Physics 576 Stellar Astrophysics Prof. James Buckley. Lecture 1 Mapping the Universe

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1 Physics 576 Stellar Astrophysics Prof. James Buckley Lecture 1 Mapping the Universe

2 Physics 476/576 Course Outline Stellar Structure and Evolution (and other topics in Astrophysics),Crow 205, 11:30-1:00 Instructor: Professor James Buckley (no TA) Office: Compton 253 Office hours: TBD Textbook: Advanced Stellar Astrophysics, William K. Rose Other Books: Radiative Processes in Astrophysics, Rybicki and Lightman, Principles of Stellar Evolution and Nucleosynthesis, Clayton, Quarks and Leptons, Halzen and Martin Course requires a knowledge of undergraduate E&M, Quantum Mechanics, Mechanics and Statistical Physics (but will review material as it arrises) Grade based on one midterm (30%), homework (40%) and final exam project (30%). Class attendance is required.

3 Physics 576 Syllabus Introduction: astronomical coordinates, distance, magnitudes and nomenclature Theory of radiation Statistical physics and thermodynamics Black-body radiation Stellar Structure: hydrostatic equilibrium, radiative transfer, convective transfer, nuclear burning, the Lane Emden equation for Polytropes Virial theorem and applications Quantum statistics Relativistic quantum mechanics, Dirac equation, fermions and bosons, quantum statistics, Einstein coefficients Reaction equilibrium, ionization equilibrium, out-of-equilibrium processes Equations of state, degenerate matter etc. Time dependent perturbation theory Perturbation expansion and Feynman diagrams Radiation absorption processes, oscillator strength, bound-bound, bound-free, freefree interactions

4 Physics 476/576 Syllabus Weak interactions, neutrinos, beta-decay Nuclear fusion, interaction rates, WKB approximation Nuclear physics Stellar stability and evolution. Mass accretion, binary systems White dwarfs and neutron stars Supernovae Explosive nucleosynthesis Stellar magnetic fields, pulsar magnetic fields. General relativity Neutron stars and black holes. Black hole formation, accretion, radiative processes

5 Reading/Homework Assignment Read chapter 1, sections 1.1, 1.2, 1.5 Homework will be assigned on Thursday.

6 Diurnal Motion of Stars Polaris West North East To a terrestrial observer stars seem affixed to a celestial sphere that revolves around an axis pointing in the direction of Polaris

7 Horizon Coordinates 3,-%4(!"#"$%&'#(5,#" 1'%%&%+2"!"#"$%&'#()*+'%,- 5'%4(,:($%'- %4-,+;4(0&;4% )#"='%&,0('%(>-'0$&% 6%'-(2-,7$(8"#,9(4,-&/,0

8 Equatorial Coordinates Equatorial Coordinates Celestial sphere NCP Star!"#$ %&$%'( )*( +$(,) %&$%'( -,..&/+ )*$"#+* )*( "01(%),/2 )*( /"$)* %('(.)&,' -"'(3 4&+*),.%(/.&"/ α "$ 45 &.,/,'"+"#. )" '"/+&)#2(,/2 &. 6(,.#$(2 (,.),'"/+ %('(.)&,' (7#,)"$ )" &/)($.(%)&"/ 8&)* )*( Earth #! *"#$ %&$%'( 9('%&/,)&"/ δ "$ 9:; &. 6(,.#$(2 /"$)* <$"6 )*( %('(.)&,' " Celestial equator (7#,)"$ SCP Υ First point of Aries, point where the sun crosses the celestial equator at the March (vernal) equinox!"#$,/+'(!,/+'( 0()8((/ %('(.)&,' "01(%),/2 )*( "0.($=($>. 6($&2(,/3?&2($(,' )&6( &. (7#,' )" )*( *"#$,/+'( "< )*( =($/,' )$,/.&) 8*(/ )*(.&2($&,' )&6( &. )*(.,6(,. )*( RA3

9 Celestial coordinates Declination Lines Polaris Right Ascension Lines DEC lines stay fixed RA lines move, making one revolution every 24 sidereal hours

10 Spherical Geometry Non-euclidean geometry " $ r=1 &! & # % '() *+,-. &/01.2 3/ &,43&/01. > &: *+ 23/.2; sin a sin A = sin b sin B = sin c sin C

11 Angular Distance Angular Distance!"#$ A #" (α, δ)%!"#$ B #" (α + α, δ + δ)!" 1 &!# %!$ '()(*"+#),-./#"0$ V " 2 # sin( α) sin( θ) = sin φ sin [90 (δ + δ)] sin( α) cos(δ + δ) = sin( θ) sin φ α θ sin φ cos δ

12 nce Angular Distance Angular Distance!"#$%#&%#' $" &() $*) (+,--,#'-),../"0%+,$%"#1 "#) 2,# 3/%$) B #" (α + α, δ,# + )0./)((%"# δ) 4"/ $*) 2*,#') %# 5)2-%#,$%"#,#5 2"+6%#) $*) /)(&-$(7!" 1 & δ = θ cos φ '()(*"+#),-./#"0$ V!# %!$ 2 # " θ sin φ = α cos δ ( θ) 2 cos 2 φ +( θ) 2 sin 2 φ = ( α cos δ) 2 +( δ) 2 ( α) ( θ) = $3"."%#$( sin φ 5%44)/%#' %# 9:,#5 ;<! 6= ( α, δ) %(7 sin [90 (δ + δ)] δ) = sin( θ)sinφ α θ sin φ 8),5%#' $" $*) %+."/$,#$ /)(&-$ $*,$ $*),#'&-,/ 5%($,#2) θ 6)$3))# ( θ) 2 ( α cos δ) 2 +( δ) 2

13 Galactic Coordinates

Aristarchus of Samos Aristarchus lived on the Greek island of Samos from 310 BC to 230 BC.

size and distance to our Sun Deduced that the points of light we see at night are not dots painted on some celestial sphere but

Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made,

His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a

14 Aristarchus of Samos Aristarchus lived on the Greek island of Samos from 310 BC to 230 BC. First to postulate that the planets orbited the Sun - not the Earth Estimated size of the Earth, size and distance to our Moon, the size and distance to our Sun Deduced that the points of light we see at night are not dots painted on some celestial sphere but stars like our Sun at enormous distances. Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the 'universe' just mentioned. His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of fixed stars, situated about the same centre as the sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the centre of the sphere bears to its surface. - Archimedes

15 Diameter of the Earth Erastothenes of Cyrene (modern day Libya) ( BC) was a Greek mathematician, astronomer, Librarian of Alexandria, friend of Archimedes. Sun visible at bottom of a well, vertical sticks cast no shadow in Syene on the summer solstice at local noon. In Alexandria, on the same day, a a stick cast a measurable shadow. From measurements of shadows in Alexandria, the angle of elevation of the Sun corresponded to 1/50 of a full circle (7 12') south of the zenith at the same time. Assuming Alexandria was due north of Syene, distance from Alexandria to Syene must be 1/50 of circumference of the Earth. The estimated distance between the cities was 5000 stadia. He rounded the result to a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. The exact size of the stadion is uncertain, but was likely about 185 m, which implies a circumference of km, only 16.3% too large. 7.2 deg Alexandria 7.2 deg Syen

Distance to Sun 3 87 Aristarchus argued, if one measured the angle between the moon and sun when the moon is exactly half illuminated then one could compute the ratio of their distances.

(Note: Degrees and trigonometry had not been invented yet) Aristarchus used an approximation (for what we call sin) and obtained the inequality: 1/18 > sin 3 > 1/20 He deduced that the sun was

16 Distance to Sun 3 87 Aristarchus argued, if one measured the angle between the moon and sun when the moon is exactly half illuminated then one could compute the ratio of their distances. Aristarchus estimated the angle at half illumination 87 so the ratio of the distances is sin(3 ). (Note: Degrees and trigonometry had not been invented yet) Aristarchus used an approximation (for what we call sin) and obtained the inequality: 1/18 > sin 3 > 1/20 He deduced that the sun was between 18 to 20 times as far away as the moon. In fact at the moment of half illumination the angle between the moon and the sun is actually 89 50' and the sun is actually about 400 times further away than the moon. Knowing the ratio of distances, and the relative angular sizes Aristarchus also deduced the radius of the Sun and Moon.

The Dark Ages Aristotle, 384-322BC Ptolemy, 85-165AD The Church Aristotle said If the stars

around the sun, we should see some displacement of the stars.

17 The Dark Ages Aristotle, BC Ptolemy, AD The Church Aristotle said If the stars affixed to the celestial sphere are not centered on the earth, and the earth is rotating around the sun, we should see some displacement of the stars. We don t see this, so unless the stars are ridiculously far away, the earth is the center of the universe! Aristotle also said The natural state of a body is to be at rest, and only the presence of a force or impulse would move it. Therefore a heavy body should fall faster than a light one, because it would have a greater pull towards Earth. Aristotle and Ptolemy prevailed with their Geocentric model of the universe until the 16th century. Everything was OK except for those darned wanderers or planets.

(years) Approx. Radius (a.u.) Earth 1.0 1.0 Mercury 0.241 0.

18 Distance to Planets Parallax distance S un Earth! Mercury Relative scales of the solar system Planet Period (years) Approx. Radius (a.u.) Earth Mercury Venus Mars Jupiter Venus transit, APOD July 20, 2004

) 1 pc = 3.08568025 x 10 18 cm 1 pc = 3.

19 Parallax Distance d = 1AU tan p 1AU p d 1pc p By definition, a star at a distance of one parsec (1 pc) will have a parallax angle of one arcsec (1 ) 1 pc = x cm 1 pc = ly Nearest star, Proxima Centauri, has a parallax angle of 0.77 and a distance of 1.3 pc or 4.2 ly

List 5 References 6 External links Nearest Stars # 1 System Designation Star Star # Stellar class Apparent magnitude (m V ) Absolute magnitude (M V ) Epoch J2000.

20 List 5 References 6 External links Nearest Stars # 1 System Designation Star Star # Stellar class Apparent magnitude (m V ) Absolute magnitude (M V ) Epoch J Right ascension [2] Declination [2] Solar System Sun G2V [2]!26.74 [2] 4.85 [2] variable: the Sun travels along the ecliptic Alpha Centauri (Rigil Kentaurus; Toliman) Proxima Centauri (V645 Centauri) # Centauri A (HD ) # Centauri B (HD ) Parallax [2][3] Arcseconds(±err) Distance [4] Light-years (±err) Additional references 1 M5.5Ve [2] [2] 14 h 29 m 43.0 s!62 40! 46" (0 29)" [5][6] (16) [7] 2 G2V [2] 0.01 [2] 4.38 [2] 14 h 39 m 36.5 s!60 50! 02" 2 K1V [2] 1.34 [2] 5.71 [2] 14 h 39 m 35.1 s!60 50! 14" (1 17)" [5][8] (68) 2 Barnard's Star (BD a) 4 M4.0Ve 9.53 [2] [2] 17 h 57 m 48.5 s ! 36" (1 00)" [5][6] (109) 3 Wolf 359 (CN Leonis) 5 M6.0V [2] [2] [2] 10 h 56 m 29.2 s ! 53" (2 10)" [5] (390) 4 Lalande (BD ) 6 M2.0V [2] 7.47 [2] [2] 11 h 03 m 20.2 s ! 12" (0 70)" [5][6] (148) has 8 planets 5 Sirius (# Canis Majoris) 6 Luyten Sirius A 7 A1V [2]!1.46 [2] 1.42 [2] 06 h 45 m 08.9 s!16 42! 58" (1 28)" [5][6] (289) Sirius B 7 DA2 [2] 8.44 [2] [2] Luyten A (BL Ceti) Luyten B (UV Ceti) 9 M5.5Ve [2] [2] 01 h 39 m 01.3 s!17 57! 01" (2 70)" [5] (631) 10 M6.0Ve [2] [2] 7 Ross 154 (V1216 Sagittarii) 11 M3.5Ve [2] [2] 18 h 49 m 49.4 s!23 50! 10" (1 78)" [5][6] (512) 8 Ross 248 (HH Andromedae) 12 M5.5Ve [2] [2] 23 h 41 m 54.7 s ! 30" (1 10)" [5] (36) 9 Epsilon Eridani (BD!09 697) 13 K2V [2] 3.73 [2] 6.19 [2] 03 h 32 m 55.8 s!09 27! 30" (0 79)" [5][6] (27) 10 Lacaille 9352 (CD! ) 14 M1.5Ve 7.34 [2] 9.75 [2] 23 h 05 m 52.0 s!35 51! 11" (0 87)" [5][6] (31) 11 Ross 128 (FI Virginis) 15 M4.0Vn [2] [2] 11 h 47 m 44.4 s ! 16" (1 35)" [5][6] (49) 12 EZ Aquarii (GJ 866, Luyten 789-6) EZ Aquarii B 16 M? [2] [2] 22 h 38 m 33.4 s!15 18! 07" (4 40)" [5] (171) EZ Aquarii A 16 M5.0Ve [2] [2] List of nearest stars - Wikipedia, the free encyclopedia EZ Aquarii C 16 M? [2] [2] has two proposed planets

21 Solar Luminosity L = erg s 1 Radient flux at Earth : F = L 4πd 2 = erg s 1 cm 2 Solar constant : F =1.36 kw m 2

22 Stellar Magnitudes In 1856, Pogson made more precise measurements verifying Hershell s result that a first magnitude star is about 100 times brighter than a 6th magnitude star. Pogson formalized the system, the ratio of brightness of two stars with apparent magnitude differing by 1, was defined to be exacly 100 1/5 =2.512, now known as the Pogson ratio. Pogson s scale was originally fixed by assigning Polaris a magnitude of 2. When Polaris was found to be variable, Vega became the standard reference with m=0. Some examples: The sun has m=-26.73, the full moon m=-12.6, maximum brightness of Jupiter m=-2.94, brightest star Sirius m=-1.47, Vega m=0.03, Andromeda galaxy m=3.44 The absolute magnitude M of a star is defined to be the apparent magnitude m that star would have if at a distance of 10 pc (typical for nearby stars). From your textbook: 100 1/5 = =2.512 F 1 /F 2 = (m 2 m 1 ) F abs /F rel = r 2 /(10 pc) 2 = (m M) M = m +5 5 log r

Magnitude Scale M=1 M=2 M=3 M=4 M=5 M=6 Aperture D Brighter Star (to be measured) 1 Aperture D 2 Reference Star Hipparchus (followed by Ptolemy) created a catalog of about 1000 stars that were

23 Magnitude Scale M=1 M=2 M=3 M=4 M=5 M=6 Aperture D Brighter Star (to be measured) 1 Aperture D 2 Reference Star Hipparchus (followed by Ptolemy) created a catalog of about 1000 stars that were grouped into six magnitude groups. Ptolemy called the brightest stars first magnitude or m=1, the second brightest m=2 and so on. In the early 19th century, William Herschel (born in Hanover, Germany built massive 48 reflector and 20 refractor) devised a naked-eye method to make quantitative measurements of magnitude Herschel s method consisted of viewing a reference star (with a stopped-down telescope) and an unknown with a star (with an identical telescope). When the aperture was adjusted so that the apparent magnitudes were the same, the apparent magnitude could be determined: F 1 πd 2 1/4 =F 2 πd 2 2/4 F 1 /F 2 =(D 2 /D 1 ) 2

24 Cosmic Distance Ladder

Standard Candles and Redshift If we know the intrinsic luminosity of stars, and measure their brightness we can measure distance Often hard to know the

Objects for which we have some basis of calibrating intrinsic luminosity are known as standard candles and can be used for measuring distance (or

25 Standard Candles and Redshift If we know the intrinsic luminosity of stars, and measure their brightness we can measure distance Often hard to know the intrinsic luminosity. Objects for which we have some basis of calibrating intrinsic luminosity are known as standard candles and can be used for measuring distance (or rigorously luminosity distance) Hubble observed more distant (fainter) galaxies appeared to recede more quickly. Now standard candles can be used to calibrate the redshift-distance relationship (Hubble s law) to map the most distant universe. Edwin Hubble, born 1989 in Marshfield, MO!

26 Big Bang Cosmology

27 Energy Budget of Universe This semester we will only study a tiny wedge of the total energy budget of the universe

Distances in our Galaxy Transitions in relative spins of electrons and protons in neutral hydrogen give rise to 21 cm (1420 MHz) radiation p e p e Sun Molecular clouds containing hydrogen, CO, etc.

28 Distances in our Galaxy Transitions in relative spins of electrons and protons in neutral hydrogen give rise to 21 cm (1420 MHz) radiation p e p e Sun Molecular clouds containing hydrogen, CO, etc. rotate around GC in Keplerian orbits. Doppler shifted 21 cm line gives line-of-sight velocity - can use Kepler s laws to reconstruct distribution of matter in galaxy, distances, enclosed mass (Dark Matter!) Association of galactic objects (e.g., supernova remnants, pulsars) with molecular clouds can give a crude distance (sometimes the only distance) to galactic objects.

29 Spectra Spectroscopy is the key to understanding the composition of stars, stellar structure, physical parameters of stars

30 Spectral Classification Harvard group expanded upon the spectral classification subdividing into 15 types labeled A through O according to the strength of the Balmer lines. M.N. Saha, an Indian physicist showed how, for a given temperature, one could calculate the most likely energy level at which an atom's electrons could be found. Annie Canon observing in At the time Wellesley students observed using a 4-inch Browning telescope that could be set up on the north or south porch of College Hall. Cecilia Payne used Saha's work to show how the strength of hydrogen lines depends on temperature. Annie Canon, who actually led the Harvard classification project, reorganized the classification scheme based on this work, rearranging the classes from hot to cold O, B, A, F, G, K, M.

31 Spectral Classification

32 Spectral Classification

33 CGS Units Quantity Symbol CGS unit CGS unit abbreviation Definition Equivalent in SI units length, position L, x centimetre cm 1/100 of metre = 10!2 m mass m gram g 1/1000 of kilogram = 10!3 kg time t second s 1 second = 1 s velocity v centimetre per second cm/s cm/s = 10!2 m/s force F dyne dyn g cm / s 2 = 10!5 N energy E erg erg g cm 2 / s 2 = 10!7 J power P erg per second erg/s g cm 2 / s 3 = 10!7 W pressure p barye Ba g / (cm s 2 ) = 10!1 Pa dynamic viscosity μ poise P g / (cm s) = 10!1 Pa s wavenumber k kayser cm!1 cm!1 = 100 m!1 Centimetre gram second system of units - Wikipedia, the free encyclopedia

Physics 556 Stellar Astrophysics Prof. James Buckley. Lecture 1 Mapping the Universe

Physics 556 Stellar Astrophysics Prof. James Buckley Lecture 1 Mapping the Universe Physics 556 Course Outline Stellar Structure and Evolution (and other topics in Astrophysics) Crow 206, 11:30-1:00 Instructor: