Debris discs and comet populations around Sun-like stars: the Solar System in context

0.25 MB·English

by  J. S. Greaves

Mon.Not.R.Astron.Soc.000,1–8(2009) Printed28January2010 (MNLATEXstylefilev2.2)
Debris discs and comet populations around Sun-like stars:
the Solar System in context
0 J. S. Greaves1⋆ & M. C. Wyatt2
1
0 1SUPA, Physics & Astronomy, Universityof St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK
2 2 Institute of Astronomy, Universityof Cambridge, Cambridge CB3 0HA, UK

n
a
J Accepted 2009.Received2009;inoriginalform2009

8
2
ABSTRACT

]
P Numerous nearby FGK dwarfs possess discs of debris generated by collisions
E among comets. Here we fit the levels of dusty excess observed by Spitzer at 70 µm
. and show that they form a rather smooth distribution. Taking into account the tran-
h
sitionofthe dustremovalprocessfromcollisionalto Poynting-Robertsondrag,allthe
p
stars may be empirically fitted by a single population with many low-excess mem-
-
o bers.Withinthisensemble,theKuiperBeltisinferredtobe suchalow-dustexample,
r among the last 10 % of stars, with a small cometary population. Analogue systems
t
s hostinggasgiantplanetsandamodestcometbeltshouldoccurforonlyafewpercent
a ofSun-likestars,andsoterrestrialplanetswithacomparablecometaryimpactrateto
[
the Earth may be uncommon. The nearest such analogue system presently known is

1 HD 154345at18pc, but accountingfor surveycompleteness,a closerexample should
v lie at around 10 pc.
7
7 Key words: planetary systems – circumstellar matter – infrared: stars
1
5
.
1
0 1 INTRODUCTION systemwillstronglyaffecttheimpactrateonanyterrestrial
0 planetspresent.Directevidenceofimpactsintheinnersys-
1 Impacts pose a hazard to life on Earth, especially in the
tems comes from detections of dust grains at temperatures
: case of an event energetic enough to destroy much of the
v of afew hundredKelvin,representingbreak-updebrisfrom
surfacecrust andoceans(Zahnle et al. 2007).Themost de-
i parentplanetesimals.Suchdetectionsviaamid-infraredex-
X structiveimpactsareassociatedwithcometsratherthanas-
cess signal above the stellar photosphere are rare, but this
r teroids,astheformerhitathighspeedswheninfallingfrom does not imply that inner system planetesimals and plane-
a theKuiperBeltregion(Jeffers et al.2001),butthepresent-
tary impacts are sparse, as the debris lifetime at a few AU
day cometary impact rate is low, largely because most of
is short (Wyatt 2005). Less directly, we can examine the
theprimordialbodieshavebeendispersed(Morbidelli et al.
far-infrared debrissignatures to assess thenumbersof bod-
2003). This is thought to have occurred in the first Gyr of
iescolliding withinthecooloutercometbelts,andconsider
theSun’slife,whenJupiterandSaturncrossedameanmo-
the influence of gas giants in perturbing comets inwards to
tion resonance, destabilising the gas giants so that Saturn
where they threaten terrestrial planets.
hadcloseencounterswithUranusandNeptune.Theexpan-
sion of their orbits perturbed the primordial Kuiper Belt Here we use the results of recent volume-limited sur-
(Gomes et al. 2005), producing the Late Heavy Bombard- veys of Sun-like stars with Spitzer by Trilling et al. (2008)
mentoftheEarthataround700Myr,afterwhichthecomet and Beichman et al. (2006) to study thedustiness of Solar-
population was greatly depleted and the impact frequency analogue systems, via the predominantly 70 µm detections
hasbeenmuchlower.However,thepresenceofthegasgiants of excess above the stellar photospheres. Various analytical
isstillsignificanttoday,asdynamicalinteractionscanbring models, as reviewed by Wyatt (2008), predict far-infrared
cometsintotheinnerSolarSystem–Horner & Jones(2008) dustluminosities asfunctionsofinitialsizeandmassof the
haverecentlyshownthattheimpactrateontheEarthwould planetesimal discandtheageofthehoststar.Thustheex-
vary significantly if the mass of Jupiterwere different. cesses detected by Spitzer can be related to the ensemble
Thus, in extrasolar systems we may expect that the of populations of comets per star. We can then place the
number of comets and the architecture of the giant-planet Sun’sKuiperBelt,forwhich therearemeasurementsof the
numbers and distribution of comets and dust particles, in
thecontext ofsimilar stars. Forexample,othersystems are
⋆ E-mail:jsg5atst-andrews.ac.uk knownthatarehundredsoftimesdustierthantheSolarSys-
2 J. S. Greaves et al.
Figure 1. Sun-likestars inorder of decreasing 70 µm excess (y-axis). The rankon the x-axis isthe star’s number (e.g. 1for the most
dusty)dividedbythenumberofstarssurveyed.Upperlimitsarenotplotted.Thediamondsshowcontiguousdebrisdetectionswhilethe
fourpointsplottedwithcircleshaveinterveningsystemswithonlyupperlimitsinE70;thespacingofthesesparsedetections isderived
asdescribedinsection3.1.Theblackcurveisapower-lawfitforstarsofE70 downto0.5,excludingthefoursparsedetections oflower
excess.Thegreylineisanextrapolationtolowerexcessesincludingdustremovaltheory(section3.4),notafittothefourcirclesymbols.
Thedashedlineshowsthe 2.5σ upper limittothenet E70 forstarswheredetections beyond x=0.3couldbemade(section 3.2). The
circle symbol (far right) is the position of the Sun in the ensemble, derived from its maximum estimated dust level (section 4.1) and
plottedatitscorrespondinglowestrankonthegreycurve.ThebarsindicatethattheSunmaybelessdustyandsoofhigherrank.
tem;dustieratgreateragethantheSun;orhavemuchlarger sigmaconfidenceinallthestars,sothereisapotentialbias
debris belts. Viewed externally as a debris disc, the Kuiper where faint stars rise above the detection threshold of to-
Belt would be faint, a result which motivates this study to tal flux only in cases of large excess. To avoid this, we se-
answerthequestionofwhethertheplanetandplanetesimal lected only the objects with F∗/δF > 3, where F∗ repre-
populationaroundtheSunisunusual,andwhetherthishas sents the photosphere and δF is the noise in the flux mea-
any role in impacts on theEarth and the evolution of life. surement. This selection includes 176 stars from the two
combined surveys, after also eliminating a number of M-
dwarfs from Beichman et al. (2006). The excesses are then
2 DATA defined as E70 = Fdust/F∗ = (Ftotal−F∗)/F∗. All further
analysis uses the fluxes and errors listed by Trilling et al.
Two major unbiased surveys of nearby Solar analogues (2008); Beichman et al. (2006) along with their othertabu-
have been made with Spitzer, with debris detection rates lated quantities, such as estimates for stellar ages.
of ≈15 % at 70 µm, for fractional excesses of a few Thesurveypapersidentifydebrissystemsasthosewith
tenths or more above the photosphere (Trilling et al. 2008; E70 at 3σ confidence, i.e. χ70 = Fdust/δF > 3, here com-
Beichman et al. 2006). The FGK targets in these two sam- prising 27 stars. Here we add 6 more candidate systems of
ples are complementary and extend out to ∼ 30 pc from slightly lower significance. A tabulation of all 176 E70 val-
the Sun; a further survey (Kim et al. 2007) will com- ues,inorderofχ70,showsthatnegativeoutliersextenddown
plete much of this volume. We neglect here results from to −2.5σ, and this distribution is quite symmetric, with 70
theFEPS project (Hillenbrand et al. 2008;Carpenter et al. stars of 0 6 χ70 6 +2.5 versus 73 of −2.5 6 χ70 < 0. Fur-
2009; Meyer et al. 2008) where stars were selected by age, ther,thisχ70distributionisclosetoaGaussiancentredona
and so there is a trend of lower sensitivity for younger and nullvalue,withmeanandsigmaof-0.03and1.2respectively.
thus rarer and more distant stars. The published nearby- We thus adopt here as candidate debris systems all those
volume samples also have some biases that are inherited with >+2.5σ significance, and estimate that the chance of
fromthegoalsoftheoriginalproposals,withmoreluminous afalse positiveis.1.5 %perstar,given that<1moreex-
stars,hostsofgiantplanetsandsinglestarsover-represented treme outliers appear among 73 negative results. With this
compared to theirtrue proportions among Sun-likestars. new selection criterion, there are 33 systems identified here
Only 70 µm data of high quality from Trilling et al. as debris hosts1 , or 19 % of thestars observed.
(2008) and Beichman et al. (2006) are discussed here, trac-
ing cool dust at tens to hundreds of AU from the host
star. The photospheric signal was not detectable with 3- 1 Those of 2.5-2.9σ confidence are HD 39091, 55575, 69830,
Comets populations around Sun-like stars 3
Figure 2. Debris properties of the sample, in logarithmic age Figure 3. Detected debris systems, showing stellar properties.
bins.Thegreybarsshow theminimum-to-maximumE70 within Small, medium and large symbols correspond to the early, mid
each bin, and the points (and Poisson error bars) indicate the and late age-bins respectively of Figure 2, and light and dark
percentage ofstarswithdebris.Thenumberofsystemsdetected greyshadings pickoutthe mostandleastluminousstars(early-
(observed)ineachagebinfromlefttorightis3(12),9(45)and F and K types respectively). Points within circles are systems
19(99), with18starshavingnotabulated ages. hostinggiantplanets(fromtheExtrasolarPlanetsEncyclopedia)
and those within squares have multiple stars (from the Catalog
ofComponents ofDoubleandMultipleStars).
3 ANALYSIS
2006) and these are likely to be the minimum inherited er-
3.1 Detected population
rorswhenattemptingtodetectlowlevelsofdebrisat70µm.
Figure 1 plots the 70 µm excesses of the stars where debris There is no strong trend of level or incidence of debris
is identified,ordered bya fractional ‘rank’. Therank is for- withparticularstellarproperties.Forexample,thereislittle
mulated as the number of the star in order of decreasing trendwithage,asalreadynotedbye.g.Trilling et al.(2008);
E70, dividedbythetotal numberof stars (176). Itis equiv- Beichman et al. (2006); Greaves & Wyatt (2003). Figure 2
alent to the fraction of stars with equal or higher E70 than shows the sample divided into three broad bins each span-
the current plotted point. However, beyond a rank of 0.1, ningafactor of ≈4in age(tominimise errorsfrom poorly-
not all the stars were observed to sufficient depth to detect dated objects). The detection rate is essentially flat with
the corresponding E70 of approximately 0.8 and below, if age over the entire main sequence, while maximum dusti-
suchexcessesarepresent.Thistendencyisinfactimplicitin ness declines mildly with age – a similar decline has been
the initial selection, as δE70 =δF/F∗ and so where F∗/δF seen for 70 µm excesses of A-type stars (Suet al. 2006).
approaches 3, only E70 > 0.83 can be detected with 2.5σ Thesetrendsagreewithrecentevolutionarymodelsassum-
confidence. In this regime, there are four debris detections marisedbyWyatt(2008),whereeachsystem’sdustinessde-
(circles in Figure 1) that are interleaved with upper limits clinesslowlywithtimeastheparentpopulationofcolliding
of similar E70, but the ranks of the non-detections can not bodies is ground away. Iftheinitial planetesimal discs have
be determined as the true debris levels are unknown. How- awiderangeofradiiandmasses, thenthereisawiderange
ever, plotting these four points as contiguous ranks causes of excess values at any one age, and the detection rate is
an artificial downturn in the trend of excess, because simi- ratherconstantwithtimeiftheupperenvelopeofmaximum
larsystemsshouldoccurinthisregionbutwerenotactually dustfluxiswellabovethedetectionlimit(Greaves & Wyatt
observed deeply enough to bedetected. Thus for these four 2003).
points,estimatedranksareplotted,byincreasingthestepon Further, there are only weak trends associated with
thex-axisfrom 1/176, to1/176 multiplied byascale factor other stellar properties, such as luminosity, binarity and
of (numberof stars still tobecounted) dividedby (number the presence of giant planets (Beichman et al. 2006;
of stars where thenext E70 could bedetected). These stars Bryden et al.2006;Trilling et al.2007).Figure3replotsthe
withE70 ≈0.4werenumbers30to33inorderofdecreasing debris hosts of Figure 1 with symbols denoting these prop-
dustiness,andtheiroriginalranksof0.17to0.19(30/176to erties,andnoobvioustrendsarevisible.Infurtheranalysis,
33/176) havebeen increased to 0.21 to 0.30. all the stars are therefore treated as a single population.
The excesses observed range from 17 down to 0.4, al-
though only about one in five stars was observed deeply
3.2 Trend in debris level
enough to detect debris at thislower bound.The minimum
detectable excess for Spitzer, where generally the dust and The ranked plot (Figure 1) shows that the excesses form a
star lie within the same telescope beam, is set by uncer- rather smoothly declining distribution, dominated by lower
tainty in the photospheric predictions plus errors in the values of E70. The steep slope can explain how the rate
shorter-wavelengthdatausedforextrapolation.Dispersions of far-infrared debris detection among Sun-like stars has
in24 µmdataofaround5% areobserved(Beichman et al. risen with improvements in sensitivity with successive in-
struments,namelytheIRAS,ISOandSpitzermissions.For
example,a typicalG-dwarf photosphere at 15 pchas aflux
114613, 173667and222237; HD69830isaconfirmeddebrissys- of approximately 30 mJy at 60 µm (Habing et al. 2001),
temwithshorter-wavelengthexcesses (Trillingetal.2008). whiletheIRASall-skysurveycoulddetectsignalsofaround
4 J. S. Greaves et al.
for the mean value and standard error on the mean3. This
KS–Test Comparison Cumulative Fraction Plot is not a significant detection of net excess, so the sugges-
1.0 tion of a typical excess of 0.05 by Aumann& Good (1990)
(at60µm)cannotbeconfirmed.However,it doesallow all
.8 systemstobeslightly dusty,orsometohavemodest excess
while others are dust-free, as well as the possibility that all
Cumulative Fraction ..64 uoaslnrriegelyhd4t)5u,4ssbtk%-uelwettsahst.aoKAtwomtalhmrodisonsggpmootrshooiretveis-veSepm2ot4isariittnlaiovarvgereetEtefsrs7ot0tmhfimenraedeasdmsiauffarpeyerrmeoinnbetnafabt(csii.ltei(t.bFydeigoea--f
brisdisc)population.Thereforethereisasyetnoconclusive
.2 result, but this does not rule out many low-dust systems.
As a small excess is characteristic of the Solar System, at-
temptingtoinfertheunderlyingpopulationisusefultoput
0
theSun in context.
0 .05 .10 .15 .20 .25
X
3.3 Single population hypothesis
Figure4.CumulativedistributionsofmeasuredE70(Xaxis)for
24 upper-limit systems discussed in the text. These have small Wefirsttestthesimplestpossiblehypothesis,thatallSolar-
E70 errorsof60.15andsothedistributionisaguidetowhether type stars have debris discs drawn from a single distribu-
a net positive excess may be present. Positive values (solidline) tion. A suitable function is sought that fits the excesses,
arecomparedtonegativevalues thathave beenmultipliedby-1 plus information in the low net excess for systems that are
(dashedline).
not detected. The single-population hypothesis is unlikely
to explain all systems completely, but provides a testable
empirical approach.
200 mJy (Wyatt 2005) and thecorresponding limit for ISO Figure 1 shows (black line) a best fit to the debris de-
wasaround90mJy(Decin et al.2000).ThusIRASandISO tections with E70 =0.5 to17, given by
could detect E60 ∼ 6 and 3 respectively. Of the stars plot-
tedinFigure1,wewouldthenexpectabout3brightexam- E70 =0.09x−1.08 (1)
ples to be discovered by IRAS, and HD 139664, 48682 and
where x is the star rank, and the correlation coefficient is
109085 were actually found. Subsequently, ISO could have
0.98.Thesingle-populationhypothesisisthusarathergood
discovered ∼6 less-dusty systems, while the sparse surveys
empirical fit to the systems detected, in spite of the wide
actually undertaken added two discoveries2, HD 30495 and
rangeofstellarages,spectraltypes,etc.TheregimeatE70 <
17925
0.5 was excluded as a different dust behaviour is predicted
The large sensitivity improvement with Spitzer has
(see below), and includes only 4 detected systems.
more than tripled the discoveries of debris systems among
If the Equation 1 fit continued for all ranks up to 1,
these nearby stars, suggesting that more fainter exam-
then the last star would have E70 of 0.09, and the mean
ples remain to be discovered. However, debris levels in the
in the undetected population at x > 0.3 would be 0.16. If
presentlyundetectedpopulation areinferred tobesmall on
thisextrapolationapplied,moredetectionsshouldhavebeen
average. Aumann & Good (1990) suggested that a net ex- made,givena3-sigmathresholdof∼0.15setbyuncertain-
cess of ∼0.05 might bepresent, from IRAS60 µm data for ties ∼ 0.05 in the photospheric levels as discussed above.
G-stars within 25 pc. The Spitzer 70 µm data now explore
Also, the true mean is unlikely to be so high, as among
this regime lying at theright of Figure 1, although individ-
the 24 stars with the smallest excess-errors, there are only
ualexcessesarestillnotdetected.Forexample,thereare24 fourobjectswithE70 measurementtsevenashighas∼0.25
stars with Spitzer observations deep enough that excesses (2.5σ upperlimits∼0.4). Thissuggests adrop industiness
rangingfrom 3%to37%could havebeendetected,ifsuch
among themajority population of stars.
dustlevelswereactually presentin thesesystems.(Herewe
neglecttheuncertaintiesduetocalibrationandjustconsider
signals of 2.5 times the noise level.) These stars are part of 3.4 Dust generation
the population at star-rank > 0.3 in Figure 1, and none of
them has a significant measurement of excess, but thedata The hypothesis above assumes one distribution for the
are deep enough that a tendency to mildly positive values amountofdustperstar,butgivensomerangeofinitialcir-
canbesearchedfor.Inparticular,stackingthedatacanshow cumstellar disc properties, it is more likely that the quan-
ifthereisevidenceforanaveragenon-zerodustinessthatis tity of comets per star forms the underlying distribution.
not apparent in each individual noisy observation. Averag- In this case, the amount of dust generated needs to take
ing the measured E70 for these 24 stars we find 0.03±0.02
3 Thenet value from all stars without debris detections is simi-
larat−0.01±0.02butismoreinfluencedbyunphysicalnegative
2 Five other fainter debris systems in Figure 1 were also in excesses, down toE70 =−0.7.These mayindicate uncertainties
fact candidates from IRAS/ISO, where fainter excesses could be in the photospheric models, with the two lowest values corre-
probed for various reasons, such as stellar proximity, or hotter spondingtostars attheextremes ofthespectral type range, for
photospheres orwarmerdustthanaverage. example.
Comets populations around Sun-like stars 5
into account the dust removal processes, and as discussed are similar at 60 and 70 µm but the photosphere is fainter
by Dominik & Decin (2003), this depends on the number byafactorof0.5±0.1intheSpitzerdata,from6G-dwarfsin
of colliding bodies. In massive discs, the dominant destruc- commonandwith nodebris.Hence,weadoptE70 =1.5for
tive mechanism is collisional and N ∝ N , while τ Ceti,whilefortheparametersofthissystemE ≈0.85,
dust comets crit
in diffuse discs where the Poynting-Robertson (light drag) and so EτCeti ≈ Ecrit×1.8. Since τ Ceti has an estimated
effect removes dust, Ndust ∝ Nc2omets. This distinction be- 1.2M⊕ ofcollidingbodiesofradiir625km(Greaves et al.
tween high- and low-mass discs, in the collisional and PR- 2004), under the assumption of a collisional cascade with
drag dust removal regimes respectively, is also discussed by incremental population dN(r) ∝ r−3.5, then E would
crit
Meyer et al. (2007). correspond to0.7M⊕.However,models (L¨ohneet al.2008,
Wyatt (2005) has shown that the discs readily de- e.g.) consider colliders up to r = 75 km, so including this
tectableinthefar-infraredareinthehigh-massregime,but extracontribution raises thecritical mass to1.3M⊕.Thus,
to extrapolate here to the whole population of stars, the withtheassumptionthatthedustinallsystemscomesfrom
dust generated in the low-mass cases must also be calcu- acollisionalcascadefedby75kmobjects,thegeneralscaling
lated.Thistransitionoccurswherethefractionalluminosity is
of the debrisis
fcrit =Ldust/L∗ =[2×104(r/dr)(r/M∗)1/2]−1 (2) E70/0.5=(Mr675km/1.3 M⊕)α (3)
where 0.5 is the generic value of E , and α is 1 for E >
crit
for disc radius and width r,dr in AU and stellar mass M∗ E and 2 for sub-critical discs.
crit
in solar masses. It is obtained from the limit where PR-
The mass in bodies of r 6 75 km per star is then pre-
drag and collision lifetimes are equal, for grains where the
dictedtorangefrom60downto0.2Earthmasses,with the
radiative force is half the gravitational force (Wyatt 2005).
detected debris discs hosting &1 M⊕ of comets. The shape
Using 11 resolved images of debris discs around Sun-like
of the population is the same as the excesses fitted in Fig-
starsobservedintheopticalandsubmillimetre(Wyatt2008;
ure 1, i.e. M approximately inversely proportional to
comets
Greaves et al. 2009), we calculated their values of f .
crit x,sothemostmassivebeltsarerare.Theprobabilitythata
These lie in the range 1 to 10 ×10−6 with an average of
star’s comets exceed a given mass is found by inverting the
5×10−6. The corresponding 70 µm ratio E can then
crit rank-mass expression to give
becalculated(Beichman et al.2006),andfordusttempera-
turesof40-80Kandstellar effectivetemperaturesimilar to P(>M )=0.26/M0.93 , (4)
comets comets
theSun,E isonaverage0.5at70µm.Hence,ifallSun-
crit
likestarspossessdebrisdiscsofsimilarscalestotheresolved applicable tothemass inbodies with r675 km.Thehigh-
systems4, thenthere should be adownturn in dustiness be- est mass appears realistic, for example it is comparable to
low E70 ≈0.5, even if there is a single smooth distribution the20-30M⊕ ofcollidersinferredaroundtheA-starFomal-
of numberof comets per star. haut(Wyatt& Dent2002),whichhostsabrightdebrisdisc
ThedottedlineinFigure1showsthisextrapolationbe- with E70 > 20 (Stapelfeldt et al. 2004). The exact masses
yond E70 = 0.5, assuming that the remaining systems are would be modified if the comets do not follow a collisional
less dusty according to E ∝ N ∝ N2 but continu- cascade–forexample,Hahn & Mahotra(2005)fitthesize-
dust comets
ingthesamepower-lawdistributionforN (x),i.e.ofa distributionfortheKuiperBeltasadoublepower-lawwith
comets
form like Equation 1. In this case, the predicted mean E70 many small bodies but a depletion at sizes greater than
is reduced from 0.16 to 0.06, in better agreement with the 65 km. Adopting this distribution for the exo-comet belts
estimate from the data of 0.03±0.02 for all the stars at would increase the fraction of the total mass that is in the
x>0.3. Thus, the single-population hypothesis taking into collider population bya factor of about 2.5.
account thedifferent regimes of dustremoval can match all
thepresent observational results.
3.6 Models
3.5 Comet populations
Although the fit used here is simply empirical, analytical
The numberof comets perstar can next beestimated from
models for evolving debris disc populations in fact pro-
the dust excess, albeit via several scalings so the the final
ducesimilartrends.ThemodelsofWyatt et al.(2007)have
values are only approximate. To connect comets and ex-
been applied to FGK stars surrounded by a range of plan-
cesses, we consider the τ Ceti debris disc, which is one of
the nearby resolved examples and has E60 = 0.75 ±0.15 etesimal discs. These discs have masses drawn from a log-
normalfunctionandsizes from apower-law distribution,as
(Habinget al. 2001). These ISO observations were made
in the previous model for debris discs of A-type host stars
with a slightly wider and shorter wavelength-centred fil-
(Wyatt et al. 2007). The model systems are sampled as if
ter than the 70 µm Spitzer/MIPS data, so we estimate a
observed at random ages and then ranked as in Figure 1.
correction using stars detected by both ISO and Spitzer
The general behaviour of a steep decline from a few very
(Habinget al. 2001; Trilling et al. 2008). The dust signals
dustysystems down toalong tailof low-debris starsis eas-
ily reproduced, adopting planetesimal populations of a few
4 Only 3 of the 11 resolved systems are in our present sample, Earth masses and discs extending out to a few tens of AU.
and there could be a bias to larger systems where the aim is to Kains et al. (in prep.) will present the final model parame-
make resolved images, although the resolved examples were not ters fitting both 70 and 24 µm debris statistics among the
chosenforobservationonsuchaprioriexpectations. Spitzer-surveyedFGK stars.
6 J. S. Greaves et al.
4 THE SOLAR SYSTEM Suchan excess, at our Solar upperlimit of 0.02, could thus
in principle be robustly detected in an hour. In practice,
4.1 Kuiper Belt properties
there are only a dozen Sun-like stars within this distance,
We now compare the 70 µm excess of the Kuiper Belt (if while beyond it a disc of Solar System dimensions would
it were viewed from outside) to the extrasolar values. The span less than three 5-arcsec telescope beams, and so un-
Solar System’s far-infrared dust flux is unfortunately not certainties in subtracting the blended stellar signal would
well established, although Landgraf et al. (2002) confirmed be re-introduced. However, Herschel will be able to explore
that Kuiper Belt dust does exist, via impacts onto the Pi- somewhat larger excesses very efficiently. For example, if
oneer spacecraft as they entered the outer Solar System. 5 % uncertainties in stellar models allow the detection of
However the emission from this dust from an Earth view- E70 ≈ 0.15, Herschel is predicted to detect debris in 35 %
point isasmall perturbation tothemuchbrighterZodiacal of systems (according to the grey line extrapolation in Fig-
flux. Aumann & Good (1990) used IRAS scans to estimate ure 1), compared to about 20 % of the stars observed with
that the peak Kuiper Belt flux is 3×10−8 W m−2 sr−1 at Spitzer.
60 µm (in a 40 µm bandpass), and the main belt on the
skyiseffectively≈10◦ wide5 (Morbidelli et al.2003).Sum-
ming over this area and dividing by the bandpass to give
5 IMPLICATIONS
a per-frequency-interval unit then gives a total flux of ap-
proximately 1 MJy (±0.5 MJy from the scatter in different The single population hypothesis discussed above fits both
scans). Subsequent COBE data with a similar 60 µm pass- the debris systems detected by Spitzer and the net upper
band favour an upper limit at the lower end of this range limitfortheremainingstars,oncetheswitchofdustremoval
(Backman et al.1995).Weassumethatthe70µmdustflux toPoynting-Robertsondragistakenintoaccount.IftheSun
willbesimilar,whiletheSolarphotosphericemission would isamemberofthishypotheticalpopulation,itmustbeone
be100 MJy if seen at the approximately 45 AUdistance of oftheleast dustysystems,withinthelasttenpercent.The
theKuiper Belt6. estimates of mass in colliding comets suggest the Kuiper
The Sun’s excess at 70 µm is therefore ≈ 0.01±0.005 Beltpopulationmayactuallybeadepopulatedoutlier,with
from IRAS, or possibly less from the COBE limit. These only a few-hundredthsof an Earth-mass in colliding bodies
values of excess for the Kuiper Belt are remarkably small. uptotensofkilometresizes.Roughlyathirdofsimilarstars
Allowinga2σuncertaintysothatE70canbeashighas0.02 are predicted to host an order of magnitude more comets;
wouldimplythatx>0.9.Hence,theSunisoneoftheleast therefore,implicationsforimpactsonanyterrestrialplanets
dusty systems (Figure 1), or possibly not a member of the need to beconsidered.
single population being tested in our hypothesis. SincetheSunis anormal mid-main sequenceG-dwarf,
The total mass in Kuiper Belt bodies has been es- these results are surprising. Further, the primordial Kuiper
timated at a few hundredths of an Earth-mass, from Belt should have been much dustier and a bright mem-
deep surveys finding objects as small as 25 km diame- ber of the inferred single population. It is estimated that
ter (Bernstein et al. 2004). The two-power-law model of at least 10 M⊕ of rocky material was needed in order for
Hahn & Mahotra (2005) can be used to estimate the to- theKuiperBeltbodiestoform(Morbidelli et al.2003),and
tal belt mass, adopting their generic albedo of 0.04. The this total belt mass would place the young Sun around
KuiperBeltwouldthensumto∼0.08M⊕ inther675km x∼0.1inFigure1.However,betweentheformationstageat
regime(orsomewhatsmallerinacollisionalcascade,orwith ∼0.1 Gyr and today, theKuiper Belt should only have de-
more recently-adopted higher albedo). In contrast, in our clinedaboutfour-foldindustluminosity(L¨ohne et al.2008),
single population hypothesis the lowest mass in colliders is so its present-day rank would be x∼0.3, inconsistent with
≈ 0.2 M⊕, and so the Kuiper Belt again appears to be an theobserved rank of x&0.9.
outlier, or at theextremeend of therange. ThekeytotheseresultsisthedispersalofmanyKuiper
Belt bodies, so that the population is now very depleted
(Morbidelli et al. 2003,e.g.). TheNicemodel(Gomes et al.
4.2 Detectability of Kuiper Belt analogues
2005) proposes that dispersal occurred when Jupiter and
Anexcessoforderonepercentabovethestellarphotosphere Saturn crossed their mutual 2:1 mean motion resonance
willbeverydifficulttodetectaroundnearbystars,evenwith as they migrated outwards; this event would have moved
the newly-launched Herschel mission. The PACS/70 chop- UranusandNeptuneontoenlargedeccentricorbitsandcon-
ping mode was predicted to detect ≈ 3 mJy sources with sequentlydisruptedthecomet belt.Thismodelcanexplain
5σ confidence in 1 hour, whereas the Sun if seen for exam- ejection of manyobjects, and can besynchronizedwith the
ple at 6 pc would have a photospheric signal of 135 mJy. Late Heavy Bombardment of the Earth-Moon system at
about 0.7 Gyr. However, the existence and timing of this
eventdependontheprecisearchitectureofthesystemofgas
5 We include only the classical belt and neglect dust that could giants (Thommes et al. 2008). Such as dispersal of around
begeneratedoverawiderbeltbycollisionsamongscattereddisc 99 % of the comet mass could readily shift the Solar Sys-
objects.Levisonetal.(2008)suggestsuchaneventcreatedare-
tem’sexcesstoalowstateandthusahighrank,asinferred
cently discovered familyof comets, but modelsarenot wellcon-
here – a process recently modelled in detail by Booth et al.
strainedbythisonedatapoint.
6 This value based on the Sun’s effective temperature was (2009).However,theyfindthat<12%ofSun-likestarscan
checkedagainstaphotosphericcalculationfortheMIPS/70pass- haveundergonesuch an event,as thereis noglobal drop in
band (Trillingetal. 2008) for the ‘Solar twin’ star HD 146233 dustinessat mature ages (Figure 2), so system clearing can
(Soubiran&Triaud2004). not have been common. G´aspa´r et al. (2009) infer roughly
Comets populations around Sun-like stars 7
similarproportions,basedonthesmallnumberofstarsthat 5.2 Analogue exo-Earths
couldbeundergoingclearouteventsinthe760-Myroldclus-
ter Praesepe. Thus in thepresent context, although comet- An analogue planet to our own is hypothesized to have a
clearing by giant planets could shift theranks of individual roughly similar impact rate. Impacts much faster than the
stars to much higher values, thedata imply that such stars rate experienced on Earth, of about one every 100 Myr for
are only a small sub-set. This may be neglected in the sin- 10 km bodies, are likely to cause a serious extinction prob-
gle population hypothesis, as the net excess at x > 0.3 is lem (e.g. halving the number of species after each event).
presentlypoorly defined,andso switchingafew percent of However, a much slower impact rate could mean that life
planet-hostingstarstoalow- orzero-dust statewould have would stay at a very simple level, with noneed to adapt to
little effect on thenet debris estimate. changesinenvironment.Hereweconsideracometarypopu-
lationcomparabletoorlowerthanthatoftheSunassimilar,
but also note that the slope of the inferred E70 is shallow
5.1 Relation to giant planets atlarge x,soaconsiderable population couldbeonly afew
From long-term trends in Doppler wobble surveys, times dustier (depending on the poorly known Solar E70).
With this basic hypothesis, we then need to link impact
Cumming et al. (2008) estimate that ≈ 18 % of Sun-like
rates to the configuration of the giant planets and comet
stars host giant planets, of above about Saturn’s mass and
belts. Unfortunately, this is computationally expensive to
orbitingwithin20AU.Hereweassumethatanysuchplanet
study for many systems (Horner& Jones 2008, e.g.). Mod-
orbiting within 3 AUwould be disruptive,for example per-
elling(Greaves,Jeffers,Horneretal.,inprep.)willcompare
turbing a terrestrial planet at ∼ 1 AU into an unstable or
the Solar System, with rather few comets but several per-
eccentric orbit, or in some migration scenarios preventing
turbing giant planets, to representative common extrasolar
ahabitableplanet from forming (Fogg & Nelson 2009).Ex-
architectures,suchasmanymorecometsbutfewerperturb-
cluding this 8 % of systems leaves 10 % of stars hosting a
ing planets. In the interim, we can consider two cases at
gas giant at 3-20 AU, among which four out of every ten
opposite extremes: one where debris and giant planets are
planets(generally aboveJupiter’smass) arealready discov-
unconnected phenomena, and one where gas giants beyond
ered (Cumming et al. 2008). A small correction should be
3 AU are a hypothetical signpost to systems where comets
made for approximately 1 % of star systems found to host
are cleared out.
another lower-mass giant that is closer in, although this is
less than theuncertainty of about 3 % in theextrapolation The results above then suggest that . 10 % of stars
toorbitsasdistantas20AU.Theresultisthat≈9±3%of haveasfewcometsastheSun(basedonitsE70upperlimit),
Sun-likestarsshouldhostgasgiantsnocloserinthan3AU, whileabout9%ofstarshostaninnermostgasgiantbeyond
and are therefore reasonably analogous to the Solar Sys- 3AU.Ifthesephenomenaareuncorrelated,thentheproduct
tem, with one-third of this population already discovered. of these rates implies that only up to ∼ 1 % of Sun-like
Hypothesizing optimistically that all these stars could also star systems would be analogous to our own, in the sense
have an unknown ice giant planet like Uranus or Neptune, of a small comet population concurrent with outer-system
the minimum conditions are met for gas giant interactions giant planets. In the alternative case where giant planets
that could end with disruption of a comet belt outside the can help to enforce a low comet population, this fraction of
ice giant (should such a belt exist). starsrisestoanupperlimitof9%,assumingfurther-outice
It is presently uncertain how giant planet systems and giantsarealso presentandso interactionscan clear out the
comet belts arerelated. Fewstarshavebothgas giants and comet belt. This estimate of 1-9 % for an analogue system
debris discs (Greaves et al. 2007; Moro-Mart´ın et al. 2007), may beoptimistic, if theexo-Earth impact rate is critically
and systems with both phenomena have similar excesses to sensitivetotheconfigurationofgasgiants;forexample,the
non-planet-hosts(Bryden et al.2009).However,therecould clearing of the Kuiper Belt required Jupiter and Saturn to
be a class of systems with many infalling comets and fre- cross a particular resonance, in the model of Gomes et al.
quent impacts on any terrestrial planet(s). One archetype (2005). Further, there may not be an exo-Earth around all
is HD 10647 which has a very high E70 of 50 and so an Sun-likestars,ornotwithintheHabitableZonewherewater
inferred > 100 M⊕ of colliders; this object is > 1 Gyr canbeliquidonthesurface;seeRaymond et al.(2007)fora
old (Liseau et al. 2008), while the four dusty planet-hosts modelpredictionthatstarsof&0.8M⊙arethemostsuitable
of Figure 3 are about mid-main sequence. Consequently, hosts.Ontheotherhand,ourestimateofonlyafewpercent
it could be very difficult for complex life to ever evolve of analogue systems is too pessimistic if in fact the single
in these systems with at least twenty times more collid- populationhypothesisdoesnotapply,andthereare≫10%
ers than the Sun, if gas giants perturb these bodies into ofSun-likestarswithlittledust.Thisisnotpossibletotest
the inner regions. (Energetic impacts more frequently than withthecurrentdata,butHerschelobservationsshouldsoon
every∼10Myrwouldprobablyhinderrecoveryofbiodiver- beable to test whether many stars host little dust.
sity (Krug& Patzkowsky 2004); however, creation of large Adopting up to 9 % as the preliminary estimate of the
heatedimpactbasinscouldfavourtheappearanceofsimple frequencyofanaloguesystemsallowsustoestimatethedis-
thermophiliclife (Abramov & Mojzsis 2009).) Ontheother tance to the nearest counterpart. In conjunction with the
hand, whether there is any connection between faint debris space density of Sun-like hosts, which for mid-F to late-K
levels and gas giants is very difficult to determine. There dwarfs is 0.01 pc−3, the nearest analogue system should lie
are 14 planets hosts in our sample that do not have debris within 13 pc. The nearest presently known analogue candi-
detections,andforthesethemeanE70is0.05±0.05,notsig- date(inthesenseofplanetandcometcontent)istheG8star
nificantlydifferentfrom0.03±0.02estimatedfornull-debris HD154345 at 18 pcdistance, which hasno obviousSpitzer
stars in general. 70µmexcessandhostsaJupiter-likeplanetat4AU.How-
8 J. S. Greaves et al.
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beyond 3 AU have so far been discovered, a completeness F., 2004, MNRAS 351, L54
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analogues as yet havepublished debrisdata. Hahn J.M., Malhotra R.,2005, AJ130, 2392
Hillenbrand L.A. et al., 2008, ApJ 677, 630
Horner J., Jones B.W., 2008, A&G49, 1.22
Jeffers S.V., Manley S.P., Bailey M.E., Asher D.J., 2001,
6 CONCLUSIONS
MNRAS327, 126
Systems roughly analogous to our own, hosting a modest Kim S.et al., 2007, BAAS 39, 814
comet population and gas giants at a few AU or beyond, Krug A.Z., Patzkowsky M.E., 2007, Paleobiology 33, 435
are inferred to be rather uncommon. If Sun-like stars of- Landgraf M., Liou J-C., Zook H.A., Gru¨n E., 2002, AJ,
tenhostterrestrialplanetsinthehabitablezone,onlyafew 123, 2857
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ACKNOWLEDGMENTS
ThommesE.W.,BrydenG.,WuY.,RasioF.A.,2008,ApJ
We thank the referee for comments that helped to clarify 675, 1538
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Trilling D.E. et al., 2007, ApJ658, 1289
Wyatt M.C., 2008, ARAA46, 339
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