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Neutron Star Phys 321: Lecture 8 Stellar Remnants Prof. Bin Chen, Tiernan Hall 101, [email protected] Evolution of a low-mass star Planetary Nebula Main SequenceEvolution and Post-Main-Sequence track of an 1 Stellar solar Evolution-mass star Post-AGB PN formation Superwind First He shell flash White dwarf TP-AGB Second dredge-up He core flash ) Pre-white dwarf L / L E-AGB ( 10 He core exhausted Log RGB Ring Nebula (M57) He core burning First Red: Nitrogen, Green: Oxygen, Blue: Helium dredge-up H shell burning SGB Core contraction H core exhausted ZAMS To white dwarf phase 1 M Log (T ) 10 e Sirius B FIGURE 4 A schematic diagram of the evolution of a low-mass star of 1 M from the zero-age main sequence to the formation of a white dwarf star. The dotted ph⊙ase of evolution represents rapid evolution following the helium core flash. The various phases of evolution are labeled as follows: Zero-Age-Main-Sequence (ZAMS), Sub-Giant Branch (SGB), Red Giant Branch (RGB), Early Asymptotic Giant Branch (E-AGB), Thermal Pulse Asymptotic Giant Branch (TP-AGB), Post- Asymptotic Giant Branch (Post-AGB), Planetary Nebula formation (PN formation), and Pre-white dwarf phase leading to white dwarf phase. and becomes nearly isothermal. At points 4 in Fig. 1, the Schönberg–Chandrasekhar limit is reached and the core begins to contract rapidly, causing the evolution to proceed on the much faster Kelvin–Helmholtz timescale. The gravitational energy released by the rapidly contracting core again causes the envelope of the star to expand and the effec- tive temperature cools, resulting in redward evolution on the H–R diagram. This phase of evolution is known as the subgiant branch (SGB). As the core contracts, a nonzero temperature gradient is soon re-established because of the release of gravitational potential energy. At the same time, the temperature and density of the hydrogen-burning shell increase, and, although the shell begins to narrow significantly, the rate at which energy is generated by the shell increases rapidly. Once again the stellar envelope expands, absorbing some of the energy produced by the shell Death of low-mass stars • Crash course by Phil Plait The discovery of Sirius B • In 1844, Friedrich Bessel found the brightest star in the night sky, Sirius, Sirius A has a companion, using precise parallax observations for ten years • In 1862, Alvan G. Clark discovered the “Pup” at its predicted position using his father’s new 18-inch refractor Sirius B • The Pup is very faint (~0.03 Lsun) so, probably cool and red? • In 1915, Walter Adams discovered that, however, the surface temperature is ~27,000 K! A hot, blue-white star! Chandra X-ray image Appendix: Astronomical and Physical Constants APPENDIX APPENDIX Astronomical and Physical Constants Physical Constants 11 2 2 Gravitational constant G 6.673(10) 10− Nm kg− APPENDIX = × 8 1 Speed of light (exact) c 2.99792458 10 ms− Astronomical and≡ Physical7 × 2 Constants Permeability of free space µ0 4π 10− NA− ≡ × 2 Permittivity of free space ϵ0 1/µ0c ≡ Astronomical Constants8.854187817 ... 10 12 Fm 1 = × − − Electric charge e 1.602176462(63) 1030 19 C Solar mass Estimating1M =radius1.9891 of ×Sirius10 −kg B Electron volt 1 eV ⊙ 1.602176462= (63×) 103 19 J 2 Solar irradiance S 1.365(2) 10 −Wm− Astronomical and= = Physical×× 34 Constants Planck’sSolar constant luminosity h 1L 6.626068763.839(52(5)) 1010−26 WJs =⊙ = ×× 15 Solar radius • Luminosity of 1RSirius4. 13566727B is 60.03.95508(16) (L26sun10) − 10eV8 m s ! = ⊙ = × 2×1/4 Solar effective temperature Te, h/2π L /(4πσR ) ≡⊙ ≡ ⊙ ⊙ 34 • Effective temperature1.054571596 is5777 27,000(822))K 10K− Js = = × 16 Astronomical Constants6.58211889(26) 10− eV s • Mass is ~1.05 solar= mass × 3 Planck’sSolar constant absolute bolometricspeed of light magnitduehc Mbol 1.239841864(.1674)30 10 eV nm Solar mass × 1M = 1=.9891 10 ×kg Solar apparent bolometric magnitude ⊙ mbol= 1240 eV nm26×.83 3 2 Solar irradiance • What is itsS radius?≃ 1=.365−(2) 10 Wm23 − 1 Boltzmann’sSolar apparent constant ultraviolet magnitudek U = 1.380650325(24×.91) 10 JK− Solar luminosity Astronomical1L = Constants3=.839−(5) 10× 26 −W Solar apparent blue magnitude B 8.617342326(153.10) 10 5 eV K 1 Solar mass ⊙ 1M== = 1−.9891× ×1030 −kg8 − Solar radiusStefan–BoltzmannSolar apparent constant visual magnitude 1Rσ V 2π65.k955084/(1526c(226.h753)) 10 m ⊙ ⊙ = × 3 2 Solar irradiance S≡= = 1−.365(2)2×110/48 Wm−2 4 Solar effectiveSolar temperature bolometric correction Te, BC 5.670400L= /(4(πσ400.)08R ×10) − 26Wm− K− Solar luminosity ⊙ 1L=≡ =⊙ 3.839− (5×)⊙ 10 W Radiation constant a ⊙ 4σ5777=/c (2) K × 8 EarthSolar mass radius Solar Radius: 1M1R== 65.95508.9736(2610) 241610kg m 3 4 ⊙ 7.565767= (54) 102−×1/4Jm− K− Solar effective temperature T= ⊕ = L /(4πσ××R ) 6 AtomicEarth mass radius unit (equatorial) Earth Radius:1u 1Re, 1.660538736.378136(13) 101027mkg ⊙⊕ ≡ ⊙ ⊙ − Solar absolute bolometric magnitdue Mbol = = 4.577774 (2) K×× 2 = 931=.494013(37) MeV/c2 4 Solar apparentAstronomical bolometric unit magnitudeUsing Stefanmbol -Boltzman’s1= AU Law26.83:1.4959787066 31 1011 m Electron mass me = 9.10938188−= L(72=) 4π10R−×σkgT Solar apparentLightSolar ultraviolet (Julian) absolute year magnitudebolometric magnitdueU 1M= lybol 25.919.4607304724.74 × 41015 m 5.485799110== This means(12) compressing10×− u the mass of the ParsecSolar apparent bolometricWe have magnitude R ~ 5.51m x= pcbol =106 m − 20626426.83 .806× AU27 Solar apparentProton mass blue magnitude BmWDp 1.67262158==26.−10 (13) 10− kg Solar apparent ultraviolet magnitude U== − entire325.0856776 .Sun91 within× 10 a 16volumem < Earth! Solar apparent visual magnitude V 1.00727646688==26.−75 (13)×u Solar apparent blue magnitude B== − 326.2615638.10 ly (Julian27 ) Neutron mass mn 1.67492716= − (13) 10− kg Solar bolometricSolar correction apparent visual magnitudeBC V= = 0.0826.75 × = 1.00866491578− (55) u = − h m s SiderealSolar bolometric day correction BC= 230.5608 04.090530927 Hydrogen mass mH 1.673532499== − (13) 10− kg Earth mass Solar day 1M = 5.97368640010 s24×kg 1.00782503214= (35) u SiderealEarth mass year ⊕ 1M== 53.9736.15581450× 10624 kg107 s Earth radiusAvogadro’s (equatorial) number 1RN 6.022141996.378136(47)10 10m23 mol 1 A ⊕ ⊕ == × ×6 − Earth radius (equatorial) 1R== 6365.378136.256308× × 10 d1 m 1 Gas constant R ⊕ 8.314472== (15) J mol× − K− 7 Tropical year = 2 3.1556925192 1110 s AstronomicalBohr radius unit 1a0 AU, 4πϵ1=.04959787066! /mee 10× 11m Astronomical unit ∞ 1≡ AU= 1365.4959787066.2421897× d 1011 m 5.291772083== (19) 10×157 m Light (Julian)JulianLight year year (Julian) year 1 ly 1= ly 9.46073047293.460730472.1557600×101010− 15ms m a = (m=≡/µ)a ××× Parsec Parsec 10 pc,H 1 pc 206264e 2062643650,.806.25.806 d AU AU ≡ ≡ ∞ 11 Gregorian year = 5.294654075= 3.1556952(20) 16101016−7 sm = 3.408567763.08567763 2!3 10× 10 mm Rydberg constant R me=≡e /64π ϵ0 c ×× ∞ ≡= 3365.2615638.2425× lyd (Julian) 1.09737315685493=≡.2615638 ly ((Julian83) )107 m 1 Note: Uncertainties in the last digits are indicated== in parentheses. For instance, × − RH (µ/m8 e)R h m s theSidereal solar radius, day 1 R , has an uncertainty of 0.≡00026 10 m.23∞56 04.0905309 Sidereal day ⊙ ± 1×.0967758323= h56m04(13.0905309) 107 ms 1 Solar day = 86400 s × − Note: Uncertainties in the last digits are indicated in parentheses.= = For instance, the universal Solar day Sidereal year 864003.15581450 s 107 s 11 2 2 gravitational constant, G, has an uncertainty of 0.010= 10 =Nm kg− . × 7 Sidereal year ± × −3.15581450365.25630810 d s = = × Tropical year 365.2563083.155692519 d 107 s = × = 365.2421897 d 7 Tropical year 3=.155692519 10 s Julian year = 3.1557600× 107 s 365≡ .2421897 d× = 365.25 d ≡ 7 Julian year Gregorian year 3.15576003.15569521010s7 s ≡ ≡ × × 365.25365 d.2425 d ≡ ≡ 7 Gregorian yearNote: Uncertainties in the last digits are indicated in parentheses.3.1556952 For instance,10 s ≡ × the solar radius, 1 R , has an uncertainty of 0.00026 365108 m..2425 d ⊙ ± ≡ × Note: Uncertainties in the last digits are indicated in parentheses. For instance, From Appendix A o f An In tro du ctio n to Mo dern Astro p hysics, Second Edition, Bradley W. Carroll, Dale A. Ostlie. Copyright © 2 007 the solar radius, 1 R , has an uncertainty of 0.00026 108 m. by Pearson Education, Inc. Published by ⊙Pearson Addison-Wesley.± All× rights reserved. From Appendix A o f An In tro du ctio n to Mo dern Astro p hysics, Second Edition, Bradley W. Carroll, Dale A. Ostlie. Copyright © 2 007 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved. From Appendix A o f An In tro du ctio n to Mo dern Astro p hysics, Second Edition, Bradley W. Carroll, Dale A. Ostlie. Copyright © 2 007 by Pearson Education, Inc. Published by Pearson Addison-Wesley. All rights reserved. APPENDIX AstronomicalAppendix: Astronomical and and Physical Physical Constants Constants Properties of white dwarfs AstronomicalDensity Constants Solar mass 1M 1.9891 1030 kg ⊙ = × 3 2 Solar irradiance Sirius B SR ~ 5.5 x 106 m1.365(2) 10 Wm− PhysicalWD Constants= × 26 Solar luminosity 1L 3.839(5) 1110 2W 2 Gravitational constant G ⊙ = 6.673(10) 10×− Nm kg8 − Solar radius 1R = 6.95508× (268) 101 m Speed of light (exact) c 2.99792458 10 ms− ⊙ ≡ = 7 × 2 2×1/4 Solar effectivePermeability temperature of free space Tµe,0 9 4π L-103 /(− 4NAπσ−R ) ρ ⊙~ 3 x≡ 10≡ kg m× ⊙2 ⊙ Permittivity of free space ϵ0 1/µ57770c (2) K ≡ 12 1 = 8.854187817 ... 10− Fm− = × 19 Electric charge Surfacee gravity: Phil1.602176462 said 100,000x(63) that10− ofC the Earth’s gravity = × 19 Solar absoluteElectron bolometric volt magnitdue M1 eVbol
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