3.1 Average magnetic fields from integrated light

  As more physical effects were included in the modeling, more sources of line broadening were treated and the magnetic parameters decreased.
But one must ask: will fB → 0 eventually?
Saar (1996bJump To The Next Citation Point)

The history of magnetic field measurements in cool and, in particular, in sun-like stars, is not easily followed. The fundamental paradigm of magnetic fields leading to chromospheric and coronal emission, as observed on the Sun, has motivated clear expectations on the presence and properties of magnetic fields. The relation between rotation and activity, hence presumably also between rotation and magnetic flux, and the difficulty to detect Zeeman signatures in rotationally broadened spectral lines causes great practical difficulty, especially in sun-like stars. In low-mass (M-type) and pre-main sequence stars, the relation between activity and rotation is presumably more observer-friendly, facilitating the detectability of Zeeman broadening. I will, therefore, distinguish between magnetic field observations in sun-like stars, low-mass stars, and pre-main sequence stars.

3.1.1 Sun-like stars

The general difficulties detecting the subtle effects of Zeeman broadening in a spectral line from the spatially unresolved stellar disk were discussed in Section 2.1. A promising way to overcome the problem of degeneracies between Zeeman broadening and other broadening agents is to compare spectral lines with different Zeeman sensitivities in the same spectrum. An enhanced width (or equivalent width) of the magnetically sensitive lines often is good indication for the presence of a magnetic field. This strategy was successfully applied to Ap stars with fields of 1 kG-strength by Preston (1971). Vogt (1980Jump To The Next Citation Point) used a multichannel photoelectric Zeeman analyzer mainly to measure polarization in sun-like stars, but also presents comparison between the widths (FWHM) of magnetically sensitive lines at 6173 Å and two nearby, magnetically less sensitive lines. Four stars were analyzed with this method finding no evidence for magnetic fields. Vogt (1980Jump To The Next Citation Point) concludes that this rules out the presence of non-coherent longitudinal fields in excess of 1000 – 1500 G and covering the entire surface, which is similar to Bf ≤ 1500 G.

Robinson Jr (1980Jump To The Next Citation Point) introduced a new method based on the comparison between magnetically sensitive and insensitive lines. Realizing that the increase in line width for fields less than several kG is very small at optical wavelengths, he suggested to employ a Fourier transform technique to easily separate the broadening effects due to magnetism from other broadening effects. The underlying principle is the very same as if one is comparing line shapes or line widths directly in the wavelength regime (instead of Fourier regime). However, the Fourier transform technique is able to cleanly separate the different broadening effects at least in principle, and thus could ideally separate magnetic broadening from other effects. The main limitation of Zeeman broadening measurements at optical wavelengths, however, cannot be overcome by this method: it is still necessary to precisely measure a magnetically non-broadened line in order to use it as a template for the (potentially stronger) broadening observed in a magnetically sensitive line. Both lines must be of very similar nature in terms of formation height and temperature response. It is, therefore, not surprising that the limitations discussed by Robinson Jr (1980Jump To The Next Citation Point) are essentially identical to the limitations arising when line widths are compared directly. Consequently, the Fourier technique was not applied to a great many spectra, but the paper became a benchmark for line comparison techniques in general because it thoroughly discusses the requirements and limitations of this technique.

What followed was a series of attempts trying to measure magnetic fields in more or less active sun-like stars. Driven by detections of chromospheric and coronal activity, active stars with relatively low rotational broadening (v sin i) were observed in order to search for the effects of Zeeman broadening. Highest obtainable data quality at this time was typically on the order of R ∼ 50 000 – 70 000 and SNR ∼ 100 – 200. A remarkable conclusion from the magnetic field observations taken during this time was pointed out by Gray (1985). Investigating the reports on magnetic field measurements, he finds that for G- and K-dwarfs, the product between the magnetic field strength B, and the areal coverage factor f , i.e., the average magnetic field strength Bf , “is a constant independent of physical parameters such as spectral type and rotational velocity”. Realizing that this is rather unlikely, he concludes that “either we have systematic misconceptions involved in our Zeeman-broadening analysis or else we have before us a remarkable magnetic conservation condition”. The value of this “magnetic constant” is roughly Bf  = 500 G. According to Equation (4View Equation), this means an extra-broadening of 700 m s–1 for a magnetically sensitive line (g = 2.5) over an insensitive line (g = 1.0) at red optical wavelengths (670 nm); this is typically between 10% and 20% of a resolution element.

This example demonstrates that searching for the subtle effects of a several hundred Gauss magnetic field is close to the theoretical detectability of the Zeeman effect, and that it is extremely difficult to judge whether differences between lines of different magnetic sensitivities are really due to magnetism. Consequently, the Zeeman analysis methods were criticized by many authors (see e.g., Saar, 1988Jump To The Next Citation Point) centering on two flaws: 1) incomplete treatment of radiative transfer, and 2) lack of correction for line blends. Saar (1988) presents a set of improved methods for the analysis of magnetic fields in cool stars. Main ingredients are radiative transfer effects, treatment of exact Zeeman patterns, and improved correction for line blends. Following up on this improvement, Basri et al. (1990) went one step further introducing a two-component analysis by applying their more detailed line-transfer analysis to the (more realistic) situation in which the magnetic component of the stellar atmosphere is not identical to the non-magnetic component. The authors also point out that the derived magnetic flux still could be in error by a factor of 2 because atmospheres from one-dimensional calculations are used for a multi-component analysis (neglecting gradients and differences in atmospheric structure); misestimates of abundance, turbulence, and subsequently magnetic field can be quite severe. A detailed parameter study estimating the accuracy of magnetic field analysis methods in detailed radiative transfer calculations with embedded fluxtubes is given by Saar and Solanki (1992) and Saar et al. (1994a).

Obviously, a straightforward way to improve magnetic field measurements is to observe at longer wavelengths (see Equation (4View Equation)). Useful lines are found for example at 1.56 µm (Fe i) and 2.22 µm (Ti i), i.e., at wavelengths a factor of 3 – 4 longer than typical red/optical observations. First suitable instrumentation at such long wavelengths became available in the early-1990s. The first detailed analysis of a high-resolution infrared spectrum in a sun-like star (for earlier work on M stars, see Section 3.1.2) was performed by Valenti et al. (1995Jump To The Next Citation Point). These authors used a high-resolution (R = 103 000), high SNR (100 – 200) spectrum (taken during several hours of exposure) to determine the magnetic field of šœ– Eri, and upper limits on the order of 100 G in two other early K-dwarfs. šœ– Eri has been subject to magnetic field investigations many times earlier at optical wavelengths. Valenti et al. (1995Jump To The Next Citation Point) also show a compilation of reports on magnetic field measurements in this star published between 1984 and their work in 1995. Interestingly, average magnetic fields of šœ– Eri decreased over time starting at ∼ 800 G in 1984 and reaching 130 G in 1995. Possible interpretations of this result are that the field in šœ– Eri is variable, or that observations reporting lower field strengths (predominantly near-IR measurements) probe a different part of the stellar atmosphere. Valenti et al. (1995Jump To The Next Citation Point) discuss possible scenarios reaching the conclusion that probably optical investigations have overestimated the magnetic flux of šœ– Eri.

A critical compilation of magnetic field measurements obtained between the paper of Robinson Jr (1980) and 1996 was attempted by Saar (1996bJump To The Next Citation Point). The selection process leading to a condensed sample of “improved” field measurements was described as follows: “I have therefore compiled a carefully selected sample of magnetic measurements from analyses which treat radiative transfer effects and use disk-integration in their models. In addition, I (ruthlessly!) neglect results from low S/N IR data, measurements using Fe I 8468 Å in K dwarfs, Zeeman/magnetic Doppler imaging results, and curve-of-growth analyses” (for the reasons why some techniques were neglected, see Saar, 1996bJump To The Next Citation Point). A similar, upgraded collection of Zeeman analyses carried out in the period 1996 – 2001 was given by Saar (2001Jump To The Next Citation Point).

For this review, I have tried in Table 1 to compile magnetic field measurements available for sun-like stars. Following Saar (1996bJump To The Next Citation Point), I include only those measurements that rely on relatively high data-quality and analysis techniques. Since apparently not very many magnetic field measurements were reported in sun-like stars after 2001, Table 1 does not contain many results in addition to the compilations by Saar (1996bJump To The Next Citation Point, 2001Jump To The Next Citation Point). However, in the light of the results reported by Valenti et al. (1995Jump To The Next Citation Point), I distinguish between work done at optical wavelengths and work done at infrared wavelengths, the former probably being more prone to overestimating the magnetic field.

View Image

Figure 12: CES spectra of 59 Vir with uncertainties overplotted by best-fit solutions. Solid blue lines represent the overall best-fit solutions, dash-dotted red lines are other solutions shown for comparison. Residuals drawn below the fits visualize differences between measured and calculated line profiles, scaled by factor 100. The purple error bar to the right shows σi. Green lines indicate the difference between overall best-fit and the comparison model, i.e., the change in line shape due the presence of magnetic flux (other fit parameters vary freely). Top: Model with identical temperature for magnetic and non-magnetic regions; best-fit: Bf  = 500 G (solid blue), comparison: Bf  = 0 G (dash-dotted red). Bottom: Best fit for model with different temperatures for magnetic and non-magnetic regions; Bf  = 120 G (blue solid), comparison: solution from upper panel (Bf  = 500 G, same temperatures, red dashed line) (from Anderson et al., 2010Jump To The Next Citation Point, reprinted with permission ā’ø ESO).

A critical re-investigation of the detectability of magnetic fields in high-quality optical spectra was carried out by Anderson et al. (2010Jump To The Next Citation Point). The data material used for this work is of much higher quality than most magnetic field investigations before, and the data therefore allows a critical view on the published results and some of the limitations of the method. Anderson et al. (2010Jump To The Next Citation Point) used optical spectra around the Fe i line at 6173 Å observed at a spectral resolving power of R = 220 000 and SNR ∼ 400. The analysis is carried out for a one-component model with the same atmosphere for the magnetic and the non-magnetic parts of the stellar surface, and also for a two-component model employing different atmospheres for the two components. The results are reproduced in Figures 12View Image and 13View Image. For the active G0 star 59 Vir, the authors find a magnetic field with Bf  ≈ 420 G for the one-component case. For the two-component analysis, they cannot exclude a zero-field solution reporting an upper limit of 300 G. Figure 12View Image shows how subtle the differences between solutions with different magnetic field strengths are if all other relevant parameters are allowed to vary freely (there is currently no way to constrain these parameters at the level required). Figure 13View Image demonstrates the relation between magnetic field strength B and filling factor f in case of a one-component atmosphere (left panel). The two-component models shown in the center and right panels, however, can lift the Bf degeneracy but manage to reproduce the spectra even without the presence of a significant magnetic field. In other words, at optical wavelengths, the signal of temperature spots on the surface of a cool star can dominate the influence of the magnetic field through Zeeman broadening. Unfortunately, we have so far no clear empirical evidence for the relation between temperature and magnetic field strength on stellar surfaces other than on the Sun.

A look at Table 1 reveals that infrared measurements are only available in six sun-likes stars, all of them are of spectral type K. Two of the six data points are actually non-detections, and three were reported in conference summaries in which, unfortunately, no comprehensive presentation of the data and its analysis is given.

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Figure 13: 2 χ-maps for 59 Vir solutions (see Figure 12View Image). Left panel: Solution using the same atmospheres for magnetic and non-magnetic regions; Center panel: the same using cool magnetic regions; Right panel: the same for warm magnetic regions (from Anderson et al., 2010Jump To The Next Citation Point, reprinted with permission ā’ø ESO).

3.1.2 M-type stars

Low-mass stars of spectral type M have radii of approximately half a solar radius and less. If the stellar dynamo depends on the value of the Rossby number, Ro = Pāˆ• τconv, the magnetic field strength expected in sun-like and low-mass stars is a function of rotational period and convective overturn time. Values for the convective overturn time are theoretically not well determined, but τconv is probably higher at lower masses (e.g., Kim and Demarque, 1996). Therefore, slower rotation is sufficient to produce larger fields in less massive stars. Furthermore, the smaller radii of less massive stars lead to lower surface velocities hence less rotational broadening at a given rotational period. Finally, less massive stars are also much cooler thus exhibiting less temperature broadening in their spectral lines. It is this combination of parameters that facilitates the detection of Zeeman splitting in M-type stars in comparison to more massive, sun-like stars; Zeeman broadening is more easily detected because of generally narrower line widths (see also Reiners, 2007Jump To The Next Citation Point).

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Figure 14: Magnetic field measurements in active M dwarfs. Left: Spectra of the flare star EV Lac and the inactive star Gl 725B in the vicinity of the magnetically sensitive Fe i line at 8468.4 Å. Right: The spectrum of EV Lac divided by the inactive star Gl 725B (solid histogram). The dashed line shows a single field fit to the data (missing the line wings), the dashed-dot line show a fit allowing a distribution of magnetic fields (from Johns-Krull and Valenti, 2000Jump To The Next Citation Point).

The first detection of Zeeman splitting in an M-type star, and also the first detection of a photospheric magnetic field in cool stars at all, was presented by Saar and Linsky (1985Jump To The Next Citation Point). They observed the early-M flare star AD Leo using a Fourier transform spectrometer. After six hours of observation they had obtained a spectrum with R = 45 000 and SNR ≈ 25 around the Ti i lines at 2.22 µm from which they measured an average magnetic field strength of Bf  = 2800 G. Similar data taken with the same instrument was obtained in a few M-stars, and Saar (1994Jump To The Next Citation Point) presented a preliminary analysis of the three M-type stars AU Mic, AD Leo, and EV Lac. Another benchmark was the investigation of the Fe i line at 8468 Å in seven early- to mid-M dwarfs by Johns-Krull and Valenti (1996Jump To The Next Citation Point). Substantial magnetic fields were detected in two stars of the sample, EV Lac and Gl 729. A refined analysis of the two stars and AD Leo and YZ Cmi was presented in Johns-Krull and Valenti (2000Jump To The Next Citation Point). The latter work assumed a distribution of magnetic fields on the stellar surface, which led to significantly higher average field values compared to Johns-Krull and Valenti (1996Jump To The Next Citation Point). The results from the 8468 Å line were comparable to the values from the 2.22 µm line within 10 – 20%.

A serious problem for the detection of Zeeman splitting in atomic spectral lines of M-type stars is the appearance of molecular bands. For example, the Fe i line at 8468 Å is embedded in a forest of TiO molecular absorption lines, which makes the modeling of Zeeman splitting in this line a delicate task. To overcome this problem, and the notorious difficulty to model TiO absorption (see Valenti et al., 1998), Johns-Krull and Valenti (1996Jump To The Next Citation Point) modeled the ratio of the flux between an active and an inactive star. Hopefully, our understanding of very cool atmospheres, molecular chemistry, and molecular line formation will in the future allow a detailed modeling of Zeeman splitting in the spectra of M dwarfs (see also Kochukhov et al., 2009Jump To The Next Citation Point; Önehag et al., 2011; Shulyak et al., 2011).

At optical wavelengths, the main opacity contributors in M dwarfs are molecular bands from TiO and VO. Analysis of Zeeman broadening in these bands, however, is difficult not only because of problems getting the line formation right, but also because the lines are not individually resolved. Nevertheless, for the detection of M star magnetic fields, it would be favorable to utilize molecular absorption bands. A molecular band that appears to be extremely useful for the analysis of M-star magnetic fields (and other purpose) is the near-infrared band of molecular FeH. Its suitability for magnetic analysis was shown by Wallace et al. (1999), and it was proposed to be a useful diagnostic at low temperatures by Valenti et al. (2001). An observational problem of FeH is that its most suitable band is located at around λ = 1µm, which is too red for most CCDs and too blue for most astronomically used infrared spectrographs. As a consequence, only very few high-resolution spectrographs can provide spectra at this wavelength, and efficiencies are typically ridiculously low. On the other hand, M dwarfs emit much of their flux at near-infrared wavelengths so that in comparison to optical measurements, the signal quality around 1µm is not much lower than around 700 nm if the spectra are obtained with an optical/near-IR echelle spectrograph like HIRES (Keck observatory) or UVES (ESO/VLT). Reiners and Basri (2006Jump To The Next Citation Point) developed a method to semi-empirically determine the magnetic fields of M dwarfs comparing FeH spectra of the targets to spectra of two template stars; one with no magnetic field and one with a known, strong magnetic field (Figure 15View Image). This method requires a known magnetic star to calibrate the Zeeman splitting amplitude. The field strength of the target star is then estimated by interpolation between the template spectra.

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Figure 15: Magnetic field measurement using the empirical method of Reiners and Basri (2006Jump To The Next Citation Point). The black histogram shows the spectrum of Gl 729. The red and blue lines are scaled spectra of the active star EV Lac and the inactive star GJ 1002, respectively. The green line is an interpolation between the red (Bf  = 3.9 kG) and blue (0 kG) lines yielding a field strength of Bf  = 2.2 kG for Gl 729 (from Reiners and Basri, 2007Jump To The Next Citation Point, reproduced by permission of the AAS).

The method of Reiners and Basri (2006) was first used in a sample of 24 M stars between spectral types M0 and M9 (Reiners and Basri, 2007Jump To The Next Citation Point). As reference, the field measurement of EV Lac measured by Johns-Krull and Valenti (2000Jump To The Next Citation Point) was used. Thus, all magnetic field measurements are relative to this reference star (āŸØB āŸ© = 3.9 kG), and magnetic fields higher than this value cannot be quantified. Obviously, systematic uncertainties of the measurements are quite large, typically several hundred Gauss, and uncertainties probably grow towards very late spectral types where the template spectra are less suited as a reference. Unfortunately, Zeeman splitting of the FeH molecule is very complicated and could not entirely be described at this point (see Berdyugina and Solanki, 2002). Meanwhile, progress has been made using an empirical approach to understand FeH absorption and line formation (Wende et al., 2009, 2010), and to model Zeeman splitting in FeH lines (Afram et al., 2009; Shulyak et al., 2010Jump To The Next Citation Point). It was suggested that the fields determined semi-empirically may be overestimated by some ∼ 20%1 (Shulyak et al., 2010).

A (probably non-exhaustive) list of magnetic field measurements from Stokes I analysis in M dwarfs is given in Table 2, and I plot the distribution of field strength as a function of spectral type in Figure 16View Image. The field strengths of young, early-M and field mid- and late-M dwarfs are on the order of a few kG. This is the main results from Zeeman analysis and consistently found using different indicators (at least in mid-M dwarfs). Compared to the Sun, the average magnetic field hence is larger by two to three orders of magnitude, an observational result that must have severe implications for our understanding of low-mass stellar activity. It is not clear whether our picture of a star with spots more or less distributed over the stellar surface is actually valid in M dwarfs. If, for example, 50% of the surface of a star with a mean magnetic field of 4 kG is covered with a “quiet” photosphere and low magnetic field, the other half of the star must have a field strength as large as ∼ 8 kG. The two components of the stellar surface on such a star probably have very different temperatures and properties, and the definition of effective temperature must be considerably different from the temperature of the “quiet” photosphere.

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Figure 16: Measurements of M dwarf average magnetic fields from integrated light measurements. Data are given in Table 2. Limits are indicated by arrows, and multiple measurements of the same star are connected with vertical lines.

In early-M dwarfs (M3 and earlier), magnetic fields were found in young stars that are still rapidly rotating. Since old, early-M dwarfs in the field are generally slowly rotating and inactive there has been no search for magnetic fields in any large sample of them. Typical field values can be expected to be on the level of a few hundred Gauss and less, which is difficult to detect with Stokes I Zeeman measurements. Many mid- and late-M stars are rapidly rotating and fields of kG-strength are ubiquitously found among them.

3.1.3 Pre-main sequence stars and young brown dwarfs

Magnetic fields of pre-main sequence stars are of particular interest because accretion of circumstellar material onto the stellar surface is believed to be controlled by the stellar magnetic field (e.g., Bouvier et al., 2007). Evidence for accretion is observed in pre-main sequence stars of very different mass including young brown dwarfs. Field strengths predicted from several models of magnetospheric accretion are on the order of several kG for T Tauri stars, and a few hundred Gauss for young brown dwarfs (Johns-Krull et al., 1999bJump To The Next Citation Point; Reiners et al., 2009bJump To The Next Citation Point). On top of this, at young ages, magnetic fields may be generated by a dynamo like in older, sun-like stars (in contrast to fossil fields), but the dynamo would probably operate similar to the one in low-mass M-type dwarfs because pre-main sequence stars are still fully convective. On the other hand, at ages of a few Myr, primordial fields may still be present and not (yet) dissipated. Magnetic fields in pre-main sequence stars may therefore carry important information about the star- and planet-formation process.

First measurements of magnetic field strengths in T Tauri stars were attempted using the equivalent width method in (red) optical absorption lines by Basri et al. (1992Jump To The Next Citation Point), and Guenther et al. (1999Jump To The Next Citation Point) were following this strategy. Johns-Krull et al. (1999bJump To The Next Citation Point) used infrared lines of Ti i at 2.22 µm to determine the magnetic field in BP Tau. Obtaining information on stellar parameters and rotation from optical lines and magnetically insensitive CO lines, they were able to disentangle the significant Zeeman broadening from other broadening agents. Similar work on other T Tauri stars using infrared spectra was done by Johns-Krull et al., much of it is summarized in Johns-Krull (2007Jump To The Next Citation Point) where additional measurements of 14 T Tauri star magnetic fields are presented. Another set of 14 magnetic field measurements in very young T Tauri stars in the Orion nebula cluster are given in Yang and Johns-Krull (2011Jump To The Next Citation Point). We will return to the results from these substantial samples in Sections 5 and 7.3. A summary of magnetic field measurements in very young stars and brown dwarfs is given in Table 3, and are shown in Figure 17View Image.

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Figure 17: Measurements of pre-main sequence and young brown dwarf magnetic fields from integrated light measurements. Data are given in Table 3. Limits are indicated by arrows, and multiple measurements of the same star are connected with vertical lines.

Using FeH measurements as laid out in Section 3.1.2, Reiners et al. (2009bJump To The Next Citation Point) attempted to find evidence for kG-strength magnetic fields in young brown dwarfs. Young brown dwarfs can be expected to harbor substantial magnetic fields (Reiners and Christensen, 2010), and no fundamental difference is known to exist in the parameters that are believed to be relevant for magnetic flux generation between very-low mass stars and young brown dwarfs. However, in contrast to pre-main sequence stars, and in contrast to older brown dwarfs, none of the young brown dwarfs investigated by Reiners et al. (2009bJump To The Next Citation Point) exhibited a field above the detection threshold that in all cases lay below the fields typically found among the other groups.

An important property of the four young brown dwarfs investigated for magnetic fields is that all of them show evidence for accretion and, therefore, harbor a circumstellar disk. Magnetic field strengths required for magnetospheric accretion in these objects are much lower than in more massive, young stars, hence there is currently no contradiction between the presence of accretion and the lack of evidence for substantial fields. Observations of radio-emission, however, indicate that fields of a few kG strength are in fact present on some L-type field (old and non-accreting) brown dwarfs (Hallinan et al., 2008; Berger et al., 2009). Direct measurement of magnetism in non-accreting brown dwarfs, both young and old, are required to further investigate whether the average fields are really weaker in young brown dwarfs or in the presence of accretion.

It is an interesting question whether the non-detection of magnetic fields in brown dwarfs is due to the presence of accretion disks around the objects observed so far. If this is the case, there ought to be some mechanism for the disk to regulate the magnetic field of the central object, which is not easily understood. Alternatively, large difference in radius may be of importance in this context because the surface area of young brown dwarfs is about an order of magnitude larger than the surface of old brown dwarfs. If magnetic flux is approximately conserved during its evolution, the average magnetic field would be an order of magnitude lower in young, large brown dwarfs than in old, small, field brown dwarfs. We come back to this point in Section 7.3.


Table 1: Average magnetic fields from Stokes I measurements in sun-like stars. Tables 17 are an attempt to collect information available on magnetic fields in cool stars. They are certainly incomplete to some extent simply because the author has overlooked many sources. The reader is encouraged to send references to papers that are missing so far and new work that appears in this field.
Star SpType Bf [kG] Reference
IR data
σ Dra K0 ≤ 0.10 Valenti et al. (1995Jump To The Next Citation Point)
40 Eri K1 ≤ 0.10 Valenti et al. (1995Jump To The Next Citation Point)
šœ– Eri K2 0.13 Valenti et al. (1995)
LQ Hya K2 2.45 Saar (1996bJump To The Next Citation Point)
ξ Boo B K4 0.46 Saar (1994Jump To The Next Citation Point)
Gl 171.2A K5 1.40 Saar (1996bJump To The Next Citation Point)
Optical data
HD 68456 F6 1.00 Anderson et al. (2010Jump To The Next Citation Point)
59 Vir G0 0.19 Linsky et al. (1994Jump To The Next Citation Point) (see Saar, 1996bJump To The Next Citation Point)
0.42 Anderson et al. (2010Jump To The Next Citation Point) (one temperature)
< 0.30 Anderson et al. (2010Jump To The Next Citation Point) (cool spot solution)
58 Eri G1 0.20 Rüedi et al. (1997Jump To The Next Citation Point)
κ Cet G5 0.36 Saar and Baliunas (1992)
61 Vir G6 < 0.15 Anderson et al. (2010)
ξ Boo A G8 0.48 Basri and Marcy (1988Jump To The Next Citation Point)
0.35 Marcy and Basri (1989Jump To The Next Citation Point)
0.34 Linsky et al. (1994) (see Saar, 1996bJump To The Next Citation Point)
70 Oph A K0 0.22 Marcy and Basri (1989Jump To The Next Citation Point)
40 Eri A K1 0.06 Rüedi et al. (1997Jump To The Next Citation Point)
36 Oph B K1 0.12 Rüedi et al. (1997Jump To The Next Citation Point)
šœ– Eri K2 0.35 Basri and Marcy (1988Jump To The Next Citation Point)
0.30 Marcy and Basri (1989Jump To The Next Citation Point)
0.17 Rüedi et al. (1997Jump To The Next Citation Point)
HD 166620 K2 0.23 Basri and Marcy (1988)
HD 17925 K2 0.25 Saar (1996bJump To The Next Citation Point)
36 Oph A K2 0.20 Marcy and Basri (1989Jump To The Next Citation Point)
HR 222 K2.5 0.19 Marcy and Basri (1989Jump To The Next Citation Point)
HR 5568 K4 0.16 Rüedi et al. (1997Jump To The Next Citation Point)
EQ Vir K5 1.38 Saar (1996bJump To The Next Citation Point)
61 Cyg A K5 0.29 Marcy and Basri (1989)
šœ– Ind K5 0.09 Rüedi et al. (1997)


Table 2: Average magnetic fields from Stokes I in M-dwarfs.
Star Other Name SpType Bf [kG] Reference
Gl 182 M0.0 2.5 Reiners and Basri (2009Jump To The Next Citation Point)
Gl 803 AU Mic M1.0 2.3 Saar (1994Jump To The Next Citation Point)
Gl 569A M2.0 1.8 Reiners and Basri (2009Jump To The Next Citation Point)
Gl 494 DT Vir M2.0 1.5 Saar (1996b)
Gl 70 M2.0 < 0.2 Reiners and Basri (2007Jump To The Next Citation Point)
Gl 873 EV Lac M3.5 3.9 Johns-Krull and Valenti (1996Jump To The Next Citation Point, 2000Jump To The Next Citation Point)
3.7 Saar (1994Jump To The Next Citation Point)
Gl 729 M3.5 2.0 Johns-Krull and Valenti (1996, 2000Jump To The Next Citation Point)
2.2 Reiners and Basri (2007Jump To The Next Citation Point)
Gl 87 M3.5 3.9 Reiners and Basri (2007Jump To The Next Citation Point)
Gl 388 AD Leo M3.5 2.8 Saar and Linsky (1985Jump To The Next Citation Point)
2.6 Saar (1994)
3.3 Johns-Krull and Valenti (2000Jump To The Next Citation Point)
2.9 Reiners and Basri (2007Jump To The Next Citation Point)
3.2 Kochukhov et al. (2009Jump To The Next Citation Point)
GJ 3379 M3.5 2.3 Reiners et al. (2009aJump To The Next Citation Point)
GJ 2069 B M4.0 2.7 Reiners et al. (2009aJump To The Next Citation Point)
Gl 876 M4.0 < 0.2 Reiners and Basri (2007Jump To The Next Citation Point)
GJ 1005A M4.0 < 0.2 Reiners and Basri (2007Jump To The Next Citation Point)
Gl 490 B G 164-31 M4.0 3.2 Phan-Bao et al. (2009Jump To The Next Citation Point)
Gl 493.1 M4.5 2.1 Reiners et al. (2009aJump To The Next Citation Point)
GJ 4053 LHS 3376 M4.5 2.0 Reiners et al. (2009aJump To The Next Citation Point)
GJ 299 M4.5 0.5 Reiners and Basri (2007Jump To The Next Citation Point)
GJ 1227 M4.5 < 0.2 Reiners and Basri (2007Jump To The Next Citation Point)
GJ 1224 M4.5 2.7 Reiners and Basri (2007Jump To The Next Citation Point)
Gl 285 YZ CMi M4.5 3.3 Johns-Krull and Valenti (2000Jump To The Next Citation Point)
> 3.9 Reiners and Basri (2007Jump To The Next Citation Point)
4.5 Kochukhov et al. (2009)
GJ 1154 A M5.0 2.1 Reiners et al. (2009aJump To The Next Citation Point)
GJ 1156 M5.0 2.1 Reiners et al. (2009aJump To The Next Citation Point)
Gl 905 M5.5 < 0.1 Reiners and Basri (2007Jump To The Next Citation Point)
GJ 1057 M5.0 < 0.2 Reiners and Basri (2007Jump To The Next Citation Point)
Gl 905 M5.5 < 0.1 Reiners and Basri (2007Jump To The Next Citation Point)
GJ 1245B M5.5 1.7 Reiners and Basri (2007Jump To The Next Citation Point)
GJ 1286 M5.5 0.4 Reiners and Basri (2007Jump To The Next Citation Point)
GJ 1002 M5.5 < 0.2 Reiners and Basri (2007Jump To The Next Citation Point)
Gl 406 M5.5 2.4 Reiners and Basri (2007Jump To The Next Citation Point)
2.1 – 2.4 Reiners et al. (2007)
Gl 412 B M6.0 > 3.9 Reiners et al. (2009aJump To The Next Citation Point)
GJ 1111 M6.0 1.7 Reiners and Basri (2007Jump To The Next Citation Point)
Gl 644 C VB 8 M7.0 2.3 Reiners and Basri (2007Jump To The Next Citation Point)
GJ 3877 LHS 3003 M7.0 1.5 Reiners and Basri (2007Jump To The Next Citation Point)
2M 0440232–053008 M7.0 1.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0741068+173845 M7.0 1.0 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0752239+161215 M7.0 3.5 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0818580+233352 M7.0 1.0 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1048126–112009 GJ 3622 M7.0 0.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1356414+434258 M7.0 2.7 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1456383–280947 M7.0 1.2 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1534570–141848 M7.0 2.0 Reiners and Basri (2010Jump To The Next Citation Point)
LHS 2645 M7.5 2.1 Reiners and Basri (2007Jump To The Next Citation Point)
2M 0331302–304238 M7.5 2.0 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0351000–005244 M7.5 1.4 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0417374–080000 M7.5 1.8 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0429184–312356A M7.5 2.5 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1006319–165326 M7.5 1.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1246517+314811 M7.5 < 0.4 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1253124+403403 M7.5 1.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1332244–044112 M7.5 1.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1546054+374946 M7.5 2.7 Reiners and Basri (2010Jump To The Next Citation Point)
LP 412-31 M8.0 > 3.9 Reiners and Basri (2007Jump To The Next Citation Point)
VB 10 M8.0 1.3 Reiners and Basri (2007Jump To The Next Citation Point)
2M 0248410–165121 M8.0 1.4 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0320596+185423 M8.0 3.7 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0517376–334902 M8.0 1.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0544115–243301 M8.0 1.2 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1016347+275149 M8.0 2.1 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1024099+181553 M8.0 < 1.4 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1141440–223215 M8.0 1.8 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1309218–233035 M8.0 1.2 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1440229+133923 M8.0 < 0.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1843221+404021 M8.0 1.2 Reiners and Basri (2010Jump To The Next Citation Point)
2M 2037071–113756 M8.0 < 0.2 Reiners and Basri (2010Jump To The Next Citation Point)
2M 2306292–050227 M8.0 0.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 2349489+122438 M8.0 1.2 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0024442–270825B M8.5 2.1 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0306115–364753 M8.5 1.6 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1124048+380805 M8.5 2.0 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1403223+300754 M8.5 2.1 Reiners and Basri (2010Jump To The Next Citation Point)
2M 2226443–750342 M8.5 1.8 Reiners and Basri (2010Jump To The Next Citation Point)
2M 2331217–274949 M8.5 3.1 Reiners and Basri (2010Jump To The Next Citation Point)
2M 2353594–083331 M8.5 2.0 Reiners and Basri (2010Jump To The Next Citation Point)
LHS 2924 M9.0 1.6 Reiners and Basri (2007Jump To The Next Citation Point)
LHS 2065 M9.0 > 3.9 Reiners and Basri (2007Jump To The Next Citation Point)
2M 0019457+521317 M9.0 3.7 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0109511–034326 M9.0 1.4 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0334114–495334 M9.0 1.4 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0443376+000205 M9.0 < 1.0 Reiners and Basri (2010Jump To The Next Citation Point)
2M 0853362–032932 M9.0 2.9 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1048147–395606 M9.0 2.3 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1224522–123835 M9.0 1.4 Reiners and Basri (2010Jump To The Next Citation Point)
2M 1438082+640836 M9.5 1.2 Reiners and Basri (2010Jump To The Next Citation Point)
2M 2237325+392239 M9.5 1.0 Reiners and Basri (2010Jump To The Next Citation Point)


Table 3: Average magnetic fields from Stokes I in pre-main sequence stars and young brown dwarfs.
Star SpType Bf [kG] Reference
TAP 10 G5 < 0.7 Basri et al. (1992Jump To The Next Citation Point)
GW Ori G5 < 1.0 Guenther et al. (1999Jump To The Next Citation Point)
T Tau K0 2.4 Johns-Krull (2007Jump To The Next Citation Point)
2.5 Guenther et al. (1999Jump To The Next Citation Point)
TAP 35 K1 1.0 Basri et al. (1992)
2MASS 05361049–0519449 K3 2.31 Yang and Johns-Krull (2011Jump To The Next Citation Point)
V1735 Orig K4 2.08 Yang and Johns-Krull (2011Jump To The Next Citation Point)
LkCa 15 K5 1.55 Guenther et al. (1999)
V1227 Ori K5-K6 2.14 Yang and Johns-Krull (2011Jump To The Next Citation Point)
OV Ori K5-K6 1.85 Yang and Johns-Krull (2011Jump To The Next Citation Point)
GI Tau K6 2.7 Johns-Krull (2007Jump To The Next Citation Point)
TW Hya K7 2.6 Johns-Krull (2007Jump To The Next Citation Point)
GK Tau K7 2.3 Johns-Krull (2007Jump To The Next Citation Point)
GM Aur K7 1.0 Johns-Krull (2007Jump To The Next Citation Point)
Hubble 4 K7 2.5 Johns-Krull et al. (2004)
AA Tau K7 2.8 Johns-Krull (2007Jump To The Next Citation Point)
BP Tau K7 2.2 Johns-Krull (2007Jump To The Next Citation Point)
2.6 Johns-Krull et al. (1999b)
DK Tau K7 2.6 Johns-Krull (2007Jump To The Next Citation Point)
GG TauA K7 1.2 Johns-Krull (2007Jump To The Next Citation Point)
TWA 9A K7 2.9 Yang et al. (2008Jump To The Next Citation Point)
TW Hya K7 2.7 Yang et al. (2008Jump To The Next Citation Point)
V1568 Ori K7 1.42 Yang and Johns-Krull (2011Jump To The Next Citation Point)
DG Tau K7.5 2.6 Johns-Krull (2007Jump To The Next Citation Point)
2MASS 05353126–0518559 K8 2.84 Yang and Johns-Krull (2011Jump To The Next Citation Point)
V1348 Ori K8 3.14 Yang and Johns-Krull (2011Jump To The Next Citation Point)
V1123 Ori M0/K8 2.51 Yang and Johns-Krull (2011Jump To The Next Citation Point)
DN Tau M0 2.0 Johns-Krull (2007Jump To The Next Citation Point)
LO Ori M0 3.45 Yang and Johns-Krull (2011Jump To The Next Citation Point)
LW Ori M0.5 1.30 Yang and Johns-Krull (2011Jump To The Next Citation Point)
2MASS 05350475–0526380 M0.5 2.79 Yang and Johns-Krull (2011Jump To The Next Citation Point)
V568 Ori M1 1.53 Yang and Johns-Krull (2011Jump To The Next Citation Point)
2MASS 05351281–0520436 M1 1.70 Yang and Johns-Krull (2011Jump To The Next Citation Point)
CY Tau M1 1.2 Johns-Krull (2007Jump To The Next Citation Point)
DF Tau M1 2.9 Johns-Krull (2007Jump To The Next Citation Point)
TWA 9B M1 3.3 Yang et al. (2008Jump To The Next Citation Point)
DH Tau M1.5 2.7 Johns-Krull (2007Jump To The Next Citation Point)
TWA 5A M1.5 4.2a Yang et al. (2008Jump To The Next Citation Point)
V1124 Ori M1.5 2.09 Yang and Johns-Krull (2011Jump To The Next Citation Point)
DE Tau M2 1.1 Johns-Krull (2007Jump To The Next Citation Point)
TWA 8A M2 2.7 Yang et al. (2008Jump To The Next Citation Point)
TWA 7 M3 2.0 Yang et al. (2008)
UpSco 55 M5.5 2.3 Reiners et al. (2009bJump To The Next Citation Point)
CFHT-BD-Tau 4 M7 < 1.8 Reiners et al. (2009bJump To The Next Citation Point)
UpSco-DENIS 160603 M7.5 < 0.4 Reiners et al. (2009bJump To The Next Citation Point)
2MASS 1207 M8 < 1.0 Reiners et al. (2009bJump To The Next Citation Point)
ρ-Oph-ISO 32 M8 < 2.4 Reiners et al. (2009bJump To The Next Citation Point)
a very high v sin i


Table 4: Magnetic field measurements not listed in Tables 1, 2, and 3.
Publication Comment
Robinson et al. (1980) ξ Boo A, 70 Oph A, 61 Vir
Vogt (1980) BY Dra, HD 88230, 61 Cyg A, HD 209813
Marcy (1981) ξ Boo A
Golub et al. (1983) λ And
Marcy (1984) 29 G- and K main sequence stars
Marcy and Bruning (1984) 8 evolved stars
Gray (1984) 18 F-, G-, and K-dwarfs
Gondoin et al. (1985) ξ Boo A, 61 UMa, λ And
Saar et al. (1986) EQ Vir
Bruning et al. (1987) 7 K- and M-dwarfs
Mathys and Solanki (1989) Preliminary results, “Stenflo–Lindegren” technique
Bopp et al. (1989) VY Ari
Saar (1990Jump To The Next Citation Point) Selection of 31 G – M star measurements; including unpublished data


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