Externally-polluted white dwarfs with dust disks
Externally-Polluted White Dwarfs With Dust Disks
M. Jura1, J. Farihi,2 & B. Zuckerman1
ABSTRACT
We report Spitzer Space Telescope photometry of eleven externally-polluted
white dwarfs. Of the nine stars for which we have IRAC photometry, we find
that GD 40, GD 133 and PG 1015+161 each has an infrared excess that can be
understood as arising from a flat, opaque, dusty disk. GD 56 also has an infrared
excess characteristic of circumstellar dust, but a flat-disk model cannot reproduce
the data unless there are grains as warm as 1700 K and perhaps not even then.
Our data support the previous suggestion that the metals in the atmosphere of
GD 40 are the result of accretion of a tidally-disrupted asteroid with a chondritic
composition.
Subject headings: circumstellar matter – asteroids – stars, white dwarfs
1. INTRODUCTION
Gravitational settling of heavy elements is so effective in white dwarfs cooler than 20,000
K that their atmospheres are expected to be pure hydrogen or pure helium (Paquette et
al. 1986), and the ∼20% of these stars which exhibit photospheric metals are thought
to be externally polluted (Wolff et al. 2002, Zuckerman et al. 2003, Koester & Wilkin
2006). A promising model to explain these data is that a minor-body is perturbed (Debes &
Sigurdsson 2002) to orbit within the tidal radius of the star where it is destroyed and a dusty
disk is produced (Jura 2003). Accretion from this disk can explain atmospheric pollutions
(Zuckerman et al. 2003) as seems likely to have occurred for GD 362 (Becklin et al. 2005,
Kilic et al. 2005, Jura et al. 2007) and G29-38 (Jura 2003, Reach et al. 2005b). While the
disrupted minor-body model is promising, despite extensive surveys, only a handful of white
dwarfs are known to display an infrared excess (Kilic et al. 2006b, Kilic & Redfield 2007,
Mullally et al. 2007, Farihi et al. 2007). We have therefore obtained Spitzer Space Telescope
data to investigate the frequency of dusty disks orbiting white dwarfs and to assess models
for the sources of the external pollution.
1Department of Physics and Astronomy and Center for Astrobiology, University of California, Los Angeles
CA 90095-1562; jura, ben @astro.ucla.edu
2Gemini Observatory, 670 North A’ohoku Place, Hilo HI 96720; jfarihi@gemini.edu
http://arxiv.org/abs/0704.1170v1
– 2 –
2. OBSERVATIONS
We observed eleven stars with atmospheric metals found in the SPY project (Koester
et al. 2005) that also show a hint of K-band excess in 2MASS photometry. We used the
IRAC (Fazio et al. 2004) and MIPS (Rieke et al. 2004) cameras on the Spitzer Space
Telescope (Werner et al. 2004) to obtain photometry at wavelengths between 3.6 µm and 24
µm. IRAC observations were executed using a 20 point cycling dither pattern of medium
step size, with 30 s individual exposures, yielding a total integration time of 600 s at all
wavelengths. MIPS observations were performed using 10 cycles of the default 14 point
dither pattern, with 10 s individual exposures, yielding a total integration time of 1400
s. The data were processed with the IRAC and MIPS calibration pipelines (both versions
14) to create single, reduced images upon which to make photometric measurements. We
removed the one dimensional artificial gradient in the sky which is a common feature of
MIPS pipelined data by subtracting a median collapsed image across the direction of the
gradient. Aperture photometry was carried out with standard IRAF tasks, and measured
fluxes were corrected for aperture size, but not for color. For IRAC detections, fluxes were
typically measured in a 3-pixel radius aperture, but a 2-pixel radius aperture was used for
faint sources or objects in a crowded field, and a 5-pixel radius aperture was used for GD
56, the brightest source. MIPS 24 µm flux was measured in a 2.45 pixel radius aperture for
GD 56, but a smaller aperture with a radius of 1.22 pixels was necessary for GD 133 because
of a nearby galaxy. The measured fluxes were corrected to the standard IRAC and MIPS
photometric apertures using corrections found in the most recent versions of the IRAC and
MIPS data handbooks. The results are listed in Table 1. IRAC data were not obtained for
two sources since they are in other Spitzer programs; these data have not yet been published.
For both the IRAC and MIPS data, the photometric errors were estimated by taking
the per pixel standard deviation in the extracted sky level and multiplying by the area of an
aperture with a radius of 2 pixels. Color corrections have been ignored and are typically less
than 1%. Our dither pattern should remove the pixel phase dependent correction as well as
the IRAC array location dependent errors described by Reach et al. (2005a). Total 1σ errors
(5% calibration plus photometric measurement errors) are listed in Table 1. Because there is
a somewhat larger scatter in the ratios of even the best-measured photospheric fluxes in the
IRAC bands for white dwarfs (Farihi et al. 2007) than expected from model atmospheres
(Tremblay & Bergeron 2007 and Bergeron 2007, private communication), to be conservative,
following Hines et al. (2006) and Silverstone et al. (2006), we adopt a 10% calibration
uncertainty in the reported fluxes, as reflected in the error bars displayed in Figures 1-4.
Upper limits for non-detections in both IRAC and MIPS images were derived identically to
the photometric errors for detections.
– 3 –
To assess the reliability of our IRAC photometry obtained with small apertures, we also
reduced our data with CCDCAP3. Although there is no significant difference with apertures
of 3 pixel-radii, it was found that IRAF reported fluxes 3% smaller than CCDCAP with
2-pixel radius apertures at the two shorter wavelength IRAC channels where undersampling
of the array is most significant. We have found that this small offset is largely mitigated
by the aperture corrections provided by the Spitzer Science Center, and the net uncertainty
introduced by using a small aperture is well below our 1σ errors. As a further check, using
2-radius pixel aperture photometry and IRAF, we have reproduced the IRAC fluxes reported
by Reach et al. (2005b) for G29-38 to within 3% at 4.5 µm and to within 1% at 7.9 µm. We
used 2-pixel radius apertures to reduce the data at 3.6 µm and 4.5 µm for only one star, PG
2354+159.
The data for PG 1015+161 are contaminated by a star ≈ 2′′ away (Kilic et al. 2006b).
Although our IRAC images are slightly elongated by 0.′′5 or 0.4 pixels at 3.6 µm and 4.5 µm
in the direction of this background star, we cannot accurately deconvolve the image, and
we adopt an alternative approach to estimate its fluxes. As shown in Figure 5, a 1995.9
epoch Keck Observatory NIRC z-band image (see Farihi, Becklin & Zuckerman 2005), the
angular separation of the background star was appreciably greater in the past, 2.′′9 vs. 1.′′8
in 2007.0. From the Keck data, we find values of z = 19.12 mag, J = 18.76 mag and K =
18.26 mag and infer a spectral type of approximately K0V. We extrapolate these measures
to IRAC wavelengths, and we list in Table 1 our results for PG 1015+161 after the estimated
contributions from the background star are subtracted from the total measured IRAC fluxes
at the position of PG 1015+161.
Both GD 133 and PG 1015+161 were suspected by Kilic et al. (2006b) to have an
infrared excess on the basis of their 2 µm spectra; our IRAC data demonstrate that these
two stars indeed have excesses. GD 56 was previously shown to have a 2 µm excess (Kilic
et al. 2006b); our data significantly extend the wavelength range over which the excess
is measured. Except for the slight hint in the 2MASS photometry, there is no previous
measurement of an infrared excess for GD 40.
3. MODELS
We first try to account for the infrared data with the passive, opaque flat disk model
of Jura (2003). Here, the disk’s potential vertical stratification is ignored, so that at each
distance from the central star all dust grains achieve the same temperature as determined by
3described at:http://www.noao.edu/noao/staff/mighell/ccdcap
http://www.noao.edu/noao/staff/mighell/ccdcap
– 4 –
the balance between radiative heating and cooling. Although a more sophisticated treatment
is required to account for data such as the strong silicate feature seen in both the infrared
spectrum of G29-38 (Reach et al. 2005b) and GD 362 (Jura et al. 2007), this simple model
accounts for the currently available data.
Since all the target stars are warmer than 7000 K, the received photospheric infrared
flux from the star, Fν(∗), is modeled to better than the 2σ measurement uncertainty as a
single-temperature blackbody (Kilic et al. 2006a, Tremblay & Bergeron 2007), Bν , so that
Fν(∗) =
Bν(T∗) (1)
where the star of radius, R∗, and effective temperature, T∗, lies at distance D from the Sun.
For a flat, opaque disk that is passively illuminated by the host star; the expected flux,
Fν(d), is (Jura 2003):
Fν(d) = 12 π
1/3 R
cos i
2 kB T∗
3 h ν
∫ xmax
ex − 1
dx (2)
where i denotes the inclination angle of the disk and i = 0◦ corresponds to a face-on con-
figuration. Here, x = (hν)/(kBTdisk) where Tdisk denotes the temperature in the disk. Since
the disk is opaque, we cannot estimate its mass.
Table 2 lists stellar parameters adopted from Friedrich, Jordan & Koester (2004),
Koester et al. (2005), and Koester & Wilken (2006) as well as our estimated disk pa-
rameters. The fits to our Spitzer data and near-infrared photometry from 2MASS or, when
available, from the more accurate observations obtained at the IRTF by Kilic et al. (2006b),
are shown in Figures 1-4. We find satisfactory fits for GD 40, GD 133 and PG 1015+161
with a range of possible model parameters that are listed in Table 2. The inner dust tem-
perature is constrained by the excess at 3.6 µm, but the fit is not unique. To fit the 4.5 µm
and 5.7 µm fluxes, there can be either a relatively broad range of temperatures with a more
edge-on disk, or a narrower range of temperatures with a more face-on disk. In order not to
over-predict the fluxes at 8 µm and 24 µm, the outer temperature cannot be too low. As
listed in Table 2, using the thermal profile given in Jura (2003), the models lie within the
tidal radius which typically is about a factor of 100 greater than the star’s radius (Davidsson
1999).
We see in Figure 1 that GD 40 can be equally well fit with a disk with an inner tem-
perature of 1200 K that is nearly edge-on or one with an inner temperature of 1000 K that
is more nearly face-on. If, however, the inner temperature is only 800 K, then we cannot
match the flux at 3.6 µm. Figure 3 displays the results for PG 1015+161. Again, there is
little difference between a model which is more nearly edge-on and an inner temperature of
– 5 –
1200 K and a model which is more nearly face-on with an inner temperature near 1000 K.
However, a disk with an inner temperature of 800 K fails to produce enough flux at 3.6 µm.
For GD 133, as shown in Figure 4, a model with an inner temperature of 1200 K that is
viewed nearly edge-on is only somewhat better than a model with an inner temperature of
800 K that is viewed nearly face-on.
Kilic et al. (2006b) have shown that GD 56 is unusual in having a particularly marked
excess at 2 µm, and as seen in Figure 2, our model Agd56 with an inner disk temperature
of 1200 K completely fails. An alternative possibility with a less than satisfactory fit is that
the inner disk temperature is larger than 1200 K, and we also show in Figure 2 the results
for model Bgd56 with an inner disk temperature of 1700 K and an outer disk temperature of
400 K (see Table 2). A better fit can be achieved if, rather than a flat disk, we assume that
the disk is substantially warped as driven by the central star’s luminosity (Pringle 1996) or
otherwise puffed up by the gravitational field of a planet. To model this scenario, we assume
a single temperature blackbody at 1000 K, and, as shown in Figure 2, we can fit the data if
this material is a disk with an angular radius of 1.4 × 10−10 radians as seen from the Earth.
Our data are inconsistent with a simple model of interstellar accretion to explain the
atmospheric metals. Assume interstellar grains are accreted at rate Ṁdust at the Bondi-Hoyle
radius, Rinit, which is typically between 1 and 10 AU (Koester & Wilken 2006) and then
drift inwards because of Poynting-Robertson drag to a final radius, Rfinal, where they are
destroyed. In this scenario, the expected (see Jura 2006) infrared flux from interstellar (IS)
accretion, Fν(IS), is:
Fν(IS) ≈
Rinit
Rfinal
Ṁdust c
This expression is valid for observations at frequencies where hν/k lies between the minimum
and maximum grain temperature. To evaluate equation (3), we adopt dust accretion rates
that are 0.01 of the rates of accretion of interstellar gas given by Koester & Wilken (2006) and
also use their estimated distances. We adopt this value of the interstellar dust to gas ratio
by mass of 0.01 from Zubko et al. (2004). For simplicity, we assume grains are destroyed
by sublimation between ∼10−2 AU and ∼10−3 AU, the region where an unshielded grain
that acts like a blackbody attains a temperature near 1200 K. We therefore adopt Rinit =
1000 Rfinal although the results are insensitive to the exact value of this ratio. We show
in Table 3, the predicted values of Fν(24 µm) and a comparison between the predicted and
observed fluxes, Fpred/Fobs, for the hydrogen-rich stars where the dwell time of metals in the
atmosphere is typically less than 100 yr (Koester & Wilken 2006) and therefore accretion
is almost certainly ongoing. In contrast, for the three helium rich stars in our sample (GD
40, G26-31, PG 2354+159), the atmospheric dwell times for metals are closer to 3 × 105
– 6 –
yr (Paquette et al. 1986), and it is possible that accretion has stopped but there are still
metals lingering in the stellar photosphere. We see that from Table 3 that the expected flux
is always at least an order of magnitude larger than observed and thus this simple model of
interstellar accretion is unsatisfactory.
4. DISCUSSION
We find that four of nine white dwarfs with fluxes measured in the IRAC bands display
evidence of circumstellar dust disks. For GD 40, the deficiency of carbon in the accreted
material (Wolff et al. 2002) is naturally understood if an asteroid of at least 1023 g with a
chondritic composition was tidally-destroyed (Jura 2006), in agreement with some previous
qualitative suggestions (Sion et al. 1990, Aannestad et al. 1993).
G29-38 was the first white dwarf found to have an infrared excess (Zuckerman & Becklin
1987) from dust while GD 362 was the second (Becklin et al. 2005, Kilic et al. 2005). With
the results reported here and other recent studies (Mullally et al. 2007, Kilic et al. 2006b,
Kilic & Redfield 2007, Farihi et al. 2007), there are now enough white dwarfs with infrared
excesses that it is possible to begin to discern some patterns. First, all the white dwarfs
with an infrared excess also display atmospheric metals, thus it is highly plausible that the
stars are accreting from reservoirs of circumstellar material. Second, Kilic et al. (2006b),
Farihi et al. (2007) and Kilic & Redfield (2007) have shown that the stars with relatively
high calcium abundances also tend to display an infrared excess. Third, the stars with an
infrared excess all have effective temperatures greater than ∼9500 K and white dwarf cooling
ages less than ∼1 Gyr4. According to the simulations of Debes & Sigurdsson (2002), most
of the orbital perturbations of asteroids would occur during the first several hundred million
yr of the white dwarf’s cooling, consistent with the data.
The scenario of a tidally-disrupted asteroid explains the data for white dwarfs with both
a relatively high photospheric calcium abundance and an infrared excess. However, the source
of the atmospheric metals of those white dwarfs without an infrared excess is uncertain. One
possibility is that the particle density is sufficiently low that mutual collisions lead to effective
dust destruction. At, for example, the typical tidal radius of a white dwarf of ∼0.01 AU,
4GD 362 previously was thought to be hydrogen-rich and have a relatively low luminosity and therefore
a cooling age well in excess of 1 Gyr (Gianninas, Dufour & Bergeron 2004). However, the star is now known
to be helium-rich and have a much larger luminosity and correspondingly shorter cooling age (Zuckerman
et al. 2007). G167-8 has an effective temperature of 7400 K, but its infrared excess, if real, is from much
cooler dust than that found in the systems described here (Farihi et al. 2007).
– 7 –
the orbital speed is near 300 km s−1, and even small deviations from circular orbits can
lead to mutual collision speeds in excess of 10 km s−1 which result in grain destruction.
For stars with an infrared excess, the disks may be so dense that the grains act more like
a granular fluid and the mutual collision speeds are small. Thus, the externally-polluted
white dwarfs without an infrared excess may have gas disks as has been found for SDSS
J122859.93+104032.9 (Gaensicke et al. 2006).
White dwarfs with a relatively low accretion rate tend not to possess an infrared excess.
Scaling the accretion rates of Koester & Wilken (2006) by 0.01 as described above, Figure 6
presents a comparison of Ṁdust vs. effective temperature for DAZs with IRAC photometry,
distinguishing between those with and without excess emission. The correlation between
having an infrared excess and Ṁdust shown in Figure 6 is closely related to the result found
by Kilic et al. (2006b) that the stars with a greater metal abundance are the ones with an
infrared excess. Although the numbers are very limited, the DAZs with Ṁdust larger than
about 3 × 108 g s−1 possess an excess while the stars with lower accretion rates do not. For
comparison, the dust production rate in the zodiacal cloud is about 3 × 106 g s−1 (Fixsen &
Dwek 2002) and considerably larger around some other main-sequence stars. Even in their
advanced evolutionary state, some white dwarfs may possess a population of eroding parent
bodies.
5. CONCLUSIONS
We have found evidence for dusty disks orbiting four externally-polluted white dwarfs.
For GD 40, the evidence lends support to the hypothesis that tidal-disruption of a carbon-
deficient asteroid has occurred.
This work has been partly supported by NASA and is based on observations made with
the Spitzer Space Telescope which is operated by the Jet Propulsion Laboratory, California
Institute of Technology, for NASA. We thank P. Bergeron for sending us models of white
dwarf atmospheres, M. Kilic for useful correspondence and T. von Hippel for a helpful
referee’s report.
REFERENCES
Aannestad, P. A., Kenyon, S. J., Hammond, G. L., & Sion, E. M. 1993, AJ, 105, 1033
Becklin, E. E., Farihi, J., Jura, M., Song, I., Weinberger, A. J., & Zuckerman, B. 2005, ApJ,
632, L119
– 8 –
Carey, S. 2006, talk presented at the Spitzer data workshop
Davidsson, B. J. R. 1999, Icarus, 142, 525
Debes, J. H. & Sigurdsson, S. 2002, ApJ, 572, 556
Debes, J. H. & Sigurdsson, S. 2007, in ASP Conf. Ser., EUROWD06,: 15th European White
Dwarf Workshop;, ed. R. Napiwotzki & M. Barstow (San Francisco: ASP), in press
Farihi, J., Becklin, E. E., & Zuckerman, B. 2005, ApJS, 161, 394
Farihi, J., Zuckerman, B., & Becklin, E. E. 2007, ApJ, submitted
Fazio, G. G. et al. 2004, ApJS, 154, 10
Fixsen, & Dwek, E. 2002, ApJ, 578, 1009
Friedrich, S., Jordan, S., & Koester, D. 2004, A&A, 424, 665
Gaensicke, B. T., Marsh, T. R., Southworth, J., & Rebassa-Mansergas, A. 2006, Science,
314, 1908
Gianninas, A., Dufour, P., & Bergeron, P. 2004, ApJ, 617, L57
Hines, D. et al. 2006, ApJ, 638, 1070
Jura, M. 2003, ApJ, 548, L91
Jura, M. 2006, ApJ, 653, 613
Jura, M., Farihi, J., Zuckerman, B., & Becklin, E. E. 2007, AJ, in press
Kilic, M., & Redfield, S. 2007, ApJ, in press
Kilic, M., von Hippel, T., Leggett, S. K., & Winget, D. E. 2005, ApJ, 632, L115
Kilic, M., von Hippel, T., Mullally, F., Reach, W. T., Kuchner, M. J., Winget, D. E., &
Burrows, A. 2006a, ApJ, 642, 1051
Kilic, M., von Hippel, T., Leggett, S. K., & Winget, D. E. 2006b, ApJ, 646, 474
Koester, D., & Wilken, D. 2006, A&A, 453, 1051
Koester, D., Rollenhagen, K., Napiwotzki, R., Voss, B., Christlieb, N., Homeier, D., &
Reimers, D. 2005, A&A, 432, 1025
– 9 –
Mullally, F., Kilic, M., Reach, W. T., Kuchner, M. J., von Hippel, T., Burrows, A., &
Winget, D. E. 2007, ApJS, in press
Pringle, J. E. 1996, MNRAS, 281, 357
Paquette, C., Pelletier, C., Fontaine, G., & Michaud, G. 1986, ApJS, 61, 197
Reach, W. T. et al. 2005a, PASP, 117, 978
Reach, W. T., Kuchner, M. J., von Hippel, T., Burrows, A., Mullally, F., Kilic, M., &
Winget, D. E. 2005, ApJ, 635, L161
Rieke, G. H. et al. 2004, ApJS, 154, 25
Silverstone, M. et al. 2006, ApJ, 639, 1138
Sion, E., Hammond, G. L., Wagner, R. M., Starrfield, S. G., & Liebert, J. 1990, ApJ, 362,
Tremblay, P.E., & Bergeron, P. 2007, ApJS, in press
von Hippel, T., Kuchner, M. J., Kilic, M., Mullally, F., & Reach, W. T. 2007, ApJ, in press
Werner, M. W. et al. 2004, ApJS, 154, 1
Wolff, B., Koester, D., & Liebert, J. 2002, A&A, 385, 995
Zubko, V., Dwek, E., & Arendt, R. G. 2004, ApJS, 152, 211
Zuckerman, B. et al. 2007, in preparation
Zuckerman, B., & Becklin, E. E. 1987, Nature, 330, 138
Zuckerman, B., Koester, D., Reid, I. N. & Hunsch, M. 2003, ApJ, 596, 477
This preprint was prepared with the AAS LATEX macros v5.2.
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Table 1 – Measured Infrared Fluxesa
Star Other Name Fν(3.6 µm) Fν(4.5 µm) Fν(5.7 µm) Fν(7.9 µm) Fν(24 µm)
(µJy) (µJy) (µJy) (µJy) (µJy)
WD 0300-013b GD 40 231(12) 199(10) 159(15) 164(17) <90
WD 0408-041 GD 56 1090(55) 1212(61) 1177(61) 1112(59) 240(80)
WD 1015+161 PG 1015+161 212(11) 177(9) 145(17) 126(19) <110
PG 1015+161c 197(11) 169(9) 140(17) 123(19) <110
WD 1116+026 GD 133 592(30) 527(26) 472(27) 464(29) 310(100)
WD 1124-293 ESO 439-80 <50
WD 1204-136 EC 12043-1337 158(5) 99(4) 72(14) 32(17) <70
WD 1225+006 HE 1225+0038 361(18) 223(12) 144(16) 79(20) <80
WD 1315-110 HE 1315-1105 210(11) 131(7) 90(15) 30(18) <80
WD 1457-086 PG 1457-086 <90
WD 2144-079b G26-31 191(10) 122(7) 65(19) 42(22) <100
WD 2354+159b PG 2354+159 73(5) 44(4) 27(17) <21 <110
a1σ errors for detections are given in parenthesis; the procedure for deriving the upper limits
is described in §2.
bHe-rich star (Koester et al. 2005)
cPG 1015+161 fluxes corrected for the background star, as discussed in §2
– 11 –
Table 2 – Stellar and Disk Properties
Star T∗ R∗ R∗/D model cos i Tmax Tmin Rmin Rmax
(K) (R⊙) (10
−12) (K) (K) (R∗) (R∗)
GD 40 15,200a 0.013b 3.6 Agd40 0.2 1200 600 18 44
Bgd40 0.4 1000 700 22 36
Cgd40 0.8 800 650 30 40
GD 56 14,400a 0.015c 3.6 Agd56 1.0 1200 300 16 104
Bgd56 1.0 1700 400 10 71
PG 1015+161 19,300a 0.014c 2.7 Apg10 0.3 1200 800 24 42
Bpg10 0.6 1000 800 31 42
Cpg10 1.0 800 700 42 50
GD 133 12,200a 0.014c 7.0 Agd133 0.2 1200 300 13 83
Bgd133 0.4 1000 600 17 33
Cgd133 0.8 800 600 23 33
aKoester et al. (2005)
bFriedrich et al. (2004)
cderived from Koester & Wilkin (2006)
– 12 –
Table 3 – Predicted Fν(24 µm) for Simple Interstellar Accretion followed by
Poynting-Robertson drag
Star D dMdust/dt Fν(24 µm) Fpred/Fobs
(pc) (109 g s−1) (mJy)
GD 56 74 0.26 9.9 41
PG 1015+161 95 2.0 46 >420
GD 133 43 0.37 42 140
ESO 439-80 34 0.13 23 >460
EC 12043-1337 52 0.23 18 >260
HE 1225+0038 29 0.0059 1.5 >19
HE 1315-1105 40 0.022 2.9 >36
PG 1457-086 117 1.5 23 >260
Distances are taken from Koester & Wilkin (2006) while the dust accretion rates are scaled
from their values as described in §3.
– 13 –
Fig. 1.— Comparison of models from Table 2 and data (2σ errors) for GD 40. The plot shows
the contribution from the stellar photosphere (dotted line), one disk model (blue dashed line
for model Agd40) and totals (solid blue for model Agd40, solid green for model Bgd40,
solid red for model Cgd40). Models Agd40 and Bgd40 are essentially indistinguishable while
model Cgd40 predicts somewhat too little flux at 3.6 µm because the warmest grains are
only 800 K.
– 14 –
Fig. 2.— Comparison of three models and data (2σ errors) for GD 56. The dotted line is the
contribution from the stellar photosphere. The sums of the circumstellar and stellar fluxes
are shown for models Agd56 (solid blue line) and Bgd56 (solid magenta line) listed in Table
2. We also show (solid black line) the flux for a model summing both the photosphere and
excess emission for an opaque dust cloud at a temperature of 1000 K with an angular radius
1.4 × 10−10 radians as seen from Earth.
– 15 –
Fig. 3.— Similar to Figure 1, but for PG 1015+161 with blue, green and red for the totals
of models Apg10, Bpg10 and Cpg10, respectively. The emission from only the disk is shown
for model Apg10
– 16 –
Fig. 4.— Similar to Figure 1, but for GD 133 with blue, green and red for the totals of
models Agd133, Bpg13s and Cpg133, respecitvely. The emission from only the disk is shown
for model Agd133.
– 17 –
Fig. 5.— KECK/NIRC z-band image, epoch 1995.9, obtained of PG 1015+161. Up lies at
P. A. = 96◦; the background star lies 2.′′9 from the white dwarf at P. A. = 270◦. The proper
motion proper motion of µ = 0.′′13 yr−1 at P. A. = 239◦ (Farihi et al. 2005) of PG 1015+161
is consistent with its position relative to the background source in our 2007.0 IRAC images.
– 18 –
Fig. 6.— Mass accretion rates (§3) vs. effective temperature for hydrogen-rich white dwarfs
with an excess (solid circles) in either ground-based or Spitzer data and without an excess
(open triangles) in published Spitzer data. GD 133 and PG 1015+161 (this paper), GD
56 (this paper and Kilic et al. 2006b), G29-38 (Zuckerman & Becklin 1987), WD 2115-560
(Mullally et al. 2007, von Hippel et al. 2007), WD 1150-153 (Kilic & Redfield 2007) have an
excess while EC 12043-1337, HE 1225+038, and HE 1315-1105 (this paper), WD 1202-232,
WD 1337+705 and WD 2149+021 (Mullally et al. 2007), and WD 0208+396, WD 0243-026,
WD 0245+541, and WD 1257+278 (Debes & Sigurdsson 2007) do not. Two helium-rich
white dwarfs (GD 40 and GD 362) that also display an excess are not shown here.
	INTRODUCTION
	OBSERVATIONS
	MODELS
	DISCUSSION
	CONCLUSIONS
