The Sun The Sun’s Spectrum Earlier in the course, I told you stellar spectra are black bodies Why are there all these features?

+ Spectral Lines High resolution solar spectrum In dense inner part, light gets randomized – black body spectrum Light passes through cooler stellar atmosphere But some wavelengths get absorbed! + -

Stellar spectra Approximate black body spectrum – color tells you temperature Red is cool, blue is hot Spectral lines tell you a lot about the star Different lines for each element (and ionization state) Strength tells you about composition and temperature

Composition of a Typical Star (Sun) 73.46% Hydrogen 24.85% Helium 0.77% Oxygen 0.29% Carbon 0.16% Iron 0.12% Neon 0.09% Nitrogen 0.07% Silicon 0.05% Magnesium ~0.14% Other

The Photosphere The point at which gas is thick enough that we can’t see through it This is a little shallower towards the edge Limb darkening Here we see shallow and cool Here we see deep and hot

The Stefan-Boltzmann Law Earlier, we discussed the energy density for black body radiation Imagine a region filled with black body radiation with a hole where it can flow out Only half of it is moving at all outwards This half is moving out at average speed ½c The flux* (power/area) for this flow is: Define the Stefan-Boltzmann constant  Then the flux is given by *Confusingly, called R in the book

Total Luminosity of a Star If the surface temperature of the star is T, we can multiply by the surface area of the star to get the total luminosity L For example, we can use this to get the surface temperature of the Sun: Solve for the surface temperature Another way to write the luminosity formula Divide by the same expression for the Sun

What Powers the Sun? The Sun has been shining for > 4 billion years Could it be chemical energy? The energy per kg is: Not nearly enough Could it be gravitational potential energy? Perhaps nuclear power? Looks likely!

The Proton-Proton Chain, Step 1 The Sun is made primarily of hydrogen Which has the most energy per nucleon Hydrogen must combine to make some heavier nucleus Simplest process: 1H + 1H  2He The problem: 2He is very unstable, and this process immediately reverses itself To stabilize it, the 2He must immediately + decay to make 2H The effective interaction (so far) is p+ p+ p+ n0 p+  e+ 1H + 1H  2H + e+ + e

Energy from Fusion Reactions For simple fusion reactions, where protons and neutrons are rearranged, easy to find the energy produced Consider a process like: From previous arguments, the energy produced would be But the charge of the nuclei is conserved, so For other processes, like + decay, we can use previously found formulas A + B  C + 

Sample Problem Find the energy for each substep in the process 1H + 1H  2H + e+ + e The two steps are The first step is a simple fusion The second step is a standard + decay Total energy for this process is 1H + 1H 2He 2He  2H + e+ + e

Why the Proton-Proton chain is slow + p+ n0 p+ + + 1H + 1H  2H + e+ + e + 0.42 MeV  e+ The protons repel each other until they get close together They therefore must be moving at high speed to get even a little close They then need to quantum tunnel the rest of the way This has a very low probability To get it to work, it then needs to immediately + decay To overcome all these difficulties, the temperature must be very hot Minimum about 10 million K In the Sun, the central temperature is about 15 million K The process is very temperature sensitive Even a small change in temperature causes a very large change in rate

The Proton-Proton Chain, Steps 2 – 4 + p+ + + p+ p+ 1H + 1H  2H + e+ + e + 0.42 MeV  e+ n0 The next few steps go much faster Step 2: The positron immediately finds an electron to annihilate with Step 3: The 2H nucleus finds another proton to combine with to make 3He Step 4: Two 3He nuclei find each other and make 4He plus two protons e+  e- + e+ + e–   +  + 1.02 MeV p+ n0 +  2H + 1H  3He +  + 5.49 MeV n0 + p+ 2 3He  4He + 2 1H + 12.86 MeV

The Proton-Proton Chain, Overview The net reaction is: The neutrinos leave and carry 2% of this energy The photons that were produced, and the kinetic energy of other products, heat the center of the Sun The 98% now works its way to the surface of the Sun 4 1H + 2 e–  4He + 2  + 26.73 MeV

Detecting the Neutrinos Neutrinos have a very low cross-section to interact with anything But there are an enormous number of them streaming towards the Earth Neutrino detectors detect a very small fraction of these neutrinos Homestake neutrino detector Sudbury Neutrino Observatory

The Sun imaged in neutrinos Neutrino Detectors The Sun imaged in neutrinos Super Kamiokande

Ways to Move Heat Three ways that heat can move: Conduction – heat by physical contact Too slow in stars Convection – the flow of fluids Important in the Sun and other stars Radiation – the flow of electromagnetic radiation

How Heat Moves in the Sun There are three regions in the interior of the Sun The core Where the energy is generated The radiative zone Heat moves by radiation Note this is largest region The convective zone Heat moves by convection