Zeeman–Doppler imaging

{{Short description|Investigative astrophysics technique}}

Image:suaur.jpg (a young star of T Tauri type), reconstructed by means of Zeeman–Doppler Imaging]]

In astrophysics, Zeeman–Doppler imaging is a tomographic technique dedicated to the cartography of stellar magnetic fields, as well as surface brightness or spots and temperature distributions.

This method makes use of the ability of magnetic fields to polarize the light emitted (or absorbed) in spectral lines formed in the stellar atmosphere (the Zeeman effect). The periodic modulation of Zeeman signatures during the stellar rotation is employed to make an iterative reconstruction of the vectorial magnetic field at stellar surface.

The method was first proposed by Marsh and Horne in 1988, as a way to interpret the emission line variations of cataclysmic variable stars.{{cite journal|last1=Marsh|first1=T. R.|last2=Horne|first2=K.|title=Images of accretion discs – II. Doppler tomography|journal=Monthly Notices of the Royal Astronomical Society|date=1 November 1988|volume=235|issue=1|pages=269–286|doi=10.1093/mnras/235.1.269|bibcode=1988MNRAS.235..269M|doi-access=free}} This techniques is based on the principle of maximum entropy image reconstruction; it yields the simplest magnetic field geometry (as a spherical harmonics expansion) among the various solutions compatible with the data.{{Cite journal |last=Donati |first=J.-F. |author2=Howarth, I. D. |author3=Jardine, M. M. |author4=Petit, P. |author5=Catala, C. |author6=Landstreet, J. D. |author7=Bouret, J.-C. |author8=Alecian, E. |author9=Barnes, J. R. |author10=Forveille, T. |author11=Paletou, F. |author12=Manset, N. |display-authors=4 |date=2006 |title=The surprising magnetic topology of τ Sco: fossil remnant or dynamo output? |journal=Monthly Notices of the Royal Astronomical Society |volume=370 |issue=2 |pages=629–644 |doi=10.1111/j.1365-2966.2006.10558.x |doi-access=free |bibcode=2006MNRAS.370..629D|arxiv = astro-ph/0606156 |s2cid=7054292 }}

This technique is the first to enable the reconstruction of the vectorial magnetic geometry of stars similar to the Sun. It now enables systematic studies of stellar magnetism and provides insights into the geometry of large arches formed by magnetic fields above stellar surfaces. To collect the observations related to Zeeman-Doppler Imaging, astronomers use stellar spectropolarimeters like ESPaDOnS {{Cite web |url=http://espadons.ast.obs-mip.fr/ |title=ESPaDOnS |access-date=2021-10-28 |archive-date=2020-02-21 |archive-url=https://web.archive.org/web/20200221200246/http://espadons.ast.obs-mip.fr/ |url-status=live }} at CFHT on Mauna Kea (Hawaii), HARPSpol {{Cite web |url=http://www.astro.uu.se/~piskunov/RESEARCH/INSTRUMENTS/HARPSpol/ |title=Archived copy |access-date=2015-09-08 |archive-date=2016-03-05 |archive-url=https://web.archive.org/web/20160305141530/http://www.astro.uu.se/~piskunov/RESEARCH/INSTRUMENTS/HARPSpol/ |url-status=live }} at the ESO's 3.6m telescope (La Silla Observatory, Chile), as well as NARVAL{{Cite web|url=http://www.ast.obs-mip.fr/projets/narval/v1/|title=Home Page of Narval|website=www.ast.obs-mip.fr|access-date=2021-10-28|archive-date=2020-07-30|archive-url=https://web.archive.org/web/20200730082938/http://www.ast.obs-mip.fr/projets/narval/v1/|url-status=live}} at Bernard Lyot Telescope (Pic du Midi de Bigorre, France).

The technique is very reliable, as the reconstruction of the magnetic field maps with different algorithms yield almost identical results, even with poorly sampled data sets.{{cite journal|last1=Hussain|first1=G. A. J.|last2=Donati|first2=J.- F.|last3=Collier Cameron|first3=A.|last4=Barnes|first4=J. R.|title=Comparisons of images derived from independent Zeeman Doppler imaging codes|journal=Monthly Notices of the Royal Astronomical Society|date=11 November 2000|volume=318|issue=4|pages=961–973|doi=10.1046/j.1365-8711.2000.03573.x|bibcode=2000MNRAS.318..961H|doi-access=free}} It makes use of high-resolution time-series spectropolarimetric observations (Stokes parameter spectra).{{Cite journal |last=Hackman |first=T. |last2=Lehtinen |first2=J. |last3=Rosén |first3=L. |last4=Kochukhov |first4=O. |last5=Käpylä |first5=M. J. |date=2016-03-01 |title=Zeeman-Doppler imaging of active young solar-type stars |url=https://www.aanda.org/articles/aa/full_html/2016/03/aa27320-15/aa27320-15.html |journal=Astronomy & Astrophysics |language=en |volume=587 |pages=A28 |doi=10.1051/0004-6361/201527320 |issn=0004-6361|arxiv=1509.02285 }} It has however been shown, from both numerical simulations{{Cite journal|last1=Kochukhov|first1=O.|last2=Piskunov|first2=N.|date=June 2002|title=Doppler Imaging of stellar magnetic fields: II. Numerical experiments|journal=Astronomy & Astrophysics|volume=388|issue=3|pages=868–888|doi=10.1051/0004-6361:20020300|bibcode=2002A&A...388..868K |issn=0004-6361|doi-access=free}} and observations,{{Cite journal|last1=Rosén|first1=L.|last2=Kochukhov|first2=O.|last3=Wade|first3=G. A.|title=First Zeeman Doppler Imaging of a Cool Star Using All Four Stokes Parameters|date=2015-05-29|url=https://iopscience.iop.org/article/10.1088/0004-637X/805/2/169|journal=The Astrophysical Journal|volume=805|issue=2|pages=169|doi=10.1088/0004-637X/805/2/169|issn=1538-4357|arxiv=1504.00176|bibcode=2015ApJ...805..169R |s2cid=118833875|access-date=2020-10-12|archive-date=2020-10-19|archive-url=https://web.archive.org/web/20201019084205/https://iopscience.iop.org/article/10.1088/0004-637X/805/2/169|url-status=live}} that the magnetic field strength and complexity is underestimated if no linear polarization spectra is available from observations. Since linear polarization signatures are weaker compared circular polarization their detections are not as reliable, particularly for cool stars. Therefore, the observations are normally limited to only Stokes IV parameters.{{Cite journal |last=Hackman |first=T. |last2=Kochukhov |first2=O. |last3=Viviani |first3=M. |last4=Warnecke |first4=J. |last5=Korpi-Lagg |first5=M. J. |last6=Lehtinen |first6=J. J. |date=2024-02-01 |title=From convective stellar dynamo simulations to Zeeman-Doppler images |url=https://www.aanda.org/articles/aa/full_html/2024/02/aa47144-23/aa47144-23.html |journal=Astronomy & Astrophysics |language=en |volume=682 |pages=A156 |doi=10.1051/0004-6361/202347144 |issn=0004-6361|arxiv=2306.07838 }} With more modern spectropolarimeters such as the recently installed SPIRou{{Cite web|last=|first=|date=|title=SPIRou|url=https://www.cfht.hawaii.edu/Instruments/SPIRou/index.php|url-status=live|archive-url=https://web.archive.org/web/20200221233123/http://www.cfht.hawaii.edu/Instruments/SPIRou/index.php|archive-date=2020-02-21|access-date=|website=}} at CFHT and CRIRES+{{Cite web |title=ESO - CRIRES+ |url=https://www.eso.org/sci/facilities/develop/instruments/crires_up.html#:~:text=CRIRES+%20is%20a%20project%20to%20transform%20the%20VLT%20instrument%20CRIRES |access-date=2024-10-02 |website=www.eso.org}} at the Very Large Telescope (Chile) the sensitivity to linear polarization will increase, allowing for more detailed studies of cool stars in the future.