a model of polarized oh maser emission in w75n

Mon. Not. R. Astron. Soc. 343, 1067–1080 (2003)

A model of polarized OH maser emission in W75N

M. D. Gray,1� B. Hutawarakorn2 and R. J. Cohen3

1Department of Physics, UMIST, PO Box 88, Manchester M60 1QD2National Electronics and Computer Technology Centre, NSTDA, 73/1 Rama VI Road, Bangkok 10400, Thailand3Jodrell Bank Observatory, University of Manchester, Macclesfield SK11 9DL

Accepted 2003 April 30. Received 2003 January 17; in original form 2002 October 10

ABSTRACTMulti-element Radio-linked Interferometer Network (MERLIN) observations of 18-cm linesof OH from the star-forming region W75N indicate a rotating molecular disc orthogonal to thebipolar molecular outflow, with the maser polarization tracing twisted magnetic field lines. Theobservations are compared with synthetic maser features generated by a polarization-dependentmodel of maser amplification, which uses input physical conditions drawn from a numericalsimulation of a star-forming disc/outflow source. The model helps to explain the complexity ofthe observed magnetic field structure on the basis of maser emission originating from severaldifferent depths within the protostellar disc. Line-ratios, spectral richness and polarization ofground-state (18-cm) masers agree broadly with observations. Although the detailed agreementis crude, the model is able to generate lines that are observed, whilst excluding those that arenot: for example, the main lines and 1720 MHz are generated in the ground state, but not1612 MHz; 4765 MHz is generated, but neither of the other 4.7-GHz lines appear as masers.

Key words: magnetic fields – masers – polarization – stars: formation – ISM: individual:W75N – radio lines: stars.

1 I N T RO D U C T I O N

The nature of OH masers associated with star formation has been thesubject of speculation for nearly 40 years. Early work established theassociation of strong OH masers with compact or ultracompact H II

regions, for example Habing et al. (1974). The prototype H II/OHregion is the source W3(OH), which exhibits all known transitions ofOH maser emission and which is arguably the best studied OH masersource. Proper-motion measurements confirm that the OH masersare expanding away from the compact H II region at speeds of a fewkm s−1 (Bloemhof, Reid & Moran 1992). However, it has becomeapparent that OH masers are also associated with other stages ofstar formation, in particular with the phase of bipolar outflow frommassive young stars. In such cases there is very good evidence thatthe OH masers trace the warm inner regions of a dense moleculardisc orthogonal to the outflow (Brebner et al. 1987). The dynamicsand physical conditions at the centre of a bipolar outflow source arelikely to be considerably different from those in a well-developedexpanding OH/H II region source. The magnetic field is likely to playa crucial role in the dynamics and evolution of bipolar molecularoutflows, in particular in collimating the flow (for example, modelsby Pudritz & Norman 1983; Uchida & Shibata 1985).

OH masers provide a unique way of probing the magnetic fieldstructure on subarcsecond scales. Zeeman splitting of the OH maserlines in the magnetic field provides a direct measure of the field

�E-mail: [email protected]

strength, provided that the splitting exceeds the maser linewidth(Elitzur 1996), while measurements of linear polarization of the OHmaser emission can give three-dimensional information on the mag-netic field direction (for example, Garcıa-Barreto et al. 1988). Multi-element Radio-linked Interferometer Network (MERLIN) measure-ments of OH masers associated with bipolar outflows in the sourcesG35.2-0.74N, W75N and NGC 7538 have established that the OHmasers lie in rotating discs, and that magnetic field vectors have atoroidal component around the disc, as predicted by the twisted fieldmodel by Uchida & Shibata (1985) (Hutawarakorn & Cohen 1999;Hutawarakorn, Cohen & Brebner 2002; Hutawarakorn & Cohen2003). The most detailed information on the magnetic field and theOH maser distribution was obtained for the source W75N, which isthe subject of the present paper.

W75N is a well-studied region of massive star formation in themolecular cloud complex DR21-W75 at an approximate distanceof 2 kpc. It has a well-defined bipolar molecular outflow at posi-tion angle of ∼65◦, which was discovered by Fischer et al. (1985)and which has been mapped at higher angular resolution by Hunteret al. (1994) and Davis, Smith & Moriarty-Schieven (1998). At thecentre of the outflow are OH, H2O and methanol masers (for exam-ple, Hunter et al. 1994; Hutawarakorn et al. 2002, and referencestherein), which are embedded in a submillimetre core of luminosity1.4 × 105 L� and an estimated mass of 1800–2500 M� (Moore,Mountain & Yamashita 1991).

The W75N OH ground-state masers were mapped in full polar-ization with MERLIN by Hutawarakorn et al. (2002). High degreesof linear polarization were detected in many of the OH masers, with

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1068 M. D. Gray, B. Hutawarakorn and R. J. Cohen

polarization angles preferentially aligned with the direction of thebipolar outflow. The observations were interpreted in terms of a ro-tating maser disc orthogonal to the outflow, with twisted magneticfield lines wound up by the disc rotation. More recent VLBA obser-vations (Slysh, Val’tts & Migenes 2001, 2002a; Slysh et al. 2002b)have resolved maser components in W75N down to a scale of 12 ×4 milliarcsec. These observations confirm the existence of stronglylinearly polarized features.

Excited-state OH masers, at 4765 MHz, were detected towardsW75N by Szymczak, Kus & Hrynek (2000). The 4765-MHz maserswere observed to flare. Follow-up observations with MERLIN indi-cate that the 4765-MHz masers are associated with the 1720-MHzground-state masers in the H II(Ba) source (Niezurawska, privatecommunication). This close spatial association between 4765- and1720-MHz masers is also found in W3(OH) (Gray et al. 2001).Excited-state OH masers at 6035 MHz were detected by Baudryet al. (1997), with a possible Zeeman pair indicating a magneticfield of 7.8 mG.

The aim of the present work is to investigate whether a model ofthe generation and amplification of polarized OH maser radiationcoupled with a disc and outflow model of the source can repro-duce the polarization characteristics, spatial distribution, line ratiosand magnetic field structure of the observed MERLIN and VLBAfeatures. Section 2 gives a brief description of the maser model,with the disc and outflow model discussed in Section 3. Section4 contains the results from the maser modelling and our compar-isons of this computational output with the observations. Finally,our conclusions are developed in Section 5.

2 M A S E R M O D E L L I N G

The maser models used in the present work are based on the prop-agation calculations in Gray & Field (1995) and references therein.The maser model employs a semiclassical formalism to describethe processes of maser amplification and saturation in the presenceof a magnetic field of moderate strength, in the sense that energyshifts depend only linearly on the applied magnetic field. In the caseof OH, the presence of a magnetic field lifts the degeneracy of thehyperfine energy levels (quantum number F), producing 2F + 1magnetic hyperfine sublevels (quantum number mF) per hyperfinelevel. The magnitudes of the energy shifts obey the formulae derivedfor the Zeeman effect of hyperfine structure. In the case of the levelsthat form the 1665-MHz transition, the energy shift corresponds toa velocity shift of 0.57 km s−1 mG−1 for two units of mF (for ex-ample, see Bloemhof et al. 1992). If 48 hyperfine levels of OH areused, Zeeman splitting produces 384 magnetic hyperfine sublevels.Einstein A coefficients and the type of collisional rate coefficientsused in the present work, derived from the theory of Dixon & Field(1979), can be split to the magnetic hyperfine level by multiplicationby the appropriate Clebsch–Gordon coefficient as in Gray & Field(1995). As yet, there is no set of rate coefficients from close-coupledscattering calculations that is both complete for 48 hyperfine levelsand calculated at the magnetic hyperfine level of detail. Switchingbetween a hyperfine-resolved set (Offer, Van Hemert & Van Dishoek1994), and a magnetic hyperfine-resolved set is not a two-way pro-cess: for those transitions where magnetic hyperfine-resolved ratecoefficients have been supplied (Offer, private communication) theless detailed set can be recovered by averaging. However, attempt-ing to generate the more detailed set from the less-detailed set, bymultiplying by Clebsch–Gordon coefficients, does not recover themagnetic hyperfine rate coefficients. Therefore, we have not usedthe set of rate coefficients from Offer et al. (1994) in this work.

A set of steady-state master equations was constructed, describingthe flow of population into and out of every magnetic sublevel inthe system via the processes of kinetic collisions, spontaneous lineemission and stimulated emission and absorption of both line andcontinuum radiation. The radiation processes are modified by theeffects of far-infrared (FIR) line overlap using the approximate the-ory of Doel, Gray & Field (1990), with modifications as requiredfor magnetic hyperfine splitting (Gray & Field 1995).

Populations also depend on the degree of saturation of maser ra-diation, and because this radiation is partially coherent in principle,the coefficients relating to the effects of the maser radiation are keptseparate from those that describe the other processes listed aboveduring solution of the master equations. The effects of saturationare treated as in Field & Gray (1988) with the following importantmodification from Gray & Field (1995): the intensity of the radia-tion is replaced by a linear combination of the Stokes parameterswith coefficients that contain the angle between the propagation di-rection of the perfectly beamed maser and the magnetic field. Theprecise form of these coefficients depends on the type of the tran-sition (σ+, σ− or π ) and whether or not the transition is subject tooverlap during propagation (see Section 2.1).

The steady-state master equations are solved using the Sobolev,or large velocity gradient (LVG), approximation. Under LVG, theoptical depth in all directions for all radiatively allowed transitions iscalculated in terms of the local velocity gradient. From the opticaldepths, a set of single-flight photon escape probabilities is calcu-lated. An iterative scheme produces a self-consistent set of energysublevel populations and photon escape probabilities. When the so-lution has been achieved, the population of each magnetic sublevelappears in the form

ρi = ρi0 exp

[∑j

T ij f j (I j , Q j , U j , Vj )

], (1)

where ρi0 is the sublevel population in the absence of saturatingmaser radiation, T i

j is a coefficient which couples the effect of tran-sition j to sublevel i and the sum

∑j is taken over all radiatively

allowed transitions. f j is a linear combination of the Stokes param-eters in transition j and the form of f j depends on whether j is atransition of σ−, σ+ or π type. In the present work, as in Gray& Field (1995), the amplification of any plane-polarized radiationfrom an individual spot is based on an axis that lies in the planecontaining the line of sight and the magnetic field local to the spot.Since this axis is based on the magnetic field and not on the globalaxis system of the source, the Stokes U component is decoupledfrom the propagation. The component of the magnetic field in theplane of the sky is recorded (see Section 3) and it is assumed thatthe polarization plane of a maser is either parallel or perpendicularto this, depending on the transition type, and does not rotate duringpropagation. Gain coefficients are computed, based on differencesof sublevel populations generated from converged solutions of themaster equations. We note that, at the magnetic hyperfine level, allpopulations have the same statistical weight of 1.

Amplification proceeds by solving a set of coupled differentialequations of the Bier–Lambert type, with positive coefficients forall transitions that are inverted. At each step, the OH sublevel pop-ulations are then modified according to the derived coefficients andthe Stokes parameters of the maser radiation with consequent ad-justment to the maser gain-coefficient matrix.

So far, the discussion in this section describes the amplifi-cation and saturation of an individual maser spot, which corre-sponds observationally to a resolved maser feature, usually at VLBI

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Polarized OH maser emission in W75N 1069

resolution. To model a source such as W75N, which supports manysuch features, the single-spot model requires several modificationsand developments. First, the largely free choice of input parameters(magnetic field, number density, kinetic temperature and contin-uum background radiation) are replaced by those applicable to astar-forming region of disc and outflow type, scaled and rotated asfar as possible to match the appearance of W75N (see Section 3).Secondly, the output of the code is arranged to resemble observa-tional data: synthetic spectra and maps are constructed.

2.1 Recent improvements to the model

Several modifications to the codes used in Gray & Field (1995), andnot reported in that work, are discussed below. These improvementshave been made to enable the modelling programs to be used withmore realistic input data.

The first major change involves the pumping radiation and theSobolev approximation. It is no longer possible in the present workto consider a medium that is isotropic, in the sense that every direc-tion yields the same optical depth. This is because, in the presentwork, each line of sight has a different velocity gradient, in general,and a different orientation with respect to the local magnetic field.Angle averaging is introduced over 21 lines of sight radiating outfrom each site of maser emission (see Section 3) in order to gener-ate an averaged photon escape probability and an averaged sourcefunction for each transition. Many transitions are subject to FIR lineoverlap and the degree of this overlap is now dependent on the cho-sen line of sight. The coordinate system is no longer based on themagnetic field, but on a set of fixed axes, so the field angle, θ B isgenerated by dotting the unit vector for each line of sight, l, on tothe magnetic field B. The orientation angle is given by

cos θB = Bx sin θ cos φ + By sin θ sin φ + Bz cos θ

|B| (2)

for polar angle θ , azimuthal angle φ and usual Cartesian magneticfield components with the origin at the maser site. For each line ofsight, overlap-dependent absorption coefficients are generated and,since the model is polarization specific, each coefficient is a 4 ×4 matrix, with each dimension corresponding to the four Stokesparameters. However, because the present work only contains termsdue to absorption and selective absorption of the Stokes parameters,only eight terms are non-zero, and of these only three are distinct.Note that because of FIR line overlap, the nature of overlappingtransitions may be a complex hybrid of the σ± and π types. ASobolev optical depth, τ S is calculated for the velocity gradientalong the line of sight, according to

τS = κi

8π

(∑i

li

∑j

l j∂vi

∂x j

)−1(c

ν

)3

(3)

noting that the optical depth is defined in terms of the absorption (di-agonal) element, κ i , of the coefficient matrix. κ i is the product of theinversion, the Einstein A-value and an overlap-dependent functionof the angle between B and the line of sight. Escape probabilitiesand source functions are then generated, for each line sight, usingthe formulae given in Gray & Field (1995) prior to averaging. Theresults are a scalar escape probability and source function for eachFIR transition, which can be applied to the master equations in thestandard manner.

Secondly, line overlap has been applied to the propagation of in-dividual polarized maser components because these lie very closein frequency, and will overlap in cases where the Zeeman splittingis inadequate to split energy levels by at least a few Doppler full

widths and possibly also due to the effect of velocity gradients inthe medium. Individual hyperfine transitions are treated as neveroverlapping, as in earlier work, which is an excellent approxima-tion except in the special case of megamaser emission, where forexample 1665- and 1667-MHz emission may be blended (for exam-ple, Baan & Haschick 1987). Within a hyperfine transition, overlapof magnetic hyperfine components, which may or may not be ofthe same type, are dealt with in two different ways. The first type ofoverlap is complete, as is the case for all the components of the sametype in a main line and this is treated as in Gray & Field (1995).Treatment of other overlapping magnetic hyperfine components,which have different rest frequencies for a non-zero magnetic field,relies on the hyperfine transitions acting as overlapping groups ofmagnetic hyperfine lines. Any of the magnetic hyperfine lines can,in principle, contribute to radiation in any of the 1001 velocity binsthat span the hyperfine transition. Suppose that the Stokes vectorSHV refers to hyperfine transition H, and velocity bin V . A Stokesmatrix gain coefficient γ

H Vcan then be defined which contains

contributions from the population inversions of all the magnetic hy-perfine transitions which have molecules moving at velocity V . Themolecular contributions can be of any type, depending on the σ±

or π nature of the magnetic hyperfine transition involved and mayalso be negative, contributing absorption if the particular transitionis not inverted. The maser propagation equation for bin V is then

dSH V

dx= γ

H VSH V (4)

and it is solved, coupled to saturation expressions such as equa-tion (1). A significant problem arises in the development of the satu-ration expressions because the saturation coefficients (T i

j in equation1), are specific to a particular transition at the magnetic hyperfinelevel and not to a selected velocity subgroup, such as V . It is thereforenecessary to develop an expression that relates the Stokes vector forthe jth magnetic hyperfine transition, S j , to the Stokes vector for thevelocity subgroup V within a hyperfine transition, SHV . The requiredrelation is

S j,V −Vj = [γH V

]−1γj,V −Vj

SH V (5)

and a derivation of equation (5) is given in the Appendix. The ve-locity subscript V−Vj in equation (5) allows for the effects of avelocity gradient in the medium shifting the response frequency ofthe saturated molecular populations, as propagation advances, andthe original Zeeman splitting.

Further minor improvements are as follows. The number of ve-locity subgroup bins has been increased from 11 to 41 to enablefrequency resolutions similar to those of typical radio astronomycorrelators. Doppler processes can shift the radiation emitted by themolecules assigned to these bins considerably due to both magneticsplittings and velocity gradients in the direction of maser propaga-tion, so 1001 radiation frequency bins are provided per hyperfinetransition, covering the range −25.0 to +25.0 km s−1 relative to thecentral frequency of the transition concerned.

3 T H E M O D E L F O R W 7 5 N

The MERLIN observations of W75N give qualitative evidencefor a rotating OH maser disc, orthogonal to the bipolar outflow(Hutawarakorn et al. 2002). The magnetic field configuration showsa degree of alignment with the outflow, together with a toroidalcomponent around the disc, as predicted in the model by Uchida& Shibata (1985). Combining the theoretical model of OH maseramplification and propagation (see Section 2 above) with the mag-netohydrodynamic disc and outflow model from Uchida & Shibata

C© 2003 RAS, MNRAS 343, 1067–1080


(1985), helps us to understand more concerning the complexity ofthe observed magnetic field structure in W75N and possibly in othersimilar sources.

3.1 Digitization of the model

The model by Uchida & Shibata (1985), which is cylindrically sym-metric, was chosen to represent the physical conditions in the mate-rial surrounding a massive young stellar object. This yielded densi-ties, three velocity components and three magnetic field componentsas functions of radius and axial distance (see figs 3 and 4 of Uchida& Shibata 1985).

The models by Uchida & Shibata (1985) depend on a set of dimen-sionless parameters (η = 2.9 × 10−3, ξ = 1.6, δ = 4.7 × 10−3). Thedimensionless parameters represent, respectively, the ratios squaredof the isothermal speed of sound, the Keplerian speed and the Alfvenspeed to the rotation speed of the model disc at its inner edge.The models may be used, with appropriate scaling, to represent adisc/outflow structure of any reasonable size and mass. One problemwith the Uchida model is that the hydrodynamics used assumes thatthe central object is vastly more massive than the disc; this is almostcertainly not true for W75N. Therefore, the dimensioned numberswhich we apply in order to scale our model can never fully matchthe observations. The three dimensioned numbers which must besupplied in order to convert the various contour heights and vectorlengths to densities, velocities and magnetic field components, arethe stellar mass M∗, the ratio of disc to stellar mass µ, and the innerdisc radius Ri. In the present work, values of M∗ = 40 M�, µ =0.1 and Ri = 1600 au have been used. The mass gives a reasonablevelocity spread in the spectra of the ground-state lines and densities,which are low enough to avoid quenching in these same lines. Themass of the actual protostar in VLA2 (Torrelles et al. 1997) shouldcorrespond to a star of type B0.5 or earlier, or more massive thanapproximately 12 M�. The remaining mass, up to M∗ = 40 M�, istaken to be disc and outflow material inside the inner disc radius Ri.These source-specific parameters are used to generate the followingphysical quantities at the inner disc radius: the Keplerian rotationspeed vK = (GM∗/Ri)1/2, leading to the inner disc rotation speedv0 = vK/ξ 1/2 and the speed of sound vs = (γ η)1/2v0, assuming aratio of specific heats, γ = 7

5 , appropriate for molecular hydrogen.The Alfven speed is then vA = δ1/2v0 and the kinetic temperature,T = mv2

s /(γ k), which is assumed to be constant throughout thedisc. The abundance of OH was also assumed to be a global con-stant equal to 10−5 with respect to H2. The mean molecular mass, mis taken to be that for molecular hydrogen and k is Boltzmann’s con-stant. This set of physical quantities is in turn used to generate gridsof values for the density, and the three components each of the mag-netic field and velocity. Unfortunately, the spacing of the contoursrepresenting the angular (φ) component of the magnetic field wasdifficult to interpret in terms of a physical interval, so this quantityis less well known than the others. Unfortunately it was not possibleto recover the scaling of these contours because the original modeloutput was no longer available (Uchida, private communication).

Each figure from Uchida & Shibata (1985) was digitized to forma grid of 20 × 20 points. For maser positions not exactly coincidentwith a grid node, bilinear interpolation was applied to find inter-mediate values. To allow for maser positions outside the range ofthe original Uchida & Shibata (1985) data, an extrapolation func-tion was added. Test positions for maser spots can be generatedat random or, as in this work, according to a sampling plan. Foreach chosen point, the radial and axial positions are supplied to thegenerating routine and the density, magnetic field and velocity are

Table 1. Physical parameters returned for a typical maser spot po-sition (see also Fig. 3).

Quantity Value Units

Radial velocity, vr −2.44 km s−1

Tangential velocity, vφ −2.73 km s−1

Axial velocity, vz −0.01 km s−1

Radial magnetic field, Br 1.85 mGTangential magnetic field, Bφ −2.00 mGAxial magnetic field, Bz 0.84 mGNumber density of H2 4.95 × 108 cm−3

returned from the interpolation or extrapolation routines as appro-priate. Values returned for a typical maser position are shown inTable 1. This spot has a radial position of 1600 au and is 25 auabove the disc plane.

3.2 Extensions to the basic model

Several additional quantities required for the maser model can bederived from the density, velocity and magnetic fields resulting fromSection 3.1. A velocity gradient tensor can be derived from the threevelocity components. This tensor has six non-zero components froma total of nine because of cylindrical symmetry. The velocity gra-dient tensor is used to supply the gradients needed for the LVGapproximation, and a projected value on to the line of sight (cho-sen to be the x-axis) is used for the velocity gradient, which affectsmaser amplification. Escape probabilities for polarized radiation area function of the angle of the beam to the local magnetic field, sothe LVG approximation requires an average over a number of linesof sight; 32 are used in the present LVG model. The maser pumpingcode allows for a background radiation source from optically thickdust local to the maser zone, which may in general be at a temper-ature different from the kinetic temperature in the disc. We haveadopted a dust temperature value of 45 K derived from observationsby Ward-Thompson & Robson (1991).

Physical conditions are extended to negative coordinate valuesaccording to the following reflection conditions:

n(−z) = n(z) (6)

vr(−z) = vr(z)

vz(−z) = −vz(z)

vφ(−z) = vφ(z) (7)

Br(−z) = −Br(z)

Bz(−z) = Bz(z)

Bφ(−z) = −Bφ(z). (8)

We chose 336 sites for possible maser emission at the followingcoordinates: eight radii (r = 1600, 2000, 2400, 2800, 3200, 3600au), eight angles (φ = 330◦, 0◦, 30◦, 60◦, 90◦, 120◦, 150◦, 180◦) andseven layers (z = +250, +100, +25, 0, −25, −100, −250 au).

Fig. 1 shows the maser sites in the r–φ plane. The physical con-ditions are derived for these points by bilinear interpolation (or forsome outer coordinates, extrapolation) from the Uchida & Shibata(1985) data. The omission of maser sites from a sector of the discamounts to an assumption that masers beam predominantly in apositive radial direction, and that there is considerable absorptionof radiation by the material in the outflow.

In W75N, the orientation of the CO(J = 3–2) outflow observedby Hunter et al. (1994) is ∼66◦ east of north. The OH masers lie

C© 2003 RAS, MNRAS 343, 1067–1080


φ=330

φ=150

φ=120

φ=90

φ=60

φ=30

φ=180φ=0Xo

Yo

24001600800 3200

Figure 1. Sites investigated for possible maser emission on the r–φ planein cylindrical coordinates (r , φ, z). The radius r is given in au.

nearly perpendicular to the axis of the CO outflow and form anarc-shape (that represents the near half of an inclined disc). The el-lipticity of the arc suggests a disc inclined ∼60◦ to the line of sight(Hutawarakorn et al. 2002). In the present paper, we model the discusing a rotation axis that is inclined at 65◦ to the line of sight andoriented 67◦ east of north in projection. Fig. 2a shows the orientationof the disc and outflow model in Cartesian coordinates (x0, y0, z0).The maser sites lie on the x0–y0 plane. The orientation in Fig. 2bwas achieved by rotating the whole model 70◦ counterclockwise inthe x0–y0 plane, and the z-axis was then rotated 293◦ in a counter-clockwise direction about the modified y-axis, resulting in the newcoordinate system (x , y, z). In the new (observer’s) coordinate sys-tem the x-axis points from the modelled object towards the observerand masers are propagated parallel to this axis from each chosen site.The distance of propagation is one of the final free parameters in themodel, so we adopted a set of five possible values: 5 × 109, 1 × 1010,5 × 1010, 1 × 1011 and 5 × 1011 m. The same set of values were usedfor all sites. We note that in the high-density regime of this model,where number densities close to the disc plane typically exceed 5 ×108 cm−3, saturation is achieved for at least one maser line at themajority of sites, even though the propagation distances are typi-cally shorter than those used for approximate outflow conditions in,for example, Gray, Field & Doel (1992).

Finally, synthetic spectra can be constructed by summing themaser output from all sites for a given line-of-sight velocity andsynthetic maps can be constructed by projecting the coordinates ofall emitting spots on to the plane of the sky, the y–z plane in theobserver’s coordinates. We note that in this present work, resultscan only be generated for the LCP, RCP and Stokes parameters I, Qand V .

4 M O D E L R E S U LT S A N D I N T E R P R E TAT I O N

The model allows the �-doublet transitions of the first three rota-tional states to act as masers, that is the 1.6-, 6.0- and the 4.7-GHzgroups. We have obtained the results for the following transitions:F1(3/2) at 1665, 1667, 1612, 1720 MHz; F1(5/2) at 6030, 6035,6017, 6049 MHz; and F2(1/2) at 4751, 4765 and 4660 MHz. Mostof the discussion here relates to the ground-state (1.6-GHz) lines,

O70

(b)

(a)

x

y

z

O293O

x

Oy

Oz

BLUE

BLUE

RED

RED

Figure 2. (a) Model of disc and bipolar outflow in Cartesian coordinates(x0, y0, z0); (b) the W75N-like orientation as a result of the rotation of 290◦in the clockwise direction on the x0–y0 plane and the rotation of 67◦ z0-axis in the clockwise direction about the modified y-axis. Dots indicate thepositions for which maser emission was calculated.

but information concerning the 4.7- and 6.0-GHz transitions appearsin the discussion of the model spectra.

From the raw output of the model, we searched for the maximumvalue of the Stokes I parameter from 336 maser sites in each tran-sition. A cut-off was set at 1 per cent of the peak intensity in eachtransition, below which the output of a maser site, in that transition,would be ignored. The input magnetic field at each maser site (takenfrom the model of Uchida & Shibata 1985) as described in Section 3produces distinct profiles for each of the Stokes parameters I, Q andV . Example spectra of one maser spot are shown in Fig. 3. This spotis, in fact, the same one from which the parameters in Table 1 weredrawn, and is computed at a gain length of 1 × 1010 m. Saturationeffects are clearly evident in the spectrum (see below) and the π , σ+

and σ− components are clearly split. The Stokes Q and V spectrashow that circular polarization is dominant in both σ components,but of opposite handedness, as expected. The π component is lin-early polarized, with Q having the opposite sign to its value in theσ components.

The spot spectrum in Fig. 3 shows a Zeeman triplet, with bothσ components and the weaker central π component being present.The velocity resolution is better by a factor of ∼4 than in MERLIN

C© 2003 RAS, MNRAS 343, 1067–1080


− 2 − 1 0 1 2 3Velocity (km/s)

− 1 x 106

− 500000

0

500000

1 x 106

1.5 x 106

Am

plif

icat

ion

Example Spot Spectrum

Figure 3. The computed Stokes I, Q and V spectra of the 1665-MHz maser from a typical spot in the z = +25 au layer of the 1600-au ring. This spot has theparameters listed in Table 1. The solid line, dotted line and dashed line correspond to the Stokes I, Q and V spectra, respectively. The π component is locatedat the rest frequency and the σ+ and σ− components are split by a magnetic field of strength 2.85 mG. The velocity scale does not include the offset of +9 kms−1 for the systemic velocity of W75N.

observations. The maser propagation was computed under the as-sumption of negligible velocity redistribution (NVR), so each veloc-ity subgroup of the molecular population is saturated independentlyof the rest. The result is a ‘hole-burning’ effect, where the line-centres of each component have decayed due to absorption, whilstamplification continues in the brighter line-wings, which are slowerto evolve. The return to absorption at the line-centre is a competitive-gain effect which could not be observed in a two-level system. Anadditional competitive effect, in the magnetically split case, is com-petition between transitions with different magnetic splittings: inthis case competition with 1667 MHz, which has a smaller splitting,produces the asymmetry, which is evident in the σ components inFig. 3. These NVR competitive effects, though intrinsically inter-esting, are not apparent in the observational data (Hutawarakornet al. 2002), which probably indicates that real maser lineshapesdevelop under conditions closer to complete velocity redistribution.Although a velocity gradient is present along the gain length, it istoo small to have a significant effect on the computed spot spectrum.

We note that complete Zeeman patterns such as those found in ourcalculations are rarely observed in interstellar OH maser sources.The probable reason for this is that real maser sources have largerlocal velocity gradients than are assumed in our model due, forexample, to small-scale turbulence. A velocity shift of ∼2 km s−1 isenough to significantly change the optical depths of pumping lines,a change that can differentiate between σ+ and σ− transitions if thevelocity gradient and magnetic field are not aligned.

Having considered a single maser spot, we now consider the com-posite spectra formed by adding the individual spectra from all thespots that contribute significantly to the model source. In Fig. 4,we show the model (on the left) and observed spectra of the threeOH ground-state lines detected towards W75N. The solid lines inthe graphs denote RHC polarization, the dotted lines, LHC polar-ization. The model spectra were computed at the second-smallestpropagation length, equal to 1 × 1010 m; of the five gain lengths, this

one gave results that resembled the observations most closely. Noemission was observed at 1612 MHz, nor was any maser output gen-erated by the model at this frequency. The model and observationalfigures can be put on the same velocity scale by applying a shift of+9 km s−1, the local standard of rest (LSR) velocity of W75N, tothe model data. The velocity resolution of the model data is 0.05 kms−1, but for the MERLIN observational spectra, the velocity reso-lution was 0.21 km s−1. The velocity extents of the model data are−3.8 to +6.0 km s−1 at 1665 MHz and from −2.7 to +4.9 km s−1

at 1667 MHz. At 1720 MHz, the model spectrum is restricted to thenarrow features that appear in the lowest panel of Fig. 4.

In Fig. 5, we plot the model spectra for all the excited-state tran-sitions which were inverted at any propagation distance. Of thefour transitions shown, detections have been made at 4765, 6030and 6035 MHz. The model masers at 4765 and 6030 MHz are toobright with respect to the ground-state lines compared with theirobservational equivalents. A slightly better overall agreement withobservations could probably be obtained by adopting a propagationlength a little shorter than 1 × 1010 m, since this virtually eliminatesthe 6016-MHz line, already very weak, and significantly reducesthe amplification factors at 4765 and 6030 MHz.

The general effect of changing the propagation distance is plot-ted in Fig. 6: we can see that at very short distances there is no1720-MHz emission. The other ground-state lines become strongerrelative to 6030 MHz, but the 1667-MHz amplification falls with the4765-MHz emission, making it very difficult to disentangle the twocurves. The agreement with observations certainly does not improveat gain lengths longer than 1010 m: the 6016-MHz transition becomesvery strong in the model, whereas it is not observed at all. The model1720-MHz maser also becomes brighter than the ground-state mainlines, which is also not observed. A strong conclusion is that a veryshort propagation distance is required: at much longer gain lengths,the spectra become dominated by 1720- and 6016-MHz masers, incontrast to what is observed. None the less, even at gain lengths

C© 2003 RAS, MNRAS 343, 1067–1080


Figure 4. Composite maser spectra: the ground-state lines with the model on the left and MERLIN observations on the right. The solid and dashed linesindicate RHC and LHC polarization, respectively. The model spectrum does not include the offset of +9 km s−1 for the systemic velocity of W75N.

of only 1010, there are obvious signs of saturation in several lines(1665, 1667, 4765 and 6030 MHz) with competitive effects.

In Fig. 7(a), we show the computed polarization characteristicsof all the significant maser spots at 1665 MHz; Fig. 7(b) showsthe same information for the 1667-MHz masers. The great majorityof 1665-MHz masers have a total polarization very close to 100per cent, and σ components dominate over π components, thoughthere are certainly many π components present. At 1667 MHz,a larger fraction of the maser spots have total polarization markedlyless then 100 per cent. Although the model produces many π

components, which are linearly polarized and restricted to themL-axis in Fig. 7, there are also a significant number of σ com-ponents with high degrees of linear polarization, particularly at1665 MHz.

From spectra, we now turn our attention to maps that show thedistribution of spot intensities and velocities, as projected on tothe plane of the sky. In any map, we expect to see some subset ofthe total number of masers, oriented as in Fig. 2(b). In Fig. 8, weshow the distribution of model maser spots in the plane of the sky at1665 MHz. The Stokes I amplification factor is indicated by thesize of the symbol, and the number by each symbol gives the line-of-sight velocity in km s−1, after 9.0 km s−1 has been added to

the velocity of each point to represent the systemic LSR velocityof W75N. The velocities marked in Fig. 8 are therefore directlycomparable with observational images generated by MERLIN andthe VLBA. Similar information is plotted for 1667 MHz in Fig. 9.

One outstanding feature of Figs 8 and 9 is that the 1665-MHz mapis more completely filled than its counterpart at 1667 MHz. This ten-dency becomes more extreme above and below the disc plane: in theoutermost layers, at ±250 au, the 1665-MHz distribution is still wellfilled, though considerably weaker than in the disc plane, but veryfew 1667-MHz spots contribute at all. This general difference indistribution produces the greater spectral richness of the 1665-MHzspectrum, relative to 1667 MHz, which we see in Fig. 4. However, in-dividual 1667-MHz spots are often brighter than those at 1665 MHz(see Figs 8 and 9). The 1667-MHz spectrum is weaker overall be-cause it is composed of far fewer spots.

The final result from the model that we show is the magneticfield structure, in Fig. 10. The grey-scale shading in Fig. 10 rep-resents the angle of the magnetic field to the line of sight, withthe darkest shade corresponding to a field pointing directly at theobserver. The size of the squares in Fig. 10 represents the mag-nitude of the magnetic field at that spot, whilst the vectors in-dicate the projection of the field direction on to the plane of the

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Figure 5. Composite model maser spectra for the excited-state lines. Thesolid and dashed lines indicate RHC and LHC polarization, respectively.The velocity scale does not include the offset of +9 km s−1 for the systemicvelocity of W75N.

sky. The scale in the bottom right-hand corner of Fig. 10(d) showssymbols, from left to right, representing fields of 1, 2, 3, 4 and5 mG. We note that the field magnitudes generated by the modelare somewhat weaker than those in the observations. This is a con-sequence of the overall mass of the model being set slightly toolow (see the problems related to fixing the model parameters inSection 3).

4.1 Comparisons with observations

In this section, we further compare various aspects of the modeloutput with observational data obtained from MERLIN. We notethat the model we have used associates the OH masers predomi-nantly with the disc; this may not be true of all OH-maser sources instar-forming regions. However, it may be more typical than was pre-viously believed, since very recent analysis of data from W3(OH)(Gray et al. 2003) suggests that even this, apparently disordered,source is dominated by a north to south rotation. None the less,W75N appears to be at an earlier stage of evolution than W3(OH):W75N has a less developed H II region, and consequently thereis less random and outward motion in the disc. Masers in the in-ner disc of W75N can operate at much higher densities and farshorter propagation distances than in W3(OH), so many of theconclusions drawn from masers in that source (for example, Gray2001) do not apply here. In particular, the idea that the masersform in an interface zone between the H II region and its precur-sor shock, with large amounts of far-infrared radiation to drive aradiative pumping scheme for the masers, may not be applicableto W75N.

The spatial extent of the model-maser distribution can be gaugedfrom Figs 8 and 9. We note that these diagrams show only maserspots in the disc plane, but the higher and lower layers generallyshow a smaller total extent of emission. At 1665 MHz, the modelmasers span a region that covers 5800 au north to south, and 3100 aueast to west. At the assumed distance of W75N (2 kpc) this cor-responds to 1.6 arcsec in RA by 2.9 arcsec in declination. Thecorresponding region containing 1665-MHz masers in W75N is(Hutawarakorn et al. 2002) 2.2 arcsec in RA, and 2.1 arcsec in dec-lination. These distributions are in reasonable agreement, thoughthe number of maser spots in the model is considerably larger thanthe number observed, a consequence of the regular model grid. It isnot surprising that the model and observational scales are roughlycomparable, since the Uchida & Shibata (1985) model was scaledto fit the observed parameters of W75N, but if the model were badlywrong, inability of the model masers to grow could have severelyrestricted the region spanned by the model masers. We find a simi-lar reasonable agreement at 1667 MHz, where the number of maserfeatures is smaller than at 1665 MHz in both the model and theobservations.

The observations show that in W75N the 1665-MHz lines are thebrightest ground-state lines, followed by the 1667- and 1720-MHzlines, with no 1612-MHz maser emission observed. This sequenceis reproduced well by the model (see Fig. 4). For the excited-statelines, the agreement is less good, with 4765 and 6030 MHz be-ing too bright in the model. Of course, the relative intensities ofthe ground- and excited-state transitions depend not only on theamplification factors but also on how bright the background seedradiation is at 1.6 GHz, compared with 4.7 and 6.0 GHz. It isnot clear from the observations whether the seed radiation hasa thermal or non-thermal spectrum. Assuming a bremsstrahlungbackground, making the amplification factors roughly compara-ble at the ground- and excited-state frequencies, the best fit to theobserved maser line ratios is probably obtained at a gain lengtha little shorter than 1010 m (see Fig. 6). The very short gainlengths required means that velocity-gradient effects during prop-agation are negligible in this model (compare with Field, Gray &de St Paer 1994).

The conditions encountered at maser sites in the present work aretypically denser and have weaker radiation fields than those treatedpreviously (for example, Gray 2001; Gray et al. 1992). Both of

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Figure 6. Variation of the velocity-integrated amplification factor with propagation distance for all the maser transitions with significant amplification.

Figure 7. Polarization characteristics of (a) model 1665-MHz masers, and (b) model 1667-MHz masers. Masers which are 100 per cent polarized are foundon the semicircular arc in each diagram.

these factors tend to make the collisional element of the pump moreimportant and, consequently, the solutions become more heavilydependent on the rate coefficients employed. It is intended to testthe results generated here against solutions that use the far better rate

coefficients generated by Offer et al. (1994), which have recentlybecome available in a magnetic-hyperfine-specific form.

The velocity widths of the ground-state spectra from the modelcompare quite well with their observational counterparts at 1667 and

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Figure 8. The distribution of model maser spots in the disc plane at 1665 MHz. Stokes I amplification factor is indicated by the size of the circles; numbersindicate the line-of-sight velocity in km s−1.

1720 MHz; at 1665 MHz the observational spectrum is broader bya factor of 1.7. In general, the model spectra are narrower, reflectingthe problems, discussed in Section 3, of assigning suitable massesfor the ‘star’ and disc. As most of the spectral width depends on therotation curve of the source (the rest results from magnetic splitting)a better agreement with observations could have been obtained byincreasing the masses in the model. The model is, however, success-ful in obtaining a spectral width for 1667 MHz, which is smallerthan the width at 1665 MHz. The model also correctly places theweak 1720-MHz emission on the red side of the spectrum. Therelative spectral richness of the ground-state lines also follows thecorrect sequence of the greatest number of features at 1665 MHz,fewer at 1667 MHz and just two features at 1720 MHz. The abso-lute spectral richness of the model is, however, much greater be-cause of the large number of regularly gridded points used (seeFig. 1).

Any model maser feature that is elliptically polarized must be ofσ -type, since a π transition can only be linearly polarized. The vastmajority of the spots modelled in the present work are therefore ofσ -character (see Fig. 7). For a σ -feature, the projected magneticfield direction on the plane of the sky is at 90◦ to the direction of thelinear polarization vector. To contrast the model results with obser-vations, we compare our Fig. 7 with figs 6 and 7 of Hutawarakornet al. (2002), in which the data are plotted in exactly the same for-mat. For 1665 MHz (our Fig. 7a and fig. 6 of Hutawarakorn et al.)we find a pattern that is reasonably similar to the observations: mostof the spots are close to 100 per cent polarized, and there is a distinctconcentration to either modest, or large degrees of linear polariza-

tion, this tendency being more pronounced in the observations thanin the model. The model has a ‘tail’ of unsaturated π componentsstretching back along the mL-axis of Fig. 7(a); the observationsonly show one good candidate for a π component: spot 4 in fig. 6of Hutawarakorn et al, with two other possible π components. At1667 MHz, the polarization distribution of the model again bearsa reasonable resemblance to the observations, with the model databeing somewhat more extreme in producing 100 per cent-polarizedfeatures. In agreement with observations, modelled spots at1667 MHz, with low degrees of circular polarization, also tend tohave weak linear polarization, so there are many spots with the ap-proximate range 40–80 per cent of total polarization lying close tothe x-axis. Most of the 100 per cent-polarized masers are predomi-nantly circularly polarized. There are also only a few π componentsin the model data at 1667 MHz.

We now consider the distribution of maser spots on the sky, com-paring our model maps Fig. 8 (1665 MHz), and Fig. 9 (1667 MHz)with the observational maps, figs 2 and 11 of Hutawarakorn et al.(2002), noting that our maps are plotted for the maser spots inthe disc plane only. Velocity information is contained in fig. 2 ofHutawarakorn et al., and the velocity distribution is similar to themodel: the bluest velocities appear for masers in the north of themap, whilst the reddest velocities appear near the centre and inthe southeast. The model does not reproduce the very blue veloc-ities found in the south-central part of the observational map, andindeed it is difficult to see how these velocities could be generatedby a pure rotational flow. The outlying spots at 1667 MHz alsohave no counterparts in the model data. There are really too few

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7.0

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8.2

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11.8

12.011.8

11.9

11.1

11.9

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12.0

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11.2

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11.3

Figure 9. The distribution of model maser spots in the disc plane at 1667 MHz. Stokes I amplification factor is indicated by the size of the circles; numbersindicate the line-of-sight velocity in km s−1.

observational spots to make a detailed comparison of the distribu-tion of intensities, but the model is certainly capable of producingthe observed mixture of bright and weak spots in close association.

Finally, we compare the magnetic field structure of the model(Fig. 10) with the magnetic field pattern derived from observations(Fig. 11). At 1665 MHz only, there are three features that are reason-able candidates to be emitting in π transitions and for these featureswe have adopted a magnetic field component in the plane of thesky parallel to the observed plane polarization vectors. All othermagnetic field components in Fig. 11 are assumed to come fromσ components, with the field direction on the sky plotted at 90◦ tothe observed orientation of the linear polarization on the sky. Wenote that the field magnitudes generated by the model are somewhatweaker than those in the observations. This is a consequence of theoverall mass of the model being set slightly too low (see problemsrelated to fixing the model parameters in Section 3).

One of the features of the observations is that spots which areclosely associated spatially can have very different planes of linearpolarization; this conclusion holds regardless of whether we assumeany of the observed 1665-MHz spots are π components. It can beseen from Fig. 10 that this aspect of the observed maser distribu-tion can be explained by assuming that what we see is the apparentsuperposition, at MERLIN resolution, of spots with very differentprojected field angles, which come from different depths in the disc.Fig. 10 is useful in demonstrating this superposition: assuming thatwe can see several layers within the disc, we could see nearby fea-tures with sky magnetic field components different by ∼90◦ nearthe middle of the map by going from Fig. 10(c) (25 au above the

disc plane) to Fig. 10(e) (25 au below the plane). Observations in-dicate that the line-of-sight component of the magnetic field tendsto change sign as we move from the north of the map to the south.This general trend is reproduced for most of the model disc layersin Fig. 10.

The model is based on the masers lying in a rotating disc. Thedistribution of the masers in the plane of the sky which results (seeFigs 8–10) appears as an extended arc, ∼1000 au (0.5 arcsec) wide.Observations also show that the masers are placed in an arc, but thisis far less well filled than the model maps, perhaps indicating a lessuniform distribution of masing gas than in the model. However, theobserved distribution of masers, in both hands of polarization andboth ground-state main lines, is consistent with an arc of similar sizeto that in the model. Overall, this model helps to reconcile the three-dimensional magnetic field proposed by Uchida & Shibata (1985)and the observed magnetic field in W75N, as deduced from maserpolarization.

5 C O N C L U S I O N S

The model of the maser emission can explain several important fea-tures of the maser emission from W75N. The model successfullyreproduces the relative line strengths of the ground-state lines, theirrelative spectral richness, and, in particular, it reproduces the weak1720-MHz features in the correct part of the velocity range. Thevelocity extents of these lines are also reproduced moderately well,being slightly narrower than the observations. For most of the sig-nificant excited-state lines, however, the observational results are

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(h)(g)

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Figure 10. The simulation results for the magnetic field. Plots (a)–(g) are for 1665-MHz model maser spots, with layers, relative to the disc plane, at heightsof 250, 100, 25, 0, −25, −100 and −250 au. Plot (h) is for 1667 MHz in the disc plane. The grey-scale bar, shown in each plot, represents the angle of themagnetic field to the line of sight (los) with the scale running from zero (black), indicating a field pointing towards us, to 180◦ (white) where the field pointsdirectly away. The size of the squares represents the magnetic field strength (see the main text).

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1720RCP

1667LEP1667REP1667LCP1667RCP

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Figure 11. The magnetic field of the W75N OH maser region as de-rived from observed planes of polarization (Hutawarakorn et al. 2002) at1665 MHz (upper), and at 1667 and 1720 MHz (lower). The size of thesquares indicates the peak flux density of the masers, while the vectors in-dicate the projected magnetic field direction, with the size of the vectorsbeing proportional to the degree of linear polarization (bars at the bottomleft corresponding to 100 per cent).

not reproduced, the model spectrum being far too rich and also toointense at 4765 and 6030 MHz. The failure to match the observedmaser strengths in the excited states may be due in part to the setof rate coefficients used, but is probably more to do with a slightmismatch of physical conditions: only one model has been run, andone with slightly different parameters could almost certainly fit theobservations better. The ability to reproduce observational resultsis gain-length-dependent, and we have to conclude that the gainlengths of masers in W75N are very short, less than approximately1010 m. Such propagation distances for masers are markedly shorter

than those usually assumed for other sources, such as W3(OH),but nevertheless result in significant saturation of several transitionsbecause of the high density in the model disc.

Polarization parameters of the observations are also reproducedreasonably well by the model. Degrees of polarization close to 100per cent are more common at 1665 MHz than at 1667 MHz, andin addition the model reproduces the tendency to produce far fewermasers with close to 100 per cent linear polarization at 1667 MHz.

One confusing property of the observed linear polarization struc-ture, and associated projected magnetic field orientation is the man-ner in which the magnetic field appears to rotate in moving clockwisearound the observed maser arc. In the west of the object, the fieldappears mainly toroidal, but moving round to the south, it appearsto develop a strong poloidal component. In terms of the model, thiscan be explained easily if we adopt the view that we can see patchesof maser emission that originate from significantly different depthswithin the disc. It is quite possible, for example, to see two featuresthat appear close in velocity and close together on the sky to haveprojected magnetic field vectors that cross almost at right angles ifthe two features come from different planes.

AC K N OW L E D G M E N T S

We thank the director and staff of MERLIN, which is operated byJodrell Bank Observatory, University of Manchester, on behalf ofthe Particle Physics and Astronomy Research Council (PPARC) ofthe United Kingdom. MDG acknowledges the award of a UniversityResearch Fellowship by the Royal Society. BH acknowledges theaward of a studentship from NECTEC, Ministry of Science, Tech-nology and Environment, Thailand. Thanks also to Sandra Etoka ofJodrell Bank Observatory for her help in producing the grey-scalefigures.

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A P P E N D I X : D E R I VAT I O N O F T H E V E L O C I T YS U B G RO U P/T R A N S I T I O N T R A N S F O R M AT I O N

In the hyperfine transition representation, the Stokes vector, SHV ,may be expressed as the sum over all magnetic hyperfine transitionsand all velocity bins within these transitions which can contributeradiation at velocity subgroup V . We can therefore write

SH V =NH∑j=1

Nv∑v=1

S j,v, (A1)

where NH is the number of magnetic transitions within hyperfinetransition H, and Nv is the number of velocity bins within eachmagnetic transition which can contribute radiation at V . A similarexpression can be formed to relate the gain-coefficient matrices inthe two representations. An important simplification, used in the

model, is that the bin-widths used in the two representations are thesame. Therefore, for any given magnetic transition, there is a uniquevelocity bin which can contribute at V , and for the jth transition, thisbin has velocity vj = V − V j, where Vj is the compensating shiftwhich takes into account the effects of energy level splitting by themagnetic field and velocity gradients. The second sum in equation(A1) can now be removed and the revised equation is

SH V =NH∑j=1

S j,V −Vj (A2)

and, as before, a similar expression applies for the gain coefficientmatrix γ

H V. Now suppose that equation (5) of the main text is true:

by pre-multiplying by γH V

this equation can be rewritten as

[γH V

]S j,V −Vj = [γj,V −Vj

]SH V . (A3)

It is now possible to sum equation (A3) over the magnetic transitions,j, such that from equation (A2) we see that we can replace thesummed Stokes vector and gain-coefficient matrix by their hyperfine(subscript HV) equivalents, leaving

SH V = [γH V

]−1γH V

SH V (A4)

so equations (A3) and (5) of the main text are correct.

This paper has been typeset from a TEX/LATEX file prepared by the author.

C© 2003 RAS, MNRAS 343, 1067–1080

a model of polarized oh maser emission in w75n

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