The Sun. Nearest Star Contains most of the mass of the solar system Source of heat and illumination

Transcription

1 The Sun Nearest Star Contains most of the mass of the solar system Source of heat and illumination Outline Properties Structure Solar Cycle Energetics Equation of Stellar Structure TBC

2 Properties of Sun Mass = 1.989x10 30 kg (333,000 Earth masses) Radius = x10 8 m (109 Earth Radii) Average Density = g cm -3 Luminosity = 3.826x10 26 Watts Escape Velocity = 6.18x10 5 m s -1. I.e., (By comparison, for the Earth)

3 Properties of Sun Surface Gravity = 2.740x10 2 m s -2. I.e., (By comparison, for the Earth) We ll return to both of the latter concepts when we discuss the general properties of planets

4 Properties of Sun Chemical Composition - Metallicity Metal poor (old) Metal Rich (young) Expressed As - 1) 2) X = H, Y = He, Z = Other Typically, X = 0.70, Y = 0.28, Z = 0.02 Number Density

5 Properties of Sun Solar Constant = 1370 W m -2. I.e., Note that every planet has its own solar constant. And like the dust grain, the flux received will play a part in the temperature of the planet. Other factors such as the planet s albedo (reflectivity) & atmospheric composition will also be important.

6 Properties of Sun Effective Temperature = 5770 K, where T e is the temperature of a blackbody having the same radiated power per area. I.e.,

7 Temperature Note that the temperature structure of the Sun is complicated

8 Interior of the Sun Core: center of Sun (15x10 6 K) Radiative zone: region of sun where energy is transported via radiation Convective zone: region of the sun where energy is transported to the photosphere via blobs of warm, rising gas Time required to move energy from the core to the surface ~ million years

9 General features of the Sun Photosphere: The region in the solar atmosphere from which most of the visible light escapes into space (5800 K) Sunspots: A region of the solar photosphere that is cooler than its surroundings & therefore appears dark (~4800 K) Sunspots can be used to determine the sun s rotation period ~ days Sunspots were discovered by Galileo Sunspots

10 Close-up of Sunspot

11 The Photosphere (Video)

12 Close-up of Photosphere Granulation: Caused by convective cells

13 X-ray image of the Sun These fields prevent convection from carrying as much heat into the sunspots

14 Corona Corona: The outer atmosphere of the Sun. It has temperatures in excess of a million degrees & extends for millions of kilometers into space Coronal gas expands & flows away from the Sun and forms the Solar Wind Note that a solar eclipse is the best time to see the corona directly

15 Corona in Visible Light (Video)

16 H! Emission (Video)

17 The Nature of Sunspots The Sun rotates faster at its equator than its pole The magnetic field lines winds up as a result of differential rotation Sunspots occur when the magnetic fields poke through the photosphere

18 Solar Cycle The 22-year cycle in which the solar magnetic field reverses direction, consisting of two 11-year sunspot cycles The Aurora (i.e., dancing light in the earth s sky caused by charged particles entering our atmosphere) are more intense during the solar maxima. Cause: Winding of magnetic fields?

19 Energetics of the Sun & Timescales So, the Sun has a L ~ 4x10 26 W & a lifetime greater than or equal to 4.6x10 9 yrs (i.e., at least as old as the Earth & moon). How is the energy generated? Consider it in terms of timescales But first, consider dynamical timescale (freefall collapse) - Chemical Energy (I.e, that bonds molecules together) -

20 Generation of Solar Energy Gravitational Energy (Kelvin-Helmholtz timescale) - Recall that the potential energy difference between two points r 1 & r 2 for objects of mass M & m is Thus, for m at r 1 = " from M, the potential energy at r = r 2 is

21 Generation of Solar Energy Gravitational Energy (Kelvin-Helmholtz timescale) - Imagine building a spherical body with constant density by laying infinitesimally thin shells of mass, on top of the sphere of mass already built. The gravitational energy released in adding this shell (or removing it) is, If the sphere is built to radius R (or taken apart), the total energy released (or required) is

22 Generation of Solar Energy Gravitational Energy (Kelvin-Helmholtz timescale) - Thus,

23 Generation of Solar Energy Nuclear Energy, I.e,. The fusion of Hydrogen into Helium - photon neutrino The conversion of mass to energy is thus Thus, the energy released per reaction is The nuclear timescale for the Sun is thus,

24 Generation of Solar Energy The actual value is, I.e, the Sun will continue burning H into He until 10% of its mass is converted into He.

25 Generation of Solar Energy Note that the process has many steps -

26 Two important points about Fusion 1) Fusion is the way by which elements heavier than hydrogen are built As stars evolve, they fuse different forms of light nuclei into heavier nuclei (such a Carbon & Iron). We ll discuss stellar evolution in detail later. Thus, without fusion, there would be no planets like the earth. I.e., planets like the Earth can exist because of fusion that occurred in stars before the solar nebula collapsed

27 Two important points about Fusion, cont. 2) The Sun is in hydrostatic equilibrium. It is this balance between the force of radiation pressure from fusion reactions & the force of gravity is what keeps stars stable Such stability is important for life on planets Given our prior calculation, the Sun has 5 billion more years to go in its present state

28 Equations of Stellar Structure 1) Continuity of Mass Mass in a spherical shell - 2) Hydrostatic Equilibrium - Upward Forces = Downward Forces

29 Equations of Stellar Structure 3) Energy Production - Define #(r) = energy production time -1 mass -1 (W kg -1 ). Power from shell is Note that, for the Sun, For humans,

30 Equations of Stellar Structure 4) Temperature Gradient - From our discussion of opacity, $, the fractional energy change in intensity is For a star (sphere), the luminosity passing through the shell is L. The fraction absorbed in the shell is!"dr. Thus, the absorbed flux is df absorbed sets up the temperature gradient.

31 Equations of Stellar Structure In equilibrium, where And in radiative equilibrium, F = B % = Planck function. Thus, We ve ignored angles in all of the above. An exact derivation gives

32 Equations of Stellar Structure Thus, there are 4 equations of stellar structure, plus the ideal gas law Variables - r, M(r ), " (r ), P(r ), T(r ), µ( r ), #(r ),!(r ). Note also that #(",T,µ) &!(",T,µ). Thus, the equations of stellar structure cannot be solved analytically.