TEMPERATURE OSCILLATIONS IN SOLAR PHOTOSPHERE CAUSED BY
PROPAGATION OF ACOUSTIC-GRAVITY WAVES OF SMALL AMPLITUDES.
Olshevsky V.L.
Main Astronomical Observatory, NAS, Ukraine, [email protected]
Abstract:
We analyze oscillations of temperature and velocity in the Solar
photosphere. We calculate oscillations using analytical solution of the
system of HD equations for isothermally stratified 1-dimentional
atmosphere model. The results of calculations are compared with data,
obtained in [1-2] by applying the inversion techniques to the observed
profiles of the K I 7699 A line [3]. In this way we investigate how well
the temperature oscillations in the photosphere can be described by
propagation of small-amplitude acoustic-gravity waves. On the other hand,
by means of such a comparison, we are able to conclude how well the
inversion methods can reproduce small-amplitude temperature oscillations.
It is shown, that calculated velocity oscillations correspond to observed
Model:
Ideal non-magnetic
HD equations:
r
r
r
dV
r
= -ÑP + g r ,
dt
r r
¶r
= -Ñ r V ,
¶t
dQ
d T R T dr
= cV
dt
dt
r dt
T1 P1 r1
= - .
T0 P0 r 0
( )
Newtonian cooling:
Up- and downflow solutions
of the dispersion relation:
Cv
dQ
= - T1
dt
tr
r 0 Cn
tn =
3
16ksT0
iw (iw + V0 z H )
i
1
kz =
±i
+
2
2H
4H
g *C*2
Exact solution:
V1z = V0 exp(ik z z + iwt )
1
æ 1
ö
ç - - ik z ÷
iw + V0 z H è H
ø
1
~
~
æ 1
*ö
P1 = P0 P V1z , P =
ç - - ik z g ÷
iw + V0 z H è H
ø
~
~
r1 = r 0 R V1z , R =
Relaxation time
(Shpiegel, 1957)
Comparison of the results of
modelling and inversion:
Ruiz Cobo et al. applied the inversion technics to the time series of K 7699A line and obtained the series of 1D photospheric
models. Using these models we have calculated the mean, undisturbed, atmosphere and computed waves propagating through
it. We have modeled propagation of monochromatic waves at six frequencies which were the most powerful in the velocity
spectrum. Oscillations were studied as function of height as well as in the scale of optical depth.
Stratification of the temperature (left) and velocity (right
panels) amplitudes and phases with optical depth. Solid line
corresponds to the results of inversion, dashed - model.
Temperature (left) and velocity (right panels) oscillations
on four fixed levels of optical depth. Note that temperature
oscillations are filtered for 6 choosen frequencies
Major conclusions:
1. The model reproduces the observed velocity oscillations well through the
whole photosphere on the optical depth scale as well as on the height scale.
2.The model can reproduce the height dependence of the temperature
oscillations only at heights above the temperature minimum, however the
inversion gives large errors at these layers.
3.The model gives large errors in the deep layers for the oscillations at levels
with fixed optical depth.
4. The local minimum of amplitudes at heights of 300-400km can not be
produced by vertical motions of the atmosphere as it was considered in [2].
Stratification of the temperature (left) and velocity (right
panels) amplitudes and phases with geometrical height. Solid line
corresponds to the results of inversion, dashed - model.
Temperature (left) and velocity (right panels) oscillations
on four fixed levels of geometrical height. Note that temperature
oscillations are filtered for 6 choosen frequencies
Panels by the left illustrate the last
conclusion: in the model atmosphere
also oscillates nearly in phase, but
there is no amplitude minimum around
300-400km heights.
References:
1. Ruiz Cobo, B.; Rodriguez Hidalgo, I. and Collados, M.// Astrophys. J.1997.488, 462.
2. Rodriguez, I.; Cobo, R.; Collados, M. and Bellot Rubio, L. // Astrophys. J. 2001.547, 491.
3. Bonet, J.A., Marquez, I., Vazquez, M., and Wehl, H. // Astron.&Astrophys. 1988.265, 23.
4. Khomenko, E. V.; Collados, M; Bellot Rubio, L. R. // Astrophys. J.2003.588, 606.
5. Mihalas D., Mihalas B.W. Foundation of Radiation Hydrodynamics. New York, 1984.
6. Spiegel, E.A. // Astrophys. J.1957.126, 202.