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# Astrophysics/Zeeman effect in sunspots

Question
Can you give me a quantitative example of how the Zeeman effect can be used to find the magnetic field strength of a sunspot?

Hello,

The classic Zeeman effect occurs in "triplet" form  and can be quantified as George Ellery Hale first showed (You can se a photograph with triplet splitting of a spectral line centered on a sunspot by googling "Zeeman Effect". Basically, the greater the spectral line splitting the greater the magnitude of the associated magnetic field.  Hale, who discovered the effect, posed the quantitative relationship in terms of the original wavelength lambda (0)  (undisturbed line) and the spread of wavelengths, Delta lambda:

Delta lambda = [lambda(o)] ^2  e H/ 4 pi  m_e c^2

Where H is the intensity of the sunspot magnetic field in gauss (to be found), e is the electron charge in e.s.u.,  m_e  is the mass of the electron in grams, and c the velocity of light in cm/ sec.

Now, consider an H-alpha line that undergoes triplet splitting in the vicinity of a sunspot. The undisturbed line is measured at: lambda (o)  =    6.62 x 10 ^-5 cm. The line shift on either side is: + 0.0025 Å. (Angstroms, where 1Å = 10^-8 cm)    We want to use this information to find the strength of the sunspot magnetic field: a) in gauss, b) in Tesla.

Solving for H:

H =  4 pi (Delta lambda)  m_e c^2 /[lambda(o])^2 e

Where: c =  3 x 10^ 10 cm/s

m_e  =    9.1 x 10^-28 g

(Delta  lambda) =  2 (0.0025 A) = 0.005 A

= 5.0 x 10^-11    cm

e = 4.8  x 10^-10 e.s.u.

Therefore: H =

4 pi(5.0 x 10^-11 cm)(9.1 x 10^-28 g)(3 x 10^10 cm/s)^2 / (6.62 x 10^-5  cm)^2 e

=  2.44  x 10^2 G

But 1 T = 10,000 G, so:

H =    2.44  x 10^ 2 G/  (10^4 G/ T) =   0.024 T

Questioner's Rating
 Rating(1-10) Knowledgeability = 10 Clarity of Response = 10 Politeness = 10 Comment Thanks! Just what I was looking for!

Astrophysics

Volunteer

#### Philip A. Stahl

##### Expertise

I specialize in stellar and solar astrophysics. Can answer questions pertaining to these areas, including: stellar structure and evolution, HR diagrams, binary systems, collapsars (black holes, neutron stars) stellar atmospheres and the spectroscopic analysis of stars – as well as the magnetohydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions. No nonsense questions accepted, i.e. pertaining to astrology, or 'UFOs' or overly speculative questions: 'traveling through or near black holes, worm holes, time travel etc. Absolutely NO questions based on the twaddle at this Canadian site: http://members.shaw.ca/warmbeach/FAQ.htm purporting to show a "new physics". Do not waste my time or yours by wasting bandwidith with reference to such bunkum.

##### Experience

Have constructed computerized stellar models; MHD research. Gave workshops in astrophysics (stellar spectroscopy, analysis) at Harry Bayley Observatory, Barbados. More than twenty years spent in solar physics research, including discovery of SID flares. Developed first ever consistent magnetic arcade model for solar flares incorporating energy dissipation and accumulation. Developed first ever loop-based solar flare model using double layers and incorporating cavity resonators. (Paper presented at Joint AGU/AAS Meeting in Baltimore, MD, May 1994)

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American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.

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Papers appearing in Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Fundamentals of Solar Physics', 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level', 'Astronomy & Astrophysics: Notes, Problems and Solutions', 'Modern Physics: Notes, Problems and Solutions'

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B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.

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Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society. Barbados Astronomical Society award for service (1977-91) as Journal editor.

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Caribbean Examinations Council (as advisor, examiner), Barbados Astronomical Society (as Journal Editor 1977-91), Trinidad & Tobago Astronomical Society (as consultant on courses, methods of instruction, and guest speaker).