It was found that statistical equilibrium at the instantaneous values
of the hydrodynamic variables was a bad approximation. At times
of compression in a wave the instantaneous values would give increased
hydrogen ionization with the energy increase absorbed by an increase
of the hydrogen ionization energy with only a small temperature
increase as a consequence. Because of the long timescales for hydrogen
ionization and recombination this is not a realistic picture. Hydrogen
does not have time to ionize in the compression phase above about 500
km height and the energy therefore goes into increased temperature
instead of into hydrogen ionization energy. This leads to a much
sharper temperature increase over shock fronts than would be the case
with infinitely fast ionization/recombination rates.
Another conclusion from the simulation work is that our traditional
picture of stellar chromospheres has to be radically rethought.
The temperature rise exhibited
in semiempirical models of the non-magnetic solar chromosphere is
mainly a result of non-linear averaging of a shock dominated
atmosphere. Enhanced chromospheric emission, which corresponds to an
outwardly increasing semi-empirical temperature structure, can be
produced by wave motion without any increase in the mean gas
temperature. Hence, the Sun may not have a classical chromosphere in
magnetic field free internetwork regions (click on figure to the
right).
The bright grains are produced by shocks near 1 Mm height.
Shocks in the mid chromosphere produce a large source
function (and therefore high emissivity) because the density is high
enough for collisions to couple the CaII populations to the local
conditions. The asymmetry of the line profile is due to velocity
gradients near 1Mm. Material motion Doppler-shifts the frequency where
atoms emit and absorb photons, so the maximum opacity is located at --
and the absorption profile is symmetric about -- the local fluid
velocity, which is shifted to the blue behind shocks. The optical
depth depends on the velocity structure higher up. Shocks propagate
generally into downflowing material, so there is little matter above to
absorb the blue Doppler-shifted radiation. The corresponding red peak
is absent because of small opacity at the source function maximum and
large optical depth due to overlying material. The brightness of the
violet peak depends on the height of shock formation. The lower the
shock, the higher the density and the larger the source function. The
position in wavelength of the bright violet peak depends on the bulk
velocity at the shock peak and the width of the atomic absorption
profile (described with the microturbulence fudge parameter).
The bright grains are produced primarily by waves near and slightly
above the acoustic cutoff frequency. The precise time and strength of
a grain depends on the interference between these waves at the acoustic
cutoff frequency and higher frequency waves. When waves near the
acoustic cutoff frequency are weak, then higher frequency waves produce
grains. The "five-minute" trapped p-mode oscillations are not
the source of the grains, although they can modify the behavior of
higher frequency waves. The wave pattern that exists at the solar
surface is due to the interference of many trapped and propagating
modes, so that the grain pattern has a stochastic nature.
We have investigated the ionization of hydrogen in a dynamic Solar
atmosphere. As in the static case we find that the ionization of
hydrogen in the chromosphere is dominated by collisional excitation in
the Lyman-&alpha transition followed by photoionization by Balmer
continuum photons --- the Lyman continuum does not play any
significant role. In the transition region, collisional ionization
from the ground state becomes the primary process.
We show that the time scale for ionization/recombination can be estimated from the eigenvalues of a modified rate matrix where the optically thick Lyman transitions that are in detailed balance have been excluded.
We find that the time scale for ionization/recombination is dominated
by the slow collisional leakage from the ground state to the first
excited state. Throughout the chromosphere the time scale is long
(10^3-10^5 s), except in shocks where the increased temperature and
density shorten the time scale for ionization/recombination,
especially in the upper chromosphere. Because the relaxation time
scale is much longer than dynamic time scales, hydrogen ionization
does not have time to reach its equilibrium value and its fluctuations
are much smaller than the variation of its statistical equilibrium
value appropriate for the instantaneous conditions. The mean electron
density is up to a factor of six higher than the electron density
calculated in statistical equilibrium from the mean atmosphere. The
simulations show that a static picture and a dynamic picture of the
chromosphere are fundamentally different and that time variations are
crucial for our understanding of the chromosphere itself and the
spectral features formed there.
Carlsson, M., Stein, R.F.: 1999,
in Solar Wind 9,
ed. S.R.Habbal, R.Esser, J.V.Hollweg, P.A.Isenberg, AIP conference proceedings
471, p.23-28:
The Dynamic Solar Chromosphere
and the Ionization of Hydrogen
Carlsson, M., Stein, R.F.: 1999,
in Solar Magnetic Fields and Oscillations,
proceedings of ASPE98 conference,
ed. B.Schmieder, A.Hofmann, J.Staude,
p. 206-210:
Wave Modes in a Chromospheric Cavity
Carlsson, M., Stein, R.F.: 1998,
in Proceedings of IAU Symposium 285, ed. F.-L. Deubner. p.435:
The New Chromosphere
Summary of the work above. Some new material on the dynamic formation of the sodium D-line and the use of the lambda-meter method to deduce velocity and temperature variations as functions of height.
Stein, R.F., Carlsson, M.: 1997,
in Proceedings of Århus Workshop on Solar Convection and
Oscillations and their Relationship, ed. J.Christensen-Dalsgaard,
F.Pijpers (in press)
The atmospheric response to convection and oscillations
Carlsson, M., Stein, R.F.: 1997,
in Solar and heliospheric plasma physics, Proceedings of the Eighth European Solar
Physics Meeting, ed. C.E.Alissandrakis, G.Simnett, L.Vlahos, Springer
(Lecture notes in physics 489) p.159
Chromospheric Dynamics -- What can we learn from numerical simulations
Skartlien, R., Carlsson, M., Stein, R.F.: 1994,
in Proceedings of the MINI-Workshop on
Chromospheric Dynamics, Oslo 6-8 June 1994, ed. M.Carlsson,
p. 79:
Calcium II Phase Relations and Chromospheric Dynamics
Carlsson, M., Stein, R.F.: 1994,
in Proceedings of the MINI-Workshop on
Chromospheric Dynamics, Oslo 6-8 June 1994, ed. M.Carlsson,
p. 47:
Radiation Shock Dynamics in the Solar Chromosphere --- Results of Numerical Simulations