3.2 Longitudinal fields and Zeeman Doppler maps from Stokes V

3.2.1 Dwarfs and subgiants

Advantages and caveats in searching for cool star magnetism through polarization measurements were discussed in the Sections above. For a detection, the detailed line shape in the unpolarized case does not have to be understood at very high level, which means that the signal of a potential field will be relatively straightforward to detect (given suitable instrumentation). The signal expected from magnetic cool stars, however, may be extremely weak because of flux cancellation and complicated field geometries.

Early programs to search for longitudinal fields in late-type stars were presented by Brown and Landstreet (1981) and Borra et al. (1984). Both works show sophisticated methods to search for circular polarization simultaneously in many spectral lines and obtain encouraging results in hot stars with known strong magnetic fields. Both programs, however, fail to detect polarization signals in late-type stars confirming the suspicion that net longitudinal fields are difficult to detect in these stars. The key idea in the two mentioned programs is to co-add information from many spectral lines in order to enhance the polarization signal. Masks transmitting only the light in the vicinity of stellar absorption lines are used so that the final signal is constructed to be something like an average signal from many lines. The basic idea is very similar to the construction of a mean line profile using the approach of Least Squares Deconvolution (Section 2.1.8).

A detection of circular polarization in a low-mass star was successful in an effort to create Zeeman Doppler Images in RS CVn binaries. Donati et al. (1990) show signals in circular polarization in three Fe i lines of HR 1099, and more successful detections in RS CVn’s are presented in Donati et al. (1992). These works obtained very high SNR data in order to detect polarization signals in individual lines. Later, the technique of Least Squares Deconvolution entered the domain of polarization measurements and Zeeman Doppler Imaging (see Section 2.1) and, since then, Stokes V signatures were investigated in many different stars (e.g., Donati et al., 1997). Table 5 gives a summary of Stokes V measurements in cool dwarfs and subgiants. It is sometimes difficult to compare the results from different projects, because results are sometimes presented in the form of surface maps and sometimes in the form of average magnetic field strengths. Note that also in this context, average fields mean the average value for the detected unsigned magnetic field, |B |, a definition similar to the value measured in Stokes I; the average value of the signed magnetic field is zero by construction.

A tremendous amount of work was put into the analysis of magnetic geometries in stars through ZDI, and the possibility of reconstructing magnetic fields on stellar surfaces is truly amazing. As laid out in Section 2.1, however, the interpretation of the field maps is very difficult, and conclusions have to be drawn with great care. Typical average field values for sun-like stars of spectral types F – K are of the order of ten Gauss, local field strengths in Doppler maps go up to several hundred Gauss. Note that most of the stars imaged with ZDI are rapid rotators that are much more active than the slow-rotating Sun.

Much work was done also on maps of magnetic fields in M stars. Results derived from time-series of Stokes V measurements are presented in Donati et al. (2008bJump To The Next Citation Point) and Morin et al. (2008Jump To The Next Citation Point, 2010Jump To The Next Citation Point). The typical average magnetic field strengths found in Stokes V measurements of M dwarfs are significantly larger than average fields from Stokes V work found in hotter, sun-like stars. Average fields up to 1.5 kG were detected, and the range of |B| in Doppler maps from Stokes V extend up to 2 kG, a value at which the weak-field approximation probably approaches its limitations.

Kochukhov et al. (2011Jump To The Next Citation Point) presented very high quality measurements of all four Stokes parameters in three sun-like stars. Using LSD, they detect circular and linear polarization in the RS CVn binary HR 1099. For the first time, linear polarization is detected in sun-like stars. Fields between 10 and 25 G are found in different observations of HR 1099. The signal detected in linear polarization is significantly more complex than the circular polarization signal and, as expected, linear polarization is weaker than circular polarization by roughly a factor 10.

3.2.2 Giants

Another class of stars in the focus of magnetic field research are giants. Some of these evolved stars can be rather active, and they possess large convection zones potentially allowing the operation of a dynamo. Stokes V observing campaigns are available in a handful of giants providing information about their magnetism. For the active FK Com star HD 199178, Petit et al. (2004Jump To The Next Citation Point) constructed Zeeman Doppler maps with field strengths up to several hundred Gauss. The other work summarized in Table 6 find mean fields that are on the order of 1 G or below, this means they are on average much weaker than the fields found in dwarfs.

3.2.3 Young stars

Pre-main sequence stars are particularly interesting objects for magnetic field measurements because fields may be of fossil origin or generated through dynamo operation, and magnetism is required for magnetospheric accretion (see Section 3.1.3). The observational situation from polarization measurements is similar to the one in main-sequence stars: results are available in the form of magnetic Doppler maps providing a range and geometry of the detected net field, and there are results reporting average field values from multiple or single polarization measurements.

A summary of magnetic field reports from circular polarization measurements in pre-main sequence stars is given in Table 7. Field strengths up to several hundred Gauss, and in the case of BP Tau up to 3 kG are found in Zeeman Doppler maps from photospheric lines. Average fields on the order of ten to several hundred Gauss have been found in the analysis of photospheric lines. A remarkable difference exists between the field strengths found in polarization measurements carried out in photospheric lines and those carried out in emission lines that are formed predominantly in the region of the accretion shock, usually the He i line at 5876 Å. In the latter, field strengths are on the order of a few kilo-Gauss similar to field strengths detected in Stokes I measurements.

Assuming the same flux values across the star, the net flux seen in the accretion region alone may be higher than the net flux averaged over the photosphere, which would mean that the difference is a purely geometric effect. The accretion column could stem from a more or less unipolar bundle of fluxtubes allowing to see the true (almost uncanceled) flux, while the photospheric lines come from the entire star and are subject to cancellation. Furthermore, field strengths may actually be higher in the region of accretion, and the differences between magnetic fields measurements from integrated light and results from circular polarization in photospheric and accretion lines may provide additional information on the magnetic field geometry in pre-main sequence stars (see e.g., Johns-Krull, 2007Jump To The Next Citation Point; Donati et al., 2011c, and references therein). We come back to this point in Section 6.


Table 5: Longitudinal magnetic fields or Zeeman Doppler maps from Stokes V for dwarfs and subgiants.
Star Other Name SpType <B> B Range Reference
      [G] [G]  
τ Boo F7V 0 – 3 Catala et al. (2007)
HR 1817 F8V 13 0 – 250 Marsden et al. (2006bJump To The Next Citation Point)
HD 73350 G0V 12b 0 – 20 Petit et al. (2008Jump To The Next Citation Point)
Suna G2V 4 Daou et al. (2006Jump To The Next Citation Point)
α Cen A G2V < 0.2 Kochukhov et al. (2011Jump To The Next Citation Point)
HD 171488 G2V 0 – 500 Marsden et al. (2006a)
31 0 – 500 Marsden et al. (2006b)
HD 146233 G2V 3.6 0 – 5 Petit et al. (2008Jump To The Next Citation Point)
HD 76151 G3V 5.6 0 – 10 Petit et al. (2008Jump To The Next Citation Point)
HD 190771 G5IV 15b 0 – 20 Petit et al. (2008)
LQ Hya K0V 0 – 800 Donati (1999Jump To The Next Citation Point)
AB Dor K0V 0 – 800 Donati et al. (1999)
HD 46375 K0V 0 – 5 Gaulme et al. (2010)
II Peg K1IV 0 – 700 Carroll et al. (2007)
HR 1099 K1IV 0 – 800 Donati (1999)
12 – 25 Kochukhov et al. (2011Jump To The Next Citation Point)
HD 189733 K2V 0 – 40 Moutou et al. (2007)
𝜖 Eri K2V –6 – 5 Kochukhov et al. (2011)
Gl 890 M0V < 18 Phan-Bao et al. (2009Jump To The Next Citation Point)
Gl 410 DS Leo M0V 100 Donati et al. (2008bJump To The Next Citation Point)
Gl 182 M0.5V 172 Donati et al. (2008bJump To The Next Citation Point)
Gl 494 DT Vir M0.5V 150 Donati et al. (2008bJump To The Next Citation Point)
Gl 49 M1.5 27 Donati et al. (2008bJump To The Next Citation Point)
GJ 9520 OT Ser M1.5 130 Donati et al. (2008bJump To The Next Citation Point)
Gl 569 A CE Boo M2.0V 103 Donati et al. (2008bJump To The Next Citation Point)
Gl 752 A LHS 473 M2.5V 16 Phan-Bao et al. (2009Jump To The Next Citation Point)
GJ 3241 KP Tau M3V 100 Phan-Bao et al. (2009Jump To The Next Citation Point)
Gl 388 AD Leo M3V 185 Morin et al. (2008Jump To The Next Citation Point)
Gl 896 A EQ Peg A M3.5V 480 Morin et al. (2008Jump To The Next Citation Point)
Gl 873 EV Lac M3.5V 18 – 40 Phan-Bao et al. (2006Jump To The Next Citation Point)
530 Morin et al. (2008Jump To The Next Citation Point)
GJ 4247 V374 Peg M4V 0 – 2000 Donati et al. (2006)
710 Morin et al. (2008Jump To The Next Citation Point)
Gl 490 B G 164-31 M4V 680 0 – 1800 Phan-Bao et al. (2009Jump To The Next Citation Point)
Gl 285 YZ CMi M4.5V 555 Morin et al. (2008Jump To The Next Citation Point)
Gl 896 B EQ Peg B M4.5V 450 Morin et al. (2008)
290 Phan-Bao et al. (2009Jump To The Next Citation Point)
2E 4498 2E 4498 M4.5V 440 Phan-Bao et al. (2009)
Gl 51 M5V 1500 Morin et al. (2010Jump To The Next Citation Point)
GJ 1156 M5V 100 Morin et al. (2010Jump To The Next Citation Point)
GJ 1245 B M5.5V 150 Morin et al. (2010Jump To The Next Citation Point)
Gl 905 HH And M5.5V < 5 Phan-Bao et al. (2006)
Gl 412 B WX UMa M6V 1000 Morin et al. (2010Jump To The Next Citation Point)
GJ 1111 DX Cnc M6V 100 Morin et al. (2010Jump To The Next Citation Point)
GJ 3622 M6.5V 55 Morin et al. (2010Jump To The Next Citation Point)
aUsing observations of Vesta
b priv. comm.


Table 6: Longitudinal magnetic fields or Zeeman Doppler maps from Stokes V for giants.
Star SpType <B> B Range Reference
    [G] [G]  
Betelgeuse M2Iab 0.5 – 1.6   Aurière et al. (2010)
HD 199178 G5III   0 – 600 Petit et al. (2004)
V390 Aur G8III 5 – 15   Konstantinova-Antova et al. (2008)
Pollux K0III 0.1 – 1.4   Aurière et al. (2009)
Arcturus K1.5III 0.4 – 0.7   Sennhauser and Berdyugina (2011)
EK Boo M5III 0.1 – 0.8   Konstantinova-Antova et al. (2010)


Table 7: Longitudinal magnetic fields or Zeeman Doppler maps from circular polarization in pre-main sequence stars.
Star SpType <B> B Range Reference
    [G] [G]  
HD 155555 A G5 0 – 500 Dunstone et al. (2008Jump To The Next Citation Point)
CV Cha G8 0 – 700 Hussain et al. (2009Jump To The Next Citation Point)
HD 155555 B K0 0 – 300 Dunstone et al. (2008)
T Tau K0 12 Daou et al. (2006)
CR Cha K2 0 – 400 Hussain et al. (2009)
V410 Tau K4 0 – 1000 Skelly et al. (2010)
V2129 Oph K5 0 – 800 Donati et al. (2007)
0 – 2000 Donati et al. (2011aJump To The Next Citation Point)
Tw Hya K6 150 Yang et al. (2007Jump To The Next Citation Point)
2000a Yang et al. (2007)
0 – 3000 Donati et al. (2011b)
BP Tau K7 500 0 – 3000 Donati et al. (2008a)
2750a Johns-Krull and Valenti (2000Jump To The Next Citation Point)
200 Johns-Krull et al. (1999aJump To The Next Citation Point)
2500a Johns-Krull et al. (1999a)
DK Tau M0 1450a Johns-Krull and Valenti (2000Jump To The Next Citation Point)
AA Tau M0 2900a Johns-Krull and Valenti (2000Jump To The Next Citation Point)
DF Tau M2 1000a Johns-Krull and Valenti (2000)
V2247 Oph M2.5 0 – 800 Donati et al. (2010)
a from accretion lines


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