A&A 371, 1012-1017 (2001)
DOI: 10.1051/0004-6361:20010451

Magnetic field structure in the outer OH maser envelope
of VXSagittarii

M. Szymczak1 - R. J. Cohen2 - A. M. S. Richards2


1 - Torun Centre for Astronomy, Nicolaus Copernicus University, ul. Gagarina 11, 87100 Torun, Poland
2 - Jodrell Bank Observatory, University of Manchester, Macclesfield, Cheshire, SK11 9DL, UK

Received 29 January 2001 / Accepted 15 March 2001

Abstract
The OH 1612MHz maser transition from the supergiant star VXSgr has been imaged in all Stokes parameters using MERLIN. Numerous elliptically polarised components are distributed in a roughly symmetric envelope of a size similar to that measured in total maser intensity. The polarisation vectors are generally tangential to the circumstellar envelope, indicating a globally ordered magnetic field at the distance of about 1400au from the supergiant. It is suggested that a predominance of projected radial magnetic lines and a displacement between the red- and blue-shifted parts of the envelope can be explained with a dipole field tilted at 20-30$^{\circ}$ to the line of sight.

Key words: masers - polarisation - stars: magnetic fields - stars: circumstellar matter - stars: supergiants -
stars: individual: VXSgr


1 Introduction

Circular polarisation is a distinctive characteristic of OH masers around late-type supergiant stars. Observations at high spectral resolution revealed several polarised features with line widths as small as 0.1kms-1 in the OH 1612MHz spectra of four supergiants including VXSgr (Cohen et al. 1987). The presence of circular polarisation was itself evidence for Zeeman splitting (Deguchi & Watson 1986) and, despite difficulties in identifying classical Zeeman patterns, provided a direct estimate of the strength and direction of the magnetic field. High angular resolution data enabled more reliable identification of Zeeman pairs in two supergiants; IRC+10420 (Kemball1992) and VXSgr (Szymczak & Cohen1997). In the latter object, the magnetic field strength was estimated to be $\sim$1mG at a distance of about 1400au from the star, directed towards the observer (Szymczak & Cohen1997; Trigilio et al.1998). The spatial distribution of the 1612MHz emission in VXSgr observed with the VLA (Zell & Fix1996) and MERLIN (Szymczak & Cohen1997) indicates a remarkable segregation between components of opposite circular polarisation, suggesting a globally ordered magnetic field.

It has been suggested that the axi-symmetric geometry of the 1612MHz maser envelope of VXSgr, reported first by Chapman & Cohen (1986), is a characteristic of radiation driven mass loss in circumstances where the effect of the circumstellar magnetic field cannot be neglected (Szymczak & Cohen1997). There is as yet no clear mechanism to explain the impact of the magnetic field on the stellar wind in the outer parts of circumstellar envelopes. The effect of the magnetic field on charged dust particles was postulated by Chapman & Cohen (1986). On the other hand, the presence of free electrons in circumstellar material (Szymczak et al.1998) would freeze the magnetic field into the outflowing gas. The magnetic field also affects the OH maser properties through the magnetic beaming phenomenon described by Gray & Field (1995).

Linearly polarised OH emission from circumstellar envelopes has rarely been studied (Cohen1989). Weak and narrow linearly polarised OH mainline masers (at 1665 and 1667MHz) are seen at the most blue-shifted velocities in Mira-type stars (Szymczak et al.1998). There are no published reports of searches for linear polarisation of OH emission towards VXSgr. However, to understand the polarisation mechanisms of OH masers and the possible role of the magnetic field in the dynamics of the circumstellar envelope, full polarisation data at high angular resolution are needed. In this paper we report the first results of the polarisation structure of VXSgr at 1612MHz observed with MERLIN in full polarisation mode and consider the morphology of inferred circumstellar magnetic field in the outer OH maser envelope.

2 Observations and data reduction

The OH 1612MHz maser transition was observed on 1999 April 24 using all seven telescopes of MERLIN, giving a minimum fringe spacing of $\sim$0.15arcsec. A spectral bandwidth of 250kHz was used, divided into 256 channels. This gave a velocity coverage of 46 km s-1 and a channel spacing of 0.18 km s-1. In order to observe the whole velocity range of emission from VXSgr, two bands centred on LSR velocities ( $V_{\rm LSR}$) of -10 and +20 km s-1 were observed alternately, switching between them every 5 min. The target was tracked for 6h. The left and right circularly polarised signals (LHC, RHC) from each pair of telescopes were correlated in full cross-polarisation mode, so that all Stokes parameters were obtained.

The initial data editing and correcting for gain-elevation effects was carried out using local programs for MERLIN data reduction. All further data processing were performed within the AIPS package in several steps (see Szymczak et al.1998 for details) taking special care to calibrate the polarisation. The flux scale was derived using 3C286 (Baars et al.1977) and the strong continuum source 3C84 was used to calibrate the bandpass. The flux of 3C84 was found to be $25.3\pm1.4$ Jy, giving a total flux scale error of $\sim$7%. The point continuum source 2134+004 was tracked for 20min at three hour angles to correct for parallactic angle rotation and instrumental feed leakage, and 3C286 was used to calibrate the polarisation angle, with a $\sigma_{\rm rms}<2^{\circ}$. These corrections were then applied to the VX Sgr data.

For both parts of the 1612MHz spectrum, the brightest channels were examined to find channels containing point-like emission, positionally coincident in LHC and RHC polarisations. Suitable channels were identified at -13.8 and 24.9kms-1 in the blue- and red-shifted data sets, respectively. (The terms blue-shifted and red-shifted are used to describe velocities relative to the stellar velocity of 5.5kms-1.) Phase only self-calibration was then carried out on these two reference channels using point models, and the solutions applied to all spectral channels of the VX Sgr data. Map cubes in all Stokes parameters were made and cleaned with 1000 cycles per channel using a 0.4arcsec circular Gaussian restoring beam. The rms noise level in a line-free channel of I Stokes was $\sim$15mJybeam-1, corresponding to a brightness temperature of 4104K. The positions of the maser components were measured with a typical accuracy of 0.05arcsec by fitting two-dimensional Gaussian components. The emission at 3.6kms-1 appeared in both the blue- and red-shifted data sets and was used to align the data cubes spatially. The measured fluxes of this component in both data cubes agree to within the flux scale errors.

3 Results


  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{MS1073f1.eps}\end{figure} Figure 1: MERLIN spectra of the polarisation of OH 1612MHz maser emission from VXSgr. The plots show a) Stokes I (total flux density), b) Stokes V (circularly polarised flux density), c) Stokes (Q2+U2)1/2 (linearly polarised flux density), d) $m_{\rm c}$ (percentage circular polarisation) and e) $m_{\rm l}$ (percentage linear polarisation)
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The spectra for individual Stokes parameters and the percentages of polarisation are shown in Fig. 1. The fractions of circular and linear polarisation are defined as $m_{\rm c} = V/I$ and $m_{\rm l} = \sqrt{Q^2+U^2}/I$, respectively. At outermost velocities the linearly polarised intensity ( $\sqrt {Q^2+U^2}$) is about one order of magnitude weaker than the total intensity. There are only a few linearly polarised features which have flux density greater than 2Jy. Nevertheless, the polarised intensity $\sqrt {Q^2+U^2}$ profile, like the Stokes V profile, reveals several narrow features. The percentage of linear polarisation is usually lower than 10% at the outermost velocities and slightly increases towards the stellar velocity exceeding 20% for a few features.

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{MS1073f2.eps}\end{figure} Figure 2: Relative positions of the OH 1612MHz linearly polarised maser components of VXSgr. The bars represent the plane of the electric field vector and have lengths proportional to the peak brightness of linearly polarised components, where $0.1\,{\rm arcsec} \equiv 0.41$Jybeam-1. The circles and squares represent the blue- and red-shifted components, respectively. The size of each symbol is proportional to the logarithm of the linearly polarised intensity. The filled circle and error bars at the diagram origin denote the inferred stellar position (see text) and its uncertainty, respectively
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  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{MS1073f3.eps}\end{figure} Figure 3: Selected linear polarisation ( $\sqrt {Q^2+U^2}$) maps of the 1612MHz maser emission of VXSgr. Contour levels are (-1, 1, 2, 4, 6)${\times }$100mJybeam-1. Bars show the orientations of the electric vectors and have lengths proportional to the linearly polarised intensities, where $0.1\,{\rm arcsec}\equiv 0.11$Jy. The central LSR velocity (kms-1) of each map is indicated inthe upper left-hand corner. The number of contiguous channels averaged is given in the upper right-hand corner
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The relative positions of linearly polarised maser components are plotted in Fig. 2. The orientation of the linear polarisation vectors defines the plane of the electric field vectors and their lengths are proportional to the linearly polarised intensity $\sqrt {Q^2+U^2}$. The origin of this map is the position of central star inferred from a symmetrical shell model applied to the present Stokes I data set as described in Szymczak & Cohen (1997). This map shows a clearly defined broad ring of emission which follows the envelope of roughly symmetric shape seen in the Stokes I parameter. The polarisation vectors are generally tangential to the circumstellar envelope, that is, perpendicular to the radial direction from the star. In addition to the strong components plotted in Fig. 2 there are also fainter regions of linearly polarised emission. Selected averaged channel maps of Stokes $\sqrt {Q^2+U^2}$ are shown in Fig. 3. The orientations of the polarisation vectors in the regions of weak and extended emission commonly follow the trend seen in Fig. 2. However in some channel maps the orientation of the polarisation vectors is clearly structured but at orientations very different from tangential (panels at -11.36 and -10kms-1 in Fig. 3). This could be due to a projection effect or complex structures in the circumstellar magnetic field.

To check more quantitatively the orientation of polarisation vectors in the envelope, we defined the deviation of the polarisation angle from the radial direction, relatively to the stellar position, as PA$_{\rm c}-$PA$_{\rm p}$, where PA$_{\rm c}$ is the position angle of a maser component around the plane of the sky and PA$_{\rm p}$ is the position angle of the polarisation vector. Figures 4 and 5 show this deviation as a function of PA$_{\rm c}$ and velocity, respectively. 104 out of 159 components (65%) have polarisation vectors orthogonal, within $\pm$30$^{\circ}$, to the radial direction, whereas only 17% of components are parallel within $\pm$30$^{\circ}$. This trend is even stronger when the brightness of linearly polarised components is considered: components with PA$_{\rm p}$ "parallel'' to PA$_{\rm c}$ are usually weaker than 0.4Jybeam-1 (Fig. 4).

A significant departure from this trend is observed in the range of PA$_{\rm c}$ from 30 to 100$^{\circ}$. 12 out of 30 components with linearly polarised brightness exceeding 0.8Jybeam-1 are not orthogonal to the radial direction (within $\pm$30$^{\circ}$). All these 12 components are seen at $V_{\rm LSR}>$23.8kms-1 (Figs. 3 and 5) and possibly mark a site of complex magnetic field structure. The PA$_{\rm c}-$PA$_{\rm p}$ of red-shifted components, in contrast to that of blue-shifted ones, exhibit a weak systematic change with the radial velocity (Fig. 5). There are 7 red-shifted components with fractional linear polarisation higher than 50%; all of them are located in the north-eastern cluster of the envelope. Neglecting these strongly polarised components, possibly associated with a local field structure or caused by a projection effect, we still notice that the mean angle PA$_{\rm c}-$PA$_{\rm p}$ is 90$^{\circ}$ for $V_{\rm LSR}<20$kms-1, but about 120$^{\circ}$ for $V_{\rm LSR}>20$kms-1.

Figure 6 shows the percentage of linear polarisation versus the percentage of circular polarisation for all 159 components with the peak brightness higher than 150mJybeam-1 in Stokes $\sqrt {Q^2+U^2}$ and V. The percentage of polarisation is shown as zero if the linearly or circularly polarised flux densities are less than the noise level. There are only 19 components (12%) with $m_{\rm l}>30\%$ and most of them are red-shifted. Strong circular polarisation ( $\vert m_{\rm c}\vert>65\%$) is visible only for blue-shifted components. Figure 6 clearly illustrates that all components are elliptically polarised and only 5 components are 100% polarised. There are 8 components with $\vert m_{\rm c}\vert<35\%$, but with high linear polarisation ( $m_{\rm l}>50\%$). 7 out of 8 components have -20$^{\circ}<$ PA$_{\rm p}<$ 20$^{\circ}$ and are located in the northern side of the envelope. If these are interpreted as ${\pi}$ components then the orientation of the magnetic field agrees very well with an overall picture of radial field geometry. We notice, however, that in the same region and range of PA$_{\rm p}$ there are many more components with low $m_{\rm l}$ which hardly can be interpreted as ${\pi}$ components.

  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{MS1073f4.eps}\end{figure} Figure 4: Deviation of polarisation angle from the radial direction (PA$_{\rm c}-$PA$_{\rm p}$) versus the position angle of maser component around the plane of the sky (PA$_{\rm c}$). The size of each circle is proportional to the logarithm of the brightness oflinearly polarised components (the largest circle corresponds to 4.13Jybeam-1)
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  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{MS1073f5.eps}\end{figure} Figure 5: Deviation of polarisation angle from the radial direction (PA$_{\rm c}-$PA$_{\rm p}$) versus the radial velocity. The size of each circle is proportional to the fractional linear polarisation (the largest circle means 88%)
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  \begin{figure}
\par\includegraphics[width=8.8cm,clip]{MS1073f6.eps}\end{figure} Figure 6: Percentage of linear versus circular polarisation of 1612MHz OH maser spots in VXSgr. Circles and crosses indicate the blue-shifted and red-shifted emission, respectively. Completely polarised components lie on the dashed line
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To determine properly the magnetic field direction from the orientations of polarisation vectors in a given portion of the envelope one needs to know whether the linearly polarised components are $\sigma$ or ${\pi}$ components of the Zeeman pattern. If the magnetic field is perpendicular to the line of sight the $\sigma$ components are linearly polarised perpendicular to the field, whereas the ${\pi}$ components are linearly polarised parallel to the field. We searched for groups of maser components of circular and linear polarisation that coincide in the sky to within measurement accuracy. In some places, likely Zeeman pairs with LHC and RHC components but without linearly polarised components were found. More details on the pairs of $\sigma$ components of opposite circular polarisation and their temporal behaviour will appear in a separate paper.

4 Discussion

The major result from MERLIN observations presented in this paper is that the morphology of the polarisation vectors of the elliptically polarised components shows a large scale order. The OH 1612MHz maser emission from VXSgr possibly traces the spatial orientation of the magnetic field in the outer parts of the circumstellar envelope. However, there is an ambiguity about the inferred field direction, depending on whether the elliptical polarisation represents ${\pi}$ or $\sigma$ components. We assume that most elliptically polarised components in our data are $\sigma$ components. This assumption appears to be consistent with observations of OH 1665MHz masers in star forming regions. Garcia-Barreto et al.(1988) found no features in W3(OH) which might be interpreted as ${\pi}$ components. Observations of G35.2-0.74N have shown that all Zeeman pairs identified contain $\sigma$ components only (Hutawarakorn & Cohen1999). Theoretical studies of polarised maser emission predict a dominance of $\sigma$ components in a wide range of values of the ratio of the Zeeman splitting to the Doppler line width ($x_{\rm B}$) and the degree of maser saturation (Elitzur1996). Suppression of ${\pi}$ components is expected especially for $x_{\rm B}>0.1$ and saturated emission, conditions usually fulfilled in OH 1612 maser regions. It is therefore plausible that in VXSgr we generally observed $\sigma$ components, in which case the projected circumstellar magnetic field has a predominantly radial geometry.

The plane of elliptical polarisation could change due to internal Faraday rotation and the apparent polarisation vectors would not then be orthogonal to the projected direction of the magnetic field. The OH 1612MHz envelope of VXSgr is asymmetric and moreover the emission at the extreme red- and blue-shifted velocities does not coincide in the plane of the sky (Chapman & Cohen1986; Szymczak & Cohen1997). Therefore, the red-shifted linearly polarised emission possibly propagates along the paths where the electron density is too low to strongly rotate the plane of linear polarisation. Indeed, PA$_{\rm c}$ for the red-shifted emission from VXSgr differs by 30-50$^{\circ}$ from the PA$_{\rm c}$ of the rest of the emission (Fig. 5). If this is interpreted as Faraday rotation then for a magnetic field of $1.1\pm 0.4$mG inferred from a Zeeman splitting (Szymczak & Cohen1997) and for the assumed maser gain length of 1016cm the required electron density is 24cm-3. We note, however, that the above value of magnetic field was evaluated with implicit assumption that $x_{\rm B}>1$. Following Elitzur's (1996) theory for $x_{\rm B}<1$ the magnetic field strength re-evaluated from that Zeeman pair is only 0.3mG for angle 45$^{\circ}$ from the direction of the magnetic field. Nevertheless, for the model of the 1612MHz maser (Elitzur et al.1976) with a gas density of 106cm-3 and the kinetic temperature 100K, a magnetic field of 0.3mG provides a magnetic pressure comparable to that caused by thermal gas motions, so that it may has non-negligible consequences on the outflow dynamics.

The orientation of the polarisation vectors might be affected by external Faraday rotation in the interstellar medium. VX Sgr is at $l=8\hbox{$.\!\!^\circ$ }34$ and $b=-1\hbox{$.\!\!^\circ$ }00$, close to the direction of the Galactic centre. The local strength of the longitudinal magnetic field is about 1.3 $\mu$G (Rand & Kulkarni1989) and the average number density of the interstellar medium is 0.5cm-3with a fractional ionisation of 10-4 (Garcia-Barreto et al. 1988). For a distance of 1.7kpc to VX Sgr, this would only rotate the polarisation vectors by about 0 $.\!\!^\circ$2. It is therefore unlikely that the observed polarisation vectors are strongly influenced by the interstellar medium. An electron density higher than 0.05cm-3, implying a fractional ionisation two orders of magnitude higher, would be required to significantly change the plane of the polarisation vectors in the manner observed towards more distant pulsars near the Galactic centre (Clegg et al.1992).

The average distance of the 1612MHz masers from VXSgr is about 1400 au. The OH mainline and H2O masers occur much closer to the star at distances of 200-400 au (Chapman & Cohen1986; Bowers et al.1993). The SiO 43GHz masers are located about 30au from the star (Greenhill et al.1995). Zeeman splitting observed in OH mainline masers (Chapman & Cohen 1986) implies the magnetic field strength of about 2mG. (In this case $x_{\rm B}\approx 1$, so any correction for propagation effects will be small (Elitzur1996;1998).) Although the magnetic field near the stellar surface can be uncertain as the SiO maser polarisation is not strongly dependent on field strength (Nedoluha & Watson1994), an estimate by Elitzur (1996) provides a value of about 10G at distance of 30au from the star. The field strength re-evaluated above from the 1612MHz data, projected back to the SiO maser envelope, accordingly to a dipole law (r-3), yields a field of about 35G. This value agrees well with Elitzur's estimate considering that only the largest Zeeman splitting is used. Therefore, a dipole field is plausible.

The morphology of linear polarisation vectors implies a predominantly radial magnetic field in the outer envelope of VXSgr. This picture is consistent with a dipole field viewed end-on. If the dipole is tilted by about 20 or 30$^{\circ}$to the line of sight we will still see a projected radial field pattern in the linear polarisation and at the same time account for the displacement between regions of high circular polarisation on the near and far sides of the OH 1612MHz shell (Zell & Fix1996; Szymczak & Cohen1997). Detailed modelling of the magnetic field configuration will need to take propagation effects into account and is postponed to a later paper. The following observational evidence will need to be explained: (i) The linear polarisation vectors of the 1612 MHz emission are predominantly tangential to the circumstellar envelope, implying a predominantly radial magnetic field. (ii) However, the field in the red-shifted NE section of the envelope departs from the generally radial field. (iii) The magnetic field is sampled only in those regions where the propagation of polarised maser emission is strongly favoured. (iv) Ordered polarisation is seen in the brightest emission: however, some regions of weaker emission do not always follow the same polarisation trends seen in the strongest emission. (v) Circular polarisation of 1612MHz emission indicates a magnetic axis projected at position angle $210 \pm 20^{\circ}$ on the plane of the sky, with the field direction towards us (Szymczak & Cohen1997; Trigilio et al.1998). (vi) OH mainline emission at 1667MHz, which samples a region five times closer to the star than 1612MHz emission, is consistent with the same magnetic axis (Richards et al. 2000).

5 Conclusions

We have obtained MERLIN images of the OH 1612MHz maser emission from VXSgr with full polarisation information. The linear polarisation vectors are predominantly tangential to the circumstellar envelope. This implies that the magnetic field geometry is predominantly radial (since we are most likely observing $\sigma$ components of the Zeeman splitting). However the polarisation vectors in regions of weak and extended emission do not always follow the trend observed in the brightest components, and there is one sector of the OH 1612MHz envelope (NE red-shifted) where strong deviations are observed from the radial field geometry. The observational evidence is broadly consistent with a dipole magnetic field not quite end-on, but tilted to the line of sight by 20 or 30$^{\circ}$. Detailed modelling is needed to confirm the magnetic field configuration more accurately and to determine the nature of the field distortions apparent in the red-shifted NE sector of the envelope. Such modelling could also incorporate magnetic field information obtained from other masers, such as OH mainlines at 1665 and 1667MHz and SiO lines near 43 and 86GHz, which originate nearer to the star, down to distances of only a few stellar radii.

Acknowledgements
We thank the MERLIN staff for help with the observations. MERLIN is a national facility operated by the University of Manchester at Jodrell Bank Observatory on behalf of PPARC.

References

 
Copyright ESO 2001