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Zeeman-Doppler Imaging

Magnetic mapping of stellar surfaces

Par Pascal Petit - 8/10/2007


Zeeman-Doppler Imaging

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Basic principle

Zeeman-Doppler Imaging (hereafter ZDI) is a method to reconstruct magnetic field maps of stellar surfaces. As most stars are much too far from the observer to be spatially resolved by direct imaging, ZDI takes advantage of the fast rotation of some stars to reconstruct the magnetic field distribution at their surface, by means of tomographic technics inspired from medical imaging.

Scientific motivations

By observing the magnetic field in a large sample of stars, we try to investigate the origin of stellar magnetism, as well as the impact of magnetic fields on stellar evolution. All collected hints may become decisive clues to better understand the solar magnetic activity, the origin of which is still incompletely understood, though it is known that solar magnetic storms have an important impact on electronic devices and that long-term changes of the solar activity (similar for instance to what happened during the Maunder minimum) may significantly affect the whole terrestrial climate.

In the present page, we propose to illustrate the principle of ZDI through a series of animations. We also present a gallery of stellar magnetic topologies.

General characteristics of the following animations

All following animations display a simulated star (top panel) and the Zeeman signature observed, in circularly polarised light, in a spectral line (lower panel). The inclinaison angle of the stellar rotation axis with respect to the line of sight is set to 30 deg. The projected rotational velocity of the star (v.sin i) is set to 100 km.s-1. The polarization is given in % of the contimuum level. The wavelength scale is given in equivalent radial velocity (in km.s-1).

Animation 1 : How to determine the longitude of a magnetic region ?

Star with a magnetic region located at latitude 30 deg. Field lines are radially oriented (i.e. orthogonal to the stellar surface).
mpeg format (2.2 mo)

The magnetic spot produces a typical double-peaked signature, first appearing in the blue wing of the spectral line (blue-shifted by the Doppler effect as the magnetic region is approaching the observer). The circularly polarised signature progressively shifts towards the red wing of the spectral line as the magnetic region is crossing the stellar disc under the effect of stellar rotation, then disappears as the magnetic region becomes hidden by the stellar disc. Therefore, from the observation of a time-series of Zeeman signatures, the observer is able to deduce the longitude of the active region on the stellar disc, e.g. by determining the time at which the Doppler shift of the Zeeman signature is equal to zero.

Note that the signature corresponding to a radial magnetic field keeps the same sign during the whole transit of the magnetic region. The amplitude of the signature is decreasing whenever the magnetic region approaches the stellar limb, owing both to a smaller observed projected area and to the limb darkening effect. Animation 2 shows how the spot latitude may also be determined.

Animation 2 : how to determine the latitude of a magnetic region ?

Same as above, but the magnetic region is now located at latitude 60 deg.
mpeg format (2.2 mo)

The Doppler shift of the Zeeman signature has now a lower amplitude, because the spot is located closer to the rotation axis. Furthermore, the magnetic region is now observable during the whole stellar rotation. The spot latitude can be measured by determining the amplitude of the Doppler shift on the time-series of observed line profiles.

Now that we have demonstrated that a magnetic region can be located at the stellar surface, we will show with the next animation how the orientation of the field lines can also be estimated.

Animation 3 : how to determine the orientation of field lines ?

The active region now hosts an azimuthal magnetic field.
mpeg format (2.2 mo)

Now the field in the magnetic region is azimuthal, i.e. field lines are horizontal and oriented along lines of constant latitude. The Zeeman signatures evolve in a rather different way than in the radial field case.

First, the sign of Zeeman signatures is reversing while the spot is crossing the line of sight, while the typical signature of a radial magnetic field keeps a constant sign along the spot transit.

Secondly, the amplitude of the spectral signature is stronger near the stellar limb, because the circular polarization is sensitive to the field component pointing towards the observer. In the case of a radial field, this longitudinal component is maximum in the centre of the stellar disc, while in the case of an azimuthal field the maximum longitudinal contribution is achieved close to the limb. Let us however stress the fact that the signature remains visible during the whole transit of the active region, though the amplitude is reduced near the center of the stellar disc (which is not a problem in case of good quality data sets, processed for instance with multi-lines technics).

It is therefore possible to distinguish between a radial and an azimuthal magnetic field. A similar example (not shown here) would show that it is also possible to tell if the field is meridional (i.e. horizontal and oriented along meridians), though in this particular case (and for low stellar inclinaisons) a partial ambiguity cannot be completely avoided with signatures of a radial field.

ZDI examples

From a series of circularly polarised spectra, it is therefore possible to reconstruct the distribution of active regions on a stellar surface as well as the field orientation inside these magnetic structures. This indirect imaging method is performed by means of spectral inversion technics based on a maximum entropy algorithm. The gallery contains brightness and magnetic maps reconstructed for a few stars by means of ZDI.



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Laboratoire Astrophysique de Toulouse - Tarbes (UMR5572)

CNRS (Midi-Pyrénées)

Univ. Paul Sabatier

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