# High-spatial-resolution imaging of thermal emission
from debris disks

Margaret M. Moerchen11affiliation: European Southern Observatory, Alonso de
Córdova 3107, Santiago, Chile 22affiliation: University of Florida, Department
of Astronomy, 211 Bryant Space Science Center, Gainesville, FL 32611, USA
<EMAIL_ADDRESS>Charles M. Telesco22affiliation: University of Florida,
Department of Astronomy, 211 Bryant Space Science Center, Gainesville, FL
32611, USA and Christopher Packham22affiliation: University of Florida,
Department of Astronomy, 211 Bryant Space Science Center, Gainesville, FL
32611, USA

###### Abstract

We have obtained sub-arcsec mid-IR images of a sample of debris disks within
100 pc. For our sample of nineteen A-type debris disk candidates chosen for
their IR excess, we have resolved, for the first time, five sources plus the
previously resolved disk around HD 141569. Two other sources in our sample
have been ruled out as debris disks since the time of sample selection. Three
of the six resolved sources have inferred radii of 1–4 AU (HD 38678, HD 71155,
and HD 181869), and one source has an inferred radius $\sim$10–30 AU (HD
141569). Among the resolved sources with detections of excess IR emission, HD
71155 appears to be comparable in size (r$\sim$2 AU) to the solar system’s
asteroid belt, thus joining $\zeta$ Lep (HD 38678, reported previously) to
comprise the only two resolved sources of that class. Two additional sources
(HD 95418 and HD 139006) show spatial extent that implies disk radii of
$\sim$1–3 AU, although the excess IR fluxes are not formally detected with
better than 2-$\sigma$ significance. For the unresolved sources, the upper
limits on the maximum radii of mid-IR disk emission are in the range
$\sim$1–20 AU, four of which are comparable in radius to the asteroid belt. We
have compared the global color temperatures of the dust to that expected for
the dust in radiative equilibrium at the distances corresponding to the
observed sizes or limits on the sizes. In most cases, the temperatures
estimated via these two methods are comparable, and therefore, we see a
generally consistent picture of the inferred morphology and the global mid-IR
emission. Finally, while our sample size is not statistically significant, we
notice that the older sources ($>$200 Myr) host much warmer dust
(T$\gtrsim$400 K) than younger sources (in the 10s of Myr).

circumstellar matter – infrared: stars – planetary systems

##  1 The Search for Resolved Disks

Studying the structure of circumstellar debris disks is proving to be a
valuable technique for inferring the presence of planets and understanding
physical processes associated with the early evolution of planetary systems
(see Wyatt 2008 for review). The detection of an infrared excess for a main-
sequence star is a strong indication that a debris disk is present. Through
relatively large IR-photometric surveys, we can assess trends in excess IR
luminosity for samples of debris disks that span a large range of ages (e.g.,
Su et al. 2006). By going a step further to image single sources with high
spatial resolution (with currently available facilities, $<$0.5” is considered
“high”), we may discover structures in the dust disk that are indicative of
the physical processes occurring in them.

There are presently several hundred photometric detections of debris disks
(e.g., Oudmaijer et al. 1992; Mannings & Barlow 1998; Zuckerman & Song 2004),
but only a small number ($\sim$20) have been spatially resolved. Debris disks
can be imaged in scattered light at optical or near-IR wavelengths, but such
observations suffer from strong photospheric contamination from the central
star, and a coronagraph typically must be employed (e.g., Weinberger et al.
1999). This problem is largely avoided by observing at mid-IR wavelengths
where there is relatively less emission from the photosphere, and thermal dust
emission dominates.

Recent observations by Currie et al. (2008) demonstrate the expected decay in
disk brightness with age. That work supports the models of Kenyon & Bromley
(2004), in which the disk luminosity rises sharply before slowly declining,
with the peak luminosity occurring at $\sim$10–15 Myr. Although such general
trends in disk brightness with age can be inferred through survey photometric
observations, the location of the dust and the physical processes that sculpt
the disks are poorly understood. For example, HR 4796A and $\beta$ Pic, both A
stars, have nearly the same 18 $\mu$m/25 $\mu$m color (Moerchen et al.,
2007a), and Wyatt (2008) notes that they occupy similar positions in the age-
vs.-24-$\mu$m-excess plot presented by Currie et al. (2008). Despite such
apparent similarities, resolved near-IR and mid-IR images of both sources
reveal significantly different dust distributions: HR 4796A has a well-defined
dust annulus at $\sim$70 AU that is 17 AU wide (Schneider et al., 1999; Wyatt
et al., 1999; Telesco et al., 2000) and the dominant mid-IR-emitting dust disk
of Beta Pic spans 20-120 AU (Lagage & Pantin, 1994; Telesco et al., 2005)
(although optically scattered light reveals a disk extending out to nearly
1500 AU [e.g., Larwood & Kalas 2001]). Thus, the excess flux levels tell only
a small part of the story, but degeneracies such as the example above can
sometimes be broken through imaging observations.

The initial goal of this research was to explore how morphological asymmetries
(or lack thereof) are generated by various physical processes such as
collisions and orbital resonances. Imaging at several wavelengths permits some
assessment of which process may dominate a particular disk or region therein.
The mid-IR regime offers the additional benefit of near-diffraction-limited
observing, and by imaging from the ground, as in this work, we can exploit
large telescopes to achieve the desired high angular resolution. For example,
the $\lambda/D$ diffraction limits at 11.7 $\mu$m and 18.3 $\mu$m at the
7.9-meter Gemini Observatory telescopes are 0.24” and 0.39”, respectively.

##  2 Observations

###  2.1 Source Sample

Seventeen of the nineteen debris disk candidates observed in this program are
associated with the stars listed in Table 2.1. They are main-sequence stars
(with the exception of HD 141569), essentially A-type (B8–A5), all within 100
pc. In the literature, HD 141569 is considered to be a transition disk, since
a significant amount of gas (e.g., CO) has been detected within it (Brittain &
Rettig, 2002; Brittain et al., 2003). All sources were observed either with
MIPS on $Spitzer$ at 24 $\mu$m or with $IRAS$ at 25 $\mu$m. The sources in
this sample were chosen both for their high disk-to-star ratio of excess
emission ($>$1.1) at 24 $\mu$m (Rieke et al., 2005) as well as their high
estimated flux densities at 10 $\mu$m ($>$10 mJy) and 18 $\mu$m ($>$40 mJy)
attributable to dust emission. Two sources, HD 172555 and HD 181296, were
chosen for their $IRAS$-discovered high fractional dust luminosities
(Oudmaijer et al., 1992; Mannings & Barlow, 1998) that were confirmed with
MIPS and/or ISO (Moór et al., 2006). The ages of the sample stars are in the
range $\sim$5–600 Myr. Since the time of sample selection, other works have
demonstrated that two of the targets that we observed (not listed in Table 1)
have infrared excesses that cannot be attributed to debris disk processes.
These instances are reviewed individually in this section, and will not be
discussed in future sections regarding debris disk analysis.

Table 1: Summary of Imaging Observations

Object | Gemini | Program ID | Filter | Timea [s] | Dates Observed
---|---|---|---|---|---
HD 38206 | S | 2005A-Q-2 | N | 900 | 19 Sep 2005
|  |  | Qa | 900 | 5 Feb 2006
HD 38678 | S | 2005A-Q-2 | N | 900 | 3 Feb 2005
|  |  | Qa | 900 | 3 Feb 2005
HD 56537 | N | 2006A-Q-10 | N′ | 900 | 4 Apr 2006
|  |  | Qa | 900 | 4 Apr 2006, 7 Apr 2006
HD 71155 | S | 2005A-Q-2 | N | 900 | 4 Mar 2006
|  |  | Qa | 900 | 5 Feb 2006
HD 75416 | S | 2005A-Q-2 | Si-5 | 300 | 22 May 2005
|  |  | Qa | 900 | 22 May 2005
HD 80950 | S | 2005A-Q-2 | N | 900 | 8 Mar 2006
|  |  | Qa | 900 | 5 Feb 2006
HD 83808 | N | 2006A-Q-10 | N′ | 900 | 4 Apr 2006
|  |  | Qa | 900 | 6 Apr 2006
HD 95418 | N | 2006A-Q-10 | N′ | 900 | 10 Jun 2006
|  |  | Qa | 900 | 7 Apr 2006
HD 102647 | N | 2006A-Q-10 | N′ | 960 | 11 Jun 2006
|  |  | Qa | 900 | 10 May 2006, 15 May 2006
HD 115892 | S | 2005A-Q-2 | Si-5 | 900 | 22 May 2005
|  |  | Qa | 1500 | 21 May 2005, 22 May 2005
HD 139006 | N | 2006A-Q-10 | N′ | 900 | 29 May 2006
|  |  | Qa | 900 | 30 Apr 2006, 12 May 2006
HD 141569 | N | 2006A-Q-10 | N′ | 900 | 12 Jun 2006
|  |  | Qa | 900 | 10 May 2006, 14 May 2006
HD 161868 | N | 2006A-Q-10 | N′ | 900 | 29 May 2006
|  |  | Qa | 900 | 30 Apr 2006, 20 May 2006
HD 172555 | S | 2007A-Q-23 | Si-5 | 680 | 1 Jul 2007
|  |  | Qa | 680 | 27 Jun 2007, 1 Jul 2007
HD 178253 | S | 2005A-Q-2 | Si-5 | 900 | 22 May 2005
|  |  | Qa | 600 | 22 May 2005
HD 181296 | S | 2007A-Q-23 | Si-5 | 700 | 28 Apr 2007
|  |  | Qa | 700 | 28 Apr 2007
HD 181869 | S | 2005A-Q-2 | N | 900 | 20 Aug 2005
|  |  | Qa | 1200 | 20 Aug 2005, 19 Mar 2006

Notes– aTime is on-source integration time.

HD 21362– The IRS (Infrared Spectrograph) instrument on $Spitzer$ obtained
low-resolution spectra of HD 21362 that showed several hydrogen emission lines
that are indicative of free-free radiation from an ionized stellar wind. Su et
al. (2006) concluded that the infrared excess previously thought to be due to
a debris disk presence is actually due to a fast-rotating B-type star with a
strong stellar wind creating a circumstellar gas disk (also known as the Be
phenomenon.) HD 21362 is not resolved in our images, and its measured flux
densities are 683 $\pm$ 68 mJy at 11.2 $\mu$m and 456 $\pm$ 68 mJy at 18.1
$\mu$m.

HD 74956– Recent $Spitzer$ MIPS images at 24 $\mu$m have demonstrated that the
observed infrared excess associated with HD 74956 (e.g., Aumann 1985, 1988;
Cote 1987; Chen et al. 2006; Su et al. 2006) is the result of this multiple-
star system traveling through an interstellar cloud and producing a bow shock
(Gáspár et al., 2008). The dust in this overdense region ($\sim$15 times the
Local Bubble density) is compressed at the shock front generated by photon
pressure and is heated by the star, which gives rise to an arc-shaped
morphology that is responsible for the infrared excess. More recently,
Kervella et al. (2009) studied the system in greater detail at both near-IR
and mid-IR wavelengths (with NACO and VISIR, respectively, at the VLT) to
determine whether some of the observed excess might still be attributable to a
disk around one of the system members. However, their final result
corroborates that of Gáspár et al. (2008): the bow shock alone is likely to be
responsible for the IR excess. HD 74956 is resolved only in our 10.4-$\mu$m
images, and the level of extension implies a dust disk radius of 1.4 AU
(simply estimated by quadratically subtracting the PSF FWHM from the source
FWHM). The measured flux densities are 8.61 $\pm$ 0.86 mJy at 10.4 $\mu$m and
2.38 $\pm$ 0.36 mJy at 10.4 $\mu$m

Table 2: Debris Disk Candidate Target List

Name | Type | Age | Age | $d$ | 24 or 25um $F_{\nu}$ | Flux | Excess RatioaaFor flux density measurements at 24 or 25 $\mu$m.
---|---|---|---|---|---|---|---
|  | [Myr] | Ref. | [pc] | [Jy] | Ref. | [$F_{total}/F_{\star}$]
HD 38206 | A0V | 9 | 2 | 69 | 0.115 | 4 | 3.34
HD 38678 | A2Vann | 231, 330 | 1, 3 | 22 | 1.160 | 9 | 2.43
HD 56537 | A3V | 560 | 3 | 29 | 0.586 | 9 | 1.32
HD 71155 | A0V | 169, 240 | 1, 3 | 38 | 0.321 | 4 | 1.54
HD 75416 | B8V | 5 | 4 | 97 | 0.128 | 4 | 3.51
HD 80950 | A0V | 80 | 2 | 81 | 0.121 | 4 | 3.79
HD 83808 | A5V+ | 400 | 3 | 41 | 1.140 | 9 | 1.16
HD 95418 | A1V | 300, 358, 380 | 5, 1, 3 | 24 | 1.400 | 9 | 1.21
HD 102647 | A3V | 50, 520 | 1, 3 | 11 | 2.320 | 9 | 1.42
HD 115892 | A2V | 350 | 3 | 18 | 0.705 | 4 | 1.2
HD 139006 | A0V | 314, 350 | 1, 3 | 23 | 1.686 | 9 | 1.29
HD 141569 | B9.5e | 5 (PMS) | 6, 7 | 99 | 1.819 | 9 | 162.4bbThese excess ratios were computed with $IRAS$ 25 $\mu$m flux density measurements and 25 $\mu$m photospheric flux densities estimated with the same method as described in §3.1. All other excess ratio values are taken from Rieke et al. 2005.
HD 161868 | A0V | 184, 305 | 1, 3 | 29 | 0.525 | 9 | 1.47
HD 172555 | A5IV-V | 12 | 8 | 29 | 1.092 | 9 | 9.66bbThese excess ratios were computed with $IRAS$ 25 $\mu$m flux density measurements and 25 $\mu$m photospheric flux densities estimated with the same method as described in §3.1. All other excess ratio values are taken from Rieke et al. 2005.
HD 178253 | A2V | 254, 320 | 1, 3 | 40 | 0.348 | 9 | 1.45bbThese excess ratios were computed with $IRAS$ 25 $\mu$m flux density measurements and 25 $\mu$m photospheric flux densities estimated with the same method as described in §3.1. All other excess ratio values are taken from Rieke et al. 2005.
HD 181296 | A0Vn | 12 | 8 | 48 | 0.491 | 9 | 8.32
HD 181869 | B8V | 110 | 3 | 52 | 0.280 | 9 | 1.46

References. — (1) Song et al. 2001; (2) Gerbaldi et al. 1999; (3) Rieke et al.
2005; (4) de Zeeuw et al. 1999; (5) King et al. 2003; (6) Weinberger et al.
2000; (7) Merín et al. 2004; (8) Zuckerman et al. 2001; (9) Moshir et al. 1989

###  2.2 The Images: General Comments

We obtained mid-IR images of 19 debris disk candidates (including HD 21362 and
HD 74956 mentioned above) in 2005, 2006, and 2007 at the Gemini North and
South facilities (program IDs: GS-2005A-Q-2, GN-2006A-Q-10, GS-2006A-Q-5,
GS-2007A-Q-23) with Michelle and T-ReCS (Thermal Region Camera and
Spectrograph), respectively. The log of the observation dates and program IDs
is given in Table 1 in the appendix. With Michelle, we used the narrowband N′
($\lambda_{c}$ = 11.2 $\mu$m, $\Delta\lambda$ = 2.4 $\mu$m) and narrowband Qa
($\lambda_{c}$ = 18.1 $\mu$m, $\Delta\lambda$ = 1.9 $\mu$m) filters. With
T-ReCS, we used the broadband N ($\lambda_{c}$ = 10.36 $\mu$m, $\Delta\lambda$
= 5.27 $\mu$m), narrowband Si-5 ($\lambda_{c}$ = 11.66 $\mu$m, $\Delta\lambda$
= 1.13 $\mu$m), and narrowband Qa ($\lambda_{c}$ = 18.30 $\mu$m,
$\Delta\lambda$ = 1.51 $\mu$m) filters. These filters were chosen to sample
the disk emission in the two atmospheric transmission windows in the mid-IR
regime, at $\sim$10 (N band) and $\sim$20 $\mu$m (Q band). Among the filters
available in the N band, the N′ filter in Michelle and the broadband N and
Si-5 filters in T-ReCS have the best sensitivity, as documented in Gemini-
provided tables. The Qa filter ($\sim$18 $\mu$m) was chosen for its relative
lack of water absorption lines in its wavelength range compared to Qb filters
at $\sim$25 $\mu$m, thus decreasing the importance of low atmospheric water
vapor content for execution of the observations. Both Michelle and T-ReCS
utilize Raytheon Si:As blocked-impurity-band (BIB) detectors with 320 x 240
pixels. With Michelle, each pixel subtends 0.10”, and the total field of view
is 32” x 24”, and with T-ReCS, each pixel subtends 0.09”, and the total field
of view is 29” x 22”.

A point-spread-function (PSF) comparison star was observed before and after
each science target observation, with three exceptions where the PSF star was
only observed either before or after (but not both) the disk target. The PSF
reference star was typically a Cohen IR standard (Cohen et al., 1999) that
also served as a flux calibrator. The observations used the standard mid-IR
technique of chopping with a chop throw of 15” and nodding (parallel to the
chopping direction) to remove time-variable sky background, telescope thermal
emission, and low-frequency detector noise. The data were reduced with the
Gemini IRAF package.

The total (disk + star) flux densities of the sources observed in this study
are given in Table 3. The flux densities were measured with aperture
photometry. The average sky background was measured in an annulus centered on
the star with a radius range of 1.5–2 times the main (source) aperture radius,
and the measured source flux density was corrected for the sky according to
the number of pixels in the aperture. Observations of the flux standards were
not repeated on each night, so we adopt nominal calibration uncertainties of
10% at 11.7 $\mu$m and 15% at 18.3 $\mu$m, which are typical for photometric
variations in the mid-IR (e.g. De Buizer et al. 2005, Packham et al. 2005).
Such variations dominate the uncertainties associated with the background shot
noise in all cases. The 1-$\sigma$ uncertainties presented in Table 3
represent the dispersion in the measurements due to fluctuations in the level
of thermal emission of the sky and the shot noise in the background photon
stream. The total 1-$\sigma$ uncertainties (the quadratic addition of both
background and photometric uncertainties) are given in Tables 4 and 5.

Table 3:  Flux DensitiesaaThe uncertainties given here are those associated with the measured background noise. Additionally, nominal calibration uncertainties of 10% at 11.7 $\mu$m and 15% at 18.3 $\mu$m were adopted, which are typical for photometric variations in the mid-IR (e.g. De Buizer et al. 2005, Packham et al. 2005). These photometric uncertainties dominate the background noise in all cases. (in mJy) of Debris Disk Candidates  Source | Gemini |  $F_{\nu}(10.4~{}\mu$m) |  $F_{\nu}(11.2~{}\mu$m) |  $F_{\nu}(11.7~{}\mu$m) |  $F_{\nu}(18.1~{}\mu$m) |  $F_{\nu}(18.3~{}\mu$m)
---|---|---|---|---|---|---
HD # |  | (N) | (N′) | (Si-5) | (Qa) | (Qa)
38206 | S | 202 $\pm$ 1 | … | … | … | 116 $\pm$ 7
38678 | S | 2147 $\pm$ 2 | … | … | … | 960 $\pm$ 10
56537 | N |  | 1432 $\pm$ 1 | … | 597 $\pm$ 12 | …
71155 | S | 1083 $\pm$ 2 | … | … | … | 375 $\pm$ 10
75416 | S | … | … | 229 $\pm$ 3 | … | 92 $\pm$ 7
80950 | S | 191 $\pm$ 13 |  | … | … | 109 $\pm$ 10
83808 | N | … | 3614 $\pm$ 3 | … | 1567 $\pm$ 13 | …
95418 | N | … | 3588 $\pm$ 2 | … | 1743 $\pm$ 10 | …
102647 | N | … | 5822 $\pm$ 3 | … | 2317 $\pm$ 17 | …
115892 | S | 2540 $\pm$ 3 | … | 2521 $\pm$ 2 | … | 1026 $\pm$ 17
139006 | N | … | 4077 $\pm$ 2 | … | 1795 $\pm$ 15 | …
141569 | N | … | 338 $\pm$ 1 | … | 883 $\pm$ 13 | …
161868 | N | … | 1105 $\pm$ 1 | … | 443 $\pm$ 11 | …
172555 | S | … | … | 1155 $\pm$ 2 | … | 1094 $\pm$ 11
178253 | S | … | … | 770 $\pm$ 2 | … | 360 $\pm$ 12
181296 | S | … | … | 395 $\pm$ 2 | … | 343 $\pm$ 16
181869 | S | 695 $\pm$ 2 | … | … | … | 202 $\pm$ 14
Table 4: Excess Emission of Debris Disk Candidates (Michelle)

|  $F_{\nu}$(11.2 $\mu$m) [mJy] |  |  $F_{\nu}$(18.1 $\mu$m) [mJy]
---|---|---|---
HD | Total | Star | Excess |  | Total | Star | Excess
56537 | 1432 $\pm$ 143 | 1154 | 278 $\pm$ 143 |  | 597 $\pm$ 91 | 440 | 157 $\pm$ 91
83808 | 3614 $\pm$ 361 | 2985 | 628 $\pm$ 361 |  | 1567 $\pm$ 235 | 1138 | 429 $\pm$ 235
95418 | 3588 $\pm$ 359 | 3650 | -62 $\pm$ 359 |  | 1743 $\pm$ 262 | 1392 | 351 $\pm$ 262
102647 | 5822 $\pm$ 582 | 5297 | 525 $\pm$ 582 |  | 2317 $\pm$ 348 | 2020 | 297 $\pm$ 348
139006 | 4077$\pm$ 408 | 3924 | 153 $\pm$ 408 |  | 1795 $\pm$ 262 | 1496 | 299 $\pm$ 262
141569 | 338 $\pm$ 34 | 56 | 282 $\pm$ 34 |  | 883 $\pm$ 147 | 22 | 861 $\pm$ 147
161868 | 1105 $\pm$ 111 | 1064 | 41 $\pm$ 111 |  | 443 $\pm$ 72 | 406 | 37 $\pm$ 72

Notes– The 1-$\sigma$ uncertainties given here are the quadratic addition of
both background and photometric uncertainties. For the measurement
uncertainties alone, see Table 3.

Table 5: Excess Emission of Debris Disk Candidates (T-ReCS)

|  $F_{\nu}$(10.4 $\mu$m) [mJy] |  |  $F_{\nu}$(11.7 $\mu$m) [mJy] |  |  $F_{\nu}$(18.3 $\mu$m) [mJy]
---|---|---|---|---|---
HD | Total | Star | Excess |  | Total | Star | Excess |  | Total | Star | Excess
38206 | 202 $\pm$ 20 | 169 | 33 $\pm$ 20 |  | … | … | … |  | 116 $\pm$ 19 | 54 | 62 $\pm$ 19
38678 | 2130 $\pm$ 190 | 1388 | 742 $\pm$ 190 |  | … | … | … |  | 960 $\pm$ 60 | 484 | 476 $\pm$ 60
71155 | 1083 $\pm$ 108 | 815 | 268 $\pm$ 108 |  | … | … | … |  | 375 $\pm$ 57 | 261 | 114 $\pm$ 57
75416 | … | … | … |  | 229 $\pm$ 23 | 141 | 88 $\pm$ 23 |  | 92 $\pm$ 15 | 58 | 34 $\pm$ 15
80950 | 191 $\pm$ 23 | 162 | 29 $\pm$ 23 |  | … | … | … |  | 109 $\pm$ 19 | 52 | 57 $\pm$ 19
115892 | 2540 $\pm$ 254 | 2748 | -208 $\pm$ 254 |  | 2521 $\pm$ 252 | 2155 | 366 $\pm$ 252 |  | 1026 $\pm$ 155 | 881 | 145 $\pm$ 155
172555 | … | … | … |  | 1155 $\pm$ 116 | 520 | 635 $\pm$ 116 |  | 1094 $\pm$ 164 | 213 | 881 $\pm$ 164
178253 | … | … | … |  | 770 $\pm$ 77 | 655 | 115 $\pm$ 77 |  | 360 $\pm$ 55 | 268 | 92 $\pm$ 55
181296 | … | … | … |  | 395 $\pm$ 40 | 271 | 124 $\pm$ 40 |  | 343 $\pm$ 54 | 111 | 232 $\pm$ 54
181869 | 695 $\pm$ 70 | 731 | -36 $\pm$ 70 |  | … | … | … |  | 202 $\pm$ 34 | 234 | -33 $\pm$ 34

Notes– The 1-$\sigma$ uncertainties given here are the quadratic addition of
both background and photometric uncertainties. For the measurement
uncertainties alone, see Table 3.

Table 6: Summary of Debris Disk Candidate IR Excess Detections

HD | N (10.4 $\mu$m) | N′ (11.2 $\mu$m) | Si-5 (11.7 $\mu$m) | Qaa (18.1 $\mu$m) | Qab (18.3 $\mu$m)
---|---|---|---|---|---
38206 | none | … | … | … | significant
38678 | significant | … | … | … | significant
56537 | … | none | … | none | …
71155 | marginal | … | … | … | marginal
75416 | … | … | significant | … | marginal
80950 | none | … | … | … | significant
83808 | … | none | … | none | …
95418 | … | none∗ | … | none∗ | …
102647 | … | none | … | none | …
115892 | … | … | none | … | none
139006 | … | none∗ | … | none∗ | …
141569 | … | significant | … | significant | …
161868 | … | none | … | none | …
172555 | … | … | significant | … | significant
178253 | … | … | none | … | none
181296 | … | … | significant | … | significant
181869 | none | … | … | … | none

Notes– a Michelle, Gemini North. b T-ReCS, Gemini South.

∗ While there is no statistically significant detection of excess emission for
these sources in our data, they do appear to be spatially resolved. This point
is discussed in §3.1 and §5.2.

Table 7: FWHM of Debris Disk Candidates & PSF Reference Stars (Michelle) | N′ FWHM [arcsec] |  | Qa FWHM [arcsec]
---|---|---|---
Name | Source | PSF |  | Source | PSF
HD 56537 | 0.365 $\pm$ 0.002 | 0.398 $\pm$ 0.013 |  | 0.545 $\pm$ 0.019 | 0.539 $\pm$ 0.004
|  |  |  | 0.609 $\pm$ 0.025 | 0.554 $\pm$ 0.006
HD 83808 | 0.347 $\pm$ 0.001 | 0.380 $\pm$ 0.009 |  | 0.537 $\pm$ 0.004 | 0.529 $\pm$ 0.005
HD 95418 | 0.339 $\pm$ 0.001 | 0.328 $\pm$ 0.002 |  | 0.539 $\pm$ 0.003 | 0.543 $\pm$ 0.003
HD 102647 | 0.361 $\pm$ 0.002 | 0.353 $\pm$ 0.008 |  | 0.533 $\pm$ 0.005 | 0.535 $\pm$ 0.002
|  |  |  | 0.531 $\pm$ 0.003 | 0.533 $\pm$ 0.003
HD 139006 | 0.419 $\pm$ 0.003 | 0.364 $\pm$ 0.006 |  | 0.574 $\pm$ 0.007 | 0.556 $\pm$ 0.004
|  |  |  | 0.516 $\pm$ 0.004 | 0.544 $\pm$ 0.003
HD 141569 | 0.436 $\pm$ 0.004 | 0.374 $\pm$ 0.016 |  | 0.807 $\pm$ 0.029 | 0.539 $\pm$ 0.005
|  |  |  | 0.818 $\pm$ 0.066 | 0.523 $\pm$ 0.003
HD 161868 | 0.386 $\pm$ 0.003 | 0.356 $\pm$ 0.006 |  | 0.518 $\pm$ 0.031 | 0.528 $\pm$ 0.003
|  |  |  | 0.537 $\pm$ 0.017 | 0.525 $\pm$ 0.006
Table 8: FWHM of Debris Disk Candidates & PSF Reference Stars (T-ReCS) | N FWHM [arcsec] |  | Si-5 FWHM [arcsec] |  | Qa FWHM [arcsec]
---|---|---|---|---|---
Name | Source | PSF |  | Source | PSF |  | Source | PSF
HD 38206 | 0.442 $\pm$ 0.008 | 0.427 $\pm$ 0.014 |  |  |  |  | 0.592 $\pm$ 0.042 | 0.534 $\pm$ 0.006
HD 38678 | 0.311 $\pm$ 0.001 | 0.308 $\pm$ 0.001 |  |  |  |  | 0.605 $\pm$ 0.015 | 0.536 $\pm$ 0.016
HD 71155 | 0.348 $\pm$ 0.003 | 0.332 $\pm$ 0.003 |  |  |  |  | 0.647 $\pm$ 0.040 | 0.583 $\pm$ 0.025
HD 75416 |  |  |  | 0.494 $\pm$ 0.014 | 0.471 $\pm$ 0.008 |  | 0.875 $\pm$ 0.097 | 0.648 $\pm$ 0.024
HD 80950 | 0.372 $\pm$ 0.008 | 0.412 $\pm$ 0.007 |  |  |  |  | 0.738 $\pm$ 0.125 | 0.617 $\pm$ 0.015
HD 115892 |  |  |  | 0.412 $\pm$ 0.010 | 0.467 $\pm$ 0.006 |  | 0.580 $\pm$ 0.016 | 0.597 $\pm$ 0.012
|  |  |  |  |  |  | 0.600 $\pm$ 0.011 | 0.616 $\pm$ 0.022
HD 172555 |  |  |  | 0.369 $\pm$ 0.002 | 0.378 $\pm$ 0.006 |  | 0.591 $\pm$ 0.014 | 0.559 $\pm$ 0.013
HD 178253 |  |  |  | 0.439 $\pm$ 0.003 | 0.446 $\pm$ 0.008 |  | 0.530 $\pm$ 0.053 | 0.584 $\pm$ 0.019
HD 181296 |  |  |  | 0.384 $\pm$ 0.002 | 0.380 $\pm$ 0.006 |  | 0.584 $\pm$ 0.192 | 0.519 $\pm$ 0.012
HD 181869 | 0.378 $\pm$ 0.003 | 0.354 $\pm$ 0.011 |  |  |  |  | 0.506 $\pm$ 0.024 | 0.613 $\pm$ 0.037

##  3 Source Measurements

###  3.1 Statistical Significance of IR Excesses

The photospheric flux densities at 10–12 $\mu$m and 18 $\mu$m were estimated
by extrapolating the $2MASS$ K-band (2.2 $\mu$m) flux densities (Cutri et al.,
2003) to 10 $\mu$m. The flux density was assumed to vary as $\nu^{1.88}$ over
this wavelength range, as is estimated by Kurucz (1979) to be appropriate for
an A0 star (e.g., Jura et al. 1998). Beyond 10 $\mu$m, we assumed a Rayleigh-
Jeans relation ($\nu^{2}$) for the photosphere. The photospheric flux density
estimate and the corresponding excess flux density estimate are given for each
source in Tables 4 and 5. As discussed in §2.2, photometric uncertainties of
10% and 15% are assumed for the 10- and 18-$\mu$m windows, respectively. We
have compared our flux density estimates for the photosphere with those
determined via Kurucz models for several sources (e.g., Smith et al. 2008),
and the difference is less than 4%, which is well below the photometric
uncertainty.

The photometric measurements, when combined with estimates of the photospheric
contribution, permit assessment of the level of excess emission attributable
to dust. For some of the sources that are known to have 24-$\mu$m excess
emission, we do not detect statistically significant excess emission at 10-
and/or 18-$\mu$m. We comment on these cases specifically later in this
section. We further confirm that the excess emission (when present) is
spatially coincident with the star and does not originate from a background
object. These sources were chosen based on space-based observations of their
infrared excess, and the lower resolution of those images (due to the
$\sim$10x smaller primary mirror) is more prone to confusion within the beam.
In §5, we consider whether the implications for the location of the dust from
photometric measurements and measurements of spatial extent present a
consistent picture for each of the sources.

The following definitions apply to our characterization of the measured IR
excesses:

• total uncertainty: The total uncertainty is the quadratic addition of the
measurement uncertainty (given in Table 3) and the photometric uncertainty for
a calibrated image. This value is referred to as $\sigma_{phot}$.

• no detected excess: A source with no detected excess is defined as having an
IR excess of less than two times the total uncertainty of the flux density
measurement.

• marginal excess: A source with marginal excess is defined as having an IR
excess of two to three times the total uncertainty of the flux density
measurement.

• significant excess: A source with significant excess is defined as having an
IR excess greater than or equal to three times the total uncertainty of the
flux density measurement.

For nine (HD 56537, HD 83808, HD 95418, HD 102647, HD 115892, HD 139006, HD
161868, HD 178253, and HD 181869) of our 17 debris disk sources, we do not
detect statistically significant excess emission in either of the bandpasses
used in this work. Two sources (HD 38206 and HD 80950) have an excess detected
in only one bandpass. The detections of excess emission are summarized in
Table 6. As discussed in §2.1, the debris disk candidates were chosen based on
excess emission observed at 24 or 25 $\mu$m. In the following sections, we
report the detection of spatial extension for several sources (HD 56537, HD
95418, HD 139006, and HD 161868) that do not have statistically significant
excess IR emission. These results are not necessarily inconsistent, due to the
uncertainties in both quantities.

###  3.2 Source Extent

Only a handful of circumstellar debris disks have been spatially resolved at a
level that permits examination of detailed structure. However, it is important
to keep in mind that valuable information is still obtained when only the
scale size is determined. A “disk” can consist of several components that
reflect the complex relationships among the dust population, the dust parent
bodies, and the planetary system, with the proposed (but still unresolved)
asteroid-belt and Kuiper-belt dust zones in the triple-planet system HD 8799
being a spectacular example (Marois et al., 2008; Chen et al., 2009;
Reidemeister et al., 2009). Establishing the existence of any of these
subsystems by constraining the emitting-region size permits assessment of
broader system properties, as illustrated in our analysis of Zeta Lep Moerchen
et al. (2007b) where the resolved dust may well betoken an asteroid belt and,
consequently, planets.

To check for the presence of an extended disk source in our targets, we
observed a source that is known to be not extended, a PSF star, in close
temporal proximity to the target observation, as described in §2.2. In most
cases, there was no obvious 2-D structure to the disk source, and the PSF
references often showed asymmetric features. Examples of asymmetric PSFs,
whose causes may be associated with chopping and nodding, are shown in Fig. 1.
A key measure of scale size is the full-width at half-maximum (FWHM) intensity
of the emitting source. Especially for fainter sources, the FWHM may be the
only available measure of source size. Given the small source sizes
anticipated in this study, we have focused exclusively on the use of the FWHM
to characterize their extent, while remaining open to the possibility that
more extended lower-level emission might be present. We used as our primary
metric the FWHM measurement from a 1-D Moffat profile fitted to the azimuthal
average of each source with an IRAF routine (i.e., we do not simply measure
directly the FWHM, which, due to noise on the profile, would be a much less
accurate measurement). Moffat profile fitting has been used frequently in mid-
IR image analysis (e.g., Radomski et al. 2008), because we find that the true
profile width at the half-maximum level is better approximated by a Moffat
profile than by a Gaussian, regardless of the overall goodness-of-fit as
evaluated by, e.g., chi-squared analysis. We have again verified this
hypothesis for several sources in the dataset presented in this work,
including the known resolved sources HD 38678 and HD 141569, and the FWHM of
the Moffat profile fit is closer to the true FWHM value in $>$90% of the
images measured. This is likewise the finding of a report on PSF image quality
in the mid-IR at Gemini South (which is summarized in Li, Telesco & Varosi
2010). We acknowledge that, in practice, one could choose a different metric
such as the full-width at quarter-maximum, for which a Moffat profile fit may
not be the optimal choice.

Figure 1: PSF observations taken at 11.2 $\mu$m with Michelle before and after
HD 141569, shown to illustrate typical asymmetries encountered. Contours on
the two PSF images are drawn logarithmically to show the structure, with the
lowest contour drawn at 0.3% of the peak surface brightness. Contours on the
residual image are drawn at linear intervals of the normalized peak surface
brightness of the two images, every 5% from 0–20%. Note that the first PSF
(left) shows slight N-S elongation in the core and a partial trefoil pattern
in the wings. The second PSF appears slightly cross-shaped in the core,
resulting in contours at the center that are more square-shaped. The residual
difference between these two peak-normalized PSFs is up to 20% of the original
peak flux within the central arcsecond.

We then compared the PSF and the disk candidate FWHM values to make an
assessment of the extent of the emission. However, the science targets are
typically at least an order of magnitude fainter than the reference star and
must be observed for correspondingly longer integration times to achieve
similar signal-to-noise ratios. Pupil rotation, incorrect guiding correction,
and changes in the quality of seeing during long observations on a science
target can result in a final image degraded by lower-frequency components that
are not accurately represented in the PSF determined from generally shorter
integration times. Minor variations may sometimes average out, but in the
majority of cases these effects broaden the source profile in a final stacked
image (see also Li, Telesco & Varosi 2010).

To estimate more robustly the profile widths and thereby assess spatial
extent, we examined the FWHM of the PSF star and the target sources throughout
their integration sequences. Usually, the smallest unit of integration time
was that corresponding to the so-called saveset image111A saveset is a stack
of chopped images, on- and off-source, taken within one telescope nod
position. Each saveset corresponds to $\sim$10 s of integration time, and
there are typically three savesets in one nod position before the telescope
switches to the opposite nod position., but in some cases it was necessary to
bin two or more savesets to achieve a signal-to-noise ratio high enough to
perform a Moffat fit to the source profile. In this way, we were able to
determine a mean FWHM and corresponding uncertainty from the set of subdivided
images for both the PSF and the debris disk target. Using all of the data
points, and taking into account the number of points in the set, we determined
the standard deviation of the mean (the standard deviation divided by
$\sqrt[]{n}$ number of measurements) for each set of FWHM measurements, and we
adopt this value as the uncertainty. The standard deviation (and standard
deviation of the mean) is valid for a Gaussian distribution of independent
values extracted from a population that does not vary with time, but the
assumption of a stationary Gaussian distribution of values for our data sets
was not always valid. The variation in FWHMs for each of our data sets in this
work sometimes revealed outlying data points, or an obvious deterioration or
improvement in image quality due to factors like seeing. However, such time-
variant changes are not observed for the majority of sources in this work, and
in particular we do not observe obvious changes in image quality in the data
sets of sources that we claim to have spatially resolved. Likewise, in an
effort to make our data quality transparent, plots of the FWHM measurements
for each source are shown in the appendix.

We have also applied a Student’s $t$-test (assuming unknown and unequal
variances) to compare the FWHM values of the source and PSF for each dataset
to better assess whether the source and PSF data are drawn from the same image
quality distribution. We quote these results for individual sources (§5) when
relevant, which occurs in two cases: (1) the PSF profile data are
systematically broader than the source profile data, and the $t$-test confirms
that the two sets are not drawn from the same population, in which case the
data are rejected, or (2) the source profile data are significantly broader
than the PSF profile data, and the $t$-test confirms that the two sets are not
drawn from the same population, in which case we consider the source spatially
resolved.

The following terms are defined, for use in characterization of the measured
extent of the sources:

• combined standard deviation of the mean: The combined standard deviation of
the mean is the combination of the standard deviation of the mean of the PSF
FWHM measurements and the standard deviation of the mean of the source FWHM
measurements, given by

$\sigma_{ext}=\sqrt[]{\sigma_{PSF}^{2}+\sigma_{source}^{2}}.$ (1)

This value is referred to as $\sigma_{ext}$ in the following discussion of
extension measurements.

• unresolved: An unresolved source is defined as having an average source FWHM
value that is greater than its corresponding PSF FWHM by less than three times
the combined standard deviation of the mean of those two measurements:

$FWHM_{source}-FWHM_{PSF}<3\sigma_{ext}$ (2)

• resolved: A resolved source is defined as having an average source FWHM
value that is greater than its corresponding PSF FWHM by three or more times
the combined standard deviation of the mean of those two measurements:

$3\sigma_{ext}\leq FWHM_{source}-FWHM_{PSF}$ (3)

Based on these FWHM measurements (Tables 7 and 8), several sources appear to
be extended. The statistical significance of these extended sources has been
assessed by breaking up the full integration time into individual images, as
described in §3.2. A list of the sources that appear to be resolved (based on
FWHM measurements of profile fits to the data) and their sizes is given in
Table 9. The images of the resolved sources, their corresponding PSFs, and the
residuals from peak-normalized subtraction of the PSFs are shown for reference
in Fig 2.

The profile widths of Moffat fits to the disk sources, their PSF stars, and
the associated uncertainties (one standard deviation of the mean) are listed
in Tables 7 and 8. The statistical significance of the difference between
target and PSF profile width is given in Table 9. Of the 17 debris disk
candidates (i.e., excluding the two sources mentioned in §2.1) that we imaged,
five sources near 10 $\mu$m ($\lambda_{c}$ = 10.7, 11.2, or 11.7 $\mu$m) and
two sources near 20 $\mu$m ($\lambda_{c}$ = 18.1 or 18.3 $\mu$m) had source
FWHM values bigger than the PSF FWHM by more than three times the combined
standard deviation of the mean for the two measurements. These sources are
discussed further in §5.

Figure 2: Images of the sources resolved in this work, the corresponding PSF stars, and the residual from peak-normalized subtraction. Contours are drawn at 3, 6, and 9$\sigma_{bkd}$ in all images.  Table 9: Sizes of Extended Sources | 10.4 $\mu$m |  | 11.2 $\mu$m |
---|---|---|---|---
| $\Delta FWHM\tablenotemark{a}$ | r |  | $\Delta FWHM\tablenotemark{a}$ | r |
HD | [arcsec] | [AU] |  | [arcsec] | [AU] |
71155 | 0.10 $\pm$ 0.01 | 1.96 $\pm$ 0.02 |  | … | … |
95418 | … | … |  | 0.09 $\pm$ 0.01 | 1.09 $\pm$ 0.01 |
139006 | … | … |  | 0.20 $\pm$ 0.01 | 2.31 $\pm$ 0.04 |
141569 | … | … |  | 0.22 $\pm$ 0.02 | 10.89 $\pm$ 0.48 |
181869 | 0.16 $\pm$ 0.01 | 4.12 $\pm$ 0.11 |  | … | … |
| 18.1 $\mu$m |  | 18.3 $\mu$m |
| $\Delta FWHM\tablenotemark{a}$ | r |  | $\Delta FWHM\tablenotemark{a}$ | r |
HD | [arcsec] | [AU] |  | [arcsec]  | [AU] |
38678  | … | … |  | 0.28 $\pm$ 0.02 | 3.01 $\pm$ 0.24 |
139006 | 0.12 $\pm$ 0.06 | 1.36 $\pm$ 0.09 |  | … | … |
141569 | 0.60 $\pm$ 0.03 | 29.7 $\pm$ 1.1 |  | … | … |
| 0.63 $\pm$ 0.07 | 31.1 $\pm$ 2.5 |  | … | … |

##  4 Expected detectability based on comparison to archetypes

Here we consider a simple assessment of how many sources from our sample we
would expect to spatially resolve if the source morphologies were similar to
those of certain archetypal disks that have already been resolved with mid-IR
imaging. We use two archetypes for comparison: (1) a possible asteroid belt
analog, $\zeta$ Lep, and (2) a possible Kuiper Belt analog, $\beta$ Pic. The
$\zeta$ Lep emission is very compact, and the evidence for a disk in this type
of a source would be found in the FWHM. In contrast, the central disk of
$\beta$ Pic is very extended but relatively faint and for the most part not
evident in a measurement of the FWHM, but rather in the wings of the profile.

###  4.1 $\zeta$ Lep Analog

$\zeta$ Lep was resolved in 18.3-$\mu$m images, and the measured spatial
extent implied a dust disk radius of 3 AU (Moerchen et al., 2007b). The disk
radius was inferred from a quadratic subtraction of the PSF FWHM from the
azimuthally averaged source FWHM:
${FWHM}_{source}^{2}-{FWHM}_{PSF}^{2}={D}_{disk}^{2}$. (Such a relationship is
strictly true for Gaussian functions, and another example of combination in
quadrature is given in Eq. 1.) Therefore, we consider whether each of the
sources in our sample (besides $\zeta$ Lep) would be spatially resolved if it
were described by a point source (the size of which is dictated by the
corresponding PSF) and a dust disk of radius 3 AU with the same brightness
relative to its host star as that of the $\zeta$ Lep system. We calculate the
FWHM for each source as the quadratic addition of its corresponding PSF FWHM
and a disk with a 3-AU radius:
${FWHM}_{PSF}^{2}+D_{6~{}AU}^{2}={FWHM}_{source}^{2}$. The point source
considered here may correspond to stellar emission and/or emission from dust
from an unresolved region near the star.

We consider a source to be spatially resolved if the value $FWHM_{source}$
(convolved PSF and 3-AU-radius-disk) is greater than its corresponding value
for $FWHM_{PSF}$ by more than 3$\sigma_{ext}$, where $\sigma_{ext}$ is the
total uncertainty associated with the FWHM measurements (discussed further in
§3.2). Based on the PSF observations associated with each source and the
assumption that they have a morphology like that of $\zeta$ Lep, we estimate
that eleven sources should have been resolved in images near 10 $\mu$m and
five sources should have been resolved in images near 18 $\mu$m. In reality,
five sources were resolved in 10-$\mu$m images, and two sources were resolved
in 18-$\mu$m images (results discussed further in §3.2). HD 141569 is in both
of these sets, and it is known from prior observations that this dust disk is
more extended (r$>$30 AU) and is not comparable in nature to $\zeta$ Lep.
Removing HD 141569 from the set of resolved sources leaves three sources
resolved in 10-$\mu$m images and one source resolved in 18-$\mu$m images. The
fact that only approximately half of the projected number of resolved Zeta-
Lep-like sources were actually resolved suggests that not all of the sources
are comparable in size to the asteroid-belt-like analog associated with
$\zeta$ Lep. However, it is also possible that some sources have a disk size
comparable to that of $\zeta$ Lep but remain undetected due to lower disk
brightness. This is a reasonable possibility, because $\zeta$ Lep has a higher
fractional IR luminosity than most of the sources in our sample.

###  4.2 $\beta$ Pic Analog

We also assess the number of sources we would expect to resolve if the disk
morphology of each target were comparable to that of the well known disk
$\beta$ Pic. For each target, we check whether extended emission (r$\sim$100
AU) like that seen around $\beta$ Pic would be significantly detected above
the background noise level in our actual source images. To be clear, this is
not spatial extent sought at the FWHM level, but emission farther out in the
brightness profile that is significantly above the level of the background. We
acknowledge that edge-on disks like $\beta$ Pic may be more detectable than
face-on disks because of the higher line-of-sight column densities, and so we
consider the disk emission levels for both an edge-on and a face-on case. We
used unaltered mid-IR images of $\beta$ Pic (Telesco et al., 2005) for the
edge-on case, since it is nearly edge-on already. For the face-on case, we
constructed simple model images of a face-on $\beta$ Pic by integrating the
measured flux density as a function of radius and then redistributing it
azimuthally. By generating this face-on model, we assume that the disk is
optically thin and its MIR emission is azimuthally symmetric. In images of
$\beta$ Pic taken from the ground with subarcsecond resolution (e.g., Telesco
et al. 2005), we see that the assumption of azimuthal symmetry is a
simplification of the disk structure but is reasonable for our purposes here.

We generated profile cuts of the edge-on and face-on images to compare the
flux density levels to the background noise measured in our target images.
Profile cuts were made by sampling the line of pixels along the major axis of
the disk for the edge-on case and along an axis bisecting the disk in the
face-on case. To account for the different central star brightness and
accordingly different disk brightness of our target sources, we scaled the
brightness of the $\beta$ Pic profiles according to the stellar flux density
of each of the sources. We expect that the 2-$\mu$m flux density is
predominantly from the photosphere, and we therefore used the $2MASS$
measurement for each target as a metric for the stellar brightness and,
accordingly, its dust heating ability. We scaled the profiles for each of the
sources by the ratio of the target source $2MASS$ flux density to that of
$\beta$ Pic, $F_{target}(2~{}\mu m)/F_{\beta~{}Pic}(2~{}\mu m)$. The width of
the extended emission profiles was also scaled for each source according to
the source distance.

We characterize a $\beta$-Pic-type source as one that we could have detected
if the extended emission of the test profile is (1) above the 5-$\sigma_{bkd}$
level (five times the per-pixel background noise measured in the actual source
images) and (2) beyond the first Airy null, since some simulated profiles
might have been bright enough for detection but were not spatially extended
beyond the Airy disk. Five-$\sigma$ levels are used to assess extension
because the mid-IR background is noisy enough that 3-$\sigma$ “blobs” that are
not associated with disk emission are relatively common. If all of the sources
in our sample had the same morphology and fractional IR luminosity as $\beta$
Pic, we would expect the following number of detections: for an edge-on
orientation, eleven at 10 $\mu$m and six at 18 $\mu$m, and for a face-on
orientation, five at 10 $\mu$m and none at 18 $\mu$m. (We note that the disk
of $\beta$ Pic itself is not detected in a face-on orientation in this test,
keeping in mind that the considerable observed levels of optically thin
emission have been redistributed azimuthally for the face-on model, resulting
in much lower surface brightnesses than in its true nearly edge-on
orientation.) In fact, our images reveal that only one source, HD 141569,
shows significant extended emission (in both bandpasses). However, a random
distribution of disks would only have approximately 10% of disks with
inclinations within ten degrees of edge-on; therefore, the number of
detections that we expect in a realistic distribution of disk inclinations
should be $\sim$10% of our predicted number of edge-on detections, $\sim$1 at
10$\mu$m and $<$1 at 18 $\mu$m. Therefore, perhaps surprisingly, our observed
results are consistent with a population composed entirely of $\beta$-Pic-type
disks with a random distribution of orientations. However, this statement is
weakened by the fact that our sample contains a relatively small number of
sources.

Our general conclusion based on comparison to $\zeta$ Lep and $\beta$ Pic
archetypes is that our results are generally consistent with the expected
detection rate of several more asteroid belt analogs like $\zeta$ Lep but only
one (HD 141569) Kuiper Belt analog like $\beta$ Pic. We examine this issue
more below.

##  5 Consistency of Spatial and Photometric Measurements

Here we assess the consistency of the observed color temperature of the excess
emission with the temperature of dust in radiative equilibrium at the distance
implied by the observed spatial disk extent. The color temperature is an upper
limit to the true temperature because it is the unique solution to the
equation

$\frac{F_{{\nu}_{1}}}{F_{{\nu}_{2}}}=\frac{Q_{{\nu}_{1}}}{Q_{{\nu}_{2}}}\frac{B_{{\nu}_{1}}(T)}{B_{{\nu}_{2}}(T)}$
(4)

where $B_{{\nu}_{1}}(T)/B_{{\nu}_{2}}(T)$ is the ratio of two points on the
Planck function for a temperature $T$, and $Q_{{\nu}_{1}}/Q_{{\nu}_{2}}$, the
ratio of the two emission efficiencies, is unity. If the particles behave as
blackbodies, then the ratio $Q_{{\nu}_{1}}/Q_{{\nu}_{2}}$ is unity. For
particles comparable in size or smaller than the emission wavelength, the
emission efficiency is sometimes described as $Q_{em}\propto\nu^{n}$, with
n=1–2, and if $\nu_{1}>\nu_{2}$, then $Q_{{\nu}_{1}}/Q_{{\nu}_{2}}$ will be
greater than unity. In this non-blackbody case, the ratio of the two points on
the Planck function $B_{{\nu}_{1}}(T)/B_{{\nu}_{2}}(T)$ would have to be
lower, and thus originate from a lower-temperature source, in order to produce
the same observed flux density ratios. Real dust particles are generally not
blackbodies, and the computed color temperature is therefore an overestimate
of the true physical temperature.

While the relationship between a disk s observed color temperature and a
“true” dust temperature depends on the distributions of particle sizes and
locations, numerous examples suggest that the observed global color
temperature of a disk can give an indication, albeit a rough one, of the
typical distances of the mid-infrared-emitting particles from the star, and
therefore of the disk size. For example, the 100-K mid-IR color temperature of
$\beta$ Pic implies that dust with blackbody behavior would be located at
$\sim$25 AU, which is within the bounds of the $\sim$100 AU radial extent of
the mid-IR disk emission (Telesco et al., 2005); likewise, the 327-K mid-IR
color temperature of $\zeta$ Lep implies a dust distance of 2.9 AU, which is
consistent with the 3-AU radial extent determined from 18-$\mu$m images
(Moerchen et al., 2007b).

Disk extent ($r_{AU}$) is estimated by quadratic subtraction of the PSF FWHM
from the source FWHM. The resulting estimate for the dust temperature $T_{d}$,
for blackbody particles at that distance from the star, is given by

$T_{d}=278~{}L_{\star}^{\frac{1}{4}}~{}r_{AU}^{-\frac{1}{2}}$ (5)

where the stellar luminosity $L_{\star}$ is in units of $L_{\odot}$, solar
luminosity, $r_{AU}$ is the radius of the dust annulus in AU, and the
equilibrium temperature at 1 AU (Earth) is 278 K. Uncertainties for this
temperature estimate are calculated by propagating the uncertainty in the disk
extent ($r_{AU}$) through Equation 5. This temperature estimate from Equation
5 is a lower limit to the true temperature, because we have assumed that the
dust particles are blackbodies. In reality, as noted above, “small” particles
are heated to higher temperatures than blackbodies at the same distance from
the star. For example, we have plotted in Figure 3 the relationship between
temperature and distance from a $\sim$7-L⊙ star (representative of an A-type
main-sequence star) for both blackbody-type particles and less efficient
emitters with characteristic sizes of 0.05, 0.075, and 0.25 $\mu$m. The
temperatures for these inefficient emitters were calculated based on equations
from Backman & Paresce (1993), which estimate particle temperature as a
function of distance based on assumptions regarding particle size and
composition, and thereby radiation efficiency. The case adopted for our purely
demonstrative calculations is that of a particle which absorbs efficiently but
emits inefficently, such as graphite or amorphous silicate. It can be seen in
this plot that for a given observed dust temperature, the implied distance
from the star depends significantly on the particle properties, especially at
the lowest temperatures, and this should be kept in mind when considering our
calculations in the following sections.

Figure 3: The expected blackbody temperature as a function of distance from a
$\sim$7-L⊙ main-sequence star (solid line), and the predicted temperatures for
efficiently absorbing but inefficiently emitting particles (as discussed in
Backman & Paresce 1993) with characteristic grain sizes of (from left to
right) 0.25 $\mu$m (long dash), 0.075 $\mu$m (medium dash), and 0.05 $\mu$m
(short dash).

In cases where we detect excess emission that is not spatially extended, we
estimate a temperature with Equation 5 and the 2-$\sigma_{ext}$ limit for the
observation. That is, we assume that any extension (source FWHM minus the PSF
FWHM) that is less than 2$\sigma_{ext}$ could escape detection. Thus, we
estimate the upper limit for disk extent as

$r_{limit}=\frac{1}{2}~{}\sqrt[]{(FWHM_{PSF}+2\sigma_{ext})^{2}-FWHM_{PSF}^{2}}.$
(6)

This estimate also yields a lower limit to the true dust temperature, because
the temperature will increase if (1) the dust is any closer to the star, or
(2) the particles are small enough that they do not behave like blackbody
emitters. The radius limits calculated with this method are summarized in
Table 10.

Table 10: Dust Radius Limit Estimates (in AU) for Unresolved Sources with IR
Excess

HD | Si-5 (11.7 $\mu$m) | Qaa (18.3 $\mu$m)
---|---|---
38206 | … | 10.8
71155 | … | 6.2
75416 | 8.6 | 26.5
80950 | … | 8.1
172555 | 1.4 | 3.1
178253 | 2.4 | 7.5
181296 | 2.3 | 17.6
181869 | … | 8.9

Notes– a T-ReCS, Gemini South. All limits were estimated with Equation 6.

###  5.1 Sources Unresolved at Both Wavelengths

HD 38206– There was no excess emission detected at 10.4 $\mu$m. We estimated a
temperature for the unresolved 18.3-$\mu$m-emitting dust by calculating the
blackbody temperature at the orbital distance corresponding to the
2-$\sigma_{ext}$ limit of the source FWHM at 18.3 $\mu$m, as described by
Equation 6. This temperature limit is 201 K.

HD 56537– HD 56537 was not resolved at either wavelength, and we did not
detect significant excess emission.

HD 75416– The equilibrium temperature at the orbital distance corresponding to
the 2-$\sigma_{ext}$ limits of the source FWHM at 11.7 $\mu$m and 18.3 $\mu$m
are 307 K and 175 K, respectively. To estimate the color temperature of 653
$\pm$ 272 K, we assumed that the particles behave as efficient absorbers and
inefficient emitters, because the color could not be fitted by a single-
temperature perfect blackbody. Since the color temperature is an upper limit
to the true dust temperature, the temperature estimates based on spatial
extension measurements are consistent.

HD 80950– For the purpose of assessing spatial resolution via FWHM
measurements, we rejected the 10.4-$\mu$m data, because the PSF was
systematically broader than the disk candidate. This was quantitatively
confirmed by a Student’s $t$-test with $p$-value of 0.0001, or greater than
99.9% certainty that the datasets are drawn from distinct image quality
distributions.

In 10.4-$\mu$m images of HD 80950, we detected two sources separated by 1.6”.
The flux density of the primary is 170 $\pm$ 18 mJy, and the flux density of
the secondary is 8 $\pm$ 1 mJy (uncertainties include both photometric and
background uncertainty). We did not detect any excess emission associated with
the primary at 10.4 $\mu$m. If both sources are measured within the same
aperture, their measured flux density is 190 $\pm$ 23 mJy, where we see a
greater contribution to the background noise due to the larger aperture. Our
flux density measurements are consistent with the $IRAS$ 12-$\mu$m flux
density (Faint Source Catalog) of 211 $\pm$ 25 mJy, and $IRAS$ would not have
distinguished the two sources due to its large beam size. Indeed, no record of
another source within the T-ReCS field is found in the $IRAS$ or $2MASS$
catalogs. It is therefore possible that the IR excess previously thought to be
associated with HD 80950 arises from this apparent companion object. We intend
to characterize this object with further mid-IR and near-IR photometry and/or
spectroscopy, but we note that the frequency of unassociated background
objects encountered in the mid-IR is low. If the unresolved 18.3-$\mu$m
emission originates with dust at an orbital distance corresponding to the
2-$\sigma_{ext}$ limit of the source FWHM, then the implied blackbody
temperature is at least 244 K.

HD 83808– While no excess emission was detected in either bandpass, the
uncertainties for the observed excess are large (Table 4). $Spitzer$ detected
excess emission at 24 $\mu$m, and there are therefore two possibilities for
why we do not detect any excess at 12 or 18 $\mu$m: (1) the dust emission is
diffuse enough that we do not have sufficient sensitivity to detect it above
the background noise, or (2) the dust is too cool to emit significantly at 12
and 18 $\mu$m. We also reject the 11.2-$\mu$m data for use in assessing
spatial extent due to the PSF being systematically broader than the disk
target, which is confirmed by a Student’s $t$-test $p$-value of 0.008.

HD 102647 ($\beta$ Leo)– We did not detect any IR excess emission associated
with the source, within our error bars. Again, the $Spitzer$ detection of
excess emission indicates that there is dust present associated with the
source, so there exist the same two possibilities as in the case of HD 83808:
low surface brightness or cool dust temperatures.

HD 115892– We rejected the 11.7-$\mu$m data for use in assessment of spatial
extent, because the PSF profile is broader than the disk source profile; this
is confirmed by a Student’s $t$-test $p$-value of 1.5 x 10-6.

We detected no excess emission within our error bars. $Spitzer$ observations
do show excess emission at 24 $\mu$m. If this excess is real, then we do not
detect the dust emission either because of low surface brightness or because
of dust temperatures that only yield emission longward of 18 $\mu$m.

HD 161868– We did not detect excess emission in either bandpass, and the
source FWHM is not greater than the PSF FWHM by more than 3$\sigma_{ext}$.

Su et al. (2008) recently resolved this debris disk with $Spitzer$ MIPS images
and estimated a disk radius of $\sim$520 AU from the 24 $\mu$m images and a
disk radius of $\gtrsim$260 AU from the 70 $\mu$m images. The color
temperature based on the 24 $\mu$m and 70 $\mu$m photometry is 81 K, which
overestimates the flux density at 28–35 $\mu$m and 55–65 $\mu$m, and the
authors note that this suggests a range of dust temperatures. Nonetheless, the
81 K blackbody fits the available SED points reasonably well. The IRS spectrum
is also shown, which indicates flux densities of $<$100 mJy at wavelengths
$<$20 $\mu$m; these spectral measurements confirm that our estimated mid-IR
excess levels are within expectations. Given that the color temperature and
the IRS spectrum (and MIPS images) indicate the presence of predominantly cold
dust, it is not surprising that we do not find strong evidence of excess
emission or resolved spatial structure in mid-IR images.

HD 172555– We detected significant IR excess in both bandpasses. We estimated
a minimum dust temperature by assuming that the dust must lie interior to the
disk size corresponding to the 2-$\sigma_{ext}$ limit of the source FWHM. The
temperature estimates based on extension measurements are 407 K (based on the
11.7 $\mu$m data) and 278 K (based on the 18.3 $\mu$m data). The color
temperature calculated from the excess emission measurements from the two
bandpasses is 274 $\pm$ 34 K. Therefore, the temperature estimate based on the
source size limit at 18.3 $\mu$m is consistent with the color temperature, but
the temperature estimate based on the 11.7-$\mu$m source size is not. It is
possible for nonspherical particles to have temperatures lower than those
expected for blackbody emission (e.g., Greenberg & Shah 1971; Voshchinnikov &
Semenov 2000), and this may be the case for the 11.7-$\mu$m-emitting particles
in HD 172555.

Wyatt et al. (2007) noted that the fractional IR luminosity of HD 172555 is
anomalously high, or eighty-six times the expected maximum fractional IR
luminosity based on steady-state evolution models. An estimate of 6 AU is
given for the disk radius, based on 24 $\mu$m and 70 $\mu$m $Spitzer$
photometry; this radius corresponds to a blackbody equilibrium temperature of
$\sim$200 K. This temperature is $\sim$75 K lower than the color temperature
estimate based on mid-IR color, but it is possible that the dust present in
the disk spans a range of radii, and therefore temperatures, and (at least)
two different populations of dust are being sampled by the 12 $\mu$m/18 $\mu$m
color and the 24 $\mu$m/70 $\mu$m color.

HD 178253– We did not detect statistically significant excess emission
associated with this source. However, if there is unresolved emission
originating from dust within the region corresponding to the size of the
2-$\sigma_{ext}$ limit of the source FWHM at each of the observed bandpasses,
then the emitting dust temperatures should be at least 432 K (based on the
11.7-$\mu$m FWHM) and 246 K (based on the 18.3-$\mu$m FWHM).

HD 181296– There is significant IR excess emission detected in both
bandpasses. The temperature estimates for dust within a region the size of the
2-$\sigma_{ext}$ limit of the source FWHM are 397 K (based on the 11.7-$\mu$m
FWHM) and 143 K (based on the 18.3-$\mu$m FWHM). Only the estimate based on
the source FWHM at 18.3 $\mu$m is consistent with the color temperature, which
is 229 $\pm$ 23 K.

Since our initial observations, HD 181296 has been resolved in Q-band images
taken in July 2007 at mid-IR wavelengths with longer (6.5x) integration times
(Smith et al., 2009a). It is likely that the initial observations did not
resolve the source because the integration time was not sufficient to detect
the surface brightness of the disk. The extended emission peaks detected by
Smith et al. (2009a) total $90~{}\pm~{}5$ mJy, and if we assume that the flux
is approximately equally distributed between the two peaks, then this emission
is less than three times our background noise level. Smith et al. (2008)
discuss in greater detail the relationship between disk morphology and the
predicted length of integration required to resolved a given source.

Models of the 18.3-$\mu$m images of the source indicate that $\sim$50% of the
excess emission originates in the resolved component in an apparently edge-on
disk with a 24-AU radius, which can be fit by a modified blackbody of
temperature $\sim$100 K. The rest of the excess emission resides in an
unresolved component of temperature 310 K, consistent with dust at 3.9 AU.
Discrepancies in temperature estimates based on the initial and follow-up data
sets exist primarily because of a 13% lower flux density measurement at 11.7
$\mu$m (from the more recent images); however, these two measurements are
still within $\sim$1$\sigma$ of each other.

###  5.2 Resolved Sources

For reference, we have plotted the azimuthally averaged radial profiles of the
resolved sources and their corresponding PSFs in Figure 5. However, we note
that the images used to generate these plots are only median stacks of all of
the subset frames that were used to assess their spatial resolution.

HD 141569– We review HD 141569 first, because its spatial extent has been
detected previously in mid-IR images (Fisher et al., 2000; Marsh et al., 2002)
and this data set can therefore provide a benchmark for comparison as a
consistent body of evidence that describes the source size.

The source FWHM appears extended in comparison to the PSF FWHM at both 11.2
$\mu$m and 18.1 $\mu$m, and the statistical significance of these extensions
are 3.6$\sigma_{ext}$ (11.2$\mu$m) and 9.1$\sigma_{ext}$ and 4.5$\sigma_{ext}$
(18.1-$\mu$m, from two nights of data). These data were not combined, because
the location of the central star could not be determined accurately, and this
location is necessary to register and stack images. Student’s $t$-tests on the
data yield the following results: at 11.2 $\mu$m, the $p$-value is 0.005 and
there is a 95% confidence interval that the source FWHM is greater than the
PSF FWHM by 0.023” to 0.100”; at 18.1 $\mu$m, the $p$-values are 6 x 10-5 and
6 x 10-4, and the 95% confidence intervals are 0.195”–0.340” and
0.151”–0.439”.

The blackbody dust temperatures at the radii inferred from the 11.2-$\mu$m
images and the 18.1-$\mu$m images are 186 $\pm$ 4 K at $\sim 11$ AU and 112
$\pm$ 3 K at $\sim$30 AU, respectively. (For comparison, Fisher et al. (2000)
determined disk radii of 17 AU and 34 AU at 10.8 $\mu$m and 18.2 $\mu$m,
respectively.) These temperatures are consistent with the color temperature
estimate for HD 141569 of 191 $\pm$ 16 K, in that the extension-implied
temperatures are a lower limit and the color temperature is an upper limit.
Indeed, the models of both Fisher et al. (2000) and Marsh et al. (2002) for
this disk suggest that the dominant particle population is composed of
inefficient emitters that would be heated to temperatures above those expected
for perfect blackbody emitters, which implies that our extent-implied
temperatures should also be higher.

HD 38678, $\zeta$ Lep– $\zeta$ Lep is unresolved at 10.4 $\mu$m but is
resolved at 18.3 $\mu$m, with a significance level of 3.1$\sigma_{ext}$. These
results are discussed in detail in a prior work (Moerchen et al., 2007b). We
have further confirmed the extent with a Student’s $t$-test, which yields a
95% confidence interval that the source FWHM is greater than the PSF FWHM by
0.035”–0.114”. The spatial extent of the 18.3-$\mu$m disk profile implies a
disk radius of 3 AU, which is comparable in location to the asteroid belt in
the solar system. Prior to the spatial resolution of HD 71155 (discussed
below), this was the only resolved debris disk spanning only a few AU (Chen &
Jura, 2001; Moerchen et al., 2007b). The color temperature for the excess
emission associated with $\zeta$ Lep is 323${}^{+27}_{-30}$ K, which is
consistent with the blackbody temperature of 320 K for dust grains at 3.0 AU.
The implied presence of large (r $\sim$ few microns) grains that emit like
blackbodies is supported by $Spitzer$ IRS spectra taken by Chen et al. (2006),
which show no silicate emission feature. Relatively large grains may not cause
silicate emission, as shown by Przygodda et al. (2003).

HD 71155– HD 71155 is resolved at 10.4 $\mu$m, at a significance level of
4.4$\sigma_{ext}$. The 95% confidence interval from a Student’s $t$-test is
0.008”-0.025”, with a $p$-value of 1 x 10-4. The extent (as computed with the
full data set) implies a disk radius of 2.0 $\pm$ 0.1 AU, at which the
blackbody temperature is 499 $\pm$ 3 K. The marginal excess emission for this
source could not be fitted by a simple single-temperature blackbody. The
excess was instead fitted with emitting particles that are efficient absorbers
but inefficient emitters. This may be the case for particles which are larger
than the peak wavelength of stellar emission but smaller than the peak
wavelength of particle thermal emission (Backman & Paresce, 1993). In the
literature, an emission efficiency of the form $Q_{em}\propto\nu^{n}$, with
n=1–2, is often assumed. The color temperature for such inefficient emitters
with n=1 is 487 $\pm$ 129 K, which is consistent with the temperature implied
by the 10.4-$\mu$m extension.

The unresolved 18.3-$\mu$m result is consistent if this emission originates
from the same location as the 10.4-$\mu$m emission; the quadratic sum of the
10.4-$\mu$m-based source size and the 18.3-$\mu$m PSF FWHM size is less than
the nominal detection limit for extension, $FHWM_{PSF}+2\sigma_{ext}$. If this
unresolved 18.3-$\mu$m-emitting dust is assumed to lie within a region
corresponding to this 2-$\sigma_{ext}$ limit of the source FWHM, then its
equilibrium temperature is at least 281 K, which is also consistent with the
upper limit set by the color temperature.

In Fig. 6, we note the possibility that the image quality has systematically
degraded around savesets #40 and #65. We tested the impact of the data in this
region by removing 25 contiguous savesets that include the peaks in FWHM and
then recomputing the mean FWHM value for the source, an exercise which
demonstrates the utility of measuring the source profile in every saveset
rather than solely in the final stacked image. We found that the source FWHM
decreased from 0.348” to 0.339”, but that the standard deviation likewise
decreases, such that the source FWHM is still greater than the PSF FWHM at a
3.1-$\sigma_{ext}$ level. When the $t$-test is repeated with the truncated
data set, the $p$-value is 0.035, and there is a 95% confidence level that the
source FWHM is greater than the PSF FWHM by 0.001”–0.015”. Nonetheless, this
result should be confirmed with deeper imaging observations.

HD 95418– The source is resolved at 11.2 $\mu$m with a statistical
significance of 6.8$\sigma_{ext}$. The results of a Student’s $t$-test on the
data are a $p$-value of 3 x 10-5 and a 95% confidence interval of
0.008”–0.016”. No excess emission associated with HD 95418 is detected in
either bandpass, but the measurement of the excess emission at 11.2$\mu$m is
within 2$\sigma_{phot}$ of a statistically significant excess detection, so
the spatial resolution at that wavelength is consistent. The dust temperature
at the orbital distance implied by this resolved result is 764 $\pm$ 2 K.

Figure 4: 11.2-$\mu$m images of HD 139006, its PSF reference star, and the
residual emission following PSF subtraction, where the PSF was scaled to match
the peak emission of the disk source. Contours are drawn at 3-$\sigma_{bkd}$
intervals from 6$\sigma_{bkd}$ to 15$\sigma_{bkd}$. Note that HD 139006 is
visibly elongated compared to the PSF in the first night of data, and less so
in the second night of data (in which the PSF also appears elongated). We
believe that these images may suffer from so-called “chop tails,” an issue
that has since been resolved at Gemini.

HD 139006– This source is resolved at 11.2 $\mu$m with a statistical
significance of 8.6$\sigma_{ext}$. A Student’s $t$-test yields a $p$-value of
2 x 10-7, with a 95% confidence interval that the source FWHM should be
broader than the PSF FWHM by 0.041”– 0.068”. However, in two sets of
18.1-$\mu$m images from two different nights, one is resolved and one is not.
We believe that this discrepancy arises from image elongation associated with
chopping and nodding procedures, which can be seen clearly in a comparison
images of HD 139006 at 18.1 $\mu$m on two different nights in Fig. 4. Indeed,
in one set, the PSF profile is broader than that of the source (confirmed by a
Student’s $t$-test $p$-value of 6 x 10-7), and thus we do not claim that the
source is spatially resolved at 18.1 $\mu$m. While the large photometric
uncertainty $\sigma_{phot}$ renders the observed excess emission statistically
insignificant, the measurements are well within 2$\sigma_{phot}$ of a formal
excess detection, so the results are consistent.

HD 181869– HD 181869 is resolved at 10.4 $\mu$m (3.1$\sigma_{ext}$) and
unresolved at 18.3 $\mu$m. A Student’s $t$-test on the 10.4-$\mu$m data yields
a $p$-value of 0.041, and a 95% confidence interval that the source FWHM
should be 0.001”–0.048” greater than the PSF FWHM. We have rejected the
profile measurement data at 18.3 $\mu$m on the basis of the PSF being broader
than the source, which was confirmed by a Student’s $t$-test with a $p$-value
of 0.029. No excess emission associated with HD 181869 was detected at either
10.4 $\mu$m or 18.3 $\mu$m, and the simultaneous resolution and lack of
detected excess seem contradictory. However, the measured excess emission at
10.4 $\mu$m is within 2$\sigma_{phot}$ of a marginal excess detection, which
is consistent with the apparent spatial resolution at that wavelength.

Figure 5: Normalized radial brightness profiles of resolved sources (open
circles) and their corresponding PSF stars (filled circles). Sources: (a) HD
71155 (10.4 $\mu$m), (b) HD 95418 (11.2 $\mu$m), (c) HD 141569 (11.2 $\mu$m),
(d) HD 139006 (11.2 $\mu$m), (e) HD 38678 (18.3 $\mu$m), (f) HD 141569 (18.1
$\mu$m), (g) HD 181869 (10.4 $\mu$m).  Figure 6: FWHM of profile fits to the
sources at 10.4 $\mu$m, per saveset. Open circles represent the PSF reference
star, and filled circles represent the debris disk target. Sources: (a) HD
38206, (b) HD 38678, (c) HD 71155, (d) HD 80950, (e) HD 181869.

##  6 Discussion

To better understand the nature of the unresolved sources (among those that
are still considered debris disk candidates), their colors were used to
compare these sources to spatially resolved debris disks whose structure is
relatively well known. In Figure 7, the mid-IR color temperature is plotted
against the age for each debris disk candidate. The resolved sources are
represented by star symbols, and the unresolved sources are represented by
filled circles. Most of the sources that have been resolved with ground-based
mid-IR imaging observations also have the cooler color temperatures. We expect
cooler dust to be more distant from the star and therefore be part of a more
extended disk that is easier to resolve. Thus, the fact that most of the
resolved sources have relatively cool dust is not surprising.

Of course, our sample is limited in number (eight, after non-disk sources and
null excesses have been culled) and biased. The sources were chosen on the
basis of their 24-$\mu$m excess, so it is already known that they have some
warm dust, although possibly not hot enough to emit significantly at 12 or 18
$\mu$m, as the null excess detections suggest. In addition, it is well known
that there are more sources with high fractional luminosities at younger ages,
especially less than 20 Myr (Rieke et al., 2005; Su et al., 2006; Currie et
al., 2008), and our sample, which was chosen with a brightness criterion,
reflects that trend. The cluster of sources toward the left of the plot, at
ages less than 100 Myr, must be considered with these biases in mind.

Figure 7: Mid-IR color temperature of dust versus system age. Age values are
the average of all estimates quoted by Rieke et al. (2005), with the exception
of HD 38678 (230 Myr). Sources represented by filled circles have standard
color temperatures as estimated for unresolved sources (see text). Sources
represented by star-shaped points have been spatially resolved by mid-IR
images from this study (and in the case of HD 141569, also by prior works).
For reference, $\beta$ Pic has an age of 12 Myr and a color temperature of
$\sim$180 K.

Although our sample is not statistically significant, the lack of sources in
Figure 7 with ages in the range $\sim$50–200 Myr is thought-provoking. In the
cluster of sources at young ages, we have resolved one source with a cool dust
temperature that is comparable in extent to the Kuiper Belt (along with
$\beta$ Pic, HR 4796A, and HD 32297, as further examples). In contrast, with
the exception of HD 75416 (5 Myr), which has a very large uncertainty in the
dust temperature, the two sources in our sample with significantly hotter dust
populations are also significantly older: HD 38678 ($\zeta$ Lep) at $\sim$230
Myr and HD 71155 at $\sim$200 Myr. HD 71155 is a new spatially resolved source
with a dust disk radius implied by its 10.4-$\mu$m extent of 2.0 $\pm$ 0.8 AU,
and this size is also comparable to the size of the solar system’s asteroid
belt. Our sample also includes two sources (HD 95418 and HD 139006) that do
not have a statistically significant detection of excess IR emission from our
data set, but whose spatial extents imply disk radii similar to that of the
asteroid belt. As mentioned in §3.1, the measurements of the excess emission
and the spatial extension are not necessarily inconsistent due to the error
bars associated with each value.

While low-resolution surveys show that the mid- and far-IR emission from disks
generally diminishes with time as the inverse of the system lifetime (Rieke et
al., 2005; Su et al., 2006), our observations of two apparent asteroid-belt
analogs in our sample imply that somewhat older ($>$ few 100 Myr) sources can
sustain significant mid-IR emission above the average levels by ongoing
production of dust in asteroid-belt-type collections of planetesimals
relatively close to the star. Whether the collisions have been occurring in a
steady state is not obvious, but the amount of the IR excess may help to
answer that question. Wyatt et al. (2007) distinguish disks as having
potentially transient dust-producing events if they have greater than 1000
times the maximum fractional IR luminosity predicted for their age that have
experienced only steady-state collisions. In the case of $\zeta$ Lep, the
24-$\mu$m excess exceeds the expected level due to steady-state collisions
alone by more than a factor of 10. However, the excess level for HD 71155
falls within the envelope of expected values for disks experiencing solely
steady-state collisions (Wyatt et al., 2007). Therefore, it may be more
plausible (but not imperative) to invoke a process such as delayed stirring or
an event analogous to the Earth and moon-progenitor collision for $\zeta$ Lep,
whereas observations of HD 71155 seem to be consistent with steady-state
evolution.

It is worth noting that the fractional IR luminosities of sources in our
sample (with formal detections of excess emission) that we consider to be
Kuiper Belt analogs (e.g., HD 32297, HR 4796A; $L_{IR}/L_{\star}\sim$10-3) are
$\sim$100 times higher than that of sources that we consider to be asteroid
belt analogs (e.g., HD 38678 [$\zeta$ Lep], HD 71155;
$L_{IR}/L_{\star}\sim$10-5). Thus, in a system that hosts both asteroid-belt-
like and Kuiper-Belt-like structures, the presence of a Kuiper Belt with a
significantly larger amount of dust may make it difficult to discern the
emission from an asteroid belt (see also Liou & Zook 1999). However, with the
advent of the next generation of ground-based telescopes ($>$30-m), the
improvement in diffraction-limited resolving power should enable MIR cameras
to distinguish both belts in such systems.

For the remaining unresolved sources that sustain statistically significant IR
excesses, what can the presence of the warm dust tell us? Ultimately, we would
like to know the distribution of the dust both radially and azimuthally in
order to investigate the planetary system’s architecture. That will hold clues
to the production of the dust (e.g. steady-state or catastrophic collisions)
and what maintains it in its current location (e.g., shepherding planets).
There are (as of the time of writing) approximately 10 disks that are known to
harbor planets (e.g., Wyatt 2008). It is currently easier to make radial
velocity planet detections (the primary detection technique) around FGK-type
stars, while it is easier to spatially resolve the thermal emission from dust
disks around the much more luminous A-type stars, and so there is
unfortunately little overlap in the detections. If information about the
planetary orbits is known, however, dynamical simulations may indicate where
the dust is likely to be stable and how and where the dust was initially
produced. Such simulations have been made for the K-star debris disk HD 69830,
which sustains a surprisingly high amount of dust for its 4–10 Gyr age in
addition to three Neptune-mass planets (Beichman et al., 2005; Lovis et al.,
2006; Lisse et al., 2007). Lovis et al. (2006) showed that, given the
locations of the planets as determined by radial velocity measurements, there
are two stable radii for dust annuli. The recent direct detection of an
orbiting body apparently sculpting the sharp inner edge of the debris disk of
Fomalhaut (Kalas et al., 2008) highlights this relationship.

In future work, observations at 8-meter facilities with longer integration
times and tighter constraints on image quality may reveal more details of the
disk structure for some of the sources in this sample, particularly for the
“borderline” cases. For example, four sources in our sample (HD 161868, HD
172555, HD 178253, and HD 181296) are not spatially resolved, but the color
temperature of their excess IR emission corresponds to that of dust particles
emitting like blackbodies in the approximate region of the asteroid belt
($\sim$1–3 AU). High-resolution imaging at other wavelengths such as the near-
IR or submillimeter may also provide a more complete picture of the disk
morphology (e.g., Maness et al. 2008, Debes et al. 2009, Fitzgerald et al.
2007). For disks with especially small angular sizes ($\lesssim$0.1”),
interferometric observations in the near-IR and mid-IR have also yielded
useful constraints on disk morphologies (e.g., Smith et al. 2009, Akeson et
al. 2009).

MMM gratefully acknowledges fellowship support from the Michelson Science
Center. This work was performed [in part] under contract with JPL funded by
NASA through the Michelson Fellowship Program. JPL is managed for NASA by the
California Institute of Technology. This research was partially supported by
NSF Grant AST 0098392 to CMT. Observations were obtained at the Gemini
Observatory, operated by AURA, Inc., under agreement with the NSF on behalf of
the Gemini partnership: NSF (US), PPARC (UK), NRC (Canada), CONICYT (Chile),
ARC (Australia), CNPq (Brazil), and CONICET (Argentina). Facilities:
Gemini:North (Michelle), Gemini:South (T-ReCS).

##  Appendix A Appendix: Detailed Profile Width Measurements

Here we provide the details of the FWHM measurements of the debris disk
candidates and their corresponding PSF reference stars (Figures 6, 8, 9, 10,
and 11). As discussed in §3.2, the total integration time for an image was
broken up into sub-images each corresponding to a fraction of the total time,
such that the FWHM of the source could be sampled as frequently as possible.

When S/N levels allowed, the smallest unit of time for a sub-image was that
corresponding to a saveset, $\sim$10 s. A saveset is a stack of chopped images
(on- and off-source), and there are typically three savesets per nod position.
For formal and final image stacking, images from both nod positions must be
combined to remove the radiative offset. However, the S/N of the sources was
high enough that the radiative offset did not affect the profile fits to the
sources. Measuring the FWHM in single savesets had the additional benefit of
not incorporating positional errors arising from telescope motion. When images
are taken at two nod positions, we expect that the source location is the same
in both images. However, there may be a slight positional inaccuracy occurring
between each nod switch, and this is avoided by not combining images from two
nod positions.

When the S/N levels were not high enough to perform a reasonable profile fit
to the source in a single saveset, these frames were binned up until a
sufficient S/N level was reached. In the following plots, the total number of
savesets is shown as a temporal series along the x-axis. If the FWHM was
measured in each saveset image, then the number of data points equals the
number of savesets. If, for example, six savesets had to be binned for a FWHM
measurement, then there will only be one data point for every six savesets,
and the data point will be shown at the center of the binned saveset group,
e.g., savesets 1–6 are binned, so the FWHM value is plotted above the “saveset
#3” tick mark.

Figure 8: FWHM of profile fits to the sources at 11.2 $\mu$m, per saveset.
Open circles represent the PSF reference star, and filled circles represent
the debris disk target. Sources: (a) HD 56537, (b) HD 83808, (c) HD 95418, (d)
HD 102647, (e) HD 139006, (f) HD 141569, (g) HD 161868.  Figure 9: FWHM of
profile fits to the sources at 11.7 $\mu$m, per saveset. Open circles
represent the PSF reference star, and filled circles represent the debris disk
target. Sources: (a) HD 75416, (b) HD 115892, (c) HD 178253.  Figure 10: FWHM
of profile fits to the sources at 18.1 $\mu$m, per saveset. Open circles
represent the PSF reference star, and filled circles represent the debris disk
target. Sources: (a) HD 56537, (b) HD 56537, (c) HD 83808, (d) HD 95418, (e)
HD 102647, (f) HD 102647, (g) HD 139006, (h) HD 139006, (i) HD 141569, (j) HD
141569, (k) HD 161868, (l) HD 161868.  Figure 11: FWHM of profile fits to the
sources at 18.3 $\mu$m, per saveset. Open circles represent the PSF reference
star, and filled circles represent the debris disk target. Sources: (a) HD
38206, (b) HD 38678, (c) HD 71155, (d) HD 75416, (e) HD 80950, (f) HD 115892,
(g) HD 115892, (h) HD 178253, (i) HD 181869.  Figure 12: FWHM of profile fits
to the sources, per saveset. Open circles represent the PSF reference star at
11.7 $\mu$m, and filled circles represent the debris disk target at 11.7
$\mu$m. Open squares represent the PSF reference star at 18.3 $\mu$m, and
filled squares represent the debris disk target at 18.3 $\mu$m. Sources: (a)
HD 172555, (b) HD 181296.

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## References

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