ENERGY TRANSPORT IN STARS

Ana Paola Mikler

http://brattahlid.tripod.com/Image179.jpg
Above: stratification of the interior of an average sized star, below: stratification of the interior of a massive star (Ediciones Orbis - Astronomia)

The energy produced by thermonuclear reactions in stars is produced in their core because only there the pressures and temperatures are high enough to sustain thermonuclear reactions. However, most of the luminous energy of stars is radiated from the thin region at the surface that we call the photosphere. How fast the energy gets out of the star determines:

A central issue for stars is how they transport the energy produced in the core to the surface. There are 4 important categories of such transport:

1. Convection

  Our Sun

2. Radiative Transport of Photons

3. Conduction

4. Radiation of Neutrinos




1. CONVECTION

Convection is the process where energy is carried from hotter regions at the bottom to cooler regions above by bulk buoyant motions of the gas. It occurs when the temperature gradient is very steep and quasistatic condition canít be maintained. Suppose there is a hot parcel of gas rising in the atmosphere, it will continue to rise if its ambient gas is cooler and denser, due to the buoyancy. Similarly, a falling parcel of gas willcontinue to fall if its ambient gas is hotter and less dense. In other words, this system is unstable. If we perturb a parcel of gas radially, instead of returning to its original position, the parcel will move further and further away from the original position. Energy is transferred in this process, because a rising hot bubble will eventually merge with its cooler environment, and, similarly, a cold descending bubble will descend and merge with its hot environment in the lower atmosphere. In convection, one has simultaneously rising hot bubbles and dropping cold bubbles.

Since convection involves the vertical motion of large packets of gas it is a very efficient method of energy transport. In most normal stars the energy transport is by radiation unless the rate at which energy is being produced in the interior exceeds a critical value, in which case the transport becomes convective however convection will start and stop at various points throughout the stars lifetime. In many stars both may operate: some regions of the interior may transport heat by convection and some by radiative transport.

On the Main Sequence, a low mass star will have convection in its outer layers, like the Sun. If it's really low mass it will have convection all the way in! A high mass star will have convection only in its core.

http://www.bramboroson.com/astro/images/stars_compare_convection.jpg

Convection is important because it can dig down into the star and bring up material from deeper down, or carry fresh material down closer to the core where temperatures are hotter.As well convection has a bif influence in the magnetic fields prodeced by our sun.

OUR SUN

In the Sun, the flows of hot plasma in the convection zone create the solar magnetic field. The moving charges are a current, and produce magnetic fields.The convection current is driven by the heat from the Sun's fusion.

Some scientist believe that convection creates the varying magnetic field at the sun's surface, but the ultimate reasons for each fluctuation in the flows and fields are not well understood yet

Sunspots

Sunspots are regions of very strong magnetic field, where the field lines get so crowded together that they push up through the surface, bringing some of the hot plasma with them in a spectacular arc, or loop. We see the end of the loop as a sunspot on the sun's photosphere. This dense bundle of field lines creates huge magnetic pressures.There are some indications that the magnetic forces hinder the convection of heat to the surface by making it harder for the hot gases to rise. Thus, the region in sunspots having strong magnetic fields tends to be cooler than the surrounding region and thus appears darker than the surrounding regions at higher temperature.

http://www.sunearthplan.net/media/tn_5863_whenthesunerupts.jpg

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2. RADIATIVE TRANSPORT OF PHOTONS

The most common method of energy transport in normal stars is by photons that are radiating away from the heat source.In average dimension stars, the layer above the central region, where the nuclear reactions are carried on is called the zone of transport through radiation (with a thickness of 360.000 to 410.000 km in the case of the Sun). In the deep interior, the stellar material is very opaque, so light travels only a small distance before it is absorbed. It is then re-emitted in a random direction, absorbed after a small distance, remitted, and so on until it reaches the surface. Therefore the gamma radiation gradually loses energy during this slow transportation process (one photon moves only 1 cm each 10 minutes). As well the process gradually enlarges the wavelength of those protons.

If we follow an average photon emitted in the core, its path outward to the surface is as follows:

  • Photon leaves the core.
  • Hits an electron or atom within ~1-mm and gets scattered.
  • Slowly staggers to the surface in a "random walk"
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit2/Images/RandomWalk.gif
http://www.oglethorpe.edu/faculty/~m_rulison/Astronomy/Chap%2016/Images/opacity.gif

On average, it takes about 200,000 years for a photon from the core to random walk its way to the surface.

Physicists have a colorful name for such a transport process: it is called the drunken sailor problem, because the path followed by the absorbed and re-emitted photons is like the one followed by someone too inebriated to stand up for long. For example, in the case of the Sun the average distance traveled by a photon between absorptions is about a centimeter, and it takes perhaps hundreds of thousands of years for the energy released in the center to make its way to the surface.

The flux Frad, can be expressed in terms of the temperature gradient and a coefficient of radiative conductivity, &lambda rad, as follows:

Frad = - λrad dT / dr

The minus sign indicates that heat flows down the temperature gradient. Assuming that all energy is transported by radiation.

The opacity, κ, is defined by the relation:

κ = 4acT3 / 3ρλ

where a is the radiation density constant.

By combining the two above equations and relating flux and luminosity, we obtain the equation of radiative transport. This will give us the temperature gradient that would arise in a star if all the energy were transported by radiation. It should be noted that the equation below also holds if a significant fraction of energy transport is due to conduction, but in this case L refers to the luminosity due to radiative and conductive energy transport and refers to the opacity to heat flow via radiation and conduction.

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3. CONDUCTION
http://science.nationalgeographic.co.uk/staticfiles/NGS/Shared/StaticFiles/Science/Images/Content/neutron-star-magnetar-ga.jpg

It is when heat is passed from atom-to-atom in a dense material from hot to cool regions.Conduction is the way in which metals transport heat. Usually it is not important in most normal stars, because the normal approximately ideal gas of a star is a good thermal insulator (like a blanket rather than like a piece of metal). However, under certain conditions involving very high densities, where the mean free path of electrons and ions are sufficiently long, the matter of a star may become what is termed degenerate. Conduction dominates energy transport in white dwarfs, neutron stars, or in the cores of massive stars, like red giants. For white dwarfs which are Ultra-dense stars (~105 g/cc) with no nuclear fusion in the core, the temperature is nearly uniform from the core to the surface.

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4. RADIATION OF NEUTRINOS

In massive stars, late in their lives the amount of energy that must be transported is sometimes larger than either radiation of photons or convection can account for. In these cases, significant amounts of energy may be transported from the center to space by the radiation of neutrinos. This is the dominant method of cooling or stars in advanced burning stages, and also plays a central role in events like supernovae associated with the death of massive stars.

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REFERENCES

http://csep10.phys.utk.edu/astr162/lect/energy/transport.html

http://74.125.93.132/search?q=cache:Ge2Kp3K0RMsJ:chandra.as.arizona.edu/~dave/535/lecture3.pdf+energy+transport+in+stars&cd=2&hl=en&ct=clnk&gl=us

http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit2/energy.html

http://www.jb.man.ac.uk/~smao/starHtml/radiativeTransfer.pdf

http://www.bramboroson.com/astro/images/stars_compare_convection.jpg

http://www.le.ac.uk/ph/faulkes/web/images/stars.jpg

http://angryastronomer.blogspot.com/2007_04_01_archive.html

http://brattahlid.tripod.com/sw3-52web.htm

http://www.vikdhillon.staff.shef.ac.uk/teaching/phy213/phy213_radiative.html

http://www.vikdhillon.staff.shef.ac.uk/teaching/phy213/phy213_radiative.html

http://cse.ssl.berkeley.edu/segwayEd/lessons/sunspots/research3.html

http://csep10.phys.utk.edu/astr162/lect/sun/magnetic.html

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