Helioseiosmology.

Helioseismology

The science studying wave oscillations in the Sun is calledhelioseismology. One can view the physical processes involved, in the same way that seismologists learn about the Earth’s interior by monitoring waves caused by earthquakes. Temperature, composition, and motions deep in the Sun influence the oscillation periods and yield insights into conditions in the solar interior.

Waves

The primary physics in both seismology and helioseismology are wave motions that are excited in the body’s (Earth or Sun) interior and that propagate through a medium. However, there are many differences in number and type of waves for both terrestrial and solar environments.

For the Earth, we usually have one (or a few) source(s) of agitation: earthquake(s).

For the Sun, no one source generates solar “seismic” waves. The sources of agitation causing the solar waves that we observe are processes in the largerconvectiveregion. Because there is no one source, we can treat the sources as a continuum, so the ringing Sun is like a bell struck continually with many tiny sand grains.

On the Sun’s surface, the waves appear as up and down oscillations of the gases, observed as Doppler shifts of spectrum lines. If one assumes that a typical visible solar spectrum line has a wavelength of about 600 nanometers and a width of about 10 picometers, then a velocity of 1 meter per second shifts the line about 0.002 picometers[Harvey, 1995, pp. 34]. In helioseismology, individual oscillation modes have amplitudes of no more than about 0.1 meters per second. Therefore the observational goal is to measure shifts of a spectrum line to an accuracy of parts per million of its width.

Oscillation Modes

The three different kinds ofwavesthat helioseismologists measure or look for are:acoustic,gravity, andsurface gravitywaves. These three waves generatep modes,g modes, andf modes, respectively, as resonant modes of oscillation because the Sun acts as a resonant cavity. There are about 10^7 p and f modes alone.[Harvey, 1995, pp. 33]. Each oscillation mode is sampling different parts of the solar interior. The spectrum of the detected oscillations arises from modes with periods ranging from about 1.5 minutes to about 20 minutes and with horizontal wavelengths of between less then a few thousand kilometers to the length of the solar globe[Gough and Toomre, p. 627, 1991].

The image below was generated by the computer to represent an acoustic wave (p modewave) resonating in the interior of the Sun.

 

The figure above shows one set of standing waves of the Sun’s vibrations. Here, the radial order isn= 14, angular degree isl= 20, and the angular order ism= 16. Red and blue show element displacements of opposite sign. The frequency of this mode determined from the MDI data is 2935.88 +/- 0.2 microHz.

(You can also download apostscriptversion of the above figure and read thepreprint, (5.7 Mb,postscript) titled:Structure and Rotation of the Solar Interior: Initial Results from the MDI Medium-L Program.)

Why does the Sun act as a resonant cavity? Acoustic waves become trapped in a region bounded on top by a large density drop near the surface, and bounded on the bottom by an increase in sound speed that refracts a downward propagating wave back toward the surface. A standing wave is created.

Physically and mathematically, one can understand the oscillation modes using spherical harmonics:l, andm, andnvalues. The spherical harmonic functions provide the nodes of standing wave patterns. The ordernis the number of nodes in the radial direction. The harmonic degree,l, indicates the number of node lines on the surface, which is the total number of planes slicing through the Sun. The azimuthal numberm, describes the number of planes slicing through the Sun longitudinally.

 


Picture credits: Noyes, Robert, “The Sun”, in _The New Solar System_, J. Kelly Beatty and A. Chaikin ed., Sky Publishing Corporation, 1990, pg. 23.

The figure on the left shows spherical harmonic numbersl= 6 andm= 0. The dark regions are the nodal boundaries, the green colors denote areas moving radially outward, and yellow colors show those areas moving radially inward. The figure on the right shows spherical harmonic numbersl= 6 andm= 3. The dark regions are the nodal boundaries, the green colors denote areas moving radially outward, and yellow colors show those areas moving radially inward.

 

Solar Structure

We can learn about many astrophysical processes by studying the Sun as a star. We can learn about nuclear energy generation, energy flows, interaction of magnetic fields with matter, and particle acceleration to high energies. The theory of stellar structure and evolution is a principal foundation of astrophysics and of much of our current understanding of the universe. And a major goal of helioseismology is to determine if our theories of stellar structure and evolution are correct.

The theories of stellar structure and evolution applied to our Sun are calledsolar models. The solar model equations must be solved numerically, and the solutions are usually tables describing solar chemical composition, density, luminosity, mass, pressure and temperature at different depths in the Sun.

Helioseismology is currently the best method for verifying those theories and for understanding the structure and interior processes within a star.

According to standard solar models, thesolar structurelooks like the following. The Sun is a sphere of solar radius R* = 6.96^10^{10} centimeters, initially composed by mass of about 70% hydrogen, 28% helium and 2% heavier elements.[Harvey, 1995, pp. 32]. About half of the mass and 98% of the energy generation (where hydrogen fuses into helium) exists in a core with a radius of about 0.25xR*. On top of the core is a stable region called the “radiative zone,” where the energy is transported by radiation. At a solar radius of 0.713xR* and upwards to near the solar surface, the temperature is low enough that convection is the dominant mechanism for transporting energy. This zone is called the “convection zone.”

Velocity Pictures of the Sun

Since each oscillation mode is sensitive to the solar interior’s physical conditions where the amplitudes of the mode are the greatest, identifying oscillation modes is the mainstay of the helioseismologist’s work.

To identify the oscillation modes, many helioseismology experiments start with avelocity picture of the Sun, where each pixel tracks the velocity of a small area on the solar surface by fixing on the Doppler shift of a spectrum line. One needs sequences of these images in order to identify oscillation modes.

DecomposingDoppler shift imagesinto spatial spherical harmonics is the next step in identifying oscillation modes.[Harvey, J. 1995, pp. 35]. The coefficients of each spherical harmonic, as a function of time, are then Fourier transformed to generate a power spectrum as a function of three variables:nu, the frequency, the spherical harmonic degreel, and azimuthal orderm.“L-nu figures”are a familiar diagram to helioseismologists- it is by using datasets like this, that oscillation modes are identified.

Inverse Problems

Inverse problems usually start with some precedure for predicting the response of a physical system with known parameters. Then we ask: how can we determine the unknown parameters from observed data? The goal of solving an inverse problem in helioseismology is to invert the observed data in order to derive the internal properties of the Sun. In other words, regard the density, temperature, sound speed (c), etc. as the unknown quantities and use the observed oscillation frequencies to obtain those unknowns.

The SOHO/SOI-MDI group have obtained results forsound speed,rotation raterate and pinning down the position of the hypotheticaldynamothrough inversions of measured frequency data.

Time-Distance Methods

The most common observation made in Earth seismology is that of the arrival time of the initial onset of the disturbance. If we know the variation of seismic velocity with depth within the earth, then we can calculate the travel time of rays between an earthquake and a receiver using geometrical approximations. So in principle, we can locate any earthquake in both time and space by by recording the arrival times of waves at stations worldwide.

Intime-distance helioseismology, the idea is the similar. One picks a point on the solar surface as the “source”, and then assumes an annulus at some great circle around the point as a destination to which a wave may have travelled. Correlations between all points in the annulus are calculated, pulses with energy show in the calculated correlation function, and then one can derive time and distance for waves flowing in different directions.

The SOHO/SOI-MDI group have obtained results forsub-surface flowsand otherhorizontal flowsusingtime-distancemethods and inversion methods.

Sunspots

Large sunspots are as big as the Earth and contain magnetic fields that are thousands of times stronger than the Earth?s magnetic field. Sunspots occasionally grow large enough to be seen with the naked eye through fog or haze, or sometimes at sunrise or sunset, when the sun?s usual brightness is heavily dimmed. But normally, you cannot look directly at the sun without severely damaging your eyes, and most sunspots are too small to be seen without telescopes, which were introduced in the early 17th century. Still, ancient Chinese records indicate that large sunspots have been observed with the unaided eye for nearly 2,000 years.
Sunspots are not by themselves directly related to the Earth?s weather, but the active regions in which they are immersed do result in violent explosions that produce space weather. The solar flares and coronal mass ejections emit powerful radiation and hurl energetic particles into interplanetary space, producing gusts and squalls in the perpetual solar winds blowing from the sun. We are shielded from this space weather by the Earth?s atmosphere and magnetic fields, which keep us safe. But out in deep space there is no place to hide, and both humans and satellites are vulnerable.
When solar explosions are directed at the Earth, they can produce geomagnetic storms, high above our atmosphere, and alter the terrestrial ionosphere, affecting radio communications.

Sunflares

Flares occur when accelerated charged particles, mainly electrons, interact with the plasma medium. Scientific research has shown that the phenomenon of magnetic reconnection is responsible for the acceleration of the charged particles. On the Sun, magnetic reconnection may happen on solar arcades ? a series of closely occurring loops of magnetic lines of force. These lines of force quickly reconnect into a low arcade of loops leaving a helix of magnetic field unconnected to the rest of the arcade. The sudden release of energy in this reconnection is the origin of the particle acceleration. The unconnected magnetic helical field and the material that it contains may violently expand outwards forming a coronal mass ejection.[5] This also explains why solar flares typically erupt from what are known as the active regions on the Sun where magnetic fields are much stronger on average.

Solarwind

It affects it by the intense clouds of high energy particles that it often contains which are produced by solar storms. When these clouds, called coronal mass ejections, make their way to the Earth in 3-4 days, they collide with the magnetic field of the Earth and cause it to change its shape. The particles then leak through the magnetic field of the Earth, particularly near the north and south poles, and cause still more changes to the magnetic field of the Earth, this time at even lower altitudes closer to the ground. These changes can produce many problems with electrical equipment. The way on which solar wind ‘plasma’ invades the Earth’s magnetic field and seeps into the inner regions where the van Allen radiation belts are located, is not very well known. Also, in the direction opposite the Sun, the Earth’s magnetic field is pulled way out into interplanetary space making it look like a comet. In this ‘geotail’ region many different electrical disturbances take place that can accelerate particles to very high speeds and energies. All of this is made much more violent by the solar wind, especially the storm clouds that the Sun launches our way from time to time!

Understanding the sun as a something we rely on but take for granted every day, is extremely important in that it can effect the earth in many ways. I am a firm believer in preventative measures, educating, and being aware of things that effect each other on any scale. The science and research derived from the study of or sun can lead to future development of technological breakthroughs, as well as keep us aware of the relationship we have with it.


* > pre list referencedhttp://soi.stanford.edu
* > pre list referencedhttp://tuftsjournal.tufts.edu/2010/03_1/professor/01/

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