Thomas Smid wrote:

Ulf Torkelsson wrote in message ...


Thomas Smid wrote:





On average, the corona actually still has a temperature less than the
(gravitational) binding energy, but there is a relatively large number
of particles with a high enough energy to escape.



No, it does not. It has been known since the 1950s that in order to
have a
stable corona you would need an external confining pressure exceeding the
pressure of the interstellar medium by many orders of magnitude. This
failure to construct a realistic model of a hydrostatic corona led Parker
to construct his solar wind model.



The kinetic energy required to escape the solar gravitational field
corresponds to temperatures in excess of 10^7 K. The coronal
temperature is well below this.

OK, yes you can construct an isothermal hydrostatic model of the solar
corona, but such a model has a finite pressure at infinity, that is higher
than the pressure of the interstellar medium surrounding the Sun,
therefore this cannot be the correct description of the solar corona, and
it rather turns out that you get a good description of the entire
heliosphere
by abandoning the assumption that the corona is hydrostatic, and instead
use a solar wind model.

Of course, for a gas in thermodynamic
equilibrium there will always be particles with an energy high enough
to escape the gravitational field. However, the loss of particles is
so insignificant that you can consider the corona (as well as the
solar wind) as quasi-stable.

Well such models do not manage to generate a solar wind, which is
as fast and as massive as is observed, so that model is out, and has
been known to wrong since the 1960s, when the solar wind was
observed.




The emission of radiation is not the cause of the cooling but merely
the consequence. Just imagine that all the atoms in a volume of gas
are in an excited atomic state. The subsequent decay of the electrons
to a lower level would only lead to an emission of radiation but leave
the kinetic energy of the atom unchanged. For the latter to be reduced
one needs inelastic collision processes of the atoms (or protons in
the solar case).



This description is inaccurate. It is the inelastic collisions that
excite
the atoms in the first place, and the energy is then lost from the plasma
for good when the atoms deexcite by emitting radiation.



The kinetic energy of the protons is lost when they collisionally
excite neutral atoms (of which there a few in the photosphere but
still some). It is irrelevant for the gas temperature what happens to
the excited atoms afterwards, i.e. if the radiation leaves the volume
or not).

No, it is not irrelevant at all. There are, in general, two ways in
which an excited atom can lose its extra energy, by radiative
deexcitation, in which case the photon carries away the energy from
the plasma for good if the plasma is optically thin, or by collisional
deexcitation, in which case it is transferred as kinetic energy to a new
atom.





Without these one would not see the sun as a sharply
defined disk but as a fuzzy ball (the latter would still radiate
though because of recombination of protons and electrons, which
however does not affect the overall temperature)



And this is plainly wrong. The reason that we see the Sun as a
sharply defined disk is that the opacity of the solar plasma drops
drastically at the photospheric temperature. Therefore over a short
interval in temperature, or equivalently radius, the plasma goes
from being opaque to being completely transparent.




No, the reason we see the sun as a sharply defined disk is the sharp
drop of gas density in and above the photosphere. This sharp density
drop is caused by the cooling due to inelastic collisions. As a
result, there is nothing left above the photosphere that you could
see.
Opacity alone could not produce the same effect. It would limit the
visibility to a certain depth but would not change anything about the
'fuzziness' above this height if there would not be sharp drop of
density.


I am sorry, but your are simply wrong here. The sharply defined
solar disc is due to the sudden drop off of the opacity, which depends
on both density and temperature. The temperature dependence of the
opacity is even easy to observe. The temperature in the solar
photosphere is lower above a sunspot, thus the opacity is smaller
there, and we are able to see to a deeper level inside the sunspot.
This results in that from our point of view the umbra, the central
part of the sunspot, is displaced towards the centre of the sun as
seen from the Earth as the sunspot approaches the solar limb. This
Wilson effect was described already in the 18th century.

Ulf Torkelsson