Set the Controls for the 
Heart of the Sun

! What is “one solar luminosity”?! What powers the Sun? Why couldn’t the Sun be powered

by combustion (e.g. burning gasoline) or by contraction?! Is fusion the process used in nuclear power plants?! What temperature does the p-p chain require? What are

the main inputs to, and products of, the p-p chain?! From the p-p chain, and the Sun’s luminosity (Energy

output per second) and mass, how can we find the Sun’s age? What is the Sun’s current age and total lifetime?

! How hot is the Sun’s core? How does energy move from the core to the photosphere? How long does this take?

! How do neutrinos prove that nuclear fusion powers the Sun? How long do neutrinos take to escape the Sun?

Learning Objectives

All of the world’s nuclear weapons: 3 x 104 megatonsThe Sun releases over 3 million times 
this every second

The Sun’s Energy Output3.85 x 1026 Watts, but how much is that?

We’ll generally refer to an energy release of 3.85 x 1026 Joules each second (Watts) as: 1L⊙ (1 Solar Luminosity)

What Powers the Sun?! The Sun’s total available energy is:

!The Sun’s total Mass (in kg) x The energy that can be released per kg (Energy per kg)

! The Sun’s lifetime in years is then:! total available energy / energy output per year

! We know the Sun’s energy output per year from how much energy hits the Earth (3.85 x 1026 Joules per second) and we know the Sun’s mass from its gravitational influence (1.99 x 1030 kg)

! The Sun’s lifetime in years turns out to be about:


1 x 10-4 x Energy (in Joules) released per kg

What Powers the Sun?

What Powers the Sun?! If the Sun were powered by combustion (e.g.,

gasoline) it would last a few thousand years! Up until the early 20th Century it was thought that

the Sun might shine due to energy released from gravitational contraction

! This gives a maximum life of about 20 million years!The Sun would contract ~20 meters per year!Some of the Earth’s rocks are older than 100

million years old (some rocks are radiometrically dated to over 4.4 billion years old)

!A new energy source was needed to explain the Sun’s incredible power output

Matter-Energy Equivalence ! The key to solar energy was 


provided by Einstein’s Theory 
of Relativity

! It said mass could be converted 
into energy (and vice-versa)!E = mc2!Tiny amounts of matter can be 


converted into tremendous amounts of energy!A single gram of matter could provide enough

energy to serve your household needs for a million years

Fusion!A helium atom has two protons and two neutrons!Hydrogen has only one proton

!But, helium is 0.7% less massive than four hydrogen atoms

! If you create 1 helium atom from 4 atoms of hydrogen the left over mass becomes energy!Based on the number of kilograms of mass the 


Sun must burn to provide its observed energy 
output, and 0.7% (0.007) of the hydrogen mass 
being converted to energy, the Sun burns 
600 billion kg of hydrogen each second

Fusion!Conclusion...the Sun burns 600 billion kg of

hydrogen each second! this is 2 x 1019 kg 


of hydrogen mass 
burning each year

!We know the mass 
and composition of 
the Sun (so we know exactly how much of the mass is currently hydrogen)! The Sun’s total mass is about 2 x 1030 kg! More than a half of this mass is still hydrogen

Note: Fusion Not Fission! Merging light nuclei:

fusion!Happens in the Sun!The hydrogen bomb

! Breaking up heavy nuclei: fission!Used in nuclear

power plants!The atom bomb

Fusion

Fission

!The Proton-Proton Chain (called the “p-p chain”)!4 hydrogen 


atoms fuse!Requires high 


temperatures 
(at least 7 million K)

!The products are a 
helium atom, energy 
(in the form of photons) 
and a particle called the 
neutrino (more about neutrinos later)

The Proton-Proton 
(p-p) Chain

Nuclear Fusion in the Sun

Solar Fusion and the p-p Chain

! The Sun is currently 
stable

! But it’s made from
gas, it’s not solid 
like the Earth

! So, why doesn’t the 
Sun collapse under
its own gravity?

! Outward pressure due 
to radiation created by
fusion balances the inwards force of gravity

! The Sun is in hydrostatic equilibrium

Why Doesn’t the Sun Collapse?

! It is simple (honest) to 
estimate the force of the 
Sun’s gravity on itself

! Also easy to estimate 
the temperature of 
gases at any pressure

! Using these estimates 
we find that inside the 
Sun’s core the temperature is about 15 million K!This is easily high enough to allow the p-p chain

The Solar Interior

The Solar Interior! The Sun’s core contains


~30% of the Sun’s mass !about 6 x 1029 kg...but 


not quite all of this 
mass started out as 
hydrogen

! Burning 2 x 1019 kg of 
hydrogen each year, 
this is enough fuel to last about 10 billion years!The Sun is currently about halfway through its

fuel supply (it’s about 5 billion years old)

! The layer of the Sun 
that lies just outside 
the fusion-driven core

! In the radiative zone, 
the temperature is too 
low for nuclear fusion

! Insulates the core, 
keeps it hot

! Quiet, stable! Energy from fusion in the 


core moves out slowly through the radiative zone

The Radiative Zone

Inside the Radiative Zone! Photons are created by fusion in the core! They are absorbed by atoms and re-

emitted as lower-energy photons 
in different directions

! This absorption and emission 
process is repeated over 
and over again

! Because of the high density 
in the radiative zone, it takes 
hundreds of thousands of 
years for energy to get from 
the core of the Sun to the 
outer layers of the Sun

The Convective Zone! Outside the 


radiative zone! Transports 


energy by 
convection 
(i.e. currents of heat) rather than by radiation

! Hot gas rises, cool gas falls! The photosphere is at the very top of the

convective zone; granules are convective gas reaching the top layer of the Sun

! For our purposes convection = boiling

Neutrinos! Nuclear fusion in the core of the Sun

also produces a particle called a neutrino! Matter is almost transparent to neutrinos! On average, it would take a block of lead

about one light-year in size to stop one half of a stream of neutrinos

! Roughly 100 billion pass through every square centimeter of you every second!

! They escape the Sun immediately, not in hundreds of thousands of years

The Sun in Neutrinos! A long exposure

picture of neutrinos emitted by the Sun

! Another confirmation 
that nuclear fusion 
is happening in 
the Sun’s core

! 500 days of data Credit: R. Svoboda and K. Gordan (LSU)

mailto:svoboda@phlash.phys.lsu.eduhttp://www.phys.lsu.edu/

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