Announcements for Labs. Phys1403 Stars and Galaxies Instructor: Dr. Goderya Lab 6 Measuring magnitude of stars as a function of time, now Due on Monday April 23 rd During class time Lab 13 Last Lab of the semester to be assigned this Thursday week. Exam 2 Wednesday April 18 th During class time 40 multiple choice questions and 1 short answer question. Chapters Light and Telescope Atoms and Starlight The Energy production in Sun The Family of Stars The Interstellar Medium The Formation and Structure of Stars Sample Questions on class webpage after Thursday 12 th April. Expect to see numerical questions: You can use 1 US Letter size cheat sheet with equations, constants and conversion factors. Bring a calculator, green scantron and pencil. Foundations of Astronomy 13e Seeds Chapter 12 Stellar Evolution Topics for Today s Class 1. Zero-Age Main-Sequence Stars (ZAMS) 2. Post Main-Sequence Evolution 3. Star Clusters: Evidence of Evolution 4. Variable Stars: Evidence of Evolution Guidepost In this chapter, you will consider how stars develop along their lifespan Why is there a main sequence of star properties? Why is there a relationship between masses and luminosities of main-sequence stars? How does a star s structure change as it uses up its hydrogen fuel? What is the evidence that stars actually evolve? 1
12-1 Main Sequence Stars Problem: Insides of stars cannot be directly observed This limits testing hypotheses about stellar interiors Solution: Make a zoo of stars and study their exteriors Studying exteriors of stars can help us understand their interiors Observe stars in different stage of their stellar evolution. So we can understand their life cycle 12-1 Underlying Principle Stars are born, evolve, and die according to their mass and structure Structure in a star refers to the temperature, density, pressure, in each layer. Because each layer, like an acrobat in a circus stunt, must support the weight of everything above, astronomers can compute the conditions in each layer from the surface down to the center. Four Laws of Stellar Structure Stellar Models of our Sun From these four laws, a stellar model can be computed A stellar model is a table of numbers that represent conditions inside a star. Such tables can be computed using the four laws of stellar structure, shown here in mathematical form. The table in this figure describes the present-day Sun. How Do We Know? 12-1, Part 1 Mathematical models A group of equations designed to mimic the behavior of objects and processes that scientists want to study Astronomers build mathematical models of stars to study the structure hidden deep inside them. Scientific models are only as good as the assumptions that go into them and must be compared with the real world at every opportunity How Do We Know? 12-1, Part 2 Models of stars are difficult to test against reality, but do predict some observable things Stellar models predict the existence of: A main sequence The mass luminosity relation The observed numbers of giant and supergiant stars The shapes of star cluster H R diagrams 2
Maximum Masses of Main-Sequence Stars, Part 1 Massive clouds -> fragment into smaller pieces during star formation Very massive stars lose mass in strong stellar winds Minimum Mass of Main-Sequence Stars, Part 2 At masses below 0.08 M sun, stellar progenitors do not get hot enough to ignite thermonuclear fusion brown dwarfs (a) This star-formation nebula in the constellation Carina contains the massive star Eta Carinae (60-70 solar mass). (b) Eta Carinae is actually two stars in a binary system, and they are so massive and luminous that they are rapidly losing mass and inflating two lobes with a disk of ejected material like a plate pressed between two basketballs. Each lobe is about half a light-year in diameter. Gas outside the lobes is high-speed gas expelled in the outburst of 1841. (a) Only 12.7 ly from the Sun, a brown dwarf orbits a low-mass M main-sequence star. Photographic effects give the brown dwarf a blue cast in the image, but if you could visit it, you would see an object slightly larger than the planet Jupiter glowing muddy red with a temperature slightly more than 1000 K. Brown Dwarfs Difficult to find because they are very faint and cool emit mostly in the infrared Have been detected in star forming regions Recall: Formation of Stars As a protostar contracts, it heats up due to free-fall contraction Evolutionary track from birth to Main Sequence state Free-fall contraction (b) Observations of brown dwarfs suggest that some have shifting weather patterns, as shown in the artist s conception. (a) This H R diagram has been extended to very low temperatures to show schematically the contraction of a dim, cool protostar. Evolution on the Main Sequence, Part 1 Evolution on the Main Sequence, Part 2 Main-sequence stars live by fusing H to He A star is called zero-age main A star s life time T ~ energy reservoir / luminosity sequence (ZAMS) when it starts fusion reaction of H. Massive stars have short lives! Conversion of H to He continues and the star becomes more Spectral Mass Luminosity Approximate Years on luminous and cooler moving Type (Sun = 1) (Sun = 1) Main Sequence towards the dash line. 0 5 40 400,000 1 times 10 superscript 6 Upper B 0 15 15,000 10 times 10 superscript 6 Once a star consumes all of the Upper A 0 2.5 25 1 times 10 superscript 6 hydrogen in its core, it can no Upper F 0 1.7 6.4 3 times 10 superscript 6 longer remain a stable mainsequence star. Upper G 01.1 1.4 9 times 10 superscript 6 Upper K 0 0.8 0.4 20 times 10 superscript 6 Ages of stars are shown. Upper M 0.5 0.05 100 times 10 superscript 6 (Evolutionary tracks adapted from 0 the work of Iko Iben.) 3
12-2 Post-Main-Sequence Evolution He Core + H-burning shell produce more energy than needed for pressure support Expansion and cooling of the outer layers of the star Red Giant When a star runs out of hydrogen at its center, it ignites a hydrogen-fusion shell. The helium core contracts and heats while the envelope expands and cools. Expansion onto the Giant Branch Our Sun will expand beyond Earth s orbit! Post main sequence evolution on H-R Diagram Massive star moves into the region of the supergiants such as Rigel and Betelgeuse. Medium-mass star moves into the region of the giants such as those shown here. (Evolutionary tracks adapted from the work of Icko Iben.) Condition in Helium Core: Degenerate Matter Matter in He core has no energy source left (No Fusion): electrons cannot be packed arbitrarily close together and have small energies Electron energy levels are arranged like rungs on a ladder. In a low-density gas, many levels are open, but in a degenerate gas all lower-energy levels are filled. That causes the strange behavior of degenerate matter. Helium Flash The onset of He fusion occurs very rapidly, in an event Stars like the Sun suffer a helium flash No He Flash in massive stars Stars less than 0.4 times the mass of the Sun cannot get hot enough to ignite helium. (Evolutionary tracks adapted from the work of Icko Iben.) Red Giant Evolution Red Giant Evolution (3 Solar-Mass Star) He fusion through the Triple-Alpha Process When a star runs out of H at its center, the core of He contracts to a small size, becomes very hot, and begins H nuclear fusion in a shell (blue). The outer layers of the star expand and cool. The red giant star shown here has an average density much lower than the air at Earth s surface. 4
Fusing Elements Heavier than Helium Requires very high temperatures; occurs only in very massive stars Energy generation in giant stars more massive than about 4 solar masses begins with carbon fusion and leads to many reactions involving heavier nuclear fuels. Eventually Gravity wins over 12-3 Star Clusters: Evidence of Stellar Evolution Stars in a star cluster all have approximately the same age all stars orbit the common center of mass of the cluster An open cluster is a collection of 10 to 1000 stars in a region about 25 pc in diameter. Some open clusters are quite small, and some are large, but they all have an open, transparent appearance because the stars are not crowded together. Star Cluster H-R Diagram The H R diagram of a star cluster can make the evolution of stars visible. Same age but masses different The H R diagram of a star cluster provides a snapshot of the evolutionary state of the stars at the time you happen to observe them. This diagram shows the 650- million-year-old star cluster called the Hyades in the constellation Taurus. The upper main sequence is missing because the more massive stars have died Very few stars in Giant phase Example: HR diagram of the star cluster M 55 High-mass stars evolved onto the giant branch Turn-off point Low-mass stars still on the main sequence Estimating the Age of a Cluster The lower on the MS the turn-off point, the older the cluster. From theoretical models of stars, you could construct a film to show how the H R diagram of a star cluster changes as it ages. You can then compare theory (left) with observation (right) to understand how stars evolve. Note that the time step for each frame in this film increases by a factor of 10. 5
Common Misconception Misconception: Stars are constant and unchanging Truth: Stellar models show that stars slowly evolve as they consume their fuels, and evidence from H R diagrams confirms these slow changes in structure Pulsating Stars Stars that grow and shrink in diameter periodically Cepheid Variables (period less than 100 days) RR Lyrae variables (period less than 1 day) Mira variables (period greater than 100 days) They are also used as standard candles (distance calibrators) On HR diagram found in the instability strip www.konkoly.hu RR Lyra Variable Cepheid Variable 12-4 Pulsating Stars: Evidence of Stellar Evolution Some stars show intrinsic brightness variations not caused by eclipsing in binary systems The star Delta Cephei changes its brightness from about magnitude 3.6 at brightest to about magnitude 4.5 at faintest, a reduction by more than a factor of 2. The magnitudes of a few other stars in the constellation Cepheus are given here for comparison. A graph of the brightness of Delta Cephei versus time shows that it varies in brightness with a period slightly longer than five days. Cepheid Variables: The Period-Luminosity Relation The variability period of a Cepheid and RR Lyrae variable is correlated with its luminosity More massive variable stars are larger and more luminous and pulsate with longer periods than less massive variables. Consequently, there is a period luminosity relation: Type I and type II Cepheids have different chemical compositions. The RR Lyrae stars have lower luminosities and shorter periods. (Evolutionary tracks adapted from the work of Icko Iben.) Pulsating Variables: The Instability Strip Pulsating Variables: The Valve Mechanism For specific combinations of radius and temperature, stars can maintain periodic oscillations. Those combinations correspond to locations in the Instability Strip Cepheids pulsate with radius changes of ~ 5 10 %. Partial He ionization zone is opaque and absorbs more energy than necessary to balance the weight from higher layers. => Expansion Upon expansion, partial He ionization zone becomes more transparent, absorbs less energy => weight from higher layers pushes it back inward. => Contraction. Upon compression, partial He ionization zone becomes more opaque again, absorbs more energy than needed for equilibrium => Expansion 6
Period Changes in Variable Stars Periods of some Variables are not constant over time because of stellar evolution Like a clock running just a bit slow, the Cepheid variable star X Cygni has been reaching maximum brightness later and later for most of this century. This is shown by the upward curve in this graph of its observed minus predicted times of maximum brightness. As it evolves to the right across the instability strip, it is slowly expanding, and its period is growing longer by 1.46 seconds per year. Acknowledgment The slides in this lecture is for Tarleton: PHYS1411/PHYS1403 class use only Images and text material have been borrowed from various sources with appropriate citations in the slides, including PowerPoint slides from Seeds/Backman text that has been adopted for class. 7