OBSERVING MAGNETIC FIELDS IN STAR-FORMING REGIONS

JIM COHEN

The University of Manchester, Jodrell Bank Observatory, Macclesfield, Cheshire, UK;E-mail: rjc@jb.man.ac.uk

(Received 16 April 2004; accepted 15 June 2004)

Abstract. Magnetic field strengths and directions can be estimated using many different observationaltechniques that span a wide range of wavelengths. Each observational method favours different regimesof scale size, density and other physical conditions. The available techniques and their ranges ofapplicability are briefly described and the current status of observations is reviewed, with particularemphasis on high-resolution observations of star-forming regions.

Keywords: magnetic fields, star-forming regions, Zeeman effect, masers, polarization

1. Introduction

In 1969 I was a vacation student at Mount Stromlo and Siding Springs Observatories,helping Don Mathewson to measure the polarization of starlight. The fact that therewas an interstellar magnetic field intrigued me, and so did the fact that starlightcarried its imprint. My next encounter with cosmic magnetic fields came in 1983when I began to study masers and bipolar molecular outflows from young stars. Ilearned that the prototype outflow, from the source L1551, has its CO emission lobesparallel to the interstellar polarization vectors in that part of the sky (Snell et al.,1980). What a connection! Checking the literature I found that other outflows werealigned with the local interstellar magnetic field. Furthermore the magnetic fieldmeasured using hydroxyl (OH) masers was strong enough to affect the dynamicsof the outflow (Cohen et al., 1984).

Magnetic fields are also important in early stages of star-formation. The balancebetween magnetic, gravitational and turbulent energy is critical for the stability ofmolecular clouds (e.g. Zweibel and McKee, 1995). Gravitational collapse of molec-ular clouds proceeds preferentially along the magnetic field lines, giving rise to largerotating disc or torus structures orthogonal to the magnetic field. The magnetic fieldcan play a key role in halting the collapse and in transferring angular momentum.It is natural to expect that there may be polarization signatures for the differentevolutionary stages of a young stellar object (Vallee and Bastien, 2000). Vallee andBastien present a sequence of possible magnetic field configurations associatedwith different evolutionary classes of object (Classes I–V). The basic idea is thatthe magnetic field starts uniform and is progressively distorted by gravitational

Astrophysics and Space Science 295: 27–36, 2004.C© Springer 2005

28 J. COHEN

collapse and rotation. It has also been suggested that magnetic reconnection(following twisting of the magnetic field lines) can power the bipolar molecularoutflows.

There are many techniques available to measure the interstellar magnetic fieldB. Some techniques give the direction of the field, some give the magnitude, somegive the component in the plane of the sky (Bsky = Bsin θ ) while others give thecomponent along the line-of-sight (Blos = Bcos θ ), where θ is the angle betweenthe field and the line-of-sight. Here we use the convention that θ = 0 for a fieldpointing away from us. The different methods of determining B are not all usuallyavailable for, or applicable to, a particular source. The polarized flux that containsthe magnetic field information is often less than 1%, so we are often struggling forsensitivity.

When interpreting any type of polarization measurement we must rememberthat the four Stokes parameters are additive. Our measurements give an averageover all emission or absorption in our beam and in our detector bandwidth. Threeof the Stokes parameters, Q, U and V , can be positive or negative, so averagingwill tend to reduce them. If there is any polarization structure that is unresolvedeither spatially or in frequency we will underestimate the true degree of polarizedflux

√Q2 + U 2 + V 2, and so underestimate the true degree of polarization.

At long wavelengths we may need to take account of the Faraday effect. Theplane of polarization is rotated by an amount �φ proportional to λ2

∫ne Bcos θds

integrated along the line-of-sight, where ne is the free electron density. Faradayrotation can be a nuisance if we do not know the rotation measure, for then ourpolarization vectors are rotated by an uncalibrated amount. However if we mea-sure the rotation measure it can be an important tool in studying the large-scalemagnetic field of the Galaxy. This has been done using the rotation measures ofextragalactic radio sources (Brown and Taylor, 2001) and in particular the rotationmeasures of pulsars (Han et al., 2002). For pulsars we can measure the dispersionproportional to λ2

∫neds, so the ratio of rotation measure to dispersion measure

gives us 〈Bcos θ〉 weighted according to ne. This a useful way to study the largescale magnetic field of the Galaxy (Brown et al., 2003). However it is not generallyuseful for small-scale studies of star-formation and will not be discussed furtherhere.

In this review I will discuss the different techniques that are available for measur-ing B in high-density regions around young stars, and review recent developments.For a more comprehensive overview the reader is referred to the review by Vallee(2003).

2. Continuum Measurements

There are two basic mechanisms that produce polarized continuum radiation: syn-chrotron radiation and the alignment of spinning dust grains.

OBSERVING MAGNETIC FIELDS 29

2.1. SYNCHROTRON EMISSION

Synchrotron radiation is produced by relativistic electrons spiralling around mag-netic field lines. We can understand the polarization in terms of a distributed current,with a resultant component of linear polarization perpendicular to the field lines.A fine example of this occurs in the galactic centre, where Lang et al. (1999) havedetected linear polarization perpendicular to the striking narrow filament called theNorthern Thread, confirming the magnetic field direction along the filament thatwas hypothesised long ago.

But unfortunately synchrotron polarization does not directly tell us the magni-tude of B, without further assumptions about the distribution of relativistic electrons(e.g. equipartition arguments). A local galactic magnetic field of a few µG (1 G≡ 10−4 T) is implied unambiguously by local measurements of the cosmic raydistribution, but all other B values deduced from synchrotron emission are indirect.

2 .2 . POLARIZATION FROM ALIGNED DUST GRAINS

At shorter wavelengths, from mm-wave through submm and infrared to optical,aligned dust grains are thought to be responsible for the polarization we observe.There are three possible scenarios:

– thermal emission, where the electric field vector E is perpendicular to B,– scattering, where E is perpendicular to B, or– extinction, the residual radiation that is not scattered, where E is parallel to B.

Polarization of starlight by extinction dominates at optical wavelengths. There aresome fine examples in the literature showing well-organized polarization vectorsthat are clearly related to the large-scale structure of the molecular clouds (e.g.Messinger et al., 1997). However only the outer layers of the clouds can be probedin this way. Once the extinction becomes too high the polarized signal becomesundetectable.

Polarization by scattering is important at optical and near infrared wavelengths.In fact because of the complicated nature of star-forming regions we often observea mixture of scattering and extinction that can be difficult to interpret. Fischer etal. (1994) showed from Monte Carlo simulations that many of the polarizationpatterns observed in the optical and near infrared wavebands can be fully explainedby multiple dust scattering and reflection from dust discs, without invoking magneticfields!

At longer wavelengths (far infrared and submm) thermal emission becomesthe dominant mechanism producing polarization. These wavebands have becomeaccessible to study in recent years. At these wavelengths the radiation really doescome from the whole molecular cloud, not just the outer layers. SCUBA results havemade a big impact, and now a new generation of polarimeters is coming on stream.

30 J. COHEN

Chuss et al. (2003) measured the 350-µm continuum polarization of the galac-tic centre using the Hertz polarimeter on the Caltech Submillimeter Observatory(CSO). They found a two-phase structure to B. Where the gas density is high B runsparallel to the galactic plane (toroidally about the centre). Where the gas density islower B runs perpendicular to the plane, as in the radio filament mapped by Langet al. (1999). Chuss et al. (2003) argue that cloud collapse along field lines canproduce a toroidal B field inside the dense molecular gas whilst leaving B poloidaloutside the molecular clouds. Their model resembles the Uchida and Shibata (1985)model for a collapsing molecular cloud. Chuss et al. argue that magnetic reconnec-tion provides the energy to power the non-thermal radio filaments, although otherinterpretations cannot be excluded.

In all these cases the polarization gives information only about the direction ofthe magnetic field. If we want to estimate the magnitude of B then we need to makeassumptions about the dust.

Crutcher et al. (2004), Vallee et al. (2003) and others have used the randomness inthe polarization vectors to estimate B, based on an argument due to Chandrasekharand Fermi (1953) concerning magneto-hydrodynamic waves. According to theseauthors we should be able to estimate the component of B in the plane of the sky,Bsin θ , from the rms deviation of polarization angles from the mean, assumingthat MHD waves are responsible for the deviations: Bsin θ ∝ n1/2δV δφ−1, wheren is the gas density, δV is the turbulent velocity and δφ is the rms deviation inthe polarization angle φ. The technique has previously been applied to far infraredphotometry by Chrysostomou et al. (1994) and Gonatas et al. (1994). Using SCUBAmeasurements at 850 µm Crutcher et al. estimate magnetic fields of 80 µG in L183and 140 µG in L1544, while Vallee et al. estimate a field of 150 µG in the BokGlobule CB 068.

3. Zeeman Measurements

The most direct measurements of the magnetic field come from the Zeeman effect.An electron in a magnetic field B processes at the Larmor frequency ωL = eB

2me(in

SI units), where e is the electronic charge and me is the mass of the electron. In theclassical Zeeman effect shown in Figure 1 a spectral line is split into three polarizedcomponents at frequencies ω0, ω0+ωL and ω0-ωL. Looking along the field lines wesee a pair of oppositely circularly polarized σ -components; looking perpendicularto B we see three linearly polarized components, the central π -component par-allel to B and the two outer σ -components perpendicular to B. In general at anangle θ we see a linearly polarized π -component and two elliptically polarizedσ -components.

If the Zeeman splitting is strong enough to separate the three line componentsthen we get a direct measurement of B. If however the Zeeman components areblended then we measure Bcos θ .

OBSERVING MAGNETIC FIELDS 31

Figure 1. The classical Zeeman effect. If the Zeeman components are blended then observations at anangle θ to the magnetic field give Bcos θ , whereas if the components are separated then observationsyield B directly.

3 .1 . THERM AL LINES

The classical Zeeman effect is a sufficient basis to understand Zeeman splittingof the 1420-MHz line of neutral atomic hydrogen. The splitting is weak, so σ -components dominate and we measure only weak circular polarization, with theStokes parameter V = zBcos θ d I

dν, where z is the splitting factor and I (ν) is the line

profile. Notice that whatever the magnetic field, the Stokes V -profile is unchanged.Increasing B simply increases the amplitude. Instrumental issues and sensitivitylimit the usefulness of 1420-MHz Zeeman studies to absorption measurements andfields exceeding ∼10 µG.

Absorption line studies by Brogan and Troland (2001) yielded Bcos θ values ofup to ∼750 µG in the star-forming region M17. Bcos θ increases towards the West-ern edge of the source, where Bsin θ (traced by 100-µm polarization) decreases.Either the magnetic field is bending around the edge of the HII region, or the dustproperties are being modified by the HII region.

Molecular line Zeeman studies require some understanding of the quantum Zee-man effect. In a magnetic field the upper and lower states of a molecular transitioneach split into 2F + 1 levels, where F is the total quantum number. The allowedtransitions are �m = ±1 (σ -components) and �m = 0 (π -components), where mis the magnetic quantum number. Because the upper and lower states have differentsplitting factors in general, the complete Zeeman can be complex.

For the mainlines of the OH ground state, at 1665 and 1667 MHz, the up-per and lower states split by equal amounts for each line, so the Zeeman pat-terns are simple and straightforward to interpret. Sarma et al. (2000) studied OH

32 J. COHEN

mainline absorption against continuum sources in NGC6334 and measured fieldsof ∼200 µG. Virial estimates suggest that the magnetic fields are of the right orderto support the molecular clouds associated with these sources against gravitationalcollapse.

A remarkable achievement was the detection of the Zeeman effect in thermalemission from the OH 1665 and 1667-MHz lines (Crutcher and Troland, 2000),using Arecibo. This technique has the potential to probe the magnetic field rightacross entire molecular clouds, not just in those regions where there are continuumsources. OH thermal emission is known over the whole Taurus complex (Wouterlootand Habing, 1985), for example, a region tens of degrees across.

The presence of many hyperfine components usually complicates the Zeemanpattern but complication can sometimes give new possibilities. The CN 1-0transition near 113 GHz has nine hyperfine components that are well separatedin velocity. Crutcher et al. argued that these lines provide the best opportunity tomeasure magnetic fields in clouds with densities of 105–106 cm−3. Because thedifferent components couple differently to B (one even goes the other way) theeffect of systematic and instrumental errors can be reduced. A clear detection ofthe Zeeman effect in these CN hyperfines was made using the Pico Veleta telescope(Crutcher et al., 1999). By fitting simultaneously to the seven major componentsCrutcher et al. found Bcos θ = 0.36 ± 0.08 mG in OMC1 and similar values inDR21(OH) and M17.

Crutcher (1999) summarized the then available Zeeman data on thermal linesand concluded that the magnetic and kinetic energies are approximately equal, withthe magnetic field scaling with gas density as B ∝ ρ0.47. This result is consistentwith ambipolar diffusion, but it can also be interpreted as saying that vAlfven =0.7 km s−1. The maser measurements described in the next section extend the rangeof validity of this relationship by four orders of magnitude.

Linear polarization of molecular spectra can also arise through a quantum me-chanical effect (Goldreich and Kylafis, 1981). The linear polarization is either par-allel or perpendicular to the magnetic field direction. The effect was first detectedin CO emission from the galactic centre (Greaves et al., 1999) and has since beenapplied to star-forming regions by Lai et al. (2003) and others. Although the polar-ization is weak, this technique has the advantage of being potentially applicable toany molecular line in any region of a molecular cloud.

3.2. MASER LINES

Masers provide the only direct measurement of B at subarcsecond resolution, prob-ing densities from ∼105–108 cm−3 for OH, to 1010 cm−3 for H2O. The Zeemaneffect gives only part of the polarization story however, since masers are nonlinear.There are other effects to consider, including magnetic beaming, saturation andblending of maser lines.

OBSERVING MAGNETIC FIELDS 33

As in the case of thermal lines, the interpretation is much cleaner if the magneticfield splits the Zeeman components by more than their thermal linewidths. This isthe case for the most commonly observed OH masers at 1665 and 1667 MHz.The maser amplification often introduces an asymmetry into the amplitudes of theZeeman features, since all molecules contributing to a particular maser beam musthave the same resonant frequency. The magnetic shift of frequency is equivalent to avelocity shift. Therefore along any given line-of-sight different molecules contributeto beams of right-hand circular (RHC) and left-hand circular (LHC) polarization.Hence the gains of the RHC and LHC beams are different in general, and oneor other Zeeman component dominates. Consequently complete Zeeman patternsare rarely seen. Furthermore, masers amplify most strongly along the magneticfield lines (Gray and Field, 1995), a phenomenon termed “magnetic beaming”. Asthe maser saturates the stronger beam (along B) increasingly dominates, so circularpolarization and σ -components dominate. Data for OH 1665-MHz masers in W75N

Figure 2. Circular polarization as a function of linear polarization for OH 1665-MHz masers inW75N, measured with MERLIN (Hutawarakorn et al., 2002). Because of magnetic beaming, OHmasers amplify most strongly along the line-of-sight, corresponding to θ ∼ 0 or θ ∼ 180 degrees.

34 J. COHEN

shown in Figure 2 illustrate the beaming effect. We see mostly σ -components withstrong circular or elliptical polarization corresponding to θ close to the line-of-sight,and very few π -components corresponding to θ � 90◦.

Because of magnetic beaming it is reasonable to assume that elliptically polar-ized components are σ -components. If that is the case then we can deduce θ , theangle of B to the line-of-sight, from the degree of circular polarization, since if themasers are not saturated then V = −2I cos θ/(1 + cos2θ ) as for thermal emission.From the linear polarization we know the projected angle of B on the plane ofthe sky, so we can in fact determine direction of the B vector in three dimensions(Garcia-Barreto et al., 1988). If we are lucky enough to see a Zeeman pair thensplitting gives us the magnitude of B, and we can determine the three-dimensionalB vector.

MERLIN observations of OH masers associated with bipolar outflows haverevealed maser tori or discs at the centre of the flows, with scale ∼2000 AU(Hutawarakorn and Cohen, 1999, 2003; Hutawarakorn et al., 2002). The direc-tion of B reverses on opposite sides of the torus, suggesting that rotation haswound up the field. Detailed modelling of the OH masers in W75N (Gray et al.,2003) supports the twisted magnetic field model proposed by Uchida and Shi-bata (1985). The NGC7538 region contains three bipolar outflows each with OHmasers (IRS1, IRS9 and IRS11) but with very different degrees of polarization.The same behaviour is seen in SCUBA data on scales 100 times larger: IRS11 haswell-organized B vectors aligned with the outflow, while IRS1 has less polariza-tion and less organized B vectors (Momose et al., 2001). It is suggested that thepolarization properties are age related, with younger sources being more highlyorganized, having stronger polarization and greater alignment with the outflowdirection.

Excited OH masers at 6.0 GHz have Zeeman splitting comparable to theirlinewidths, so that Zeeman pairs are common. Caswell (2003) carried out an ex-tensive search for 6.0-GHz OH masers and found many cases of matching Zeemanpairs at 6035 and 6030 MHz, from which reliable B values can be deduced evenwithout interferometry.

Blending of maser lines (including hyperfine components) is difficult to dealwith. The greater the blending and the greater the degree of saturation, thebigger have been the disagreements over how to interpret the data. A sum-mary of the current theoretical situation is given by Gray (2003). The strongH2O masers at 22 GHz show weak polarization, both circular (Sarma et al.,2002) and linear (Imai et al., 2003), but the interpretation is complicated bythe presence of blended hyperfine components, and will not be considered fur-ther here. See however Imai, these proceedings. Likewise polarization of SiOand CH3OH masers will not be discussed here, despite exciting new observa-tional results from Plambeck et al. (2003) and Gaylard and Goedhart (theseproceedings).

OBSERVING MAGNETIC FIELDS 35

4. Conclusions

Sensitivity limits three-dimensional magnetic field studies at present, but the po-tential to probe a wide range of densities up to at least ∼1010 cm−3 has beendemonstrated. Major new facilities such as ALMA should bridge the gap betweenmasers and other molecular lines, enabling us finally to see the magnetic field struc-ture of whole molecular cloud complexes, on angular scales from degrees down tomilliarcseconds.

Key questions for the future include the treatment of overlapping hyperfinecomponents, and the issues that got me started in this field in the first place, therelation of the magnetic field in star-forming regions to the general galactic fieldand to the evolution of the young stars.

Acknowledgements

I thank Malcolm Gray and Busaba Kramer (nee Hutawakorn) for interesting dis-cussions.

References

Brogan, C.L. and Troland, T.H.: 2001, ApJ 560, 821.Brown, J.C., Taylor, A.R., Wielebinski, R. and Muller, P.: 2003, ApJ 592, L29.Brown, J.C. and Taylor, A.R.: 2001, ApJ 563, L31.Caswell, J.L.: 2003, MNRAS 341, 551.Chandrasekhar, S. and Fermi, E.: 1953, ApJ 118, 113.Chrysostomou, A., Hough, J.H., Burton, M.G. and Tamura, M.: 1994, MNRAS 268, 325.Chuss, D.T., Davidson, J.A., Dotson, J.L., Dowell, C.D., Hildebrand, R.H., Novak, G. and Vaillancourt,

J.E.: 2003, ApJ 599, 1116.Cohen, R.J., Rowland, P.R. and Blair, M.M.: 1984, MNRAS 210, 424.Crutcher, R.M.: 1999, ApJ 520, 706.Crutcher, R.M., Nutter, D.J., Ward-Thompson, D. and Kirk, J.M.: 2004, ApJ 600, 279.Crutcher, R.M. and Troland, T.H.: 2000, ApJ 537, L139.Crutcher, R.M., Troland, T.H., Lazareff, B. and Kazes, I.: 1996, ApJ 456, 217.Crutcher, R.M., Troland, T.H., Lazareff, B., Paubert G. and Kazes, I.: 1999, ApJ 514, L121.Fischer, O., Henning, Th. and Yorke, H.W.: 1994, A&A 284, 187.Garcia-Barreto, J.A., Burke, B.F., Reid, M.J., Moran, J.M., Haschick, A.D. and Schilizzi, R.T.: 1988,

ApJ 326, 954.Goldreich, P. and Kylafis, N.D.: 1981, ApJ 243, L75.Gonatas, D.P., Engargiola, G.A., Hildebrand, R.H., Platt, S.R., Wu, X.D., Davidson, J.A., Novak, G.,

Aitken, D.K. and Smith, C.: 1994, ApJ 357, 132.Gray, M.D.: 2003, MNRAS 343, L33.Gray, M.D. and Field, D.: 1995, A&A 298, 243.Gray, M.D., Hutawarakorn, B. and Cohen, R.J.: 2003, MNRAS 343, 1067.

36 J. COHEN

Greaves, J.S., Holland, W.S., Friberg, P. and Dent, W.R.F.: 1999, ApJ, 512, L139.Han, J.L., Manchester, R.N., Lyne, A.G. and Qiao, G.J.: 2002, ApJ 570, L17.Hutawarakorn, B., Cohen, R.J. and Brebner, G.C.: 2002, MNRAS 330, 349.Hutawarakorn, B. and Cohen, R.J.L.: 1999, MNRAS 303, 845.Hutawarakorn, B. and Cohen, R.J.: 2003, MNRAS 345, 175.Imai, H., Horiuchi, S., Deguchi, S. and Kameya, O.: 2003, ApJ 595, 285.Lang, C.C., Morris, M. and Echevarria, L.: 1999, ApJ 526, 727.Lai, S.P., Girart, J.M. and Crutcher, R.M.: 2003, ApJ 598, 392.Messinger, D.W., Whittet, D.C.B. and Roberge, W.G.: 1997, ApJ 487, 314.Momose, M., Tamura, M., Kameya, O., Greaves, J.S., Chrysostomou, A., Hough, J.H. and Morino,

J.-I.: 2001, ApJ 555, 855.Plambeck, R.L., Wricht, M.C.H. and Rao, R.: 2003, ApJ 594, 911.Sarma, A.P., Troland, T.H., Crutcher, R.M. and Roberts, D.A.: 2002, ApJ 580, 928.Sarma, A.P., Troland, T.H., Roberts, D.A. and Crutcher, R.M.: 2000, ApJ 533, 271.Snell, R.L., Loren, R.B. and Plambeck, R.L.: 1980, ApJ 239, L17.Uchida, Y. and Shibata, K.: 1985, PASJ 37, 515.Vallee, J.P.: 2003, New Astron Rev 47, 85.Vallee, J.P. and Bastien, P.: 2000, ApJ 530, 806.Vallee, J.P., Greaves, J.S. and Fiege, J.D.: 2003, ApJ 588, 910.Wouterloot, J.G.A. and Habing, H.J.: 1985, A&AS 60, 43.Zweibel, E.G. and McKee, C.F.: 1995, ApJ 439, 779.