Astronomy 12- Interior of the Sun

  • Calculations reveal that the temperature in the Sun's core is about 15.5x10^6 K.  It also has an incredible amount of pressure caused by the remaining 75% of the Sun pushing down on it through gravity.  At these high temperatures and pressures, the nuclei of the Sun's hydrogen fuse together to produce nuclei of the element helium.  In this reaction a tiny amount of mass is lost:  It is transformed into a very large amount of energy -- the energy of the Sun.

  •  …if you take the parts of an atom (all the protons, neutrons and electrons) and add their individual masses up, you end up with a mass larger than the actual atom.  The difference is the Mass Defect.

    Mass Defect:  The difference between the mass of an atom and the mass of its individual parts.

  • It takes energy to keep the atom together, or more specifically the nucleus of the atom together.  This energy is called Binding Energy.  This binding energy is directly related to Einstein's equation E=mc2.  In fact the missing mass (Mass Defect) from the sum of the particles can be found using E=mc2.  All you need to do is rearrange this equation to find mass.

  • Thermonuclear Fusion:

    The most common reaction of any type, chemical or nuclear, in the universe is fusion.  This is the combination of light atomic nuclei into heavier ones and it is what powers all the stars in the universe!  Our Sun fuses hydrogen into helium resulting in the release of tremendous amounts of energy. 

    The process of fusing nuclei at such extreme temperatures is called thermonuclear fusion.  In particular, conversion of hydrogen into helium is called hydrogen fusion, and the same process provides the devastating energy of a hydrogen bomb.  The energy generated by hydrogen fusion in the Sun's core eventually escapes through the photosphere into space and that energy makes the Sun shine.  

    You may have heard comments that mass is always conserved or that energy is always conserved in a reaction.  We know that both of these concepts are inaccurate, because mass can be converted into energy and vise versa.  What is true, however, is that the total amount of mass plus energy is conserved.  So, the destruction of mass by the Sun does not violate any laws of nature.

    Hydrogen fusion is also called hydrogen burning, even though nothing is actually burned in the conventional sense.

  • Proton-Proton Chain reaction

    This reaction looks very complicated but that is because it takes a couple of steps.  More particles are produced and energy is given off in more than one stage.

    The nuclear transformations inside the Sun follow several routes, but each beings with the simplest atom, hydrogen (H).  Most hydrogen nuclei consist of a single proton.  The outcome of fusion is the creation of the next simplest nucleus, helium (He), consisting of two protons and two neutrons.  The fusion of hydrogen into helium takes several steps.  This particular sequence is called the proton-proton chain, and is the most common fusion process in the Sun.

  • Step 1:

    Two protons fuse to make a Hydrogen-2 nucleus (1 proton and 1 neutron -- also called a deuterium nucleus).  This also releases a positively charged electron, e+, called a positron and a neutral, nearly massless particle called a neutrino, ν.  We will get back to the neutrinos later.  For now, let's go back to the positron.  When a positron encounters a regular electron in the Sun's core, both particles are annihilated and their mass is converted into energy in the form of a gamma-ray photon.

    Step 2:

    The newly formed hydrogen 2 nucleus fuses with a second single proton to produce a Helium-3 nucleus which has two protons and 1 neutron.  A gamma ray is given off in the process as well.

    Step 3: 

    Steps 1 and 2 are happening all over the Sun's core so there are billions of these reactions taking place at 1 time.  Why this is important is because we need 2 Helium-3 nuclei for the third step.

    Two Helium-3 nuclei are fused together to form a Helium-4 nucleus (2 protons and 2 neutrons).  This reaction also releases 2 new single protons which can be used in another reaction.

  • Hydrostatic Equilibrium:  A scientific description of the Sun's interior, called a solar model, explains how the energy from nuclear fusion gets to the photosphere.  The model begins with the inward force of the Sun's gravity.  This force raises the pressure and temperature in the Sun's core.  However, because the Sun is not shrinking today, an outward force must counter the inward force of gravity.  That outward force is produced by the gamma-ray photons created during fusion.

    These photons slam into nearby ions and electrons in the solar core.  These particles absorb the energy of the photons and rebound at very high speeds.  Because they are densely packed together, they do not travel far before striking other particles.  In each collision, the particles exert forces on each other.  They then rebound, emitting photons and colliding with other particles.  The result of the frequent interactions is an outward force sufficient to counterbalance gravity.  The balance between the inward force of gravity and the outward force of the motion of the hot gas is called hydrostatic equilibrium.

  •  Random Walk in the Radiation Zone:

    • Once a gamma ray is released inside the core after a nuclear reaction has happened it must make its way out of the Sun.  Photons (particles of light) do not travel in a straight line however.  Because the density is so high inside the Sun there are a lot of particles that the photon can bump into.  When it does it is absorbed by that particle momentarily and then re-radiated with slightly less energy than it had before.  The energy that the photon loses is what provides the outward force keeping the Sun in equilibrium.  That means a lot of photons must be losing energy.  So a photon isn't absorbed just once.  It is absorbed millions of times as it makes its way from the core to the convection zone of the Sun's interior.  This is referred to as the Random Walk because the photon takes a zigzag path from the core to the convection zone that can't be predicted.  This path typically takes about 170 000 year

  • In the convection zone, the motion of particles is caused by the motion of hot gases rather than flying energetic photons.  So photons are able to pass through the convection zone relatively easily.  Particles however travel both in an upward and downward direction as a result of convection.

    • Convection is the result of moving hot gases or liquids (fluids).  Fluids are heated from underneath and they expand becoming less dense and therefore rising.  Once they reach the colder surface above they release some of their heat, as infrared photons, to that surface, become cooler,  so they condense and sink back down.  Each one of the circles in the above diagram is called a convection cell.

  • Convection Zone in the Sun:

    • There are approximately 4 million of these convection cells in the convection zone at any given time.  The grainy appearance of the Sun's photosphere is produced by the tops of these convection cells and is called granulation. 

  • Granulation on the photosphere:

    • The rising part of the granules are located in the center where the plasma (hot ionized gas) is hotter.  The outer edge of the granules is darker due to the cooler descending plasma.  A typical granule on the Sun has a diameter of about 1500 km and lasts between 8 - 20 minutes before dissipating.  Below the photosphere is a layer of "supergranules" up to 30 000 km (twice the diameter of the Earth) in diameter with a lifespan of up to 24 hours.  This is the top of the convection zone.  

  • Model of supergranules.

    • Different gamma rays created in the Sun's core lose different amounts of energy as they and their successors travel upward through the Sun.  Therefore, the photons emitted from the photosphere have a wide range of energy and wavelengths.  The most intense emission is in the visible part of the electromagnetic spectrum.  This is the origin of the blackbody nature of the photosphere's spectrum.  More on this in the next unit.

  • As explained in the proton-proton chain that powers the Sun, there are three things emitted during the nuclear reaction.  They were gamma rays, a positron, and a neutrino.  The positron would bump into an electron and annihilate through matter antimatter annihilation.  So that new gamma ray would do the random walk to get out of the Sun as well.  The third particle is the neutrino.  Neutrinos have no electric charge, and they are extraordinarily difficult to detect because they rarely interact with ordinary matter.  In fact, neutrinos interact so infrequently with matter that they can easily pass through the entire Earth as if it were not there.  The Sun is also largely transparent to neutrinos, allowing these particles to stream outward, unimpeded, from its core.