**EXTRASOLAR ZODIACAL EMISSION - NASA PANEL REPORT**

**[Panel Members]{.underline}**

Dana Backman F&M College, chair Paul Kalas MPIA, Heidelberg

Chas Beichman Caltech-IPAC Hal Levison South-West Research Inst.

Pierre Bély STScI Bill Reach Caltech-IPAC

Chris Burrows STScI George Rieke Univ. of Arizona

Mark Colavita NASA-JPL Dave Sandler Thermotrex Inc.

Stan Dermott Univ. of Florida Harley Thronson NASA-HQ

Christ Ftaclas Michigan Tech. Univ. Wes Traub Harvard-CfA

**I. Executive Summary**

The zodiacal dust cloud is the most prominent sign of the presence of
planetesimal-sized objects in our solar system. Although its total mass
is relatively tiny, the thermal emission and scattered light from a
portion of the zodiacal cloud a few x 0.1 AU across is comparable to
that from a terrestrial planet.

Our best knowledge of the zodiacal cloud is of the material near
Earth\'s orbit, at heliocentric radii from about 0.9 to 2 AU. The
detailed structure of the cloud is only now being explored. The relative
contributions of various dust creation and destruction mechanisms are
not yet well understood. What can be said at present is that most of the
dust near 1 AU is from main belt asteroid collisions and erosion, comets
are an important secondary source, and Poynting-Robertson (PR) radiation
drag inducing drift toward the Sun is the most important local removal
mechanism.

Simple back-of-the-envelope arguments presented below indicate that the
observed zodiacal dust density is probably about the norm (within a
factor of \~2) for the past Gyr. This is quite uncertain, however.
Individual asteroid collisions, giant comets, and comet showers may
produce large enhancements lasting 107 yr or more.

We cannot easily derive the density of the local zodiacal cloud in the
past because the main process (aside from collisions) that removes the
dust\'s planetesimal parent bodies is the \"chaotic\" influence of
planetary perturbations. Early in the history of the solar system the
zodiacal cloud could have been 106 times as dense and bright as at
present, based on an estimate of the maximum plausible original mass in
the asteroid belt. Models of the construction of a planetary system
indicate, however, that the presence of an asteroid belt is not
guaranteed. Thus, there is apparently a large possible range in mass of
original asteroid populations in planetary systems otherwise resembling
ours, along with an unpredictable rate of removal of asteroids and
comets and the likelihood of occasional substantial transient increases
in dust injection rate.

The above concerns lead to the main conclusion of this report: **it is
impossible to predict the density of dust at terrestrial temperatures in
extrasolar planetary systems**, even assuming the arrangement and
characteristics of major planets resemble those in our system. The
necessary presence of comets might imply a very uncertain general lower
limit of 1/10 the solar zodiacal dust density, and IRAS measurements
indicate few cases among nearby main sequence stars of more than several
x 100-zodi clouds of warm dust. Thus, our solar system\'s zodiacal
cloud, which would pose some problem for external detection of the
Earth, is probably near the low end of the possible range of system
densities although the distribution within that range is not even
guessable at this point.

It can be stated safely that the average zodiacal density should
steadily decrease over Gyr time scales in each system due to a decrease
in the mass of dust parent body populations. This implies that
planet-search instruments should be directed first at older systems.

**A planet-search interferometer should have precursor studies to
identify those systems with the least dust emission**. Dust emission at
1- to 100-zodi levels is not easily detected by unresolved photometry
because the corresponding fractional dust excess over stellar
photospheres would be only 10-4 to 10-2, smaller than the uncertainty in
stellar mid-IR spectral energy distributions. Thus, high spatial
resolution is necessary to separate exozodiacal emission from stellar
brightness. The optical and IR brightness contrasts between planets and
dust are comparable because the albedo and temperature of the dust are
like those of planets. Finding planets and finding exozodiacal clouds
will be of similar difficulty for spatial resolutions of order 0.1 AU
and dust densities like those in the solar system\'s zodiacal cloud.

Possible instruments to carry out the necessary preliminary exozodiacal
dust surveys include the Keck, Magellan, LBT, and VLT interferometers
working on the ground in the thermal-IR, and HST plus coronagraph in the
visual and near-IR. NGST at visual and near-IR wavelengths with
coronagraph and \"slow\" adaptive optics to compensate for its modest
optical smoothness could also be sensitive to exozodiacal clouds.
Ground-based IR interferometers can probably reach the 100- or 10-zodi
level for systems within 10 pc using simple and already-understood
Bracewell (chromatic) interferometry. Levels down to 10- to 1-zodi
appear feasible with implementation of achromatic interferometry in a
dual-nuller configuration.

A space-based exozodiacal mapper would be a useful intermediate step
between exozodiacal detection from the ground and planet detection from
space. Maps of exozodiacal emission could exploit expected dynamical
effects of extrasolar planets on their surrounding dust clouds to infer
the presence, orbit locations and orientation, and even masses of the
planets.

**II. Introduction**

It takes very little mass in the form of small grains in a circumstellar
environment to produce substantial scattered light and thermal infrared
emission. The surface brightness of the solar system\'s zodiacal cloud,
with a total mass equal only to that of a single small asteroid, would
make it difficult to detect Earth directly from neighboring stars at
both optical and IR wavelengths.

On the other hand, the presence of small dust grains with lifetimes much
shorter than the age of the solar system would instantly indicate to an
external observer that at least planetesimal-sized bodies exist in our
system as reservoirs for the dust material. And if planetesimals, then
why not planets? Furthermore, large masses embedded in the dust make
their presence known through their gravitational effects on the cloud\'s
morphology.

Thus, a planetary system\'s dust can both obscure and indicate the
presence of planets. This report will attempt to summarize the current
state of knowledge about our solar system\'s dust component, relate it
to dust discovered around some nearby main sequence stars, and compare
methods for detecting and characterizing extrasolar zodiacal clouds on
the road to finding extrasolar earth-like planets.

**III. Solar System Dust**

Interplanetary dust particles (IDP) are evident in the optical and IR
surface brightness of zodiacal light easily observed from the Earth. The
total IR-emitting (effective) cross-sectional area of grains between 1
and 2 AU from the Sun is about 2 x 1020 cm2. The grains characterizing
the IR emission near Earth\'s orbit have typical sizes of 10-100 µm. The
surface area given above thus corresponds to a mass of roughly 1018 -
1019 g for a density of 3 g cm-3, equivalent to a single solid body only
5-10 km in radius. The dust in the 1-2 AU annulus has an areal surface
density (vertical optical depth) of \~ 1 x 10-7, increasing slowly
toward the Sun. These characteristics will be referred to here as a
\"1-zodi\" cloud (Good 1994; Backman *et al.* 1997).

Table 1 gives the COBE DIRBE team\'s results (Kelsall *et al.* 1998) for
albedo and emissivity of the zodiacal grains at 1-3 AU. The albedo in
the near-IR is about twice that in the visible. Absolute emissivity
should equal 1 - Albedo.

Table 1: IDP Albedos and Emissivities

  ------------------------ ------------------------ ---------------------
  λ, µm                    Albedo                   Relative Emissivity

  1.25                     0.20                     

  2.2                      0.26                     

  3.5                      0.21                     1.66

  4.9                                               1.00

  12                                                0.96

  25                                                1.00

  60                                                0.73

  100                                               0.65

  140                                               0.68

  240                                               0.52
  ------------------------ ------------------------ ---------------------

The bolometric luminosity ratio Ldust/Lsun is \~ 2 x 10-8 for the 1-2 AU
annulus and is estimated to be about 1 x 10-7 for the entire zodiacal
cloud. The latter value depends strongly on the dust density and density
gradient close to the Sun. The luminosity of the hottest dust may not be
a crucial issue in interferometric detection of exozodiacal systems and
extrasolar planets because a central null intended to block stellar
emission will also block the inner reaches of exozodiacal clouds.

COBE and IRAS observations have little to say about the amount of dust
at r \< 0.9 AU. There are, however, constraints on the variation of dust
density from 1 AU to 0.3 AU which imply that the volume density varies
roughly as r-1.3 (Leinert *et al.* 1981). If the geometry of the cloud
is a \"wedge\" (Figure 1; constant opening angle subtended at the Sun,
scale height \'h\' proportional to \'r\'), then that volume density
gradient is equivalent to face-on surface density varying as r-0.3.

We do not know the position of the inner cutoff of the dust
distribution, although it may correspond simply to the vaporization
temperature of silicate grains. Observations close to the Sun during
eclipses show the zodiacal dust merging smoothly into the F-corona,
continuing in to 3 solar radii (0.015 AU) with volume density slope
flattening slightly to r-1.0 (Mann *et al.* 1996).

The details of dust density beyond 2-3 AU are also not well known. There
is a result from Pioneer 10 observations that the radial decrease of
zodiacal light intensity is about r-2.5 in the visible, equivalent to an
r-1.5 volume density law (Hanner *et al.* 1976). Table 2 gives estimated
polar zodiacal light surface brightnesses as if viewed from various
positions out to 3.5 AU based on Pioneer, Helios, and COBE DIRBE data.

Table 2: Polar Zodiacal Surface Brightness versus R

  ------------------ ----------------- ----------------- -----------------
                     Sν, MJy sr-1                        

  R, AU              4.9 µm            12 µm             25 µm

  0.5                6.5               46                51

  1.0                0.33              11                18

  1.5                0.04              4.0               9.2

  2.0                \~0               1.9               5.3

  2.5                \~0               1.0               3.4

  3.0                \~0               0.57              2.3

  3.5                \~0               \~0.35            \~1.6
  ------------------ ----------------- ----------------- -----------------

A patch of the zodiacal cloud in our solar system at 1 AU with diameter
0.3 AU (viewed face-on) would have the same brightness as the planet
Earth. This would be roughly true for both IR thermal emission and
optical scattered light to the extent that the material has
approximately the same albedo and temperature as Earth. Detecting
earth-like planets around other stars in the face of this emission thus
requires spatial resolution with this scale as well as strategies for
distinguishing moving emitters from \"fixed-pattern\" brightness.

**III.A. Sources and Sinks for Planetary Dust}**

The sources of IDP include at least: asteroid collisions, comet activity
and collisions in the inner solar system, comet collisions in the Kuiper
Belt (KB), and ISM grains. The main physical processes affecting IDP
are: expulsion by radiation pressure, inward Poynting-Robertson
![](media/image1.pct){width="101.0in" height="26.0in"}radiation drag,
solar wind pressure (including significant electromagnetic effects),
sublimation, mutual collisions, and gravitational influence of planets.

No rigorous accounting has been made of the relative strengths of the
grain sources, nor of the effects of the various destruction and
dynamical processes on the equilibrium spatial distribution of the dust.
Difficulties arise not simply because of complex cloud structure but
also from problems in comparing multi-wavelength data sets which do not
measure precisely the same lines-of-sight simultaneously and are often
subject to large calibration error. Very different models of the spatial
distribution of the material have produced acceptable fits to visual and
IR data (e.g. Giese and Kniessel 1989). Much work remains to be done
combining observational data with *a priori* models of the spatial
distribution based on dynamical evolution of the grains.

**III.A.1. Processes Affecting Grains**

The direct radiation \"overpressure\" factor β = F~rad~ /Fgrav is a
function of grain size, density, and albedo (Burns *et al.* 1979).
Values of β greater than 0.5 result in expulsion from the solar system
of a grain released from a parent body in a circular solar orbit. Such
values obtain for silicate grains smaller than roughly 1 µm radius. The
time scale for expulsion is only of order the orbit period, i.e.
essentially instantaneous compared with other time scales. Thus, this
process effectively produces a lower limit to the grain size commonly
found in solar orbit.

Grains large enough not to be expelled spiral toward the Sun under the
influence of PR drag. The PR time to de-orbit a black 30 µm-radius
(typical) grain with density 3 g cm-3 starting from 1 AU is about 105 yr
(Burns *et al.* 1979). This time scale is proportional to grain size for
a given grain composition and proportional to the square of the initial
orbit radius. The drift speed increases as r-1. In a \"wedge\" geometry,
equilibrium between a constant dust creation rate and destruction via PR
drag would produce a surface density proportional to r0, approximately
as observed in Earth\'s vicinity.

The dust mutual collision time scale is of order the orbit period
divided by the cloud optical depth perpendicular to the symmetry plane
(e.g. Backman and Paresce 1993). This is about 107 - 108 yr for the
local zodiacal cloud, much longer than the PR drag time scale. This
further indicates that local evolution is controlled mainly by PR drag.
Those particles which do collide can produce fragments smaller than the
radiation pressure \"blowout\" size and that material then exits the
system rapidly.

**III.A.2. Dust Sources**

Approximately 50% (15-75%) of IDP in the 10-100 µm size range come from
the asteroid belt, and 10% (5-25%) of the asteroidal dust comes from 3
known asteroid collision families representing ongoing interactions of
debris from significant collisions in the past (Dermott *et al.* 1996a;
Durda and Dermott 1997). The scale height of dust near the Earth
indicates at least some of the local dust is cometary (Liou *et al.*
1995). *The relative contributions of these and other sources are not
well known*.

The Trojan asteroids (Jupiter Lagrangian population) may also be a
significant source of collision debris drifting past Earth toward the
Sun because their encounter times are orders of magnitude shorter than
for main belt asteroids. The Trojan encounter velocities are not as
large, however, so their fragment size spectrum will probably have a
different shape than for main belt debris and the proportion of grains
in the size range producing substantial mid-IR emission is
unpredictable.

Comet dust grains almost certainly have different characteristic sizes,
compositions, and albedos from asteroid dust, and thus may behave
differently in response to the various forces discussed above.
Perihelion passage of a large comet such as P/Halley releases grains
with surface area of order 10-5 of that in the entire zodiacal cloud. If
the PR destruction time scale of typical cometary grains is assumed to
be roughly 105 yr (as for asteroidal grains) then P/Halley may
contribute 1% of the equilibrium zodiacal dust population during its
(maximum) life of 105 yr \~ 103 orbits.

Lower and upper limits on the Kuiper Belt dust parent body (comet
nuclei) population (Cochran *et al.* 1995 and Backman *et al.* 1995,
respectively) imply that the surface density of collisionally-produced
KB dust is comparable to that in the inner solar system zodiacal cloud.
These grains should drift toward the Sun via PR drag. However, for them
to make a noticeable contribution to the inner solar system dust
population, they must survive: a) collisions with interstellar grains,
which may be especially important for larger and more slowly-drifting KB
grains that are exposed to bombardment for longer intervals, and b)
gravitational perturbation by the Jovian planets that can trap grains in
resonances and/or eject them from the solar system; again, this should
be more important for slowly-drifting large grains. Both effects are the
subject of present modeling efforts (e.g. Liou *et al.* 1996). Gauging
their efficiency is important because without these effects the relative
densities indicate that a significant fraction of the inner solar system
dust could actually be originally from the KB (Flynn 1996; Backman *et
al.* 1997).

Interstellar grains are expected to be a significant source of the
smallest particles in the outer solar system. Ulysses detected ISM dust
in the outer solar system coming from the direction of the solar motion
through the galaxy (Grün *et al.* 1994). In-situ measurements indicate
that ISM dust surface density is only of order 0.1% of IDP density at 1
AU (Grogan *et al.* 1996).

**III.B. Fluctuations in the General Zodiacal Cloud Density**

The following argument leads to a conclusion that the present state of
our solar system zodiacal cloud is probably comparable to its \"normal\"
state over the past \~ 109 yr:

\(1\) Most of the present dust in the terrestrial-temperature zone is
asteroidal rather than cometary. This is supported by Galileo and
Ulysses observations, characteristics of the Earth\'s resonant ring, and
properties of particles caught in Earth orbit by the LDEF (Long Duration
Exposure Facility).

\(2\) Collisions of 10 km-radius bodies should occur in the main belt
approximately every 107 yr (\"particle-in-a-box\" approximation,
assuming 104 such objects spread uniformly between 2.0 and 3.5 AU). One
such collision could completely recreate the present zodiacal cloud. An
example of a model history of the zodiacal cloud density (actually, of
one family of collision debris) showing a general decline punctuated by
large transient increases is presented in Figure 2.

\(3\) The presence of 3 obvious asteroid collision debris families
indicates that complete dispersal of one of these families occupies a
time span very roughly 3 x the 107-yr interval between their initiation,
much longer than the 106-yr time scale for clearing 10-100 µm grains
from the main belt by PR drag. This is consistent with the expectation
that dust from a major collision is released slowly via grinding of
large co-orbiting fragments rather than immediately in the initial
collision.

\(4\) Although the 3 known collision families are directly responsible
for about 10% of the general dust population, fragments from those
families may be responsible indirectly for much more of the zodiacal
cloud via erosion of other asteroids (\"erosional cascade\"). If that is
actually the case, the general cloud density could be connected directly
to the number and density of active collision debris families.

\(5\) Zodiacal cloud enhancements by significant collisions last long
enough to overlap in time so the overall normal state of the cloud is
probably determined by the average of a number of collision families in
various degrees of relaxation.

\(6\) A crude estimate might then indicate that the normal variation
about the present state would be 3 ± √3 major collision families active
at a given time (with associated general belt asteroid erosion), i.e.
variation by a factor of \~ 2.

\(7\) Increases in the zodiacal cloud density by factors of 10 or more
due to exceptionally large asteroid collisions, giant comets, or comet
showers probably occupy only a small fraction of the total time.

Thus, the tentative conclusion is that **the present zodi cloud density
and brightness is probably the normal state, within approximately a
factor of 2, for the present asteroid and comet population**.

**III.C. Long-term Evolution of the Zodiacal Cloud**

The history of the zodiacal dust cloud over the age of the solar system
is likely to have been closely connected to the history of the main
asteroid belt. It is safe to state that the total mass of the asteroid
population has steadily decreased and will continue to decrease due to
mutual collisions and planetary perturbations. A \"bulge\" in the
asteroid size distribution (Zellner 1979) provides evidence that the
original population of the asteroid belt had a size spectrum
concentrated between 50-100 km radius. Many if not all of the presently
abundant asteroids smaller than that size range are not primordial but
are collision fragments.

The total main belt asteroid population now has a collisional evolution
time scale (population e-fold time) of a few x 1010 yr. The fact that
this is significantly longer than the age of the system means that the
evolution of the population is not \"controlled\" by mutual interactions
but by something external, i.e. the planets. Many calculations have
shown that asteroids in secular resonance with Jupiter (in the Kirkwood
gaps) will eventually be thrown into planet-crossing orbits, some to
exit the solar system. The winnowing of the asteroid belt is not just by
collisions but also by planetary perturbations, so it is \"chaotic\" and
*the density of the asteroid belt and associated zodiacal cloud cannot
be easily derived for past epochs*.

The present total mass of main belt asteroids is estimated to be 5 x
10-4 M⊕. It is possible that the original asteroid belt mass was 1000
times larger than present, i.e. 0.5 M⊕. The zodiacal dust released
collisionally by that population could have been as much as 106 denser
than the present cloud because collision rates depend on the square of
the number of colliding bodies. Thus, *the zodiacal cloud might have
been enormously brighter earlier in the history of the solar system*
without a large belt mass relative to the major planets. A simple
implication of this is that **planet searches should be directed toward
older stellar systems to avoid high dust density**.

**III.D. Signs of Planets**

The large-scale structure of the zodiacal cloud is determined by
planetary perturbations. The plane of symmetry of the cloud is inclined
to the ecliptic and slightly warped, and the Sun is offset from the
cloud\'s center of rotational symmetry (Dermott *et al.* 1996b). These
offsets might be discernible in some circumstances in other systems and
allow inference of the existence of planets.

COBE observations (Figure 3) have recently confirmed that the zodiacal
cloud near Earth has a marked trailing/leading asymmetry due to the
trapping of dust particles with small orbit eccentricities into orbital
resonances with Earth (Figure 4) (Dermott *et al.* 1994; Reach *et al.*
1995). There is a ring of dust that co-revolves with Earth around the
Sun; Earth resides in a cavity in this ring and a cloud of enhanced dust
density permanently trails the Earth in its orbit. The dust number
density in the trailing feature peaks about 0.2 AU behind the Earth and
is estimated to add between 10% and 40% (Dermott *et al.* 1994 and Reach
*et al.* 1995, respectively) to the local smooth cloud density over an
ecliptic plane area several x 0.1 AU diameter.

Additional work is needed to better define the true size of the wake
signals, but the Earth\'s wake has an IR signal at least 0.1x that of
Earth. Each planet probably has such a wake. The width and relative
enhancement of a wake is determined by the orbital period of the planet,
the typical grain PR drift velocity, and the mass of the planet. The
absolute wake density probably remains proportional to the smooth cloud
density, within some limits, as the latter varies with fluctuations in
intensity of grain injection processes. Wakes in exozodi clouds could be
mistaken for planets, depending on spatial resolution, but it is
important to note that **a wake can be a prominent indicator of the
presence of a planetary mass**. The wakes should be distinguishable from
planets via spectroscopy.

**IV. Other Stars**

At least 15% of nearby normal main sequence stars of all spectral types
have cold dust populations with spatial scales corresponding to our
system\'s Kuiper Belt (30-100 AU) (Backman and Paresce 1993) (Figure 5).
These are sometimes called \"Vega / β Pic\" disks after two nearby
especially prominent prototypes. The IRAS detection limit for dust
around nearby stars corresponds to a fractional dust luminosity limit of
Ldust/Lstar \> 10-5, about 100x the value for our zodiacal cloud and
also 100x a model upper limit on the amount of dust in our KB (Backman
*et al.* 1995). There is no obvious correlation within the present
small-number statistics between stellar type and average amount of dust.
Only a few main sequence stars have warm circumstellar dust (i.e., at
terrestrial temperatures) detectable with IRAS sensitivity (Aumann and
Probst 1991). Three examples, β Pic, ζ Lep, and 51 Oph, have Ldust/Lstar
values for warm dust in the range 10-5 to several x 10-4 (Fajardo-Acosta
*et al.* 1998).

It is crucial to note that some models of the construction of the
planets in our solar system indicate that **the presence of an asteroid
belt is not guaranteed**. Numerical experiments by Wetherill (1992)
yield one or more large bodies instead of an asteroid population in 50%
of runs. This is counter to the common intuition that an asteroid belt
must form just inside the orbit of the first ice giant due to
gravitational disturbances by that planet. These model systems otherwise
resemble ours, with a set of terrestrial planets and a set of Jovian
planets. Thus, complementing the point raised in section III.C that
planetary systems can have much larger asteroid and asteroidal dust
populations than does our system, present knowledge indicates that **a
system with an earth-like planet could also have much less
terrestrial-temperature dust than ours does**.

Recent discovery of nearby planetary systems containing \"hot
Jupiters\", Jovian-mass or larger objects at 0.05 to 2.5 AU from the
stars, indicates the variety of planetary systems that is apparently
possible (Butler *et al.* 1997). Of course such systems will show up
first and most easily in radial velocity searches, so their true
prevalence is unknown. However, recent theoretical work by Lin *et al.*
(1997) and Tremaine (1997) explain these objects as results of processes
of large-planet migration in the protoplanetary disk caused by drag from
either remnant gas or dense planetesimal populations. In \"hot Jupiter\"
systems, terrestrial material (planets, asteroids, and dust) would
likely have been erased by the inward migration of the large planets.

In contrast, a KB-like zone of planetesimals seemingly is guaranteed
beyond the planets in the region where the protoplanetary disk density
was too low and encounter times too long to support construction of
planets. It seems possible that cold dust like in the \"Vega / β Pic\"
systems may be detected eventually around most main sequence stars
(Dominik *et al.* 1998).

KB-like systems with Ldust/Lstar \< 10-5 would be expected to send
grains via PR drag toward their central stars because the mutual grain
collision time scale would be longer than the PR time scale. However, as
noted above, few main sequence KB-systems have significant grain
populations at temperatures above 150 K, indicating that central
\"voids\" are common. This can be explained as being due to a
combination of: a) erosion of inbound grains by interstellar dust, b)
dynamical influence of large outer planets preventing grains from
drifting close to the primary stars, and c) present inability to detect
zodiacal systems with Ldust/Lstar much below 10-5 such that KB-supplied
inner zodiacal clouds could have escaped notice to date.

Thus, it seems that the amount of cold dust in a system cannot be used
to predict the amount of hot dust because the presence of hot dust is
not guaranteed even if there is a planetary system, and the cold dust
may not be able to drift close enough to the star to become hot dust. In
terms of the planet-finding problem, observational and theoretical
studies of both the \"Vega / β Pic\" KB-like dust disks and of the dust
population in our outer solar system should help us discover whether
KB-like systems are necessarily remnants of the planet-formation process
and thus signposts of planetary systems, and whether central \"voids\"
require the influence of planets for their maintenance.

IRAS and ISO have not been able to detect hot dust at the 1-zodi level
around nearby stars because their low spatial resolutions prevent
separation of dust emission from stellar photospheres. The best these
instruments can manage in the face of uncertainty about photospheric
fluxes is to discover nearby dust systems down to the few x 100-zodi
level. SIRTF, on the other hand, will have detector arrays with
sub-diffraction pixels. With this resolution and higher sensitivity it
should be better than its predecessors at detecting thin dust around
some of the nearest stars (Backman *et al.* 1997). Unfortunately α
Centauri, the nearest system (1.3 pc), lies at a galactic latitude of
-0.7o and is projected against very bright interstellar background
emission, so it may not be easily investigated.

**V. Optical Detection Techniques**

**V.A. Zodiacal Scattered Light**

A 1-zodi cloud would have a face-on surface brightness of about V = +22
mags arcsec-2 at 1 AU from the primary star. This would be entirely
scattered/reflected light from the primary. Figure 6 gives the zodiacal
surface brightness at 1, 2, 3, 4, and 5 AU from the Sun (upper to lower
curves, respectively) as a function of wavelength. The reflected
sunlight component from about 0.4 to 4 µm is modeled from the observed
visible zodiacal light, and the thermal infrared emission from 5-20 µm
is based on the IRAS model. The transition from scattered light to
thermal emission occurs at about 3.5 µm for our local zodiacal cloud.
The near-IR brightness is about the same or slightly brighter than in
the visible because the grains are grey or slightly red. The surface
brightness of exozodiacal light (extended emission) with a given optical
depth at a chosen *angular* distance from a primary star will be
proportional to the stellar *apparent* brightness.

Exozodiacal optical surface brightness will not be easily distinguished
from background and instrumental sources of scattered light without
detecting a radial \"edge\" or azimuthal asymmetry in the exozodiacal
cloud. Based on experience with galaxy surface photometry, detection is
probably possible to exozodiacal surface brightness as low as 6 mags
arcsec-2 below the background, which will require a dramatic reduction
in the normal background for the relevant wavelengths, apertures, and
angular scales. Exozodiacal cloud detection will be much more difficult
than, e.g., finding galaxies around quasars (Ftaclas 1998).

**V.B. HST and NGST**

The superior surface accuracy of HST plus advanced-technology
coronagraphic cameras expected in the near future can probably reach the
10-zodi level. An 8-m NGST with coronagraph and \"slow\" adaptive optics
might detect the visual-λ surface brightness of a 1-zodi cloud at 10 pc
in a diffraction-limited beam if the instrument can compensate for
NGST\'s expected modest surface accuracy compared with HST.

The envisioned NGST instrumentation includes an adaptive mirror for
\"static\" wavefront correction over a very small field (1 arcsec
diameter). The post-correction background brightness would consist of
residual diffraction and scatter from actuator noise (wavefront sensor
errors, position errors, etc.). A critical concern is the unknown
angular-scale power spectrum of that post-correction background. If it
is \"white noise\" (Figure 7a), calculations show that the adaptive
mirror needs to be corrected to an accuracy of about 2 Å. This
requirement could be relaxed in some cases of background spatial noise
that is not \"white\" (Figure 7b). Note that the exozodiacal detection
problem at visual wavelengths with an 8-m aperture is more difficult
than directly detecting Jovian planets and comparable to detecting
individual terrestrial planets (Ftaclas 1998).

**VI. IR Interferometric Detection**

**VI.A. Zodiacal IR Emission**

The most relevant feature of the exozodiacal measurement problem in the
IR is the strong 10 µm foreground. The preferred wavelength band for
these measurements is around 10 µm because of: a) favorable contrast
ratio between the exozodiacal signal and the star, b) presence of a
terrestrial atmospheric window, and c) existence of spectral features of
substances such as O3 and CH4 that might indicate a non-equilibrium
atmosphere and the presence of life (ExNPS 1996). However, the 10 µm
exozodiacal signal will be deeply embedded in foreground terrestrial and
local zodiacal emission.

Figure 8a shows the face-on optical depth of the smoothly varying
portion of the solar system zodiacal dust as a function of radius from
near the Sun to 100 AU (Traub *et al.* 1996) for the COBE model
parameters (Kelsall *et al.* 1998). The COBE model spatial distribution

τ⊥ \~ (0.71 x 10-7)(rAU-0.39) was assumed valid from near the Sun to 100
AU. That figure also shows typical temperatures in the cloud assuming
emissivity = 1 (cf. Table 1). The inset scale gives angular radii for an
observer at a distance of 10 pc; thus the Earth lies at a radius of 100
mas and the solar radius is 0.44 mas. Figure 8b displays the
corresponding face-on surface brightness (also called specific intensity
or spectral radiance) in frequency units at wavelengths of 8, 10, and 12
µm. Note the steep fall-off with radius caused by weak blackbody flux at
10 µm for temperatures below about 300 K.

The IRAS zodiacal model has a steeper radial gradient, τ⊥ \~ (1.12 x
10-7)(rAU-0.80), than the COBE model. The COBE and IRAS models are both
constrained by observations relevant to material between about 0.9 and 2
AU and are similar in that region. Extrapolations of these models down
to a few solar radii is evidently dangerous: they differ there by almost
a factor of 10 in surface density. Also, to the extent that much of the
dust originates in the asteroid belt or in solar-activated comets, there
is probably a substantial break in density beyond 3-5 AU.

Figure 9 shows the integral power density from the Sun\'s surface
outward for the IRAS model. Note that 50% of the power comes from the
region inside 0.1-0.2 AU, depending on the wavelength, and 90% of the
total power is included inside a radius of 0.5-1.5 AU. For the COBE
model (not shown) the corresponding radii are 0.2-0.5 AU for the 50%
points and 1.0-2.0 AU for the 90% points. An exozodiacal dust-detecting
interferometer needs to be sensitive in this range of radii.

**VI.B. Bracewell Interferometry - Magellan**

As a specific example of a potential exozodiacal interferometer, Figure
10a displays the antenna pattern of the 6.5-m Magellan I telescope and
Figure 10b the fringe pattern formed by the 60-m separation of Magellan
I and II. The single-telescope \"beam gain\" is rotationally symmetric,
being just the diffraction pattern of a centrally obscured circular
aperture. The two-telescope \"fringe gain\" is a linear pattern of
interference fringes projected onto the sky, where the fringe
orientation is perpendicular to the projected baseline between the
telescopes and additionally averaged in azimuth. The product of these
two gains can be directly multiplied point-by-point across a model
exozodiacal map to obtain the signal in a single detector element. The
fringe phase is adjusted to give a central null on the star, blocking
most of the star\'s glare.

Note that the single-telescope diffraction-limited beam extends out to
about 200 mas, or about 2 AU radius at 10 pc, which is sufficient to
accept essentially all of the model dust emission at 10 µm. Also note
that (in star-nulling mode) the inner interference fringe has a
transmission peak at about 10 mas or 0.1 AU, which is an excellent match
to the 50% power points of the dust emission noted above. The product of
the IRAS model dust emission at 10 pc and the antenna pattern of the
Magellan interferometer results in reduction of total IRAS model power
observed at 10 µm from about 0.20 mJy to about 0.06 mJy due to the
interferometer gain pattern.

Finally, note that stellar leakage through the central null of an ideal
sinusoidal interference pattern varies as the square of the ratio of the
projected star diameter to fringe period. Wavefront perturbations
determine a Strehl ratio (on-axis relative power), the departure from
unity of which governs how much additional star light leaks into the
central diffraction-limited mode. Here the combined leakages are a
factor of a few greater than the dust emission signal, showing that the
initial contrast ratio of star/dust \~ 10,000 can be reduced to a more
manageable value in the range 1-10. A 3σ detection of the partly-nulled
10 µm flux given above for a 1-zodi cloud at 10 pc is possible in about
2 hours assuming smooth telescope mirrors, a cooled interferometer, and
noise dominated by fluctuations in telescope thermal photon emission
(Traub *et al.* 1996).

**VI.C. IR Space Interferometer**

A thermal-IR interferometer located in space would have obvious
advantages in sensitivity to exozodiacal clouds and extrasolar planets
over ground-based facilities (Bély *et al.* 1998). For a space mission
where telescope diameter is especially critical to cost, the background
power needs to be well known in advance for the success of the mission
because noise depends on the ratio of (background intensity) to (4th
power of telescope diameter).

Figures 11a and 11b compare the signal/noise ratios for exozodiacal dust
detection by interferometers located at 1 and 5 AU from the Sun,
respectively. The set of curves illustrate performance by a range of
sizes for the 4 unit telescopes in a baseline Terrestrial Planet Finder
(TPF) instrument design (ExNPS 1996).

An important performance criterion for exozodiacal dust and extrasolar
planet detection is that telescope noise should be less than local
zodiacal noise. By equating the corresponding surface brightnesses and
solving for the temperature, an upper limit for the telescope
temperature in terms of the telescope emissivity and local zodiacal
brightness can be found. For a nominal value of emissivity the telescope
temperature must be Ttel ≤ 69 K if the spacecraft is at 1 AU or ≤ 54 K
if at 5 AU. There is no clear need to cool a space interferometer\'s
telescopes much below these values (Traub *et al.* 1996).

**VI.D. Achromatic Interferometery - Keck**

The Keck Interferometer will have the following unique features relevant
to the detection of the zodiacal emission around other stars:

High Strehl (phasing): Adaptive optics at each aperture to provide
accurately phased wavefronts.

Phase-referenced operation (cophasing): Phase referencing, using
high-bandwidth fringe tracking on an off-axis star or on the target star
at a different wavelength, to cophase the interferometer and provide
high sensitivity and high path-length stability.

Interferometric nulling between the two apertures reduces the dynamic
range between the central star and the exozodiacal signal to enhance
detection. Additional nulling interferometers at each aperture can be
used to calibrate the background and the residual leakage of the central
star. With this approach, detection of exozodiacal signals as small as
10- or even 1-zodi should be possible.

The Supplement section to this report compares achromatic single and
dual-nulling operation of an instrument with the baseline
characteristics of the Keck Interferometer.

**VII. Panel Recommendations**

\(1\) Support should be given for implementation of one or more
ground-based large-aperture IR interferometers capable of surveying main
sequence stars within 10 pc to detect exozodiacal clouds to a
sensitivity level of 10-zodi or better. This will allow identification
of the least dusty systems as a precursor to IR searches for earth-like
planets.

\(2\) A space-based exozodiacal mapper less sensitive than a
planet-search instrument could find cloud asymmetries and planetary dust
\"wakes\" that would indicate the presence and locations of planets and
discern the orbit plane orientation in systems toward which the
planet-search instrument could then be directed.

\(3\) Extensive observational and theoretical studies of the structure
and history of our local zodiacal cloud should be made to: a) allow
better interpretation of observations of exozodiacal clouds, and b)
better characterize foreground emission that will interfere with
exozodiacal mapping and extrasolar planet searches, especially allowing
determination of the best location in our solar system for a
planet-search instrument.

\(4\) Some support should be given to projects aimed at determining the
age of field stars of solar type because the average dust surface
brightness should decrease with time in each system. Searches for
earth-like planets should be directed first toward older systems.

**S. Technical Supplement Regarding IR Interferometry**

**S.1. Assumptions about the Instrument and Target System**

Table S1 displays assumptions about a facility with characteristics like
the planned Keck Interferometer on Mauna Kea on which sensitivity
estimates below are based.

Table S1: Instrument assumptions

+---------------------------------+----------------+------------------+
| > Aperture                      | d              | 10 m             |
+---------------------------------+----------------+------------------+
| > Baseline                      | D              | 85 m             |
+---------------------------------+----------------+------------------+
| > Center λ                      | λο             | 10 µm            |
+---------------------------------+----------------+------------------+
| > Fractional bandwidth          | ∆λ / λο        | 0.3              |
+---------------------------------+----------------+------------------+
| > Background temperature        | T              | 273 K            |
+---------------------------------+----------------+------------------+
| > Etendue                       | AΩ             | 1 λ2             |
+---------------------------------+----------------+------------------+
| > Emissivity                    | ε              | 0.5              |
+---------------------------------+----------------+------------------+
| > AO Strehl ratio at λο         | S              | 0.984            |
+---------------------------------+----------------+------------------+
| > Effective efficiency          | η              | 0.1              |
+---------------------------------+----------------+------------------+

The value for etendue in Table S1 assumes a single-mode filter as
discussed in section S2, and the adaptive optics Strehl ratio assumes
200 nm rms wavefront errors. The effective efficiency includes adaptive
optics system transmission, starlight relay transmission, diffraction
losses, dewar internal losses, coupling losses into the single-mode
filters, and detector quantum efficiency (assumed to be 0.75). A further
efficiency factor of 0.5 is included to account for use of a nulling
beam combiner for the exozodiacal signal.

Table S2 gives the signal and signal/noise ratios if the observation
target is assumed to be the portion of an exozodiacal cloud located 1 AU
from a sun-like star at a distance of 10 pc. The background flux \'B\'
and the flux from the central star \'S\' in two apertures is 7 x 1010
and 1.5 x 108 electrons s-1, respectively.

Table S2: Fluxes and Signal/Noise Ratios *without Nulling*

+---------------------------------+-----------+-----------+-----------+
| > Exozodi density (solar zodi   | 100       | 10        | 1         |
| > units)                        |           |           |           |
+---------------------------------+-----------+-----------+-----------+
| > Exozodi flux Z (2 apertures,  | 1.3 x 106 | 1.3 x 105 | 1.3 x 104 |
| > e- s-1)                       |           |           |           |
+---------------------------------+-----------+-----------+-----------+
| > Exozodi photometric S/N (t =  | 500       | 50        | 5         |
| > 104 s)                        |           |           |           |
+---------------------------------+-----------+-----------+-----------+
| > Exozodi excess over star      | 1%        | 0.1%      | 0.01%     |
| > (Z/S)                         |           |           |           |
+---------------------------------+-----------+-----------+-----------+
| > Exozodi-to-background ratio   | 2 x 10-5  | 2 x 10-6  | 2 x 10-7  |
| > (Z/B)                         |           |           |           |
+---------------------------------+-----------+-----------+-----------+

From a strictly photometric perspective, detection of the excess from a
1-zodi cloud is possible. From a practical perspective, two points need
to be addressed: 1) the small relative size of the exozodiacal excess
relative to the star (0.01% for the 1-zodi case), and 2) the small
relative size of the exozodiacal excess relative to the mean IR
background (2 x 10-7 for the 1-zodi case). The latter point is probably
the most challenging. An approach to problem 1) involves a nulling beam
combiner between the two apertures to suppress the light from the
central star, increasing the relative size of the exozodiacal excess. An
approach to problem 2) adds additional nullers at the individual
apertures. These nullers serve as source choppers to provide an accurate
calibration of the background using only OPD (optical path differential)
modulation.

**S.2. Single-nuller Configuration**

Figure S1 is a block diagram of an interferometer configuration using an
achromatic nulling beam combiner to combine light from the two
apertures. The nulling combiner is similar in principle to a Bracewell
interferometer that combines the light from the two apertures
out-of-phase in order to provide starlight cancellation. However, the
achromatic nulling configuration uses polarization rather than a
physical path delay to generate an achromatic 180o phase shift, allowing
nulling over a wide spectral band. The delay lines in the figure
maintain equality between the two arms of the interferometer. The depth
of the achieved null is limited by the size of the source as well as
various instrumental and residual atmospheric errors, as discussed in
the next section.

**S.3. Limitations to Null Depth**

[Finite star diameter]{.underline}: Null depth is limited by the
relative spatial extent of the object. For star diameter θ = 1 mas and
λo/D = 24 mas, the null depth is δθ = 0.002.

[Optical path jitter]{.underline}: Deep nulls require a high degree of
pathlength stability between the two arms of the interferometer. The
amount of variation is a function of the atmospheric parameters and the
bandwidth of the interferometer fringe tracker. For median seeing at
Mauna Kea and a 1 kHz closed-loop bandwidth the null depth δΟ = 1.2 x
10-5. Note that there will be adequate photon flux from a bright central
star for at least a factor of 10 faster fringe tracking than this
example, and aggressive tracker algorithms can provide deeper nulls for
the same sampling rate.

[Wavefront aberration]{.underline}: Corrugations in the stellar
wavefront caused by imperfect optics reduce the interferometer fringe
visibility and hence the null depth. Relative to the combined intensity
of the two beams, the null depth δS = 1 - S, where S is the Strehl ratio
of an individual telescope with its AO system. Without further
compensation, this limits the null depth δS to 0.016. However, it is
possible to do significantly better by using a single-mode spatial
filter to remove wavefront aberrations.

[Scintillation]{.underline}: Unequal intensities between the two beams
of the interferometer produce imperfect fringe visibility. We can
approximate the instantaneous scintillation as the instantaneous change
in the Strehl ratio. For the example above with S = 0.984, the estimated
scintillation standard deviation would be 0.008, which would set the
null depth to 1.6 x 10-5. This yields a total null depth random
component of δL \~ 3 x 10-5 when combined with the path jitter from the
1 kHz fringe tracker described above.

Table S3 repeats the calculation in Table S2 but with the nulling in
place. The background is still assumed to be 7 x 1010 electrons s-1. We
assume systematic leakage δθ = 2 x 10-3 and a total random leakage δL =
3 x 10-5. As a result, the components of starlight leakage will be δθS =
3 x 10-5 and δLS = 5 x 103 electrons s-1, respectively. We now find that
the exozodiacal excess is readily detectable compared to the star.

Table S3: Fluxes and Signal/Noise Ratios *with Nulling*

+---------------------------------------+---------+---------+---------+
| > Exozodi density (solar zodi units)  | 100     | 10      | 1       |
+---------------------------------------+---------+---------+---------+
| > Exozodi flux Z (2 apertures, e-     | 7 x 105 | 7 x 104 | 7 x 103 |
| > s-1)                                |         |         |         |
+---------------------------------------+---------+---------+---------+
| > Exozodi photometric S/N (t = 104 s) | 250     | 25      | 2.5     |
+---------------------------------------+---------+---------+---------+
| > Exozodi excess over starover star   | 200%    | 20%     | 2%      |
| > (Z/systematic)                      |         |         |         |
+---------------------------------------+---------+---------+---------+
| > Exozodi excess over star            | 10000%  | 1000%   | 100%    |
| > (Z/leakage)                         |         |         |         |
+---------------------------------------+---------+---------+---------+
| > Exozodi-to-background ratio (Z/B)   | 1 x     | 1 x     | 1 x     |
|                                       | 10-5    | 10-6    | 10-7    |
+---------------------------------------+---------+---------+---------+

The exozodiacal signal is reduced in Table S3 relative to Table S2 by a
factor of 2 to represent some of the near-star dust emission being
nulled along with the star. Important problems remaining to be
considered (section S.4) include calibrating the background and the
amount of random leakage through the null.

**S.4. Dual-nuller Configuration**

Figure S2 shows a configuration that results when additional nullers are
added to the individual apertures. In this configuration, each aperture
is divided in the pupil plane and its light fed into nulling combiners.
The effective baseline for these interferometers is approximately D\' =
5 m. The output of these aperture nullers is then fed into the
interferometer nuller already described. A second interferometer nuller
is added to use the second nulled output of each aperture nuller. Four
delay lines are shown in the system, one preceding each input of the
aperture nullers. The nullers themselves maintain fixed internal
pathlengths for background stability. By adjusting the optical delay
lines, all combinations of aperture nulling \"on\" or \"off\" and
interferometer nulling \"on\" or \"off\" can be achieved.

As discussed above, the interferometer nuller cancels most of the
starlight, leaving residuals δθ (finite stellar diameter) and δL (into
which are lumped the leakage terms attributable to path jitter and
scintillation). Part of the dust emission also gets nulled, leaving
residual αZ where α \~ 0.5. With their much smaller baseline, the
aperture nullers will cancel all the star light \[strictly, a factor of
(D/D\')2 more than provided by the interferometer nuller\] as well as
some of the exozodiacal emission, leaving residual εZ. Signals provided
by the various nulling combinations are listed in Table S4.

Table S4: Signals for Various Nulling Combinations

+---------------+--------------+--------------+----------------------+
| Mode          | Aperture     | In           | Signal               |
|               |              | terferometer |                      |
|               | Nuller       |              |                      |
|               |              | Nuller       |                      |
+---------------+--------------+--------------+----------------------+
| \(a\)         | off          | on           | 2S + Z + B           |
+---------------+--------------+--------------+----------------------+
| \(b\)         | off          | on           | δθS + δLS + αZ + B   |
+---------------+--------------+--------------+----------------------+
| \(c\)         | on           | off          | δLS + εZ + B         |
+---------------+--------------+--------------+----------------------+
| \(d\)         | on           | on           | δLS + εZ + B         |
+---------------+--------------+--------------+----------------------+

Switching among these combinations requires only changes in pathlength
delay, not pointing. It is accomplished by motion of a PZT transducer by
5 µm and can occur quickly. If only OPD modulation external to the
nulling interferometers is used the background does not change; thus,
this approach can be used as a source chopper in order to calibrate the
background. This procedure is essential to allow detection of faint
exozodiacal signals.

The same approach can also be used to calibrate the random star leakage.
For changes in the instrument background and star leakage slower than
the chop rate, the difference between modes (b) - (d) is a \"white
noise\" process which should average out with integration time as 1/√t.
In addition, since S \>\> Z, mode (a) can be used to calibrate S, which,
along with knowledge of the star\'s diameter, can be used to calibrate
the exozodiacal excess. This dual-nuller approach therefore should allow
the detection of a weak exozodiacal signal embedded in a strong
background.

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**Figure Captions**

[Figure 1]{.underline}: Model cross-section of the solar system zodiacal
dust cloud showing a \"wedge\" shape consistent with grain drift inward
from the asteroid belt under the influence of PR drag. Densities at the
latitude extrema are enhanced, reflecting orbits inclined to the mean
plane executing simple harmonic motion along the vertical axis. The
inner cutoff represents termination of the model calculation rather than
a real discontinuity in the cloud.

[Figure 2]{.underline}: Model evolution of the total cross-section area
of dust and other objects in a debris family generated by collision of
two large asteroids at t = 0. The declining trend represents steady
removal of particles by PR drag. The transient increases result from
later collisions of large fragments within the swarm.

[Figure 3]{.underline}: COBE 25 µm surface brightness of the zodiacal
dust at ecliptic latitude 0o as a function of Earth\'s orbital
longitude. The upper and lower curves represent observations pointing
directly behind and in front of the Earth along its orbit, respectively.
The clear difference reveals the presence of a \"wake\" of dust trapped
in orbital resonance behind the earth. The sinusoid pattern around the
year results from Earth\'s vertical motion relative to the symmetry
plane of the cloud which is not quite identical to the ecliptic.

[Figure 4]{.underline}: Model of the motion of a particle trapped in a
resonance with the Earth, relative to a coordinate frame revolving with
Earth. The axis units are AU. The resonance holds the particle in a ring
at \~ 1 AU, temporarily interrupting its journey via PR drag from the
asteroid belt into the Sun.

[Figure 5]{.underline}: IRAS 25/60 µm versus 12/25 µm color-color
diagram for A, F, G and K main sequence stars in the Bright Star Catalog
surrounded by planetary material. The excluded region contains the
colors of free-free (plasma) emission. The color of a pure photosphere
with no circumstellar dust would be off the diagram to the upper right.
The trajectories trace colors of disks structurally identical to the
ones around β Pic and α PsA but with varying total amounts of dust in
contrast to the stellar photospheres.

[Figure 6]{.underline}: Spectral energy distribution of the zodiacal
cloud surface brightness as a function of wavelength and of distance
from the Sun. The nested curves are for dust at 1 AU (highest) to 5 AU
(lowest) from the sun. Each SED has a minimum in the near-IR at the
transition from scattered solar light to intrinsic thermal emission; the
transition moves to longer wavelengths for cooler dust.

[Figure 7]{.underline}: Zodiacal light surface brightness at visual
wavelengths compared with solar and planetary diffraction patterns seen
from 10 pc by an NGST-class telescope. a) Solar diffraction reduced by
\"slow\" adaptive optics in the case of system noise with a \"white\"
spatial spectrum. b) Same, but for a plausible case of \"non-white\"
noise.

[Figure 8]{.underline}: Thermal model of a 1-zodi cloud around a
solar-type star viewed from 10 pc based on the COBE zodiacal model. a)
Disk vertical optical depth (τ⊥) and temperature versus distance from
the central star, compared with a possible profile of the β Pic disk. b)
Thermal emission surface brightness versus distance from the star for
several wavelengths around 10 µm.

[Figure 9]{.underline}: Integral power versus distance from the star for
a 1-zodi cloud around a solar-type primary viewed from 10 pc, based on
the IRAS zodiacal model.

[Figure 10]{.underline}: Magellan telescope diffraction and fringe
pattern sensitivities versus distance from a central star viewed from 10
pc. a) Single telescope diffraction. b) Interferometer fringes from both
Magellan telescopes combined, employing central Bracewell nulling.

[Figure 11]{.underline}: Signal/Noise ratio for a space IR
interferometer detecting Earth at 10 µm from a distance of 10 pc in 104
seconds integration. The family of curves shows sensitivies for a range
of sizes of 4 unit telescopes along a 75-meter array baseline. The
horizontal axis is density of the exozodiacal cloud in which the
earth-like planet is embedded, in multiples of our 1-zodi cloud.
\"Struct = 0.0\" means these models assume the exozodiacal cloud is
perfectly smooth and structureless. a) Case of an interferometer located
at r = 1 AU. b) Interferometer located at 5 AU.

[Figure S1]{.underline}: Block diagram for achromatic single-nulling on
a 2-telescope interferometer.

[Figure S2]{.underline}: Block diagram for achromatic dual-nulling (once
at each aperture plus once for the 2-telescope interferometer as a
whole).