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Measuring stellar magnetic fields

JD L

23/02/09

Leverhulme Lectures on Stellar Magnetism


Outline








We have now looked at atomic physics needed to detect magnetic fields in non-degenerate stars -- but this does not completely solve our problem How does this microphysics allow us to actually measure fields in stars, and what exactly do we me as ure ? What kind of instrumentation is needed for magnetic field measurements? How are the polarimetric and intensity measurements that we actually make described?

23/02/09

Leverhulme Lectures on Stellar Magnetism


Zeeman splitting in HD 94660








We have seen that a strong field (>~ 2 kG) produces direct Zeeman splitting This leads to a simple measurement of Question: what kind of an average is ?? Question: what do we do if the field of interest is far too small to detect this way??
Leverhulme Lectures on Stellar Magnetism

23/02/09


How to use Zeeman polarisation to get field measurement?






Zeeman effect in spectral lines can alter stellar lines even if the stellar lines are not split--> For greatest detection sensitivity we need to obtain polarised spectra Need a combination of polarisation analyser (polarimeter) with spectrograph = spectropolarimeter
Leverhulme Lectures on Stellar Magnetism

23/02/09


Polarimeters




Simplest polarimeter is a device that rejects one sense of polarisation (circular, linear, etc) or separates two beams from the initial one, differing in polarisation state (e.g. Iceland spar) --> Iceland spar = crystalline calcite is birefringent: speed of light depends on polarisation state
Leverhulme Lectures on Stellar Magnetism

23/02/09


A (really) simple polarimeter










Simple linear polarimeter is a polarisation analyser built from calcite wedges to transmit one polarisation state and reflect the other (Glan-Thompson prism) Get spectrum of star with polariser in front of entrance slit, rotate polariser 90o, then compare the two spectra Question: is this a good polarimeter?? Question: what would improve it? Question: how to measure circular polarisation?
Leverhulme Lectures on Stellar Magnetism

23/02/09


Second essential component of a polarimeter: a retarder






A retarder has two axes such that e-wave has higher speed through substance than o-wave E is projected on these axes and each projected component travels separately When recombined at other side, polarisation state of wave is changed
Leverhulme Lectures on Stellar Magnetism

23/02/09


Circular polarimetry








To do circular polarimetry we can convert circular polarisation into linear and then analyse the linear polarisation A quarter-wave plate resolves circular polarisation into two linear beams at right angles, 90o different in phase After the wave-plate, the two beams are in phase, converting a beam of circularly polarised light to linearly polarised light Also operates in reverse
Leverhulme Lectures on Stellar Magnetism

23/02/09


A simple but real polarimeter


First lens collimates beam ­ electro-optic crystal is a modulating quarter wave plate ­ Wollaston prism is linearly polarising beam splitter ­ filters define wavelengths ­ second lens focusses light on phototube cathodes

23/02/09

Leverhulme Lectures on Stellar Magnetism


A real spectropolarimeter: polarisation module followed by spectrograph

23/02/09

Leverhulme Lectures on Stellar Magnetism


Recent advances in observational capabilities








Major advance during past 10 years has been development of facility instruments capable of high resolution stellar spectropolarimetry in all four Stokes parameters Most important: MuSiCoS spectropolarimeter and its successors, ESPaDOnS and Narval, all due to J-F Donati. MuSiCoS provided spectra with R = 35000 for window 4600 ­ 6600 е. Main limit was low efficiency, but provided wholly new types of data, provoked several major breakthroughs. ESPaDOnS and Narval observe region 3700 to 10400 е with R = 68000 and far higher efficiency.

23/02/09

Leverhulme Lectures on Stellar Magnetism


ESPaDOnS: a spectropolarimeter at Canada France Hawaii Telescope

23/02/09

Leverhulme Lectures on Stellar Magnetism


Degree of polarisation






It is very convenient to work with idea of "fractional polarisation" rather than with spectra in right & left polarised light Last row shows how polarised spectra may be combined to describe degree of polarisation of light in spectrum Define this polarisation for linear & circular polarisation
Leverhulme Lectures on Stellar Magnetism

23/02/09


The Stokes vector










Specifically, to described polarised light mathematically we use the Stokes parameter description: [I, Q, U, V] I is the total intensity of light in the beam For Q and U, measure the intensity of the beam through perfect linear polarisers (polarising analysers) orientated at 0, 45, 90, and 135 degrees. Q = I0 ­ I90, U = I45 ­ I135. Measure the intensity of the beam thorough two perfect circular polarisers. V = Iright ­ Ileft. [I, Q, U, V] describe the polarisation state of a light beam adequately for modelling its interactions with matter [I, Q, U, V] are functions of frequency and direction Q, U, V are sometimes normalised to I (Q -> Q/I, etc).
Leverhulme Lectures on Stellar Magnetism

23/02/09


Field measurements in stars: a simple approximation






How can we use spectral observations of (usually circular) polarisation to deduce some value of magnetic field strength in the observed star? Since circular polarisation is produced by line-of-sight field component, we expect that the measurement deduced from circular polarisation will describe a mean of this field component over surface of star: (mean longitudinal field) Question: what kind of average is ? Question: what should we measure to determine longitudinal field strength?
Leverhulme Lectures on Stellar Magnetism

23/02/09


Zeeman pattern in one sense of circularly polarised light




Figure shows Zeeman pattern seen in one sense of circularly polarised light, in transverse (upper) & longitudinal (lower) field As direction of field shifts from transverse to longitudinal, mean position of observed line moves away from non-magnetic position
Leverhulme Lectures on Stellar Magnetism

23/02/09


Deducing field strength from polarimetry








Objective is to use circular polarisation observations to derive a mean line-of-sight field strength for observed star From previous figure, one can accept that the separation between the position of the spectral line as seen in right and in left circularly polarised light is given by the mean separation of the sigma components multiplied by the cosine of the angle between the field and the line of sight This leads directly to the formula = 2 x 4.67 10-13 z 2 B cos where is in A units, and z is a suitable average Lande factor Assume that this is approximately correct for spectral lines even if they are strong enough to be saturated
Leverhulme Lectures on Stellar Magnetism

23/02/09


Field measurement in Ap stars weak field limit


If the field is very weak, so splitting is small compared to (local) line width, the separation of the two circularly analysed components is as shown below. A measurement of net circular polarisation V in the line wing yields a field estimate through where all wavelengths ar e m eas ure d i n A . (cf Landstreet 1982, ApJ 258, 639; Bagnulo et al 2002, A&A 389, 191)

V 9.34 10-13 z 2 dI / d B z

23/02/09

Leverhulme Lectures on Stellar Magnetism