The velocity grows slowly without bound for as far out as the temperature is maintained. \) The momentum equation can then be written in the form \) Denote the critical radius \(R\ ,\) where the right hand side vanishes, by \(R = GM_0/2U^2\. Then \(U\) is a constant, and it is convenient to write \(V(r) = v(r)/U\. To illustrate these principles with a simple solution, consider the isothermal corona, in which the temperature \(T(r)\) is a constant. Note, then, that the factor in parenthesis on the left hand side crosses zero at the sonic point somewhere along the way from small to large \(r\ ,\) and, if \(dv/dr\) is to remain finite where \(v\) crosses over \(U\ ,\) then that sonic point must occur at the same location as the zero of the right hand side. Hence the right hand side starts out negative at small \(r\) and becomes positive at large \(r\ ,\) passing through zero along the way. \) It is also evident that, if the temperature \(T(r)\) varies asymptotically as \(1/r^\alpha\ ,\) where \(\alpha < 1\ ,\) the first term on the right hand side dominates the second term at large \(r\ ,\) and the right hand side is positive. The wind velocity and density vary widely between a slow dense phase, issuing from the vicinity of magnetic active regions on the Sun, and a fast tenuous phase issuing from the broad regions of weak magnetic field ( 0\. The helium abundance varies and is usually well below the normal solar abundance. The wind is mostly hydrogen, with a small percentage of helium by number, and smaller percentages of heavier elements. Those measurements established the theoretical prediction from the hydrodynamics of the solar corona that the expansion of the corona produces an ongoing supersonic wind blowing outward through the solar system. The first unambiguous verification of the existence of the solar wind was made from the Venus Mariner, or Mariner II, in 1962. Instruments carried on spacecraft give direct measures of the speed, density, temperature, and atomic composition of the solar wind. The region dominated by the solar wind is called the heliosphere. The solar wind spreads out as it races off into space, eventually being halted at distances of the order of 10 2 AU by the feeble pressure of the interstellar wind and magnetic field. But even during a month of inactivity at the Sun, the geomagnetic activity never ceases, and there is always an aurora to be seen on any cloudless night at high latitude, implying a continuing wind. Were it not for the wind, that part of the field should quiet down between outbursts from solar flares. Another indication of the solar wind is the ongoing rattling of the magnetic field of Earth, particularly at high geomagnetic latitudes, from where the lines of force extend far out into space. This fact was one of the principal clues leading to recognition of the wind as a simple hydrodynamic phenomenon. The solar wind blows the gaseous tails of comets into the antisolar direction, regardless of the existence or absence of flares or the general level of magnetic activity of the Sun. The solar wind sweeps out through the solar system, ruffling the magnetic fields of the planets and sweeping back the interstellar gas and magnetic field. The million degree outer atmosphere of the Sun (the corona) continually expands to produce the supersonic solar wind. 8 Interaction with the interstellar wind.4 Heat input and the origin of coronal expansion.
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