Exo--Zodiacal Dust Levels for Nearby Main Sequence Stars

Abstract

The Keck Interferometer Nuller (KIN) was used to survey 25 nearby main
sequence stars in the mid-infrared, in order to assess the prevalence of warm
circumstellar (exozodiacal) dust around nearby solar-type stars. The KIN
measures circumstellar emission by spatially blocking the star but transmitting
the circumstellar flux in a region typically 0.1 - 4 AU from the star. We find
one significant detection (eta Crv), two marginal detections (gamma Oph and
alpha Aql), and 22 clear non-detections. Using a model of our own Solar
System's zodiacal cloud, scaled to the luminosity of each target star, we
estimate the equivalent number of target zodis needed to match our
observations. Our three zodi detections are eta Crv (1250 +/- 260), gamma Oph
(200 +/- 80) and alpha Aql (600 +/- 200), where the uncertainties are 1-sigma.
The 22 non-detected targets have an ensemble weighted average consistent with
zero, with an average individual uncertainty of 160 zodis (1-sigma). These
measurements represent the best limits to date on exozodi levels for a sample
of nearby main sequence stars. A statistical analysis of the population of 23
stars not previously known to contain circumstellar dust (excluding eta Crv and
gamma Oph) suggests that, if the measurement errors are uncorrelated (for which
we provide evidence) and if these 23 stars are representative of a single class
with respect to the level of exozodi brightness, the mean exozodi level for the
class is <150 zodis (3-sigma upper-limit, corresponding to 99% confidence under
the additional assumption that the measurement errors are Gaussian). We also
demonstrate that this conclusion is largely independent of the shape and mean
level of the (unknown) true underlying exozodi distribution.

Full text

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Exo–Zodiacal Dust Levels for Nearby Main–Sequence Stars: A
Survey with the Keck Interferometer Nuller
R. Millan-Gabet
California Institute of Technology, NASA Exoplanet Science Institute, Pasadena, CA
91125, USA
R.Millan-Gabet@caltech.edu
E. Serabyn, B. Mennesson, W. A. Traub
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,
Pasadena, CA 91109, USA
R. K. Barry, W. C. Danchi, M. Kuchner
NASA Goddard Space Flight Center, Exoplanets and Stellar Astrophysics Laboratory,
Code 667, Greenbelt, MD 20771, USA
S. Ragland, M. Hrynevych, J. Woillez
Keck Observatory, 65-1120 Mamalahoa Hwy, Kamuela, HI 96743, USA
and
K. Stapelfeldt, G. Bryden, M. M. Colavita, A. J. Booth
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive,
Pasadena, CA 91109, USA
Received
;accepted
Accepted by ApJ April 7 2011

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ABSTRACT
The Keck Interferometer Nuller (KIN) was used to survey 25 nearby main
sequence stars in the mid–infrared, in order to assess the prevalence of warm
circumstellar (exozodiacal) dust around nearby solar–type stars. The KIN mea-
sures circumstellar emission by spatially blocking the star but transmitting the
circumstellar flux in a region typically 0.1 − 4 AU from the star. We find one
significant detection (η Crv), two marginal detections (γ Oph and α Aql), and
22 clear non–detections. Using a model of our own Solar System’s zodiacal cloud,
scaled to the luminosity of each target star, we estimate the equivalent number
of target zodis needed to match our observations. Our three zodi detections
are η Crv (1250 ± 260), γ Oph (200 ± 80) and α Aql (600 ± 200), where the
uncertainties are 1σ. The 22 non–detected targets have an ensemble weighted
average consistent with zero, with an average individual uncertainty of 160 zodis
(1σ). These measurements represent the best limits to date on exozodi levels
for a sample of nearby main sequence stars. A statistical analysis of the popu-
lation of 23 stars not previously known to contain circumstellar dust (excluding
η Crv and γ Oph) suggests that, if the measurement errors are uncorrelated (for
which we provide evidence) and if these 23 stars are representative of a single
class with respect to the level of exozodi brightness, the mean exozodi level for
the class is < 150 zodis (3σ upper–limit, corresponding to 99% confidence under
the additional assumption that the measurement errors are Gaussian). We also
demonstrate that this conclusion is largely independent of the shape and mean
level of the (unknown) true underlying exozodi distribution.
Subject headings: techniques: high angular resolution — planetary systems: zodiacal
dust — stars: circumstellar matter

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1.Introduction
The present day Solar System contains interplanetary dust. The term zodiacal usually
refers to the dust present in the inner Solar System, out to
∼ 5 AU. It currently has a
fractional luminosity of Ldust/L?∼ 10−7(Backman & Paresce 1993) and 10−10the mass of
the planets, but an infrared luminosity 100× larger. Because the survival times for small
particles in the radiation and wind environment of the star is a few 100 to a few 1000 yrs,
any such circumstellar dust observed in stars older than a few tens of millions of years must
be recently formed and continuously generated. The presence of prominent dust bands in
the solar zodiacal cloud associated with asteroid families suggest that the zodiacal cloud
arises from the breakup of main belt asteroids (see e.g. Dermott et al. 1984). However,
recent models of zodiacal dust production imply that the splitting of short period comets
could be the dominant source (Nesvorny et al. 2010).
Circumstellar dust around other mature stars was originally discovered, unexpectedly,
by IRAS (Aumann et al. (1984), see e.g. the review by Backman & Paresce (1993)), and
has since been observationally studied by a variety of ground and space observatories, via
both their thermal and scattered emission. Most commonly, the phenomenon reveals itself
as long–wavelength fluxes in excess of what is expected from the stellar photosphere alone,
but spatially resolved images of the outer disk regions have also been obtained for a few of
the most extreme systems (see e.g. the review by Zuckerman 2001). The term debris disk
usually refers to the entire dust distribution, extending to 100s of astronomical units (AU)
from the Sun.
The presence of high levels of cold outer dust around main sequence stars is now known
to be a ubiquitous phenomenon (e.g. 30% of all A–stars, and 13% of solar–type stars Rieke
et al. 2005; Su et al. 2006; Bryden et al. 2006; Beichman et al. 2006b). However, very
few stars have had positive detections of excess flux at wavelengths < 30µm (Beichman

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et al. 2006a; Lawler et al. 2009). Although this rarity appears to be consistent with
evolution models and detection thresholds, the fact remains that much less is known about
levels of inner warm dust, of most interest to extra–solar terrestrial planets searches. The
measurement is difficult, because the dust emission is close to and faint compared to the
parent star. Thus, we currently have no firm estimates of the warm zodi brightness around
nearby stars, or around any stars. Interestingly, the few systems that have been imaged
in some detail at sub–mm wavelengths display a striking variety of complex morphological
features. This forces caution when interpreting spatially unresolved observations, and
highlights the difficulties in attempting to infer levels of inner warm dust from measurements
made at wavelengths which probe very different spatial scales.
Searches for exozodiacal emission from warm inner dust have been attempted from the
ground (e.g. Kuchner et al. 1998; Liu et al. 2004) and space (e.g. Beichman et al. 2006a;
Lawler et al. 2009). Due to current limitations of the observational techniques, known
exozodi disks have much higher dust densities than the Solar System (e.g. Ldust/L?> 10−4
from the Lawler et al. (2009) survey); the present–day Solar System zodiacal levels would
be currently undetectable around other stars.
Studying exozodi clouds is of interest for a variety of reasons. Among them, the
time–scales for debris disk evolution may help understand terrestrial planet formation (see
e.g. Wyatt 2008), and disk structure may be used to infer the presence of perturbing unseen
exo–planets (Wolf et al. 2007; Stark & Kuchner 2008), examples of which have now been
directly imaged (Marois et al. 2008; Kalas et al. 2008). Moreover, both the levels of exozodi
emission and their spatial structure act as sources of noise that may hinder the direct
detection and characterization of terrestrial exoplanets by spaced–based coronographic
or interferometric techniques (e.g. Beckwith 2008). Indeed the largest uncertainty in
estimating planet detection efficiencies is due to exozodi dust. Since exozodi photons impact

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the required integration times and sample sizes for a given mission lifetime, knowledge
of exozodi levels and structure for all candidate stars would allow a greatly optimized
instrument and observing strategy design.
Mid–infrared interferometry has provided exozodi measurements at high spatial
resolution for specific known high–dust stars (Stark et al. 2009; Smith et al. 2009).
Interferometric techniques have also enabled the identification of an intriguing source of
near–infrared excess around some main sequence stars (Absil et al. 2008, 2006; Akeson et
al. 2009; Absil et al. 2009). Obtaining exozodi measurements for relatively large samples
of representative nearby main sequence stars was the primary scientific driver for the
development of the Keck Interferometer Nuller (KIN), and for the execution of a 1–year
long intensive Key Science observing campaign shared among three selected proposals.
This paper summarizes the results from one of three Key Science programs selected (“The
Keck Interferometer Nuller Survey of Exozodiacal Dust around Nearby Stars ”, Principal
Investigator: G. Serabyn).
2. The Sample
Of all nearby stars, ∼ 85 dwarfs and sub–dwarfs fall within the sensitivity and
observability limits of the KIN. Given the expected time allocation for the Key Science
programs, we down–selected this list to 40 high priority objects, containing systems
both with and without known debris disk emission (a.k.a “high dust” and “low dust”,
respectively) as inferred from mid–infrared spectrophotometric measurements. The selecting
committee ultimately assigned 5 high dust and 24 low dust objects to the program described
here. Of those, 25 systems were actually observed, 2 high dust (η Crv and γ Oph) and
23 low dust. Observations took place in service mode during the period February 2008 –
January 2009, over 32 nights shared with the other two Key Science programs. Table 1

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describes our list of observed targets, including all the brightnesses relevant to the various
KIN subsystems, and the stellar parameters relevant to our modeling approach.
3. The Keck Interferometer Nuller
3.1. Instrument Overview
The Keck Interferometer Nuller (Colavita et al. 2009) operates in N–band (8.0−13.0µm)
and combines the light from the two Keck telescopes as an interferometer with a physical
baseline length B ∼ 85 m. The KIN produces a dark fringe through the phase center
(“Nulling”). The adjacent bright fringe (through which flux is transmitted), projects onto
the sky at an angular separation λ/2B = 10 mas, or 0.1 AU at the median distance to the
stars in our sample (10.5 pc), and for λ = 8.5µm (the effective wavelength of the KIN
bandpass). Thus, the instrument is sensitive to circumstellar dust located as close to the
central star as these spatial scales (i.e. “inner working angle”). Blackbody emission peaks
at 8.5µm for T ∼ 432 K. For the median luminosity of the stars in our sample (2.2L?),
dust particles in thermal equilibrium at this temperature are located at a stellocentric
radius of 0.3 AU. Therefore, the KIN fringe spacing matches well the expected location of
relatively warm dust, located in the inner disk regions. The KIN can observe objects as
faint as N(flux) = 1.7 Jy, as long as they also have Kmag < 6 (K–band co–phasing limit)
and Jmag < 8.5 (angle tracking limit).1
The response of any interferometer may be understood by projecting the fringe
pattern on the sky: what is measured is the astrophysical flux from the surface brightness
transmitted through the fringe pattern. For the work presented here, we measure and
1see http://nexsci.caltech.edu/software/KISupport/nulling/ for a full description of the
instrument parameters.

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calibrate the transmitted flux (expected to be small) due to dust surrounding the central
target stars. Thus, we refer to the basic observable as the “flux leakage” or simply the
“leak” (the inverse quantity, the null depth, is an equivalent and also frequently used term,
i.e. leak = 0.01 implies null depth 100:1). The amount of flux leakage not attributable to
the finite size of the central stars is referred to as “excess leakage”, and by measuring it we
can learn about the amounts of circumstellar dust present.
In order to achieve good accuracy of the calibrated leak measurements, the KIN
utilizes an architecture in which each Keck pupil is split into two halves, resulting in two
Keck–Keck long baselines, and two short baselines (4 m) formed between the two halves
of each Keck telescope. In order to accommodate the large dynamic range between a star
and any surrounding dust, the star is nulled on the Keck–Keck baselines. In order to detect
small leakage signals in the presence of the large mid–infrared background, the nulled
outputs are combined on the short baselines in a standard Michelson combiner (a.k.a. the
“cross–combiner”, or XC) with fast optical path difference modulation (i.e. “interferometric
chopping”, see also Mennesson et al. 2005). The output of the short baseline combiners (for
which any object appears essentially unresolved) when the long baselines are “at peak” also
provide the necessary flux normalization of the leak measurement. In essence then, the KIN
measurement is the ratio of the amplitudes of the short baseline combiner fringes when the
long baseline combiner is set at null, divided by the same quantity when the long baseline
combiner is set at peak:
Lraw=XC fringe amplitude at null
XC fringe amplitude at peak
(1)
The many details involved in making this measurement are described in Colavita et al.
(2009) and Colavita et al. (2010). As emphasized in those references, in a ground–based
background limited environment, achieving a high level of suppression of the central star

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(i.e. deep nulls) is not the most important consideration. Equally important is being
able to calibrate the leaks well; and the KIN four–beam architecture results in a better
calibration of the measured leakages (or equivalent visibilities) compared to standard
Michelson interferometry at mid–infrared wavelengths.
Due to various instrumental factors (diffraction, material absorption, pinhole mode
matching), the KIN spectral responsivity is strongly peaked toward the blue end of the
bandpass; the 8 − 9µm bin contains most of the signal–to–noise ratio (SNR). Also, the
red end of the spectrum is affected by poorer calibration quality (believed to be caused by
residual correlation in the short baseline combiners arising from telescope thermal emission).
Thus, for the analysis presented here, we only use the 8 − 9µm spectral bin, most sensitive
to exozodi detection.
3.2. Sky Response
As noted above, the KIN response may be understood as the flux from the astrophysical
source that is transmitted through its fringe pattern projected on the sky. Due to its
four–beam architecture, the KIN beam pattern consists of three terms:
1. Point spread function (PSF) of each Keck half–aperture (TPSF); this is well
approximated at 8.5µm by an elliptical Gaussian of FWHM = 490 × 440 mas. For
the observations presented here, the Keck rotator angles are oriented such that this
pattern has the major–axis along the East–West direction, and rotates as the target
moves across the sky such that the minor–axis always points toward North.
2. Fringes of the short baseline combiner (TXC):
TXC= cos(2π(x · uxc+ y · vxc)) (2)

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where (x,y) are coordinate offsets in right ascension and declination, and (uxc,vxc) are
the corresponding short baseline spatial frequencies. These fringes are perpendicular
to the half–pupil PSF major–axis, and rotate in the same way. Projected on the sky,
this fringe pattern is relatively “broad”: at 8.5µm the fringe spacing for the physical
4 m short baseline is 440 mas.
3. Fringes of the long baseline combiner (Tlong):
Tlong=1
2· (1 ∓ cos(2π(x · u + y · v))(3)
where (u,v) are the long baseline spatial frequencies, and the ∓ corresponds to the
null/peak configuration, respectively. This fringe pattern can have any orientation
with respect to TPSF and TXC. As mentioned above, in this “fine” fringe pattern the
dark and bright fringes are spaced by an angular separation projected on the sky of
10 mas, at 8.5µm and for the physical 85 m KI baseline.
The total KIN transmission pattern is thus:
T(x,y,u,v,uxc,vxc,λ) = TPSF· TXC· Tlong
(4)
Through the dependence on the spatial frequencies, the instantaneous KIN pattern
depends on wavelength (8.5µm) and on the hour angle and declination of the target being
observed. Figure 1 shows an example of the KIN pattern terms. The KIN is sensitive to
circumstellar dust by its ability to measure its flux transmitted through the total KIN fringe
pattern (center panel of Figure 1) i.e. dust located from ∼ 10 mas (0.1 AU at 10 pc) out
to the ∼ 490 × 440 mas field–of–view. However, the short baseline fringes (TXC) also act
to limit the KIN’s ability to detect outer dust. Indeed, in the example shown in Figure 1

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(top–right panel), TXCgoes to zero at ∼ 110 mas along the small baseline direction, so that
the “effective FOV” is only ∼ 110 × 440 mas (∼ 1.1 × 4.4 AU at 10 pc).
For an object with a brightness distribution I(x,y,λ), the expected monochromatic
leak is thus:
Lcalculated(u,v,uxc,vxc,λ) =
? ?I(x,y,λ) · T(x,y,u,v,uxc,vxc,λ)nulldxdy
? ?I(x,y,λ) · T(x,y,u,v,uxc,vxc,λ)peakdxdy
(5)
where the double integral is performed over the KIN field–of–view, set by the the
half–pupil PSF, as described above.
In order to provide some physical intuition, we note that for an object of angular size
much smaller than the fringe spacing of the long baseline, the nulled signal would ideally
be zero, resulting in L = 0. If, on the other hand, the object is large and its brightness
distribution spans many long baseline fringes, the flux transmitted at null or at peak are
similar and L = 1.0. Detailed descriptions of the theory behind the nuller measurement
may also be found in Traub & Oppenheimer (2010) and Serabyn et al. (2011).
3.3.Data Reduction, Calibration and Errors
End–to–end data reduction and calibration was performed by the Keck Interferometer
Project using their pipeline and external calibration package (nullCalib2). Here we
summarize the steps involved and the various sources of measurement error.
During observing, a micro–sequence is executed during which the short baseline optical
path modulation is always active (one fringe measurement every 25 msec), and the nullers
alternate between the null and peak states (for 250 msec and 50 msec, respectively).
2http://nexsci.caltech.edu/software/V2calib/nullCalib/

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Depending on the object brightness, this sequence is repeated for 10–15 min, thus many
thousand independent estimates of the leak are formed for each observation. From
the scatter of these measurements a “formal” error is estimated for the average leak
measurement corresponding to each observation.
Following standard practice, in order to monitor and subtract the instrument’s transfer
function (i.e. the non–zero leak that is measured when observing a point source located at
the phase center), observations of targets of interest were interleaved with observations of
calibrator stars of known N–band angular diameters. Thus, the calibrated leak is:
Lcalibrated= (Ltarget
raw
− Lsystem)(6)
where Lsystem, at the time of the target observations, is obtained by interpolation from
the net leak measurements of the bracketing calibrator stars, after subtracting the calibrator
leak expected given its angular diameter. This calculation is described in more detail in
Appendix C of Colavita et al. (2009), and all the steps are applied by the package nullCalib.
The required calibrator angular diameters were measured using the simultaneous
K–band fringe tracker data, and converted to N–band diameters using standard limb–
darkening relations. The procedure is described in detail in Appendix A of Colavita et al.
(2009); for clarity we repeat here some of the most relevant aspects. The approach was to
treat the nulling targets as calibrators, since at K–band they are expected to effectively be
simple naked stars. Although some of the calibrators are small (< 1 mas) compared to the
KI resolution, for such small calibrators the 20–30% precision obtained in those cases results
in uncertainties on the calibrated leaks well below the leak measurement errors (best–case
0.2%, see below). At the other end of the size range, for a 3 mas calibrator, the largest in
our sample, the diameter only needs to be known with 10% precision or better in order to
not add significant error to the calibrated leaks. Thus, the calibration procedure is largely

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insensitive to resonable errors in the adopted calibrator angular diameters. The accuracy
of our measured calibrator angular diameters was evaluated against estimates obtained
using surface brightness relations; in all cases the discrepancies also result in a calibrated
leakage differences smaller than the best–case measurement error. The uncertainties in the
calibrator diameters are taken into account and propagated into the formal error of the
calibrated leaks. The relevant parameters for the calibrators used for our sample are listed
in Table 2.
We note that we make the assumption that there is no source of calibrator leak other
than its angular extent, i.e. the calibrators have no excess N–band emission, which if
unaccounted for would directly lead to underestimated exozodi emission levels. However,
of 56 calibrators used in this study, one is a main–sequence star and all others are giants
(i.e. none are super–giants), and all but three have spectral types K0–M0; both of which
minimize the possibility of infrared emission above photospheric levels (e.g. Cohen et al.
1999, and references therein). Furthermore, all the calibrators used have been selected to
have IRAS 12µm/25µm flux ratios that agree, within the photometric errors, with that
of a blackbody of the calibrator effective temperature. These methods, however, do not
insure that our calibrators are free from low level dust emission at N–band (few percent
or less), undetected in the K–band diameter comparisons and IRAS flux ratios. But we
can use our own data to place some limits on the possible level of exozodi emission around
our calibrators. Indeed, if calibrator exozodi emission were high, and variable from star to
star, this would be apparent in correspondingly large leak fluctuations among the different
calibrators. Specifically, we have compared the variations in system leak estimates made
when same calibrator is used on either side of the target observation (only instrument
variations expected) with the same quantity computed when two different calibrators are
used (variations due to instrument plus calibrator exozodi level). Within measurement
errors, we see no difference between those two cases, implying that our calibrators do not

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contain large amounts of exozodi dust (in the language of Section 5, ? 100 zodi impact on
average on the exozodi levels derived for the target stars).
We also include “external” errors in the calibrated leaks, which have been estimated
from the night–to–night repeatability of multiple sets of calibrated data taken on the
same star (Colavita et al. 2009, 2010). In summary then, the errors on Lcalibratedcontain
two terms: (a) a formal error derived from the scatter of the leak measurements in each
observation, and which also contains the uncertainties associated with the estimate of
the system leak (mainly due to calibrator diameter uncertainties), and (b) the external
error just described. Table 3 shows the measured calibrated leak and errors for each
observation. As can be seen, for the stars in our sample the formal error is typically
σformal
Lcalibrated= 0.001 to 0.004. The external errors are wavelength and flux dependent; for the
stars in our sample they are in the range: σext.
Lcalibrated= 0.002 to 0.0035.
Validation of the KIN response and calibration was evaluated by the project using a
test system for which the expected leak could be calculated; in this case a binary system
with a well known orbit (Appendix B of Colavita et al. 2009).
Table 3 also contains the calculated leak expected from the target star itself (L?),
which is needed in order to derive the excess leak due to the exozodi cloud, as described
below. The calibrated leak data are also shown in Figure 2. We emphasize that at this
stage we do not average the multiple leak measurements that are available for a given
target, because variations among leaks measured at various times may in principle contain
a contribution from the changing projected baseline fringe spacing and orientation. Thus
we first model our measurements for a specific exozodi model, and average the results after
this conversion, as described in Section 4.4. Figure 3 also summarizes our measurements
but only for the wideband (8 − 9µm) channel used in the analysis presented here.

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4.Data Modeling
4.1.Modeling Exozodi Clouds
In order to interpret our measurements and compare them to the Solar System case,
we use the Zodipic code3to create images of zodi clouds around each of our targets. Zodipic
synthesizes brightness distributions of exozodiacal clouds based on the empirical fits to the
observations of the solar zodiacal cloud made by COBE (Kelsall et al. 1998).
When Zodipic generates a model brightness distribution for a zodi disk analog around
a star other than the Sun, the dust has the same optical depth at 1 AU and radial density
profile as in the Solar System. As a convenient unit, we refer to this model as corresponding
to “1–zodi”, which we denote z = 1. Zodipic scales the radial temperature profile with
stellar luminosity, and the inner dust radius is set by a dust sublimation temperature set
at 1500 K (the dust inner radius is thus dependent on stellar spectral type, but z = 1
models around any star have a fractional dust luminosity Ldust/L?? 10−7, the Solar System
value). In the Zodipic code the dust density can be treated as a free parameter, allowing
to generate brightness distributions for scaled version of the Solar System (the total flux
due to the circumstellar dust scales linearly with z). In the next section, we describe our
procedure for converting the calibrated leaks to an exozodi dust density, parametrized in
terms of a number (z) of zodis.
We note that the zodiacal models used here include only the smooth component of
interest, i.e. the Earth trailing blob and asteroidal dust bands are not included. We also
note that increasing the optical depth of the cloud increases the collision rate, which affects
the cloud structure, a physical process which is not taken into account by Zodipic. In a
zodiacal cloud, grain–grain collisions become important for grains above a critical size,
3http://ssc.spitzer.caltech.edu/dataanalysistools/tools/contributed/general/zodipic/

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∼ 30−150µm in the solar zodiacal cloud (Fixsen & Dwek 2002), and which scales inversely
as the optical depth of the disk (Kuchner & Stark 2010). Since this critical grain size
reaches 10µm for a disk with about 3–15 zodis worth of dust, we expect that disks with
more than roughly a few tens of zodis should begin to show morphological changes at KIN
wavelengths because of the collision destruction of grains in the center of the disk. Our
models, from Zodipic, are strictly linear in the dust density, and do not take this collisional
depletion into account; this level of analysis is left to future studies.
We also note that our procedure assumes that the exo–zodi density in the inner–most
regions of KIN sensitivity (∼ 10 mas or 0.1 AU at 10 pc, as described above) follows
the same radial density profile of the Kelsall et al. (1998) model, which was based on
COBE/DIRBE measurements made at larger stellocentric radii, 0.9 AU or larger. However,
measurements of the Solar zodiacal cloud made by the Helios probes as close as 0.3 AU
(Leinert et al. 1981), and measurements in the solar F corona (MacQueen & Greeley 1995),
both find radial density profiles with exponents of ∼ 1.3, in agreement with the Kelsall et
al. (1998) model.
The Zodipic images generated are 512 × 512 pixels, with a scale of 2 mas/pixel, i.e.
10× finer than the long baseline fringe spacing. The image size is thus 1024 × 1024 mas,
a good match to the KIN field–of–view (given by TPSF). Figure 1 includes an example
Zodipic image for a Solar System analog at 10 pc. We note that this image size (in pixels)
keeps the computation times short, but at this spatial resolution the stellar disk would not
be well sampled. Therefore, the Zodipic images generated do not include the central stars,
they represent only the exozodi brightness distribution (Izodi).