HST/ACS Multiband Coronagraphic Imaging of the Debris Disk around Beta Pictoris

Abstract

(Abridged.) We present F435W (B), F606W (Broad V), and F814W (Broad I) coronagraphic images of the debris disk around Beta Pictoris obtained with HST's Advanced Camera for Surveys. We confirm that the previously reported warp in the inner disk is a distinct secondary disk inclined by ~5 deg from the main disk. The main disk's northeast extension is linear from 80 to 250 AU, but the southwest extension is distinctly bowed with an amplitude of ~1 AU over the same region. Both extensions of the secondary disk appear linear, but not collinear, from 80 to 150 AU. Within ~120 AU of the star, the main disk is ~50% thinner than previously reported. The surface-brightness profiles along the spine of the main disk are fitted with four distinct radial power laws between 40 and 250 AU, while those of the secondary disk between 80 and 150 AU are fitted with single power laws. These discrepancies suggest that the two disks have different grain compositions or size distributions. The F606W/F435W and F814W/F435W flux ratios of the composite disk are nonuniform and asymmetric about both projected axes of the disk. Within ~120 AU, the m_F435W-m_F606W and m_F435W-m_F814W colors along the spine of the main disk are ~10% and ~20% redder, respectively, than those of Beta Pic. These colors increasingly redden beyond ~120 AU, becoming 25% and 40% redder, respectively, than the star at 250 AU. We compare the observed red colors within ~120 AU with the simulated colors of non-icy grains having a radial number density ~r^-3 and different compositions, porosities, and minimum grain sizes. The observed colors are consistent with those of compact or moderately porous grains of astronomical silicate and/or graphite with sizes >0.15-0.20 um, but the colors are inconsistent with the blue colors expected from grains with porosities >90%. Comment: 38 pages (including 21 figures and 4 tables) in EmulateApJ format, accepted for publication in The Astronomical Journal. Full-resolution figures and fully processed FITS images (with error maps) are available at http://acs.pha.jhu.edu/~dag/betapic Version 2: Added 4 references and some clarifying text. Basic facts and conclusions are unchanged

Full text

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arXiv:astro-ph/0602292v2 1 Mar 2006
TO BE PUBLISHED IN The Astronomical Journal.
Preprint typeset using LATEX style emulateapj v. 08/13/06
HST/ACS MULTIBAND CORONAGRAPHIC IMAGING OF THE DEBRIS DISK AROUND BETA PICTORIS1
D. A. GOLIMOWSKI,2D. R. ARDILA,3J. E. KRIST,4M. CLAMPIN,5H. C. FORD,2G. D. ILLINGWORTH,6F. BARTKO,7N. BENÍTEZ,8
J. P. BLAKESLEE,9R. J. BOUWENS,6L. D. BRADLEY,2T. J. BROADHURST,10R. A. BROWN,11C. J. BURROWS,12E. S. CHENG,13
N. J. G. CROSS,14R. DEMARCO,2P. D. FELDMAN,2M. FRANX,15T. GOTO,16C. GRONWALL,17G. F. HARTIG,11B. P. HOLDEN,6
N. L. HOMEIER,2L. INFANTE,18M. J. JEE,2R. A. KIMBLE,5M. P. LESSER,19A. R. MARTEL,2S. MEI,2F. MENANTEAU,2
G. R. MEURER,2G. K. MILEY,15V. MOTTA,18M. POSTMAN,11P. ROSATI,20M. SIRIANNI,11W. B. SPARKS,11H. D. TRAN,21
Z. I. TSVETANOV,2R. L. WHITE,11W. ZHENG,2AND A. W. ZIRM2
To be published in The Astronomical Journal.
ABSTRACT
We present F435W (B), F606W (Broad V), and F814W (Broad I) coronagraphic images of the debris disk
around β Pictoris obtained with the Hubble Space Telescope’s Advanced Camera for Surveys. These images
provide the most photometrically accurate and morphologically detailed views of the disk between 30 and
300 AU from the star ever recordedin scattered light. We confirm that the previouslyreportedwarp in the inner
disk is a distinct secondary disk inclined by ∼ 5◦from the main disk. The projected spine of the secondary
disk coincides with the isophotal inflections, or “butterfly asymmetry,” previously seen at large distances from
the star. We also confirm that the opposing extensions of the main disk have different position angles, but we
find that this “wing-tilt asymmetry”is centered on the star rather than offset from it as previouslyreported. The
main disk’s northeast extension is linear from 80 to 250 AU, but the southwest extension is distinctly bowed
with an amplitude of ∼ 1 AU over the same region. Both extensions of the secondary disk appear linear, but
not collinear, from 80 to 150 AU. Within ∼ 120 AU of the star, the main disk is ∼ 50% thinner than previously
reported. The surface-brightness profiles along the spine of the main disk are fitted with four distinct radial
power laws between 40 and 250 AU, while those of the secondary disk between 80 and 150 AU are fitted with
single power laws. These discrepancies suggest that the two disks have different grain compositions or size
distributions. The F606W/F435W and F814W/F435W flux ratios of the composite disk are nonuniform and
asymmetric about both projected axes of the disk. The disk’s northwest region appears 20–30% redder than
its southeast region, which is inconsistent with the notion that forward scattering from the nearer northwest
side of the disk should diminish with increasing wavelength. Within ∼ 120 AU, the mF435W–mF606Wand
mF435W–mF814Wcolors along the spine of the main disk are ∼ 10% and ∼ 20% redder, respectively, than those
of β Pic. These colors increasingly redden beyond ∼ 120 AU, becoming 25% and 40% redder, respectively,
than the star at 250 AU. These measurements overrule previous determinations that the disk is composed of
neutrally scattering grains. The change in color gradient at ∼ 120 AU nearly coincides with the prominent
inflection in the surface-brightness profile at ∼ 115 AU and the expected water-ice sublimation boundary. We
compare the observed red colors within ∼ 120 AU with the simulated colors of non-icy grains having a radial
number density ∝ r−3and different compositions, porosities, and minimum grain sizes. The observed colors
are consistent with those of compact or moderately porous grains of astronomical silicate and/or graphite with
sizes ? 0.15–0.20µm, but the colors are inconsistent with the blue colors expected from grains with porosities
? 90%. The increasingly red colors beyond the ice-sublimation zone may indicate the condensation of icy
mantles on the refractory grains, or they may reflect an increasing minimum grain size caused by the cessation
of cometary activity.
Subject headings: circumstellar matter — planetary systems: formation — planetary systems: protoplanetary
disks — stars: individual (β Pictoris)
1Based on guaranteed observing time awarded by NASA to the ACS In-
vestigation Definition Team (HST program 9987).
2Department of Physics and Astronomy, The Johns Hopkins University,
3400 North Charles Street, Baltimore, MD 21218-2686
3Spitzer Science Center, Infrared Processing and Analysis Center, MS
220-6, California Institute of Technology, Pasadena, CA 91125
4
Jet Propulsion Laboratory, 4800 Oak Grove Drive, M/S 183-900,
Pasadena, CA 91109
5NASA’s Goddard Space Flight Center, Code 681, Greenbelt, MD 20771
6Lick Observatory, University of California at Santa Cruz, 1156 High
Street, Santa Cruz, CA 95064
7Bartko Science & Technology, 14520 Akron Street, Brighton, CO 80602
8Instituto de Astrofísica de Andalucía (CSIC), Camino Bajo de Huétor,
24, Granada 18008, Spain
9Department of Physics and Astronomy, Washington State University,
Pullman, WA 99164
10School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978,
Israel
11Space Telescope Science Institute, 3700 San Martin Drive, Baltimore,
MD 21218
12Metajiva, 12320 Scenic Drive, Edmonds, WA 98026
13Conceptual Analytics LLC, 8209 Woburn Abbey Road, Glenn Dale,
MD 20769
14Royal Observatory Edinburgh, Blackford Hill, Edinburgh EH9 3HJ,
UK
15Leiden Observatory, Postbus 9513, 2300 RA Leiden, Netherlands
16Institute of Space and Astronautical Science, Japan Aerospace Explo-
ration Agency, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan
17Department of Astronomy and Astrophysics, The Pennsylvania State
University, 525 Davey Lab, University Park, PA 16802
18
Departmento de Astronomía y Astrofísica, Pontificia Universidad
Católica de Chile, Casilla 306, Santiago 22, Chile
19Steward Observatory, University of Arizona, Tucson, AZ 85721
20European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-
85748 Garching, Germany
21W. M. Keck Observatory, 65-1120 Mamalahoa Hwy, Kamuela, HI

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2GOLIMOWSKI ET AL.
1. INTRODUCTION
Since the initial discoveries of cool (∼ 100 K) dust around
nearby stars by the Infrared Astronomical Satellite (Aumann
1985), β Pictoris has been the foremost example of a young,
main-sequencestar with a resolved circumstellar disk of dust.
The disk likely comprises the debris from disintegrating bod-
ies in a nascent planetary system rather than primordial dust
from the dissipating protostellar nebula (Backman & Paresce
1993; Artymowicz 1997; Lagrange et al. 2000; Zuckerman
2001).Spectroscopic evidence of multitudinous star-
grazing comets (Lagrange-Henriet al. 1988; Beust et al.
1990; Vidal-Madjar et al. 1994, and references therein) has
motivated models of the disk as an admixture of gas and
dust from colliding and evaporating comets located within
a few tens of AU from β Pic (Lecavelier des Etangs et al.
1996; Beust & Morbidelli 1996; Thébault et al. 2003). The
cometary origin of the dust is supported by the detec-
tion of broad, 10 µm silicate emission like that observed
in the spectra of comets Halley, Kohoutek, and others
(Telesco & Knacke 1991; Knacke et al. 1993; Aitken et al.
1993; Weinberger et al. 2003; Okamoto et al. 2004).
Ground-based, coronagraphic images of β Pic reveal
an asymmetric, flared disk extending at least 1800 AU
from the star and viewed nearly “edge-on” (Smith & Terrile
1984; Paresce & Burrows 1987; Golimowski et al. 1993;
Kalas & Jewitt 1995; Mouillet et al.1997a; Larwood & Kalas
2001). High-resolution Hubble Space Telescope (HST) and
adaptive-optics images show that the inner part of the disk
(∼ 20–100 AU from β Pic) is warped in a manner consis-
tent with the presence of a secondary disk that is inclined by
∼ 4◦from the main disk and perhaps sustained by a massive
planet in a similarly inclined, eccentric orbit (Burrows et al.
1995; Mouillet et al. 1997b; Heap et al. 2000; Augereau et al.
2001). HST and ground-based images also reveal concentra-
tions of dust along the northeast extension of the disk about
500–800 AU from the star that have been interpreted as an
asymmetric system of rings formed, along with other asym-
metries in the disk, after a close encounter with a passing star
(Kalas et al. 2000, 2001; Larwood & Kalas 2001). Spatially
resolved mid-infrared images show an asymmetric inner disk
having depleteddust within 40 AU of β Pic (Lagage & Pantin
1994; Pantin et al. 1997) and oblique clumps of emission 20–
80 AU from the star (Wahhaj et al. 2003; Weinberger et al.
2003; Telesco et al. 2005). These features suggest the pres-
ence of noncoplanar dust rings whose locations conform to
the mean-motion resonances of a putative planetary system.
Constraints on the sizes of the dust grains observed
in scattered light have been based upon multiband
(BVRI) imaging studies of the disk in both unpolarized
(Paresce & Burrows 1987; Lecavelier des Etangs et al. 1993)
and polarized (Gledhill et al. 1991; Wolstencroft et al. 1995)
light. The unpolarized images indicate that the disk is col-
orless (within uncertainties of 20–30%) at distances 100–
300 AU from β Pic, thoughits B-bandbrightness may be sup-
pressed at 50 AU from the star.22This neutral scattering by
96743
22Throughout this paper, we compute the projected dimensions of the
disk in astronomical units (AU) using the trigonometric parallax of π =
0.′′05187 ± 0.′′00051 (or 1/π = 19.28 ± 0.19 pc) reported for β Pic by
Crifo et al. (1997) based on astrometric measurements conducted with the
Hipparcos satellite. Consequently, the projected distances reported in this pa-
per may differ from those appearing in papers published before 1997, which
were based on an erroneous distance of 16.4 pc to the star.
thedisk has beencustomarilyviewedas evidencethat thedust
grains are much larger than the wavelengths of the scattered
light (≫ 1 µm). However, Chini et al. (1991) noted that the
B-, V-, and I-band scattering efficiencies of silicate spheres
were similar for grains with radii of 0.2–0.3 µm. Attempts
to reconcile the neutral colors of the disk with the 10–25%
polarization of scattered light from the disk have been prob-
lematic. Voshchinnikov & Krügel (1999) and Krivova et al.
(2000) found that, although the polarization alone is best fit-
ted with a grain size distribution with a lower limit of a few
microns, the observed neutral colors can only be replicated
by adding submicron-sized grains and lowering either the re-
fractive index of the grains or the proportion of the smallest
grains. Given the adjustments needed to match the polariza-
tion models with the highly uncertain disk colors, a more pre-
cise multicolor imaging study of the β Pic disk is warranted.
In this paper, we present multiband coronagraphic images
of β Pic’s circumstellar disk obtained with HST’s Advanced
Camera for Surveys (ACS) (Ford et al. 2003; Gonzaga et al.
2005). These images reveal the disk between 30 and 300 AU
fromthe star with unprecedentedspatial resolution, scattered-
light suppression, and photometric precision. These qualities
permit the measurement of the disk’s optical colors with 3–10
times better precision than previously reported from ground-
based observations. By deconvolving the instrumental point-
spread function (PSF) from each image, we accurately deter-
mine the brightnesses, morphologies, and asymmetries of the
two disk components associated with the warp in the inner
disk. Our fully-processed images and results will likely serve
as the empiricalstandardsfor subsequentscattered-lightmod-
els of the inner disk until the next generation of space-based
coronagraphicimagers is deployed.
2. OBSERVATIONS AND DATA PROCESSING
2.1. ACS Imaging Strategy and Reduction
Multiband, coronagraphic images of the A5V star β Pic
were recorded on UT 2003 October 1 using the High Resolu-
tion Channel (HRC) of ACS (Ford et al. 2003; Gonzaga et al.
2005). The HRC features a 1024×1024-pixel CCD detector
whose pixels subtend an area of 0.′′028 × 0.′′025, providing
a ∼ 29′′×26′′field of view (FOV). Beta Pic was acquired in
the standard “peak-up” mode with the coronagraph assembly
deployed in the focal plane of the aberrated beam. The star
was then positioned behind the small (0.′′9 radius) occulting
spot located approximatelyat the center of the FOV. HST was
oriented so that the disk’s midplane appeared approximately
perpendicularto the 5′′occulting finger and the large (1.′′5 ra-
dius) occulting spot that also lie in the FOV. Short, medium,
and long exposures were recorded through the F435W (B),
F606W (Broad V), and F814W (Broad I) filters over three
consecutive HST orbits. All images were digitized using the
default analog-to-digital conversion of 2 e−DN−1. This se-
quence of exposures was promptly repeated after rolling HST
about the line of sight by ∼ 10◦. This offset changed the
orientation of the disk in the FOV by ∼ 10◦and facilitated
the discrimination of features associated with the disk from
those intrinsic to the coronagraphic PSF. Immediately before
the exposures of β Pic, coronagraphicimages of the A7IV star
α Pictoris were recorded through the same filters to provide
reference images of a star having colors similar to those of
β Pic but no known circumstellar dust. A log of all HRC ex-
posures is given in Table 1.
The initial stages of image reduction (i.e., subtraction of
bias and dark frames and division by a noncoronagraphic

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MULTIBAND IMAGES OF DISK AROUND β PICTORIS3
flat field) were performed by the ACS image calibration
pipeline at the Space Telescope Science Institute (STScI)
(Pavlovsky et al. 2005). To correct the vignetting caused by
the occulting spots, we divided the images by normalized
“spot flats” that were appropriately registered to the approx-
imate locations of the migratory occulting spots on the date
of our observations (Krist et al. 2004). We then averaged the
constituent images of each set of exposures listed in Table 1
after interpolating over static bad pixels and eliminating tran-
sient bad pixels with a conventional 3σ rejection algorithm.
We then normalized the averaged images to unit exposure
time and replaced saturated pixels in the long-exposure im-
ages with unsaturated pixels at corresponding locations in
the shorter-exposure images. Throughout this process, we
tracked the uncertainties associated with each image pixel. In
this manner, we created cosmetically clean, high-contrast im-
ages and meaningful error maps for each combination of star,
filter, and roll angle. Figure 1 shows 29′′×10′′sections of the
reduced F606W images of β Pic and α Pic obtained at each
roll angle.
2.2. Subtraction of the Coronagraphic PSF
To distinguish the brightness and morphology of the disk
from the diffracted and scattered light of β Pic, the occulted
star’s PSF must be removed from each image. By observing
α Pic and β Pic in consecutive HST orbits, we limited the dif-
ferences between the coronagraphicPSFs of the two stars that
would otherwise be caused by inconsistent redeployment of
the coronagraphassembly, gradual migration of the occulting
spot, or changes in HST’s thermally drivenfocus cycles (Krist
2002). We measured the positions of the stars behind the oc-
culting spot using the central peaks of the reduced corona-
graphic PSFs (Figure 1) that result from the reimaging of in-
completely occulted, spherically aberrated starlight by ACS’s
corrective optics (Krist 2000). The positions of β Pic and
α Pic differed by ∼ 0.8 pixel (∼ 0.′′02). This offset causes
differences between the coronagraphic PSFs that are large in
the immediate vicinity of the occulting spot, but the residual
light at larger field angles (? 5′′from the star) after PSF sub-
traction is ∼ 103.5times fainter than the disk’s midplane at
those field angles (Krist 2000).
Optimal subtraction of the coronagraphic PSF requires ac-
curate normalization and registration of the filter images of
the reference star α Pic with the corresponding images of
β Pic. Because direct images of the two stars were not ob-
tained, we estimated the brightnesses of each star in each
ACS bandpass using the HST synthetic photometry pack-
age, Synphot, which has been developed and distributed by
STScI (Bushouse et al. 1998). In doing so, we used the op-
tical spectra of the A5V stars θ1Serpentis and Praesepe 154
(Gunn & Stryker 1983) to approximatethe spectrum of β Pic.
Likewise, we approximated the spectrum of α Pic with that
of the A5IV star HD 165475B. These proxies yielded syn-
thetic Johnson–Cousins photometry that closely match the
Cousins BVRI measurements of α Pic and β Pic reported by
Bessel (1990). Assuming V magnitudes of 3.27 and 3.86 for
α Pic and β Pic, respectively, we computed synthetic flux ra-
tios, Fα/Fβ, of 1.65, 1.75, and 1.90 for F435W, F606W, and
F814W, respectively. We then divided the images of α Pic by
these ratios to bring the integrated brightnesses of the refer-
ence PSFs into conformity with those of β Pic.
We aligned the normalized images of α Pic with the cor-
responding images of β Pic using an interactive routine that
permits orthogonal shifts of an image with subpixel resolu-
tion and cubic convolution interpolation. The shift intervals
and normalization factors (i.e., Fα/Fβ) were progressively re-
fined throughout the iterative process. We assessed the qual-
ityofthenormalizationandregistrationbyvisuallyinspecting
the difference image created after each shift or normalization
adjustment. Convergence was reached when the subtraction
residuals were visibly minimized and refinements of the shift
interval or normalization factor had inconsequential effects.
Based on these qualitative assessments, we estimate that the
uncertainty of the registration along each axis is 0.125 pixel
and the uncertainty of Fα/Fβin each bandpass is 2%.
After subtracting the coronagraphicPSFs from each image,
we transformed the images to correct the pronounced geo-
metric distortion in the HRC image plane. In doing so, we
used the coefficients of the biquartic-polynomial distortion
map provided by STScI (Meurer et al. 2002) and cubic con-
volution interpolation to conserve the imaged flux. We then
combined the images obtained at each HST roll angle by ro-
tating the images of the second group clockwise by 9◦.7 (Ta-
ble 1), aligning the respective pairs of images according to
the previously measured stellar centroids, and averaging the
image pairs after rejecting pixels that exceeded their local 3σ
values. Again, we tracked the uncertainties associated with
each stage of image processing to maintain a meaningful map
of random pixel errors.
We combined in quadrature the final random-error maps
withestimatesofthesystematicerrorscausedbyuncertainties
in the normalization and registration of the reference PSFs.
Other systematic errors from cyclic changes of HST’s focus
and differences between the field positions and broadband
colorsofαPicandβ Picarenegligiblecomparedwiththesur-
face brightness of β Pic’s disk over most of the HRC’s FOV
(Krist 2000). Our systematic-error maps represent the con-
volveddifferencesbetweenthe optimalPSF-subtractedimage
of β Pic and three nonoptimal ones generated by purpose-
fully misaligning (along each axis) or misscaling the images
of α Pic by amounts equal to our estimated uncertainties in
PSF registration and Fα/Fβ. The total systematic errors are
1–5 times larger than the random errors within ∼ 3′′of β Pic,
but they diminish to 10–25% of the random errors beyond
∼ 6′′of the star. We refer to the combined maps of random
and systematic errors as total-error maps.
Figure 2 shows the reduced and PSF-subtracted images of
the disk in each ACS bandpass. Each image has been rotated
so that the northeast extension of the disk is displayed hor-
izontally to the left of each panel. The images have been
divided by the brightness of β Pic in each bandpass derived
from Synphot.23The alternating light and dark bands near
the occulting spot reflect imperfect PSF subtraction caused
by the slightly mismatched colors and centroids of α Pic and
β Pic. The bands perpendicular to the disk have amplitudes
that are ∼ 50–100% of the midplane surface brightnesses at
similar distances from β Pic. These residuals preclude ac-
curate photometry of the disk within 1.′′5 (∼ 30 AU) of the
star and anywhere along the direction of the occulting finger.
Along the midplane of the disk, the photometric uncertainties
due to PSF subtraction are ∼ 5–10% at a radius of r = 30 AU
and less than 1% for r > 60 AU.
23All calibrated surface brightnesses and colors presented in this paper are
based upon the following Vega-based apparent magnitudes for β Pic obtained
from Synphot: mF435W= 4.05, mF606W= 3.81, and mF814W= 3.68. The sys-
tematic zero-point errors are < 2% (Sirianni et al. 2005), and the estimated
errors from imperfectly matched reference spectra are ∼ 1–2%.

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4 GOLIMOWSKI ET AL.
Figure 3 shows alternate views of the disk in which the ver-
tical scale is expanded by a factor of four over that presented
in Figure 2 and the vertical dimension of the disk’s surface
brightness is normalized by the brightness measured along
the“spine”ofthedisk. (Thespinecomprisestheverticalloca-
tionsofthemaximumdiskbrightnessmeasuredalongthehor-
izontal axis of each image, after smoothing with a 3×3 pixel
boxcar.) The expanded vertical scale exaggerates the warp
in the inner disk first observed in images taken with HST’s
Wide Field Planetary Camera 2 (WFPC2) by Burrows et al.
(1995). The multiband images shown in Figures 2 and 3 may
be directly compared with the unfiltered optical image of the
diskobtainedwiththeSpaceTelescopeImagingSpectrograph
(STIS)coronagraph(Grady et al.2003)andshowninFigure8
of Heap et al. (2000).
2.3. Deconvolution of the “Off-Spot” PSF
Accurate assessment of the chromatic dependencies of the
disk’s color and morphology requires the deconvolution of
the unocculted instrumental PSF from each HRC filter im-
age. This deconvolution of the “off-spot” PSF is especially
important for the F814W images, because very red photons
(λ ? 0.7 µm) passing through the HRC’s CCD detector are
scattered diffusely from the CCD substrate into a large halo
that contributes significantly to the wide-angle component
of the PSF (Sirianni et al. 2005). Unfortunately, no collec-
tion of empirical off-spot reference PSFs exists yet for the
HRC coronagraph. Consequently, we can deconvolvethe off-
spot PSFs only approximatelyby using synthetic PSFs gener-
ated by the Tiny Tim software package distributed by STScI
(Krist & Hook 2004). Tiny Tim employs a simplistic model
of the red halo that does not consider its known asymmetries
(Krist et al. 2005b), but this model is sufficient for assessing
the general impact of the red halo on our images of β Pic’s
disk.
We generated model off-spot PSFs using the optical pre-
scriptions, filter transmission curves, and sample A5V source
spectrum incorporated in TinyTim. For simplicity, we ap-
proximated the weakly field-dependent PSF in each band-
pass with single model PSFs characteristic of the center of the
FOV. The model PSFs extended to an angular radius of 10′′.
We corrected the geometrically distorted model PSFs in the
manner described in §2.2, and then deconvolved them from
the PSF-subtracted images of β Pic obtained at each roll an-
gle. In doing so, we applied the Lucy–Richardsondeconvolu-
tion algorithm (Richardson 1972; Lucy 1974) to each image
outside a circular region of radius 1.′′5 centered on the sub-
tracted star. (The amplitudes and spatial frequencies of the
PSF-subtraction residuals within this region were too large to
yield credible deconvolved data.) The imaged FOV lacked
any bright point-sources by which we could judge conver-
gence of the deconvolution, so we terminated the computa-
tion after 50 iterations. Examinationof intermediate stages of
the process showed no perceptible change in the deconvolved
images after ∼ 45 iterations.
Figures 4 and 5 are the deconvolved counterparts of Fig-
ures 2 and 3, respectively. The compensating effect of the
deconvolutionis especially evident when comparing the mor-
phologies of the disk in Figures 3 and 5. The color-coded
isophotes of the disk in each bandpass are much more similar
in the deconvolvedimages than in the convolved images. The
amplified, correlated noise in the deconvolvedimages is char-
acteristic of the Lucy–Richardson algorithm when applied to
faint, extendedsources. It is a consequence of the algorithm’s
requirements of a low background signal, nonzero pixel val-
ues, and flux conservation on both local and global scales.
These requirements also account for the disappearance of the
negative PSF-subtraction residuals near the occulting spot.
The requirement of local flux conservation ensures reliable
photometryin regions where the ratio of signal to noise (S/N)
is large and where PSF-subtraction residuals are small, but it
makesphotometricmeasurementselsewhereless accurateand
their uncertainties nonanalytic.
3. IMAGE ANALYSIS
The processed ACS/HRC images shown in Figures 2 and 3
are the finest multiband, scattered-light images of β Pic’s in-
ner disk obtained to date.24Earlier ground-based, scattered-
light images show the usual effects of coarse spatial resolu-
tion and PSF instability caused by variable atmospheric and
local conditions (Smith & Terrile 1984; Paresce & Burrows
1987; Golimowski et al. 1993; Lecavelier des Etangs et al.
1993; Kalas & Jewitt 1995; Mouillet et al. 1997a,b). The un-
published BVRI WFPC2 images of the disk described by
Burrows et al. (1995) have comparatively low S/N ratios be-
cause WFPC2 lacks a coronagraphic mode and directly im-
aged starlight scatters irregularlyalong the surface of its CCD
detectors. These conditions forced short exposure times to
avoid excessive detector saturation and created irreproducible
artifacts in the PSF-subtracted images. Moreover, the con-
struction of a WFPC2 reference PSF from images of β Pic
obtainedat severalroll angles allowedpossible contamination
of the reference PSF by the innermost region of the disk. The
unfiltered STIS images of the disk (Heap et al. 2000) com-
pare favorably with our HRC images, notwithstanding their
lack of chromatic information and partial pupil apodization
(Grady et al. 2003). Both sets ofimagesshowthe sameregion
of the disk, though STIS’s narrow occulting wedge permitted
imaging of the disk’s midplane about 0.′′4 (8 AU) closer to
the star. The HRC’s circular occulting spot and Lyot stop ex-
posed the regions around the projected minor axis of the disk
that were obscured in the STIS images by diffraction spikes
and the shadow of the occulting bar. The HRC images have
twice the spatial resolution of the STIS images, and they ex-
hibit better S/N ratios in the regions of the disk between 150
and 250 AU from the star.
3.1. Disk Morphology
Figure 6 shows isophotal maps of our F606W images of
the disk before and after deconvolution of the off-spot PSF.
These maps are qualitatively similar to those generated from
our F435W and F814W images. They confirm the morphol-
ogy and asymmetries of the disk reported previously by sev-
eral groups and described in detail by Kalas & Jewitt (1995)
and Heap et al. (2000). The brightness asymmetry between
the disk’s opposing extensions is particularly evident along
the spine beyond ∼ 100 AU of β Pic. The asymmetric cur-
vature of the isophotes on opposite sides of the spine and the
inversionof this asymmetryacrossthe projectedminoraxis of
the disk are also apparent. Kalas & Jewitt (1995) referred to
this diametrical antisymmetry as the “butterfly asymmetry.”
Our images provide the first credible look at the sur-
face brightness along the disk’s projected minor axis. The
convex isophotes in this region indicate that the pinched
appearances of the disk in the images of Smith & Terrile
24Fully processed images and error maps in FITS format can be obtained
via the World Wide Web at http://acs.pha.jhu.edu/∼dag/betapic.

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MULTIBAND IMAGES OF DISK AROUND β PICTORIS5
(1984), Golimowski et al. (1993), Lecavelier des Etangs et al.
(1993), Mouillet et al. (1997a,b), and, to a lesser degree,
Kalas & Jewitt (1995) are artifacts of oversubtraction of the
reference PSF and/or self-subtraction of the disk along its mi-
nor axis. Other scattered-light images yielded no information
in this region because of obscuration by coronagraphicmasks
(Paresce & Burrows 1987; Gledhill et al. 1991; Heap et al.
2000). Our images are tinged by residuals from the im-
perfect subtraction of the linear PSF feature seen in Fig-
ure 1, but these residuals do not affect the overall contours
of the isophotes. The isophotes are more widely spaced along
the northwestern semiminor axis than along the southeastern
semiminor axis. Such brightness asymmetry in optically thin
disks is often attributed to the enhanced forward-scattering
efficiency of the dust, which implies that the side of the disk
closer to Earth is inclined slightly northwest from the line of
sight to the star. This deduction is consistent with the in-
clination determined by Kalas & Jewitt (1995) from single-
scatteringmodelsofthesurfacebrightnessalongtheprojected
major axis of the disk.
3.1.1. The Main and Secondary Disks
Mouillet et al.(1997b)viewedtheinnerwarpas adeformed
and thickened region of the disk, perhaps caused and sus-
tained by a planet in an inclined, eccentric orbit within 20 AU
of β Pic. Heap et al. (2000) subsequentlyinterpretedthe warp
as a blend of two separate disk components, the lesser of
which is inclined from the main component by 4◦.6. The lat-
ter interpretation is supported by Figure 7, which shows the
ratios of our HRC images after and before deconvolution of
the off-spot PSF. The division of the PSF-deconvolved filter
images (Figure 4) by their corresponding convolved images
(Figure 2) accentuates the small or narrow features in the disk
that are most affected by blurring from the instrumental PSF.
Thus the sharply-peaked midplane of the outer disk appears
prominently in Figure 7. The midplane of the inner warp is
not as well defined as that of the outer disk, but the apparent
separation of the midplanes beyond ∼ 80 AU from the star
indicates that the warp is a distinct secondary disk inclined
from, and perhaps originating within, the main disk.
Mimicking Heap et al. (2000), we determined the contribu-
tions of the main and secondary disks to the composite verti-
cal scattered-light profile (i.e., the scattered-light distribution
perpendicular to the midplane of the disk) by fitting two sim-
ilar, vertically symmetric profiles to the composite profile as
a function of distance from the star. In doing so, we assigned
a shape to the individual profiles by qualitatively assessing
various analytic functions at a few locations along the disk
in our PSF-deconvolved images. We found that a “hybrid-
Lorentzian” function – two Lorentzians of different widths
whose top and bottom parts, respectively,are smoothly joined
at an arbitrary distance from their common centers – satisfac-
torily matched each individual profile. (We ascribe no physi-
cal significance to this hybrid-Lorentzianfunction, nor do we
claim that it uniquely or optimally characterizes each profile.)
We used a non-linear least-squares fitting algorithm based on
the Levenberg–Marquardttechnique (Press et al. 1992) to de-
termine the positions, amplitudes, widths, and top-to-bottom
transition zones of the main and secondary hybrid-Lorentzian
profiles at distances of 30–250 AU from β Pic. The resulting
fits of the composite vertical profiles were best in the regions
80–130 AU from the star, where the two disk components are
sufficiently bright and separated to allow unambiguous dis-
crimination of both components. Figure 8 shows the best fits
to the composite vertical profiles of both extensions of the
disk observed in our F606W image at distances of 100 AU
from the star.
Figure 9 shows the relative positions of the fitted compo-
nentsofthecompositeverticalprofileasafunctionofdistance
from β Pic. For each filter image and disk extension, we per-
formed linear least-squares fits to the traces of the main and
secondary disks within the regions where they are accurately
identified (80–250 AU for the main disk and approximately
80–130AU for the secondary disk). These fits are overplotted
in Figure 9. The relative position angles of the main disk’s
northeast and southwest extensions (measured counterclock-
wise from the horizontal axis) are about −0◦.4 and 0◦.5, re-
spectively. The difference between these position angles is
similar to the “wing-tilt asymmetry” noted by Kalas & Jewitt
(1995) at distances of 100–450 AU from β Pic. However, our
fittedlinesappeartointersectatapointalmostcoincidentwith
thestar, ratherthanatapointinthesouthwestextension,as re-
ported by Kalas & Jewitt. Expanding the vertical scale of our
tracesof themain diskin the F606Wimage(Figure10)shows
that thespine of the northeastextensionconformsto the linear
fit down to ∼ 80 AU, at which point the main and secondary
disks can no longer be credibly distinguished. However, the
spine of the southwest extension exhibits more curved than
linear behavior over the range of the fit. This bow in the
southwest extension appears in our F435W and F814W im-
ages with equal clarity and therefore does not appear to be
an artifact of our decomposition of the vertical scattered-light
profile.
Table 2 lists the position angles of the linear fits along each
extension of the secondary disk relative to the correspond-
ing fits along the main disk. The average tilt of the sec-
ondary disk’s southwest extension matches the 4◦.6 derived
by Heap et al. (2000) for both extensions. However, we find
that the average tilt of the northeast extension is ∼ 25% larger
than the values obtained by Heap et al. (2000) and by us for
the southwest extension. Extrapolating the linear fits to the
secondary disk outward (Figure 6) shows that the convex in-
flections of the butterfly asymmetry are aligned with the sec-
ondary disk, which supports the notion that the asymmetry is
caused by radiatively expelled dust from the secondary disk
(Augereau et al. 2001). On the other hand, extending the lin-
ear fits to the secondary disk toward β Pic (Figure 9) shows
that its nonparallel extensions would not converge near the
star if they extended sufficiently inward. Instead, the north-
east extension would intersect the northeast extension of the
main disk at a distance of ∼ 30 AU from β Pic. Corona-
graphic images with a smaller occulting spot and higher pixel
resolutionare neededto determine if this intersection actually
occurs.
Although our analysis of the two-component structure of
the disk qualitatively supports that of Heap et al. (2000), our
results reveal some errors in the presentation and interpre-
tation of their results. These errors stem from the incorrect
portrayal of the secondary disk’s tilt relative to the northeast
and southwest extensions of the main disk in Figures 11–
13 of Heap et al. (2000). In these figures, the plotted data
– and consequently the relative slope of the secondary disk
– are inverted about the midplane of the main disk. The ori-
entations of the main and secondary disks should appear as
they do in Figures 7–9 of this paper and in Figures 8 and 10
of Heap et al. (2000). Because of this inversion, Heap et al.
concluded that the disk’s southeast side was brighter than its
northwest side and, consequently, that the southeast side was

Page 6

6 GOLIMOWSKI ET AL.
inclined toward the line of sight. These conclusions are not
supported by our isophotal map of the disk (Figure 6) or by
the single-scattering models of Kalas & Jewitt (1995).
3.1.2. Thickness of the Main Disk
Previous scattered-light studies indicated that the com-
posite disk is uniformly thick within 7′′(135 AU) of
β Pic and flared beyond that region (Smith & Terrile
1984; Paresce & Burrows 1987; Artymowicz et al. 1990;
Golimowski et al. 1993; Kalas & Jewitt 1995; Mouillet et al.
1997a; Heap et al. 2000). These characteristics are evident
in Figures 3 and 5. Previous measurements of the disk’s full
width at half its midplane (FWHM) brightness vary signifi-
cantly, however, which suggests that the disk’s intrinsic pro-
jected width is less than or comparableto the resolutionof the
images from which the measurements were made. Our de-
convolution of the off-spot PSF from the HRC images – the
first such effort exhibited for scattered-light images of β Pic’s
disk – permits us to assess this resolution dependency and to
measure more accurately the intrinsic width of the disk as a
function of distance from β Pic.
Figure 11 shows the full widths of each extension of the
composite disk at half and one tenth of the maximum bright-
ness of the midplane at distances 20–250 AU from the star.
These widths are shown in the panels labeled “FWHM” and
“FW0.1M,” respectively. The associated pairs of thin solid
anddashedcurvesshow thewidths ofthe northeastand south-
west extensions obtained from the F606W image before and
after PSF deconvolution. The short, thick curves show the
measured widths of the hybrid-Lorentzian curves that best
fit the main component of the composite disk in the region
80–150 AU from β Pic (§3.1.1). The FWHM and FW0.1M
plots show progressive reductions in the measured width of
the main disk after PSF deconvolution and decomposition of
the main and secondary disks. The up-to-30% reduction in
the FWHM after deconvolution of the narrow off-spot PSF
(FWHM ≈ 0.′′05) shows that previously reported measure-
ments, particularly those obtained from the ground, reflect
more the angular resolution of the observations than the in-
trinsic thickness of the disk.
The deconvolved and decomposed curves show that the
FWHM and FW0.1M of both disk extensions are nearly con-
stant (∼ 11–13 AU and ∼ 50–60 AU, respectively) within
∼ 120 AU of β Pic, and they increase approximately linearly
with distance beyond∼120 AU. This behavioris consistently
seen in the F435W, F606W, and F814W images. The south-
west extensionappearsto thickenmorerapidlythanthenorth-
east extension beyond ∼ 160 AU, as noted by Kalas & Jewitt
(1995), but the correlated noise injected into the deconvolved
images by the Lucy–Richardson algorithm (Figure 5) pre-
cludes accurate quantification of the FWHMs from those im-
ages. Reverting to the PSF-convolved images, we find that
the FWHM and FW0.1M of the southwest extension are
∼ 10 AU and ∼ 60 AU larger, respectively, than the corre-
spondingvalues of northwest extension 250 AU from the star.
Our finding is consistent with the FWHM measurements of
Kalas & Jewitt (1995) when the different angular resolutions
of the two sets of observations are considered. Heap et al.
(2000) reportedno suchthickness asymmetryfromtheirSTIS
images. Their measurements of FWHM at discrete locations
50–200AU fromβ Pic are consistentwith ourPSF-convolved
measurements of the narrower northeast extension. However,
their FW0.1M measurements at these locations are 20–60%
smaller than our PSF-convolved measurements at the same
locations in each extension. These discrepancies may reflect
differences between the S/N ratios of the HRC and STIS im-
ages at scattered-light levels below ∼ 10−9of the stellar flux.
3.1.3. Planetesimal Belts or Rings
Reexamining earlier WFPC2 and ground-based corona-
graphic images of β Pic, Kalas et al. (2000) noted several
localized density enhancements along the midplane of the
disk’s northeast extension at distances of 500–800 AU from
the star. They did not see this structure in the southwest ex-
tension, so they interpreted the clumps as a system of eccen-
tric, nested rings formed in the aftermath of a close encounter
between the disk and a passing star. Wahhaj et al. (2003) and
Weinberger et al.(2003)later reportedmid-infraredimagesof
thedisk that show a distinct warp within20 AU ofthe star that
is oppositely tilted from the secondary disk seen in Figure 7.
Wahhaj et al. (2003) also noted clumps of emission in both
disk extensions within 100 AU of β Pic that are arranged in
diametrically opposite pairs centered on the star. They inter-
preted these clumps as a series of noncoplanar rings caused
by gravitational interactions of the disk with a planetary sys-
tem. Telesco et al. (2005) did not observe the innermost warp
in their mid-infrared images of the disk, but they attributed a
brightclumpof12–18µmemissionat 52AU insouthwestex-
tension to a concentration of 0.1–0.2 µm silicate and organic
refractory grains heated to ∼ 190 K. High-spatial-resolution,
mid-infrared spectra of the disk recorded at 3 AU intervals
along the inner 30 AU of each extension also show con-
centrated regions of emission from 0.1–2 µm silicate grains
(Okamoto et al. 2004). The presence of such concentrations
of small grains in the face of expulsive stellar-radiation pres-
sure suggests that the grains are continuously created by col-
lisions of planetesimals confined to rings or belts within the
otherwise depleted inner region of the dust disk.
The bright clumps detected by Kalas et al. (2000) in the
northeast extension of the disk lie outside the FOV of
our HRC images, and the innermost warp reported by
Wahhaj et al. (2003) and Weinberger et al. (2003) is obscured
by the HRC’s occulting spot.
mid-infrared emission located 30–100 AU from the star
(Wahhaj et al. 2003; Telesco et al. 2005) are potentially ob-
servable in our HRC images.
map of the inner region of the disk obtained from our PSF-
deconvolvedF606W imageaftersmoothingwith a 3×3-pixel
boxcar. The isophotal interval is 0.2 mag arcsec−2, which is
similar to the interval between isophotes of 18 µm emission
from the same region of the disk presented by Wahhaj et al.
(2003) and Telesco et al. (2005). The locations of the clumps
of 18 µm emission are marked with the letters assigned to
them by Wahhaj et al. Our F606W isophotes show no evi-
dence of such clumping in scattered optical light. Adjusting
the isophotal interval and the smoothing factor does not alter
this conclusion. Our images do not refute the existence of the
clumps, however, because the scattered optical light and mid-
infrared emission may emanate from different regions of the
disk (Pantin et al. 1997).
However, the clumps of
Figure 12 is an isophotal
3.2. Surface Brightness and Asymmetry
Because β Pic’s disk is viewed nearly “edge-on,” its
surface brightness has traditionally been parametrized with
one or more power laws fitted along the midplanes
(or spines) of its opposing extensions (Smith & Terrile
1984; Artymowicz et al. 1989, 1990; Gledhill et al. 1991;
Golimowski et al. 1993; Lecavelier des Etangs et al. 1993;

Page 7

MULTIBAND IMAGES OF DISK AROUND β PICTORIS7
Kalas & Jewitt 1995; Mouillet et al. 1997a; Heap et al. 2000).
The number of fitted power laws and their indices have varied
considerably, mostly because such fits are sensitive to errors
inthestellar PSF subtraction. TheinnatestabilityofHST’sin-
strumental PSFs reduce these errors substantially, so we com-
pare our quantitative measurements of the disk’s spine (as de-
fined in §2.2) with those obtained from the STIS images of
Heap et al. (2000). To do so, we assess the surface bright-
nesses of the spines of both extensions from our ACS images
both before and after PSF deconvolution. We initially ignore
the two-component structure of the disk described in §3.1.1,
because the two components cannot be distinguished by our
profile-fitting algorithm within 80 AU of the star (§3.1.1) and
because the main disk dominates the surface brightness be-
yond 80 AU. We then compare our results for the composite
disk with those obtained for its main and secondary compo-
nents over the region in which they are credibly resolved.
3.2.1. Horizontal Profiles of the Composite Disk
Figure 13 shows the logarithmic surface brightness pro-
files measured along the spines of each extension of the
composite disk before PSF deconvolution. The accompa-
nying ±1σ error profiles, which are derived from the total-
error maps of the images (§2.2) and include ∼ 3% uncer-
tainty in the photometric calibration, show that these profiles
are very accurate beyond ∼ 1.′′5 (∼ 30 AU) from the star.
The profiles clearly do not indicate a single power-law de-
pendence of surface brightness with distance, as was deter-
mined in some of the earliest ground-based imaging studies
of the disk (Smith & Terrile 1984; Artymowicz et al. 1989;
Gledhill et al. 1991; Lecavelier des Etangs et al. 1993). In-
stead, the logarithmic profiles exhibit distinctly different lin-
ear behavior at angular distances of 2′′–3.′′5, 3.′′7–5.′′6, 6.′′6–
10′′, and 10′′–13.′′4, with smooth transitions in slope be-
tween these regions. Table 3 lists the slopes of the lin-
ear least-squares fits to the logarithmic data (i.e., the in-
dices of the radial power laws, r−α, that best fit the surface-
brightness profiles) within these four regions. The promi-
nent changes in α at ∼ 6′′(∼ 115 AU) from the star are
well documented (Artymowicz et al. 1990; Golimowski et al.
1993; Kalas & Jewitt 1995; Heap et al. 2000), but the more
subtle changes at ∼ 3.′′6 (∼ 70 AU) and ∼ 10′′(∼ 195 AU)
are noted here for the first time. Conversely, the pronounced
decrease in the disk’s B-band surface brightness within 7.′′3
(?140 AU) reported by Lecavelier des Etangs et al. (1993) is
not observed in our F435W image.
The prominent inflections in the profiles at ∼ 115 AU are
possible evidence for the sublimation of water ice from com-
posite grains at dust temperatures greater than 100–150 K
(Nakano 1988; Artymowicz et al. 1990; Golimowski et al.
1993; Pantin et al. 1997; Li & Greenberg 1998). Applying
their cometary dust model to β Pic’s disk, Li & Greenberg
(1998) noted that the relative compositions of the grains
should vary across several regions of the disk, as the inner
and outer mantles of various ices and organic refractory ma-
terial successively evaporate from, or condense upon, their
silicate cores in accordance with the local dust temperature
and stellar-radiation pressure. The more subtle changes in α
at ∼ 70 AU and ∼ 195 AU may therefore mark the bound-
aries over which such changes in composition (and conse-
quently albedo) occur. On the other hand, the decrease in
α within ∼ 70 AU may indicate a decrease in the number
density of the grains caused by an interior planetary system
(Lagage & Pantin 1994; Roques et al. 1994; Lazzaro et al.
1994) or, as we discuss in §3.2.2, the unresolved superposi-
tion of the main and secondary disks.
The changes in α at angular distances of ∼ 3.′′6, 6′′, and
10′′from β Pic are also apparent in the midplane surface-
brightnessprofiles extractedfrom the STIS images of the disk
(Heap et al. 2000). To facilitate comparison with previous
studies, Heap et al. fitted power-lawfunctionsto three regions
of each extension. Two of these regions coincide approxi-
mately with our regions 1 and 3 defined in Table 3; the third
region bridges our regions 1 and 2. Our values of α in re-
gion 1 (2′′–3.′′5, or 39–67 AU, from β Pic) of both extensions
differby ?5% fromthose computedbyHeap et al. (2000) for
the positions of maximum flux along each extension. How-
ever, our values of α in region 3 (6.′′6–10′′, or 127–193 AU,
from β Pic) are ∼ 10–15% smaller than those of Heap et al.
for both extensions, i.e., our power-law fits in this region are
significantly less steep than those determined from the STIS
images. This discrepancy is puzzling, especially as this outer
region of the disk is relatively insensitive to moderate errors
in the PSF subtraction.
To investigate the possible effect of the convolved instru-
mental PSF on our power-law fits, we repeated this analy-
sis on our PSF-deconvolved images in each bandpass. The
surface-brightness profiles along the spines of each decon-
volved disk extension are shown in Figure 14. The corre-
sponding values of α for each region of the deconvolved im-
ages are listed in Table 3. These values are significantly dif-
ferentfromtheirPSF-convolvedcounterpartsonlyinregion4,
where the S/N ratios are low and, consequently, the efficacy
of the Lucy–Richardson algorithm is suspect. In region 3,
the average difference between the associated convolved and
deconvolved indices is ∼ 1%, so it is unlikely that differ-
ences between the HRC and STIS coronagraphic PSFs cause
the ∼ 10–15% discrepancies in the values of α reported by
Heap et al. (2000) and us for this region.
Figure 15 displays the PSF-deconvolved profiles in a man-
ner that facilitates comparison of the two disk extensions in
the F435W, F606W, and F814W images. The plots show the
effects of the asymmetric values of α on the relative bright-
nesses of the two extensions at equal distances from β Pic.
The southwest extension is brighter than the northwest ex-
tension in the region ∼ 50–100 AU from the star, whereas
the opposite condition exists for r ? 150 AU. At r = 6′′
(∼ 115 AU), the surface brightnesses of each extension are
14.9, 14.6, and 14.4 mag arcsec−2in F435W, F606W, and
F814W, respectively. These values are 0.2–0.3 mag arcsec−2
brighter than the corresponding brightnesses measured from
the PSF-convolved images. The latter measurements com-
pare favorably with the ground-based, R-band measurements
of Golimowski et al. (1993) and Kalas & Jewitt (1995) at r =
6′′, but are ∼ 1.5 mag arcsec−2brighter than the R- and I-
band measurements reported by Paresce & Burrows (1987)
and Smith & Terrile (1984), respectively, for this fiducial dis-
tance. The outer distance limits of our photometric measure-
ments (260 AU and 300 AU for the northeast and southwest
extensions, respectively) are set by the HRC’s FOV; they do
not reflect an intrinsic asymmetry in the physical sizes of the
extensions.
Although the values of α within ∼ 110 AU of β Pic (re-
gions 1 and 2) are nearly constant across F435W, F606W, and
F814W, those between 125 and 200 AU (region 3) decrease
nonuniformly with increasing wavelength. These trends in-
dicate that the optical colors of the disk are constant within
∼ 110 AU of the star, but they redden considerably between

Page 8

8GOLIMOWSKI ET AL.
125 and 200 AU. The color gradient appears to flatten again
from ∼ 200 to 250 AU (region 4), but the relatively large un-
certainties attached to α in this region preclude a definitive
assessment. We confirm these trends in our subsequent anal-
ysis of the disk’s color (§3.3).
3.2.2. Horizontal Profiles of the Component Disks
The resolution of the inner disk into two components
prompts an assessment of the contributions of each compo-
nent to the horizontal surface-brightness profiles of the com-
posite disk. Figure 16 shows the multiband, logarithmic pro-
files of the main and secondarydisks, extractedfromthe PSF-
deconvolved images. The curves trace the maxima of the
hybrid-Lorentzian profiles that best fit the vertical surface-
brightness profiles of the two disks at 80–150 AU from β Pic
(§3.1.1). The secondary disk is ∼ 1.5 mag arcsec−2fainter
than the main disk at 100 AU, as indicated in Figure 8. The
profiles of the main disk show the same inflections at ∼ 6′′
(∼ 115 AU) exhibited by the composite disk, but the sec-
ondary disk’s profiles appear linear throughout this region.
Whereas the relative brightnesses of the main disk’s exten-
sions invert at ∼115 AU (as noted in §3.2.1for the composite
disk), the southwest extensionof the secondarydisk is consis-
tentlybrighterthanits northeastextensionfrom80 to150AU.
We fitted power laws to the profiles of both extensions of
the main and secondary disks over the regions displayed in
Figure 16, taking care to avoid the inflection of the main disk
at ∼ 115 AU. Table 4 lists the indices, α, of these power
laws. The main disk’s indices at 80–108 AU are 15-35%
smaller than those of the composite disk in the mostly over-
lapping region 2 (defined in Table 3), whereas its indices at
127–150 AU are 5–20% larger than those of the composite
disk in region 3. These indices are nearly constant across the
B, V, and I bands at 80–108 AU, but they progressively de-
crease with increasing wavelength at 127–150 AU. This be-
havior mimics that of the composite disk in regions 2 and 3
(§3.2.1), which indicates that the main disk’s colors progres-
sively redden beyond the inflection at ∼ 115 AU. Conversely,
the secondary disk’s indices progressively increase with in-
creasing wavelength within the entire 80–150 AU region of
the northeast extension, but they are effectively constant in
the southwest extension. The former trend suggests that the
colorsinthenortheastextensionbecomebluerwithincreasing
distance from β Pic. Altogether, these characteristics indicate
that the grain populationsand/or distributions in the main and
secondary disks differ significantly at common projected dis-
tances from the star. Moreover, if unresolved, the secondary
diskcansignificantlyaffectmodelsthat usethescattered-light
profiles to constrain the spatial distribution and composition
of dust in the main disk.
3.3. Optical Colors of the Disk
Previous multiband-imagingstudies of β Pic’s disk showed
that the optical colors of the star and disk are indistin-
guishable within the studies’ estimated photometric errors
(Paresce & Burrows 1987; Lecavelier des Etangs et al. 1993).
These errors ranged from 20 to 30%, so actual color differ-
ences of a few tenths of a magnitude would not have been
deemed credible. The greater photometric precision of our
ACS study enables a correspondingly more precise assess-
ment of the disk’s optical colors and scattering properties. We
first examine the ACS colors of the composite disk to enable
a comparison with the earlier ground-based studies. We then
examinethe colorsofthe mainandsecondarycomponentsde-
rived from our decomposition of the disk’s vertical scattered-
light profile (§3.1.1).
3.3.1. Two-Band Flux Ratios of the Composite Disk
Figure 17 shows the F606W/F435W and F814W/F435W
flux ratios of the disk obtainedfrom the PSF-deconvolvedim-
ages shown in Figure 4. Because the images in Figure 4 are
separately normalizedby the stellar flux in each bandpass, the
images in Figure 17 represent the flux ratios of the disk rela-
tiveto those ofthe star. Consequently,regionsofthe disk hav-
ing a flux ratio of 1.0 exhibit the same mF435W–mF606Wand
mF435W–mF814W colors (hereafter denoted F435W–F606W
and F435W–F814W) as β Pic itself. Although the flux ra-
tios along the projected minor axis of the disk are obscured
by the residual artifacts of the PSF subtraction, those along
the projected major axis are clear and uncorrupted. The im-
ages show that the flux ratios are asymmetric about both pro-
jected axes, with the largest ratios appearing in the north-
northeast quadrant of the disk. Within ∼ 150 AU of the star,
the F606W/F435W and F814W/F435W ratios on the south-
east side of the disk are ∼ 1.0–1.1 times those of the star,
while the ratios on the northwest side are ∼ 1.2–1.4 times
those of the star. The uncertainties of these ratios range from
∼ 5–10% along the spine to ∼ 25% at projected vertical dis-
tances of ±50 AU from the spine. Beyond ∼ 150 AU from
the star, the color asymmetry between the two sides dimin-
ishes substantially, but the uncertainties away from the spine
are comparatively large (∼ 25–75%).
Figures 6 and 17 show that the northwest side of the disk
within ∼ 150 AU of β Pic is both brighter and redder than its
southeast counterpart. If the brightness asymmetry indicates
that the side of the disk nearer to Earth is tipped northwest-
erly (§3.1), then the color asymmetry within ∼ 150 AU indi-
cates that the ensemble of dust grains in that region becomes
increasingly forward-scattering with increasing wavelength.
This behavior is inconsistent with the expected scattering
properties of both compact and porous interstellar grains
(Draine & Lee 1984; Wolff et al. 1998; Voshchinnikov et al.
2005), so its cause is not evident.
The vertical asymmetry of the composite disk’s colors is
strikingly well aligned with the spine of the disk, which ap-
pears prominently in both panels of Figure 17. As the S/N
ratios of our flux measurements are largest along the spine,
we hereafter restrict our analysis of the disk’s colors to that
region in order to assess their dependence on the horizontal
projected distance from the star. Focusing on the spine also
allows us to assess the impact of PSF convolution on the col-
ors measured along this narrow feature of the composite disk.
3.3.2. Colors along the Spine of the Composite Disk
Figure 18 shows the F435W–F606W and F435W–F814W
colors of the composite disk relative to those of β Pic, before
and after deconvolutionof the off-spot PSF. We measured the
colors along the spines of each disk extension after smooth-
ing the F606W/F435W and F814W/F435W ratio images with
a 7×7-pixel boxcar. Although the PSF-convolved colors are
less accurate than their deconvolvedcounterparts,their uncer-
tainties are more suitably compared with those from previ-
ous studies in which PSF deconvolution was not performed.
The average uncertainties of both colors before PSF decon-
volution are ∼ 3% at 40–150 AU and ∼ 8% at 150–250 AU,
i.e., 3–10 times better than those obtained in previous studies

Page 9

MULTIBAND IMAGES OF DISK AROUND β PICTORIS9
(Paresce & Burrows 1987; Lecavelier des Etangs et al. 1993).
PSF deconvolution increases the differences between the
F435W–F606W and F435W–F814W colors of the disk and
star by ∼ 0.03 and ∼ 0.1 mag, respectively, at the cost
of increased uncertainty. The relatively large increase in
∆(F435W–F814W) is due to the correction of blurring from
both the instrumental PSF and the HRC’s red-halo anomaly
(§2.3).The general similarity of the respective solid and
dashed curves in Figure 18 shows that the color variations as
a functionof distance from β Pic are not significantly affected
by PSF deconvolution. This condition is consistent with the
practically invariant power-law indices that parametrize the
midplane surface-brightness profiles in regions 1–3 of the
composite disk before and after PSF deconvolution (Table 3).
The PSF-deconvolved curves in Figure 18 show that the
F435W–F606W and F435W–F814W colors of the disk are
∼ 0.1 mag and ∼ 0.2 mag redder, respectively, than those
of β Pic at distances of ∼ 40–120 AU from the star. These
color excesses are nearly constant within this region and have
average uncertainties of ∼ 8%.
F435W–F814W excesses respectively increase to ∼ 0.2 mag
and ∼ 0.35 mag at 250 AU in the northeast extension and
to ∼ 0.25 mag and ∼ 0.4 mag at 250 AU in the southwest
extension. The average uncertainties of both excesses be-
yond 150 AU from the star are ∼ 23%, i.e., ∼ 0.05–0.09 mag
at 250 AU. The constancy of F435W–F606W and F435W–
F814W within ∼ 120 AU is consistent with the chromatically
invariantpower-lawindicesassociated with regions1 and2 of
the composite disk (Table 3). Likewise, the steadily redden-
ing colors from∼120–250AU are consistent with the inverse
proportionality of α and wavelength in region 3 of the disk.
Our results contradict the longstanding notion that β Pic’s
disk scatters visible light neutrally and uniformly. Its red
optical colors (relative to the star) are generally consis-
tent with the colors of the disks surrounding the B9 Ve
star HD 141569A (Clampin et al. 2003) and the G2 V star
HD 107146 (Ardila et al. 2004, 2005), although those disks
do not exhibit spatial color gradients like those seen in
β Pic’s disk beyond ∼ 120 AU. The relatively red col-
ors of β Pic’s disk contrast markedly with the relatively
blue colors of the edge-on disk surrounding AU Microscopii
(Krist et al. 2005a), an M dwarf in a co-moving group of
stars that includes β Pic (Barrado y Navascués et al. 1999;
Zuckerman et al. 2001). In §4.2.6, we speculate that the dis-
parate colors of the disks surroundingβ Pic and AU Mic may
be caused by small differences between the minimum sizes of
dust grains in the two disks.
The F435W–F606W and
3.3.3. Colors along the Spines of the Component Disks
Figure 19 shows the F435W–F606W and F435W–F814W
colors of each extension of the main and secondary disks in
the region 80–150 AU from β Pic. The colors are derived
from the maxima of the hybrid-Lorentzian profiles that best
fitted these components of the vertical-scattered light profiles
of the composite disk (§3.1.1). Because the colors depend
upon the robustness of our fitting algorithm at each position
along the spine of the composite disk, their uncertainties can-
not be analytically determined. We estimate these uncertain-
ties from the root-mean-squared (RMS) deviations computed
for each disk extension. For the main disk, σ(F435W−F606W)≈
σ(F435W−F814W)≈ 0.02 over both extensions. For the sec-
ondary disk, σ(F435W−F606W)≈ 0.1 over both extensions, and
σ(F435W−F814W)≈ 0.1 and 0.2 over the southwest and north-
east extensions, respectively.
The colors of the main disk conform to those of the com-
posite disk between 80 and 150 AU, as expected from its
nearly fivefold superiority in brightness over the secondary
disk. The colors of the secondary disk’s southwest extension
also match those of the main disk, but its northeast extension
appearsbluerthanthemaindiskby∼0.1–0.2maginF435W–
F606W and ∼ 0.1–0.4 mag in F435W–F814W.Moreover,the
F435W–F814W color of this extension apparently becomes
bluerwithincreasingdistancefromthestar,as previouslysug-
gested by its steepening midplane surface-brightness gradient
(§3.2.2 and Table 4). However, the relatively large uncertain-
ties in this region of the disk preclude a definitive assessment
ofthecolorsandtrendsofthesecondarydisk. Withinouresti-
mated errors, the colors of the secondary disk are also consis-
tent with being neutral and constant between 80 and 150 AU.
4. DISCUSSION
4.1. Impact of PSF deconvolution on observations and
models
Our analysis demonstratesthat PSF deconvolutionis an im-
portantstep toward accuratelycharacterizingthin debris disks
viewed edge-on or, more generally, less-inclined disks having
narrow or compact structural elements. It is especially im-
portant for multiband imaging studies designed to map the
chromatic dependencies of a disk’s morphology and surface
brightness. For example, PSF deconvolution dispels the il-
lusion that β Pic’s disk thickens with increasing wavelength
(Figures3and5)byrestoringthedisplacedredfluxtoitsorig-
inallocationalongthedisk’sspine. Thisrestorationofthetrue
surface-brightness distribution contributes largely to our ob-
servation that the main disk component is significantly redder
thanpreviouslydeterminedfromground-basedmeasurements
(Paresce & Burrows 1987; Lecavelier des Etangs et al. 1993).
It also provides refined empirical constraints for past and fu-
ture dynamical models that alternatively view the inner warp
as a uniform, propagating deformation of a single disk or as
two distinctly separate, inclined disks (Mouillet et al. 1997b;
Augereau et al. 2001).
The improved measurements of the disk’s morphology and
surface brightness obtained from our PSF deconvolved im-
ages provide a basis for improved scattered-light models of
β Pic’s disk. However, deriving the spatial distribution and
scattering properties of dust in an edge-on disk is compli-
cated by the integrated effects of variations in both charac-
teristics along the line of sight. This complication is com-
pounded by the many asymmetries between the opposing
extensions of β Pic’s disk and by the existence of an in-
clined secondary disk. Consequently, three-dimensional scat-
tering models based on axisymmetric dust distributions –
like those previously developed for the disks around β Pic
(Artymowicz et al. 1989; Kalas & Jewitt 1995) and AU Mic
(Krist et al. 2005a) – have limited utility in the face of the
morphologicaland photometriccomplexityof β Pic’s disk re-
vealed by our HRC images.
Multicomponent, nonaxisymmetric models are clearly
needed to reproduce the complicated scattered-light distribu-
tion associated with β Pic’s disk. Development of such mod-
els is beyond the scope of this paper, but we identify several
issues raised by our observations that should be addressed by
future modelling efforts:
1. The horizontal surface-brightness profiles of the main
disk within ∼ 150 AU are sensitive to contamination
by flux from the secondary disk. Models of the dust

Page 10

10GOLIMOWSKI ET AL.
distribution within either disk should be based on de-
convolvedand deblendedcomponentsof scattered light
from both disks.
2. The spines of the opposing extensions of the secondary
disk are not collinear. While the misaligned spines of
the main disk (dubbed the “wing-tilt” asymmetry by
Kalas & Jewitt 1995) are attributed to forward scatter-
ing from a slightly inclineddisk, those of the secondary
disk are not as easily explained. The possible optical
and/or dynamical causes of this phenomenon need to
be explored.
3. The clumpiness noted in mid-infrared images of
the disk is not observed in optical scattered light,
even though the grains believed responsible for the
clumps of mid-infraredemission (Okamoto et al. 2004;
Telesco et al. 2005) have sizes commensurate with ef-
ficient scattering of optical light. This apparent incom-
patibility may indicate that the scattered light and ther-
malemissioncomefromdifferentregionsalongtheline
of sight (Pantin et al. 1997). If so, these disparate ob-
servations may constrain the mean scattering properties
of the grains.
4. The optical colors of the composite disk are asymmet-
ric about both projected axes of the disk. The gener-
ally redder and brighter appearance of the northwest
half of the disk is inconsistent with the expectation that
the dust grains scatter red light more isotropically than
blue light. This peculiar behavior may place interesting
constraints on the sizes and compositions of the grains
throughout the disk.
5. The prominent changes in the horizontal surface-
brightness profiles and color gradients at ∼ 115 AU
from β Pic suggest that these phenomena may have a
common cause. The expected sublimation of water ice
from micron-sized grains lying within ∼ 100 AU of the
star (Pantin et al. 1997; Li & Greenberg 1998) is one
possible cause, but color variations caused by changes
in the grain-size distribution must also be investigated.
Although we defer these issues to future theoretical inves-
tigations, we partly address the last issue here via a one-
dimensional analysis of the colors observed along the spines
of the component disks.
4.2. Colors and Properties of the Dust
Li & Greenberg (1998) successfully modeled the disk’s
continuum emission from near-infrared to millimeter wave-
lengths and its 10 µm silicate emission feature by assuming
that the dust is continually replenished by comets orbiting
near, or falling onto, β Pic. In this scenario, the cometary
dust grains are highly porous aggregates of primitive inter-
stellar dust whose composition, molecular structure, and size
and spatial distributions are altered by the stellar radiation
environments into which they are sputtered and transported.
Li & Greenberg (1998) did not apply this dust model to the
disk’s appearance in scattered light because the scattering
properties of highly porous grains with appropriate compo-
sitions had not been fully determined. Subsequent modeling
of these properties (Wolff et al. 1998; Voshchinnikov et al.
2005) now enables us to examine the porous-grain model
from the perspective of the disk’s optical colors.
We begin by deriving a parameter that, in the absence of a
detailed three-dimensionalmodel of the disk, links the optical
propertiesofavarietyofgrainswiththecolorsobservedalong
the spine of the disk. We apply this parameter first to the
colors of the composite disk (Figure 18), as these colors are
largely attributable to the main disk and their uncertainties
are well established. Afterwards, we examine the less-certain
colors measured for the secondary disk (Figure 19).
4.2.1. Effective Scattering Efficiency of Midplane Grains
The intensity of singly-scattered light measured along the
midplane of an optically thin, edge-on disk is
I(ǫ) =
?
n(r) σscaΦ(θ) F0
?r
r0
?−2
dx,
(1)
where ǫ is the angular distance from the star, n(r) is the num-
ber density of grains at a distance r from the star, σscais the
scattering cross section of grains of a given size and compo-
sition, Φ(θ) is the phase function of the scattering angle θ, F0
is the stellar flux at an arbitrary radius r0, and x traverses the
disk along the line of sight. The complicated and asymmetric
surface brightness profiles of β Pic’s disk suggest that n(r)
cannot be expressed as a single analytic function throughout
the disk. However, constraining n(r) within each region of
each disk extension requires a complex modelling effort that
is beyond the scope of this paper.
Fora less rigorousanalysis ofthe disk’s colors, we approxi-
mate the surface brightness and numberdensity profiles along
the midplanes of both extensions with single radial power
laws having fixed indices −α and −ν, respectively. Because
the outer radius of the disk is ? 1800 AU (Larwood & Kalas
2001), our lines of sight mostly traverse regions of the disk
that lie well beyond the projected distances at which we see
prominent inflections in the surface brightness profiles. The
effective index α should therefore be biased toward the in-
dices observed in the outer regions of the disk, i.e., α ≈ 4
(Smith & Terrile 1984; Kalas & Jewitt 1995). Nakano (1990)
determined that ν = α−1 if the observed scattered light orig-
inates mostly from dust along those parts of line of sight
near β Pic. This condition is valid unless the dust grains
are strongly forward-scattering. Some models indicate that
the scattered light is dominated by such grains (Pantin et al.
1997), but the relationships between the sizes, compositions,
and optical properties of the grains remain uncertain. Assum-
ing for simplicity that the disk comprises grains that are at
most moderately forward-scattering, we obtain
n(r) = n0
?r
r0
?−3
.
(2)
Adopting the disk geometry portrayed in Figure 1 of
Buitrago & Mediavilla (1986), we rewrite Equation (1) as
I(ǫ) =F0n0r5
R4sin4ǫ
0
?π−θ0
θ0
σscaΦ(θ) sin3θ dθ,
(3)
where R is the distance to β Pic, and θ0is the scattering angle
at the outer edge of the disk. The radius of the disk greatly
exceeds the FOV of our images, so θ0≈ 0. The integral is
then solely dependent upon the scattering properties of the
grains, so we define the grains’ effective scattering efficiency
as

Page 11

MULTIBAND IMAGES OF DISK AROUND β PICTORIS11
Qeff=
?π
0
QscaΦ(θ) sin3θ dθ,
(4)
where Qsca= σsca/πa2, and a is the grain size (radius). We
use a common scattering phase function for small grains,
Φ(θ) =
1−g2
4π (1+g2−2g cos θ)3/2,
(5)
where g is the scattering asymmetry parameter defined by
g = ?cos θ? =
?
4πΦ(θ) cos θ dΩ
(6)
and dΩ is the unit solid angle (Henyey & Greenstein 1941).
Values of g = −1, 0, and 1 correspond respectively to back-
ward, isotropic, and forward scattering.
Substituting Equation (5) into Equation (4) and evaluating
the integral, we obtain
Qeff=Qsca
3π
(1−g2).
(7)
This result indicates that our view of the edge-on disk is pro-
duced by mostly isotropic scatterers, which conforms to our
initial assumption that the grains in the disk are not strongly
forward-scattering. Its analytic form is a fortunate conse-
quence of our choice of ν = 3, but the bias against forward-
scattering grains is maintained for any choice of ν > 1. Both
Qscaand g are functions of the dimensionless parameter x =
2πa/λ, where λ is the wavelength of the scattered light. The
mean Qefffor grains of size a, weighted by the stellar flux in
a given bandpass, is
?Qeff? =
?QeffFλTλdλ
?FλTλdλ
,
(8)
where Fλis the flux spectrum of β Pic and Tλis the filter
transmission profile. We now compare ?Qeff? for grains of
various compositions and porosities in the ACS B, Broad-V,
and Broad-I bands.
4.2.2. Dust Grains within the Ice-Sublimation Zone
Figure 20 shows ?Qeff? as a function of a for the F435W,
F606W, and F814W filters and five combinations of porosity
and composition. None of these combinations includes icy
mantles, so they are applicable only to the region of the disk
within the ice sublimation limit (? 100 AU for micron-sized
grains; Pantin et al. 1997; Li & Greenberg1998). Figures 20a
and 20b depict ?Qeff? for compact (0% porosity) grains com-
posed, respectively, of pure astronomical silicate (“astrosil”)
andequalpartsastrosil andamorphouscarbon(graphite). The
curvesarederivedfromtabulatedvaluesofQscaandgforeach
composition based upon the work of Draine & Lee (1984).25
Figures 20c and 20e show ?Qeff? for 33% and 90% porous
grains with equal amounts of astrosil and graphite inclusions,
based on the values of Qscaand g for such grains computedby
Voshchinnikov et al. (2005). Figure 20d depicts an intermedi-
ate case of 60% porosityand pure astrosil derivedfromvalues
of Qscaand g computed by Wolff et al. (1998). For x > 25,
we extrapolated the tabulated values of Qscaand g for porous
grains to the geometric-opticslimits of Qsca→1 and g→1 as
25As of this writing, tabulated values of Qsca and g for compact
grains of astrosil and graphite are available on the World Wide Web at
http://www.astro.princeton.edu/∼draine/dust/dust.diel.html.
x→∞. Thisextrapolationisacceptablebecauseeventhemost
porous grains are expected to be strongly forward-scattering
for x ≫ 25 (N. Voshchinnikov, personal communication) and
thus, for ν = 3, contribute negligibly to our edge-on view of
the disk.
Figures 20a and b represent the grain characteristics most
often invoked when modelling scattered-light images of de-
bris disks. When viewed edge-on, disks comprising com-
pact grains with a ≫ 1 µm exhibit similar scattering effi-
ciencies in F435W, F606W, and F814W, i.e, they are neu-
tral, albeit relatively inefficient, scatterers at optical wave-
lengths. This condition is the basis of previous assertions
that the reportedly neutral colors of β Pic’s disk reflect a
minimum grain size of several microns (Paresce & Burrows
1987; Lecavelier des Etangs et al. 1993). However, as noted
by Chini et al. (1991), the values of ?Qeff? for smaller grains
(a ≈ 0.2–0.3 µm) are also similar among the broad optical
bands, so some submicron-sized grains are also neutral scat-
terers at these wavelengths. Moreover, because small grains
likely dominate the size distribution of grains in the disk
(Dohnanyi 1969; Li & Greenberg 1998), they more strongly
influence the overall color of the disk than supermicron-sized
grains. Nevertheless, the truly red colors of β Pic’s composite
disk (Figure 18) makes the debate over the cause of neutral
colors in this case irrelevant.
Figures 20c, d, and e show that increasing porosity has two
dramatic effects on ?Qeff?. First, the pronounced peak at 0.2–
0.4 µm diminishes rapidly for porosities ? 60%. This phe-
nomenon is caused by the similar behavior of Qscafor x ? 10
as porosity increases (Wolff et al. 1998; Voshchinnikov et al.
2005). Second, the peak broadens as it diminishes, caus-
ing the ranges of predominantly blue-, neutral-, and red-
scattering grains to broaden and shift to larger grain sizes.
For 90% porosity, almost all grains with a ? 3 µm scatter
light in F435W more efficiently than in F606W and F814W,
and grains with a?3 µm are neutral scatterers. The values of
?Qeff? for blue-scattering grains with a ? 1 µm are less than
half those of the neutrally-scattering grains, but no distribu-
tion of sizes for 90% porous grains will yield a disk with red
colors.
To compare the colors of an ensemble of grains having uni-
form porosity and composition with the observed colors of
β Pic’s disk, we must determine for each bandpass the mean
scattering cross section of the ensemble using ?Qeff? and a
reasonable grain-size distribution. Applying this quantity to
Equation (3), we express the intensity of scattered-light from
the disk relative to the stellar flux in a given bandpass as,
I =I(ǫ)
F∗
=
r3
0
R2sin4ǫ
?amax
amin
πa2?Qeff?dn0
dada,
(9)
where F∗= F0r2
dn0/da is the grain-size distribution, and aminand amaxare
the minimum and maximum sizes of the grains. The intrinsic
color of the disk between bandpasses 1 and 2 is therefore,
0/R2is the stellar flux measured at Earth,
m1−m2= −2.5 log
?I1
I2
?
.
(10)
Figure 21 shows the simulated F435W–F606W and
F435W–F814W colors of the inner disk as functions of mini-
mum grain size for the grain compositions and porosities pre-
viously considered. To compute these colors, we assumed the
values of ?Qeff? fromFigure 20 and a power-law size distribu-
tion, dn0∝ a−3.5da, commonly attributed to dust produced

Page 12

12GOLIMOWSKI ET AL.
from planetesimal and particle collisions (Dohnanyi 1969).
We computed the integral in Equation9 for amin= 0.01, 0.02,
..., 5.00 µm and an arbitrary amax= 100 µm.26Except for the
case of 90% porosity, the observed colors along the spine of
thecompositediskwithin120AU (F435W–F606W≈0.1and
F435W–F814W ≈ 0.2; Figure 18) are simultaneously repro-
duced by all combinations of porosity and composition when
amin=0.15–0.20µm. The 90% porous grains yield only blue
or neutral colors for any choice of amin(as presaged by Fig-
ure 20e), and therefore alone fail to explain the observed red
colors of the inner disk.
Our measured colors along the spine of the composite disk
within 120 AU are, by themselves, insufficient to constrain
tightly the composition and porosity of the grains in that re-
gion. However, they do show that very porous grains do not
contribute significantly to the integrated scattered light along
the spine. This conclusion does not necessarily imply a lack
of very porous grains, because the values of ?Qeff? for such
grains with a ? 2 µm are 10–20 times smaller than those of
compact and moderately porous grains of similar size (Fig-
ure 20). Thus, our results do not necessarily contradict those
of Li & Greenberg (1998), who found that the dust models
that best fitted the observed continuum and 10 µm silicate
emissionfromthedisk arethosethatfeatureextremelyporous
(> 95%) grains. It remains to be seen, however, whether a
distribution of grain porosities can simultaneously satisfy the
constraints provided by scattered-light and thermal images of
the inner disk.
4.2.3. Dust Grains beyond the Ice-Sublimation Zone
Our estimate of amin= 0.15–0.20 µm within 120 AU
matches that obtained by Voshchinnikov & Krügel (1999)
using ground-based observations of the disk’s colors and
polarization beyond 115 AU (Paresce & Burrows 1987;
Lecavelier des Etangs et al. 1993; Wolstencroft et al. 1995)
anda dustmodelfeaturinganR-bandrefractiveindexofmR=
1.152−0.005i and a grain-size distribution of dn ∝ a−3.2da.
This refractive index is descriptive of both “dirty-ice” grains
with 50% porosity and astrosil grains of 76% porosity. How-
ever, our HRC images show that the disk steadily reddens
beyond 120 AU, so the other dust models considered by
Voshchinnikov & Krügel (1999) – and rejected because they
produced colors that were too red compared with the nearly
neutral colors observed from the ground – are in fact poten-
tially viable models for this region of the disk. These mod-
els feature larger refractive indices (corresponding to various
combinationsof compact and moderatelyporous grains of as-
trosil, mixed or layered with dirty ice) and larger amin. In an-
otherstudyofthe disk’spolarizationandcolors,Krivova et al.
(2000) also favored models with moderate refractive indices,
porosities ? 50%, and depleted numbers of grains smaller
than 2–3 µm.
Although tabulated values of Qscaand g have not yet been
published for moderately porous astrosil grains with icy man-
tles, it is reasonable to expect that the optical colors of an
edge-on disk of such grains vary with aminin a manner sim-
ilar to those depicted in Figures 21a–d. If so, then the in-
creasingly red color gradient observed in β Pic’s disk beyond
26We repeated this exercise for the porous-grain cases using the grain-
mass distribution derived by Li & Greenberg (1998) from their thermal dust
model that assumed 97.5% porosity and n(r) ∝ r−1.8within the region 46 ≤
r ≤ 115 AU (Figure 11c of Li & Greenberg 1998). The results were nearly
identical to those obtained for the grain-size distribution of Dohnanyi (1969),
so we discuss them no further.
120 AU (Figure 18) may reflect values of aminthat increase
with distance from ∼ 0.15 µm to perhaps ∼ 2 µm at 250 AU
(Voshchinnikov & Krügel 1999). A similar trend was pro-
posed by Weinberger et al. (2003), based on the disappear-
ance of the 10 µm silicate emission feature beyond 20 AU of
the star. These phenomena are consistent with the scenario
of a diminished presence of small (a ? 2–3 µm) grains near
the ice-sublimation zone (? 100 AU), where cometary activ-
ity ceases (Li & Greenberg 1998) and radiation pressure sets
aminto 1–10 µm, depending on porosity (Artymowicz 1988).
The steeper color gradients in the southwest extension of the
disk suggest that aminincreases more rapidly in that exten-
sion, i.e., the number of small grains in the southwest exten-
sion is smaller than in the northeast extension. This sugges-
tion is consistent with the observed asymmetry between the
polarizationsof the two extensions (Wolstencroft et al. 1995),
which has been attributed to a 20-30% larger population of
small grains in the northeast extension (Krivova et al. 2000).
4.2.4. Dust Grains in the Secondary Disk
The largely uncertain colors of the secondary disk (§3.3.3)
preventusfromrigorouslycomparingthegraincharacteristics
of the main and secondary disks. However, the lack of inflec-
tions in the secondarydisk’s colorand surface-brightnesspro-
files (Figure16) indicatesthatthe grainpopulationsofthetwo
component disks are fundamentally different at 80–150 AU
from the star. If the inflections in the main disk’s profiles
at ∼ 115 AU are solely caused by ice sublimation, then the
composition and/or size distribution of the secondary disk’s
grains must be sufficiently different from those of the main
disk that the ice-sublimation boundary in the secondary disk
(if it exists) lies within or beyond the 80–150 AU range of
our analysis. More precise photometry of the secondary disk
is needed to determine whether the differences in the grains’
composition or size distribution required for such a boundary
shift are compatible with the colors of the disk.
Artymowicz (1997) argued that icy grains should not exist
anywherein β Pic’s disk becausetheyquicklyphotoevaporate
intheface ofthestar’s strongultravioletfluxandbecausethey
are structurallybrittle and unableto survivehigh-velocitycol-
lisions with other grains. If so, then other causes of the differ-
ences between the color and surface-brightnessprofiles of the
main and secondary disks must be considered. For example,
the inflections in the main disk’s profiles at ∼115AU may re-
flect a sharp decrease in the number density of grains within
that distancefromthe star. Lecavelier des Etangs et al. (1996)
successfully modeled the inflection in the surface-brightness
profile by imposing a lower limit on the sizes of comets or
asteroids that travel from outer regions of the disk and re-
tain enough volatile material to evaporate within 110 AU. If
this scenario is correct, then the lack of inflections in the sec-
ondary disk’s profiles suggests that most of its dust is pro-
duced by colliding or evaporating planetesimals orbiting near
the star rather than by evaporating comets with large, ec-
centric orbits. This interpretation is consistent with the hy-
pothesis that the “warp” in the composite disk is caused by
radiation-blown dust from colliding planetesimals that have
been perturbed from the the innermost part of the main disk
by a giant planet in an inclined orbit (Mouillet et al. 1997b;
Augereau et al. 2001).
4.2.5. Possible Effect of Irradiation on Disk Colors
Recent photometric studies of Kuiper Belt Objects (KBOs)
reveal that these objects exhibit a broad range of optical and

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MULTIBAND IMAGES OF DISK AROUND β PICTORIS 13
near-infrared colors (Luu & Jewitt 1996; Jewitt & Luu 1998,
2001; Tegler & Romanishin 1998, 2003; Barucci et al. 2001;
Delsanti et al. 2004). Growing (but controversial) evidence
suggests that KBOs are divided by their perihelia, q, into two
color populations: KBOs with q < 40 AU have neutral-to-
red intrinsic colors, and KBOs with q > 40 AU have only
red intrinsic colors (0.5 ? B–R ? 0.75, relative to the Sun;
Tegler & Romanishin 1998, 2003; Delsanti et al. 2004). A
possible cause of this color trend is the diminution of col-
lisions and/or cometary activity in the outer Kuiper Belt
(Luu & Jewitt 1996; Stern 2002; Delsanti et al. 2004). This
hypothesis rests on the notion that the “dirty-ice” surfaces of
KBOs are progressively polymerized and reddened by high-
energy solar and cosmic radiation unless they are recoated
with primordial dust ejected by collisions between KBOs or
the sublimation of H2O, CO2, and CO ices.
The observed reddening of β Pic’s disk beyond its ice-
sublimation zone suggests a possible connectionwith the red-
dening of distant KBOs. Could the reddening of β Pic’s disk
beyond ∼ 115 AU be the result of irradiative polymerization
rather than an increasing minimum grain size? Luu & Jewitt
(1996) simulated the rate of irradiative reddening of KBOs
using an inverse exponential function with an e-folding time
of ∼ 108yr. Because the radiation is overwhelmingly solar
within the heliopause (Gil-Hutton 2002), we crudely apply
this function to the region of β Pic’s disk in our FOV by as-
suming that the e-folding time scales with luminosity and the
distance fromthe star. In this situation, the B–V color of long-
lived icy grains orbiting β Pic (L/L⊙= 8.7; Crifo et al. 1997)
would increase by ∼ 0.3 mag in a few times 108yr. The life-
times ofgrainsnotquicklyexpelledfromthe diskbyradiation
pressure are limited by either Poynting–Robertsondrag or in-
tergraincollisions,dependingontheirsizeandlocationwithin
the disk. At 120–250 AU, the minimum lifetimes of grains
larger than ∼ 0.2 µm are constrained by collisions to ∼ 0.2–
2 Myr (Backman & Paresce 1993). Thus, the lifetimes of the
grains observedin ourHRC images are much too short for the
observedcolor gradient to be caused by irradiative reddening.
This condition likely persists throughout the outer disk, be-
cause the grain lifetimes beyond ∼ 500 AU (which are lim-
ited by Poynting–Robertson drag) are ∼ 1% of the irradiative
e-folding times at those distances.
4.2.6. Comparing the disks around β Pic and AU Mic
The disk around the M dwarf AU Mic, whose spa-
tial velocity and age are similar to those of β Pic
(Barrado y Navascués et al. 1999), is the only known debris
disk exhibiting blue colors at optical wavelengths (Krist et al.
2005a). Moreover, the disk’s F435W–F814W color becomes
bluer with increasing distance from the star. The disk ex-
tends at least 210 AU from the star and is viewed almost
edge-on (Kalas et al. 2004), so the predicted F435W–F814W
colors shown in Figure 21 can be compared to the observed
ACS colors of the disk if the grains are not icy. In this case,
the measured F435W–F814W = −0.3 at 30 AU (Krist et al.
2005a) from AU Mic suggests that the disk may be com-
posed of astrosil and/or graphite grains with amin< 0.1 µm
for porosities ? 60% or amin≈ 0.2 µm for 90% porosity.
The possibility that AU Mic’s disk contains smaller or more
porous grains than are evident in β Pic’s inner disk (§4.2.2)
is consistent with the much lower radiation pressure exerted
on such grains by AU Mic than by β Pic (Kalas et al. 2004;
Krist et al. 2005a). On the other hand, the measured F435W–
F814W = −0.5 at 60 AU from the star cannot be produced by
any combination of grain composition and porosity shown in
Figure21, so the grainsin AU Mic’s disk may have a different
mineral composition altogether.
5. SUMMARY AND CONCLUDING REMARKS
We have presented B-, BroadV-, and Broad I-band corona-
graphic images of the dusty debris disk around β Pictoris ob-
tained with the High Resolution Channel of HST’s Advanced
Camera for Surveys. We have exploited the HRC’s image
resolution and stability by subtracting a well-matched coron-
agraphic reference image and deconvolving the instrumental
PSF from the multiband images. The resultant images pro-
vide the most morphologically detailed and photometrically
accurate views of the disk between 30 and 300 AU from the
star obtained to date.
Our PSF-deconvolved images confirm that the appar-
ent warp in the disk ? 100 AU from the star, which
was previously observed by Burrows et al. (1995) and
Heap et al. (2000) and modelled by Mouillet et al. (1997b)
and Augereau et al. (2001), is a distinct secondary disk in-
clined to the main disk by ∼ 5◦. The opposing extensions of
the secondary disk are not collinear, but their outwardly pro-
jected midplanes (spines) are coincident with the isophotal
inflections previously seen at large distances and commonly
called the “butterfly asymmetry” (Kalas & Jewitt 1995). The
surface brightness profiles along the spines of the secondary
disk from80 to 150AU can be fit with single power-lawfunc-
tions having indices of −3.7 < −α < −5.0. The lack of inflec-
tions in the surface brightness profiles around the expected
ice-sublimation boundary (∼ 100 AU) suggests that the com-
position and/or size distribution of grains in the secondary
disk is differentfromthoseof the main disk. Altogether,these
phenomenasupport the notion that the secondary disk and the
butterfly asymmetry comprise radiatively expelled dust from
colliding planetesimals in inclined orbits near the star rather
than from evaporating comets in large, eccentric orbits.
We confirm the “wing-tilt asymmetry” between the oppos-
ing extensions of the main disk, but we find that the effect
is centered on the star rather than offset toward the south-
west extension (Kalas & Jewitt 1995). While the spine of
the northeast extension appears linear 80–250 AU from the
star, the southwest spine is distinctly bowed with an ampli-
tude of ∼ 1 AU. The vertical width of the main disk within
∼ 120 AU is nearly constant and is up to 50% narrower than
previously reported. The clumpy structures observed in mid-
infrared images and spectra of the disk (Wahhaj et al. 2003;
Weinberger et al. 2003; Okamoto et al. 2004; Telesco et al.
2005) are not seen in our optical scattered-light images. The
surface-brightnessprofiles along the spines of the main disk’s
extensions can be fit by four distinct power laws separated by
inflections at ∼ 70, 117, and 193 AU. The power-law indices,
α, match those of Heap et al. (2000) well within 70 AU of
β Pic, butare10–15%smallerthanthoseofHeap et al. (2000)
at 127–193 AU. This discrepancy cannot be attributed to dif-
ferencesin the instrumentalPSFs. The indices within 150 AU
change significantly after removing the contribution from the
secondary disk, so the superposed effects of both disks must
be considered in future models of β Pic’s circumstellar dust
distribution.
The two-dimensional F606W/F435W and F814W/F435W
flux ratios of the composite disk are nonuniform and asym-
metric about the projected major and minor axes of the disk.
Within 150 AU of β Pic, the ratios on the southeast side of
the disk are ∼ 1.0–1.1 times those of the star, while those

Page 14

14GOLIMOWSKI ET AL.
on the northwest side are ∼ 1.2–1.4 times those of the star.
The redder appearance of the nearer northwest side of the
disk is inconsistent with the expectation that forward scatter-
ing from disk grains should diminish with increasing wave-
length. TheF435W–F606WandF435W–F814Wcolorsalong
the spine of the disk are ∼ 0.1 mag and ∼ 0.2 mag red-
der, respectively, than those of β Pic at ∼ 40–120 AU from
the star. These color excesses increase steadily beyond ∼
120 AU, respectively reaching ∼ 0.2–0.35 mag and ∼ 0.25–
0.4 mag at 250 AU. These results contradict the longstand-
ing notion that the disk consists of neutrally scattering grains
with sizes larger than several µm (Paresce & Burrows 1987;
Lecavelier des Etangs et al. 1993).
We have compared the colors measured along the spine of
the composite disk with those expected for non-icy grains
having a number density ∝ r−3and different compositions,
porosities, and minimum grain sizes. We find that the ob-
served F435W–F606Wand F435W–F814W colors within the
ice-sublimation zone (? 100 AU) are consistent with those of
compactor moderatelyporous(P?60%)grains ofastronom-
ical silicate and/or graphite with minimum sizes of ∼ 0.15–
0.20 µm. The observed colors are inconsistent with the blue
colors expected from the very porous grains (P ? 90%) that
best reproduce the 10 µm silicate emission feature observed
within ∼ 35 AU of the star (Li & Greenberg 1998). The red-
dening colors beyond ∼ 120 AU may reflect the formation
of “dirty ice” grains or an increasing minimum grain size be-
yond the ice-sublimation boundary. The latter condition is
consistent with the decreased production of submicron grains
as cometary activity diminishes. It is unlikely that the redden-
ing of disk beyond ∼ 120 AU is caused by irradiative poly-
merization (as has been postulated for the reddest and most
distant Kuiper Belt Objects) because the required irradiation
time is hundreds of times longer than the expected lifetimes
of the grains at those distances.
Our ACS/HRC coronagraphic images of β Pic’s disk are
the finest multiband, scattered-light images of its inner region
(30–300 AU) ever recorded. These images will not be su-
perseded by the Terrestrial Planet Finder or other proposed
extrasolar-planet imaging missions because the fields of view
of those missions will lie well within the region obscured by
the HRC’s occulting spot. Comparable infrared images of the
disk are expectedfromthe James Webb SpaceTelescope if the
current specifications for its coronagraphic-imaging modes
are maintained. Thus, our observations and derived results
should be standard references for comparative and theoreti-
cal studies of circumstellar debris disks for at least the next
decade.
We thank N. Voshchinnikov for his advice regarding the
optical properties of porous grains. We also thank E. Pantin
for his comments on the manuscript. ACS was developed un-
der NASA contract NAS 5-32865, and this research has been
supported by NASA grant NAG5-7697 and by an equipment
grant from Sun Microsystems, Inc. The STScI is operated by
AURA Inc., under NASA contract NAS5-26555.
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