Signatures of planets in protoplanetary and debris disks

ARTICLE IN PRESS

0032-0633/$ - se

doi:10.1016/j.ps

�CorrespondE-mail addr

[email protected]

gennaro@astro

Planetary and Space Science 55 (2007) 569–581

www.elsevier.com/locate/pss

Signatures of planets in protoplanetary and debris disks

Sebastian Wolfa,�, Amaya Moro-Martınb, Gennaro D’Angeloc,d

aMax Planck Institute for Astronomy, Konigstuhl 17, 69117 Heidelberg, GermanybDepartment of Astrophysical Sciences, Peyton Hall, Ivy Lane, Princeton University, Princeton, NJ 08544, USA

cSchool of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UKdNASA Ames Research Center, Space Science and Astrobiology Division, MS 245-3, Moffett Field,CA 94035, USA

Received 17 November 2005; accepted 3 April 2006

Available online 27 October 2006

Abstract

We discuss selected possibilities to detect planets in circumstellar disks. We consider the search for characteristic signatures in these

disks caused by the interaction of giant planets with the disk as the most promising approach. Numerical simulations show that these

signatures are usually much larger in size than the planet itself and thus much easier to detect. The particular result of the planet–disk

interaction depends on the evolutionary stage of the disk. Primary signatures of planets embedded in disks are gaps in the case of young

disks and characteristic asymmetric density patterns in debris disks.

We present simulations which demonstrate that high spatial resolution observations performed with instruments/telescopes that will

become available in the near future will be able to trace the location and other properties of young and evolved planets. These

observations will allow to directly investigate the formation and evolution of planets in protoplanetary and debris disks.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: Protoplanetary disk; Debris disk; Planet formation; Planet–disk interaction; Radiative transfer simulation

1. Introduction

Planets are expected to form in circumstellar disks,which are considered as the natural outcome of theprotostellar evolution, at least in the case of low andintermediate mass stars (e.g., Adams et al., 1987; Lissauer,1993). While a detailed picture of the evolution of thecircumstellar environment, in particular of circumstellardisks, has been developed already, the planet formationprocess is in major parts still under discussion. Inparticular, adequate constraints from observations arerequired in order to either verify or rule out currentlydiscussed planet formation scenarios (e.g., Pollack et al.,1996; Weidenschilling, 1997; Goldreich and Ward, 1973;Youdin and Shu, 2002).

Although many extra-solar planet candidates have beendetected indirectly by radial velocity variations of stars

e front matter r 2006 Elsevier Ltd. All rights reserved.

s.2006.04.035

ing author. Tel.: +496221 528406; fax: +49 6221 528246.

esses: [email protected] (S. Wolf),

rinceton.edu (A. Moro-Martın),

.ex.ac.uk (G. D’Angelo).

(e.g., review by Marcy et al., 2005) no firm direct imagingdetection of a planet has been obtained so far. The maindifficulty is the large brightness contrast between a star anda planet combined with their small angular distance. Onecan try to avoid this problem for example by searching forplanetary companions around nearby stars, making use ofhigh-resolution imaging techniques, nulling interferometry,or coronagraphy. Furthermore, the brightness ratiobetween the star and the presumed planetary companioncan be decreased by choosing a proper wavelength range,spectral type of the star, and age/evolutionary stage of theplanet (e.g., Hubbard et al., 2002).Finding and imaging planets which are still embedded in

a circumstellar disk is by far more difficult, because thedust continuum radiation dominates the whole spectralrange from the ultraviolet to millimeter wavelengths: In theultraviolet to the near-infrared by scattering of the stellarradiation and at longer wavelengths by thermal reemission.Thus, in the preparation of observations of planets in diskseven more constraints have to be taken into account,describing the properties of the disk, such as the opticalparameters of the dust (chemical composition, size

www.elsevier.com/locate/pss

dx.doi.org/10.1016/j.pss.2006.04.035

mailto:[email protected]



ARTICLE IN PRESS

Fig. 1. Azimuthally averaged disk surface density hSi for planets with

masses from 0.01 to 1 MJupiter, around a solar-mass star (rP is the radius of

the planetary orbit). In physical units, hSi ¼ 10�4 corresponds to

33 g cm�2. The depth and width of the density gap depend mainly on

the planet’s mass (as the plot indicates), the disk temperature, and the

viscosity of the disk material. Notice that, in a cold disk with low viscosity

also a planet with a mass of a few times 10MEarth could open a deep gap.

1see, e.g., http://www.alma.nrao.edu/.

S. Wolf et al. / Planetary and Space Science 55 (2007) 569–581570

distribution) and its spatial temperature and densitydistribution. In the case of young, optically thick circum-stellar disks, the disk inclination and possible accretion onthe planet have to be considered as well.

Despite these obvious problems to investigate planetsduring the final stages of their formation or early evolutionthrough direct imaging, the following approach is currentlyunder discussion. During recent years, numerical simula-tions and analytical studies of planet–disk interactionshave shown that planets may cause characteristic large-scale signatures in the density distribution of circumstellardisks. The most important of these signatures are gaps andspiral density waves in young, also called ‘‘protoplanetary’’disks and resonance structures in evolved systems, so-called‘‘debris disks’’. The importance of investigating thesesignatures lies in the possibility to use them in the searchfor embedded planets. Therefore, disk features can provideconstraints on the processes and timescales of planetformation.

In the following sections we discuss characteristicsignatures in circumstellar disks caused by the planetaryperturbation. Moreover, we focus on the question whetherthese signatures could be observed and thus be used astracers for planets and the physical conditions in their closevicinity. In Section 2 we consider protoplanetary disks, andin Section 3 debris disks. This distinction is helpful sincethe main physical processes dominating the structure of adisk with an embedded planet are different in both cases,resulting in different characteristic features.

2. Protoplanetary disks

Protoplanetary disks are accretion disks which have beenfound around TTauri and Herbig Ae/Be stars. Hydro-dynamic simulations of gaseous, viscous protoplanetarydisks with an embedded protoplanet show that planets withmasses \0:1MJupiter produce significant perturbations inthe disk’s surface density. In particular, they may open andmaintain a large gap as illustrated in Fig. 1. (e.g., Brydenet al., 1999; Kley, 1999; D’Angelo et al., 2002; Bate et al.,2003). This gap, which is located along the orbit of theplanet, may extend up to several astronomical units inwidth, depending on the mass of the planet and thehydrodynamic properties of the disk (see caption of Fig. 1for further details). Nevertheless, the disk mass flow ontothe planet continues through the gap with high efficiency.Nearly all of the flow through the gap is accreted by theplanet at a rate comparable to the rate at which massaccretion would occur in the disk without a planet. The gasaccretion on the planet can continue to planet masses of theorder of 10MJupiter, at which point tidal forces aresufficiently strong to prevent flow into the gap. However,planets with final masses of the order of 1MJupiter wouldundergo migration on a timescale of about 105 years, whichcould make survival difficult.

Protoplanets also launch spiral waves in the disk (seeFig. 2 (left)). However, in the presence of turbulence, these

waves appear to be diffused (Nelson and Papaloizou,2003). Furthermore, D’Angelo et al. (2002) found smaller-scale spirals in the vicinity of the planet that are detachedfrom the main ones: Along these small spirals the gas orbitsthe planet, forming a circumplanetary disk (see Fig. 2(right); see also Lubow et al., 1999).The observability of the features outlined above has been

first investigated by Wolf et al. (2002). It was shown thathigh-resolution images in the submillimeter wavelengthrange, as to be obtained with the Atacama Large Millimeter

Array1 (ALMA), will allow to trace the gap but not thelarge-scale spiral structure.We perform further simulations with the goal of

answering the question whether the planet itself and/orthe circumplanetary environment heated by the planet,through its contraction and/or via accretion onto it, couldbe detected. The detection of a gap would already representa strong indication of the existence of a planet, thus givinginformation such as planetary mass, disk viscosity, andpressure scale-height of the disk. The detection/non-detection of warm dust close to the planet, however, wouldadditionally provide valuable constraints on the tempera-ture and luminosity of the planet, the accretion process,and the density structure of the surrounding medium.This study is motivated also by the assumption that

young giant planets are expected to be very hot, comparedto their old counterparts, such as Jupiter. Even moreimportantly, the accretion onto the planet is expected torelease enough energy to sufficiently heat the circumplane-tary environment. Thus, the planet surroundings might be

http://www.alma.nrao.edu/

ARTICLE IN PRESS

Fig. 2. (Left) Surface density of a circumstellar disk with an embedded 1MJupiter planet, which shows the planet, the gap, and the spiral-wave pattern

excited by the planet. (Right) Density in the planet’s Roche lobe that shows the circumplanetary disk (with selected streamlines), i.e., the disk around the

planet. The density scale on top of each panel is linear (left) and logarithmic (right). The physical units are as in Fig. 1.

S. Wolf et al. / Planetary and Space Science 55 (2007) 569–581 571

observable in the (far-)infrared wavelength range throughthermal dust reemission. Provided that the mass of theplanet is large enough to open a significantly large and low-density gap (on the order of a Jupiter mass), the contrastbetween the gap and the dust heated by the planet might besufficiently high to allow one to distinguish both compo-nents, i.e., the gap and the dust distribution around theplanet.

We test different environments of a planet located in acircumstellar disk for the resulting temperature structurewhich, in combination with the density distribution, mainlydetermines the likelihood to detect any of the featurescharacterizing the embedded planet. The models consideredhere cover a broad range of different, most reasonablescenarios. A detailed description of all considered modelconfigurations and the resulting observational consequencesis given in Wolf and D’Angelo (2005). In the following, weconcentrate on the most significant results of this study.

2.1. The planetary accretion region as a hotspot in a young

disk

The evolution of a circumstellar disk with an embeddedplanet can be formally described by the Navier–Stokesequations for the density and the velocity field components(see, e.g., D’Angelo et al., 2002 for details). For thepurpose of the present study, the disk is treated as a two-dimensional viscous fluid in the equatorial plane. Diskmaterial is supposed to have a constant kinematic viscositythat is equivalent to a Shakura and Sunyaev parametera ¼ 4� 10�3 at the location of the planet.

A planet-sized object with mass MP revolves around thecentral star, moving on a circular orbit whose radius is rP.It perturbs the surrounding environment via its point-massgravitational potential. The ratio of MP to M� is 2� 10�3,hence MP ¼ 1Mjup if M� ¼ 0:5Msun. We base this studyon two-dimensional models because, by means of high-resolution three-dimensional simulations, D’Angelo et al.(2003) demonstrated that computations in two dimensionsgive a satisfactory description of disk–planet interactionswhen dealing with heavy planets (MP=M�410�4) in thindisks (aspect-ratio � 0:05).The simulations are started from a purely Keplerian

disk. Due to the angular momentum transfer among theinner disk (rorP), the planet, and the outer disk (r4rP), adeep density gap is soon carved in along the orbital path.Characteristic spiral features, spreading both interior andexterior to the planet’s orbit are excited by the gravitationalpotential of the planet (Fig. 2, left panel). The diskdepletion interior to the planet’s orbit (rorP), due both togravitational torques exerted by the planet on the diskmaterial and to viscous diffusion towards the star, isaccounted for by allowing material to flow out of the innerborder of the simulated disk domain, thus accounting foraccretion onto the central star. These calculations alsosimulate the growth rate of the planet due to the feedingprocess by its surroundings. A fraction of the matterorbiting the planet inside of an accretion region is removedon a timescale on the order of a tenth of the orbital period.Since the accretion process is a highly localized phenom-enon, the accretion region must be small. Therefore, wechoose a radius raccP equal to 6� 10�2 rH, where the Hill

ARTICLE IN PRESSS. Wolf et al. / Planetary and Space Science 55 (2007) 569–581572

radius rH ¼ rPffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiMP=ð3M�Þ

3p

¼ 8:7� 10�2 rP approxi-mately characterizes the sphere of gravitational influenceof the planet. In order to achieve the necessary resolutionto study the flow dynamics on these short length scales,without neglecting the global circulation within the disk,we utilized a nested-grid technique (D’Angelo et al., 2002,2003). We obtain a planetary accretion rate, _MP, on theorder of 10�9Msun yr

�1.Since a measure of the planetary accretion rate is

available through our simulations, it is possible to evaluatethe accretion luminosity of the planet Lacc. For a planetwith a radius of a few Jupiter radii (e.g., Burrows et al.,1997), MP ¼ 1Mjup (orbiting a M� ¼ 0:5Msun star) andrP ¼ 5AU, we get Lacc � 10�4 Lsun. However, the accretionrate is observed to slowly diminish with time, due to thedepletion of the disk and the deepening of the gap. Hence,the accretion luminosity decays with the time. As anexample, extrapolating _MP after a few 104 years, the aboveestimate of Lacc becomes � 10�5 Lsun. This value for theplanetary accretion luminosity is on the same order ofmagnitude as the luminosity derived by Burrows et al.(1997) for a young Jupiter-mass planet.

Based on the density structure obtained from thehydrodynamical simulations we derive a self-consistenttemperature structure in the disk. For this purpose we usethe three-dimensional continuum radiative transfer codeMC3D (Wolf, 2003; see also Wolf et al., 1999). We derivethe disk temperature structure resulting from stellarheating on a global grid covering the whole disk, butsimulate the additional heating due to the planet on a muchsmaller grid centered on the planet, which sufficientlyresolves the temperature gradient in its vicinity.

We now discuss observable quantities under the assump-tion that the disk is seen face-on since this orientationallows a direct view on the planetary region. The thermaldust reemission of circumstellar disks can be mapped with(sub) millimeter observations and it has been performedsuccessfully for a large number of young stellar objects(e.g., Beckwith et al., 1990). The only observatory,however, which—because of its aspired resolution andsensitivity—might have the capability in the near future todetect features as small as a gap induced by a planet in ayoung disk, will be ALMA. For this reason, we performradiative transfer simulations in order to obtain images at afrequency of 900GHz, which marks the planned upperlimit of the frequency range to be covered by ALMA. Thisfrequency is required for our simulations because it allowsto obtain the highest spatial resolution. The trade-off is therelatively high system temperature (�1200K; Guilloteau,2002) which adds a significant amount of noise to thesimulated observations. Therefore, long observing times(8 h in our simulations) are mandatory. To investigate theresulting maps to be obtained with ALMA, we use theALMA simulation software developed by Pety et al. (2001)and chose an observation setup according to the directionsand suggestions given by Guilloteau (2002). Furthermore,we introduce a random pointing error during the observa-

tion with a maximum value of 0:600 in each direction, 30�

phase noise, and further error sources, such as amplitudeerrors and ‘‘anomalous’’ refraction (due to the variationof the refractive index of the wet air along the line ofsight). The observations are simulated for continuousobservations centered on the meridian transit of theobject. The object passes the meridian in zenith where anopacity of 0.15 is assumed. The bandwidth amounts to8GHz.Based on these simulations, whose outcomes are shown

in Figs. 3 and 4, we make the following predictions aboutthe observability of a giant planet in young circumstellardisks:

(1)
The resolution of the images to be obtained withALMA will allow detection of the warm dust in thevicinity of the planet only if the object is at a distance ofnot more than about 50–100 pc. For larger distances,the contrast between the planetary region and theadjacent disk in any of the considered planet/star/diskconfigurations will be too low to be detectable.However, the more pronounced, larger gap can beobserved also for objects at larger distances, such as innearby rich star-forming region (e.g., Taurus; Wolfet al., 2002).
(2)
Even at a distance of 50 pc a resolution being highenough to allow a study of the circumplanetary regioncan be obtained only for those configurations with theplanet on a Jupiter-like orbit but not when it is as closeas 1AU to the central star. This is mainly due to thesize of the beam (�0:0200 for the ALMA configurationas described above).
(3)
The observation of the emission from the dust in thevicinity of the planet will be possible only in case of themost massive and thus young circumstellar disks(�10�3–10�2Msun).
2.2. Influence of the planet on the spectral energy

distribution

The contribution of the planet to the net flux at900GHz—by direct or scattered radiation and reemissionof the heated dust in its vicinity—is p0:4% (depending onthe particular model) than that from the small region of thedisk considered in our simulations. Furthermore, theplanetary radiation significantly affects the dust reemissionspectral energy distribution (SED) only in the near to mid-infrared wavelength range (see Fig. 5). However, since thisspectral region is influenced also by the warm upper layersof the disk and the inner disk structure, the planetarycontribution and thus the temperature/luminosity of theplanet cannot be derived from the SED alone.

2.3. Inner cavities in young circumstellar disks?

Observed mid-infrared SEDs of selected disks aroundTTauri and debris-type disks show hints of inner cavities

ARTICLE IN PRESS

Fig. 4. Simulation of ALMA observations with a close-up view of the region around the planet. MP=M� ¼ 1Mjup=0:5Msun, Comparison of disks, seen at

two different distances (left map: 50 pc, right map: 100 pc). The size of the displayed region amounts to 6AU� 6AU. The asterisk marks the position of

the planet. The contour lines mark selected signal-to-noise levels (from Wolf and D’Angelo, 2005).

Fig. 3. Simulation of ALMA observations of a disk with an embedded planet with a mass of 1Mjup around a 0:5Msun star (orbital radius: 5AU). The

assumed distance is 50 pc (left)/100pc (right). The disk mass amounts to Mdisk ¼ 1:0� 10�2 Msun. Only structures above the 2s-level are shown. The sizeof the combined beam is symbolized in the lower left edge of each image. Note the reproduced shape of the spiral wave near the planet and the slightly

shadowed region behind the planet in the left image (from Wolf and D’Angelo, 2005).


(void of small dust grains) such that the inner radius of thedisk is apparently much larger than the sublimationradius—at least of selected dust species. Examples amongTTauri disks are GM Aurigae (Koerner et al., 1993; Riceet al., 2003) and TW Hya (Calvet et al., 2002). Twoalternatives are discussed to explain these inner ‘‘holes’’: (a)

dust evolution (mainly grain growth) resulting in adepletion of small grains and (b) the influence of a giantplanet in the inner region. In Fig. 6 the reconstructed imageof a circumstellar disk with an inner hole is shown whichcould be obtained with the VLTI combining up to fourAuxiliary Telescopes (Wolf et al., 2006).

ARTICLE IN PRESS

Fig. 5. Spectral energy distribution of protoplanetary disks with embedded planets (simulations). Left: MP=M� ¼ 1Mjup=0:5Msun, Mdisk ¼ 10�2 Msun

(same model as used for Fig. 4, left column); Right: MP=M� ¼ 1Mjup=0:5Msun, Mdisk ¼ 10�6 Msun. The planet is located at a distance of 5AU from the

central star. Solid line: net SED; long dashed line: disk reemission; short dashed line: direct (attenuated) and scattered radiation originating from the

protoplanet (due to planetary radiation and/or accretion); dot-dashed line: (re)emission from the planet and the dust within the sphere with a radius of

0.5AU centered on the planet. The assumed distance is 140 pc (from Wolf and D’Angelo, 2005).

Fig. 6. Simulated 10mm image of the inner region of a TTauri circumstellar disk with a cleared inner region (radius: 4AU), seen under an inclination of

60� (assumed distance: 140 pc). Left: original image; right: reconstructed image (not scaled), based on simulated mid-infrared VLTI observations

combining four Telescope (MATISSE concept study; see e.g., Lopez et al., 2006) (from Wolf et al., 2006).


3. Debris disks

3.1. General overview

Debris disks are solar system sized dust disks producedas by-products of collisions between asteroid-like bodiesand the activity of comets left over from the planetformation process. In the case of our solar system, thedebris of Jupiter-family short-period comets and collidingasteroids represents the dominant source of zodiacal dustlocated inside the Jupiter orbit. A second belt of dust islocated beyond the orbit of Neptune (e.g., Dermott et al.,

1992; Liou et al., 1995). Besides the solar system, optical tomid-infrared images of b Pic and AU Mic (e.g., Kalas andJewitt, 1995; Weinberger et al., 2003; Kalas et al., 2004)and (sub)millimeter images of Vega, Fomalhaut, � Eri, andb Pic (Holland et al., 1998; Greaves et al., 1998; Liseau etal., 2003) have revealed spatially resolved debris diskswhich were first inferred from observations of infrared fluxexcesses above photospheric values with IRAS. Based onstudies with ISO, the disk fraction is thought to decreasesignificantly with age, amounting to much less than 10%for stars with ages X1Gyr (e.g., Spangler et al., 2001; seealso Habing et al., 2001; Greaves et al., 2004; Dominik and

ARTICLE IN PRESS

Fig. 7. The annually averaged spectrum of the zodiacal light, normalized

to that of a 240K blackbody. Diamonds represent DIRBE data, and the

solid error bars represent the FIRAS spectrum. At wavelengths below

�150mm, the zodiacal spectrum is that of a graybody with an optical

depth of �3� 10�7 (similar to the value 10�7 quoted by Leinert, 1996). At

longer wavelengths the dust emissivity falls off as l�2, as shown by the

solid line (from Fixsen and Dwek, 2002).


Decin, 2003). Planetary debris disks are assumed torepresent the almost final stage of the circumstellar diskevolution process, i.e., they are the evolutionary productsof ongoing or completed planet formation.

In contrast to optically thick young circumstellar disksaround Herbig Ae/Be and TTauri stars with spatialstructures dominated by gas dynamics, the much loweroptical depth and lower gas-to-dust mass ratio in debrisdisks (Zuckerman et al., 1995; Dent et al., 1995;Artymowicz, 1997; Liseau and Artymowicz, 1998; Greaveset al., 2000a; Lecavelier des Etangs et al., 2001) let thestellar radiation—in addition to gravity—be responsiblefor the disk structure. Besides, fragmentation becomes atypical outcome of particle collisions, because relativevelocities of grains are no longer damped by gas. ThePoynting–Robertson (P–R) effect, radiation pressure,collisions, and gravitational stirring by embedded planetsare all important in determining the dust population anddisk structure (Liou and Zook, 1999; Grady et al., 2000;Moro-Martın and Malhotra, 2002).

Since the mass of small grains in debris disks andtherefore the thermal dust reemission from these disks aremuch smaller than in case of TTauri disks, only a verylimited sample of observations existed in the recent past, asIRAS and ISO could only probe the brightest and closestsystem. However, because of the unprecedented sensitivityof the mid-infrared detectors aboard the Spitzer Space

Telescope there has been a substantial increase in the totalnumber of detected debris disks. As an example, the A-Starand FGK GTO Surveys and the FEPS Legacy Survey (cf.Meyer et al., 2004) are allowing to extend the search fordisks around stars to greater distances and more tenuousdisks, achieving detections rates adequate to establish diskfrequency and properties on a sound statistical basis (e.g.,Rieke et al., 2005; Bryden et al., 2006; Beichman et al.,2005).

In the simplest model of debris disks, their structure iscontrolled by gravity, radiation pressure, and P–R drag. Ina collisionless system without sources and sinks and withgrains in circular orbits, the radial density distribution rðrÞdecreases as 1=r due to P–R drag (e.g., Briggs, 1962). This‘‘classical solution’’ approximately represents the overalldistribution of dust in the solar system (e.g., Ishimoto,2000). Another simply structured debris disk would be acloud of grains moving outward from the center inhyperbolic trajectories. This solution, which applies to so-called b-meteoroids in the interplanetary space is describedby rðrÞ / r�2 (e.g., Lecavelier des Etangs et al., 1998;Ishimoto, 2000). However, as for instance Gor’kavyi et al.(1997) pointed out, there exist several effects that maychange the distribution considerably, including resonanceeffects with planets, gravitational encounters with planetswhich occur in the form of elastic gravitational scattering,mutual collisions of particles, evaporation of dust grains,and existence of sources of dust with highly eccentric orbits(such as the Encke comet in the case of the solar system;e.g., Whipple, 1976; Sykes, 1988; Epifani et al., 2001). The

resulting density distribution is in most cases no longerdescribed by a single power-law, but depends strongly onthe properties (mainly the orbits and masses of planets anddust sources) of each particular disk/planetary system. Inthe case of b Pic, visible observations of the scatteredstarlight and mid-infrared images show a decrease of themid-plane number density profile with increasing distancefrom the central star (Artymowicz et al., 1989; Kalas andJewitt, 1995), possibly indicating that most of the dustsources are located in the inner disk.Although debris disks represent a rich source of

information about the formation and evolution of plane-tary systems, they also impose problems on the observa-tions of exoplanetary systems. First, zodiacal light of ourown solar system has a potential serious impact on theability of space-born observations to detect and study theirtargets. It is attributed to the scattering of sunlight in theUV to near-IR, and—important for mid-IR missions suchas DARWIN (e.g., Fridlund, 2000)—the thermal dustreemission in the mid to far-IR. At infrared wavelengthsfrom approximately 1mm, the signal from the zodiacal lightis a major contributor to the diffuse sky brightness anddominates the mid-IR sky in nearly all directions, exceptfor very low galactic latitudes (Gurfil et al., 2002). Based onmeasurements obtained with the COBE satellite, Fixsenand Dwek (2002) derived an annually averaged spectrumof the zodiacal cloud in the 10–100mm wavelength range.The spectrum exhibits a break at �150mm that indicates aknee in the dust size distribution at a radius of about 30mm(see Fig. 7).Second, the exozodiacal dust disk around a target star,

even at solar level, will likely be the dominant signaloriginating from the extrasolar system. In the case of asolar system twin, its overall flux over the first 5AU isabout 400 times larger than the emission of the Earth at

ARTICLE IN PRESS

Fig. 8. Four basic resonant structures in debris disks: (I) low-mass planet

on a low-eccentricity orbit, (II) high-mass planet on a low-eccentricity

orbit, (III) low-mass planet on a moderate-eccentricity orbit, and (IV)

high-mass planet on a moderate-eccentricity orbit (from Kuchner and

Holman, 2003).


10mm. Although the factor reduces to a few tens afterpartial rejection by usage of a nulling interferometer, onestill has to make sure that the exo-zodiacal signature willnot mimic planetary signals such as would be the case if thedisk is significantly clumpy (as almost always found in theouter regions of debris disk—e.g., Holland et al., 1998,2003; Greaves et al., 1998). If the origin of this clumpinessis in perturbations of planets, then detecting clumps canhelp to pinpoint those planets (e.g., Wyatt, 2003). In thiscontext one has to be aware that collisionally regenerateddebris disks are also intrinsically clumpy because dustcreated by collisions between large planetesimals starts outin a clumpy dust distribution (Wyatt and Dent, 2002).

3.2. Structure of debris disks with embedded planets

The high-resolution images of debris disks in scatteredlight in the optical/near-IR and in thermal emission at mid-IR to millimeter wavelengths show density structures, suchas rings, gaps, arcs, warps, offset asymmetries and clumpsof dust (e.g., Greaves et al., 1998; Schneider et al., 1999;Wilner et al., 2002; Holland et al., 1998, 2003; Koerneret al., 2001). In evolved, optically thin debris disks some ofthese features are likely to be the result of gravitationalperturbations by one or more massive planets on the dustdisk. There are several mechanisms by which giant planetscan sculpt the disks: (a) capture of dust in mean motionresonances (MMRs) with the planet, as the dust particlesdrift toward the central star due to P–R drag; (b)gravitational scattering of dust particles by the planet; (c)resonance capture of dust-producing planetesimals due toplanet migration; and (d) secular (long-term) planetaryperturbations. The resulting characteristic density patternsare expected to provide the strongest indirect hints on theexistence of planets embedded in these disks (see e.g., Liouand Zook, 1999; Wyatt et al., 1999; Ozernoy et al., 2000;Moro-Martın and Malhotra., 2002, 2003, 2005; Wilneret al., 2002; Quillen and Thorndike, 2002; Sremcevic et al.,2002; Kuchner and Holman, 2003).

Resonant trapping takes place when the orbital period ofthe planet is ðpþ qÞ=p times that of the particle, where p

and q are integers, p40 and pþ qX1. Taking into accountradiation pressure force, a=ap ¼ ½ðpþ qÞ=p�2=3 � ð1� bÞ1=3,where a and ap are the semimajor axis of the orbit of theparticle and of the planet, respectively, and b is the ratio ofthe radiation pressure force to the gravitational force. Eachresonance has a libration width Da, that depends on theparticle eccentricity and the planet mass, in which resonantorbits are stable, while resonance overlapping makes theregion close to the planet chaotic. When trapped in outerMMRs (q40), the dust particle receives energy from theinner planet, balancing the energy loss due to P–R drag.This makes the lifetime of particles trapped in outerMMRs longer than in inner MMRs, with the formerdominating the disk structure.

Kuchner and Holman (2003) pointed out that four basicresonant structures probably represent the range of high-

contrast resonant structures a planet with eccentricityt0:6can create in a disk of dust released on low eccentric orbits:(i) A ring with a gap at the location of the planet, (ii) asmooth ring, (iii) a clumpy eccentric ring, and (iv) an offsetring plus a pair of clumps. The appearance/dominance ofone of these structures mainly depends on the mass of theplanet and the eccentricity of its orbit (Fig. 8).The dust disk produced by the Kuiper Belt objects in our

own Solar System is an example of a debris disk withembedded massive planets in circular orbits. In the SolarSystem, the planet dominating the trapping of particles inMMRs is the outermost massive planet Neptune. Dyna-mical models show that the dust disk density is enhanced ina ring-like structure between 35–50AU, with someazimuthal variation due to the trapping into MMRs andthe fact that trapped particles tend to avoid the resonanceplanet, creating a minimum density at Neptune’s position.The effect of trapping into MMRs can clearly be seen in the‘‘equilibrium’’ semimajor axis distributions shown in Fig. 9and the disk surface density distributions shown in Fig. 10(from Moro-Martın and Malhotra, 2002). Both figuresshow how the dust disk structure is more pronounced forlarger particle sizes (smaller b) as the trapping in MMRs ismore efficient when the drag forces are small.One of the most prominent features in Figs. 9 and 10 is

the strong depletion of dust inside 10AU due to gravita-tional scattering of dust particles by Jupiter and Saturn.Moro-Martın and Malhotra (2005) explored how thiseffect depends on planet mass, semimajor-axis, eccentricity,

ARTICLE IN PRESSS. Wolf et al. / Planetary and Space Science 55 (2007) 569–581 577

and particle size. They found that planets with masses of3–10MJup located between 1–30AU eject 490% of theparticles that go past their orbits, while a 1MJup planet at30AU ejects 480% of the particles, and about 50–90% iflocated at 1AU, with these results being valid for particles

Fig. 9. Semimajor-axis distribution of Kuiper Belt dust particles, showing

the percentage of particles (in log scale) found at a particular semimajor-

axis. The different colors and line weights represent different particle sizes

or b-values with the black (thin), red (medium) and blue (heavy) lines

corresponding to b-values of 0.00156, 0.025 and 0.4, respectively (which

for astronomical silicates would correspond to particle sizes of 135, 8.8,

and 0:7mm, respectively) [from Moro-Martın et al., in prep.]

Fig. 10. Number density distribution of Kuiper Belt dust grains of different pa

center indicates the position of Neptune. As in the previous figure, the trappi

particles in the inner 10AU due to gravitational scattering with Jupiter and Sa

2002).

with b-values between 0.00156 and 0.4 (see Fig. 11). Thisresults in a lower dust number density within the planet’sorbit, as the dust grains drifting inward due to the P–Reffect are likely to be scattered into larger orbits.Inner cleared regions have been found in several debris

disks: b Pic (inner radius: 20AU), HR 4796A (30–50AU), �Eri (50AU), Vega (80AU), and Fomalhaut (125AU)—e.g., Dent et al. (2000), Greaves et al. (2000b), Wilner et al.(2002), Holland et al. (2003). These cavities may be createdby gravitational scattering with an inner planet.Krivov et al. (2000) pointed out that the P–R effect can

be ignored in disks with optical depths larger than about10�4 (see also Artymowicz, 1997). However, for SolarSystem analogs, fainter than the disks observed to date andthat telescopes like ALMA and DARWIN will be able todetect, P–R drag dominates the dynamics of the dustparticles and therefore, in that density regime, gravitationalscattering with massive planets is likely responsible for thecreation of inner cavities (if observed).Another two prominent examples for which the possible

influence of a planet on the disk structure has beendiscussed are the debris disks around Vega and b Pictoris.The first shows two dominating emission peaks/densityenhancements in spatially resolved submillimeter maps

rticle sizes, corresponding to different b-values. The dot to the right of the

ng of particles in the exterior MMRs with Neptune and the depletion of

turn are the most prominent features (from Moro-Martın and Malhotra,

ARTICLE IN PRESS

Fig. 11. (Left) Percentage of ejected particles (with b ¼ 0:044) as a function of planet mass for systems consisting on an outer belt of dust-producing

planetesimals and a single massive planet in a circular orbit. The different colors and line weights correspond to different planet semimajor-axis. (Right)

Percentage of ejected particles as a function of planet semimajor axis. The different colors and line weights correspond to different planet eccentricities

(from Moro-Martın and Malhotra, 2005).

2Single aperture far infrared telescope.3Terrestrial planet finder.4James Webb space telescope.


(Holland et al., 1998; Wilner et al., 2002). However, Suet al. (2005) did not confirm the existence of thesestructures, but found a circular, smooth brightnessdistribution without indications of clumpiness in highspatial resolution mid- and far-infrared images obtainedwith MIPS/Spitzer. The b Pictoris disk is seen nearly edge-on and extends to at least a distance of 100AU from thecentral star (Zuckerman and Becklin, 1993; Holland et al.,1998; Dent et al., 2000; Pantin et al., 1997). The northeastand southwest extensions of the dust disk have been foundto be asymmetric in scattered light as well as in thermalemission. This warp is assumed to be caused by a giantplanet on an inclined orbit that gravitationally perturbs thedust disk (Augereau et al., 2001; Mouillet et al., 1997, seealso Lubow and Ogilvie, 2001).

3.3. Signatures of planets in spatially unresolved debris disks

Besides high-resolution imaging of debris disks, mid-infrared spectroscopy is a valuable tool to deduce theexistence of an inner gap, since the deficiency of hot dust inthe stellar vicinity causes a decrease of the mid-infrared fluxcompared to an undisturbed disk. With increasing gap sizethe emission spectrum is shifted toward longer wavelengthsand the mid-infrared flux is reduced (see Fig. 12). Detailedstudies of the influence of planets on the SED of debrisdisks have been performed by Wolf and Hillenbrand (2003)and Moro-Martın et al. (2005). Moro-Martın et al. (2005),carried out a study on how the dust density structurecarved by massive planets affects the shape of the diskSED. The disk SED depends on the grain properties(chemical composition, density, and size distribution), themass, and location of the perturbing planet. They foundthat (1) the SED of a debris disk with embedded giantplanets is fundamentally different from that of a diskwithout planets, the former showing a significant decrease

of the near/mid-IR flux due to the clearing of dust insidethe planet’s orbit. (2) The SED is particularly sensitive tothe location of the planet, i.e., to the area interior to theplanet’s orbit that is depleted in dust (see Fig. 13, fromMoro-Martın et al., 2005). (3) There exist some degen-eracies that can complicate the interpretation of the SED interms of planet location. For example, the SED of a dustdisk dominated by weakly absorbing grains (e.g., Fe-poorsilicates) has its minimum at wavelengths longer than thoseof a disk dominated by strongly absorbing grains (e.g.,carbonaceous and Fe-rich silicate). Because the SEDminimum also shifts to longer wavelengths when the gapradius increases (owing to a decrease in the meantemperature of the disk), there might be a degeneracybetween the dust grain chemical composition and thesemimajor axis of the planet clearing the gap (see Fig. 14,from Moro-Martın et al., 2005).The Spitzer space telescope is carrying out spectro-

photometric observations of hundreds of circumstellardisks most of which are spatially unresolved. The study ofthese SEDs can help us diagnose the radial distribution ofdust, allowing us to identify targets where the dynamicalimprints of embedded giant planets may be present (e.g.,Kim et al., 2005; Beichman et al., 2005). But because theSEDs are degenerate, to unambigously constrain the planetlocation we need to obtain high resolution images able tospatially resolve the disk. In the future, telescopes likeALMA, SAFIR2, TPF3, DARWIN and JWST4 will be ableto image the dust in planetary systems analogous to ourown. If observed from afar, the Kuiper Belt dust diskwould be the brightest extended feature in the solar system,and its structure, if spatially resolved, could be recognized

ARTICLE IN PRESS

Fig. 12. Influence of an inner gap on the SED of a debris disk. Inner disk radius: dust sublimation radius (solid line), 0.1AU (dotted), 1AU (dashed), and

10AU (dash-dotted). Left/right column: Fe-poor silicate (MgSiO3)/Fe-rich Silicate (Olivine, MgFeSiO4). Top: a ¼ 0:1mm, Bottom: a ¼ 1mm. Disk mass:

10�10Msun. The central star has a solar-type SED (we use the solar SED published by Labs and Neckel (1968), extended by a blackbody SED beyond

151mm). The distance to the system is assumed to be 50 pc (from Wolf and Hillenbrand, 2003).

Fig. 13. SEDs of dust disks in the presence of different planetary

configurations (solid: 3MJup at 1AU; dashed: 3MJup at 5AU; dashed-

dotted: 3MJup at 30AU; dotted: system without planets). Results are

shown for three grain chemical compositions (indicated in each panel),

and particle size distribution given by nðbÞdb ¼ n0b�q with q ¼ 3:0. In all

cases the system is at a distance of 50 pc and has a total disk mass of 10�10

Msun (from Moro-Martın et al., 2005).


as harboring at least two giant planets: an inner planet(Jupiter plus Saturn) and outer planet (Neptune) (Liouet al., 1996; Moro-Martın and Malhotra, 2002). The goal isthat high-resolution, high-sensitivity imaging of debrisdisks around other stars will help us to learn about thefrequency and diversity of planetary systems, helping usplace our solar system into context.

4. Summary

Numerical simulations convincingly demonstrate thathigh-resolution imaging performed with instruments/tele-scopes that will become available in the near future willallow detection of planets in circumstellar disks. However,scattering of stellar light and thermal emission by smallgrains—in the case of optically thick disks seen at highinclination also absorption—will make direct planet detec-tion via imaging hardly feasible. But planets cause large-scale perturbations in the disks which will be observablewith observatories like the Stratospheric Observatory For

Infrared Astronomy (SOFIA), the James Webb Space

Telescope (JWST), but also ground-based observatories/

ARTICLE IN PRESS

Fig. 14. Left: Possible degeneracy between the grain chemical composition and the location of the planet clearing the gap. Solid line: SED of a dust disk

composed of MgSiO3 grains with a 3MJup planet at 1AU; dashed line: same for MgFeSiO4 grains with a 3MJup planet at 30AU. In both cases q ¼ 2:5.Right: brightness density distributions at 70mm (assuming graybody emission from 12mm grains) expected from a disk with a 3MJup planet at 1AU (top)

and 30AU (bottom), respectively (shown in arbitrary units). High resolution images are needed to solve the degeneracy (from Moro-Martın et al., 2005).


interferometers, such as ALMA or the VLTI by spatiallyresolved mapping of the dust reemission. The particulartype of perturbation depends on the evolutionary stage ofthe disk. The most prominent signatures of planetsembedded in disks are gaps and circumplanetary accretiondisks in the case of young disks and characteristicasymmetric density patterns in debris disks. Furthersignatures are, for instance, spiral structures in youngdisks or warps due to planets on inclined orbits.

Acknowledgement

S.W. is supported by the German Research Foundation(DFG) through the Emmy Noether Grant WO 857/2-1.A.M.M. is under contract with the Jet PropulsionLaboratory (JPL) funded by NASA through the MichelsonFellowship Program. JPL is managed for NASA by theCalifornia Institute of Technology. AMM is also sup-ported by the Lyman Spitzer Fellowship at PrincetonUniversity. G.D. is grateful to the Leverhulme Trust forsupport under a UKAFF (UK Astrophysical FluidsFacility) Fellowship.

References

Adams, F.C., Lada, C.J., Shu, F.H., 1987. Astrophys. J. 312, 788.

Artymowicz, P., 1997. Annu. Rev. Earth Planet. Sci. 25, 175.

Artymowicz, P., Burrows, C., Paresce, F., 1989. Astrophys. J. 337, 494.

Augereau, J.C., Nelson, R.P., Lagrange, A.M., Papaloizou, J.C.B.,

Mouillet, D., 2001. Astrono. Astrophys. 370, 447.

Bate, M.R., Lubow, S.H., Ogilvie, G.I., Miller, K.A., 2003. Mon. Not. R.

Astron. Soc. 341, 213.

Beckwith, S.V.W., Sargent, A.I., Chini, R.S., Guesten, R., 1990. Astron. J.

99, 924.

Beichman, C.A., Bryden, G., Rieke, G.H., Stansberry, J.A., Trilling, D.E.,

Stapelfeldt, K.R., Werner, M.W., Engelbracht, C.W., Blaylock, M.,

Gordon, K.D., Chen, C.H., Su, K.Y.L., Hines, D.C., 2005. Astrophys.

J. 622, 1160.

Briggs, R.E., 1962. Astron. J. 67, 710.

Bryden, G., Chen, X., Lin, D.N.C., Nelson, R.P., Papaloizou, J.C.B.,

1999. Astrophys. J. 514, 344.

Bryden, G., Beichman, C.A., Trilling, D.E., Rieke, G.H., Holmes, E.K.,

Lawler, S.M., Stapelfeldt, K.R., Werner, M.W., Gautier, T.N.,

Blaylock, M., Gordon, K.D., Stansberry, J.A., Su, K.Y.L., 2006.

ApJ 636, 1098.

Burrows, A., Marley, M., Hubbard, W.B., Lunine, J.I., Guillot, T., et al.,

1997. Astrophys. J. 491, 856.

Calvet, N., D’Alessio, P., Hartmann, L., Wilner, D., Walsh, A., Sitko, M.,

2002. ApJ 568, 1008.

D’Angelo, G., Henning, Th., Kley, W., 2002. Astrono. Astrophys. 385,

647.

D’Angelo, G., Kley, W., Henning, Th., 2003. Astrophys. J. 586, 540.

Dent, W.R.F., Greaves, J.S., Mannings, V., Coulson, I.M., Walther,

D.M., 1995. Mon. Not. R. Astron. Soc. 277, L25.

Dent, W.R.F., Walker, H.J., Holland, W.S., Greaves, J.S., 2000. Mon.

Not. R. Astron. Soc. 314, 702.

Dermott, S.F., Durda, D.D., Gustafson, B.A., Jayaraman, S., Xu, Y.L.,

Gomes, R.S., Nicholson, P.D., 1992. In: Harris, A.W., Bowell, E.

(Eds.), Asteroids, Comets, Meteors, p. 153.

Dominik, C., Decin, G., 2003. Astrophys. J. 598, 626.

Epifani, E., Colangeli, L., Fulle, M., Brucato, J.R., Bussoletti, E., de

Sanctis, M.C., Mennella, V., Palomba, E., Palumbo, P., Rotundi, A.,

2001. Icarus 149, 339.

Fixsen, D.J., Dwek, E., 2002. Astrophys. J. 578, 1009.

Fridlund, C.V.M., 2000. Darwin—The Infrared Space Interferometry

Mission. ESA Bull. 103, 20.

Goldreich, P., Ward, W.R., 1973. Astrophys. J. 183, 1051.

Gor’kavyi, N.N., Ozernoy, L.M., Mather, J.C., Taidakova, T., 1997.

Astrophys. J. 488, 268.

Grady, C.A., Sitko, M.L., Russell, R.W., Lynch, D.K., Hanner, M.S.,

Perez, M.R., Bjorkman, K.S., de Winter, D., 2000. In: Mannings, V.,

Boss, A.P., Russell, S.S. (Eds.), Protostars and Planets IV. University

of Arizona Press, p. 613.

ARTICLE IN PRESSS. Wolf et al. / Planetary and Space Science 55 (2007) 569–581 581

Greaves, J.S., Holland, W.S., Moriarty-Schieven, G., Jenness, T., Dent,

W.R.F., Zuckerman, B., McCarthy, C., Webb, R.A., Butner, H.M.,

Gear, W.K., Walker, H.J., 1998. Astrophys. J. 506, L133.

Greaves, J.S., Coulson, I.M., Holland, W.S., 2000a. Mon. Not. R. Astron.

Soc. 312, L1.

Greaves, J.S., Mannings, V., Holland, W.S., 2000b. Icarus 143, 155.

Greaves, J.S., Holland, W.S., Jayawardhana, R., Wyatt, M.C., Dent,

W.R.F., 2004. Mon. Not. R. Astron. Soc. 348, 1097.

Guilloteau, S., 2002. ALMA Memo, 393.

Gurfil, P., Kasdin, J., Arrell, R., Seager, S., Nissanke, S.M., 2002.


Habing, H.J., Dominik, C., Jourdain de Muizon, M., Laureijs, R.J.,

Kessler, M.F., Leech, K., Metcalfe, L., Salama, A., Siebenmorgen, R.,

Trams, N., Bouchet, P., 2001. Astrono. Astrophys. 365, 545.

Holland, W.S., Greaves, J.S., Zuckerman, B., Webb, R.A., McCarthy, C.,

Coulson, I.M., Walther, D.M., Dent, W.R.F., Gear, W.K., Robson, I.,

1998. Nature 392, 788.

Holland, W.S., Greaves, J.S., Dent, W.R.F., Wyatt, M.C., Zuckerman, B.,

Webb, R.A., McCarthy, C., Coulson, I.M., Robson, E.I., Gear, W.K.,

2003. Astrophys. J. 582, 1141.

Hubbard, W.B., Burrows, A., Lunine, J.I., 2002. Annu. Rev. Astronomy

Astrophys. 40, 103.

Ishimoto, H., 2000. Astrono. Astrophys. 362, 1158.

Kalas, P., Jewitt, D., 1995. Astrophys. J. 110, 794.

Kalas, P., Liu, M.C., Matthews, B.C., 2004. Science 303, 1990.

Kim, J.S., Dean, D.C., Backman, D.E., et al., 2005. Astrophys. J. 632,

659.

Kley, W., 1999. Mon. Not. R. Astron. Soc. 303, 696.

Koerner, D.W., Sargent, A.I., Beckwith, S.V.W., 1993. Icarus 106, 2.

Koerner, D.W., Sargent, A.I., Ostroff, N.A., 2001. Astrophys. J. 560,

L181.

Krivov, A.V., Mann, I., Krivova, N.A., 2000. Astrono. Astrophys. 362,

1127.

Kuchner, M.J., Holman, M.J., 2003. Astrophys. J. 588, 110.

Labs, D., Neckel, H., 1968. Zeitschrift fur Astrophysik 69, 1.

Lecavelier des Etangs, A., Vidal-Madjar, A., Ferlet, R., 1998. Astrono.

Astrophys. 339, 477.

Lecavelier des Etangs, A., Vidal-Madjar, A., Roberge, A., Feldman, P.D.,

Deleuil, M., Andre, M., Blair, W.P., Bouret, J.-C., Desert, J.-M.,

Ferlet, R., Friedman, S., Hebrard, G., Lemoine, M., Moos, H.W.,

2001. Nature 412, 706.

Liou, J.C., Zook, H.A., 1999. Astron. J. 118, 580.

Liou, J.-C., Dermott, S.F., Xu, Y.-L., 1995. Planet. Space Sci. 43, 717.

Liou, J.C., Zook, H.A., Dermott, S.F., 1996. Icarus 124, 429.

Liseau, R., Artymowicz, P., 1998. Astrono. Astrophys. 334, 935.

Liseau, R., Brandeker, A., Fridlund, M., Olofsson, G., Takeuchi, T.,

Artymowicz, P., 2003. A&A 402, 183.

Lissauer, J.J., 1993. Annu. Rev. Astronomy Astrophys. 31, 129.

Lopez, B., Wolf, S., Dugue, M., Graser, U., Mathias, Ph., et al. 2006.

Aperture synthesis in the MID-infrared (10mm) with the VLTI. In:

Proceedings of The Power of Optical/Infrared Interferometry: Recent

Scientific Results and Second Generation VLT Instrumentation.

Garching, 2005, in press, Germany.

Lubow, S.H., Ogilvie, G.I., 2001. Astrophys. J. 560, 997.

Lubow, S.H., Seibert, M., Artymowicz, P., 1999. Astrophys. J. 526, 1001.

Marcy, G., Butler, R.P., Fischer, D., Vogt, S., Wright, J.T., Tinney, C.G.,

Jones, H.R.A., 2005. Prog. Theoret. Phys. Suppl. 158, 24.

Meyer, M.R., Hillenbrand, L.A., Backman, D.E., Beckwith, S.V.W.,

Bouwman, J., Brooke, T.J., Carpenter, J.M., Cohen, M., Gorti, U.,

Henning, Th., Hines, D.C., Hollenbach, D., Kim, J.S., Lunine, J.,

Malhotra, R., Mamajek, E.E., Metchev, S., Moro-Martın, A., Morris,

P., Najita, J., Padgett, D.L., Rodmann, J., Silverstone, M.D.,

Soderblom, D.R., Stauffer, J.R., Stobie, E.B., Strom, S.E., Watson,

D.M., Weidenschilling, S.J., Wolf, S., Young, E., Engelbracht, C.W.,

Gordon, K.D., Misselt, K., Morrison, J., Muzerolle, J., Su, K., 2004.

Astrophys. J. Suppl. Ser. 154, 422.

Moro-Martın, A., Malhotra, R., 2002. Astron. J. 124, 2305.

Moro-Martın, A., Malhotra, R., 2003. Astron. J. 125, 2255.

Moro-Martın, A., Malhotra, R., 2005. Astrophys. J. 633, 1150.

Moro-Martın, A., Wolf, S., Malhotra, R., 2005. Astrophys. J. 621, 1079.

Moro-Martın, A., Wolf, S., Malhotra, R., 2006, in preparation.

Mouillet, D., Larwood, J.D., Papaloizou, J.C.B., Lagrange, A.M., 1997.

Mon. Not. R. Astron. Soc. 292, 896.

Nelson, R.P., Papaloizou, J.C.B., 2003. Mon. Not. R. Astron. Soc. 339,

993.

Ozernoy, L.M., Gorkavyi, N.N., Mather, J.C., Taidakova, T.A., 2000.


Pantin, E., Lagage, P.O., Artymowicz, P., 1997. Astrophys. J. 327, 1123.

Pety, J., Gueth, F., Guilloteau, S., 2001. ALMA Memo. 398.

Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak,

M., Greenzweig, Y., 1996. Icarus 124, 62.

Quillen, A.C., Thorndike, S., 2002. Astrophys. J. Lett. 578, 149.

Rice, W.K.M., Wood, K., Armitage, P.J., Whitney, B.A., Bjorkman,

J.E., 2003. MNRAS 342, 79.

Rieke, G.H., Su, K.Y.L., Stansberry, J.A., et al., 2005. Astrophys. J. 620,

1010.

Schneider, G., Smith, B.A., Becklin, E.E., et al., 1999. Astrophys. J. 513,

L127.

Spangler, C., Sargent, A.I., Silverstone, M.D., Becklin, E.E., Zuckerman,

B., 2001. Astrophys. J. 555, 932.

Sremcevic, M., Spahn, F., Duschl, W.J., 2002. Mon. Not. R. Astron. Soc.

337, 1139.

Su, K.Y.L., Rieke, G.H., Misselt, K.A., Stansberry, J.A., Moro-Martin,

A., et al., 2005. Astrophys. J. 628, 487.

Sykes, M.V., 1988. Astrophys. J. 334, L55.

Weidenschilling, S., 1997. Icarus 127, 290.

Weinberger, A.J., Becklin, E.E., Zuckerman, B., 2003. Astrophys. J. 584,

L33.

Whipple, F.L., 1976. In: Interplanetary Dust and Zodiacal Light.

Springer, Berlin, New York, 1976, p. 403.

Wilner, D.J., Holman, M.J., Kuchner, M.J., Ho, P.T.P., 2002. Astrophys.

J. 569, L115.

Wolf, S., 2003. Comput. Phys. Comm. 150, 99.

Wolf, S., D’Angelo, G., 2005. Astrophys. J. 619, 1114.

Wolf, S., Hillenbrand, L.A., 2003. Astrophys. J. 596, 603.

Wolf, S., Henning, Th., Stecklum, B., 1999. Astrono. Astrophys. 349,

839.

Wolf, S., Gueth, F., Henning, Th., Kley, W., 2002. Astrophys. J. 566, L97.

Wolf, S., Lopez, B., and The MATISSE Consortium, 2006. MATISSE.

Interferometric imaging in the mid-infrared. In: Rouan, D., Foresto,

V. (Eds.), Proceedings of the Conference on Visions for Infrared

Astronomy, in press.

Wyatt, M.C., 2003. Astrophys. J. 598, 1321.

Wyatt, M.C., Dent, W.R.F., 2002. Mon. Not. R. Astron. Soc. 334, 589.

Wyatt, M.C., Dermott, S.F., Telesco, C.M., 1999. Astrophys. J. 527, 918.

Youdin, A.N., Shu, F.H., 2002. Astrophys. J. 580, 494.

Zuckerman, B., Becklin, E.E., 1993. Astrophys. J. 414, 793.

Zuckerman, B., Forveille, T., Kastner, J.H., 1995. Nature 373, 494.

Documents

Signatures of planets in protoplanetary and debris disks