Multi-spectral Observations of Lunar Occultations: I. Resolving
The Dust Shell Around AFGL 5440
Paul M. Harvey1 and Andrew Oldag1
ABSTRACT
We present observations and modeling of a lunar occultation of the dust-
enshrouded carbon star AFGL 5440. The observations were made over a contin-
uous range of wavelengths from 1 – 4µm with a high-speed spectrophotometer
designed expressly for this purpose. We find that the occultation fringes cannot
be fit by any single-size model. We use the DUSTY radiative transfer code to
model a circumstellar shell and fit both the observed occultation light curves and
the spectral energy distribution described in the literature. We find a strong
constraint on the inner radius of the dust shell, Tmax = 950 K ± 50K, and op-
tical depth at 5µm of 0.5 ± 0.1. The observations are best fit by models with
a density gradient of ρ ∝ r−2 or the gradient derived by Ivezić & Elitzur for a
radiatively driven hydrodynamic outflow. Our models cannot fit the observed
IRAS 60µm flux without assuming a substantial abundance of graphite or by
assuming a substantially higher mass-loss rate in the past.
Subject headings: stars: AGB and post-AGB – techniques: high angular resolu-
tion – stars: mass loss
1. Introduction
Mass loss from post-main-sequence stars provides a large fraction of the heavy element
abundance and solid particle content of the interstellar medium (e.g. Wallerstein & Knapp
1998; Ferrarotti & Gail 2006). The mechanism(s) of the mass loss during the AGB phase of
stellar evolution are thought to involve both radiation pressure and stellar pulsation (Suh
1997; Wallerstein & Knapp 1998; Schröder et al. 1998), but most details of this process are
not well understood. Many uncertainties about these processes can be clarified by studies of
the spatial structure of circumstellar mass-loss shells. For example, a number of molecular
1Astronomy Department, University of Texas at Austin, 1 University Station C1400, Austin, TX 78712-
0259; pmh@astro.as.utexas.edu, feardrew@astro.as.utexas.edu
http://arxiv.org/abs/0704.0256v1
– 2 –
line studies of the extended envelopes around AGB stars have found strong evidence for
periodic variations in mass-loss rates leading to the appearance of “rings” in the radial
distribution of molecular emission lines, (e.g. Fong, Meixner & Shah 2003, Olofsson et al.
1996). Very deep, sensitive imaging studies have also found similar phenomena in the dust
around the most nearby extreme example of these objects IRC+10216 (Mauron & Huggins
2000). In order to study the inner regions of these circumstellar shells, however, angular
resolutions well under 1 arcsec are required. For example, at a distance of 1 kpc, the
dust evaporation radius around a 104 L⊙ star corresponds to an angular radius of 20 milli-
arcsec (mas). Speckle interferometry and more recently adaptive optics observations have
enabled resolutions of order 0.1 arcsec (Hofmann et al. 2001; Biller et al. 2005), while lunar
occultation observations and multi-aperture interferometry have pushed angular resolutions
to the milli-arcsecond level, e.g. reviews by Quirrenbach (2004) and Monnier (2003).
Until recently most interferometric observations have been made in typically one or two
relatively broad bands. We present here observations of a lunar occultation of the star AFGL
5440 (aka OH 06.86-1.5, IRAS 18036-2344), made with a high-speed infrared spectropho-
tometer, pMIRAS (Harvey & Wilson 2003), developed as a prototype for a more ambitious
instrument now nearing completion. This star has been classified as a carbon-rich AGB
star on the basis of its IRAS LRS spectrum (Zuckerman & Dyck 1986; Volk & Cohen 1989;
Kwok, Volk & Bidelman 1997). Groenewegen et al. (2002) have estimated the distance to
be 2.25 kpc. Near-infrared through far-infrared photometry of the source has been summa-
rized by Guglielmo et al. (1993) and more recently by Guandalini et al. (2006), including a
combination of ground based photometry, the IRAS values, and more recent MSX results.
The reported distance and photometry imply a luminosity of 1.4×104 L⊙.
In addition to the observations of AFGL 5440, we also discuss observations that we
have made of two “calibration” stars in order to understand the limitations of our obser-
vation/analysis process. These objects are cool stars with no detectable circumstellar dust
shell based on their near-infrared and IRAS colors, IRC+00233 (M7) and HD 155292 (K2).
Our observations cover the entire 1 - 4µm spectral region with a resolving power that
varies from ∼ 20 at the shortest wavelengths to ∼ 100 at the long end. Our time resolution
of 8 msec permits an effective angular resolution of a couple milli-arcsec, with the exact
resolution being a strong function of the signal-to-noise ratio as discussed later. The broad
wavelength coverage allows us to observe simultaneously the Fresnel fringe pattern of the
obscured central star at the shorter wavelengths together with the circumstellar dust emis-
sion from the warmest part of the dust distribution. In §2 we describe the details of the
observations and instrumental parameters and the basic data reduction process. Then in §3
we describe various ways we have modelled the star+shell in order to determine the limits
– 3 –
on the circumstellar shell structure placed by our observations. Finally in §4 we summarize
the implications of these results for the mass loss of this object.
2. Observations and Data Reduction
The observations of AFGL 5440 were made during an immersion occultation event
on 28 Aug 2001 at approximately 02:44:00 UT. The elevation of the Moon at the time of
the event was 36◦, and the Sun was 17◦ below the horizon. The sky conditions were not
completely photometric but cloud cover was minimal and intermittent. The position angle
of the occultation event on the lunar limb was 54◦, and the lunar phase was 0.72. We used
the pMIRAS instrument on the McDonald Observatory 2.7-m telescope. The details of the
instrument have been described by Harvey & Wilson (2003), but we summarize the most
important characteristics here. The instrument is essentially a long/wide slit, high-speed
spectrophotometer using a NaCl prism to disperse the light from the slit, which is then
imaged onto a 32×100 pixel portion of a 2562 InSb array detector. The slit width is chosen
to be the minimum acceptable in order to minimize the background on the detector within
the limitations imposed by the seeing conditions. For these observations the slit width was
set at about 5 arcsec for the typical seeing of 1.5 arcsec. The detector is read-out every 8
msec, with photon integration occuring over essentially the full 8 msec time. Therefore, the
Fresnel occultation fringe pattern is averaged over this 8 msec time (as well as over the 2.7-m
telescope aperture). Because we use a refractive dispersive element, the dispersion/spectral
resolution is not equal at all wavelengths; the highest dispersion is at the longest wavelengths,
a feature that minimizes the background photon count at those wavelengths. On average
over the 1 – 4µm waveband covered by the instrument, one pixel corresponds roughly to
λ/∆λ = 100. Because of uncompensated seeing effects and the lower spectral dispersion
at shorter wavelengths, the true resolving power at the shortest wavelengths is R ∼ 20.
In the spatial direction the plate scale is 0.4 arcsec/pixel. The instrument is read-noise
limited shortward of 2.5µm and background-limited longward of 3µm. A typical observation
consists of taking 5000 frames at a time roughly centered on the occultation event. This
is accomplished by using a buffer that holds the most recent 5000 frames and terminating
the data acquisition a few seconds after the event is observed on a real-time display. This
is an important feature since the predicted times of occultation events are often in error by
as much as 10 seconds due to irregularities in the lunar limb as well as imperfect stellar
astrometry. Our observations of the occultation event of the comparison star, IRC+00233,
were obtained during an immersion event on 29 Jun 2001, and those of HD 155292 were
obtained during an immersion event on 26 Aug 2001.
– 4 –
The data reduction process consists of several typical steps. Because the spectrum is
being observed with much higher time resolution than the seeing timescale, the spectrum
moves around by several pixels over the course of an occultation event. Therefore, to con-
struct a light curve with minimal spectral blurring, the images must be shifted to correspond
to the same wavelength/pixel scale. This is done with a simple cross-correlation algorithm
that works well for the high S/N data discussed here. The spectrum is also not perfectly
aligned with the X/Y axes of the detector, so we take out this tilt as well during the pro-
cessing to simplify later steps. Because we use a “long slit”, ∼ 10 arcsec, we can use the sky
measurements on either side of the stellar spectrum to provide an accurate and high-time-
resolution sky subtraction. For the data discussed here we produce a weighted average in
the spectral direction that is two pixels wide and sum the pixels in the spatial direction that
have detectable signal. We have experimented with more elaborate photometric extraction
schemes, but this technique appears to produce S/N ratios as high as any more complex
algorithms. We have also experimented with various flat-fielding methods but have found
only a small improvement in S/N with these methods. The end result of the data reduc-
tion process is a sequence of ∼ 100 light curves for which we extract a few hundred frames
centered on the occultation event. The frames that are taken well before the Fresnel fringe
pattern of the occultation becomes evident are used to estimate the noise level in the data,
due both to read-noise, background photon statistics, and the often non-negligible amount
of seeing/scintillation noise caused by the atmosphere.
Because the exact location of the spectrum on the detector varies both due to seeing
and between observing runs after adjustments to the instrument, we perform the wavelength
calibration by fitting the NaCl dispersion function to the observed positions of the J, H, K,
and L atmospheric transmission maxima in the actual data for each occultation event. The
accuracy of this calibration is probably good to ± .01 λ throughout the 1 – 4µm region that
is observed. Because of variable instrumental efficiency depending on the placement of the
star image on the input slit, and the common occurrence of non-photometric sky conditions
during occultation events, we specifically do not attempt to derive a flux calibration for our
data. We have, however, compared the relative signal from AFGL 5440 to that of relatively
well characterized stars observed on the same night and conclude that the stellar magnitudes
in the published literature for AFGL 5440 are consistent with values that we would have
derived from our signal strengths to within ± 30%.
– 5 –
3. Source Modeling
The fringe pattern of a lunar occultation event is a convolution of the pattern for a point
source over several parameters that all act to blur the fringes. These parameters include:
the telescope aperture, the integration time of the detector, the wavelength bandwidth of
the observation, and, most importantly, the source size/structure. In order to extract the
source size or more detailed properties of the spatial structure, the typical procedure is to
model the combination of all the above “blurring” parameters with various possible source
models to find the best fit to the data (e.g. Nather & McCants 1970; Richichi et al. 1995).
An additional uncertainty in the observations is the basic frequency of the fringe pattern,
i.e. the speed of the lunar shadow. Although this parameter is calculated by the software
that we use to predict occultation events, small uncertainties in the shape of the lunar limb
(roughness due to craters, etc) can produce differences in the predicted shadow speed up
to several tens of percent. Therefore, this parameter must also be fit in addition to the
parameters that blur the fringes.
We began our modeling process by assuming a uniform disk as the simplest possible
model with which to try fitting the data for the observed objects, AFGL 5440, IRC+00233,
and HD 155292. We use a simple χ2 test for the best model, allowing one or more parameters
to vary during the process. Typically we first allow both the size and lunar shadow velocity
to vary until we find an approximate fit to both. This fit can be done either individually at
each wavelength or globally using the entire waveband.
3.1. Comparison Stars
For IRC+00233 and HD 155292 we assumed that a single source size was likely to be
appropriate for the entire wavelength range within our observational uncertainties, and we fit
the observations globally for source size and lunar velocity. Rough estimates of the angular
sizes of these two stars can be derived simply by assuming that they are blackbodies of the
effective temperatures given by their spectral types. Using the empirical relation between
angular size and B-K color from van Belle (1999) for IRC+00233 (B = 11.06, K = 1.95), we
would expect an angular size of 3.5 mas; the star is, however, likely to be mildly variable, so
the size at the time of our observations might have been different by ± 20%. For HD155292
(B = 11.0, K = 4.9) a similar calculation gives an angular size of 0.6 mas. Since typical
departures from a uniform disk model are at the level of 10 – 30% (e.g. Thompson, Creech-
Eakland & van Belle 2003; and Scholz 2003), the resolution required to detect them reliably
for even IRC+00233 is below 1 mas. Based on tests we have done with model data, this is
beyond the capabilities of our current data set which is limited by both spectral resolution
– 6 –
and signal-to-noise ratio to accuracies on the order of ±2 mas.
The best fit size for IRC+00233 is between 4.5 and 5.0 mas. Figure 1 shows observed
and model light curves for a model assuming a 4.5 mas uniform disk for a subset of the
wavelengths observed. Figure 2 shows the χ2 and signal-to-noise ratio as a function of
wavelength over the entire observed band for this model. Both figures show that this model
provides a very good fit to the observations except for a small range of wavelengths around
∼ 1.7µm where a substantially larger size would provide a better fit. We do not have a
good explanation for this discrepancy; it may be due to some systematic noise effect or to
a real difference in the stellar photosphere in that region. For comparison Schmidtke et al.
(1986) observed this same star in an occultation event using narrow-band filters near 1.6 and
2.2µm. They found a size at those wavelengths of ∼ 3 mas, similar to but smaller than our
calculated blackbody size. For HD 155292 all uniform-disk models with a size less than about
3 mas were able to fit the data reasonably well (Figures 3 and 4). Since the blackbody size
of the star is less than a milli-arcsecond, this is consistent with the expected uncertainties in
our data and modeling. The signal-to-noise ratio for this star was low enough that we had
no effective narrow-band information beyond 2.5µm, and at the shorter wavelengths some
periodic electronic pickup had a non-negligible effect on the observed fringe patterns as well.
Note that for both these comparison stars there are wavelengths with reasonable S/N as
shown in Figures 1 and 3 where there is a less than adequate fit, so these are difficult to
explain solely as due to telluric atmospheric absorption effects.
3.2. AFGL 5440
For AFGL 5440 a quick glance at the observed light curves (Figure 5) indicated that a
single source size was unlikely to fit over the entire 1 – 4µm bandwidth (Harvey & Wilson
2003). This suggests that we are seeing the combination of the emission from the central
star and a circumstellar shell of material due to mass loss from the star. To demonstrate
the poor fit with a single size uniform disk, we show in Figures 5 and 6 the results of trying
to fit the data with one example uniform disk, 11 mas. As can be seen in the plots of χ2
as well as the observed versus model light curves, the 11 mas disk provides a passable fit in
the mid-range of wavelengths, 2.5 – 3.2µm, but produces fringes that are too sharp at the
longer wavelengths and too broadened at the shortest wavelengths.
This result motivated us to pursue a full radiative transfer model for the object that
could be used to compare both the size constraints provided by our occultation data and the
spectral energy distribution (Guandalini et al. 2006) which contains important and different
information about the relative amount of dust at different temperatures. The DUSTY code
– 7 –
(Ivezić, Nenkova & Elitzur 1999) was originally created, in fact, for modeling the emission
from AGB stars surrounded by mass-loss shells. Its output includes model source images
as well as the total energy distribution, so it is ideal for our purposes. Our approach to
using the code was to choose a particular combination of input parameters and then vary
the dust optical depth to find the best fit to the energy distribution for those parameters.
We then used the output source images that were computed as a function of wavelength
to calculate expected occultation fringes for the model and compared those to the observed
fringes. Since AFGL 5440 has been classified as a carbon-rich star, we assumed a carbon-
rich dust composition, typically some combination of amorphous carbon, silicon carbide, and
graphite as the major constituents. The other critical parameters for the models are the dust
temperature at the inner radius and the radial density gradient. The outer radius of the dust
shell makes essentially no difference to the observed characteristics at λ < 60µm as long as it
is at least 100 times the inner radius. The goal of our modeling was to find some reasonable
fit to our occultation data and the rough spectral energy distribution for the circumstellar
dust shell; we have not attempted to extract details of the stellar photosphere or attempt
a thorough examination of all possible dust size/composition models since our data do not
bear directly on those issues for reasons of wavelength coverage and spectral resolution. In
particular, we did not try to find any better than superficial agreement with the IRAS LRS
data.
We explored more than 200 models to understand the effect of varying the input pa-
rameters on the quality of the fit. Basically all the models that provided an approximate fit
to the occultation observations and the spectral energy distribution had several features in
common. First, the dust temperature at the inner radius of the dust shell was of order 950K
± 50K. Models with a maximum dust temperature below 900 K did not have enough hot
dust to fit the occultation fringes at the longer wavelengths, while models with hotter inner
edges had even more difficulty than the best-fit model in reproducing the energy distribu-
tion longward of 10µm. Secondly, the radial density gradient of models with a reasonable
fit was close to r−2 (or to DUSTY’s calculation of the gradient appropriate for a radiatively
driven wind which approximates an r−2 distribution for large radii). Models with a density
gradient of r−1.8 came closer to producing the IRAS 60µm flux, but did not fit the shape of
the 5 – 20µm energy distribution well. Models with a density gradient of r−2.2 can fit the
energy distribution out to 20µm and also provide a good fit to the occultation results, but
have substantially worse fits to the IRAS 60µm flux than our best fit models. The optical
depth for best fit at the fiducial wavelength of 5µm was typically in the range 0.3 – 0.6.
Finally, the dust composition that provided the best fit included a small amount of SiC
together with comparable amounts of amorphous carbon and graphite. Other carbon-rich
compositions produced reasonable fits except at the longest wavelengths or in the 11µm SiC
– 8 –
feature. Note that there is a range of optical properties for different forms of amorphous car-
bon (Andersen, Liodl,& Hofner 1999) that we did not explore. We experimented with two
grain size distributions, the MRN slope (Mathis, Rumpl & Nordsieck 1977), and another,
the KMH shape (Kim, Martin & Hendry 1994), used by Ivezić & Elitzur (1996) for models
of IRC+10216, that has a smoother fall-off on each end. We found that we could obtain
reasonably good fits with either distribution. Figures 7 and 8 show the fits to the spectral
energy distribution and to the occultation light curves for the best-fit model. Figure 9 shows
the quality of the fit versus wavelength, and figure 10 illustrates the spatial profiles of this
best-fit model. Figures 11 and 12 likewise show for comparison the fits for a model discussed
below that does not use any graphite. Finally, figures 13 and 14 show results for a third
model that fits the energy distribution but gives a poor fit to the occultation results because
of a lack of enough warm dust close to the star.
4. Discussion and Summary
Model dust shells have been computed for a number of carbon-rich AGB stars by various
authors. Le Bertre, Gougeon, & Le Sidaner (1995) and Le Bertre (1997) found that the
energy distributions for nearly two dozen carbon-rich stars could be modelled with very
similar dust shell parameters. They found a common value of maximum dust temperature
of order 950 K with shell density gradient of ρ ∝ r−2 for spherically symmetric shells. The
best fit dust property implied a dust emissivity, ǫ ∝ λ−1.3, consistent with that expected for
an amorphous carbon-rich dust composition as also found by Jura (2004). These conclusions
were enhanced by their ability to fit the energy distributions over a range of phases of the
observed variability of many of the stars. On the other hand, Suh (1997) suggested that a
“superwind” phase of mass loss could improve model fits to the energy distributions for a
number of carbon-rich AGB dust shells by enhancing the emission shortward of 30µm because
of a high rate of mass loss in recent times, e.g. at small radii where most of the emission
would be due to hotter dust. Ivezić & Elitzur (1996) used a self-consistent radiatively driven
hydrodynamic model for the density distribution around IRC+10216 and were able to fit both
the spectral energy distribution and the near-infrared angular visibility data from speckle
observations. Interestingly they derived an inner dust shell temperature substantially lower
than ours and most other studies, ∼ 750K. Winters et al. (1997) computed a full time-
dependent model of periodic outflow from AFGL 3068 and were able to produce a good fit
to the energy distribution and observed light curves. Virtually all of these modeling efforts
used dust emissivities appropriate for some form of amorphous carbon (usually including
SiC), but with no graphite (see also Lorenz-Martins 2001), contrary to our best model fit
above. The model of Ivezić & Elitzur (1996) utilized a grain size distribution that included
– 9 –
substantially larger grains than most earlier models.
Our lunar occultation observations add constraints to these results most directly in
defining the amount of dust in the innermost region around AFGL 5440, since our longest
observed wavelength is 4µm. Basically, our data imply that the density of grains emitting
in the 3 – 4µm spectral region must be sufficiently large to produce the substantial fringe
“blurring” observed in our light curves. Graphically, this amount of emission is illustrated
in figure 10 showing the source profiles for the best-fit model. For any given assumed dust
emissivity, this constraint then implies a fairly narrow range of optical depth and ratio of
near-infrared to mid-infrared dust emission. Thus, we constrain the dust density gradient in
the innermost part of the circumstellar shell. Finally, as mentioned above, the fact that we
were unable to find a satisfactory fit to the data with any model having a maximum dust
temperature lower than 900 K is a strong constraint on the location of the inner edge of
the dust shell. This result follows from the fact that dust cooler than 900 K cannot emit
sufficiently to produce the required amount of 3 – 4µm emission. Note that this temperature
is nearly a factor of two below the expected condensation temperatures for dust around these
stars (Egan & Leung 1995). The physical value of this inner radius for AFGL 5440 for the
dust properties of the best-fit model is 3.7×1014 cm, or an angular radius at the assumed
distance of 2.25 kpc of 11 mas. For reference the angular diameter of the central star is of
order 3 mas, based on a blackbody approximation for its likely photospheric temperature of
2500K ± 300K and 2µm magnitude.
Since our modeling is the first of which we are aware for this particular star over the
entire infrared wavelength region, we also discuss here the constraints on the circumstellar
cloud properties implied by the overall energy distribution. As mentioned above, our best-fit
model utilized roughly equal amounts of amorphous carbon and graphite in addition to the
small amount of SiC required to fit the 11µm feature seen in the IRAS LRS spectrum. This
result is contrary to the large amount of evidence against substantial amounts of graphite
in stars like AFGL 5440. The factor that drove us to include graphite was its relatively flat
emissivity vs. wavelength dependence between 10 and 50µm that enabled us to fit the IRAS
60µm flux. Models with only amorphous carbon and SiC failed to fit that flux by factors of
3 or more. Figures 11 and 12 discussed above show the energy distribution and model light
curves for the best-fitting model that uses only amorphous carbon and SiC, and which uses
the radiatively driven hydrodynamic density gradient of Ivezic & Elitzur (1996) as computed
by DUSTY. The light curves fit the observed occultation data nearly as well as those for the
best-fit model.
Clearly, however, the IRAS 60µm flux cannot be fit by any similar model without
graphite, and substantial modifications would have to be made to the assumed density law
– 10 –
in the outer regions or to the dust emissivity in order to come close to fitting the 60µm
flux. Explaining this problem is beyond the scope of our study, but the fact that there is
abundant evidence for non-constant outflow from carbon stars (Fong, Meixner & Shah 2003;
Mauron & Huggins 2000) provides a convenient (if ad hoc) explanation. If the mass-loss rate
were greater in the past, then the amount of dust at radii appropriate for emission at 60µm
might well be larger than a simple extrapolation from the dust responsible for the 3 – 20µm
emission. This would describe the opposite situation from that proposed by (Suh 1997) who
suggested higher mass-loss rates in the recent past to explain observations of a number of
other similar carbon stars. The radial location of dust emitting strongly at 60µm is of order
1 to a few arcseconds from the star. For an assumed distance of 2.25 kpc and its measured
outflow velocity of 22 km s−1 (Groenewegen et al. 2002), this would correspond to a time
of order 500 years to a couple thousand years in the past for the proposed higher mass-loss
rate. This time scale is comparable to the period of fluctuation seen by Mauron & Huggins
(2000) for IRC+10216.
The fact that we have constrained the absolute value and radial dependence of the dust
density with our observations means that we have constrained the recent dust mass-loss
rate for AFGL 5440 as well. The dust mass-loss rate implied by our derived optical depth
and radial density dependence is Ṁdust = 6.5 × 10
−8 M⊙/yr for the optical constants of
amorphous carbon used by DUSTY (Ivezić, Nenkova & Elitzur 1999). Groenewegen et al.
(2002) computed dust and gas mass-loss rates individually for AFGL 5440 on the basis of the
IRAS 60µm flux for the dust, and millimeter CO observations for the gas. They derived a
gas mass-loss rate of 3.1×10−5 M⊙/yr and dust mass-loss rate of 5.1×10
−8 M⊙/yr implying
a gas-to-dust mass ratio of 600. Interestingly, their dust mass-loss rate is slightly lower than
the value we have derived in spite of their using the 60µm IRAS flux for normalization. This
result reinforces the overall uncertainties in model assumptions and absolute dust opacties,
particularly at longer infrared wavelengths. In any case, a dust mass-loss rate of order 5 –
10×10−8M⊙/yr and gas mass-loss rate a few hundred times larger are consistent with the
data.
In summary, our observations have separately resolved the stellar photosphere and the
inner edge of the circumstellar dust shell around AFGL 5440. We have strongly constrained
the inner radius of the dust shell surrounding the star as well as the near-infrared optical
depth. Our constraints together with the spectral energy distribution suggest a dust density
gradient consistent with that expected for radiatively driven mass loss with the exception
that the far-infrared flux may imply a recent decrease in mass-loss rate from the time when
the far-ir-emitting dust was ejected.
– 11 –
5. Acknowledgments
We thank a number of people and institutions that have supported this work since its
earliest stages. M. Simon greatly encouraged our efforts and provided many useful comments
over the course of this work. He also provided the basic prediction software (developed by L.
Cassar) that we use for determining the times and elements of occultation events. We also
acknowledge illuminating conversations with A. Richichi, S. Guilloteau, D. Evans, and R.
E. Nather and very helpful suggestions from two anonymous referees. D. Wilson developed
the initial versions of a number of the reduction algorithms used in this work and provided
a great deal of assistance during the observations. C. Young provided help in the intricacies
of DUSTY. This project has been supported by: internal McDonald Observatory funding,
NASA Grant NAG5-10458, and NSF grant AST-0096626. We also acknowledge extensive use
of the NASA Astrophysics Data System and SIMBAD, and P. Harvey thanks the University
of Colorado’s Center for Astrophysics and Space Astronomy for graciously hosting him during
a sabbatical while much of this paper was written.
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van Belle, G.T. 1999, PASP, 111, 1515
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This preprint was prepared with the AAS LATEX macros v5.2.
– 13 –
Table 1. DUSTY Models of AFGL 5440
Model Tmax ρ ∝ r
−N τ Amorph C Graphite SiC Size Dist.
K @5µm % %) %)
194 950 -2.0 0.41 40 50 10 MRN1
200 950 -2.0 0.55 95 0 5 KMH2
206 850 rad-flow3 0.45 95 0 5 KMH2
Note. — 1Mathis, Rumpl & Nordsieck (1977) with amin = .005µm; amax =
0.25µm.
2Kim, Martin & Hendry (1994) with amin = .005µm; amax = 0.2µm.
3 Radiatively driven outflow computed by DUSTY as described by
Ivezić & Elitzur (1996)
– 14 –
Fig. 1.— Plots of observed light curves (crosses) versus computed model light curves for
the 4.5 mas uniform disk model of IRC+00233 at a sampling of the range of wavelengths
observed between 1 and 4µm. In each panel the lower curve of triangles shows the difference
of observed minus model.
– 15 –
Fig. 2.— Plots of the χ2 (solid) for the model fit of the 4.5 mas uniform disk to the observed
light curve for IRC+00233 over the range of wavelengths observed between 1 and 4µm.
The observed signal-to-noise ratio is also shown (dashed) as a function of wavelength for
comparison.
– 16 –
Fig. 3.— Plots of observed light curves (crosses) versus computed model light curves for
the 2.0 mas uniform disk model of HD155292 at a sampling of the range of wavelengths
observed between 1 and 4µm. In each panel the lower curve of triangles shows the difference
of observed minus model.
– 17 –
Fig. 4.— Plots of the χ2 (solid) for the model fit of the 2.0 mas uniform disk to the
observed light curve for HD155292 over the range of wavelengths observed between 1 and
4µm. The observed signal-to-noise ratio is also shown (dashed) as a function of wavelength
for comparison.
– 18 –
Fig. 5.— Plots of observed light curves (crosses) versus computed model light curves for
the 11 mas uniform disk model for AFGL 5440 at a sampling of the range of wavelengths
observed between 1 and 4µm. In each panel the lower curve of triangles shows the difference
of observed minus model.
– 19 –
Fig. 6.— Plots of the χ2 (solid) for the model fit of the 11 mas uniform disk to the observed
light curve for AFGL 5440 over the range of wavelengths observed between 1 and 4µm.
The observed signal-to-noise ratio is also shown (dashed) as a function of wavelength for
comparison.
– 20 –
Fig. 7.— Plot of the observed spectral energy distribution of AFGL 5440 versus that
predicted by model 194, the best fit model. The open diamonds show the values from
Guandalini et al. (2006) and Guglielmo et al. (1993). The light grey line indicates the IRAS
LRS spectrum.
– 21 –
Fig. 8.— Plots of observed light curves (crosses) versus computed model light curves for
model 194 for AFGL 5440 at a sampling of the range of wavelengths observed between 1
and 4µm. In each panel the lower curve of triangles shows the difference of observed minus
model.
– 22 –
Fig. 9.— Plots of the χ2 (solid) for the fit of model 194 (the best fit) to the observed
light curve for AFGL 5440 over the range of wavelengths observed between 1 and 4µm.
The observed signal-to-noise ratio is also shown (dashed) as a function of wavelength for
comparison.
– 23 –
Fig. 10.— Plots of the model spatial distributions for AFGL 5440 predicted by model 194,
the best fit model. The curves are drawn for 1.0 and 1.2µm (solid, 1.0µm is the more
extended), and 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, and 4.0µm, with the
longest wavelengths being the most extended of these.
– 24 –
Fig. 11.— Plot of the observed spectral energy distribution of AFGL 5440 versus that
predicted by model 200, the best fit model that does not use graphite as for fig. 7.
– 25 –
Fig. 12.— Plots of observed light curves (crosses) versus computed model light curves for
model 200 for AFGL 5440 at a sampling of the range of wavelengths observed between 1
and 4µm. In each panel the lower curve of triangles shows the difference of observed minus
model.
– 26 –
Fig. 13.— Plot of the observed spectral energy distribution of AFGL 5440 versus that
predicted by model 206, illustrating the fit for a shell with a cooler inner dust temperature
as for fig. 7.
– 27 –
Fig. 14.— Plots of observed light curves (crosses) versus computed model light curves for
model 206 for AFGL 5440 at a sampling of the range of wavelengths observed between 1
and 4µm. In each panel the lower curve of triangles shows the difference of observed minus
model. Note the larger residuals at the longer wavelengths than for the best fit model 194.
	Introduction
	Observations and Data Reduction
	Source Modeling
	Comparison Stars
	AFGL 5440
	Discussion and Summary
	Acknowledgments

  We present observations and modeling of a lunar occultation of the
dust-enshrouded carbon star AFGL 5440. The observations were made over a
continuous range of wavelengths from 1 - 4um with a high-speed
spectrophotometer designed expressly for this purpose. We find that the
occultation fringes cannot be fit by any single-size model. We use the DUSTY
radiative transfer code to model a circumstellar shell and fit both the
observed occultation light curves and the spectral energy distribution
described in the literature. We find a strong constraint on the inner radius of
the dust shell, Tmax = 950 K +/- 50K, and optical depth at 5um of 0.5 +/- 0.1.
The observations are best fit by models with a density gradient of r^-2 or the
gradient derived by Ivezic & Elitzur for a radiatively driven hydrodynamic
outflow. Our models cannot fit the observed IRAS 60um flux without assuming a
substantial abundance of graphite or by assuming a substantially higher
mass-loss rate in the past.

Introduction
Mass loss from post-main-sequence stars provides a large fraction of the heavy element
abundance and solid particle content of the interstellar medium (e.g. Wallerstein & Knapp
1998; Ferrarotti & Gail 2006). The mechanism(s) of the mass loss during the AGB phase of
stellar evolution are thought to involve both radiation pressure and stellar pulsation (Suh
1997; Wallerstein & Knapp 1998; Schröder et al. 1998), but most details of this process are
not well understood. Many uncertainties about these processes can be clarified by studies of
the spatial structure of circumstellar mass-loss shells. For example, a number of molecular
1Astronomy Department, University of Texas at Austin, 1 University Station C1400, Austin, TX 78712-
0259; pmh@astro.as.utexas.edu, feardrew@astro.as.utexas.edu
http://arxiv.org/abs/0704.0256v1
– 2 –
line studies of the extended envelopes around AGB stars have found strong evidence for
periodic variations in mass-loss rates leading to the appearance of “rings” in the radial
distribution of molecular emission lines, (e.g. Fong, Meixner & Shah 2003, Olofsson et al.
1996). Very deep, sensitive imaging studies have also found similar phenomena in the dust
around the most nearby extreme example of these objects IRC+10216 (Mauron & Huggins
2000). In order to study the inner regions of these circumstellar shells, however, angular
resolutions well under 1 arcsec are required. For example, at a distance of 1 kpc, the
dust evaporation radius around a 104 L⊙ star corresponds to an angular radius of 20 milli-
arcsec (mas). Speckle interferometry and more recently adaptive optics observations have
enabled resolutions of order 0.1 arcsec (Hofmann et al. 2001; Biller et al. 2005), while lunar
occultation observations and multi-aperture interferometry have pushed angular resolutions
to the milli-arcsecond level, e.g. reviews by Quirrenbach (2004) and Monnier (2003).
Until recently most interferometric observations have been made in typically one or two
relatively broad bands. We present here observations of a lunar occultation of the star AFGL
5440 (aka OH 06.86-1.5, IRAS 18036-2344), made with a high-speed infrared spectropho-
tometer, pMIRAS (Harvey & Wilson 2003), developed as a prototype for a more ambitious
instrument now nearing completion. This star has been classified as a carbon-rich AGB
star on the basis of its IRAS LRS spectrum (Zuckerman & Dyck 1986; Volk & Cohen 1989;
Kwok, Volk & Bidelman 1997). Groenewegen et al. (2002) have estimated the distance to
be 2.25 kpc. Near-infrared through far-infrared photometry of the source has been summa-
rized by Guglielmo et al. (1993) and more recently by Guandalini et al. (2006), including a
combination of ground based photometry, the IRAS values, and more recent MSX results.
The reported distance and photometry imply a luminosity of 1.4×104 L⊙.
In addition to the observations of AFGL 5440, we also discuss observations that we
have made of two “calibration” stars in order to understand the limitations of our obser-
vation/analysis process. These objects are cool stars with no detectable circumstellar dust
shell based on their near-infrared and IRAS colors, IRC+00233 (M7) and HD 155292 (K2).
Our observations cover the entire 1 - 4µm spectral region with a resolving power that
varies from ∼ 20 at the shortest wavelengths to ∼ 100 at the long end. Our time resolution
of 8 msec permits an effective angular resolution of a couple milli-arcsec, with the exact
resolution being a strong function of the signal-to-noise ratio as discussed later. The broad
wavelength coverage allows us to observe simultaneously the Fresnel fringe pattern of the
obscured central star at the shorter wavelengths together with the circumstellar dust emis-
sion from the warmest part of the dust distribution. In §2 we describe the details of the
observations and instrumental parameters and the basic data reduction process. Then in §3
we describe various ways we have modelled the star+shell in order to determine the limits
– 3 –
on the circumstellar shell structure placed by our observations. Finally in §4 we summarize
the implications of these results for the mass loss of this object.
2. Observations and Data Reduction
The observations of AFGL 5440 were made during an immersion occultation event
on 28 Aug 2001 at approximately 02:44:00 UT. The elevation of the Moon at the time of
the event was 36◦, and the Sun was 17◦ below the horizon. The sky conditions were not
completely photometric but cloud cover was minimal and intermittent. The position angle
of the occultation event on the lunar limb was 54◦, and the lunar phase was 0.72. We used
the pMIRAS instrument on the McDonald Observatory 2.7-m telescope. The details of the
instrument have been described by Harvey & Wilson (2003), but we summarize the most
important characteristics here. The instrument is essentially a long/wide slit, high-speed
spectrophotometer using a NaCl prism to disperse the light from the slit, which is then
imaged onto a 32×100 pixel portion of a 2562 InSb array detector. The slit width is chosen
to be the minimum acceptable in order to minimize the background on the detector within
the limitations imposed by the seeing conditions. For these observations the slit width was
set at about 5 arcsec for the typical seeing of 1.5 arcsec. The detector is read-out every 8
msec, with photon integration occuring over essentially the full 8 msec time. Therefore, the
Fresnel occultation fringe pattern is averaged over this 8 msec time (as well as over the 2.7-m
telescope aperture). Because we use a refractive dispersive element, the dispersion/spectral
resolution is not equal at all wavelengths; the highest dispersion is at the longest wavelengths,
a feature that minimizes the background photon count at those wavelengths. On average
over the 1 – 4µm waveband covered by the instrument, one pixel corresponds roughly to
λ/∆λ = 100. Because of uncompensated seeing effects and the lower spectral dispersion
at shorter wavelengths, the true resolving power at the shortest wavelengths is R ∼ 20.
In the spatial direction the plate scale is 0.4 arcsec/pixel. The instrument is read-noise
limited shortward of 2.5µm and background-limited longward of 3µm. A typical observation
consists of taking 5000 frames at a time roughly centered on the occultation event. This
is accomplished by using a buffer that holds the most recent 5000 frames and terminating
the data acquisition a few seconds after the event is observed on a real-time display. This
is an important feature since the predicted times of occultation events are often in error by
as much as 10 seconds due to irregularities in the lunar limb as well as imperfect stellar
astrometry. Our observations of the occultation event of the comparison star, IRC+00233,
were obtained during an immersion event on 29 Jun 2001, and those of HD 155292 were
obtained during an immersion event on 26 Aug 2001.
– 4 –
The data reduction process consists of several typical steps. Because the spectrum is
being observed with much higher time resolution than the seeing timescale, the spectrum
moves around by several pixels over the course of an occultation event. Therefore, to con-
struct a light curve with minimal spectral blurring, the images must be shifted to correspond
to the same wavelength/pixel scale. This is done with a simple cross-correlation algorithm
that works well for the high S/N data discussed here. The spectrum is also not perfectly
aligned with the X/Y axes of the detector, so we take out this tilt as well during the pro-
cessing to simplify later steps. Because we use a “long slit”, ∼ 10 arcsec, we can use the sky
measurements on either side of the stellar spectrum to provide an accurate and high-time-
resolution sky subtraction. For the data discussed here we produce a weighted average in
the spectral direction that is two pixels wide and sum the pixels in the spatial direction that
have detectable signal. We have experimented with more elaborate photometric extraction
schemes, but this technique appears to produce S/N ratios as high as any more complex
algorithms. We have also experimented with various flat-fielding methods but have found
only a small improvement in S/N with these methods. The end result of the data reduc-
tion process is a sequence of ∼ 100 light curves for which we extract a few hundred frames
centered on the occultation event. The frames that are taken well before the Fresnel fringe
pattern of the occultation becomes evident are used to estimate the noise level in the data,
due both to read-noise, background photon statistics, and the often non-negligible amount
of seeing/scintillation noise caused by the atmosphere.
Because the exact location of the spectrum on the detector varies both due to seeing
and between observing runs after adjustments to the instrument, we perform the wavelength
calibration by fitting the NaCl dispersion function to the observed positions of the J, H, K,
and L atmospheric transmission maxima in the actual data for each occultation event. The
accuracy of this calibration is probably good to ± .01 λ throughout the 1 – 4µm region that
is observed. Because of variable instrumental efficiency depending on the placement of the
star image on the input slit, and the common occurrence of non-photometric sky conditions
during occultation events, we specifically do not attempt to derive a flux calibration for our
data. We have, however, compared the relative signal from AFGL 5440 to that of relatively
well characterized stars observed on the same night and conclude that the stellar magnitudes
in the published literature for AFGL 5440 are consistent with values that we would have
derived from our signal strengths to within ± 30%.
– 5 –
3. Source Modeling
The fringe pattern of a lunar occultation event is a convolution of the pattern for a point
source over several parameters that all act to blur the fringes. These parameters include:
the telescope aperture, the integration time of the detector, the wavelength bandwidth of
the observation, and, most importantly, the source size/structure. In order to extract the
source size or more detailed properties of the spatial structure, the typical procedure is to
model the combination of all the above “blurring” parameters with various possible source
models to find the best fit to the data (e.g. Nather & McCants 1970; Richichi et al. 1995).
An additional uncertainty in the observations is the basic frequency of the fringe pattern,
i.e. the speed of the lunar shadow. Although this parameter is calculated by the software
that we use to predict occultation events, small uncertainties in the shape of the lunar limb
(roughness due to craters, etc) can produce differences in the predicted shadow speed up
to several tens of percent. Therefore, this parameter must also be fit in addition to the
parameters that blur the fringes.
We began our modeling process by assuming a uniform disk as the simplest possible
model with which to try fitting the data for the observed objects, AFGL 5440, IRC+00233,
and HD 155292. We use a simple χ2 test for the best model, allowing one or more parameters
to vary during the process. Typically we first allow both the size and lunar shadow velocity
to vary until we find an approximate fit to both. This fit can be done either individually at
each wavelength or globally using the entire waveband.
3.1. Comparison Stars
For IRC+00233 and HD 155292 we assumed that a single source size was likely to be
appropriate for the entire wavelength range within our observational uncertainties, and we fit
the observations globally for source size and lunar velocity. Rough estimates of the angular
sizes of these two stars can be derived simply by assuming that they are blackbodies of the
effective temperatures given by their spectral types. Using the empirical relation between
angular size and B-K color from van Belle (1999) for IRC+00233 (B = 11.06, K = 1.95), we
would expect an angular size of 3.5 mas; the star is, however, likely to be mildly variable, so
the size at the time of our observations might have been different by ± 20%. For HD155292
(B = 11.0, K = 4.9) a similar calculation gives an angular size of 0.6 mas. Since typical
departures from a uniform disk model are at the level of 10 – 30% (e.g. Thompson, Creech-
Eakland & van Belle 2003; and Scholz 2003), the resolution required to detect them reliably
for even IRC+00233 is below 1 mas. Based on tests we have done with model data, this is
beyond the capabilities of our current data set which is limited by both spectral resolution
– 6 –
and signal-to-noise ratio to accuracies on the order of ±2 mas.
The best fit size for IRC+00233 is between 4.5 and 5.0 mas. Figure 1 shows observed
and model light curves for a model assuming a 4.5 mas uniform disk for a subset of the
wavelengths observed. Figure 2 shows the χ2 and signal-to-noise ratio as a function of
wavelength over the entire observed band for this model. Both figures show that this model
provides a very good fit to the observations except for a small range of wavelengths around
∼ 1.7µm where a substantially larger size would provide a better fit. We do not have a
good explanation for this discrepancy; it may be due to some systematic noise effect or to
a real difference in the stellar photosphere in that region. For comparison Schmidtke et al.
(1986) observed this same star in an occultation event using narrow-band filters near 1.6 and
2.2µm. They found a size at those wavelengths of ∼ 3 mas, similar to but smaller than our
calculated blackbody size. For HD 155292 all uniform-disk models with a size less than about
3 mas were able to fit the data reasonably well (Figures 3 and 4). Since the blackbody size
of the star is less than a milli-arcsecond, this is consistent with the expected uncertainties in
our data and modeling. The signal-to-noise ratio for this star was low enough that we had
no effective narrow-band information beyond 2.5µm, and at the shorter wavelengths some
periodic electronic pickup had a non-negligible effect on the observed fringe patterns as well.
Note that for both these comparison stars there are wavelengths with reasonable S/N as
shown in Figures 1 and 3 where there is a less than adequate fit, so these are difficult to
explain solely as due to telluric atmospheric absorption effects.
3.2. AFGL 5440
For AFGL 5440 a quick glance at the observed light curves (Figure 5) indicated that a
single source size was unlikely to fit over the entire 1 – 4µm bandwidth (Harvey & Wilson
2003). This suggests that we are seeing the combination of the emission from the central
star and a circumstellar shell of material due to mass loss from the star. To demonstrate
the poor fit with a single size uniform disk, we show in Figures 5 and 6 the results of trying
to fit the data with one example uniform disk, 11 mas. As can be seen in the plots of χ2
as well as the observed versus model light curves, the 11 mas disk provides a passable fit in
the mid-range of wavelengths, 2.5 – 3.2µm, but produces fringes that are too sharp at the
longer wavelengths and too broadened at the shortest wavelengths.
This result motivated us to pursue a full radiative transfer model for the object that
could be used to compare both the size constraints provided by our occultation data and the
spectral energy distribution (Guandalini et al. 2006) which contains important and different
information about the relative amount of dust at different temperatures. The DUSTY code
– 7 –
(Ivezić, Nenkova & Elitzur 1999) was originally created, in fact, for modeling the emission
from AGB stars surrounded by mass-loss shells. Its output includes model source images
as well as the total energy distribution, so it is ideal for our purposes. Our approach to
using the code was to choose a particular combination of input parameters and then vary
the dust optical depth to find the best fit to the energy distribution for those parameters.
We then used the output source images that were computed as a function of wavelength
to calculate expected occultation fringes for the model and compared those to the observed
fringes. Since AFGL 5440 has been classified as a carbon-rich star, we assumed a carbon-
rich dust composition, typically some combination of amorphous carbon, silicon carbide, and
graphite as the major constituents. The other critical parameters for the models are the dust
temperature at the inner radius and the radial density gradient. The outer radius of the dust
shell makes essentially no difference to the observed characteristics at λ < 60µm as long as it
is at least 100 times the inner radius. The goal of our modeling was to find some reasonable
fit to our occultation data and the rough spectral energy distribution for the circumstellar
dust shell; we have not attempted to extract details of the stellar photosphere or attempt
a thorough examination of all possible dust size/composition models since our data do not
bear directly on those issues for reasons of wavelength coverage and spectral resolution. In
particular, we did not try to find any better than superficial agreement with the IRAS LRS
data.
We explored more than 200 models to understand the effect of varying the input pa-
rameters on the quality of the fit. Basically all the models that provided an approximate fit
to the occultation observations and the spectral energy distribution had several features in
common. First, the dust temperature at the inner radius of the dust shell was of order 950K
± 50K. Models with a maximum dust temperature below 900 K did not have enough hot
dust to fit the occultation fringes at the longer wavelengths, while models with hotter inner
edges had even more difficulty than the best-fit model in reproducing the energy distribu-
tion longward of 10µm. Secondly, the radial density gradient of models with a reasonable
fit was close to r−2 (or to DUSTY’s calculation of the gradient appropriate for a radiatively
driven wind which approximates an r−2 distribution for large radii). Models with a density
gradient of r−1.8 came closer to producing the IRAS 60µm flux, but did not fit the shape of
the 5 – 20µm energy distribution well. Models with a density gradient of r−2.2 can fit the
energy distribution out to 20µm and also provide a good fit to the occultation results, but
have substantially worse fits to the IRAS 60µm flux than our best fit models. The optical
depth for best fit at the fiducial wavelength of 5µm was typically in the range 0.3 – 0.6.
Finally, the dust composition that provided the best fit included a small amount of SiC
together with comparable amounts of amorphous carbon and graphite. Other carbon-rich
compositions produced reasonable fits except at the longest wavelengths or in the 11µm SiC
– 8 –
feature. Note that there is a range of optical properties for different forms of amorphous car-
bon (Andersen, Liodl,& Hofner 1999) that we did not explore. We experimented with two
grain size distributions, the MRN slope (Mathis, Rumpl & Nordsieck 1977), and another,
the KMH shape (Kim, Martin & Hendry 1994), used by Ivezić & Elitzur (1996) for models
of IRC+10216, that has a smoother fall-off on each end. We found that we could obtain
reasonably good fits with either distribution. Figures 7 and 8 show the fits to the spectral
energy distribution and to the occultation light curves for the best-fit model. Figure 9 shows
the quality of the fit versus wavelength, and figure 10 illustrates the spatial profiles of this
best-fit model. Figures 11 and 12 likewise show for comparison the fits for a model discussed
below that does not use any graphite. Finally, figures 13 and 14 show results for a third
model that fits the energy distribution but gives a poor fit to the occultation results because
of a lack of enough warm dust close to the star.
4. Discussion and Summary
Model dust shells have been computed for a number of carbon-rich AGB stars by various
authors. Le Bertre, Gougeon, & Le Sidaner (1995) and Le Bertre (1997) found that the
energy distributions for nearly two dozen carbon-rich stars could be modelled with very
similar dust shell parameters. They found a common value of maximum dust temperature
of order 950 K with shell density gradient of ρ ∝ r−2 for spherically symmetric shells. The
best fit dust property implied a dust emissivity, ǫ ∝ λ−1.3, consistent with that expected for
an amorphous carbon-rich dust composition as also found by Jura (2004). These conclusions
were enhanced by their ability to fit the energy distributions over a range of phases of the
observed variability of many of the stars. On the other hand, Suh (1997) suggested that a
“superwind” phase of mass loss could improve model fits to the energy distributions for a
number of carbon-rich AGB dust shells by enhancing the emission shortward of 30µm because
of a high rate of mass loss in recent times, e.g. at small radii where most of the emission
would be due to hotter dust. Ivezić & Elitzur (1996) used a self-consistent radiatively driven
hydrodynamic model for the density distribution around IRC+10216 and were able to fit both
the spectral energy distribution and the near-infrared angular visibility data from speckle
observations. Interestingly they derived an inner dust shell temperature substantially lower
than ours and most other studies, ∼ 750K. Winters et al. (1997) computed a full time-
dependent model of periodic outflow from AFGL 3068 and were able to produce a good fit
to the energy distribution and observed light curves. Virtually all of these modeling efforts
used dust emissivities appropriate for some form of amorphous carbon (usually including
SiC), but with no graphite (see also Lorenz-Martins 2001), contrary to our best model fit
above. The model of Ivezić & Elitzur (1996) utilized a grain size distribution that included
– 9 –
substantially larger grains than most earlier models.
Our lunar occultation observations add constraints to these results most directly in
defining the amount of dust in the innermost region around AFGL 5440, since our longest
observed wavelength is 4µm. Basically, our data imply that the density of grains emitting
in the 3 – 4µm spectral region must be sufficiently large to produce the substantial fringe
“blurring” observed in our light curves. Graphically, this amount of emission is illustrated
in figure 10 showing the source profiles for the best-fit model. For any given assumed dust
emissivity, this constraint then implies a fairly narrow range of optical depth and ratio of
near-infrared to mid-infrared dust emission. Thus, we constrain the dust density gradient in
the innermost part of the circumstellar shell. Finally, as mentioned above, the fact that we
were unable to find a satisfactory fit to the data with any model having a maximum dust
temperature lower than 900 K is a strong constraint on the location of the inner edge of
the dust shell. This result follows from the fact that dust cooler than 900 K cannot emit
sufficiently to produce the required amount of 3 – 4µm emission. Note that this temperature
is nearly a factor of two below the expected condensation temperatures for dust around these
stars (Egan & Leung 1995). The physical value of this inner radius for AFGL 5440 for the
dust properties of the best-fit model is 3.7×1014 cm, or an angular radius at the assumed
distance of 2.25 kpc of 11 mas. For reference the angular diameter of the central star is of
order 3 mas, based on a blackbody approximation for its likely photospheric temperature of
2500K ± 300K and 2µm magnitude.
Since our modeling is the first of which we are aware for this particular star over the
entire infrared wavelength region, we also discuss here the constraints on the circumstellar
cloud properties implied by the overall energy distribution. As mentioned above, our best-fit
model utilized roughly equal amounts of amorphous carbon and graphite in addition to the
small amount of SiC required to fit the 11µm feature seen in the IRAS LRS spectrum. This
result is contrary to the large amount of evidence against substantial amounts of graphite
in stars like AFGL 5440. The factor that drove us to include graphite was its relatively flat
emissivity vs. wavelength dependence between 10 and 50µm that enabled us to fit the IRAS
60µm flux. Models with only amorphous carbon and SiC failed to fit that flux by factors of
3 or more. Figures 11 and 12 discussed above show the energy distribution and model light
curves for the best-fitting model that uses only amorphous carbon and SiC, and which uses
the radiatively driven hydrodynamic density gradient of Ivezic & Elitzur (1996) as computed
by DUSTY. The light curves fit the observed occultation data nearly as well as those for the
best-fit model.
Clearly, however, the IRAS 60µm flux cannot be fit by any similar model without
graphite, and substantial modifications would have to be made to the assumed density law
– 10 –
in the outer regions or to the dust emissivity in order to come close to fitting the 60µm
flux. Explaining this problem is beyond the scope of our study, but the fact that there is
abundant evidence for non-constant outflow from carbon stars (Fong, Meixner & Shah 2003;
Mauron & Huggins 2000) provides a convenient (if ad hoc) explanation. If the mass-loss rate
were greater in the past, then the amount of dust at radii appropriate for emission at 60µm
might well be larger than a simple extrapolation from the dust responsible for the 3 – 20µm
emission. This would describe the opposite situation from that proposed by (Suh 1997) who
suggested higher mass-loss rates in the recent past to explain observations of a number of
other similar carbon stars. The radial location of dust emitting strongly at 60µm is of order
1 to a few arcseconds from the star. For an assumed distance of 2.25 kpc and its measured
outflow velocity of 22 km s−1 (Groenewegen et al. 2002), this would correspond to a time
of order 500 years to a couple thousand years in the past for the proposed higher mass-loss
rate. This time scale is comparable to the period of fluctuation seen by Mauron & Huggins
(2000) for IRC+10216.
The fact that we have constrained the absolute value and radial dependence of the dust
density with our observations means that we have constrained the recent dust mass-loss
rate for AFGL 5440 as well. The dust mass-loss rate implied by our derived optical depth
and radial density dependence is Ṁdust = 6.5 × 10
−8 M⊙/yr for the optical constants of
amorphous carbon used by DUSTY (Ivezić, Nenkova & Elitzur 1999). Groenewegen et al.
(2002) computed dust and gas mass-loss rates individually for AFGL 5440 on the basis of the
IRAS 60µm flux for the dust, and millimeter CO observations for the gas. They derived a
gas mass-loss rate of 3.1×10−5 M⊙/yr and dust mass-loss rate of 5.1×10
−8 M⊙/yr implying
a gas-to-dust mass ratio of 600. Interestingly, their dust mass-loss rate is slightly lower than
the value we have derived in spite of their using the 60µm IRAS flux for normalization. This
result reinforces the overall uncertainties in model assumptions and absolute dust opacties,
particularly at longer infrared wavelengths. In any case, a dust mass-loss rate of order 5 –
10×10−8M⊙/yr and gas mass-loss rate a few hundred times larger are consistent with the
data.
In summary, our observations have separately resolved the stellar photosphere and the
inner edge of the circumstellar dust shell around AFGL 5440. We have strongly constrained
the inner radius of the dust shell surrounding the star as well as the near-infrared optical
depth. Our constraints together with the spectral energy distribution suggest a dust density
gradient consistent with that expected for radiatively driven mass loss with the exception
that the far-infrared flux may imply a recent decrease in mass-loss rate from the time when
the far-ir-emitting dust was ejected.
– 11 –
5. Acknowledgments
We thank a number of people and institutions that have supported this work since its
earliest stages. M. Simon greatly encouraged our efforts and provided many useful comments
over the course of this work. He also provided the basic prediction software (developed by L.
Cassar) that we use for determining the times and elements of occultation events. We also
acknowledge illuminating conversations with A. Richichi, S. Guilloteau, D. Evans, and R.
E. Nather and very helpful suggestions from two anonymous referees. D. Wilson developed
the initial versions of a number of the reduction algorithms used in this work and provided
a great deal of assistance during the observations. C. Young provided help in the intricacies
of DUSTY. This project has been supported by: internal McDonald Observatory funding,
NASA Grant NAG5-10458, and NSF grant AST-0096626. We also acknowledge extensive use
of the NASA Astrophysics Data System and SIMBAD, and P. Harvey thanks the University
of Colorado’s Center for Astrophysics and Space Astronomy for graciously hosting him during
a sabbatical while much of this paper was written.
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This preprint was prepared with the AAS LATEX macros v5.2.
– 13 –
Table 1. DUSTY Models of AFGL 5440
Model Tmax ρ ∝ r
−N τ Amorph C Graphite SiC Size Dist.
K @5µm % %) %)
194 950 -2.0 0.41 40 50 10 MRN1
200 950 -2.0 0.55 95 0 5 KMH2
206 850 rad-flow3 0.45 95 0 5 KMH2
Note. — 1Mathis, Rumpl & Nordsieck (1977) with amin = .005µm; amax =
0.25µm.
2Kim, Martin & Hendry (1994) with amin = .005µm; amax = 0.2µm.
3 Radiatively driven outflow computed by DUSTY as described by
Ivezić & Elitzur (1996)
– 14 –
Fig. 1.— Plots of observed light curves (crosses) versus computed model light curves for
the 4.5 mas uniform disk model of IRC+00233 at a sampling of the range of wavelengths
observed between 1 and 4µm. In each panel the lower curve of triangles shows the difference
of observed minus model.
– 15 –
Fig. 2.— Plots of the χ2 (solid) for the model fit of the 4.5 mas uniform disk to the observed
light curve for IRC+00233 over the range of wavelengths observed between 1 and 4µm.
The observed signal-to-noise ratio is also shown (dashed) as a function of wavelength for
comparison.
– 16 –
Fig. 3.— Plots of observed light curves (crosses) versus computed model light curves for
the 2.0 mas uniform disk model of HD155292 at a sampling of the range of wavelengths
observed between 1 and 4µm. In each panel the lower curve of triangles shows the difference
of observed minus model.
– 17 –
Fig. 4.— Plots of the χ2 (solid) for the model fit of the 2.0 mas uniform disk to the
observed light curve for HD155292 over the range of wavelengths observed between 1 and
4µm. The observed signal-to-noise ratio is also shown (dashed) as a function of wavelength
for comparison.
– 18 –
Fig. 5.— Plots of observed light curves (crosses) versus computed model light curves for
the 11 mas uniform disk model for AFGL 5440 at a sampling of the range of wavelengths
observed between 1 and 4µm. In each panel the lower curve of triangles shows the difference
of observed minus model.
– 19 –
Fig. 6.— Plots of the χ2 (solid) for the model fit of the 11 mas uniform disk to the observed
light curve for AFGL 5440 over the range of wavelengths observed between 1 and 4µm.
The observed signal-to-noise ratio is also shown (dashed) as a function of wavelength for
comparison.
– 20 –
Fig. 7.— Plot of the observed spectral energy distribution of AFGL 5440 versus that
predicted by model 194, the best fit model. The open diamonds show the values from
Guandalini et al. (2006) and Guglielmo et al. (1993). The light grey line indicates the IRAS
LRS spectrum.
– 21 –
Fig. 8.— Plots of observed light curves (crosses) versus computed model light curves for
model 194 for AFGL 5440 at a sampling of the range of wavelengths observed between 1
and 4µm. In each panel the lower curve of triangles shows the difference of observed minus
model.
– 22 –
Fig. 9.— Plots of the χ2 (solid) for the fit of model 194 (the best fit) to the observed
light curve for AFGL 5440 over the range of wavelengths observed between 1 and 4µm.
The observed signal-to-noise ratio is also shown (dashed) as a function of wavelength for
comparison.
– 23 –
Fig. 10.— Plots of the model spatial distributions for AFGL 5440 predicted by model 194,
the best fit model. The curves are drawn for 1.0 and 1.2µm (solid, 1.0µm is the more
extended), and 1.4, 1.6, 1.8, 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, and 4.0µm, with the
longest wavelengths being the most extended of these.
– 24 –
Fig. 11.— Plot of the observed spectral energy distribution of AFGL 5440 versus that
predicted by model 200, the best fit model that does not use graphite as for fig. 7.
– 25 –
Fig. 12.— Plots of observed light curves (crosses) versus computed model light curves for
model 200 for AFGL 5440 at a sampling of the range of wavelengths observed between 1
and 4µm. In each panel the lower curve of triangles shows the difference of observed minus
model.
– 26 –
Fig. 13.— Plot of the observed spectral energy distribution of AFGL 5440 versus that
predicted by model 206, illustrating the fit for a shell with a cooler inner dust temperature
as for fig. 7.
– 27 –
Fig. 14.— Plots of observed light curves (crosses) versus computed model light curves for
model 206 for AFGL 5440 at a sampling of the range of wavelengths observed between 1
and 4µm. In each panel the lower curve of triangles shows the difference of observed minus
model. Note the larger residuals at the longer wavelengths than for the best fit model 194.
	Introduction
	Observations and Data Reduction
	Source Modeling
	Comparison Stars
	AFGL 5440
	Discussion and Summary
	Acknowledgments
