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Can magnetic waves in aurorae transform into acoustic waves?
Jada Maxwell & E.J. Zita, The Evergreen State College, Olympia, WA 98505
Contact: Jada Maxwell, [email protected], http://academic.evergreen.edu/m/maxjad02; Dr. E.J. Zita, [email protected], http://academic.evergreen.edu/z/zita
Abstract
Waves Observed with Aurorae
CMEs cause Magnetohydrodynamic
Waves
There are two basic types of
magnetohydrodynamic (MHD) waves, Alfvén
waves and magnetosonic waves. Alfvén waves
are transverse magnetic waves; they move along a
magnetic field line like a wave along a plucked
string (Fig. 7) with a velocity of
Alfven speed  v A 
Fig. 1 Aurora borealis over northern
Michigan, 7 November 2004.
Image courtesy of Shawn Malone
B
0 
where B is the magnetic field, μ0 is the magnetic
permeability and ρ is the mass density.
Magnetosonic waves are longitudinal
magnetic waves; they travel across magnetic field
lines and cause perturbations to the magnetic
pressure.
Both Alfvén and magnetosonic waves
have been observed in the ionosphere during
geomagnetic storms caused by CMEs4.
Acoustic Waves
CMEs are magnetized blobs of plasma. Plasma
is often called the fourth state of matter and is the state
in which most of the matter in the universe exists. It
is an overall neutrally charged, ionized gas of negative
electrons and positive ions. One characteristic of
plasma is that it creates and is affected by magnetic
and electric fields. The disturbances to the
magnetosphere caused by CMEs are called
geomagnetic storms - the magnetic field of the CME
is interacting with the magnetosphere. This interaction
takes place through magnetic reconnection (Fig. 5-6).
Waves are created in the magnetic field of Earth
during geomagnetic storms. Our question involves
these waves: Can magnetic waves in the auroral
region transform into sound waves?
Acoustic speed  cS 
APS NW Section Meeting
Victoria, B.C.
13-14 May 2005
observed
Aurorae
Tk
MHD waves have an associated electric field perturbation E1
and pressure gradients. In Alfvén waves the field E1 is perpendicular
to the direction of propagation k and velocity perturbation v1 of the
wave (Fig. 9). In magnetosonic waves the field E1 is perpendicular to
k and parallel to v1. In acoustic waves, the pressure gradient is antiparallel to the electric field.
MHD waves can drive acoustic waves via both electric field
perturbations E1 and velocity perturbations v1 (Fig. 10).
mi
where γ is the ratio of specific heats in an ideal
gas, T is the temperature, k is the Boltzmann
constant and mi is the ion mass.
The sound waves that have been
detected5 in association with aurorae are in the
infrasonic frequency range (<~20 Hz). Humans,
having hearing ranges from about 20 Hz to 20
kHz, cannot hear infrasound.
Chart 1: Magnetic-to-acoustic wave transformation can occur at
about 120 km, where the gas pressure and magnetic pressure are
comparable, ~1.
Image: Halliday/Resnick/Walker, 449
Fig. 7 Alfvén waves
Fig. 9 Alfvén wave propagation and
associated electric field
Fig. 10 Alfvénic electric field perturbations
can drive acoustic waves
Image: Chen, 137
Images courtesy of Georgia State University
Conclusions & Ongoing Research
Atmospheric (Gas) Pressure above Fairbanks, AK
Calculating Gas Pressure (PG)
Fig. 2 Coronal mass ejection (CME)
Illustration by Steele Hill
Solar Acoustic-to-Magnetic Wave Transformation
The surface of the Sun is around 5800 Kelvin (K), yet between 103 and
104 km from the surface there is a dramatic spike in the temperature of the
corona, to more than 1 million K. One source of this heating probably involves
the transformation of acoustic waves to magnetic waves.
Acoustic waves are created by convection under the surface of the Sun.
These waves travel away from the Sun, into the chromosphere, until the
atmosphere is no longer dense enough for them to propagate through. At an
altitude where the pressure of the atmosphere is comparable to the pressure of
the magnetic field, where ~1, these acoustic waves transform into magnetic
waves.
Fig. 3 The magnetosphere of Earth is
shaped by the solar wind.
Image courtesy of Minnesota Technolog
Where is β~1 in Earth’s Atmosphere?
, the ratio of gas pressure to magnetic pressure, is about equal
to one at the altitude where acoustic waves transform into magnetic
waves in the solar atmosphere. A place in Earth’s atmosphere where
~1 would be a good indication of the possibility for magnetic-toacoustic wave transformation.
Pgas
Pmagnetic
2
2 CS

2
 VA
=1
Resonant
Condition
Fig. 5 The magnetic component of a CME
that is anti-parallel to the dayside
magnetosphere allows for magnetic
reconnection. Dayside field lines become
“open” field lines and are dragged into the
magnetotail.
Fig. 6 Magnetic flux increases in the
magnetotail as dayside field lines
become part of the magnetotail. The
magnetotail is compressed and magnetic
reconnection occurs on the nightside of
Earth.
We find that ~1 around 120 km above Fairbanks. This height
is reasonable because the bottom of the aurora reaches only down to
about 100 km.
pressure (N/m^2)
1.00E+06
Fairbanks, Alaska, is a location which is subject to more auroral
displays than almost any other inhabited place on Earth. Infrasound has
also been detected and recorded in Fairbanks. For these reasons, we
have calculated  in Earth’s atmosphere above Fairbanks (Chart 1).
Image: Halliday/Resnick/Walker, 746
Infrasound
observed
Fig. 8 Acoustic (sound) waves

Fig. 4 Electrons spiral down
Earth’s magnetic field lines.
CMEs
Acoustic waves, or sound waves, are
longitudinal mechanical waves. As they
propagate through a medium they cause particle
displacement and pressure variations (Fig. 8).
The velocity of sound waves is
What is the aurora?
Aurorae are created when a coronal mass
ejection (CME, Fig. 2) from the Sun interacts with the
protective magnetic shield around Earth, called the
magnetosphere (Fig. 3). Auroral potential structures
accelerate charged particles down the magnetic field
lines of Earth toward the north and south poles (Fig.
4). As these particles travel toward the poles they
interact with atoms and molecules in the upper
atmosphere, or ionosphere. These interactions excite
the atoms and molecules, which then emit the energy
as light. This is the visible aurora (Fig. 1).
?
observed
1.00E+04
n  mi  particle density
Pg
1.00E+02
  mass density
PG  nkT
1.00E+00
0
50
70
90
120
m i  ion mass
150
1.00E-02
k  1.38 x10  23 J/K
1.00E-04
altitude (km)
• Waves can transform where β~1
• β~1 in the ionosphere at ~120 km, at 67ºN latitude
- CMEs create ionospheric Alfvén waves
- CMEs create aurorae
- Acoustic waves are observed with some aurorae
 Alfvén waves may create auroral acoustic waves
Chart 2
Calculating Magnetic Pressure (PB)
Magnetic Pressure above Fairbanks, AK
magnetic pressure (N/m^2)
Acoustic waves from the Sun's photosphere
transform into magnetic waves in the
chromosphere1-3. While there is no clear evidence
of audible sound in aurorae (e.g. northern &
southern lights), infrasound (acoustic waves below
20 Hertz) emanating from aurorae has been
detected. How are these auroral acoustic waves
created? Alfvén waves in the Earth's magnetosphere
have been observed to arise from solar magnetic
storms. Can these magnetic waves similarly
transform into acoustic waves? On the Sun, this
acoustic-to-magnetic wave transformation occurs
where the atmospheric pressure and the magnetic
pressure are comparable (~1), in the
chromosphere. This wave transformation is crucial
for transporting photospheric energy to the hot
corona. We investigate evidence and mechanisms
for magnetic-to-acoustic wave transformation in the
Earth's ionosphere, where ~1.
MHD Waves
Auroral Magnetic-to-Acoustic Wave
Transformation
3.10E-03
3.00E-03
PB
2.90E-03
 r0 
Br  2 B0 cos   
r
3
 r0 
B  B0 sin   
r
2.80E-03
2.70E-03
2.60E-03
(radial component
of magnetic field)
3
(theta component
of magnetic field)
2.50E-03
B  Br  B
2
2.40E-03
0
50
Chart 3
70
90
altitude (km)
120
150
2
(total magnetic field)
We plan to:
• Gather data from satellite observations of resonant acoustic and Alfvén
waves in a single CME induced geomagnetic event
• Evaluate how wave velocities, frequencies and wavelengths change as
altitude and β changes
• Use data of auroral infrasound observed at Earth’s surface to extrapolate
speeds in the ionosphere and compare to MHD wave speeds
• Include magnetosonic waves and their contribution to acoustic waves
2
B
PB 
20
(magnetic pressure)
References:
Image sources:
1 Bogdan, T.J., et al.; Waves in magnetic flux concentrations: The critical role of
mode mixing and interference, Astronomische Nachrichten 323 (2002)
Chen, Francis F. Introduction to Plasma Physics and Controlled Fusion. Plenum
Press, 1984
2 ---. “Waves In The Magnetized Solar Atmosphere II: Waves from Localized
Sources in Magnetic Flux Concentrations.” The Astrophysical Journal 599 (10
December 2003): 626-660
Georgia State University
<http://hyperphysics.phy-astr.gsu.edu/hbase/sound/tralon.html>
3 Johnson, M.C., S. Petty-Powell, and E.J. Zita. “Energy Transport by MHD Waves
Above the Photosphere Numerical Simulations.” (17 October 2002)
4 Ofman, L. “Alfvén waves in the solar corona, the solar wind, and the
magnetosphere.” American Geophysical Union, Fall Meeting 2004, #SM44A-02
5 Wilson, C.R. and J.V. Olson. “Auroral Infrasound Observed at I53US Fairbanks,
Alaska.” American Geophysical Union, Fall Meeting 2003, #U31B-0009
Halliday, D., R. Resnick, and J. Walker. Fundamentals of Physics (ed. 7). John
Wiley & Sons, 2005
Malone, Shawn. Online image. Lake Superior Photo.
<http://www.lakesuperiorphoto.com>
Minnesota Technolog
<http://technolog.it.umn.edu/technolog/novdec97/cover.htm>
Steele Hill, courtesy of NASA
<http://sohowww.nascom.nasa.gov/localinfo/steele.html>