Longitudinal fields and Zeeman Doppler maps from Stokes V

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. (2008b ) and Morin et al. (2008 , 2010 ). 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. (2011 ) 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. (2004 ) 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, 2007 ; 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. (2006b )
HD 73350		G0V	12^b	0 – 20	Petit et al. (2008 )
Sun^a		G2V	4		Daou et al. (2006 )
$α$ Cen A		G2V	< 0.2		Kochukhov et al. (2011 )
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. (2008 )
HD 76151		G3V	5.6	0 – 10	Petit et al. (2008 )
HD 190771		G5IV	15^b	0 – 20	Petit et al. (2008 )
LQ Hya		K0V		0 – 800	Donati (1999 )
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. (2011 )
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. (2009 )
Gl 410	DS Leo	M0V	100		Donati et al. (2008b )
Gl 182		M0.5V	172		Donati et al. (2008b )
Gl 494	DT Vir	M0.5V	150		Donati et al. (2008b )
Gl 49		M1.5	27		Donati et al. (2008b )
GJ 9520	OT Ser	M1.5	130		Donati et al. (2008b )
Gl 569 A	CE Boo	M2.0V	103		Donati et al. (2008b )
Gl 752 A	LHS 473	M2.5V	16		Phan-Bao et al. (2009 )
GJ 3241	KP Tau	M3V	100		Phan-Bao et al. (2009 )
Gl 388	AD Leo	M3V	185		Morin et al. (2008 )
Gl 896 A	EQ Peg A	M3.5V	480		Morin et al. (2008 )
Gl 873	EV Lac	M3.5V	18 – 40		Phan-Bao et al. (2006 )
			530		Morin et al. (2008 )
GJ 4247	V374 Peg	M4V		0 – 2000	Donati et al. (2006 )
			710		Morin et al. (2008 )
Gl 490 B	G 164-31	M4V	680	0 – 1800	Phan-Bao et al. (2009 )
Gl 285	YZ CMi	M4.5V	555		Morin et al. (2008 )
Gl 896 B	EQ Peg B	M4.5V	450		Morin et al. (2008 )
			290		Phan-Bao et al. (2009 )
2E 4498	2E 4498	M4.5V	440		Phan-Bao et al. (2009 )
Gl 51		M5V	1500		Morin et al. (2010 )
GJ 1156		M5V	100		Morin et al. (2010 )
GJ 1245 B		M5.5V	150		Morin et al. (2010 )
Gl 905	HH And	M5.5V	< 5		Phan-Bao et al. (2006 )
Gl 412 B	WX UMa	M6V	1000		Morin et al. (2010 )
GJ 1111	DX Cnc	M6V	100		Morin et al. (2010 )
GJ 3622		M6.5V	55		Morin et al. (2010 )
^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. (2008 )
CV Cha	G8		0 – 700	Hussain et al. (2009 )
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. (2011a )
Tw Hya	K6	150		Yang et al. (2007 )
		2000^a		Yang et al. (2007 )
			0 – 3000	Donati et al. (2011b )
BP Tau	K7	500	0 – 3000	Donati et al. (2008a )
		2750^a		Johns-Krull and Valenti (2000 )
		200		Johns-Krull et al. (1999a )
		2500^a		Johns-Krull et al. (1999a )
DK Tau	M0	1450^a		Johns-Krull and Valenti (2000 )
AA Tau	M0	2900^a		Johns-Krull and Valenti (2000 )
DF Tau	M2	1000^a		Johns-Krull and Valenti (2000 )
V2247 Oph	M2.5		0 – 800	Donati et al. (2010 )
^a from accretion lines