Can magnetic waves in aurorae transform into acoustic waves?Jada Maxwell & E.J. Zita, The Evergreen State College, Olympia, WA 98505Contact: Jada Maxwell, maxjad02@evergreen.edu, http://academic.evergreen.edu/m/maxjad02; Dr. E.J. Zita, zita@evergreen.edu, http://academic.evergreen.edu/z/zita

Abstract

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.

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).

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?

Fig. 2 Coronal mass ejection (CME)Illustration by Steele Hill

Fig. 3 The magnetosphere of Earth is shaped by the solar wind.

Image courtesy of Minnesota Technolog

Fig. 4 Electrons spiral down Earth’s magnetic field lines.

Image: Halliday/Resnick/Walker, 746

Fig. 1 Aurora borealis over northern Michigan, 7 November 2004.

Image courtesy of Shawn Malone

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.

Waves Observed with Aurorae

Fig. 7 Alfvén wavesImages courtesy of Georgia State University

Fig. 8 Acoustic (sound) wavesImage: Halliday/Resnick/Walker, 449

Solar Acoustic-to-Magnetic Wave TransformationThe 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.

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-to-acoustic wave transformation.

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).

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.

Magnetic Pressure above Fairbanks, AK

2.40E-03

2.50E-03

2.60E-03

2.70E-03

2.80E-03

2.90E-03

3.00E-03

3.10E-03

0 50 70 90 120 150

altitude (km)

mag

net

ic p

ress

ure

(N

/m^

2)

PB

Atmospheric (Gas) Pressure above Fairbanks, AK

1.00E-04

1.00E-02

1.00E+00

1.00E+02

1.00E+04

1.00E+06

0 50 70 90 120 150

altitude (km)

pre

ssu

re (

N/m

^2) Pg

APS NW Section MeetingVictoria, B.C.13-14 May 2005

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

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.

0

speedAlfven B

vA

Acoustic WavesAcoustic 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

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.

iS m

Tkc

speed Acoustic

Auroral Magnetic-to-Acoustic Wave Transformation

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 anti-parallel to the electric field.

MHD waves can drive acoustic waves via both electric field perturbations E1 and velocity perturbations v1 (Fig. 10).

Fig. 9 Alfvén wave propagation and associated electric field

Image: Chen, 137

Fig. 10 Alfvénic electric field perturbations can drive acoustic waves

References:

1 Bogdan, T.J., et al.; Waves in magnetic flux concentrations: The critical role of mode mixing and interference, Astronomische Nachrichten 323 (2002)

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

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

Image sources:

Chen, Francis F. Introduction to Plasma Physics and Controlled Fusion. Plenum Press, 1984

Georgia State University<http://hyperphysics.phy-astr.gsu.edu/hbase/sound/tralon.html>

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>

Conclusions & Ongoing Research• 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

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

Calculating Gas Pressure (PG)

J/K1038.1

massion m

density mass

density particle

23

i

xk

mn i

nkTPG

Calculating Magnetic Pressure (PB)

(magnetic pressure)

(radial component of magnetic field)

(theta component of magnetic field)

(total magnetic field)

Chart 3

CMEs

Aurorae

MHD Waves

Infrasound

?

observed observed

observed

Chart 2

0

2

2B

PB

22BBB r

3

00 sin

r

rBB

3

00 cos2

r

rBBr

2

22

A

S

magnetic

gas

V

C

P

P

=1ResonantCondition

Chart 1: Magnetic-to-acoustic wave transformation can occur at about 120 km, where the gas pressure and magnetic pressure are comparable, ~1.