AboutPhilip A. Stahl Expertise I specialize in stellar and solar astrophysics. Can answer any questions pertaining to these areas, the spectroscopic analysis of stars – as well as the magneto-hydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions.
Experience Have published papers on the relationship between sunspot morphology and solar flares; discovery of SID flares related to this, constructed computerized stellar models; MHD research.
Organizations American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.
Publications Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France)
Education/Credentials B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.
Awards and Honors Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society
Now take the strip and put a kink or half-twist into it about two –thirds from one end, then tape the free ends. What you will have is called a Moebius strip.
The Moebius strip has one part twist and one part writhe and this is the fundamental basis of helicity. You can get a pictorial idea by going to:
“Magnetic helicity” was probably first introduced by K. Moffat in the late 1950s as a topological invariant that describes the complexity of a magnetic field. Like the pure tolpological helicity, this magnetic helicity also has “twist” and “writhe” components. It is written as a function of the vector potential (A) and the magnetic field (B), and measures the topological linkage of magnetic fluxes (F)
The magnetic helicity H of a field with characteristic magnetic induction B within a volume V is defined:
H = INT_ V A*B dV
where INT denotes integral over the volume V and A is the vector potential, B is the magnetic induction.
In actual working solar conditions, one prefers a gauge-invariant form of H and this is provided by the “relative helicity” – wherein one subtracts the helicity of some reference field (B (o), e.g. associated with the force-free parameter alpha = 0) and having the same distribution of the normal component of B on the surface (S). Thus,
H_r = [INT _V A*B dV - INT V_o A_ o B_o dV_o]
It is hypothesized that shearing and twisting of the field “injects” helicity and that this may be useful in quantifying: a) how much magnetic free energy becomes available, and b) whether instability can be predicted based on observed indicators of helicity at the level of the photosphere-chromosphere.
H(R) can then be resolved into two components such that:
d H(R)/ dt = d H(R) [T] / dt + d H(R) [W] / dt
where term 1 on the RHS refers to the “twist” and term 2 to the “writhe”
We see evidence of the Sun’s magnetic helicity in the solar corona as well as the solar wind that streams past Earth. In eruptive prominences, for example, we actually have images that show the twist and writhe (or helical structure) associated with topological helicity – and which is magnetic helicity in the Sun’s magnetic environment.
For example, if you carefully inspect and study the prominence in the upper right of the image below, you can discern both twist and writhe in the plasma filaments. Evidently then, prominences are capable of transporting magnetic helicity in the solar corona.
Solar eruption, especially coronal mass ejections (CMEs) carry magnetic flux as well as helicity from the Sun. When the erupted magnetic field reaches the Earth it interacts with the magnetosphere, causing magnetic substorms and auroras.
Some recent research also reveals remarkable aspects of magnetic helicity in the solar environment. For example, it seems that magnetic helicity of different signs or polarities (+ or -) can occur, depending on which hemisphere of the Sun it’s measured.
When you think about it, though, this makes eminent sense. (Think of the Coriolis force causing a preferred sign or handedness, relative to convective flows in the northern and southern hemispheres of a planet like Earth) If there is a preferred “handedness” (or chirality) associated with magnetic flux, it would be expected to exhibit a different sign in each hemisphere.
Observations confirm that this sign asymmetry exists throughout the solar atmosphere: in the corona, the solar wind and the photosphere. (For the latter evidence, see, e.g. A.A. Pevtsov et al, The Astrophysical Journal, Vol. 473, p. 533, 1996)
Lastly, it is possible that magnetic helicity exchange may lead to instability in a system with higher helicity. In this way, some solar flares may be understood in terms of arising from a helicity exchange process. We will learn more as lab plasma experiments continue, especially those that seek to duplicate "solar prominences" in the laboratory - so we can then more closely study the effects of magnetic helicity on stability.
