Measurement of energies of MHD waves

1
6th SOLAR-B Science Meeting, Nov. 8-11, 2005,
Kyoto
Measurement of energies of MHD waves generated by
a microflare by SOLAR-B Takaaki Yokoyama
(University of Tokyo)
The dissipation of MHD waves is suggested as a
possible mechanism of the coronal heating. The
measurement of the wave energy and its
dissipation rate is one of the most important
subjects that have to be studied during the
SOLAR-B project. In this paper, we will discuss
how to measure by SOLAR-B the wave energy
generated by a flare or a microflare. By using
the three-dimensional simulations of propagation
of linear MHD waves, the predicted profiles of
SOLAR-B/EIS data as a function of the wavelength,
time, and space are presented.
Introduction
MHD simulation of Alfven-wave generation by
reconnection (Yokoyama Shibata 1998)
Waves Generated by a Microflare
The dissipation of MHD waves is suggested as a
possible mechanism of the coronal heating (e. g.
Ionson 1978 Heyvaerts Priest 1983). Magnetic
reconnections in the corona and/or in the
chromosphere can be a source mechanism for the
generation of such waves (e. g. Sturrock 1999).
From the results of two-dimensional MHD
simulations, more than 10 of the released energy
is given to the waves (Yokoyama Shibata 1998
Kigure et al. 2005). The measurement of the
wave energy and its dissipation rate is one of
the most important subjects that have to be
studied during the SOLAR-B project in the context
of the coronal heating problem. In this paper, we
will discuss how to measure by SOLAR-B the wave
energy generated by a flare or a microflare. By
using the three-dimensional simulations of
propagation of linear MHD waves, the predicted
profiles of SOLAR-B/EIS data as a function of the
wavelength, time, and space are presented.
(TRACE)
Color map velocities normal to B in
the simulation plane. normal to the
plane

• The EIS slit is set near an active region.
• Put where the magnetic structure is uniform.
• A spatial scanning is not necessary.
• As short cadence as possible.

Fast-mode Alfven waves
Alfven wave
Fast-mode MHD wave
Measurement is done at x5w. The z-axis is along
the line-of-sight, and the y-axis is along the
slit.
pressure perturbation (dp/p6e-2, width w) at
(x0, y0, z0) on uniform plasma (B, p, r are
constant)
velocity perturbation (Vz/Cs1e-3, width w) at
(x0, y0, z0) on uniform plasma (B, p, r are
constant)
Fast-mode MHD wave
t/ts
t/ts
tsd/Cs
tsd/Cs
y/w
t/ts
y/w
Alfven wave
Vz/Cs
t/ts
t/ts
Vz/Cs
Vz/Cs
Derivation of Physical Variables
tA
(2) The arrival time of the Alfven wave tA is
obtained from the plot of I Vz(Dl), yyB, t.
From the formula , Bx/B is
obtained.

• (0) Measure following variables from imaging
  observations
• apparent distance between the flare site and the
  slit position d
• position of the crossing point of the field line
  with the slit yB and the crossing angle fB

t/ts
Vz/Cs
And from , By/B can
be also obtained. Then, Bz/B can be calculated.
(3) From the duration of Alfven wave detection,
the spatial scale of the wave wA can be
estimated. The amplitude uA is also measured
directly.
wA/CA
wf/Cf
(1) Using EIS data cube, make a plot I Vz(Dl)0,
y, t and fit the edge to determine Cf. In case
of low b , it is reasonable to take CA Cf .
tf
uf
t/ts
uA
The energy of Alfven wave is
Vz/Cs
(4) In the similar way, the parameters for the
fast-mode MHD sonic wave, i.e. wf and uf can be
measured. The energy of the fast-mode wave is
EIS Observation
References

• Necessary to resolve the wave amplitude with a
  velocity of (maybe) several percents of
• The wave signal will be strong enough if the
  spatial scale (along the line-of-sight) of the
  wave packet is larger than 1e4km.
• Simultaneous observations of imaging instruments
  in the EUV range are critical. The best is with
  TRACE.
• Farther studies are necessary on the subjects of
• the effect of non-uniform magnetic field and
• the effect of reflection waves at the
  chromosphere-corona boundary.

Heyvaerts Priest, 1983, AAp, 117, 220 Ionson,
1978, ApJ, 226, 650 Kigure et al. 2005,
submitted Sturrock, 1999, ApJ, 521, 451 Yokoyama
Shibata, 1998, in solar Jets and Coronal
Plumes, p215