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Stellar Structure

The structure of stars can be illustrated by a pictures, which divide the body into zones as shown in Figure 08-04a and will be described in the followings for each zone within a typical star like the Sun. However, the diagram in Figure 08-04b conveys a little bit more information by plotting the variation of temperature and density for four different types of stars.
Stellar Structure Temperature-Density Diagram In the diagram, each line represents a star starting at the right with a point for the center and ending at the left with another point for the photosphere. The four intermediate points divide the star into five zones of equal mass. The dashed lines represent transitions in the equation of state. The dotted line separates two different kinds of opacity (electron scattering in the upper portion, bound-free/free-free transitions below). The crosses on the Sun and Red Giant indicate the transition from the convective layer to the radiative zone.

Figure 08-04a Stellar Structure
[view large image]

Figure 08-04b Density-Temperature Diagram [view large image]

Table 08-01 below lists some characteristics of main-sequence stars as the function of mass.

Mass (Msun) Energy Transport Zones Spectral Type Surface Temperature (1000 oC) Luminosity (Lsun) Diameter (Dsun) Central Density (Water=1) Lifetime (109 yrs)
0.1 M7 2.5 0.0001 0.1 60 1000
0.5 K8 3.8 0.03 0.7 80 100
1 G2 5.7 1 1 90 10
1.5 F3 6.3 5 1.3 85 1.8
2 A6 8.0 17 1.7 70 0.8
5 B8 9.5 500 3 20 0.075
10 B5 15.0 5000 5 9 0.02
15 B1 28.0 20000 10 6 0.01
30 O8 40.0 100000 15 3 0.004

Table 08-01 Characteristics of Main-Sequence Stars

    Stellar structure can be roughly divided into six zones according to some characteristics :

  1. Core - This is the region where energy is generated. It is in the inner most 30% of the radius (for Sun-like star). The nuclear reactions
    Stellar Fuel Residual Fuel involve mainly the p-p chain and CNO cycle (see Figure 08-04c and "Thermo-nuclear Fusion"). Near the end of the stellar life span, the core becomes the dumping site for the helium byproduct, the nuclear burning occurs in the envelope, and the star turns into a red giant. For massive stars heavier than 15 Msun, more residuals from helium to iron are deposited into the core, those stars are the supergiants.

    Figure 08-04c Stellar Fuel
    [view large image]

    Figure 08-04d Residual Fuel [view large image]

  2. Radiative Zone - The layer next to the core is the radiative zone where energy is primarily transported toward the exterior by means of radiative diffusion. The photons are absorbed and re-emitted in a slow process, which takes an average of 170,000 years for gamma rays
    Radiative Zone from the core of the Sun to leave the radiation zone (Figure 08-04-left). On top of this layer is a thin shell called Tachocline. This is the region where solid rotation passes over to differential motion in fluid. Many theories about the origin of the solar magnetic field have failed to account for its durability. Recent observations suggests that the sheared magnetic field lines in these two regions can account for this long lasting and strong magnetic field about 2000 times stronger than the Earth's (see Figure 08-04c-right, and "NASA's Issue #60 : Where Does The Sun's Magnetic Field Come From ?").

    Figure 08-04e Radiative Zone
    [view large image]

    Depending on the stability of the radiative process, the radiative and convective zones can be arranged differently according to different kinds of stars (Figure 08-04a). In term of the temperature T and pressure P, the criterion for stable radiative layer is :

    The curve for the B1 main sequence star with a mass of 15 Msun in Figure 08-04b clearly violates this radiative equilibrium condition near the core, thus the inner layer becomes convective as shown in Figure 08-04a. In the same diagram, the crosses on the Sun and Red Giant indicate the transition from the convective envelope to the radiative interior as the result of the bending of the steeper slope.

  3. Convective Zone - Convection occurs every time when we boil water in a pot. An element of fluid receives heat from the bottom,
    Convective Zone it expends into a spherical volume to equalize the pressure outside. The reduction in density inside allows the bubble to rise until the heat is released to the cooler environment at the surface and falls back to the bottom without the bubbly appearence (Figure 08-04f). Thus, the criterion for the formation of convective cell is the inequality of the densities environment > bubble (which is equivalent to the stable radiative condition) . The motion of photons are still impeded by interactions with the atoms there until they reach the boundary with the photosphere where the convective cells appear as granules. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma (see insert in Figure 08-04f).

    Figure 08-04f Convective Zone
    [view large image]

  4. Photosphere - The region under the photosphere is opaque up to the bottom of this layer from where radiation streams outward in the form
    Sunspots Formation of 6000 K blackbody spectrum (Figure 08-04h). The magnetic flux generated deep inside the convective zone becomes visible in the photosphere as a pair (corresponding to the two opposite polarity) of dark spots due to lower temperature compared to the surroundings. As shown in Figure 08-04g the spot where the magnetic field line emerges is cooler because the rising convective cell is block out. These sunspots move across the surface of the Sun with a life time from days to months and the number varies in 11-year cycle.

    Figure 08-04g Sunspots Fromation

    As the ionization energy of 13.6 ev for the ground level of hydrogen corresponds to a temperature of about 0.15x106 K, the number of neutral hydrogen atoms gradually increases from the bottom of the convective zone at 106 K to 6000 K at the bottom of the photosphere until most of them settle down to un-ionized state at the edge of the photosphere with a temperature of about 4000 K (see Figure 08-04i).
    Blackbody Spectrum Photosphere Photosphere The neutral atoms of various chemical elements in the cooler region would absorb radiation with specific wavelength creating the Fraunhofer absorption lines (see insert in Figure 08-04h). Figure 08-04j portrays the relationship between the photosphere and the formation of the absorption line.

    Figure 08-04h Blackbody Spectrum [view large image]

    Figure 08-04i Photosphere

    Figure 08-04j Absorption Lines Formation [view large image]

  5. Chromosphere - Temperature decreases to about 4000 K at the top of the photosphere. Then a curious phenomena occurs where instead of
    Chromosphere falling continuously as expected, the temperature starts rising to 3x104 K (Figure 08-04i). Nobody can offer a satifatory explanation except a hand-waving suggestion of broken magnetic field lines to provide the energy. This kind of rising temperature in rarefied gas occurs twice in the Earth's atmosphere. The same also happens within the inter-galactic cluster space, where the temperature can reach 108 K. The particle density there is even lower at 10-3 cm-3 (comparing to 1017 cm-3 (at bottom) - 1011 cm-3 (at top) in the chromosphere, and ~ 1019 cm-3 at sea-level on Earth). The energy supple in the intracluster medium is suggested to be gravitational in origin.

    Figure 08-04k Chromosphere
    [view large image]

    Due to the overwhelming brightness of the photosphere, the chromosphere is normally invisible except during a total eclipse (Figure 08-04k,a). However, many features show up by using special equipment (Figure 08-04k). Such detailed structures cannot be seen from other stars which appear point-like to us, its presence is detected only via the radiation originated at the photosphere. Followings are brief descriptions for some of those features, most of them have something to do with the magnetic field.
  • Corona - This layer is also invisible except during a total eclipse (insert in Figure 08-04l). The trend of rising temperature and falling density continuous until reaching some 106 K at the top (~ million km from the photosphere). Since there is a huge heat sink in the interplanetary space at about 150 K, this trend of rising temperature cannot maintain itself indefinitely. It is the open magnetic field line called "coronal hole",
    Corona Heliopause which channel the energy outward in the form of solar wind (Figure 08-04l). The point where the solar wind's strength is no longer great enough to push back the interstellar medium at about 120 AU is known as the heliopause (Figure 08-04m) and is often considered to be the outer border of the Solar System. At the boundary of collision, the shock wave generates lot of energy to rise the temperature again to about one million Kelvin.

    Figure 08-04l Corona
    [view large image]

    Figure 08-04m Heliosphere

    Oort Cloud Objects
      Terminlogy for Figure 08-04m :
    • Termination shock - the solar wind collides for the first time with the interstellar medium, slows down and changes direction.
    • Heliosheath - the outer region of the heliosphere; the solar wind is compressed and turbulant.
    • Heliopause - the boundary between solar wind and interstellar wind where they are in equilibrium.
    • Bow shock - the shock wave caused by the heliosphere in the direction it travels.

    Figure 08-04n Oort Cloud Objects [view large image]

    By definition, the heliopause is the edge of the solar system, which is now explored by the Pioneer and Voyager spacecrafts. Actually, there are cometary objects going around the Sun in the Oort cloud out to 50,000 AU (Figure 08-04n).

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