Stellar structure

Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star. Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star. Different layers of the stars transport heat up and outwards in different ways, primarily convection and radiative transfer, but thermal conduction is important in white dwarfs. Convection is the dominant mode of energy transport when the temperature gradient is steep enough so that a given parcel of gas within the star will continue to rise if it rises slightly via an adiabatic process. In this case, the rising parcel is buoyant and continues to rise if it is warmer than the surrounding gas; if the rising particle is cooler than the surrounding gas, it will fall back to its original height. In regions with a low temperature gradient and a low enough opacity to allow energy transport via radiation, radiation is the dominant mode of energy transport. The internal structure of a main sequence star depends upon the mass of the star. In stars with masses of 0.3–1.5 solar masses (M☉), including the Sun, hydrogen-to-helium fusion occurs primarily via proton–proton chains, which do not establish a steep temperature gradient. Thus, radiation dominates in the inner portion of solar mass stars. The outer portion of solar mass stars is cool enough that hydrogen is neutral and thus opaque to ultraviolet photons, so convection dominates. Therefore, solar mass stars have radiative cores with convective envelopes in the outer portion of the star. In massive stars (greater than about 1.5 M☉), the core temperature is above about 1.8×107 K, so hydrogen-to-helium fusion occurs primarily via the CNO cycle. In the CNO cycle, the energy generation rate scales as the temperature to the 15th power, whereas the rate scales as the temperature to the 4th power in the proton-proton chains. Due to the strong temperature sensitivity of the CNO cycle, the temperature gradient in the inner portion of the star is steep enough to make the core convective. In the outer portion of the star, the temperature gradient is shallower but the temperature is high enough that the hydrogen is nearly fully ionized, so the star remains transparent to ultraviolet radiation. Thus, massive stars have a radiative envelope. The lowest mass main sequence stars have no radiation zone; the dominant energy transport mechanism throughout the star is convection. The simplest commonly used model of stellar structure is the spherically symmetric quasi-static model, which assumes that a star is in a steady state and that it is spherically symmetric. It contains four basic first-order differential equations: two represent how matter and pressure vary with radius; two represent how temperature and luminosity vary with radius. In forming the stellar structure equations (exploiting the assumed spherical symmetry), one considers the matter density ρ ( r ) {displaystyle ho (r)} , temperature T ( r ) {displaystyle T(r)} , total pressure (matter plus radiation) P ( r ) {displaystyle P(r)} , luminosity l ( r ) {displaystyle l(r)} , and energy generation rate per unit mass ϵ ( r ) {displaystyle epsilon (r)} in a spherical shell of a thickness d r {displaystyle {mbox{d}}r} at a distance r {displaystyle r} from the center of the star. The star is assumed to be in local thermodynamic equilibrium (LTE) so the temperature is identical for matter and photons. Although LTE does not strictly hold because the temperature a given shell 'sees' below itself is always hotter than the temperature above, this approximation is normally excellent because the photon mean free path, λ {displaystyle lambda } , is much smaller than the length over which the temperature varies considerably, i. e. λ ≪ T / | ∇ T | {displaystyle lambda ll T/| abla T|} .