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Overview of solar physics

Overview of solar physics. K. B. Ramesh Indian Institute of Astrophysics Bangalore kbramesh@iiap.res.in. Measured/Estimated solar parameters. Sun-Earth distance Radius of the Sun Shape of the Sun Mass and Density of the Sun Irradiance, Luminosity and Effective Temperature

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Overview of solar physics

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  1. Overview of solar physics K. B. Ramesh Indian Institute of Astrophysics Bangalore kbramesh@iiap.res.in

  2. Measured/Estimated solar parameters • Sun-Earth distance • Radius of the Sun • Shape of the Sun • Mass and Density of the Sun • Irradiance, Luminosity and Effective Temperature • Acceleration due to gravity of the Sun • Central temperature • Abundance • Age of the Sun • Life of the Sun

  3. Sun-Earth Distance (1 AU)1 AU = 149,597,870.691 kilometers Cos D/a V o D E S a D = ct/2 c = 3 x 108ms-1 Radar signal travel time “t” sec

  4. Solar diameter = 13.9136 x 108m 1 AU f = 1 AU x I/DS Sun /2 /2 DS I d f Ds = 1.496x1011x I /f Ds= 1.496x1011x 0.1 m / 10.686 m = 14 x 108 m

  5. Sun’s angular extent AU D  D = AU x   = ½ degree 32 arc min 1919 arc sec Linear scale 1919 “  13.9136 x 105 km  1” = 729 km on the Sun

  6. Shape of the Sun Early 1960s,  = 4.2 x 10-5  30 km 30 km  30/729 = 0.04 arc sec

  7. Circular Orbit Mass of the Sun M = 1.9884 x 1033 gm

  8. Mean density of the Sun

  9. Measuring solar irradiance • Radiation energy received in an area of 1 m2 at a distance of 1 AU Q = MST a.Er = (W1.S1 + W2.S2 )(T2-T1)(t2-t1) • Radiometer Detectors • Normal Incidence Pyrheliometer • Thermo-Electric Detectors

  10. Solar Luminosity • Irradiance (I) = Energy received per square meter at 1 AU Rate at which the Sun emits energy (Luminosity) = I x 4d2 d = 1 AU = 1368 x 4 x (1.496 x 1011)2 Watts = 3.854 x 1026 Watts

  11. Sun’s effective temperature • Stefan-Boltzmann Law : The energy radiated by a blackbody radiator per sec per unit area is proportional to the fourth power of the absolute temperature and is given by • Luminosity = 4R2  T4  = 5.6703 x 10-8 W m-2 K-4 R = 6.955 x 108 m L = 3.854 x 1026 W T = 5780o K

  12. Surface gravity gs = 274.2 m sec-2 gV = 8.9 m s-2 gE = 9.8 m s-2 gM = 1.62 km s-2

  13. Escape velocity VS = 617 km s-1 VE = 11.2 km s-1 VM = 2.37 km s-1

  14. Sun’s central temperature • Assuming proton must be hot enough and fast enough to counteract the gravitational compression • Thermal energy = Gravitational potential energy TC = 1.56 x 107 oK

  15. Solar abundances • 70% Hydrogen, • 28% Helium, • 1.5% Carbon, Nitrogen and Oxygen, and • 0.5% All other elements

  16. Line profile of a spectrum Intensity Abundances Intensity 5860 5870 5880 5890 5900 5910 5920 Location Element identification Wavelength 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

  17. Standard Solar Model • If the model can accurately predict what is observed, then it is reasonable to assume that it can accurately tell astronomers about what they cannot observe, both inside the Sun and its behavior at other epochs. • This model is known as the standard solar model, and it has been in a state of constant evolution since its inception

  18. Standard Solar Model • Treats the interior of the Sun as if it were composed of spherical layers like the inside of an onion, with conditions slowly changing from layer to layer. • The laws of physics relate each layer to the others, providing the mathematical equations that allow each physical quantity to be numerically determined in each layer

  19. Mass continuity, the addition of mass to M(r) is equal to the density times the surface area of the layer times its thickness. • Hydrostatic equilibriumstates that gas pressure (force per unit area) in each layer must balance the inward gravitational pull or weight of all overlying layers.  • Thermal equilibriumrelates the change of energy per second flowing outward through each layer (that is, the luminosity) to the energy generation rate in that layer. • The equation of stateprescribes the relation of gas pressure to the temperature and particle density at any point • The opacitya measure of how opaque the material is

  20. Basic Assumptions The standard solar model has FOUR basic assumptions. • The sun evolves in hydrostatic equilibrium. • Energy can be transferred in the star via radiation, conduction, convection, and neutrino losses • Thermonuclear reactions are the only source of energy production inside the star (the Sun)

  21. Basic Assumptions Since heavy elements are neither created nor destroyed in the thermonuclear reactions in a solar-type star, they provide a record of the initial abundances, and only the relative amounts of hydrogen and helium are an indicator of stellar evolution

  22. Gravity Gas Pressure

  23. Locally determined properties • To complete our description of the laws which govern the physical nature of the solar interior, • the pressure ‘p’, • the rate of energy generation per unit mass, and • the opacity, must be defined. • These three properties can be specified purely in terms of the local values of the density, temperature, and composition.

  24. 1. Hydrostatic equilibrium • The local balance between Pressure and Gravity MG/r2 is the local value of gravity g(r)

  25. 1. Hydrostatic equilibrium Pressure For an ideal gas, the pressure p = NkT N – number of particles per unit volume k – Boltzmann constant The density can be specified in terms of a mean atomic weight, , which essentially is the average mass per particle in units of proton mass mH Hence  = mHN H = kT/mHg

  26. 1. Hydrostatic equilibrium Pressure For an ideal gas, the pressure p = NkT N – number of particles per unit volume k – Boltzmann constant The density can be specified in terms of a mean atomic weight, , which essentially is the average mass per particle in units of proton mass mH Hence  = mHN H = kT/mHg

  27. 1. Hydrostatic equilibrium Conservation of Mass • The most straightforward relation is mass balance involving all of the mass inside a sphere of radius “r” r r+dr (r) - mass per unit volume at r for the present Sun M(RS) = MS

  28. 1. Hydrostatic equilibrium Mass Balance • The radius or a star can change in the course of its life. • Mass of stars (particularly low-mass stars like the Sun) do not change much. • Therefore it is customary to use mass rather than the radius as the independent variable

  29. 2. Energy Balance • L - luminosity at r •  – rate of energy production • ergs gr -1 sec-1 Thus the rate of change of luminosity L with r

  30. Temperature variation 2. Energy Balance • The rate of temperature variation is determined depending upon the mode of energy transport. • Convection • Radiation Conduction is negligible in the present Sun though is important in high density stars.

  31. 2. Energy Transfer When Radiative transfer is dominant c – velocity of light,  – absorption coefficient • – opacity or mass absorption coefficient. 1/  - photon mean free path  Stefan-Boltzmann constant

  32. 2. Energy Transfer When convective transfer is dominant This blob of gas carries its excess heat upward and deposits it in its surroundings by radiation and when it eventually breaks up and dissolves by direct mixing. When an element of gas undergoes an adiabatic change (no heat is transferred across its boundaries), the temperature and pressure changes are related by

  33. 2. Energy Transfer The adiabatic temperature gradient is the criterion for the existence of convective instability is

  34. 2. Energy Transfer This instability results primarily from the recombination of electrons with bare nuclei and ions to form ions of the heavier nuclei which readily absorb radiation. This greatly increases the opacity k and causes |dT/dr|rad to become large.

  35. Locally determined properties The element abundances are defined by X (hydrogen mass fraction), Y (helium mass fraction), and Z (metal mass fraction) where X+Y+Z=1 The explicit dependence of the pressure on the composition can be explained by examining the factors which determine the mean atomic weight . There are two factors which cause . to change with radius in the Sun. The composition of the core differs from that of the remainder of the sun because of the effect of nuclear transmutations over the past 4 ½ billion years. Also, because the density and temperature are not uniform, the degree of ionization of each element also varies with the radius.

  36. 3. Energy generation The energy () production per unit mass, is attributed to the energy released in nuclear fusion reactions. • There are two processes, or chains of reactions, that are responsible for the fusion in our Sun, • The proton-proton (pp) chain and • The carbon-nitrogen-oxygen (CNO) chain.

  37. Energy generation 3. Energy generation Nuclear reactions are limited to very high temperature regions of stars (> 107 K) and usually to nuclear charges of 7 or less (nitrogen nucleus). Also, for the collision rate to be appreciable, the density must be high. Initially, the sun achieved a high central temperature from the potential energy given up through gravitational contraction. However, once conditions for nuclear reactions became favorable, gravitational contraction became negligible with respect to nuclear reactions

  38. 3. Energy generation Bridging the Coulomb gap

  39. 3. Energy generation Bridging the Coulomb gap • For collisions between two protons the critical speed, Vc is • Critical speed is determined by two fundamental constants of nature. • More interestingly its numerical value is nearly equal to the escape velocity of the Sun • If rms speeds of protons < Vc, nuclear reactions are not possible

  40. 3. Energy generation Because of high availability and low nuclear charge, the most likely candidates for nuclear reaction are hydrogen nuclei (protons) which combine to form helium in the following series of steps.

  41. 3. Energy generation Source of Sun’s Energy • 4P He4 + 6 + 2e 41

  42. Energy generation 2 X

  43. Energy generation However, each neutrino carries away 0.26 MeV (on the average) so that the actual energy liberated for every 4He formed is 26.7 MeV. The first step is the slowest and therefore determines the rate at which the whole chain reaction proceeds. Based on this first step, the rate at which mass is converted to energy by the proton-proton cycle is X – mass fraction of Hydrogen to helium

  44. Energy generation A second possible mechanism for producing helium from hydrogen is the carbon cycle,. It proceeds by the following steps in which carbon acts as a catalyst: 26.73 MeV

  45. 0 5 10 15 20 25 30 35 Temperature (in millions of degrees)

  46. Energy generation The net effect is just the same as that shown by equation. However, each neutrino carries away 1. 7 MeV on the average, so that 25.0 MeV is liberated for every 4He nucleus formed. The rate of energy generation per unit mass by the carbon cycle is given by

  47. Energy generation The total rate of energy generation is the sum of the two production processes  = pp + cno Thus, like the pressure,  is a function of , T, and the composition. Because a proton requires much more energy to overcome the potential barrier of 14N than of another proton, the carbon cycle requires relatively higher temperatures to be operative.

  48. Opacity Locally determined properties • Opacity  - impedes the radiative flow of generated energy toward the surface. The tendency of the solar gases to inhibit the flow of radiant energy is primarily dependent upon four processes which operate simultaneously: • This is done by a calculation of the probability that a photon of energy h is absorbed (photo- excitation or photo-ionization) or • scattered by individual atoms, ions, or electrons.

  49. A model of the present Sun

  50. The quantities p, , and are defined in terms of the local values of , T, and the composition. The description of the interior will be complete when the appropriate boundary conditions for the above equations are specified. at the center r = 0 M=0L=0and on the surface a r = RS M = MS L(RS) = LS For an age of 4.5 x 109 years r = RS

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