A&A 434, 1029-1038 (2005)
DOI: 10.1051/0004-6361:20042488
W. H. T. Vlemmings1 - H. J. van Langevelde2 - P. J. Diamond3
1 - Department of Astronomy, Cornell University, Ithaca, NY 14853, USA
2 -
Joint Institute for VLBI in Europe, Postbus 2, 7990 AA Dwingeloo, The Netherlands
3 -
Jodrell Bank Observatory, University of Manchester, Macclesfield, Cheshire, SK11 9DL, UK
Received 6 December 2004 / Accepted 20 January 2005
Abstract
Through polarization observations, circumstellar masers
are excellent probes of the magnetic field in the envelopes of
late-type stars. Whereas observations of the polarization of the SiO
masers close to the star and on the OH masers much further out were
fairly commonplace, observations of the magnetic field strength in the
intermediate density and temperature region where the 22 GHz H2O
masers occur have only recently become possible. Here we present the
analysis of the circular polarization, due to Zeeman splitting, of the
H2O masers around the Mira variable stars U Her and U Ori and the
supergiant VX Sgr. We present an upper limit of the field around U Her
that is lower but consistent with previous measurements, reflecting
possible changes in the circumstellar envelope. The field strengths
around U Ori and VX Sgr are shown to be of the order of several
Gauss. Moreover, we show for the first time that large scale magnetic
fields permeate the circumstellar envelopes of an evolved star; the
polarization of the H2O masers around VX Sgr reveals a dipole field
structure. We discuss the coupling of the magnetic field with the
stellar outflow, as such fields could possibly be the cause of
distinctly aspherical mass-loss.
Key words: masers - polarization - stars: circumstellar matter - stars: magnetic fields - stars: AGB and post-AGB
At the end of their evolution, a large majority of stars go through a
period of high mass loss while climbing the asymptotic giant branch
(AGB). This mass loss, of the order of 10-7 to
yr-1,
is responsible for the formation of a
circumstellar envelope (CSE). It is also the main source for
replenishing interstellar space with processed material. AGB stars
such as the Mira variable stars, with main sequence masses less than a
few
,
will eventually develop as planetary nebulae (PNe). The
heavier evolved stars such as the supergiants will eventually explode
as a supernova (SN). The exact role of magnetic fields in the mass
loss mechanism and the formation of CSEs is still unclear but could be
considerable. The study of several maser species found in CSEs has
revealed important information about the strength and structure of
magnetic fields throughout the envelopes surrounding the late-type
stars. At distances from the central star of up to several thousands
of AU, measurements of the Zeeman effect on OH masers indicate
magnetic fields strengths of a few milliGauss (e.g. Szymczak & Cohen 1997; Masheder et al. 1999). Additionally, weak alignment with the CSE structure is found
(e.g. Etoka & Diamond 2004). Observations of SiO maser polarization have shown
highly ordered magnetic fields close to the central star, at radii of
5-10 AU where the SiO maser emission occurs
(e.g. Barvainis et al. 1987; Kemball & Diamond 1997). When interpreting the circular polarization
of the SiO masers as standard Zeeman splitting, the magnetic field
strength determined from these observations could be up to several
tens of Gauss. However, a non-Zeeman interpretation can explain the
observations by magnetic field strengths of only several tens of
milliGauss (Wiebe & Watson 1998).
Table 1: Star sample.
Recently, high circular polarization of circumstellar H2O
masers was observed for a small sample of late-type stars
(Vlemmings et al. 2002, hereafter V02).
H2O masers occur at intermediate distances in the CSE, in gas that
is a factor of 10-1000 more dense than the gas in which OH masers
occur. Vlemmings et al. (2001, hereafter V01) managed to detect the Zeeman
splitting of the circumstellar H2O maser around the supergiant star
S Per, even though for typical field strengths of a few hundred mG the
H2O Zeeman splitting is extremely small, only 10-3times the typical half-power width of the H2O maser line
(
kHz). Additional detections were discussed
in V02 and typical field strength of between 0.2 and 1 G were
found, using the full, non-LTE radiative transfer equations from
Nedoluha & Watson (1992).
Such high magnetic field strengths at a few hundred AU from the
central star give strong support for the standard Zeeman
interpretation of the SiO maser polarization.
The results from V02 indicate that the magnetic field strengths measured in the circumstellar maser regions are consistent with either a r-2 field strength dependence on the increasing distance to the star, similar to a solar-type magnetic field or possibly an r-3dependence as produced by a dipole magnetic field. This implies surface magnetic fields of hundreds to several thousand Gauss, indicating that the magnetic field pressure dominates the thermal and radiation pressure at the surface of the star. As a result, the magnetic field likely plays a very important role in driving the late-type star mass loss. Additionally, magnetic fields possibly play an important role in shaping the CSEs. This will also affect the formation of PNe, that are often observed to have distinctly non-spherical shapes.
Here we present new results on the magnetic field strength in the envelopes of several late-type stars. We discuss the observations and data calibration in Sect. 2 and the analysis method in Sect. 3. The new and previous results for our sources are presented in Sect. 4. In Sect. 5 the specific results on the supergiant VX Sgr are discussed, where the maser polarization observations allow for the investigation of the morphology of the magnetic field. The consequences of these measurements are discussed in Sect. 6 and are followed by our conclusions in Sect. 7.
The observations were performed at the NRAO Very Long Baseline Array
(VLBA) on April 20 2003. The average beam width is
mas at the frequency of the
616-523 rotational
transition of H2O, 22.235 GHz. We used 4 baseband filters of 1 MHz
width, which were overlapped to get a velocity coverage of
44 km s-1, covering most of the velocity range of the H2O
masers. Similar to the observations in V02, the data were correlated
multiple times. The initial correlation was performed with modest
(
km s-1) spectral resolution, which enabled us to
generate all 4 polarization combinations (RR, LL, RL and LR). Two
additional correlator runs were performed with high spectral
resolution (
km s-1) which therefore only contained
the two polarization combinations RR and LL. This was necessary to be
able to detect the signature of the H2O Zeeman splitting in the
circular polarization data and to cover the entire velocity range of
the H2O masers. Each source-calibrator pair was observed for 6 h.
The calibrator was observed for 1.5 h in a number of
scans equally distributed over the 6 h.
The data analysis path is described in detail in V02. It follows the method of Kemball et al. (1995) and was performed in the Astronomical Image Processing Software package (AIPS). The calibration steps were performed on the data-set with modest spectral resolution. We were also forced to flag several channels that suffered from strong interference. Fringe fitting and self-calibration were performed on a strong maser feature. The calibration solutions were then copied and applied to the high spectral resolution data-set. Finally, corrections were made for instrumental feed polarization using a range of frequency channels on the maser source, in which the expected frequency averaged linear polarization is close to zero. Then image cubes were created for stokes I, Q, U and V in the modest spectral resolution data set, and for stokes I and V in the high spectral resolution data-set.
We observed 4 late-type stars, the supergiant VX Sgr and the Mira
variable stars U Ori, R Cas and U Her. U Her was previously observed
in December 1998 as part of the observations described in
V02. Unfortunately, we were unable to detect the H2O masers of
R Cas, presumably due to source variability. In Table 1 we
list the observed sources with type, position, distance, period and
velocity, as well as the peak H2O maser flux at the epoch of
observation. In the high spectral resolution total intensity channel
maps, the noise is dominated by dynamic range effects and is 60 mJy.
In the circular polarization polarization maps the rms noise
is
20 mJy.
The polarization of the OH masers of our sources has previously been
observed and SiO maser polarization measurements have been performed
on VX Sgr. Polarization of the 1612 MHz OH masers around U Ori
indicate a magnetic field of
mG (Reid et al. 1979),
while Palen & Fix (2000) found a field of
mG on the
1665 and 1667 MHz OH masers around U Her. The magnetic fields in the
main-line and satellite-line OH maser regions around VX Sgr were
measured using MERLIN (Trigilio et al. 1998; Szymczak et al. 2001; Chapman & Cohen 1986) and the VLA
(Zell & Fix 1996). The polarization of the 1665 and 1667 MHz OH masers
indicated a field strength of
mG, while the
field in the 1612 MHz maser region is
mG. In the
single dish observations of the circular polarization of SiO masers by
Barvainis et al. (1987), they observe a circular polarization
percentage of 8.7%. This indicates
G for
VX Sgr.
For the analysis of the polarization spectra we used both the basic
LTE interpretation and the full radiative transfer non-LTE
interpretation, which were thoroughly described in V02. The LTE
analysis consists of a standard Zeeman interpretation assuming LTE. As
a result, the narrowing and rebroadening of the maser profile caused
by saturation are not reproduced. We have included the
possibility of multiple masing hyperfine lines. In this analysis, the
magnetic field strengths are determined by fitting a synthetic
V-spectrum, proportional to
,
to the polarization
spectra. The magnetic field strengths follow from
Table 2: Results.
For the non-LTE analysis, the coupled equations of state for the 99
magnetic substates of the three dominant hyperfine components from
Nedoluha & Watson (1992) were solved for a linear maser in the
presence of a magnetic field. The modeled spectra were then directly
fitted to the observed spectra. When a direct model fit was not
possible, we used Eq. (1) with
,
which is
the corresponding best estimate for the coefficient in the non-LTE
case.
The spectral fitting for both the non-LTE as well as the LTE analysis requires the removal of the scaled down total power spectrum from the V-spectrum to correct for small residual gain errors between the right- and left-polarized antenna feeds. It was found in V01 and in V02 that generally, the V-spectra were narrower than expected in the LTE case. This could be partly explained by introducing the non-LTE method, however, some narrowing remained. In V02, we attributed this to the application of uni-directional maser propagation in the modeling, and we found that a bi-directional maser could explain some of the narrowing. However, for computational efficiency we continue to use the uni-directional method, while allowing for additional narrowing of the V-spectrum, as we found that the estimates for the fractional circular polarization are robust.
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Figure 1: Total intensity image of the H2O maser features around U Her. The inlay shows the total intensity spectrum of the U Her H2O masers, where the solid vertical line indicates the stellar velocity and the dashed vertical line indicates the velocity of the maser feature that was found to be coincident with stellar position in Vlemmings et al. (2002). |
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We have determined the magnetic field strength on the strongest maser
features in the band (44 km s-1 wide). The results of both the LTE and
non-LTE analysis are shown in Table 2 for features
with peak fluxes down to
of the brightest maser spot. As
seen in Col. 6, the percentage circular polarization is relatively
large and varies between 0.3% and 20% with the highest polarization
being detected for U Ori. Magnetic field strengths obtained using the LTE
Zeeman method are given in Col. 7 while the results obtained using
the non-LTE models are shown in Col. 8. Features that did not show
circular polarization at a level higher than 3 times the rms noise in
the V-spectrum are considered non-detections. However, the formal
errors on the magnetic field strength also include the errors
on total intensity and line width, and are thus larger, resulting in
occasional magnetic field strengths around the
noise level. For the
non-detections we have determined the absolute upper limits
using the
coefficient obtained in the non-LTE radiative
transfer models. In the LTE analysis the limits would be larger by a
factor of
1.4
Maser features that had circular polarization spectra that could not
be fitted accurately are labeled in Table. 2. This
is likely due to blending of several features, both spatially and
along the velocity axis. The values for the magnetic field strength
for those features were determined using only the minimum
and maximum
of the V-spectrum after it was forced
to be point symmetric. The features labeled ** (VX Sgr n, shown in
Fig. 4 and VX Sgr w) suffered from external
interference, most of which we managed to remove. Some effects remain
however, and it is unclear if this had an effect on the measured
magnetic field strength for those features.
As in V02, we were unable to detect any significant linear
polarization above a limit of
for the strongest maser
features and a few % for most of the weakest. There was a hint of
linear polarization on the strongest maser feature of U Ori, but as
the level of polarization was at most only at the
level of
it cannot unambigiously be classified as a detection.
After the observations of U Her in V02 revealed a magnetic field in
the H2O maser region of 1.5 G, U Her was observed again in
our second observational run. The integrated total intensity map of
the H2O maser features is shown in Fig. 1.
Even though the strength of the U Her maser features is similar in both
observational epochs, we did not detect any significant circular
polarization in the observations presented here. The upper limit we
find is
130 mG on the strongest and
600 mG on the
weakest maser feature. However, the spectrum and spatial distribution
of the masers has changed significantly in the more than 4 years
between the observational epoch of December 13th 1998 and April 20th
2003. The velocity of the maser features observed in V02
(between -19.3 and -17.6 km s-1) was several km s-1 more blue-shifted than the maser
features observed here, that are close to the stellar radial velocity
of -14.5 km s-1. Whereas the spatial distribution of the maser spots
in V02 showed an elongated structure in the N-S direction,
Fig. 1 indicates a significantly different structure.
The weakest VLBI feature detected at -15.82 km s-1 (labeled c in
Fig. 1) corresponds in velocity to the feature that was
found to be the strongest in the MERLIN observations of
Vlemmings et al. (2002). In those observations, this feature was found to be
aligned with the optical position to within 15 mas and interpreted
as the amplified stellar image.
Assuming that the current feature at -15.82 km s-1 is also the
amplified stellar image we obtain a lower limit on the distance on
the sky between the brighter H2O maser features and the star. For a
distance to U Her of 277 pc, the projected separation between the
star and the two brightest maser features is
16 AU. Since
the velocity of these maser features is close to the stellar velocity,
we expect the true separation to be similar. Assuming that the maximum
magnetic field strength in V02 was measured at the inner edge of the
H2O maser region, which was found to be
12.5 AU
(Bains et al. 2003), the expected magnetic field strength at 16 AU is
700 mG assuming a dipole magnetic field configuration. The
difference between the expected field strength and the measured upper
limits could be due to a large angle
between the
magnetic field lines and the line of sight. Alternatively, some of the
magnetic field strength difference could be due to different maser
clump density by up to a factor of
10, if the magnetic field lines
are frozen into the dense clumps. We could also be observing actual
variability in the magnetic field.
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Figure 2: ( left) Total intensity image of the H2O maser features around U Ori. ( right) Total power (I) and V-spectra for selected maser features of U Ori. The bottom panel shows the best fitting synthetic V-spectrum produced by the standard LTE Zeeman interpretation (dashed line). The middle panel shows the best non-LTE model fit (dotted line). The corresponding total power fits are shown in the top panel. The V-spectra in the lower two panels are adjusted by removing a scaled down version of the total power spectrum as indicated in Sect. 3, which is different for the LTE and non-LTE fits. The solid vertical lines show the expected position of the minimum and maximum of the V-spectrum in the general LTE interpretation. |
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Figure 2 shows the integrated total intensity H2O maser map of
U Ori. Very little structure is observed and the maserfeatures seem
to be somewhat blended both spatially as well as in velocity. Strong
circular polarization up to
is detected on the three
bright central features where interestingly the features b and c,
to the left and right of the brightest feature a, show an opposite sign for
the magnetic field. The total intensity and circular polarization
spectra for these features are also shown in Fig. 2. From
these we estimate the absolute magnetic field strength in the
maser region to be
3.5 G. While the central feature a does
not show such a high field strength, the feature seems to be a blend
of two features with oppositely directed magnetic fields. The more
complex circular polarization spectrum of U Ori a can be explained
by two features with a magnetic field of
800 mG of opposite
sign. The high magnetic field strength measured for the Mira variable
star U Ori is consistent with the high field (10 mG) measured using the
OH masers (Reid et al. 1979) assuming a dipole r-3 dependence of
the magnetic field on the distance to the star. This assumes that the
H2O masers occur in a shell with an outer edge of 30 AU, as
determined by Bains et al. (2003).
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Figure 3: Similar to Fig. 2 for VX Sgr. |
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Figure 4: Similar to the spectra in Figs. 2 and 3 for additional maser features around VX Sgr. Feature VX Sgr n suffers from some interference effect in the right wing of the spectrum but this does not affect the magnetic field determination. |
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The integrated total intensity H2O maser map of the supergiant
VX Sgr is shown in Fig. 3. VX Sgr shows a rich structure
of strong H2O maser features in a
mas ellipse,
corresponding to
AU at a distance of 1.7 kpc. The
maser feature distribution is similar to that seen in the MERLIN
observation by Murakawa et al. (2003, hereafter M03). Circular polarization
was detected ranging from 0.3-
for a large number of maser features
as seen in Table 2. Several of the spectra are shown
in Figs. 3 and 4. As mentioned above,
a few of the maser features suffered from blending or external
interference. The maximum magnetic field strength measured is
4 G. Across the maser features we find a clear transition between a
negative magnetic field in the S-E to a positive magnetic field in the
N-W. This is the first detection of a large scale magnetic field in a
circumstellar H2O maser region.
The maser shell of VX Sgr has been studied extensively with MERLIN
and VLA observations (e.g. Lane 1984; Trigilio et al. 1998; Zell & Fix 1996; Chapman & Cohen 1986, M03). The recent
observations of M03 indicate that the H2O masers arise in a thick
shell between 100 AU and 325 AU from the star. In this shell, the
H2O masers seem to be accelerated from 10 km s-1 to 20 km s-1.
The H2O maser shell shows a clear elliptical asymmetry which was
modeled in M03 as a spheroidal maser distribution intersected with an
under-dense bi-conical region at an inclination angle
from the line of sight and rotated
on the plane of the sky. Marvel (1996) also observed the
elliptical H2O maser distribution with the VLBA and, constrained by
proper motions, fitted the emission region using an oblate spheroid
with a maximum radius of 250 mas at an inclination angle
and projected position angle
.
Observations of the 1612 MHz OH masers at 1400 AU from the
star also show the elliptical asymmetry observed in the H2O masers.
The magnetic field strength in the 1612 MHz OH maser region was
estimated to be of the order of a milliGauss (Trigilio et al. 1998).
Szymczak et al. (2001) observed the linear polarization of the OH
masers and found structure that could be explained by a dipole
magnetic field with an inclination axis of about
or
.
Additionally, the observations of Zeeman pairs in the OH
emission indicates a change in magnetic field direction across the
maser region.
This was suggested to be the signature of a dipole magnetic field
(Zell & Fix 1996). Further observations indicated that the magnetic
axis was projected at a position angle
(Szymczak & Cohen 1997). Observations of the OH mainline masers
emission at 1667 MHz closer to the star are consistent with the same
magnetic angle (Richards et al. 2000).
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Figure 5:
The best fitted dipole magnetic field for the H2O
maser observations around VX Sgr (denoted by the solid circle). ( left)
The distribution of the H2O maser features indicating the measured
magnetic field strengths. Open symbols denote a positive magnetic
field while the closed symbols correspond to a negative magnetic
field. The crosses represent the upper limits. The symbols have been
scaled relative to the magnetic field strength. ( right) The
distribution of the H2O maser features indicating the velocity
structure of the maser features. The open symbols are the red-shifted
features and the solid symbols are the blue-shifted features. The size
indicates the velocity difference with the stellar velocity (
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We have fitted a dipole magnetic field to our H2O maser magnetic
field observations of VX Sgr. As the positions of the maser features
in the shell along the line of sight are unknown, we used the
accelerating spherical outflow model of Chapman & Cohen (1986) to describe the
velocity structure of the maser shell. Thus, the observed radial
velocity of the maser features directly maps into the third spatial
dimension, allowing for a three dimensional fit. A maximum likelihood
fit was made to the dipole field, solving for the stellar position,
the inclination and position angle of the magnetic field and the field
strength at the surface of VX Sgr. The stellar radius was fixed at
16 AU, in agreement with the observations by Danchi et al. (1994) and
Greenhill et al. (1995). In the fits we also included the maser features for which
we only determined an absolute upper limit. The errors on the
magnetic field strength were taken from our analysis, while we
included errors of 1 km s-1 on the velocity of the maser features to
take into account turbulent velocities and small deviations from the
spherical outflow model. Figures 5 show the structure of
the magnetic field as well as the radial velocity structure observed
for the H2O maser features. The best fitted model for a dipole
magnetic field is overplotted. While the magnetic field strengths can
be fit reasonably well, the model has a harder time simultaneously
fitting the velocity structure. Our fits show the stellar position to
be offset from the center of the H2O maser emission by
mas to the NE. The magnetic axis of the dipole field is
pointed toward us at an inclination angle
,
and a
position angle of
.
The indicated errors
are the formal
errors from the fit. However, as both the
magnetic field and the outflow velocity structure are likely to have
small scale structure, the exact errors are strongly model dependent
and are hard to quantify.
The fitted values are remarkably consistent with the values found for
the magnetic field determined from OH masers, as well as with the
orientation angle determined from the H2O maser distribution in M03
and Marvel (1996). We find that the magnetic field strength at the
surface of VX Sgr corresponds to
kG. For the
r-3 magnetic field strength dependence of the dipole field, this
is consistent with the observations of the magnetic field on the OH
masers as well as the SiO masers (Barvainis et al. 1987). In addition to a dipole
magnetic field, we also considered a solar-type magnetic field with a
magnetic field strength dependence of r-2 on the distance to the
star. This resulted in a significantly lower likelihood.
Our ability to perform such a fit of VX Sgr indicates that an ordered large scale magnetic field exists. Previously, an alternative model explained the magnetism in terms of local fields, frozen in high density pockets (Soker 2002). Although such small scale structure could still be important, we conclude that it is likely that large scale magnetic fields permeate the CSEs.
The observations reveal circular polarization percentages up to .
Using the non-LTE radiative transfer method this indicates
magnetic field strengths along the maser line of sight up to
4 G, while the fields determined using the LTE approximation are
generally
higher. As shown in V02, the non-LTE circular
polarization spectra are typically not symmetric, while the LTE method
produces spectra with an point symmetric S-curve shape. However, due
to the data processing and the necessary removal of a scaled down
replica of the total power, it is impossible to directly observe the
non-symmetric non-LTE spectra. Still, we confirm that the non-LTE
spectra produce better fits to the observed V-spectra, as can be seen
in several of the spectra presented in
Figs. 2-4. Most of
the observed V-spectra also show narrowing that cannot be reproduced
in the LTE analysis, as was first found in V01. Similar to earlier
results (e.g. Vlemmings & van Langevelde 2005; Spencer et al. 1979), we find that the H2O masers are mostly
unsaturated after an analysis of the line widths and shapes of the
total intensity spectra.
We confirm in these observations again the absence of linear
polarization to a limit of ,
which provides
compelling evidence against the non-Zeeman interpretation, considered
by Wiebe & Watson (1998) for the SiO masers, as the cause for the observed high
circular polarization of the H2O masers. The fact that no
significant linear polarization is observed is an additional
indication that the circumstellar H2O masers are unsaturated
(Nedoluha & Watson 1991).
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Figure 6: Magnetic field strength, B, as function of distance, R, from the center of the star. Dashed-dotted boxes are the estimates for the magnetic fields in the OH and SiO maser regions of Mira stars, solid boxes are those for the supergiants. The dashed-dotted line indicates a solar-type magnetic field and the dotted line indicates the dipole field. The solid symbols are the previously observed stars (U Her: triangles; S Per: squares; VY CMa: crosses and NML Cyg: hexagonals). The open symbols indicate the stars of the sample presented here (U Her: triangle; VX Sgr: hexagonal and U Ori: circle). Note that the open triangle only indicates the upper limit determined for the most recent observation of U Her. Also note that the magnetic field strength observed on the OH masers of U Ori is larger than the typically observed fields for Mira variables. The dashed lines represent estimates of the stellar radius. |
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The observed magnetic field strengths on the H2O masers are
consistent with the results for the other maser species assuming a
dependence of the field strength on the distance to
the star. As the magnetic field strength determined for the SiO,
H2O and OH maser features depends on the angle between the magnetic
field and the maser propagation axis, it is difficult to exactly
determine the value of
.
In Fig. 6 we show an
updated version of Fig. 15 from V02 including the results from the
sources observed for this paper. The open symbols indicate the stars
in the sample presented here. The points for the H2O masers are
drawn at the outer radius of the maser region, which for VX Sgr was
determined in M03. For U Ori we used the value of
30 AU from
Bains et al. (2003). The arrows indicate a typical width of the H2O maser
region. The SiO maser location of
50 AU for VX Sgr was taken
from Doeleman et al. (1998) and its OH maser extent (
1400 AU) from
Szymczak et al. (2001). The OH masers around U Ori were found to exist at
65 AU (Chapman et al. 1991). For the other sources the references are
listed in the relevant section of V02. We indicate a solar-type
magnetic field (
)
and a dipole field (
). The
observations of VX Sgr indicate (as shown in Sect. 5) that a
dipole field best fits the shape of the field in the H2O maser
region. Extrapolating the observed magnetic field strengths to the
stellar surface, we find that Mira variable stars have surface field
strengths up to several times 102 G, while supergiant stars have
fields of the order of 103 G.
The origin of the strong, large scale magnetic fields around evolved
stars remains a topic of debate. The generation of an axisymmetric
magnetic field requires a magnetic dynamo in the interior of the
star. One of the main arguments against a dynamo generated magnetic
field is the slow rotation of the late-type star based on conservation
of angular momentum (Soker & Harpaz 1992). However, models by Blackman et al. (2001)
consider the strong differential rotation created when the degenerated
stellar core contracts while the envelope expands. In this case the
dynamo is the result of the interaction between the differential
rotation ()
and turbulence in the convection zone around
the degenerated core (
). This
-dynamo action can produce a strong magnetic field
similar to the one observed using the circumstellar masers. It has
been argued that such strong magnetic fields should produce strong
X-ray emission. Although Mira is a weak X-ray source (Soker & Kastner 2003),
observations of TX Cam and T Cas did not reveal any X-ray emission
(Kastner & Soker 2004). However, as the optical depth for X-ray emission around
evolved stars is expected to be high, it has been shown that this
non-detection cannot rule out the strong magnetic fields produced by
the
-dynamo (Blackman et al. 2001). The above models include
the interaction with a degenerated core, while the core of supergiants
such as VX Sgr is supposedly not degenerate. However, a similar dynamo
action for supergiants, driven by the differential rotation between
the contracting non-degenerate core and the expanding outer envelope
has been shown to also be able to generate strong magnetic fields
(Uchida & Bappu 1982).
In contrast to the
-dynamo, several papers have
examined a
-dynamo, under the assumption that
the rotation of the envelope only marginally contributes to the dynamo
action (Soker 2002; Soker & Zoabi 2002). These models produce magnetic fields that
are several orders of magnitude lower than the models using the
-dynamo. The observed magnetic field strength in the
maser regions of the CSE are then argued to be due to localized,
magnetized wind clumps that are produced in magnetic spots on the
surface of the star that can have local field strengths of up to
10 G. Using another model, dynamo action of giant-cell convection at
the surface of a late-type supergiant star has recently been shown to
be able to produce fields up to
500 G in localized spots on the
stellar surface (Dorch 2004). Models that produce local strong field
however, do not readily explain the observations of large scale
magnetic field structure such as seen around VX Sgr. Alternatively, in
the case of the
-dynamo a strong magnetic field
can be generated when the star is spun up by a close binary. The
sources in our sample do not however, show any indication of binarity,
although this cannot be ruled out.
The magnetic field strength of several Gauss measured in the H2O
maser region implies that the magnetic pressure dominates the thermal
pressure of the circumstellar gas throughout a large part of the CSE
of both regular AGB stars and supergiants. The ratio between the
thermal and magnetic pressure is given by
,
with k the Boltzman constant. Assuming a gas density
of
cm-3 and a temperature of
K
at the inner edge of the H2O maser region, a magnetic field between
B=0.5 and 1 G gives
,
indicating that
the magnetic pressure dominates the thermal pressure by factors of
80 or more. In the lower density non-masing regions this
factor will be even higher unless the magnetic field is frozen into
the high density clumps. Still, in that case, when
with
(Mouschovias 1987),
will be of the
same order of magnitude.
The effects of magnetic fields on the stellar outflow and the shaping
of the distinctly aspherical PNe have been discussed in several papers
(e.g. García-Segura 1997; Pascoli 1987; Chevalier & Luo 1994). PNe are thought to be formed due to
the interaction of the slow AGB wind ( km s-1) with a
subsequent fast wind (
km s-1) generated when the central
star evolves into a white dwarf (Kwok et al. 1978). Strong, large scale,
magnetic fields around AGB stars could directly affect the fast wind
and as a result shape the PN (Chevalier & Luo 1994; García-Segura et al. 2003). Only recently,
magnetic field strengths of 1-3 kG have been detected at the
surface of the central star of several PNe (Jordan et al. 2005).
Another mechanism in which magnetism can play a role in shaping PNe is
described in Matt et al. (2000). In the models presented in that paper, a
large scale dipole magnetic field is responsible for creating an
equatorial density enhancement in the initial, slow, AGB wind. For the
magnetic field to influence the stellar outflow, the outflow must be
sufficiently ionized, which is likely the case close to the surface of
the star. A dipole magnetic field will then only need to have
sufficient magnetic pressure (
)
to produce an equatorial
disk. The interaction of the later fast wind with this disk has been
shown to be able to easily create aspherical, cylindrical symmetric
PNe (e.g. Soker & Livio 1989; Mellema et al. 1991; Icke 1988). Furthermore, under the influence
of the large scale magnetic field, the circumstellar disk could become
warped (Lai 2003), and the interaction of the fast wind with such a
disk has been shown by Icke (2003) to be able to explain the multipolar shape observed for several PNe, such as NGC 7027
(Cox et al. 2002). Although we have not directly observed the morphology of
the magnetic field for the AGB stars in our sample, the magnetic field
strengths measured on U Ori, are fully consistent with a dipole
magnetic field such as found around the supergiant VX Sgr. As seen in
Fig.3, we observe indeed that the H2O masers around
VX Sgr occur in a oblate spheroid, which could be an indication of the
equatorial density enhancement expected in a CSE that has been shaped
by a dipole magnetic field.
We have measured the magnetic field around the late-type stars U Her,
U Ori and VX Sgr using observations of the circular polarization of
their H2O masers. Although we only find an upper limit in the case
of U Her, we find strong magnetic fields of 3.5 and 4 G for
U Ori and VX Sgr respectively. The rich structure of the H2O masers
around the supergiant VX Sgr enabled us to determine the shape of the
magnetic field around this supergiant star. The observations are best
represented by a dipole magnetic field at angles that are remarkably
consistent with those of the dipole field used to explain previous OH
maser polarization observations at much larger distances from the
central star. This confirms the presence of an ordered magnetic field
close to the star. Additionally, the ellipsoidal structure of the
H2O masers around VX Sgr is aligned with the equatorial plane of
the dipole field, which could indicate the equatorial density
enhancement caused by the magnetic field as described by
Matt et al. (2000). The magnetic field strengths determined in the H2O
maser regions around U Ori and U Her, lower mass evolved stars that
are the progenitors of PNe, are also consistent with a dipole field,
such as found around VX Sgr. As a result, also for those stars, the
magnetic fields can cause aspherical density structures that result
in non spherically symmetric PNe.
Acknowledgements
W.V. acknowledges the hospitality of the Harvard-Smithsonian CfA during his visit which was supported by the Niels Stensen Foundation.