A magnetically collimated jet from an evolved star

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1

A magnetically collimated jet
from
an evolved star

Wouter H.T. Vlemmings*, Philip J. Diamond* & Hiroshi Imai**

*Jodrell Bank Observatory, University of Manchester, Macclesfield, Cheshire SK11
9DL, UK

**Department of Physics, Faculty of Science, Kagoshima U
niversity, Kagoshima 890
-
0065, Japan

Planetary nebulae often have asymmetric shapes, which could arise due to
collimated jets from evolved stars before evolution to the planetary nebula phase
1
-
3
. The source of jet collimation in these stars is unknown. Mag
netic fields are
thought to collimate outflows that are observed in many other astrophysical
sources, such as active galactic nuclei
4
-
7
and proto
-
stars
8, 9
, although hitherto there
are no direct observations of both the magnetic field direction and strengt
h in any
collimated jet. Theoretical models have shown that magnetic fields could also be
the dominant source of collimation of jet in evolved stars
10, 11
. Here we report
measurements of the polarization of water vapour masers that trace the precessing
jet
emanating from the asymptotic giant branch star W43A at 2.6 kpc from the
Sun, which is undergoing rapid evolution into a planetary nebula
2, 12
. The masers
occur in two clusters at opposing tips of the jets, ~1,000 AU from the star. We find
direct evidence
that the magnetic field is collimating the jet.


The 22 GHz H
2
O masers can be observed at high angular resolution and
can
be used to
trace the magnetic field strength and structure at small scales
13
-
15
. Circular polarization
is caused by the Zeeman effect
, observations of which yield the magnetic field strength
along the line of sight
13, 14, 16
. The linear polarization vectors describe the direction of
the magnetic field.

2

We have used the Very Long Baseline Array (VLBA) of the National Radio Astronomy
Obs
ervatory to determine both the linear and circular polarization of the 22 GHz H
2
O
masers in the jet of W43A (Figs 1 and 2). In our linear polarization spectra we
achieve

a r.m.s. noise of approximately 10 mJy beam
-
1
, and we detect linear polarization in t
he 6
brightest maser features (peak flux > 6 Jy beam
-
1
), with a weighted mean linear
polarization fraction of 0.66

0.07%. The 3
σ
r.m.s. upper limits of the linear
polarization fraction on the other 14 detected but weaker features range upwards from
0.68
%. The linear polarization vectors are predominantly aligned with the jet.
According to maser theory, the linear polarization vectors are either parallel or
perpendicular to the magnetic field direction
17
. The strongest linear polarization is
typically fou
nd when the polarization vector is perpendicular to the magnetic field
direction on the sky
13, 16
. We thus conclude that most of the observed linear polarization
vectors are perpendicular to the magnetic field direction as shown in panel
c
and
d
of
Fig. 1.
Across the brightest maser feature we observe a 90

flip of the polarization
angle. Here, as predicted by the theory and as previously observed in SiO masers
18
, the
linear polarization vector changes from parallel to perpendicular with respect to the
magn
etic field across the maser. We find the median, error weighted, position angle of
the magnetic field to be
-
27

12º east of north. This
error estimate
includes the
systematic error (8º) introduced after polarization calibration with respect to the
calibr
ator J1743
-
0350. The magnetic field direction is thus almost perfectly
perpendicular to the jet, which is consistent with a toroidal magnetic field configuration.
We have also detected a fractional circular polarization
P
V
= 0.33

0.09

%
in one of the
ma
ser features in the southern tip of the collimated jet (Fig. 2). Using a full 22 GHz
H
2
O maser radiative transfer code, that does not assume thermal equilibrium, to fit to
the circular polarization
13
-
16
, we find the magnetic field strength along the line o
f sight
in the maser
B
||
=
B
cos
θ
= 85

33 mG, where
θ
is the angle between the line of sight
and the magnetic field direction. We estimate
θ


65º using the linear polarization
3

fraction (0.64

0.19

%
) of the maser and our polarization model fit results
. Thus, the
magnetic field in the H
2
O masers at one position within the collimated jet is
B


200


75 mG. This implies that, depending on the hydrogen number density

in the H
2
O maser
regions of the jet, the magnetic pressure dominates the gas pressure by
a factor of 2
-
200,
as expected in the case of magnetic collimation
11
.

H
2
O masers at 22 GHz are excited in gas with a hydrogen number density
n

10
8
-
10
10

cm
-
3
19
. The H
2
O masers in the collimated jet of W43A likely arise when the jet has
swept up enough mate
rial previously expelled from the star so that conditions at the tip
of the jet have become favourable for H
2
O masers to occur
2
. As the typical hydrogen
number density at 1,000 AU from the star is
n

10
5
cm
-
3
, the swept up material has
increased the densi
ty in the maser region by a factor between

10
3
-
10
5
. When the
magnetic field is partially coupled to the gas, compression of the magnetic field lines
increases the field strength in the maser region, with the relation between the magnetic
field strength an
d density
B



n
k
. Theoretical and observational considerations indicate
that the coefficient
k
can range between 0.3 and 1. An empirical relation, which has
k
=
0.4
7
, was determined from observations of magnetic fields in star
-
forming regions
20
.
Using this
relation, the magnetic field strength in the lower density region outside the jet
is
B


0.9
-
2.6 mG. This is consistent with values measured in the OH maser region at
similar distances
from the star in other systems
. Alternatively, the masers
may
occur in

a shock, similar to the H
2
O masers found in star
-
forming regions
21
.

Such shocks might
exist
between the collimated jet and dense material in the outer circumstellar envelope.
For
a
shock model we calculate, using H
2
O shock excitation models
21
, that the pr
e
-
shock hydrogen density is

3 10
6
cm
-
3
and the pre
-
shock magnetic field strength is
B



0.07 mG.

A rotating magnetic field in the outflow of a star can be described by two components
:
a
toroidal component
B
ϕ
(


r
-
1
) and a radial component
B
r
(


r
-
2
). Due
to the
4

dependencies on distance (
r
) from the star the radial component can be effectively
neglected at distances of 1,000 AU. This is consistent with the observed magnetic field
directions, which are fully toroidal. Using the
r
-
1
dependence, we can estimat
e the
magnetic field strength
B
ϕ
s
at the base of the collimated jet on the surface of the star (
R


1 AU) to be

1.5 G
if
the jet H
2
O masers are excited in swept up material, or

70 mG
if the H
2
O masers occur in shocks. The stellar toroidal magnetic field
strength has a
latitude dependence of the form
B
ϕ
s
(
θ
s
) =
B
s
sin
θ
s
, where
B
s
is the strength at the
equator
θ
s
=
π
/2. Assuming we measure the magnetic field at the edge of the collimated
jet with an opening angle of

5º, this implies
B
s


35 or 1.6 G. The
higher value is in
excellent agreement with measurements extrapolated from previous maser polarization
observations
14, 15, 18, 22
.

The magnetic field and jet characteristics of W43A support the recent theoretical
models that use magnetically collimated j
ets from evolved stars to explain the shaping
of asymmetric planetary nebulae
11, 23, 24
. These models also explain the shapes of a large
number of other proto
-
planetary nebulae, such as He 3
-
401
25
. However, the origin of the
stellar magnetic field is still
a matter of debate. Magnetic dynamo models invoking the
differential rotation between a rapidly rotating core and a more slowly rotating outer
layer have been shown to be able to produce magnetic fields in evolved stars similar in
strength to those found
in our observations
10
. Other models stress the need for a binary
companion or heavy planet for a sufficient magnetic field to be attained
26
. The presence
of a heavy planet in orbit around W43A could also be the cause of the observed jet
precession
2, 27
.

D
ifferent models have described the collimation of jets by magnetic fields around AGN
5

and proto
-
stars
28
. These models have been shown to be able to produce many of the
observed characteristics of sources, such as the collimated proto
-
star HH212
9
and a
larg
e sample of active galactic nuclei (AGN)
6
. Additionally, recent laboratory work has
5

been able to produce jets collimated by toroidal magnetic fields
29
. For the jets produced
by AGN there are many indications that magnetic collimation is occurring
6, 7, 30
,
however, no observations yet exist of the magnetic field strength. There is also no direct
evidence of magnetic collimation of proto
-
stellar jets. The characteristics of the jet of
W43A are similar to those found in star
-
forming environments
9
, and as magne
tic fields
of similar strengths are found in those regions
13
, magnetic collimation such as described
here likely also occurs during star
-
formation.


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Acknowledgements: NRAO is a facility of the National Science Foundation, operated under cooperative
agreement by Associate
d Universities, Inc. W.V. was financially supported by a Marie
-
Curie Intra
-
European fellowship.

Competing interests statement: The authors declare that they have no competing financial interests.

Correspondence and requests for materials should be addresse
d to W.V. (e
-
mail:
wouter@jb.man.ac.uk
).

9

Figure 1
: The spatial distribution, linear polarization vectors and inferred
magnetic field direction of the H
2
O masers in the jet of W43A. H
2
O maser
emission (6
16
-
5
23
l
ine at 22.235080 GHz) was observed with the VLBA with an
angular resolution of 0.5 milliarcsecond (mas) in right ascension (
α
) and 1.0
mas in declination (
δ
). In panel
a
-
d
the maser features are indicated by coloured
10

hexagons, scaled logarithmically accord
ing to their flux density in Jy beam
-
1
.
The maser features in panel
e
are indicated by coloured dots. The colour
denotes the radial velocity
V
lsr
with respect to the local standard of rest (LSR).
The dashed
-
dotted line indicates the model of the precessin
g jet of W43A (
v
=
145 km s
-
1
, inclination
39

, position angle 65º east of north, 5º precession with a
55 year period)
. The cross in panel
e
denotes the location of W43A at
approximately
27

α
(J2000)=18
h
47
m
41.166
s
and
δ
(J2000)=
-
01º45’11.7”. In panel
a
and
b
the logarithmically scaled linear polarization vectors are shown. In
panel
c
and
d
we indicate the derived magnetic field direction with red vectors.
The vectors reveal a toroidal magnetic field along the jet. The perpendicular
magnetic field direction o
f the Northern
-
most maser feature indicates that these
masers are likely located at the edge of the jet, where the magnetic field
direction is along the projected jet direction due to shear between the
compressed toroidal field lines inside and the uncompr
essed field lines outside
the jet. This indicates a

5º jet opening angle. The magnetic field strength
derived from the circular polarization (Fig.2) is indicated in panel
d
. In panel
c
-
e

the ellipses show the toroidal magnetic field component along the je
t. The sizes
of the ellipses scale according to a
r

-
1
decrease of the magnetic field strength
with increasing distance
r
from the star.

11


Figure 2
: The total power (I) and circular polarization spectrum (V) of a 22 GHz
H
2
O maser feature in the southern ti
p of the collimated jet of W43A. The spectra
have a velocity resolution of 0.027 km s
-
1
and a r.m.s. noise of 14 mJy beam
-
1
.
The feature has a peak flux of 10.85 Jy beam
-
1
and a radial velocity
V
lsr
=
-
57.19
km s
-
1
. The thick solid line in the lower panel is
the best fit model to the circular
polarization spectrum giving a circular polarization fraction P
V
= 0.33

0.09

%.
The s.d. error is determined from the r.m.s. noise on the total intensity and
circular polarization spectra. The resulting magnetic field
strength on the maser
feature is
B
||
= 85

33 mG, where the increased s.d. error is the result of an
added uncertainty due to the H
2
O maser radiative transfer model used in the fit.