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Modelling stellar magnetic fields using spectrum synthesis

JD L

16/03/09

Leverhulme Lectures on Stellar Magnetism


Basic idea of spectrum synthesis












We have a spectrum from a star, and we want to extract as much information as possible from it Basic strategy: starting from basic physics, compute the spectrum expected for this star if it conforms to our theories Expected spectrum may contain a number of adjustable parameters (abundance table, v sin i, even Teff or log g) Compare computed spectrum with observed spectrum, fit adjustable parameters If fit is good, we have a plausible model (but it may not be unique ­ this is an ill-posed problem) & parameter values If not, we have left out some essential physics which we need to find
Leverhulme Lectures on Stellar Magnetism

16/03/09


Computing an emergent spectrum: what is needed




Starting with a suitable model atmosphere (Teff, log g, abundances), what do we have to do to compute the emergent polarised spectrum of a magnetic star (forward computation)? ­ Assume some magnetic field structure, and calculate the vector field at many (50+) grid points on the visible hemisphere ­ For each grid point compute detailed run of polarised opacities and retardances at all relevant depths (60+) at closely spaced frequencies or wavelengths (0.01 е is barely adequate wavelength grid in visible). A window of 100 е might be a useful size. ­ Then compute the emergent spectrum along the ray towards observer at each surface grid point, by solving the EOTs outward along the ray, for each wavelength in the window A lot of bookkeeping is required!
Leverhulme Lectures on Stellar Magnetism

16/03/09


Details of local integration (basic idea)


For unpolarised transfer dv = v dz, where absorption coefficient includes atomic effects of both continuum and line absorption In "local thermodynamic equilibrium" (LTE), Sv is simply the Planck function Sv = Bv(T) = (2h3/c2)/[exp(h/kT) 1] Unpolarised equation of transfer can be integrated using the integrating factor exp(v /), since Sv is a known function of





I = e


/






S ' e

- ' /

d ' /

With lower limit 0, we get specific intensity emerging from surface Situation is closely analogous for polarised equations of transfer: we have four coupled, linear, firstorder DEs, which we solve numerically starting from blackbody conditions deep inside
Leverhulme Lectures on Stellar Magnetism

16/03/09


Computing the emergent spectrum: techniques


Several aspects of this problem require special considerations
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Need to have a suitable list of spectral lines, with gf values and LandИ splitting factors. Usual source is VALD database at http://ams.astro.univie.ac.at/vald/ which supplies both data from a variety of sources (some are better than others...) Because one must compute the Voigt and Faraday-Voigt functions millions of times, an efficient algorithm is needed Solving the equations of transfer numerically may be done with standard packages or methods (e.g. Runge-Kutta), but again this has to be done so many times that efficiency is essential, and you want a technique that does not require a very dense depth grid
Leverhulme Lectures on Stellar Magnetism



Descriptions of common codes discuss these points

16/03/09


Example of a spectrum synthesis code: Zeeman


Zeeman (Landstreet 1988, ApJ 326, 967) is a simple magnetic line synthesis code available on course Web page
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16/03/09

Contains simple parametrised field structures (colinear dipole, quadrupole, etc), also abundance tables specified on rings colinear with field axis (simple model of non-uniform abundances, needed for magnetic Ap stars) Reads in fundamental parameters of star, assumed magnetic field parameters, spectral window to compute Computes I, Q, U, V spectrum including line splitting and polarised transfer, using precomputed ATLAS atmosphere and VALD line list Compares computed spectrum with an observed spectrum, selects best fit v sin i, radial velocity, and 2 of fit If desired, can iterate fit to optimise field or abundance parameters
Leverhulme Lectures on Stellar Magnetism


Simple model assumed by Zeeman




Field is axisymmetric, a sum of low-order multipole components; parameters are orientations of rotation and magnetic axis, strengths of multipole components Abundance of elements to study is constant on rings symmetric about magnetic axis
Leverhulme Lectures on Stellar Magnetism

16/03/09


Examples of magnetic line profiles




Example of line synthesis ­ Cr II 4588 in A0 star ­ Dipole field, polar field strength 1000 G (0.1 T) ­ Star not rotating ­ View from four inclinations from magnetic pole: 90, 60, 30, 0 degrees ­ Q, U, V all multiplied by 10; Q & U shifted up Note how much larger V is than Q or U
Leverhulme Lectures on Stellar Magnetism

16/03/09


Modelling a normal star: Sirius as an example








Synthesis fits to non-magnetic stars may be very accurate Require good choices of Teff, log g, abundances, radial velocity, v sin i, and microturbulence parameter Teff and log g often chosen from available Stromgren or Geneva photometry calibrations Automated iterative fitting of most remaining parameters works well for such stars
Leverhulme Lectures on Stellar Magnetism

16/03/09


Modelling a magnetic star






Example of a fit to a series of spectra of a strongly magnetic B3 star, HD 175362 Mg, Si, Ti, Cr all mildly variable over surface Spectral line strength strongly affected by presence of magnetic field which reaches = +5 and -7 kG as star rotates
Leverhulme Lectures on Stellar Magnetism

16/03/09


Modelling a magnetic star: tests of parametrised models






Using MuSiCoS (or ESPaDOnS) data we can now return to problem of modelling magnetic stars We can test models derived from simple field measurements (, B, or other field moments) by observing [I, Q, U, V] spectra as a function of rotational phase and then computing predicted line profiles using the model derived from moments (example: 53 Cam) Result: poor fits, especially to Q, U.... Simple field models from field average measurements are only first approximations to real structure
Leverhulme Lectures on Stellar Magnetism

16/03/09


Basic idea of 2D mapping








How is it possible to deduce 2D map using only integrated light?? Basic idea: longitude of a feature derived from when it is most visible in spectrum Latitude derived from length of time feature is visible, and from extreme Doppler shifts Could use this idea to "map" Earth with only point source observations
Leverhulme Lectures on Stellar Magnetism

16/03/09


Mapping a magnetic star: detailed surface maps




To map surface structure of star, create mapping code that can fit spectra of all 4 Stokes parameters at many rotational phases by iterative adjustment of abundance and field maps Requires many cycles of forward computation, comparison, backwards feedback to improve maps, then through cycle again (Kochukhov et al 2004, A&A 414, 613)
Leverhulme Lectures on Stellar Magnetism



16/03/09


Further results for 53 Cam





Above: Fe distribution from 3 lines of multiplet 42 as function of rotational phase Right: magnetic field strength and orientation from same three lines
Leverhulme Lectures on Stellar Magnetism

16/03/09


Least squares deconvolution (LSD)




Donati et al (1997) have developed a very powerful tool for using spectropolarimetric data to detect weak fields even when polarisation signal is hardly visible: LSD Example of weak signal in faint cluster Ap star
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Even in very strong Fe II line at 4923, V hardly detectable When signals from thousands of lines are averaged, field signature easily visible



16/03/

Found that LSD V signal (but not Q, U) may be modelled like single l9 0ine Leverhulme Lectures on Stel

lar Magnetism


Measurement of really weak fields






16/03/09

The bright Ap star Uma shows power of LSD Although it is extremely bright (mV = 1.85) it was really difficult to detect with single- or few-line techniques (large error bars on curve at right) With LSD data from Musicos, the field is very obvious and the uncertainty in decreases by about one order of magnitude (small error bars on curve)

Leverhulme Lectures on Stellar Magnetism


Modelling of cool stars




A code for mapping magnetic fields from LSD spectropolarimetry of cool stars has been developed by Donati This has been used to map I and V LSD spectra of active cool stars, as in the map of HR 1099 to right (Petit et al 2004, MNRAS 348, 1175), where the observations at the bottom are the thin lines and the fitted model gives the bold lines
Leverhulme Lectures on Stellar Magnetism

16/03/09


Summary






The point of this lecture is that computation of spectra of magnetic stars using a good underlying physical model is quite practical, and with sophisticated mapping techniques is beginning to yield detailed maps of both hot (well, tepid) and cool magnetic stars The first such maps reinforce the conclusion that magnetic Ap stars have topologically simple fields that are really very different from the complex fields of cool, solar-like stars. But: recall that this is an ill-posed problem, and maps do not provide unique solutions to data, particularly at level of fine detail. In practice maps have limited spatial resolution ­ the finer the detail, the less certain it is.
Leverhulme Lectures on Stellar Magnetism

16/03/09