Download Mid-infrared imaging of the dust shell around the post

Mon. Not. R. Astron. Soc. 343, 880–890 (2003)
Mid-infrared imaging of the dust shell around the post-asymptotic
giant branch star HD 161796
T. M. Gledhill1 and J. A. Yates2
1 Department
2 Department
of Physical Sciences, University of Hertfordshire, College Lane, Hatfield, Hertfordshire AL10 9AB
of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT
Accepted 2003 April 16. Received 2003 April 11; in original form 2002 August 10
ABSTRACT
We present mid-infrared (IR) images of HD 161796 (IRAS 17436+5003), taken with the
OSCIR imager on the Gemini North Telescope, that resolve for the first time the thermal
emission structure of the dust shell around this post-asymptotic giant branch (AGB) star. As
well as a basic axisymmetric structure, the observations show deviations from axisymmetry in
the dust density and a twist in the symmetry axis. Modelling of the mid-IR images and of the
spectral energy distribution from ultraviolet to submillimetre wavelengths reproduces all of
the axisymmetric features with an equator-to-pole density contrast of 6 : 1 and an inclination
of the symmetry axis of 10◦ to the plane of the sky. We find that a model incorporating small
(0.01µm) grains and a steep (∝ a −6 ) power-law size distribution can successfully account
for the thermal emission and for the observed degrees of near-IR polarization. Assuming a
distance of 1.2 kpc to HD 161796, the stellar luminosity is 3.4 × 103 L and the mass of the
shell is ∼0.7 M . This is consistent with a star of initial mass between 1 and 2 M that has
undergone an intensive (2.2 × 10−4 M yr−1 ) phase of mass loss lasting about 3000 yr at the
end of the AGB. A current stellar mass of 0.56 M , as indicated by the luminosity, suggests
that HD 161796 is a few hundred years into its post-AGB evolution and will take about 5000 yr
to evolve from its present temperature of 7500 K to become the central star of an extended
elliptical planetary nebula.
Key words: radiative transfer – stars: AGB and post-AGB – circumstellar matter – stars:
individual: HD 161796 – stars: individual: IRAS 17436+5003 – stars: mass-loss.
1 INTRODUCTION
The sharp decrease in mass-loss rate, from ∼10−4 M yr−1 at the
end of the asymptotic giant branch (AGB), to ∼10−7 M yr−1 in the
post-AGB phase, leads to a detached circumstellar envelope (CSE)
of gas and dust, slowly expanding away from the star (e.g. Blöcker
1995; Steffen, Szczerba & Schönberner 1998). In this immediate
post-AGB phase, the star has yet to develop a fast wind or become
hot enough to photoionize the gas, so that the CSE provides a relatively undisturbed cumulative history of the mass-loss events that
created it. By imaging the CSE in this phase, we can obtain an improved understanding of how the mass-loss rate varies at the end
of the AGB. A number of imaging studies of post-AGB objects, or
protoplanetary nebulae (PPN), have now been made at optical (Ueta,
Meixner & Bobrowsky 2000), near-infrared (Gledhill et al. 2001)
and mid-infrared (e.g. Dayal et al. 1998; Meixner et al. 1999; Jura,
Chen & Werner 2000; Ueta et al. 2001) wavelengths. These studies
have shown the CSE to have an axisymmetric dust distribution, in E-mail: [email protected]
dicating that the shift from spherically symmetric to axisymmetric
mass loss occurs at the end of the AGB.
The cause of the shift to axisymmetric outflow is not known,
although a number of possible models have been advanced. Most
involve a binary companion to the mass-losing AGB star, in either
a detached or a common-envelope configuration (e.g. Mastrodemos
& Morris 1999, and references therein). It has also been proposed
that the stellar magnetic field may play an important role in the formation of an equatorial outflow (Matt et al. 2000; Blackman, Frank
& Welch 2001; Gardiner & Frank 2001). In order to aid discrimination between possible models, we need to know the detailed density
structure of the CSE close to the end of the AGB. This is the precise
region probed by mid-infrared (IR) studies, where emission originates from warm dust at the inner edge of the expanding dust shell.
In the post-AGB phase, the inner radius of the CSE is expected to be
∼1016 cm (Steffen et al. 1998), so that sub-arcsecond angular resolution is required to image this region. With the recent availability
of mid-IR imagers on 8-m class telescopes, this is now possible.
HD 161796 (IRAS 17436+5003) is a post-AGB star with an
F3Ib spectral type (Fernie & Garrison 1984) and the double-peaked
IR spectral energy distribution (SED) characteristic of emission
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2003 RAS
Mid-IR imaging of post-AGB star HD 161796
from a detached CSE (van der Veen, Habing & Geballe 1989;
Hrivnak, Kwok & Volk 1989). The envelope has an O-rich chemistry
(Justtanont et al. 1992) and appears as a reflection nebula at optical
and near-IR wavelengths (Ueta et al. 2000; Gledhill et al. 2001).
Previous mid-IR imaging with the 3.8-m UK Infrared Telescope
(UKIRT), at 8, 10 and 12 µm, detected the detached CSE and, using image deconvolution techniques, allowed the radius of the inner
boundary to be estimated (Skinner et al. 1994). A detailed fit to the
SED from ultraviolet (UV) to submillimetre (sub-mm) wavelengths,
including emission-line features revealed by ISO observations, has
provided evidence for the presence of crystalline water ice and silicates in the CSE of the star (Hoogzaad et al. 2002). Meixner et al.
(2002) have recently modelled the UKIRT imaging data of Skinner
et al. (1994) to provide a structural model of the CSE.
In this paper, we present mid-IR imaging of HD 161796 using the
OSCIR camera on the 8.1-m Gemini North Telescope. The resulting
spatial resolution allows us to image the thermal emission from the
warm dust and to resolve the structure of the inner envelope. The
observations are modelled using an axisymmetric radiation transport
(RT) code to determine the detailed density distribution of dust
within the CSE.
2 O B S E RVAT I O N S A N D DATA R E D U C T I O N
Imaging observations of HD 161796 were made on 2001 July 12
using the University of Florida mid-IR camera OSCIR, mounted
at the Cassegrain focus of the 8.1-m Gemini North Telescope on
Mauna Kea, Hawaii. This arrangement provides an image scale of
0.084 arcsec pixel−1 and a field of view of 11 × 11 arcsec2 . The
standard chopping and nodding technique was used to correct for the
thermal background with a chop frequency of 3 Hz and a chop throw
of 15 arcsec. Frame times were 10 and 26 ms, respectively, through
the broad- and narrow-band filters, with approximately 4 min of onsource exposure time for each filter. Flat-field images were obtained
for each filter by exposing on sky and on a polystyrene flat-field
source without chopping and nodding and the flat-field constructed
using the OFLAT task, which is part of the GEMINI package within
IRAF. The observing details are summarized in Table 1.
The observations were reduced using the OREDUCE tasks in the
GEMINI IRAF package to produce a single flat-field-corrected image,
comprising the average of the chop and nod differences, for each
filter. Flux calibration was achieved by observing Vega before and
after HD 161796. We found that the Vega fluxes increased by up to
a factor of 3 (depending on filter) between the two measurements,
suggesting that the atmospheric transmission improved substantially
during our observations of HD 161796. We have assumed that this
improvement was linear with time and have interpolated to get a
calibration factor for each filter. Although atmospheric transmission
varied during the observations, the image quality remained stable.
Table 1. Details of the observations of HD 161796 through each
filter, showing the central wavelength (λc ), bandpass (λ) and the
integrated flux. The FWHM of the PSF, estimated from observations
of Vega, are also given.
C
Filter
λc
(µm)
λ
(µm)
FWHM
(arcsec)
N wide
S 7.9
S 9.8
S 11.7
Q3
10.75
7.91
9.80
11.70
20.80
5.23
0.76
0.95
1.11
1.65
0.52
0.48
0.48
0.52
0.85
2003 RAS, MNRAS 343, 880–890
Flux
(Jy)
5.9
0.5
8.0
8.1
168.7
881
We have used the Vega observations as an indication of the point
spread function (PSF) and the full width at half-maximum (FWHM)
is quoted for each filter in Table 1. The fluxes obtained by integrating
within a circular aperture containing all of the visible emission at
each wavelength are shown in Table 1. Owing to the uncertainty in
the flux calibration factor, the errors on the fluxes could be as high
as ±50 per cent.
3 R E S U LT S A N D A N A LY S I S
Fig. 1 shows images of HD 161796 through the narrow-band S 7.9,
S 9.8 and S 11.7 filters and the wide-band N and Q3 filters. In the
bottom right of each panel we show a contour plot of the Vega
observation as an indication of the PSF shape. In the S 7.9 filter, an
unresolved peak is seen, which we attribute to emission from the star
itself, with some evidence of faint surrounding nebulosity. This is
consistent with the double-peaked nature of the SED (e.g. Hrivnak
et al. 1989) and the position of the S 7.9 filter at the minimum
between the optical/near-IR and mid-IR parts of the SED, so that
it may contain both photospheric and circumstellar emission. The
slight north-east to south-west (NE–SW) elongation of the peak
resembles the elongation of the PSF, which also indicates that we are
seeing the star. With the assumption that the star is coincident with
the 7.9-µm flux peak, this forms the origin of the coordinate system.
In order to align all of the filters on to a common coordinate system,
a shift in image position on the detector, which occurs between filter
settings, was compensated for using the observations of Vega.
Apart from the short-wavelength S 7.9 filter image, the mid-IR
images are dominated by the extended thermal emission from the
dust shell around HD 161796. In the 10-µm region (S 9.8, S 11.7
and N filters), the appearance is of a round nebulosity with a diameter
of approximately 3 arcsec. The most striking features are the two arcs
of emission positioned either side of the star and superimposed upon
a central brightness plateau. These arcs correspond to the ‘brightness
enhancements’ seen in the deconvolved UKIRT images of Skinner
et al. (1994), which are resolved here for the first time. Beyond the
arcs the surface brightness falls off rapidly. The object has similar
structure at 20 µm but appears more extended with a fainter halo
surrounding the bright central region. The faint halo is elongated in
a N–S direction, giving a total extent at 20 µm of 4.6 × 6.0 arcsec2 .
3.1 Detailed brightness structure
In the N wide image, there is a central ‘spur’ of nebulosity extending
from the eastern arc towards the position of the star. It is possible that
this image contains emission from the star itself, since the N wide
filter includes emission from wavelengths down to 8.1 µm. However,
a similar co-spatial structure is also seen in the 9.8-µm narrow-band
image (which is included within the wavelength range of the N wide
filter) but is broadened into a bar-like structure joining the two arcs
on either side of the stellar position. The structure is absent in the
11.7-µm image and may, therefore, be due to a particular silicate
dust feature radiating within the S 9.8 band.
In Fig. 2 we show both radial and azimuthal profiles passing
through the bright arcs, the peaks of which appear in the same
position relative to the coordinate centre in each filter. The locations
of the profiles are shown in the bottom right panel of Fig. 1. The
radial profile is taken along a line at position angle (PA) 120◦ , which
passes to the south of the coordinate origin, since the peaks are
not positioned diametrically opposite the star. The separation of the
peaks is 1.2 arcsec. It is also clear that, in each filter, the eastern peak
is brighter than the western peak, the intensity ratio being 1.3 ± 0.1.
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T. M. Gledhill and J. A. Yates
S_7.9
N–wide
S_9.8
Q3
S_11.7
Figure 1. Images of HD 161796 and its dust shell through five mid-IR filters. Note that the Q3 filter image has a larger scale so as to show the extended faint
emission. Contours of equal surface brightness are linearly spaced, in mJy pixel−1 and have the following values: N wide – 2 to 14 in intervals of 1; Q3 – 10 to
230 in intervals of 20; S 7.9 – 5, 8, 11; S 9.8 – 2 to 18 in intervals of 2; S 11.7 – 2 to 18 in intervals of 2. The PSF is shown contoured in the lower right corner
of each panel. The bottom right panel shows the location of the radial and azimuthal profiles in Fig. 2, superimposed on the 11.7-µm image with selected
contours. This figure is available in colour in the online version of the journal on Synergy.
The azimuthal profile is taken using a circular annulus with inner and
outer radii of 0.59 and 0.76 arcsec, centred on the coordinate origin.
This profile illustrates the variation in surface brightness with PA
around the star, in particular the contrast between the peaks along
PA 120◦ and the intervening ‘troughs’. The ratio of maximum to
minimum surface brightness from the azimuthal profiles is 2 ± 0.1,
with the exception of the Q3 filter, where it is 1.4 ± 0.1. In addition,
the trough to the NE is deeper than that to the SW.
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2003 RAS, MNRAS 343, 880–890
Mid-IR imaging of post-AGB star HD 161796
883
Q3
S_11.7
S_9.8
N–wide
S_7.9
Figure 3. The dust temperature distribution obtained from the ratio of flux
in the S 11.7 and Q3 filters (see text). Contours are at 95, 100, 105, 110 and
115 K.
Q3
the line joining the peaks. We already know that the dust emission
is not truly axisymmetric, since one peak is brighter than the other,
but it also seems that there must be more than one axis, with a twist
in orientation between the central and outer regions. The bright arcs
are also seen in near-IR polarized light images (Gledhill et al. 2001),
which were interpreted in terms of scattering from the inner edge of
a detached circumstellar dust shell. The near-IR images also show
a tendency for a twist in the symmetry axis between that defined by
the arcs and that of the outer faint halo.
3.2 Dust temperature
S_11.7
S_9.8
N–wide
The multiwavelength imaging can be used to estimate the temperature of the circumstellar dust by making a number of simplifying
assumptions. Assuming that the dust is isothermal along a line of
sight, with temperature T d , that it is optically thin and that the emissivity has a power-law variation with frequency, with index p, then
we can write
Td = (hc/k)(1/λ2 − 1/λ1 )/ ln (Iλ1 /Iλ2 )(λ1 /λ2 ) p+3 ,
Figure 2. Radial (upper) and azimuthal (lower) surface brightness profiles
through the bright arcs in each filter. The locations of the profiles are shown
in the lower right panel of Fig. 1. The data values for the Q3 filter are divided
by 10. This figure is available in colour in the online version of the journal
on Synergy.
(1)
where I λ1 and I λ2 are surface brightnesses at wavelengths λ1 and
λ2 (Dayal et al. 1998). We use the S 11.7 and Q3 band images to
compute the dust temperature, since these contain emission from
circumstellar dust but not from the star and are on the steeply rising
(Wien) part of the SED. If we assume p lies between 0 and 1, then
with p = 0.5 the temperature distribution shown in Fig. 3 is obtained,
with a maximum dust temperature of 120 K. Despite the number
of assumptions, the result is fairly robust: variation of p by ±0.5
results in a temperature variation of ∓20 K.
4 AN AXISYMMETRIC DUST MODEL
The faint outer halo, seen in the Q3 image, is elongated at a
PA of 5◦ , and has a similar spatial extent and orientation to both the
optical (Ueta et al. 2000) and near-IR (Gledhill et al. 2001) reflection
nebulosities. This is to be expected if the scattered light and thermal
emission originate from the same optically thin distribution of dust.
However, the two brightness peaks, seen in all filters apart from the
short 7.9-µm filter, define an axis at a PA of 30◦ , perpendicular to
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2003 RAS, MNRAS 343, 880–890
A 2D (axisymmetric) radiation transport (RT) code is used to model
the thermal emission from the dust in the CSE around HD 161796.
This is based on an original code by Efstathiou & Rowan-Robinson
(1990), modified to include a power-law size distribution of dust
grains, with up to seven different grain materials. The dust temperature for each grain material is calculated separately by the RT
code.
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T. M. Gledhill and J. A. Yates
4.1 Model description and parameters
In order to simulate the observations, we use a simple model for
an axisymmetric shell based on the density distribution of Kahn &
West (1985), with inner and outer radii of r 1 and r 2 . Within the shell
(r 1 r r 2 ), the number density of dust grains, n, is a function of
radial distance from the star, r, and polar angle, θ , such that
n = n 1 (r/r1 )−α (1 + sinγ θ ),
(2)
where n 1 is the dust density at r1 . The radial density fall-off is
controlled by α, and a density contrast of (1 + ) is created between
the equator and pole. The parameter γ determines how quickly the
dust density falls off from the equator to the pole and, therefore,
how much material is concentrated in the equatorial regions.
We assume that the dust grains are spherical with a single powerlaw distribution of grain sizes for all grain materials. Grain radii
range from a min to a max with power-law index q. A dust model
based on silicate grains is adopted in view of the well-established
O-rich chemistry of the CSE of HD 161796 (e.g. Justtanont et al.
1992). Hoogzaad et al. (2002) used a spherically symmetric RT
code to model the UV to sub-mm SED, including the detailed emission features revealed in the ISO spectrum. These authors used
a four-component dust model incorporating amorphous silicates
(Ossenkopf, Henning & Mathis 1992), water ice (Bertie, Labbé &
Whalley 1969; Warren 1984) and a small proportion (10 per cent)
of crystalline enstatite and forsterite, to fit the emission features. We
have used the same basic components in our model. The water ice
is assumed to exist as a coating on a proportion of the amorphous
silicate grains, with the remainder being uncoated. The radius of
the coated grains is assumed to be proportional to the core radius,
a c , so that a = f a c , and the coating thickness is a c ( f − 1). The
relative proportion of each grain type, the coating thickness and the
grain size distribution are treated as free parameters, since our 2D
RT calculation may be expected to yield different constraints to the
spherically symmetric model of Hoogzaad et al. (2002). For each
grain material the absorption and scattering efficiencies are calculated for the size distribution using Mie theory. We have used the
BHMIE (bare grains) and BHCOAT (coated grains) programs (Bohren
& Huffman 1983) to do this.
Once the grain model is fixed, then T d at each point in the shell is
determined by the stellar temperature, T ∗ , the stellar SED and the
ratio of the inner shell radius r 1 to the stellar radius r ∗ .
4.2 Fitting the SED
A two-stage approach to determining the best model fit was adopted.
First we found the best fit to the observed SED and then the resulting
2D model was used to find the best fit to our OSCIR imaging observations. This approach was successful since the parameters used
to tune the fit to the images (θ , , γ ) have only a small effect on the
SED.
The fit to the 10–20 µm region of the SED depends strongly on
the dust temperature, which is determined mainly by the ratio of the
stellar radius to the inner shell radius, r ∗ /r 1 . The ratio of flux in the
11.7- and 20.8-µm OSCIR filters indicates a maximum dust temperature of T d = 120 ± 20 K (Section 3.2). The best fit to the SED
was achieved with r ∗ /r 1 = 1.8 × 10−4 , giving dust temperatures of
126, 117 and 77 K at the inner shell boundary for the bare amorphous silicates, water ice-coated silicates and crystalline silicates,
respectively. The crystalline silicates are cooler since they absorb
less efficiently (than O-rich silicates) in the UV–optical region, but
radiate more efficiently at longer wavelengths.
The proportion of water ice-coated grains was determined by the
need to fit the 43- and 60-µm water ice emission features and the
3-µm absorption feature. We found that including more than 40 per
cent by number of water ice-coated grains resulted in a 3-µm absorption feature that was too deep (such a feature is not evident in
the ISO spectrum). Conversely we find that less than 40 per cent of
coated grains in the mixture results in a 60-µm feature that is too
weak. The strength of the water ice features also depends directly
on the coating thickness. We find that if f 1.3 then the 43- and
60-µm features can be fitted reasonably well, but the 3-µm absorption feature is too strong. A mixture with 40 per cent by number of
grains with an ice coating given by f = 1.2 is the best compromise.
The modelled fit to the 43-µm feature appears broader than the data
(in part due to insufficient resolution in our wavelength grid) and
may indicate that a more sophisticated dust model is required with,
for example, different grain size distributions in the inner and outer
envelope.
A proportion of crystalline silicate grains are included in the grain
mixture. The wavelength grid used in our RT calculation is too
coarse to sample and fit the crystalline silicate emission features
seen in the ISO spectrum. However, the fit to the 10-µm amorphous
silicate feature places an upper limit of 40 per cent by number of
amorphous grains in the mixture; including a higher proportion of
amorphous silicates results in a 10-µm bump that is too strong.
We therefore conclude that the remaining 20 per cent of grains are
crystalline silicate.
The grain size distribution and dust density are constrained by
the need to fit simultaneously the UV/optical/near-IR region of the
SED and the mid-IR flux peak between 20 and 60 µm. The height
of the mid-IR peak depends strongly on the total amount of dust
in the shell and hence on the optical extinction (AV ). Increasing
AV results in more mid-IR flux but also increased extinction in the
UV/optical region. We found that only a very limited range of grain
size parameters and extinctions could satisfy both requirements. In
particular, the fit to the UV/optical region required a large population
of small (∼0.01 µm) grains and a steep size distribution power-law
index (q = −6.0). Such a steep power-law index means that the
upper grain size limit is only poorly constrained, and so we have
assumed a max = 2 µm.
With this small grain model, we found that the best fit to the
UV emission was obtained by assuming a Kurucz profile for the
stellar spectrum with an effective temperature of T eff = 7500 K and
log(g) = 0.5. Although this gives a good fit to the UV section of
the SED, too much flux is produced in the visible by the model,
suggesting that the Kurucz approximation may not be appropriate
in this region. We have assumed a value of α = 2.0, corresponding
to constant mass loss, since our observations do not constrain this
parameter particularly well.
The outer dimension of the shell, r 2 , influences the shape of the
SED in the far-IR region (longward of 60 µm). Increasing r 2 results
in a larger proportion of cooler dust and more far-IR emission. The
need to fit the 850-µm SCUBA flux point leads to r 1 /r 2 = 0.08. The
final fit to the SED is shown in Fig. 4, with the model parameters
given in Table 2.
4.3 Fitting the OSCIR images
In Fig. 5 we show model images at a wavelength of 11.7 µm, for
comparison with the OSCIR 11.7-µm image. The model images
have an equivalent pixel scale to the OSCIR data and have been
smoothed to simulate the 0.5-arcsec seeing of the observations. The
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Mid-IR imaging of post-AGB star HD 161796
Figure 4. The final model fit to the spectrum of HD 161796 from UV to
sub-mm (solid line). The squares are IUE data and the thick solid spectrum
is SWS and LWS ISO data (Hoogzaad et al. 2002). Asterisks represent the
optical and near-IR flux points (Fernie & Garrison 1984) and the triangle is
the 850-µm flux (Gledhill et al. 2002). The open circles are fluxes from our
OSCIR measurements. The model parameters are given in Table 2.
Table 2. Parameter values for the best-fitting model and derived
parameters assuming a distance of 1.2 kpc to HD 161796. Numbers
in brackets are powers of 10.
Parameter
Value
Model parameters
1.8 (−4)
r ∗ /r 1
r 1 /r 2
8.0 (−2)
α
2.0
5.0
γ
3.0
θ (deg)
10
AV (mag)
1.2
7500 K
T eff
Dust parameters
Bare Sil
0.4
Coated Sil
0.4
f
1.2
Cryst. Sil
0.2
a min (µm)
0.01
2
a max (µm)
q
−6.0
Derived parameters
r 1 (cm)
1.35 (16)
1.68 (17)
r 2 (cm)
1.52 (−4)
n 1 (cm−3 )
M d (M )
2.96 (−3)
35
r ∗ (R )
L (L )
3.44 (3)
Description
Ratio of stellar to inner shell radius
Ratio of inner to outer shell radius
Radial density fall-off (assumed)
Equator-to-pole density contrast
Equatorial density enhancement
Inclination angle
Equatorial extinction
Effective stellar temperature
Number fraction
Number fraction
Ice mantle thickness parameter
Number fraction
Minimum grain radius
Maximum grain radius (assumed)
Grain size power-law index
Inner shell radius
Outer shell radius
Grain number density at r 1
Mass of dust in shell
Stellar radius
Stellar luminosity
polar axis of the shell has been rotated in the plane of the sky to PA
30◦ to match the orientation of the dust shell of HD 161796. Four
values of the inclination angle, θ , are shown: θ = 0 is ‘edge-on’ with
the polar axis in the plane of the sky, whereas θ = 30 has the polar
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2003 RAS, MNRAS 343, 880–890
885
axis tilted out of the plane of the sky by 30◦ , with the NE quadrant
pointing towards us.
As the model is tilted out of the plane of the sky (increasing θ ), the
peaks move so that the line joining them no longer passes through
the star, but to the SW of it. At the same time, the trough between
the peaks to the SW becomes shallower. Both of these effects are
seen in the data and can be used to determine accurately the tilt of
the dust shell as well as the density contrast, (1 + ), between the
equatorial and polar regions.
To determine the best values for the tilt and density contrast, we
calculate azimuthal profiles through the model images, for comparison with the azimuthal profile through the 11.7-µm OSCIR image
(Fig. 2). The results are shown in Fig. 6 for = 5 and four values of the inclination angle, θ. The profiles show clearly how the
peaks move closer together with increasing inclination angle and
how the troughs between the peaks become progressively asymmetric. In particular, the trough closest to the two peaks gradually
fills in. Increasing/decreasing the value of has the effect of increasing/decreasing the maximum ratio of peak to trough. Increasing the
inclination, θ, causes the peaks to move closer together and the
troughs to become more asymmetric. The best fit to the OSCIR
image is achieved for θ = 10◦ and = 5. In the OSCIR images,
the SE peak is brighter than the NW peak by a factor of 1.3. The
model fits indicate that this increased brightness is an excess over
that expected for the best-fitting model, and is most likely due to an
increase in dust density in the SE peak over and above that produced
by an axisymmetric model.
In Fig. 7 we show model images at wavelengths of 7.9, 9.8, 11.7
and 20.0 µm, using the inclination of θ = 10◦ determined above, for
comparison with the OSCIR images in Fig. 1. At 7.9 µm, the star is
visible as a central peak, with the shell seen faintly to either side, as
in the OSCIR images. At wavelengths longer than 9 µm the circumstellar emission dominates and the equatorial density enhancement
produces two arcs of emission, one on either side of the star, which
is no longer visible as a separate peak. The asymmetry caused by
the tilt of the shell, with the emission peaks lying along a line that
passes to the SW of the star (detailed above), is particularly evident
in the 9.8-µm image, becoming less evident at longer wavelengths.
This confirms that these asymmetries, evident for a tilted shell, are
optical depth effects. For a completely optically thin shell, no such
asymmetry with tilt should be observed. For the small grain model
we have used, the optical depth at 11.6 µm is still ∼0.5. The 20-µm
model image appears more extended, as is the case in the OSCIR
images, due to the contribution from cooler dust further from the
star. The contour levels in the model images have been chosen to
represent the same fractional peak brightness as those in the data.
5 DISCUSSION
5.1 Dust grain sizes
Fitting to the optical portion of the SED fixes the value of AV through
the envelope. This then places constraints on the range of grain
sizes that can produce the mid-IR flux peak. In particular, the grain
model must have the correct balance between extinction efficiencies
in the optical and mid-IR. For silicate grains, the ratio of extinction efficiency, Q ext , at 20 and 0.55 µm increases with decreasing
grain size so that small grains are more capable of producing large
mid-IR flux for a given optical extinction. Specifically, we find that
a min = 0.01 and q = −6 produces the best fit to the optical and
mid-IR parts of the SED, with an equatorial extinction of AV = 1.2.
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T. M. Gledhill and J. A. Yates
θ=0
θ= 10
θ = 20
θ = 30
Figure 5. Model images at 11.7 µm and four inclination angles. The images have been smoothed and rotated to match the OSCIR 11.7-µm image shown in
Fig. 1. The contour levels are at the same fractional brightness of the NW peak as those in Fig. 1.
θ = 30
θ = 20
θ = 10
θ=0
Figure 6. Azimuthal profiles through the 11.7-µm model images shown in
Fig. 5 (dashed lines) and the 11.7-µm OSCIR image in Fig. 2 (solid line).
This compares with AV = 1.4 obtained by Meixner et al. (2002).
If larger grains are used, then for AV = 1.2 too little mid-IR flux
is produced. Increasing the value of AV to compensate produces
too much extinction in the UV/optical part of the SED. This emphasizes the importance of considering the UV/optical part of the
SED when determining the best grain size parameters. In addition,
careful consideration should be given to the stellar spectrum. Using a blackbody approximation will result in too much input stellar UV flux, compared with that expected for an F-type supergiant
spectrum, so that any fit to the UV/optical part of the SED will be
affected.
Both Hoogzaad et al. (2002) and Meixner et al. (2002) used larger
grains in their RT models of HD 161796, choosing q = −3.5 and
a min = 0.18 and 0.2 µm, respectively. Meixner et al. (2002) used a
T eff = 7000 K blackbody source so that their model includes too
much UV flux. The model of Hoogzaad et al. (2002) is spherically
symmetric, which may account for some differences between their
fit and ours, but they do fit to the UV data. However, they find that
their model predicts a colour excess of only E(B − V ) = 0.06 and
invoke the existence of an additional component of interstellar extinction to fit the observed E(B − V ) = 0.19 (assuming their value
for T eff = 6750 K). For a standard value of the ratio of selective
to total extinction, R = 3.1, the additional colour excess implies an
interstellar extinction of AV = 0.4. However, extinction estimates
for three stars within 5◦ of HD 161796 indicate <0.13 mag of interstellar extinction (Neckel, Klare & Sarcander 1980). An alternative
explanation is that smaller grains are required, since the differential
extinction between B and V is larger for small grains (0.01 µm cf.
0.1 µm). The small grain model used in this paper produces a good
fit to the SED from UV through to submillimetre wavelengths with
no additional component of extinction.
However, the most compelling argument for the existence of small
grains is provided by the observed high degrees of near-IR linear
polarization. Imaging polarimetry in the J and K bands (Gledhill
et al. 2001) indicates up to 20 per cent polarization in the envelope,
even without correction for the unpolarized flux from the PSF of
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Mid-IR imaging of post-AGB star HD 161796
7.9 um
9.8 um
11.7 um
20.0 um
887
Figure 7. Model images at the four OSCIR wavelengths using the parameters given in Table 2 and an inclination angle of θ = 10◦ . The images have been
smoothed and rotated to match the OSCIR data shown in Fig. 1. The contours levels are at the same fractional brightness of the NW peak as those in Fig. 1.
the central star. A similar degree of uncorrected polarization was
observed in the envelope around HD 179821, which, when corrected
for the diluting effects of the overlying stellar PSF, resulted in an
intrinsic envelope polarization of ∼40 per cent (Gledhill & Takami
2001). In order to produce 40 per cent polarization by scattering in
a 3D geometry such as a shell, the grain model has to be capable of
a maximum polarization of between 60 and 80 per cent. To produce
this amount of linear polarization in the near-IR, the grains must
have radii a < 0.2 µm (see fig. 7 of Gledhill & Takami 2001). A
silicate grain model with q = −3.5 produces very little polarization
in the near-IR since too many grains with a > 0.2 µm are included,
which dominate the scattered light even for small a min (0.01). A
steep power-law index (q = −6) ensures that only small grains
contribute, resulting in large degrees of near-IR polarization. Linear
polarization as a function of scattering angle is shown in Fig. 8 for
grains with a min = 0.01 and 0.1 µm and q = −6 and −3.5.
The dust grain model used is, therefore, consistent with near-IR
(scattered light) polarimetry observations and can produce the observed degrees of linear polarization. In addition, scattering within
the detached CSE model will give rise to the observed nebula structure at optical and near-IR wavelengths (Ueta et al. 2000; Gledhill
et al. 2001), producing a centrally brightened nebula in total flux
and a limb-brightened shell structure in polarized flux. This was
demonstrated for the similar case of a detached CSE around the
star HD 179821, where a dust grain size distribution with a steep
power-law fall-off (q = −6) was also required (Gledhill & Takami
2001). We note, however, that our envelope model will not give rise
to the observed elongation along PA 5◦ seen in both the optical and
near-IR images, and which may be due to a prolate elliptical shell
of dust (which is not included in our model).
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2003 RAS, MNRAS 343, 880–890
Figure 8. Linear polarization at 1.2 µm as a function of scattering angle
for four grain size distributions. The solid curves have a min = 0.01 and
the dashed curves have a min = 0.1. The upper curves have q = −6 and
produce high polarization, whereas the lower curves have q = −3.5 and
produce little polarization. The double-peaked structure in the q = −3.5
curves results from a sign change in polarization and will result in a further
decrease in net polarization for this grain model when a range of scattering
angles are summed.
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T. M. Gledhill and J. A. Yates
5.2 Derived star and shell parameters
Hoogzaad et al. (2002) and Skinner et al. (1994) adopt a distance
to HD 161796 of 1.2 kpc. Assuming this distance, we can then
use the angular separation of the emission peaks in the OSCIR
images (1.2 arcsec) to determine the physical parameters of the
envelope. The model results show that the emission peaks occur
at the inner radius of the shell, r 1 , but after smoothing appear to
move inwards slightly. Therefore, the separation of the peaks in
the OSCIR images slightly underestimates the true value of r 1
due to the smoothing caused by the telescope PSF. By matching the pixel scale of the observations and then smoothing the
model results to account for the PSF, we estimate that the true inner radius is a factor of 1.25 larger than indicated by the OSCIR
images, or 0.75 arcsec. The derived parameters are summarized in
Table 2.
Assuming D = 1.2 Kpc then r 1 = 1.35 × 1016 cm, or 900 au.
This lies between the estimates of 586 au (Skinner et al. 1994)
and 1400 au (Hoogzaad et al. 2002) but agrees with the ∼900 au
obtained by Meixner et al. (2002), who also used an axisymmetric
dust model. However, our outer shell radius is larger than that of
previous models, since we require r 2 /r 1 ∼ 12 to fit the 850-µm flux
point, whereas both Meixner et al. (2002) and Hoogzaad et al. (2002)
use r 2 /r 1 < 4. With our derived value for r 2 , the outer boundary
of the shell subtends an angle of 15 arcsec at 1.2 kpc. We note that
this is larger than the 6.5-arcsec (half-intensity) extent indicated
by CO observations (Bujarrabal, Alcolea & Planesas 1992). The
model images (Fig. 5) show that, at 11.7 µm, the surface brightness
falls below a detectable level beyond an offset of ∼1.2 arcsec from
the star, so, even though the shell has a maximum angular extent
of 15 arcsec in our model, only the bright 3-arcsec extent region
is seen.
Likkel et al. (1991) measure an expansion velocity of V exp =
15 Km s−1 from the CO (1–0) profile. Assuming that this value can
also be used for the dust velocity within the shell, then our value
of r 1 implies that the high mass-loss phase responsible for the shell
terminated 285 yr ago, at which point the shell became detached. The
age of the shell (out to r 2 ) is 3565 yr. If the dust has decoupled from
the gas and is travelling faster than indicated by the CO expansion
velocity, then these time-scales will be shorter.
Our derived value for the stellar radius, r ∗ = 2.42 × 1012 cm
(35 R ), when combined with T eff = 7500 K, fixes the luminosity
at L = 3.44 × 103 L . This lies between the values of 3.0 × 103
and 3.6 × 103 L obtained by Hoogzaad et al. (2002) and Skinner
et al. (1994), respectively, for D = 1.2 K pc.
For the grain and envelope model used (Table 2), the number
density of dust grains required to produce an equatorial extinction
of AV = 1.2 is n 1 = 1.52 × 10−4 cm−3 , giving a dust mass in the shell
of M d = 2.96 × 10−3 M (assuming a bulk density of 3 g cm−3 for
silicates and 1 g cm−3 for water ice). This is greater than the M d =
1.7 × 10−3 M obtained by Hoogzaad et al. (2002), which can be
accounted for by our larger (factor of 3) estimate for r 2 . The dust
masses obtained from fits to the full SED are considerably greater
than mass estimates obtained from the far-IR flux. Gledhill, Bains &
Yates (2002) obtained M d = 4.4 × 10−4 M from the 850-µm flux,
which is in agreement with the M d = 3.2 × 10−4 M estimated from
the 60-µm flux (Likkel et al. 1991). For the small grain model used
here, the opacity at 850 µm is χ 850 = 0.54 cm2 g−1 , which is three
times smaller than the value estimated by Gledhill et al. (2001) on
the basis of an approximate grain model. This accounts for a factor
of 3 difference in the dust mass estimate. The remainder may be
due to the approximate nature of the submillimetre flux estimate
(an isothermal assumption) as opposed to the exact RT calculation
obtained in this paper.
A gas-to-dust mass ratio of 240 has been derived for HD 161796
(Hoogzaad et al. 2002), giving a total envelope mass of 0.71 M .
This is in agreement with the CO mass estimate of 0.68 M
(Bujarrabal et al. 2001), especially given the uncertainty in the gasto-dust mass ratio. Taking V exp = 15 Km s−1 , the mass-loss episode
responsible for the shell lasted 3280 yr, which corresponds to an
average mass-loss rate of 2.2 × 10−4 M yr−1 .
5.3 Evolution
The actual mass lost from the star will be greater than we have
calculated, since significant mass loss will have been occurring for
a longer duration than the estimated ∼3000 yr lifetime of the detectable envelope. However, the simulations of Steffen et al. (1998)
show that the mass-loss rate, Ṁ, rises almost linearly over the
∼104 yr prior to envelope detachment, so it is the last stages of mass
loss that contribute most to the envelope mass. In the post-AGB
phase this leads to a steeper density law, at radii beyond ∼1017 cm,
than the r −2 law expected for constant mass-loss rate. This break
in the density law could be taken to delineate the ‘superwind shell’
produced in the final mass-loss phase, and it is the mass of this shell
that we have estimated. Our RT models reproduce the abrupt fall-off
in surface brightness beyond the central 1-arcsec radius bright shell,
using an r −2 density law, suggesting approximately constant massloss rate just before envelope detachment. This is also in agreement
with the Steffen et al. (1998) model (their fig. 19) where Ṁ peaks
at ∼10−4 M yr−1 , giving a constant mass-loss rate for ∼500 yr,
before declining rapidly.
Using the post-AGB mass–luminosity relation of Vassiliadis &
Wood (1994), which they define from their simulations, gives a core
mass M c = 0.56 M for our value of log (L) = 3.54. This would be
consistent with an initial mass in the range 1–2 M , depending on
the mass-loss history on the AGB (Blöcker 1995). This core mass
is very close to the lower limit for the mass of a central star of
a planetary nebula (PN), M c = 0.55 M , below which evolution
to high temperature takes longer than a PN lifetime (Schönberner
1983). However, the evolutionary rate along the constant-luminosity
track is very sensitive to core mass, with the Schönberner (1983)
M c = 0.565 M model evolving to T eff = 3 × 104 K in about
5 × 103 yr. By that time, the inner radius of the dust shell will have
moved out to >1017 cm, so that HD 161796 may become the central
star of a large extended PN.
The decline in mass-loss rate and the subsequent post-AGB evolution are expected to lead to the gradual disappearance of features
such as maser emission from the CSE. Likkel (1989) detected OH
maser emission at 1667 MHz with a velocity of −26 Km s−1 , suggesting that it originated from the redshifted side of the shell. More
recent (1999) measurements with the MERLIN interferometer have
failed to detect this emission (Bains et al. 2003), indicating that the
OH masers may, indeed, have turned off at some point in the last
10 yr.
5.4 Deviations from axisymmetry
The tilted axisymmetric model reproduces most of the observed
mid-IR structure of the dust shell around HD 161796, including
the position and shape of the flux peaks, but cannot reproduce nonaxisymmetric features, such as the difference in brightness between
the two peaks. In this respect, HD 161796 is remarkably similar to
the post-AGB carbon star HD 56126 (IRAS 07134+1005), which
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Mid-IR imaging of post-AGB star HD 161796
also has a dust shell with one peak brighter than the other (Jura, Chen
& Werner 2000). Similar asymmetric brightness structure, although
less pronounced, is also seen in mid-IR images of the young PN,
IRAS 21282+5050 (Meixner et al. 1993). One possible explanation
for the brightness asymmetry in these objects is that the brighter peak
is closer to the star than the fainter one, and therefore hotter. Jura
et al. (2000) suggest that this is possible if the post-AGB star is
in a wide binary and, therefore, not central within the dust shell.
However, the temperature image shown in Fig. 2 indicates that both
peaks have the same dust temperature to within 5 K, so that, in
the case of HD 161796 at least, the brighter peak must have more
dust. Dayal et al. (1998) also reproduce the brightness asymmetry in
HD 56126 using a simple cylindrical model with 30 per cent more
dust in one half of the cylinder. The question then is how to generate
a non-axisymmetric dust distribution. The usual interpretation of the
axisymmetric dust shell model (e.g. Dayal et al. 1998; Meixner et al.
1997, 2002; this paper) is that mass loss from the stellar equator is
enhanced relative to that from the poles, so that the polar axis lies
perpendicular to the line joining the peaks in the mid-IR image.
Jura et al. (2000) suggest an alternative explanation in which the
peaks result from a polar outflow that persists for 500 yr after the
equatorial flow has abated, so that the polar axis is now along the
line joining the mid-IR peaks. If the outflow from one pole is greater
than from the other, then an asymmetric dust density could result.
In this scheme, the elongated elliptical nebula seen in the optical
and near-IR images (Ueta et al. 2000; Gledhill et al. 2001) and in
longer-wavelength mid-IR images (e.g. the Q3 band image of Fig. 1)
results from the equatorial flow. One difference between these two
models is that in the Jura et al. (2000) model the elliptical shell will
be oblate, whereas in the ‘conventional’ interpretation it is prolate.
Imaging polarimetry results for HD 161796 (Gledhill et al. 2001)
show that the degree of polarization is higher along PA 5◦ than along
the orthogonal direction. The simplest explanation for this is that
scattering is occurring in a prolate geometry, where scattering angles
at the poles (PA 5◦ ) are more confined than those at the equator. In
the case of HD 161796 this then favours an interpretation in which
an equatorial density enhancement is responsible for the mid-IR
peaks, but does not explain why one peak is brighter than the other.
Meixner et al. (2002) use a density distribution incorporating an
elliptical ‘mid-shell’ to simulate the optical images of HD 161796.
As already mentioned, this elliptical nebula is also seen in the Q3
band images (Fig. 1) and so must represent a dust density enhancement along PA 5◦ . However, it is not clear how this elliptical midshell would arise in conjunction with the inner, orthogonal, equatorial dust enhancement (responsible for the mid-IR peaks) unless
there were both polar and equatorial flows during the final stages of
AGB mass loss. However, magnetohydrodynamic (MHD) simulations of the η Car nebula suggest that in some cases such simultaneous outflows are possible (Matt & Balick 2002). An alternative
explanation is that the extension along PA 5◦ is due to a faster
wind operating after the star has left the AGB, and after the massloss phase responsible for the equatorial density enhancement has
ceased. With a current stellar radius of 35 R and mass 0.56 M ,
the escape velocity is now V esc = 78 Km s−1 . The relationship derived by Vassiliadis & Wood (1994) suggests that the wind velocity
V w ∼ V esc for M c = 0.6 M and log(T eff ) = 3.88. There is evidence
for a faster wind component in the broadened wings of the CO profile (Likkel et al. 1991), which extend 25 km s−1 from line centre,
and Bujarrabal et al. (2001) estimate that the fast flow may account
for ∼15 per cent of the envelope mass. The interaction of this faster
wind with the dense, slower, equatorially enhanced AGB wind is
exactly the scenario described by the generalized interacting stellar
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winds (GISW) model (e.g. Kahn & West 1985; Mellema & Frank
1995) developed to explain the bipolar morphologies of PNe. The
faster and more tenuous wind ( Ṁ ∼ 10−7 M yr−1 at this stage)
would be deflected by the equatorially concentrated AGB shell and
blow mainly along the polar direction, extending the inner dust shell
in this direction.
Several mechanisms for the formation of equator-to-pole density contrasts involve binary companions that can either spin-up the
mass-losing star to create an axisymmetric wind or interact tidally
with the spherical AGB wind (see Frank 1999, for a review). In simulations of the interaction of a detached binary with an AGB wind,
Mastrodemos & Morris (1999) create envelope geometries ranging
from mildly aspherical to highly bipolar. Their intermediate ‘elliptical’ geometry, with a typical density contrast of between 5 and 7,
corresponds closely with our envelope model for HD 161796 (factor of 6 density enhancement). Interaction of a post-AGB wind with
this envelope will lead to a prolate shell, as observed.
We have already mentioned a twist in axis between the inner and
outer regions of the dust shell around HD 161796 (Section 3.1),
which is particularly apparent in the Q3 band image (Fig. 1). A
curving polar axis is perhaps not surprising if the AGB torus is
irregular, with more dust to the SE of the star than to the NW,
as suggested. Alternatively, the post-AGB wind could in itself be
asymmetric and precessing, if it originates from magnetic cool spots
for example (Soker 1998). It remains to be seen whether binary
models can produce the sort of non-axisymmetric structure that we
see in HD 161796 and in other similar objects such as HD 56126
and IRAS 21282+5050.
6 CONCLUSIONS
Resolved images of the mid-IR thermal emission from the dust shell
around the post-AGB star HD 161796 are presented that clearly
show the inner boundary of a detached CSE (radius 0.6 arcsec). A
basic axisymmetric structure is revealed with a pair of bright peaks
seen on either side of the star. However, deviations from axisymmetry are evident, with the SE peak being ∼1.3 times brighter than
the NW peak along with a gradual twist in the symmetry axis between the central region and the fainter outer halo visible in the
longer-wavelength 20-µm image.
We model the mid-IR images, along with the SED from UV to
submillimetre wavelengths, using an axisymmetric radiation transport (RT) code. We find that the SED is best-fitted using a small
grain model, with minimum grain size 0.01µm and a steep (∝a −6 )
power-law size index. Support for small grains is also provided by
previous imaging polarimetry observations, which indicate up to
40 per cent linear polarization in the shell. The models reproduce
all of the axisymmetric features seen in the images, in particular the
detailed appearance and location of the mid-IR flux peaks. We find
that the strength and position of these peaks (relative to the star)
places strong constraints on the equator-to-pole density contrast
(6 : 1) and on the inclination of the symmetry axis to the plane of
the sky (10◦ ).
By assuming a distance of 1.2 kpc to HD 161796, we determine the physical parameters of the star and envelope. The derived
luminosity of 3.44 × 103 L indicates a current stellar mass of
0.56 M . The results are consistent with a star of initial mass between 1 and 2 M that lost ∼0.7 M at the end of the AGB and
is now a few hundred years into its post-AGB evolution. Given the
low core mass, it is likely that HD 161796 will take about 5000
yr to evolve to a temperature of ∼30 000 K, by which time it will
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T. M. Gledhill and J. A. Yates
be the central star of an extended (>15 arcse diameter) and mildly
asymmetric PN.
We suggest that the equatorial density enhancement is most likely
due to tidal interaction between the AGB wind from HD 161796 and
a detached binary. In addition, the elliptical shell extended along PA
5◦ may result from the interaction of a faster, post-AGB wind with
the AGB shell. The object may then be in the early stages of an
interacting stellar winds phase in which the appearance of a future
PN is being shaped.
AC K N OW L E D G M E N T S
We thank the staff of the Gemini Observatory, which is operated by
the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini
Partnership. Observations were made with the mid-infrared camera
OSCIR, developed by the University of Florida with support from
NASA. We especially thank the OSCIR support team, and in particular Scott Fischer, for their expert help with the observations and
subsequent advice on data reduction. Seppe Hoogzaad is thanked
for providing the ISO and IUE data in electronic form. We thank
Andreas Efstathiou for allowing us to use and modify his original radiation transport code. Calculations were performed using
the HiPerSPACE Computing Facility located at University College
London. The referee is thanked for many helpful comments.
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