1. CSI661/ASTR530 Spring, 2009 Chap. 2 An Overview of Stellar Evolution Jan 28, 2009 Jie Zhang Copyright ©

2. Outline Basics (from “Universe” by Freedman & Kaufmann) Young Stellar Objects Zero-Age Main Sequence Leaving the Main Sequence Red Giants and Supergiants Helium Flash Later Phase and Advanced Phase Core Collapse and Nucleosynthesis Variable Stars Novae and Supernovae White dwarfs, neutron stars and black holes Binary Stars

4. Parallax The apparent displacement of a nearby object against a distant fixed background from two different viewpoints.

5. Stellar Parallax The apparent position shift of a star as the Earth moves from one side of its orbit to the other (the largest separation of two viewpoints possibly from the Earth)

6. Distances to the nearer stars can be determined by parallax, the apparent shift of a star against the background stars observed as the Earth moves along its orbit 1 pc = 3.26 ly 1 pc = 206,265 AU = 3.09 X 10 13 km Stellar Parallax and Distance

7. Once a star’s distance is known ….. Luminosity and brightness A star’s luminosity (total light output), apparent brightness, and distance from the Earth are related by the inverse- square law If any two of these quantities are known, the third can be calculated

8. Luminosity, Brightness and Distance Many visible stars turn out to be more luminous than the Sun

9. Magnitude Scale to Denote brightness Apparent magnitude scale is a traditional way to denote a star’s apparent brightness (~ 200 B.C. by Greek astronomer Hipparchus) First magnitude, the brightest Second magnitude, less bright Sixth magnitude, the dimmest one human naked eyes see

11. Apparent Magnitude and Absolute Magnitude Apparent magnitude is a measure of a star’s apparent brightness as seen from Earth –the magnitude depends on the distance of the star Absolute magnitude is the apparent magnitude a star would have if it were located exactly 10 parsecs from Earth –This magnitude is independent of the distance –One way to denote the intrinsic luminosity of a star in the unit of magnitude The Sun’s apparent magnitude is -26.7 The Sun absolute magnitude is +4.8

12. A star’s color depends on its surface temperature Wien’s Law

14. Photometry, Filters and Color Ratios Photometry measures the apparent brightness of a star Standard filters, such as U (Ultraviolet), B (Blue) and V (Visual, yellow-green) filters, Color ratios of a star are the ratios of brightness values obtained through different filters These ratios are a good measure of the star’s surface temperature; this is an easy way to get temperature

15. Stellar Spectrum E.g., Balmer lines: Hydrogen lines of transition from higher orbits to n=2 orbit; Hα (orbit 3 -> 2) at 656 nm

16. The spectral class and type of a star is directly related to its surface temperature: O stars are the hottest and M stars are the coolest Classic Spectral Types

17. O B A F G K M (Oh, Be A Fine Girl, Kiss Me!) (mnemonic) Spectral type is directly related to temperature From O to M, the temperature decreases O type, the hottest, blue color, Temp ~ 25000 K M type, the coolest, red color, Temp ~ 3000 K Sub-classes, e.g. B0, B1…B9, A0, A1…A9 The Sun is a G2 type of star (temp. 5800 K)

18. Luminosity, Radius, and Surface Temperature Reminder: Stefan-Boltzmann law states that a blackbody radiates electromagnetic waves with a total energy flux F directly proportional to the fourth power of the Kelvin temperature T of the object: F =  T 4

19. Luminosity, Radius, and Surface Temperature A more luminous star could be due to –Larger size (in radius) –Higher Surface Temperature Example: The first magnitude reddish star Betelgeuse is 60,000 time more luminous than the Sun and has a surface temperature of 3500 K, what is its radius (in unit of the solar radius)? R = 670 Rs (radius of the Sun) A Supergiant star

20. Finding Key Properties of Nearby Stars

21. Hertzsprung-Russell (H-R) diagrams reveal the patterns of stars The H-R diagram is a graph plotting the absolute magnitudes of stars against their spectral types—or, equivalently, their luminosities against surface temperatures There are patterns

22. The size can be denoted (dotted lines) 0.001 Rs To 1000 Rs Hertzsprung-Russell (H-R) diagram the patterns of stars

23. Main Sequence: the band stretching diagonally from top-left (high luminosity and high surface temperature) to bottom-right (low luminosity and low surface temperature) –90% stars in this band –The Sun is one of main sequence stars –Hydrogen burning as energy source Hertzsprung-Russell (H-R) diagram the patterns of stars

24. Main Sequence Giants –upper- right side –Luminous (100 – 1000 Lsun) –Cool (3000 to 6000 K) –Large size (10 – 100 Rsun) Supergiants –Most upper-right side –Luminous (10000 - 100000 Lsun) –Cool (3000 to 6000 K) –Huge (1000 Rsun) White Dwarfs –Lower-middle –Dim (0.01 Ls) –Hot (10000 K) –Small (0.01 Rs) Hertzsprung-Russell (H-R) diagram the patterns of stars

25. A way to obtain the MASS of stars Binary Star System Period: ~ 80 days

26. Binary Stars Binary stars are two stars which are held in orbit around each other by their mutual gravitational attraction, are surprisingly common Visual binaries: those that can be resolved into two distinct star images by a telescope Each of the two stars in a binary system moves in an elliptical orbit about the center of mass of the system

27. Binary Stars Each of the two stars in a binary system moves in an elliptical orbit about the center of mass of the system

28. Binary star systems: stellar masses The masses can be computed from measurements of the orbital period and orbital size of the system The mass ratio of M1 and M2 is inversely proportional to the distance of stars to the center of mass This formula is a generalized format of Kepler’s 3 rd law When M1+M2 = 1 Msun, it reduces to a 3 = P 2

29. Mass-Luminosity Relation for Main- Sequence Stars The greater the mass of a main- sequence star, the greater its luminosity

30. Masses from 0.2 M Θ to 60 M Θ The greater the mass The greater the luminosity The greater the surface temperature The greater the radius Mass-Luminosity Relation for Main- Sequence Stars

31. Note: This is the end of the basics, which is from “Universe” by Freedman & Kaufmann Feb. 11, 2009 (continued)

32. (2.1) Young Stellar Objects Four stages of star formation 1.Form proto-star core within molecular cloud 2.Core grows from surrounding rotating disk 3.Bipolar flow along rotation axis 4.New star clears away the surrounding nebular material http://www.skyofplenty.com/wp-content/uploads/2008/09/esa_- _star_formation1.jpg

33. (2.1) Young Stellar Objects Energy source for a proto-star is gravitational potential energy. The contract life is about 0.1% its potential nuclear life at the main sequence Proto-stars are convective throughout, thus a new star is chemically homogeneous Proto-star Evolution Track

34. (2.2) ZAMS Zero-age main sequence star: a star just ignites the hydrogen fusion In practice, “zero-age” means that the star has changed so little in radius, effective temperature and luminosity –Means a few thousand years for a massive star –Means 10 million years for the Sun –Means 1 billion years for the least massive stars

35. (2.2.1) Main Sequence Two kinds of nuclear fusion converting H to He 1.pp-chain –for stars less than 1.5 Msun 2.CNO cycle For stars more than 1.5 Msun, Tc > 1.8 X 10 7 K Fusion is much faster than PP-chain C, N, O act as catalysts Because of P=nKT=ρ/μ N A KT, number density decreases Temperature must increase to maintain the pressure Core must slowly contract and heat up Faster energy generation, more luminous star

36. (2.2.2) Brown Dwarfs Proto-stars which never get hot enough to fuse hydrogen to helium The brown dwarf/main sequence cut is about 0.085 Msun

37. (2.3) Post-main Sequence < 0.05: No 2 D fusion  “planet” <0.085: No 1 H Fusion  brown dwarf =0.85: Hubble time scale <1.50: PP chain, Helium flash, radiative core, He WD <5.0: CNO cycle, no He flash, convective core, Carbon WD <8.0: planetary nebula, O, Ne, Mg WD <25: supernovae, neutron star > 25: supernovae, black hole Mass Cut versus star fate (also see Fig. 2.4)

38. (2.3.1) Cluster HR Diagram Fig. 2.7. HR diagram of globular cluster M3 Stars in a cluster form at nearly the same time “TOP” turnoff point can be used to determine the age of a cluster SGB: sub-giant branch RGB: red-giant branch –H-shell burning Horizontal Branch –Helium core burning AGB: Asymptotic Giant Branch –Helium shell burning –Variable stars caused RR Lyrae –by thermal instability

39. (2.3.1) Cluster HR Diagram Fig. 2.8: theoretical HR for clusters

40. (2.4) Red Giants The stage that hydrogen shell burning ignites The shell burning adds helium ash into the core, causing the dormant core to contract The shell burning causes the outer envelope to expand and thus cooling, producing red giants The hydrogen shell burning occurs via the CNO cycle, the main source of N in the universe

41. Chap. 2 (continued) Feb.18, 2009

42. (2.5) Helium Flash Core contracts, and density increases Core becomes degenerate, that is the electron degeneracy pressure is larger than the gas thermal pressure Degeneracy pressure is caused by the electron momentum associated with the Heisenberg uncertainty principle (ΔxΔp=ħ). It is also associated with Pauli- exclusive principle

43. (2.5) Helium Flash Star M < 0.4 Msun –core degenerate (ρ > 10 6 g cm -3 ) –but low temperature (< 10 7 K) –no further helium burning, produce helium white dwarf Star M > 1.5 Msun –core not degenerate (ρ < 10 6 g cm -3 ) –but high temperature (> 10 8 K), ignite helium burning –Peaceful transition to helium burning Star 0.4 Msun < M < 1.5 Msun –core degenerate (ρ < 10 6 g cm -3 ) –and high temperature (> 10 8 K) –helium flash: explosive helium burning

44. (2.5) Helium Flash For a degenerate gas, the ignition of helium burning will heat the gas, but do not cause expand The increased temperature makes the reaction go faster, which further heats the gas, which makes the reaction goes faster. This cycle of explosive nuclear reaction continues until temperature is high enough so that thermal pressure exceeds degenerate pressure. After helium flash, the core expands to a density about 10 3 g cm -3 It is mirrored by envelope contraction Luminosity decreases, and effective temperature increases; the star heads to the left in the HR diagram

45. (2.5) Helium Flash Density Evolution for model 1 Msun, z=0.02

46. (2.5.1) Horizontal Branches (HB) Giant stars with Helium burning in the core –Through triple-α reaction –3 4 He  12 C and 12 C ( 4 He, γ) 16 O Hydrogen burning in the surrounding shell through CNO cycle

47. (2.5.2) Asymptotic Giant Branches (AGB) When helium core is exhausted, HB star becomes AGB The C-O core contracts and heats up Double shell burning Helium burning in the shell surrounding the core Hydrogen burning in the shell surrounding He shell

48. (2.5.2) AGB Fig. 2.14. Double Shell Burning

49. (2.6) Later Phases, Initial Masses 6-10 Msun During the Giant star phases, a star may lose a large fraction of mass through –Super wind –Pulsation The blown-off envelope becomes planetary nebula (PN) The residual core becomes a white dwarf –Composition: Carbon-oxygen –Mass: 0.55 – 1.3 Ms –Radius: 10 -2 Rsun, or the size of the Earth –Energy source: residual heat of the atomic nuclei Luminosity: 10 -5 Lsun Fading time: 10 10 years

50. (2.6) Planetary Nebula NGC 6543 IC 418

51. (2.6.1) White Dwarfs Fig. 2.15. Color-Magnitude HR diagram

52. Chap. 2 (continued) Apr. 8, 2009

53. (2.7) Advanced Evolution Phases, Initial Masses Greater Than 6-10 Msun The core is composed of iron-peak elevemts Silicon burning is taking place, adding to the iron core Lighter elements are burning progressively in outer layers

54. (2.8) Core Collapse and Nucleosynthesis The core collapses at about ρ c =6 x 10 9 g cm -3 and T c =8 x 10 9 K The core collapses catastrophically Inner core mass 1.2 Msun Density from 10 9 to 10 15 g cm -3 Dynamic time scale is only a few seconds Forming neutron stars Releasing 10 53 ergs gravitational energy –Most comes out in neutrinos –1% in kinetic energy –0.1% in visible light and other EM radiation

55. (2.11.2) Supernovae Further collapse is effectively halted by the very stiff equation of state of nuclear matter To convert 1 Ms iron core to all neutrons (binding energy 9 Mev/nucleon) requires 10 52 ergs energy As core material reaches the nuclear density, it “bounces” and collide with informing material thus forming a shock Shock propagates outward lifting most or all of the remainder of the star

56. (2.11.2) Supernovae Crab Nebula – supernova in 1054 AD; a pulsar or neutron star is at the center

57. Neutron Star or Pulsar

58. Chap. 2 (to be continued)

59. End of Chap. 2 Note: