each of these particles in succession "froze out" when the photon energy became too low to have sufficient energy to form that type of particle. Within the first four minutes after the expansion began, nuclear fusion reactions took place, starting with hydrogen (protons) and forming deuterium, helium, and traces of lithium. Reactions then stopped, for two reasons: there are no stable nuclei with mass number 8; and the universe became too cool and rarefied for fusion to continue. Thus the end of nuclear reactions during the big bang left the universe composed of about 78 percent hydrogen and 22 percent helium, with only small traces of anything else - and no heavy elements (as found by Ralph Alpher and George Gamow in the late 1940s).
Finally, the transition from the early big bang to the modern universe: At an age of about 300,000 years the free electrons and protons were able to combine and no longer be separated (ionized), which allowed radiation for the first time to travel freely over long distances (before this time, the free electrons, which scatter photons, had kept the universe opaque, like being in a dense but bright fog). Once the electrons became bonded to the protons, suddenly the universe was transparent, and thereafter the matter and the radiation were independent of each other, which is why this event is called decoupling. Today we see the radiation as the cosmic microwave background, and the matter as a combination of visible galaxies (organized into large-scale structures) and dark matter (we don't yet know how dark energy fits into this picture).
We know from the cosmic microwave background observations that the universe already had density fluctuations in it at the time of decoupling. Apparently these were triggered by quantum fluctuations in the pre-inflationary period and were then propagated and grew in size as inflation and then the standard big bang expansion proceeded. It is fascinating to realize that the 100-million light year sized structures we see in today's universe started from quantum fluctuations when the universe was in the first 10^-30 seconds of its history.
We finished with some brief remarks on the future of the universe. It will keep expanding forever; eventually (at about 10^14 years) all the hydrogen will be used up and star formation will stop, after which all the baryonic matter will reside in compact stellar remnants; at about 10^18 years planetary systems and galaxies will have dissipated due to gravitational encounters and tidal disruption; and at somewhere around 10^100 years all the stellar remnants, even the black holes, will have evaporated due to quantum mechanical tunneling. The final (permanent and perpetual) end state of the universe will be a sea of leptons (electrons and positrons) and very low-energy photons (as the cosmic background radiation approaches a temperature of 0 K).
So, we finished off the universe and our course right on time. It's been fun!
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