Stellar Structure and Evolution

Transcription

1 Stellar Structure and Evolution Birth Life Death

2 Part I: Stellar Atmospheres

3 Part I: Stellar Atmospheres Jan. 23: Intro and Overview of Observational Data (Chapters 3 and 5) Jan. 28: Basics of Stellar Spectra I (Chapter 8) Jan. 30: Basics of Stellar Spectra II (Chapter 8) Feb. 1: First PS due at 5:00 P.M. Feb. 4: Specific Intensity, Flux (Chapter 9.1) Feb. 6: Optical Depth (Chapter 9.1) Feb. 8: Second PS due at 5:00 P.M. Feb. 11: Radiative Transfer, Kirchoff s Laws (Chapter 9.3 and 9.4) Feb. 13: The Gray Atmosphere Problem (Mihalas paper from ApJ Issue) Feb. 15: Third PS due at 5:00 P.M. Feb. 18: Continuum Opacity and Stellar Atmospheres (Chapter 9.2) Feb. 20: Line Absorption, Line Profiles (Chapter 9.5) Feb. 25: First Test (Covers Section I, incl. Chapters 3, 5, 8 and 9)

4 Part II: Stellar Interiors

5 Part II: Stellar Interiors Feb. 27: Line Absorption: Equivalent Width, Abundances (Chapter 9.5) Mar. 3: Hydrostatic Equilibrium I. (Chapter 10.1 and 10.2) Mar. 5: Hydrostatic Equilibrium II. Mar. 7: Fourth PS Due at 5:00 P.M. Spring Break Mar. 24: Radiative and Convective Energy Transport (Chapter 10.4) Mar. 26: Nuclear Reactions (Chapter 10.3) Mar. 28: Fifth PS Due at 5:00 P.M. Mar. 31: Stellar Structure (Chapter 10.5 and 10.6) Apr. 2: Main Sequence Stars (Chapter 13.1) Apr. 7: The Sun I. (Chapter 11) Apr. 9: Second Test (Emphasis on Section II, incl. Chapters 10 and 13.1)

6 Part III: The Sun and Stellar Evolution

7 Part III: The Sun and Stellar Evolution Apr. 14: Post-Main Sequence Evolution (Chapter 13.2) Apr. 16: Red Giants/ AGB stars/ Planetary Nebulae Apr. 18: Seventh PS Due at 5:00 P.M. Apr. 21: White Dwarfs (Chapters ) Apr. 23: Supernovae, Neutron Stars, Pulsars, Black Holes (Chapters and 18.5, 16.6, 16.7, 17.3) Apr. 25: Eighth PS Due at 5:00 P.M. Apr. 28: Star Formation (Chapter 12.1 and 12.2) Apr. 30: Student Presentations (by graduate students) May 5: Star and Planet Formation (Chapter 12.3) TBD: Final Exam (3 hours) (1/2 of Final will emphasize Section III and 1/2 will be a comprehensive overview of the course.)

8 Text: An Introduction to Modern Astrophysics (2nd Ed.) by Carroll & Ostlie Grading: Homework (8) 36% Term Tests (2) 30% Final Exam (1) 34% Project for Graduate Students: Class Presentation on Apr. 30 Homework Policies: (1) You MAY work in groups but everyone should contribute and everyone hands in their own papers. Some questions will require short essays and must be written entirely on your own, although you may discuss these issues with others in the class. In fact, I ENCOURAGE you to work with others on the homework, to get used to the mode of collaborative learning that is common in science. (2) All Homework is due Friday by 5:00 P.M. NO LATE PAPERS WILL BE ACCEPTED... NOT EVEN BY 1 minute! If you have not finished everything by the deadline, then hand in what you have finished.

9 Test Policies: Tests will be closed book and will require a calculator. Term tests are 80 minutes long and the Final is 3 hours. Unlike the problem sets, tests are individual effort, not group effort. Studying for the tests is best done by a) reviewing all the problem sets and their solutions, b) reviewing your class lecture notes and c) doing the reading. Office Hours: My schedule is that I will generally be unavailable for help with the class material during the mornings or early afternoons of class days (Monday and Wednesday) or on weekends. I will generally be available at all other times. You may feel free to come to my office if I am in or to send e- mail to schedule a meeting time. It will be easiest to contact me by usually. In an emergency you may also call my office number (x3672) or my home phone (at polite calling hours please!) which is and is a local call from Middletown.

10 Lecture 1: Overview of Observations The Flux (F) of a star is a measure of how bright it is. In cgs units it is: F (ergs) (cm 2 sec) Brightness as measured at Earth (apparent brightness) in magnitudes (m) m = 2.5log(F ) + const To make the constant go away, the magnitude equation is almost always used for the difference of magnitude of two stars, which depends only on the ratio of their fluxes: m 1 m 2 = 2.5log F 1 F 2 If one of the stars is a standard star, such as Vega, whose magnitude is defined to be, say, zero through a standard filter, then one can just speak of a standard magnitude. The most common standard magnitude system is UBVRI.

11 Brightness as measured at 10 pc (absolute brightness) is defined as absolute magnitude (M), so using the fact that flux declines as one over distance squared increases yields the equation for the distance modulus (m-m): m M = 5logd 5 Note that if interstellar absorption is present then the apparent brightness is diminished by an amount in magnitudes (A) in which case: m M = 5logd 5 + A These quantities are often expressed for a particular wavelength region, commonly U,B,V, R or I in the optical or J, H, K, L in the Infrared. As an example, in the V band the apparent magnitude is written as V and the distance modulus equation becomes: V M V = 5logd 5 + A V Colors are used to report ratios of fluxes in different band passes, e.g. B and V B V = 2.5log( F B F V )

12 The term bolometric refers to integration over all wavelengths. A bolometric correction (BC) is needed to convert, say, V magnitude to bolometric magnitude (mbol). The sign convention varies but the BC is usually added (as a negative number) to V to get bolometric magnitude. m bol = V + BC The absolute bolometric magnitude Mbol is a measure of the total power of a star, or its luminosity (L), which has the units ergs/sec in cgs or Watts in mks. M bol M = 2.5log L L is a useful equation for relating the absolute bolometric magnitude of a star to its luminosity. Distance (d) measured in parsecs (pc) by parallax method for nearby stars: d(in pc) = 1 p.a.(in arcsec)

13 Important physical properties of a star are mass (M), radius (R), luminosity (L) and effective temperature (Te), as well as chemical composition and age. Of course there is much more we would like to know (e.g. internal structure, rotation rate, magnetic field strength, mass loss, planets??, etc., etc., but... :) Mass is only obtained directly from binary stars. We use them to calibrate a mass-luminosity relation for main sequence stars and then infer a mass for most stars from that. Many times we just don t know what the mass of a star is. Chemical composition is determined by analysis of the spectra of stars and we will discuss this later in some detail. The composition of stars does not vary too much. They are about 75% Hydrogen and 25% Helium by mass. Only the percentage of metals (everything other than hydrogen and helium) varies from about 0.01% to about 2% by mass. Most stars in the solar neighborhood have metal abundances similar to the Sun (2%) and are regarded as Population I stars. Those with significantly smaller metal abundances are called Population II. This is inferred to mean that they are generally older, having formed at a time in the Galaxy s history before many supernovae had exploded to create the metals.

14 Age is inferred from location on the HR diagram based on stellar evolution theory, as we will discuss. Most stars are billions (Gy) of years old. The Sun is 4.57 Gy. The age of the Universe is 13.7 Gy so all stars are younger than that. An important relationship exists between the other three stellar parameters: L = 4πR 2 σt 4 e This essentially defines effective temperature. In practice, we need either the spectral type or the true color (i.e. corrected for interstellar reddening) of a star to infer Te, and the apparent magnitude and distance to infer luminosity. Bolometric corrections come from the spectral type or color and the extinction correction comes from a comparison of the measured color and true color assuming a normal interstellar extinction law.

15 Here s an outline of how it usually works for a common case in which the observed quantities are the spectral type (SpT) and the magnitude in at least two colors (e.g. B and V): SpT ----> Te, (B-V)o, BC, (Mv sometimes) Color excess or E(B-V) = (B-V) - (B-V)o Extinction in V in a normal interstellar extinction law is: Av = R x E(B-V), where R is usually taken to be about 3, and Vo = V - Av Distance comes from Vo - Mv = 5 log d - 5, or alternatively, if d is measured independently (by parallax, for example) then Mv may be calculated from this relationship, rather than from SpT. Luminosity comes from calculating Mbol = Mv + BC and using solar calibration from equation above. Radius is calculated from L = 4πR 2 σt 4 e