Class notes
Loss of energy from a star.
- Course
- Astro 101 (ASTRO101)
- Institution
- University Of Alberta (UofA)
Loss of energy from a star.
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At the core of all stars, there's a glowing nuclear furnace. We can be sure of this because we canmeasure how many neutrinos are streaming out of the sun with experiments like the Sudbury
Neutrino Observatory. This property of neutrinos, that they can pass through the core of the star
virtually unimpeded, is because neutrinos are weakly interacting particles. Which is to say that they
do not interact with electromagnetic forces. Light particles or photons do interact
electromagnetically and thus they have a very di cult time leaving the core of a star. Let's carve
into our own sun and examine how the energy produced at the core is radiated away as the light
that we see here on Earth. The innermost region of the sun extending from the center to about one
quarter of the radius of the sun, is the region where nuclear fusion takes place. This is aptly named
the thermonuclear energy core. In this innermost region, the temperature, pressure, and density are
extremely high, suitable for elements to combine in the process of fusion. The temperature has
been estimated to be 1.55 x 10 to the power of 7 K, roughly 15 million degrees. The density of the
material is nearly 14 times the density of lead and the pressure is almost a billion times the
atmospheric pressure here on Earth. Needless to say, you wouldn't want to go there but if you did
nd yourself there, you'd want to escape pretty fast. In order for energy to escape from this region,
it needs to be carried away by one of three processes: conduction, convection, and radiation.
Conduction, which is the propagation of heat through a solid, is ine cient in the sun because, well,
the sun isn't a solid. In this centermost region, extending to about three quarters of the diameter of
the sun, energy is carried away by radiative processes, the motion of photons. Extending outward
from the thermonuclear energy core, the radiative zone is a region of the sun where photons
dominate the energy ow towards the surface of the sun. You would think that light, travelling at just
over a billion kilometers per hour, wouldn't take long to escape from the core of the sun. And
indeed, if there was nothing impeding the progress of photons inside the sun, they would take
about 2.3 seconds to cross the sun's nearly 700,000 kilometer radius. But photons are impeded by
the materials of the sun. Instead of 2.3 seconds, photons take an average of 170,000 years to
escape into space. That's right, the energy we observe in the form of sunlight has been working its
way to the surface of the sun for hundreds of thousands of years. Within the rst three-quarters of
the diameter of the sun, photons bounce around on very short paths, randomly walking
their way towards the surface. Each step taken by a photon amounts to about 1 centimeter and the
energy must be carried nearly 700,000 kilometers. Just like the balls in this toy version of a rain
stick, photons jostle through the materials of the sun, colliding and careening their way to the
surface. Not every step will be directed towards the surface of the sun, though. But photons will
preferentially migrate towards the surface due to the temperature gradient. If you consider that this
rain stick has a gravity radiant, instead of a temperature one, it's not a bad analogy for the motion
of photons within the sun. Have a look at the math. If you took a 1 centimeter step every second, it
would take you over 2,000 years to walk 700,000 kilometres. But that's assuming that you
would walk in a straight line. If you stumbled around randomly, say, after getting o a dizzying
rollercoaster, it would take you quite a bit longer to get where you want to go. Eventually, the energy
from the core of the sun stumbles its way to the surface. From the centermost thermonuclear
energy core, encompassing the rst one quarter of the sun's radius, through the radiative zone,
from one quarter to about seven tenths of the sun, photons encounter the convective zone, the
outermost layer of the sun's surface. As you move outward, the average temperature of the sun
drops. And at the boundary of the convective zone, it's cool enough for electrons and protons to
join into hydrogen atoms which happen to be very good at absorbing photons. Radiative energy
transfer is no longer the dominant process and convection takes over. Atoms heated at the bottom
of the convective zone become buoyant and the mass of the hot atoms and plasma rise to the
surface like bubbles in a lava lamp. Cooler gas at the surface of the sun sinks down to replace the
hot gas that's rising and the process repeats. Once the hot gas reaches the sun's surface, energy
stored in the heat of the gas is emitted as black body photons which can then travel across the vast
distances of space, virtually unimpeded. Now that there are nally some photons escaping the sun,
let's put on our safe solar ltering glasses and have a look.
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