Open Issues in the Physics of the Solar Interior

Transcription

1 Open Issues in the Physics of the Solar Interior Werner Däppen Department of Physics and Astronomy University of Southern California Talk given at the APS Far West Meeting, Reno NV, 25 Oct. 2014

2 Disclaimer: No rotation No magnetic fields No solar cycle!

3 Inside the Sun

4 Prelude

5 The solar center: hellish or not? Judge by yourself! Sun s luminosity: Sun s mass: Mass in core: W kg kg Energy production: 2 mw / kg!!!

6 Before discussing specific energy sources Virial theorem Therefore With the expression (to a decent approximation)

7 This explains the cause for solar and stellar evolution!

8 In other words: The Arrow of Time in solar and stellar evolution!

9 Open issue of the past

10 Chemical Sun? Distance to Sun: km Solar radius: km Solar mass: kg Solar luminosity: W Thermal equiv. (gas): J/kg Tot. chemical energy: J/kg Lifetime of the Sun: 5000 years!! WRONG PHYSICS!!

11 Gravitational Potential Energy at Work!

12 J.R. Mayer, J.J. Waterson, H. von Helmholtz, W. Thomson (later Lord Kelvin) [ ] Assumption: Suppose the Sun lives from the potential energy of its own mass, released in its own gravitational field RIGHT PHYSICS??

13 Kelvin vs. Darwin

14 Charles Darwin ( ) Origin of Species (1859)

15 Darwin s Weald Source: public photo

16 From the Origin of Species (Ch. 9) Hence, under ordinary circumstances, I conclude that for a cliff 500 feet in height, a denudation of one inch per century for the whole length would be an ample allowance. At this rate, on the above data, the denudation of the Weald must have required 306,662,400 years; or say three hundred million years

17 FF to the 20 th and 21 st centuries

18 Helioseismology - a high-precision tool to probe the solar interior

19 Helioseismology Discovery: 1960 Leighton, Noyes & Simon Irregular, quasi-periodic motion Hence name: 5-minute oscillations

20 State of the art High spatial resolution (>1024 X 1024) Measure line-of-sight velocity at every pixel, at least once every 30s Doppler effect on given absorption line:

21

22

23

24 4 typical oscillation modes l=2 m=0 l=10 m=5 l=20 m=0 l=100 m=100

25 Analogy (2-D): bell (from G. Houdek) Hz Hz Hz

26 Time dependence of a single mode Project the velocity pattern on a single mode, for each fixed l and m (analogous to Fourier coefficient)

27 No Sun at night! What to do? South Pole Networking (GONG) Space (SOHO)

28 South Pole

29 GONG Stations

30 GONG Instruments

31 SOHO Instrument

32 SOHO Launch (Dec 2, 1995)

33 Time-series of one oscillation mode Source: SOHO/MDI instrument

34 Power spectrum after Fourier transform From: SOHO/GOLF instrument

35 Summary of Observations

36 Mode frequencies: properties More than 10 7 modes observed Single mode velocity tiny: Incoherently, the amplitudes add up to the observed total velocity of Data represented in so-called diagrams High Q value (weeks of coherence!)

37 Modern diagram Source SOHO/MDI instrument

38 Mid 1980s

39 Dawn of helioseismology (1977) from: Rhodes, E.J., Jr, Ulrich, R.K., Simon, G.W. 1977, Astrophys. J. 218, 901

40 Main methods of helioseismology Geometrical optics (sorry: acoustics): qualitative + approximative Solar modeling: structure frequencies Inversions: frequencies structure

41 Crash course in inversions geometrical acoustics: paths

42 Geometrical acoustics: results without proof Features Refraction, turning point Relation between Determination of n inside radial at surface All modes sample the surface region equally: good statistics! Gateway to inversions Better than 10% accuracy

43 Result for internal sound speed (using geometrical acoustics) Figure from: Gough, D.O. et al. 1996, Science 272, 1296

44 Tool to test physics! Why?

45 Thermodynamics Equation-of-state diagnosis possible, because Acoustic modes (largely) governed by the adiabatic sound speed (often denoted by )

46 No competition from laboratories (yet)

47 Fortunate situation In the convection zone, the Sun is (largely) adiabatically stratified, its structure is mainly determined by thermodynamics. Little contamination from opacity Helioseismology can probe locally

48 Elementary stellar thermodynamics In stellar physics, before 1975, normal (non-degenerate) stars were successfully modeled by Provided: Good to 90% accuracy! from Saha equation:

49 In early helioseismology From , more refined equations of state, mainly Detailed chemical composition Fermi-Dirac electrons Debye-Hückel screening good to 95-99% accuracy!

50 The dominant non-ideal effect turned out to be...dh! Screened Coulomb potential (=the [static] Debye-Hückel approximation)

51 Digression: O-C Diagrams

52 model frequencies (theory) Figure: J. Christensen-Dalsgaard

53 Data allow O-C Diagrams O = Observation C = Computation (Qnl is a scale factor. Details see: Christensen-Dalsgaard & Däppen 1992, A&A Rev. 4, 267)

54 Impact: two similar solar models Identical models, except for their equations of state. One is with Debye-Hückel screening, one without. Their adiabatic exponents are: Dashed: with screening Solid: without screening From: Christensen-Dalsgaard & Däppen 1992, A&A Rev. 4, 267

55 and their O-C diagrams without screening with screening from: Christensen-Dalsgaard & Däppen 1992, A&A Rev. 4, 267

56 To my chagrin, in 1988, the physicists were not overwhelmed!

57 ENTER: Serious Thermodynamics

58 Two main approaches: introduction Free-energy minimization chemical picture intuitive, but highly practical Grand-canonical expansions Physical picture systematic method for non-ideal corrections

59 Chemical picture Treat compounds as fundamental entities Reactions Constraints Minimize!!!subject to constraints!!! In practice, cook a free energy (intuition!) Consistent (formally!)

60 Example: MHD Fairly conventional realization (chemical picture) Key ingredient: occupation probabilities Hummer, D.G. & Mihalas, D.M. 1988, ApJ 331, 794; Mihalas, D.M., Däppen, W. & Hummer, D.G. 1988, ApJ 331, 815 Däppen,W., Mihalas, D.M., Hummer, D.G. & Mihalas, B.W. 1988, ApJ 332, 261

61 Physical picture Only electrons and nuclei are fundamental No reactions Quantum mechanics and statistical mechanics dealt with simultaneously Nothing to minimize Consistent (not just formally!)

62 Example: OPAL/ACTEX First successful stellar modeling with an equation of state in the physical picture (LLNL) Rogers, F.J. 1986, ApJ 310, 723; Rogers, F.J., Swenson, F.J. & Iglesias, C.A. 1996, ApJ 456, 902 Rogers, F.J. & Nayfonov, A. 2002, ApJ 576, 1064 Key points: systematic expansions (z = activity) Planck-Larkin Partition Function

63 MHD vs. OPAL

64 Figure from: S. Basu Inversions (numerical; Sun-Model)

65 OPAL fares better than MHD Why? Likely answer: There is no PLPF in MHD There are no scattering states in MHD Open question: is it fundamentally impossible to find PLPF entirely from within the chemical picture?

66 More precisely: consider 3 states of a H atom 1: ground state 2: weakly bound 3: continuum

67 Force law for electrons (C=Coulomb, F=free) SIMPLE MHD OPAL 1: ground state C C C 2: weakly bound F C C 3: continuum F F C Treatment of excited states: OPAL good, SIMPLE is at least consistent, but MHD is inconsistent* *as are all chemical picture formalisms with excited states but without PLPF

68 Preliminary Conclusions Even today, there is no perfect solar model Standard model is excellent, but not perfect, because data are so much better Independent verification with neutrinos

69 Neutrinos (very brief!!) Problem of solar neutrinos Chlorine- and gallium experiments Cerenkov radiation (Kamiokande) Neutrino scattering on deuterium (SNO) Together: neutrino spectroscopy: => Solar neutrino problem solved (2001)

70 Kamiokande Neutrino Experiment

71 Neutrino Sun

72 Back to helioseismology: another demonstration of its power

73 Relativistic electrons in the Sun Relativistic corrections are expected to be small, central temperature And yet: the effect can be observed!! (Elliot & Kosovichev 1998, ApJ, 500 L199)

74 Models with and without relativistic electrons Figures from: Elliot, J.R. & Kosovichev, A.G. 1998, ApJ, 500 L199

75 Quantum tunneling presents another open issue

76 Problem: Coulomb repulsion! Temperature K 1 kev Energy to bring 2 protons together 1 MeV

77 With Maxwell alone

78 No tunnel effect - no nothing! (Gamov, Atkinson & Houtermans, )

79 Quantum tunneling

80 Gamov peak

81 History I: CNO cycle H. Bethe & C.F. Weizsäcker 1938

82 History II: pp chain

83 History III: in the Sun, pp wins demonstrated by E. Salpeter in 1952

84 Back to tunneling!

85 Salpeter uses static screening to enhance nuclear reactions

86 Reduced Coulomb potential Debye Length =

87 What about dynamic?

88 .well, individual collisions NOT governed by!!! Debye Length =

89 Basic quasi-classical hypothesis (Hugh DeWitt 1973) Each tunneling event has the same probability as that of a coherent stream of incoming particles scattering at the same potential. As long as the Coulomb mountain is static, this makes sense, but if dynamical effects are considered, the assumption becomes less obvious.

90 Shaviv & Shaviv (1990s) Apply MD techniques to solar core numerically determine screening avoid mean field assumptions 90

91 Shaviv & Shaviv Apply MD techniques to solar core numerically determine screening avoid mean field assumptions Results differ from Salpeter s screening 91

92 Shaviv & Shaviv Apply MD techniques to solar core numerically determine screening avoid mean field assumptions Results differ from Salpeter s screening Dynamic effects 92

93 USC simulations they confirm Shaviv s numerical results (K. Mussack, D. Mao) 3D box protons and electrons Coulomb interactions T=15 million K n=1/a 3 0 Effective potential for electrons 93

94 Dynamic screening energy at the turning point for pairs of protons with a given relative kinetic energy. Mao, D., Mussack, K. & Däppen, W., Astrophys. J. 701 (2009) 1204

95 Screening energies and the ratio of screened to unscreened nuclear reaction rates for solar p-p reactions. Mussack, K. & Däppen, W., Astrophys. J. 729 (2011) is nearly 1!

96 nobody believed us * * with the sole unwelcome exception of NSF!!

97 Why? not least because of the heavy guns: L. S. Brown and R. F. Sawyer: Nuclear reaction rates in a plasma, Rev. Mod. Phys. 69, (1997)

98 Their original tone: [ ] in the so-called basically classical approach, there are conceptual problems raised by the division of the problem into a quantum-mechanical and a classical part. [ ] The literature lacks any development that begins with a correct general expression for the rate

99 Key idea The authors claim to compute the relevant observable rigorously, i.e., the nuclear energy production rate

100 4 pages like this, and that is just the Appendix of a 25-page paper

101 and the claim is [ ] we find no dynamical modifications of the Salpeter result [ ].

102 But is it really so? Counter-example: could one do molecular physics without Born- Oppenheimer? And that very accurately, say, to study isotope effects? Just asking!

103 Maybe it is! Is it like in the double slit experiment? After all, the observable is nuclear energy generation. Perhaps looking at the relative velocity and the v-dependent tunneling probability at the same time is forbidden by some uncertainty relation!

104 PS: a completely different alternative approach Anderegg, F., Driscoll, C. F., Dubin, D. H. E., & O Neil, T.M., Phys. Plasmas 17 (2010) Used an apparent duality to infer the solar screening results The duality occurs in experiments on a laser-cooled ionic system when observing the propagation of magnetization The authors interpret these experiments in the sense that they confirm Salpeter's view

105 Critique of this approach Their work is based on the assumption of a faithful mapping between two entirely different physical systems Present state of their experiments corresponds to plasmas that are quite stronger coupled than those found in the center of the Sun The last word has therefore not been spoken!

106 Conclusions Probing of the solar interior Detailed tests of the theory of stellar structure and evolution Far-reaching consequences, e.g. in cosmology But above all: the Sun itself is a wonderful physics laboratory!