Dynamical Properties of Stellar Coronas and Stellar Winds. II. Integration of the Heat-Flow Equation.

Abstract

view Abstract Citations (134) References (26) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Dynamical Properties of Stellar Coronas and Stellar Winds. II. Integration of the Heat-Flow Equation. Parker, E. N. Abstract The temperature T(r) in a stellar corona is computed under the circumstances that energy is supplied outward from the base of the corona only by thermal conduction. The heat-flow equation is solved analytically under a variety of circumstances. It is shown that the energy flow to infinity is non-vanishing for finite coronal density and thermal conductivity. The temperature declines less rapidly than 1/r, and a supersonic stellar wind is the only available solution of the equations compatible with negligible pressure at r = A variety of asymptotic cases are worked out to illustrate some of the temperature proffles T(r) to be expected under various circumstances. For instance, in a corona of very low density the energy consumed by expansion of the corona can be neglected and T(r) , as in Chapman's original static coronal model. The result is a supersonic stellar wind with a velocity v( ) of the same order as the gravitational escape velocity 21!2w. In a corona with medium density and sufficiently low temperature that v('0) is small compared to w, a near region, in which T(r) extends for some distance outward from the star before the far region, T(r) , takes over. The result is a supersonic stellar wind velocity v( ) of the same order as the characteristic thermal velocity C0 at the base of the corona. In a corona which is exceedingly dense, an intermediate region in which T(r) appears between the near and the far regions, which has the result of extending to large distance the point at which the coronal expansion becomes supersonic. In a corona which is exceedingly hot (cc w) the expansion becomes so violent that thermal conduction becomes negligible and the behavior of the corona is approximately adiabatic. It is shown that any effect which tends to reduce the thermal conductivity of the coronal gases at large distance from the star has the effect of enhancing the velocity of the stellar wind. Comparison with Chamberlain's earlier discussion of the solution of the momentum and heat-flow equations in his "solar-breeze" model shows that he made two self-consistent errors in his assumption that the energy flux in the solar wind is identically zero and that the gas motion is adiabatic at large radial distances from the sun. It is shown that neither assumption is correct in a corona of finite density. It is shown, however, that the analytical form T(r) 1/r suggested by Chamberlain is obtained in the limit as the density of the corona is made large without limit, in which case all motion in the corona approaches zero. Application of the solutions of the heat-flow equation to the sun-assuming that the solar corona is heated solely by thermal conduction-show that at least under present conditions the solar corona and wind lie in the middle ground between high and low density and temperature. Assuming that they have coronas heated solely by conduction it is suggested that some of the giant stars with the low gravitational escape velocities, may fall into the high-density case, and certain dwarfs into the low-density case. Some of the very active stars may fall into the high-temperature quasi-adiabatic case. Publication: The Astrophysical Journal Pub Date: January 1964 DOI: 10.1086/147741 Bibcode: 1964ApJ...139...93P full text sources ADS | Related Materials (4) Part 1: 1964ApJ...139...72P Part 3: 1964ApJ...139..690P Part 4: 1965ApJ...141.1463P Part 5: 1966ApJ...143...32P