The warm gas atmosphere of the HD 100546 disk seen by Herschel (Evidence of a gas-rich, carbon-poor atmosphere?)

3 MB·English

by  Simon Bruderer

Astronomy&Astrophysicsmanuscriptno.hd100546 c ESO2012
(cid:13)
January25,2012
The warm gas atmosphere of the HD 100546 disk seen by
⋆
Herschel
Evidence of a gas-rich, carbon-poor atmosphere?
SimonBruderer1,2,EwineF.vanDishoeck3,1,StevenD.Doty4,andGregoryJ.Herczeg1
1 MaxPlanckInstitutfu¨rExtraterrestrischePhysik,Giessenbachstrasse1,85748Garching,Germany
2 InstituteofAstronomy,ETHZurich,8093Zurich,Switzerland
2 3 LeidenObservatory,LeidenUniversity,POBox9513,2300RALeiden,TheNetherlands
1 4 DepartmentofPhysicsandAstronomy,DenisonUniversity,Granville,OH43023,USA
0
2 Submittedon7October2011/AcceptedtoA&Aon5January2012

n
ABSTRACT
a
J
Context.With the Herschel Space Observatory, lines of simple molecules (C+, O, and high-J lines of CO, Jup & 14) have been
3 observedintheatmosphereofprotoplanetarydisks.Whencombinedwithground-baseddataon[CI],allprincipleformsofcarbon
2 canbestudied.Thesedataallowustotestmodelpredictionsforthemaincarbon-bearingspeciesandverifythepresenceofawarm
surfacelayer.Theabsenceofneutralcarbon[CI],whichispredictedbymodelstobestrong,canthenbeinterpretedtogetherwith

] ionizedcarbon[CII]andcarbonmonoxide.
R
Aims.Westudy thegastemperature, excitation, and chemical abundance of thesimplecarbon-bearing species C,C+,and CO,as
S well asO by themethod of chemical-physical modeling. Using themodels, weexplore the sensitivityof the linestothe entering
. parametersandconstraintheregionfromwhichthelineradiationemerges.
h
Methods.Numericalmodelsoftheradiativetransferinthelinesanddustareusedtogetherwithachemicalnetworksimulationand
p
acalculationofthegasenergeticstoobtainthegastemperature.Wepresentournewmodel,whichisbasedonourpreviousmodels
-
o butincludesseveralimprovementsthatwereportindetail,togetherwiththeresultsofbenchmarktests.
r Results.AmodelofthediskaroundtheHerbigBestarHD100546isabletoreproducetheCOladdertogetherwiththeatomicfine-
t structurelinesof[OI]andeither[CI]or[CII].Wefindthatthehigh-J linesofCOcanonlybereproducedbyawarmatmosphere
s
a withTgas ≫ Tdust.Thelow-JlinesofCO,observablefromtheground,aredominatedbytheouterdiskwitharadiusofseveral100
[ AU,whilethehigh-JCOobservablewithHerschel-PACSaredominatedfromregionswithinsometensofAU.Thespectralprofiles
ofhigh-J linesofCOarepredictedtobebroaderthanthoseofthelow-J lines.Westudytheeffectofseveralparametersincluding
1 thesizeofthedisk,thegasmassofthedisk,thePAHabundanceanddistribution,andtheamountofcarboninthegasphase.
v Conclusions.Themain conclusions of our work are(i) only awarmatmosphere withT T can reproduce theCO ladder.
0 (ii)TheCOladdertogetherwith[OI]andtheupperlimitto[CI]canbereproducedbymgoadse≫lswidtuhstahighgas/dustratioandalow
6 abundanceofvolatilecarbon.Thesemodelshoweverproducetoosmallamountsof[CII].Modelswithalowgas/dustratioandmore
8 volatilecarbonalsoreproduceCOand[OI],areincloseragreementwithobservationsof[CII],butoverproduce[CI].Owingtothe
4 uncertainoriginofthe[CII]emission,wepreferthehighgas/dustratiomodels,indicatingalowabundanceofvolatilecarbon.
.
1
Keywords.Protoplanetarydisks–Stars:formation–Astrochemistry–Methods:numerical
0
2
1
: 1. Introduction violet(UV)radiationandX-rays.Throughheatingofthedisk’s
v
upperatmosphere,adisk-windisdriven,whichmayeventually
i At an important phase of a young low-mass star’s life, the na-
X disperse the disk (Alexanderetal. 2006; Ercolanoetal. 2008;
talenvelopehasdispersed,butthestarisstillsurroundedbyan
Gorti&Hollenbach 2009). The most abundant species tracing
r optically thick protoplanetary disk, which is thought to be the
a theionizingradiationandwarmtemperatureofafew100Kare
location of planet formation (see Dullemond&Monnier 2010 (ionized)atomiccarbon(C,C+),atomicoxygen(O),andhigh-J
and Armitage 2010 for recent reviews). Our own solar system linesofCO (with J & 14).Apartfromneutralcarbon,which
up
containsbothgaseousgiantsandrockyplanets.Itisthusevident
isaccessibletoground-basedtelescopes,thesespeciescannow
thatboththedustandthegascontentofthediskneedtobestud-
be observed using the PACS instrument (Poglitschetal. 2010)
iedinordertounderstandplanetformation.Thefeedbackofthe
onboardtheHerschelSpaceObservatory(Pilbrattetal.2010).
forming star onto the disk can help decide the disk’s fate. The
Themainformsofcarbon(C,C+,andCO)canthusbeob-
starirradiatesthedisk,heatingboththegasanddustandchang-
served for the first time and through high-J CO lines also in
ing the chemical composition of the gas by high-energy ultra-
warm regions. This allows us to probe the carbon chemistry
and the physicalstructureof planet- and comet-formingzones,
Sendoffprintrequeststo:SimonBruderer,
e-mail:[email protected] which were previously inaccessible to us. The carbon budget
⋆ Herschel is an ESA space observatory with science instruments is important for planet formation, since the terrestrial planets
providedbyEuropean-ledPrincipalInvestigatorconsortiaandwithim- in the inner Solar System are known to have a deficit in car-
portantparticipationfromNASA. bonofthreeordersofmagnituderelativetothesolarabundance
1
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
(Alle`greetal. 2001). Indications of a carbon deficit are also lyzed scattered-light images in the optical using ACS/Hubble
foundtowardsotherplanetarysystems(Jura2008).Inthediffuse finding evidence of minimal grain sizes larger than those of
ISM,about40 60%ofthecarbonislockedintoamorphouscar- typicalISMgrains.Thescatteredlightobservationsalso reveal
−
bon grains (Savage&Sembach 1996; Sofiaetal. 2004, 2011). structuresresemblingspiral armspossibly caused by either the
TobeconsistentwiththeEarth’scomposition,thesegrainsneed perturbationsof a companion(Quillenetal. 2005) or a warped
tohavebeendestroyedbeforeplanetformation.Incomets,how- disk structure (Quillen 2006). Features in the near-infrared
ever,carbongrainshavebeendetected,suggestingthatgrainde- (NIR) reveal a high crystalline silicate dust fraction in the in-
structionmechanismsplaynorole(Leeetal.2010). nerdisksurfacelayers(Bouwmanetal.2003)andanabundant
What region of the disk does the far-infrared (FIR) C, C+, amountofPAHswhoseemissionisdetectedonextendedscales
CO and O lines trace? How does the partitioning between (Geersetal. 2007). A wealth of continuum images in the near
volatile and refractory carbon vary from clouds to disks? The andmid-IR(e.g.Pantinetal.2000;Gradyetal.2001;Liuetal.
simultaneous measurement of the species tracing a significant 2003; Gradyetal. 2005) have helped to constrain the structure
fractionofthe disk mayprovideanswersto these questions.In of the inner disk using SED fitting. They reveal a large inner
addition, besides the hard to observe H , these simple species hole of radius 10 AU (Malfaitetal. 1998; Bouwmanetal.
2 ∼
formthe mostabundantconstituentsof the gas. Their lines are 2003), which possibly has a Jupiter-sized planet orbiting in-
thus importanttracers of the physical structure of the disk and side (Acke&vandenAncker 2006). Interferometric observa-
allow us to finally test the predictions made by many exist- tions(VLT-AMBERandMIDI,Leinertetal.2004;Petrovetal.
ingphysical-chemicalmodelsofdisks.Neutralcarbon[CI],for 2007) confirm the presence of the inner hole directly and set
example, is predicted to be strong by models with a range of r 13 AU (Benistyetal. 2010). Some CO ro-vibrational
hole
∼
gas masses and dust settling (Jonkheidetal. 2007) but is not emission at 4.7 µm was reported by vanderPlasetal. (2009)
detected in observationsof HD 100546 (Panic´etal. 2010) and and Brittainetal. (2009). The latter paper inferredthat the CO
CQTau(Chapillonetal.2010).Inadditiontothesubmillimeter emissionoriginatesfromradiiof13-100AU,whichisconsistent
lines discussed in our work, neutral carbon also has forbidden withtheinnerholeseeninthedustcontinuum.Theyfoundahot
lines in the near-infrared (at 8729, 9826, 9852 Å), which are rotational temperature of 1000 K and indications that both
∼
predicted to have detectable strengths (Ercolanoetal. 2009b). UVfluorescenceandcollisionalexcitationareimportantforthe
Todate,onlyafewdetectionstowardspre-main-sequencestars excitation.Hotgasinthedisksurfacelayersisalsodetectedby
havebeenreported(Looperetal.2010). observingtheH v=1 0S(1)lineat2.12µmbyCarmonaetal.
2
−
The physics and chemistry of gas in protoplanetary disks, (2011).
which is irradiated by the central star, is similar to the in- Thebulkofthediskmassisatcoldtemperatures,astraced
terface of general molecular clouds, where nearby massive bysubmillimeterlinesandcontinuum.Submillimetercontinuum
stars heat and photoionize the gas. Modeling the infrared wasreportedbyHenningetal.(1994,1998),whoderivedadust
(IR) response of gas irradiated by UV and X-rays has been massofa fewtimes10−4 M . Thegasupto 100Kis traced
developed in the context of these photo-dominated or disso- byCOrotationallinesuptoJ⊙=7 6,asrepor∼tedbyPanic´etal.
ciation regions (PDRs) and X-ray dominated regions (XDRs) (2010). They derived a gas mass −of > 10−3 M and concluded
(e.g. Tielens&Hollenbach 1985; Sternberg&Dalgarno 1989; fromthehigh12COJ =6 5/12COJ =3 2ratio⊙thatthediskat-
− −
Kaufmanetal.1999;Meijerink&Spaans2005).Thesemodels mosphereneedstobewarmerthaninTTauristars,probablyow-
simulate the infrared line emission by solving the coupled ingtophotoelectricheatingofthegasbythestrongUVfieldof
system of chemical evolution and thermal balance. The theformingB9star.Stronghigher-JlinesuptoCO J =30 29
−
coupling is the result of the cooling rates for the thermal were detected by Sturmetal. 2010 using the PACS instrument
balance depending on the abundance of the coolants, which onboardHerschel.Thedetectedlineshaveupperlevelenergies
is determined by the chemical network that itself also de- ofupto2500K.
pends on the temperature. These physical-chemical models Inthiswork,we studythe chemistryandexcitationofsim-
were applied in the context of protostars by Spaansetal. ple species (C, C+, CO, and O) in the disk arounda pre-main-
(1995) and Brudereretal. (2009a, 2010) to the walls along sequenceHerbig Ae/Be star. Our approachis twofold.We first
outflows, irradiated by UV radiation arising from either want to interpret the PACS observationsof Sturmetal. (2010)
accretion hot-spots or the protostar’s photosphere. For pro- and the ground-basedobservations of Panic´etal. (2010) taken
toplanetary disks, physical-chemical models have been towardsHD100546andsearchforevidenceofawarmdiskat-
applied by e.g. Kamp&vanZadelhoff (2001), Glassgoldetal. mosphere from the CO ladder, which probes a wide range of
(2004), Kamp&Dullemond (2004), Gorti&Hollenbach temperatures.Wehoweveralsowishtostudythedependenceof
(2004), Nomura&Millar (2005), Aikawa&Nomura (2006), the lines on certain parameters such as the carbon abundance
Jonkheidetal. (2004), Jonkheidetal. (2006), Jonkheidetal. in the gas phase, the gas/dust ratio, and others. In Section 2,
(2007), Gorti&Hollenbach (2008), Woitkeetal. (2009a), we briefly summarize the modeling approach and describe the
Woods&Willacy(2009),andErcolanoetal.(2009a). observations. In Section 3, we first present the results for one
Thewell-studiedintermediate-masspre-main-sequencestar particular model that agrees reasonably well with the observa-
HD 100546 is the focus of our present study. The B9.5Vne tions in Section 3 and then discuss the parameter dependences
type star of 2.2 M , L 27 L , and T = 10500 K inSection4and5.InSection6,wesummarizeourresults.
bol eff
(vandenAnckereta⊙l. 1997)∼is at its⊙distance of 103 6 pc
±
(Hipparcos) one of the closest Herbig Ae/Be sources. The
2. Modelandobservations
star and disk have been extensively observed at all wave-
lengths in lines and the continuum. X-ray observations are re- For this work, we use a new model based on Brudereretal.
ported in Stelzeretal. (2006). Both FUSE and IUE observed (2009b,a,2010),withseveralchangesandimprovementsimple-
HD100546 in the UV, detecting absorption in electronic tran- mented. The section provides a short summary of the model.
sitions of H probingthe warm gas with a temperature of sev- DetailsandresultsofbenchmarktestsarereportedinAppendix
2
eral 100 K (Martin-Za¨ıdietal. 2008). Ardilaetal. (2007) ana- A.
2
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
Ourphysical-chemicalmodelstartswith(i)adustradiative Muldersetal.(2011).Thesurfacedensitypower-lawistakento
transfercalculationforagivendustandgasdistributiontoobtain be Σ r 1, whichfits theVISIRimages. Anotherdustdensity
−
∝
thelocalUVradiationfield andthedusttemperature.Usingan structurefortheHD100546diskwasproposedbyBenistyetal.
initialguessofthegastemperature,(ii)thechemicalabundances (2010), basedon a analyticaldiskstructure andfitted to the IR
arecalculated,whichserveasinputforamolecular/atomicexci- interferometricdata.Theirmainconclusionsabouttheinnerdisk
tationcalculationtoobtainthecoolingrates.Next,(iii)thether- were incorporatedintothe Muldersetal. (2011) modelthatwe
malbalanceiscalculatedtoobtainanimprovedguessforthegas use. It is well-known that SED fitting yields degenerate solu-
temperature.Steps(ii)and(iii)arerepeateduntilconvergenceis tionsandtheobtainedduststructuredoesnotnecessarilyreflect
achieved.Raytracingandconvolutiontothetelescopebeamthen thegasstructure,e.g.owingtodustsettlingeffects.Inaddition,
yieldslinefluxesthatcanbeobservedwithobservations.These thestructureofthediskislikelynon-axisymmetric(Panic´etal.
modelingstepsaresummarizedinFigureA.1. 2010; Quanzetal. 2011) and with substructures (Ardilaetal.
DifferencesfromthestudyofBrudereretal.(2009b,a,2010) 2007).However,thisapproximateapproachisareasonableone
are that we solve the chemical network for the steady-state forstudyingthemaincharacteristicsofthegasemission,given
solution instead of interpolating from a pre-calculated grid of thelargeuncertaintiesinthegaslinemodeling(Section5.5).
abundances (Brudereretal. 2009b). This new approach allows We adopted a Hipparcos distance of 103 pc to HD 100546
us to include detailed photodissociation and ionization rates (vandenAnckeretal.1998).Theinclinationandpositionangle
based on the local wavelength-dependentUV field and the ac- weretakentobe42 and145 ,respectively(Pantinetal.2000).
◦ ◦
tual column densities for the self-shielding factors. The ther- WeusedaKeplerianvelocityfieldarounda2.5 M star,which
malbalanceisrefinedbyobtainingatomicandmolecularcool- was found by Panic´etal. (2010) to closely reprod⊙uce the ob-
ing rates from the excitation calculation used in Brudereretal. served spectra. The outer radius is uncertain but estimated to
(2010). This (approximate)method, which is similar to that of bebetween200AUand400AU(Pantinetal.2000;Panic´etal.
Poelman&Spaans(2005),allowsustocalculatethemolecular 2010).
excitation quickly and with reasonable accuracy. We can now
Inside the large inner hole of the HD 100546 disk, a
includethedetailedvelocitystructureintothe excitationcalcu-
smaller innerdiskextendingfrom0.25AU to 4AU was found
lationandaccountforheatingof thegasbythe IRpumpingof
(Benistyetal. 2010). We run models including the inner disk,
molecules, which is then followed by collisional deexcitation.
butfoundthatmorethan99%ofthefluxofthelinesdiscussed
Themethodcouplescellsatdifferentradiiofthedisk,unlikethe
in this work emerges from the outer disk. We thus considered
“verticaldirectiononly”escapeprobabilityapproachemployed
only the outer disk starting at 13 AU for this work. The dust
inmostpreviousdiskmodeling.Thedisadvantageofourmethod
opacityoftheinnerdiskwashoweverincludedtocalculatethe
is that we need to iterate over the entire chemical structure to
localUVfield.
derive the local gas temperature, which increases the calcula-
Asinputstellarradiationfield(Figure1),weanalyzeddered-
tion time. However, the method allows us to calculate models
withanarbitrarygeometryincludinge.g.disksembeddedinen- dened FUSE observationsfor wavelengths 911-1200Å, which
velopes. Since our code contains all geometrical properties in had been previouslyanalyzed by Deleuiletal. (2004) and IUE
onemodule,itcanbeextendedtothree-dimensionalstructuresin observations(Valentietal.2003)forlongerwavelengths(1200-
thefuture.Thechemicalnetworkinthenewcodehasalsobeen 3200 Å). The spectra were dereddened using the extinction of
extendedbyincorporatinghydrogenationreactionsongrainsur- AV = 0.36(Ardilaetal.2007)andtheextinctionlawofDraine
faces,photodesorptionofspeciesfrozen-outontograins,andvi- (2003) for R = 3.1. The FUSE/IUE spectra were extendedto
V
brationallyexcitedmolecularhydrogen(H ),whichcanbeused longer wavelengths using the B9V template of Pickles (1998).
∗2
toovercomeactivationbarriers. TheX-rayluminosityhadbeenfoundtobelog(LX) = 28.9erg
Inthisstudy,weconcentrateontherotationalladderofCO s−1 (Stelzeretal. 2006). Since the plasma temperature had not
and do not consider vibration-rotationlines detected in the M- beenwell-constrainedbyobservations,weassumedaratherhigh
bandat4.7µm,sincefluorescentexcitationbyUVphotonsplays temperatureofkTX = 6keV.ThishardspectraallowsX-raysto
asignificantroleintheirpopulation.Wenotethattheexcitation penetratedeepintotheatmosphere.Nevertheless,thelinesstud-
of the rotationalladderis determinedby collisions and the rel- ied in this work change by less than 5 % by switching on
∼
ative population of CO in the ν = 1 state is small at 4 % for X-rays.Thus,theassumptionontheshape(plasmatemperature)
athermalizedpopulationat1000K(Brittainetal.2009).Thus, of the X-ray spectra does not affect our results (Section 3.1).
the results presented in this work would not changeby includ- Inadditiontothestellarradiationfield,wealsoaccountforthe
ingvibrationallyexcitedlevelsofCO.Forthesamereasons,we interstellarradiationfield(Draine1978).Anothersourceofion-
also do notmodelthe H2 2.12 µm line. In addition,this line is izationarecosmicrays,forwhicharateofζc.r. = 5×10−17 s−1
verysensitive to the depthatwhich the dustbecomesoptically isadopted.
thick and a quantitative comparison to the far-infrared lines is Thedustopacitiescontrolthepenetrationofthephotonsand
thusdifficult. thus both the photodissociation and ionization of molecules as
well as the dust temperature. The dust grains used in the SED
fittingbyMuldersetal.(2011)aresilicateswitha5%(inmass)
2.1.ParametersfortheHD100546model
compositionof carbonaceousmaterial. For gas/dust= 100 and
To model HD 100546,we chose to use the dust density distri- apresent-daysolarphotospherecarbonabundanceof2.7 10 4
−
×
bution obtained by Muldersetal. (2011). They fit the SED us- relativetohydrogen(Asplundetal.2009),thisamountstoabout
ingadustradiativetransfercalculationwithaverticalstructure 15 % carbon bound in this population of grains. The grains
that obeys hydrostatic equilibrium assuming that T = T . have a size of 0.1 - 1.5 µm with a distribution proportional to
gas dust
Dropping this assumption results in a density structure with a a 3.5, employing the Mathis, Rumpl and Nordsieck size distri-
−
puffed-up inner rim with about 10 AU (Kampetal. 2010), but bution (Mathisetal. 1977). The opticalconstants are for irreg-
this regiondoesnotcontributesignificantlyto the emission we ularly shaped distributions of hollow spheres (DHS, Minetal.
probehere.Forconsistency,wealsousethedusttemperatureof 2005). The DHS dust modelhas been adoptedto be consistent
3
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
of recombinationreactions. We adopta 5 % PAH-to-dust ratio
104 FUV(Photoelectricheating)
) CHp.d. within 100 AU and 1% outside 100 AU, following a simulta-
−1 CH2p.d. neous fitting of Spitzer and VISIR N-band observations using
˚A H2p.d.,COp.d.,Cp.i.
−2 103 the NC = 100 opacities of Draine&Li (2007) (Gijs Mulders,
m pers. comm.). The PAH-to-dustmass ratio of 5 % corresponds
c
−1 102 approximately to the average Galactic PAH-to-dust mass ratio
s of 4.6 %, which in turn represents about 50 ppm of C per H
g
er Blackbody8000K nucleon bound in PAHs (Draine&Li 2007) and 15 % of the
13 101 Blackbody10500K present-day solar photosphere carbon abundance (for gas/dust
−
10 Blackbody12000K = 100). The PAHs are only excited by UV in the uppermost
x( 100 FUSE layer of the disk (Visseretal. 2007) and the observed features
Flu IUE thustracethisregion.Inadditiontothelargeuncertaintiesinthe
B9Vtemplate
molecular properties of the PAHs, the PAH abundance is only
10−1
poorlydeterminedintheregionfromwhichthelinesdiscussed
1000 2000 5000
in this study emerge. We thus choose to scale the PAH abun-
Wavelength(˚A) dance with the gas/dustratio, such that gaswith gas/dust= 20
contains five times smaller amount of PAHs than for gas/dust
Fig.1.UV spectraofHD 100546atthe sourcedistance of103
= 100 (Jonkheidetal. 2007). We examine the influence of the
pc.We indicatethefarultraviolet(FUV)wavelengthrangeim-
PAH abundance separately in Section 4.3. We assume PAHs
portantforgasheatingandthewavelengthrangeofphotodisso-
to be photodestroyed in regions with integrated far ultraviolet
ciation(p.d.)andphotoionization(p.i.)cross-sectionsfordiffer-
(FUV)fluxes> 106 ISRF,followingtheresultsofamorecom-
entmolecules.
plete PAH chemistry by Visseretal. (2007). This affects how-
ever only the upperlayer of the disk and we find that the lines
discussed in this work are unaffected by this assumption. We
with the SED fitting of Muldersetal. (2011). This dust popu-
lation has a mass of 10 4 M , which agrees with observations notethattheemissionofalllinesstudiedhereemergesfromz/r
−
ofsmallgrainsbyDominike⊙tal.(2003).However,muchofthe lowerthantheregionofPAHdestruction(Section3.1,3.4).
masscanbeinlargergrains,andthegas/dustratiosgivenrela-
tivetothispopulationofgrainsarethusupperlimits.Thispop-
ulationofgrainsdoesnotcontainthe UV/visualattenuationby
2.2.Observations
verysmallgrains(VSGs)andpolycyclicaromatichydrocarbons
(PAHs).WethusalsouseR =3.1and5.5opacitiesafterDraine
V
(2003)at wavelengths. 1 µm (Figure2) to includeVSG/PAH
Spectrally resolvedobservationsof the low-J 12CO J = 7 6,
absorption.Using these opacities at short wavelengthsonly af- −
J = 6 5, and J = 3 2 lines were obtained with the 12m
fects(i.e.increases)thedusttemperatureintheuppermostlayer, − −
APEX telescopebyPanic´etal. (2010) anddisplayeda double-
abovetheregionfromwhichthelineemissiondiscussedinthis
peakedlineshape,thatisconsistentwitharotatingdisk.Wenote
work emerges, as we checked. For simplicity, we thus use the
that the uncertainty in the J = 7 6 line is considerable and
samedusttemperatureforallmodelstakenfromMuldersetal. −
the J = 6 5 line is detectedat a much highersignal-to-noise
(2011). −
ratio. Theyhavealso searchedforthe 370 µm (809GHz) [CI]
3P 3P line, but were unable to detect it. We note that they
2 1
−
105 havebeenusingpositionswitchingwithanoffposition16′from
) the source. Thus, it is unlikely that the emission at the source
1
−
g hadbeencanceledoutbyextendedemission.The609µm(492
2m 104 GHz)3P1 3P0lineofneutralcarbonwasnotobserved.
c −
(
t
fficien 103 andT1h4e5[µCmII3]P158µ3mP 2lPin3e/2s−an2dPm1/2id,-thJ/eh[iOghI-]J6l3inµemso3fPC1O−w3Pit2h,
0 1
e −
co 0.1−1.5µm(κabs) Jup = 14 to 30 were observed by Sturmetal. (2010) with the
ction 102 0R.V1−=13..51µ(mκab(sσ)scat) PanAdCgSasinisntrtuimmee”nt(DonIGboITar)dkeHyerpsrcohgerlamas(PpaI:rtNo.fEtvhaens“)D.Tushte, iCcOe,
Massextin 101 RRRVVV===355...155(((σκσssaccbaastt))) l4nJi1on4t=ee−at3hn31ad0t3−Ct.hOT3e0haeJplsipne=aetrwew2no3atsjl−uibnm2lee2spndaiwnreeadCstOwhpuioltsihtnetnetahtkflieaeulnOlxyaHasbtl3Jue/pn>2pd,ee27rd5/l2wimm+iat−ihyts.5Hh/aW22vO−ee
been introduced by uncertainties in the PACS flux calibration
0.1 0.2 0.5 1 2 5 10 20 50 100
when the first PACS results were published,includingthose of
Wavelength(µm)
Sturmetal. (2010). The larger uncertainty in these lines does
Fig.2. Adopted dust opacities. The solid lines give absorption however not affect any of our conclusions. The PACS data are
mass extinction coefficients, while dashed lines indicated scat- spectrally unresolved.Except for [CII], all lines are consistent
teringmassextinctioncoefficients. withtheiremergencefromwithinthecentral9′.′4pixel.Tocor-
rect for extended emission in [CII], we subtracted the pixels
neighboring the central pixel. We also accounted for emission
ThePAHabundanceaffectsboththeheatingbymeansofthe leakingfromthecenterpixelowingtotheextendedpointspread
photoelectriceffect,aswellastheionizationbalance,bymeans function.Theoriginofthe[CII]lineisdiscussedinSection5.3.
4
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
Table1.LinefluxesmeasuredtowardsHD100546. the disk, X-rays can however be neglected, since the luminos-
ity in theFUV band(6-13.6eV) isat 4 1034 ergs 1 much
−
Species Line Wavelengtha Flux/Errorb higherthantheX-rayluminosity.Neve∼rthel×ess,theconsiderable
[µm] 10−17[Wm−2] ionization rate may affect the chemistry and for example lead
APEX(Panic´etal.2010) to a destruction of water (e.g. Sta¨uberetal. 2006). The simple
CO J=3 2 866.96 0.0149 0.003 speciesconsideredinthisworkarehoweverlittleaffectedbyX-
CCOO JJ==67−−56 433731..5665 0.103.211±±0.00.0072 raysandwefindthattheCO,C,C+,andOfluxeschangebyless
[CI] 3P2−−3P1 370.42 <±0.009 thanT∼he5(%intweghreanteXd)-rFaUysVarfleusxwiintcuhneditsoffof. the interstellar radia-
HerschelPACS(Sturmetal.2010)
CO J=14 13 186.00 7.4 0.9 tion field (Draine 1978; 1 ISRF 2.7 10−3 erg s−1 cm−2) is
CO J=15−14 173.63 11.5±0.8 showninFigure3d.VeryhighFU∼Vflux×esofupto108ISRFare
CO J=16−15 162.81 8.3±0.9 reachedinthesurfaceoftheinneredgeofthedisk.Intheupper
CO J=17−16 153.27 10.5±0.8 atmosphereof the outerdisk at r = 400 AU and z/r = 0.3 the
CO J=18−17 144.78 9.9±1.0 FUVfluxstillreaches105 ISRFatadensityofafewtimes105
CO J=19−18 137.20 8.9±0.7 cm 3.WenotethattheseareroughlytheconditionsoftheOrion
CO J=20−19 130.37 7.1±0.7 −
bar PDR (Hogerheijdeetal. 1995; Jansenetal. 1995). Similar
CO J=21−20 124.19 5.9±0.6
CO J=22−21 118.58 5.9±0.9 conditions are also predicted for the outflow walls, the “dense
CO J=23−22 113.46 <4.8±1.2 PDR” along the outflow of a high-mass star forming region
CO J=24−23 108.76 10.6±1.3 (Brudereretal.2009a).
CO J=26−25 100.46 12.7±2.4 Figure3egivestheFUVextinctioninunitsof AV,obtained
CO J=27−26 96.77 10.2±1.4 by defining τ = log(I /I ), with the attenuated FUV
CO J=28−27 93.35 10.0±1.0 flux I and thFUeVFUV−flux caottrreucntaettd only for geometrical dilu-
CO J=29−28 90.16 11.8±1.6 tionIatt (e.g.Brudereretal.2009a,Eq.2).ConversiontoA is
CO J=30−29 87.19 8.5±1.0 unatt V
CO J=31−30 84.41 <4.9±1.5 donebyscalingwiththedustopacitiesat2070Å and555Å and
[[OCIII]] 32PP3/2−3P−2P1/2 15673..7148 13.55±54±1.5c5 dacucroinugnttihnegcfaolrcuAlVati∼on,1b.0e8c6aτuVse. TthheepUhVotoeixotninizcatitoionnisanndotdiussseod-
[OI] 3P1−3P2 145.53 35.7 ±1.3 ciationratesarecalculatedfromthewavelength-dependentUV
0− 1 ± spectra.TheFUVextinctionhowevershowsthatowingtoscat-
Notes.(a)Restfrequency(b)Formalerrors,notincludingsystematicer- tering, FUV photons can penetrate much further into the disk,
rors(c)Extendedemissionsubtracted,seetext. particularlyintheouterparts(e.g.vanZadelhoffetal.2003).
Figure 3f shows the adopted PAH abundance. The drop in
the inner, upper disk is due to the photodissociation of PAHs.
3. Results:Arepresentativemodel Thedropat100AUisobservationallyconstrained(Section2.1).
The dustand gastemperatureare presented in Figure 3g/h.
We now present the details of a representative model of HD
100546. By representative, we mean that it reproduces suffi- Figure3ishowstheratioofthegastodusttemperature.Thedust
temperaturedoesnotexceed 250K, butstays above 30K
cientlywelltheobservationsenablingustostudythemainphys-
∼ ∼
icalandchemicaleffects.Itishowevernotmeanttobeabestfit acrossthe entiremodel.Thus,CO doesnotfreeze outontothe
dust grains. The gas temperature exceeds the dust temperature
model.Thedependenceontheparametersassumedhereisdis-
byfactorsofup to 50in the innerupperdisk andreachestem-
cussedinthenextsection.Theouterradiusoftherepresentative
peratures of up to 6000 K. In the outer upper disk, the gas
model is assumed to be 400 AU. We define the depletion fac-
∼
temperatureisstillT 1000Kandthusaboutafactoroften
tor δ as the carbon abundancein the gas phase relative to the gas
C ∼
present-daysolarphotosphereabundanceof2.7 10 4 relative higherthanTdust.Deeperwithinthedisk,belowz/r =0.15,col-
−
× lisions between gas and dust grains result in a coupling of the
tohydrogen(Asplundetal.2009).Inthissection,weassumea
carbongasphaseabundanceof1.3 10 4 relativetohydrogen gasanddusttemperature(Tgas =Tdust).
−
×
(δ 0.5),whichischaracteristicofthediffuseISM.Adopting
C
gas/d∼ust= 20,wegetagasmassof 2 10 3 M .Weusethe
R =5.5dustextinctionlawforthis∼mod×el. − ⊙ 3.2.Chemicalstructure
V
Fractional abundancesof C+, C, CO, O, H , and electrons rel-
2
ative to the total hydrogen density (n = n(H) + 2n(H )) are
3.1.Physicalstructure H 2
shown in Figure 4. As found by previous chemical models of
Thephysicalconditionsoftherepresentativemodelareshownin protoplanetarydisksthechemicalstructureresemblesaclassical
Figure3.Onlyonequadrantofthediskisgivenandonlyregions PDRintheverticaldirection(e.g.Jonkheidetal.2007).Below
withgasdensity>105cm−3areshown.Wepresentthegasden- a toplayerofatomichydrogen,H2 forms,asself-shieldingbe-
sityinFigure3a/bbothinlinear(r,z)aswellasin(log(r),z/r)- comes sufficient. In the outer disk, the inward column is also
space.Thelatterhastheadvantagethattheinnerpartandupper large enough to prevent H2 from photodissociation and hydro-
diskcanbeseenclearly.Directraysfromthestartothediskcor- genisinmolecularform.
respondtoverticallines.Thedensityreachesuptoafewtimes Carbonintheupperdisk(z/r 0.2)ismainlyintheformof
1010cm 3inthismodelintheinnerpartofthediskmidplane. C+, followedbyneutralcarbonan∼dCO deeperwithinthedisk.
−
TheX-rayionizationrateisgiveninFigure3c. Despitethe Anexceptionisthe“warmfinger”ofCOintheouterdisk(r >
low X-ray luminosity of this source of 8 1028 erg s 1, the 100 AU, z/r > 0.25).In this region,CO forms throughthe re-
−
ionizationrateduetoX-raysintheinner∼disk×isstillaboutthree actionofC+ with H toCH+,followedbyareactionwithO to
2
ordersofmagnitudehigherthanthestandardcosmicrayioniza- form CO+ which then reacts with H to form HCO+ and sub-
2
tionrateof5 10 17s 1.Fortheheatingandcoolingbudgetof sequentlyCO(seeJonkheidetal.2007).Theinitiatingreaction
− −
×
5
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
Fig.3.Physicalconditionsintherepresentativemodel.Thecontourlinesareshownforvaluesindicatedinthelabelbysmallarrows.
Thethindashedlineindicatesz/r = 0.15,0.2,and0.25.Thepanelsshow:a.)Gasdensityb.)Gasdensityinlinearscale.c.)Total
ionizationrate.d.)LocalFUVfluxe.)FUVextinctionf.)PAHabundanceinunitsoftheISMabundanceg.)Dusttemperatureh.)
Gastemperaturei.)Ratioofthegastodusttemperature.
isstronglyendothermicwithanenergybarriercorrespondingto 13AU<r<20AUandz/r<0.1,gasanddustareatatempera-
4640 K, thus requires a high temperature to proceed. The OH ture>100KandthegasisnotexposedtostrongFUVradiation.
formation at high temperature, by means of the reaction of O Inthispartofthedisk,oxygenislockedintowater.Furtherout,
andH ,leadstoadditionalCO+ forthischainofreactions.The waterfreezesoutandlocksmostoftheoxygenintowaterice.In
2
OHreactswithC+ toformCO+.Attheinneredgeofthediskat thisregion,thecarbonisintheformofgaseousCH .
4
13AUbelowz/r 0.1,COisshieldedfromphotodissociation
∼
owingtoshadowingbytheinnerdisk.Thehigherabundanceof
COatr =13AUandz/r =0.2isduetotheadoptedH forma-
2
tionrate:since the stickingcoefficientdecreasesabove 3000
∼ TheelectronfractionroughlyfollowstheabundanceofC+.
K(Cuppenetal.2010),thelowergastemperatureathigherz/r
ChargeexchangewithPAHsisanotherimportantreactiontype
leadstoanincreaseinH andsubsequentlyinCO.
2 for the ionization balance. The PAHs are positively charged in
Atomicoxygenhasaconsiderablyhighabundancethrough- theupperatmosphere,neutralatintermediateheights,andnega-
outthedisk,exceptforthemidplane.Thisisbecausetheelemen- tivelychargedatgreaterdepthswithinthediskduetocharging
talabundanceofoxygenishigherthanthatofcarbonandnotall byelectronattachment.Sincetheelectronabundanceisverylow
oxygen can be locked into CO, which is almost unaffected by inthemidplane,thePAHscanagainbecomeneutral.Chargeex-
photodissociation,bymeansofself-shielding.Inaddition,oxy- changeC++PAH0 C+PAH+andrecombinationC++PAH
−
gencannotbeionizeddirectlybyFUVphotonssinceitsioniza- C+PAH0 areth→etworeactionsthataffectthesimplecarbon
→
tionenergyisslightlyhigherthan13.6eV.Intheinnerdiskwith chemistrymost,leadingahigherabundanceofneutralcarbon.
6
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
Fig.4.FractionalabundancesofC+,C,CO,O,H ,andelectronsrelativetothetotalhydrogendensity(n = n(H)+2n(H )).The
2 H 2
thindashedlineindicatez/r=0.15,0.2,and0.25.AbruptchangesatR=100AUareduetoavaryingPAHabundance,seetext.
3.3.Warmatmosphereversusdusttemperature 2011) and OH (Sturmetal. 2010) towards this disk, which are
bothformedinendothermicreactionswithH .
2
Linefluxespredictedbytherepresentativemodelarepresented
in Figure 5. The figure givesthe CO ladder on the left and the 3.4.Originofthelineemission
[CI], [CII], and [OI] atomic fine-structure lines on the right.
Atomicfine-structurelinesofCandCOlinesuptoJ =7 6are Where does the observed line emission originate? The angular
convolvedtotheAPEXbeamandallotherlinestotheHe−rschel resolutionofHerschel,correspondingtoabout1000AU for63
beam.Inadditiontothemodelwiththecalculatedgastempera- µmatthedistanceofHD100546,doesnotresolvethedisk.The
ture,amodelthatassumesthatthegastemperatureisequaltothe model however, may help us to locate the region of emission.
dusttemperatureisshown.Afactoroftwoaroundtheobserved Figure 6 gives the relative contribution to the observed fluxes.
fluxesisshownbyagrayshadedregion.Weconsiderthisregion We show the integrated contribution function (ICF), which in-
as a goodagreementto observationsgivenall the uncertainties corporates all the effects involved in the line formation: abun-
indataandmodeling(seeSection5.5). dance of the molecule, excitation, and opacity. In addition, we
providethetworadiidelineatingtheregionfromwhich75%of
The modelwith the calculatedgastemperaturefits the data theemissionemerges,eitherinsideoroutside.
well, with the exception of the high-J CO lines with J > 25 The ICF, discussed in Tafallaetal. (2006) and
(see Sections 4.5 and 5.5). However,the cool atmosphere with Pavlyuchenkovetal. (2008), shows the relative contribu-
T set to T fails to reproduce the high-J CO ladder. The tiontothelineemissionalongaray.Weobtainfromtheformal
gas dust
J =16 15transitionwithE 750K(Table2)isalreadyun- solutionoftheradiativetransferequation(Eq.A.14)
up
− ∼
derproducedby aboutan order of magnitude,and the higher-J
lines are underpredictedevenmore.For example, J = 25 24 ICF= (Sν Sdust)e−τν 1 e−∆τν dν, (1)
(Eup 1800 K) is underpredictedby more than two orde−rs of Zline − (cid:16) − (cid:17)
∼
magnitude.Theatomicfine-structurelineshaveupperlevelen- wherethesourcefunctionisS ,thedustsourcefunctionisS ,
ν dust
ergiesthataremuchlowerthanthehigh-JlinesofCO.Boththe theopacitytotheobserverisτ andtheopacitywithinonecellis
ν
[CI]and[CII]lineshave E < 100K andthe line fluxescal- ∆τ .Theintegrationisperformedoverfrequency.Forsimplicity,
up ν
culatedwithacoolandwarmatmosphereareverysimilar.The we take the disk to be face on and allow the rays to propagate
[CII] line is somewhatunderproducedand [CI] overproduced. parallel to the z axis (as e.g. in Panic´etal. 2010). This avoids
However,[OI]hasanupperlevelenergyof327K(145µm)and complications with the adopted Keplerian velocity profile but
227K(63µm).Consequently,the[OI]linesforthecoolatmo- conservesthemainphysicalconclusions.Thecontributiontothe
spheredifferbyan orderof magnitudefromthoseobtainedfor observedlinefluxfromanannuluslocatedataradialdistancer
thewarmatmosphere.Weconcludethattheprominentemission isgivenby2πI(r)rdr,withthefluxI(r)atradiusr.Thus,therel-
inhigh-J COand[OI]atomicfine-structurelinesisstrongevi- ative contributionto the observedflux is I(r)dr. In Figure6,
∝
denceofahighertemperatureofthegasintheupperatmosphere wethusshowthecontributionfunctiontimestheradius(r ICF),
ofthedisk.ThisagreestotherecentdetectionofCH+(Thietal. scaledtoitspeakvalue. ×
7
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
10−13
Warmatmosphere(Tgas>Tdust)
10−14 Coldatmosphere(Tgas=Tdust)
ObservedFluxes
−2) 10−15
m
W
( 10−16
x
u
Linefl 10−17 Ffriogm.5t.heInrteepgrreasteedntalitniveeflmuoxdeesl.oTbhtaeinleefdt
part of the figure shows the CO ladder
10−18 and the right part atomic fine-structure
lines. Observations are indicated by
blackcrosses. Theredlineandsquares
10−19
showmodelfluxesforamodelwithcal-
0 5 10 C1O5-Jup 20 25 30 µ370m µ810m µ158m µ63m µ145m caunldatterdianggalsestewmitpherTagtausres,etthtoeTbdluuset. Tlihnee
[CI] [CI] [CII] [OI] [OI] gtwraoytoshtahdeeodbrseegrvioendiflnudxiceast.esafactorof
The low-J emission of CO J = 3 2 originates at radii1 Table2.Linepropertiesandorigins
−
between r 70 220 AU at z/r 0.15 0.25. The density
∼ − ∼ −
above this region is too low to contribute significantly to the Line λ E A n a Origin
up ul crit
emission,sincetheregionsbelowareshieldedbythelineopac- [µm] [K] [s 1] [cm 3] [AU]
− −
ity. Thus, the far side of the disk does not contribute much to CO J=3 2 867 33 3(-6) 2(4) 70-220
the emission, except for some radiation in line wings. Owing CO J=16− 15 163 752 4(-4) 1(6) 35-80
to the increasing density and temperaturetowardsthe inner re- CO J=30−29 87 2565 2(-3) 4(6) 20-50
gionatagivenz/r,evenspatiallysmallerregionsatradii< 100 [[CCIII]]32PP1−3−P22P 135780 9612 23((--67)) 51((33)) 115500--330000
AUcontributetotheobservableemission.Mid-J lines,e.g.CO [OI] 3P3/23−P 1/2 63 228 9(-5) 5(5) 50-180
aJn=do1n6ly−m1o5lweciuthleEswupit∼hi7n5r0K3,5are8n0oAtUexccoitnetdriibnuttehetootuhteeremdiissk- [OI] 3P10−−3P21 145 327 2(-5) 5(4) 80-210
∼ −
sion.Theselinesreachlineopacitiesofaroundunityandthefar
Notes. a(b) means a 10b. (a) Critical density (A / C ) for colli-
sideofthediskdoesnotcontributetotheemissionintheinner- sion with H at the te×mperature of E . Atomic/muloleclulaurl data from
2 up P
mostregions(radii< 30AU).Thehighest-J emission,e.g.CO Scho¨ieretal.(2005).
J = 30 29with E 2800K, detectedtowardsHD100546
up
− ∼
emerges from the inner r 20 50 AU in a thin layer at the
∼ −
surfaceofthedisk.There,COisformedbutthegastemperature
isstill sufficientlyhighto excitethelines.Theopacityofthese
linesisopticallythinandthedustextinctionisnotlarge.Thus, illustration purposes, we however also show CO J = 30 29,
emissionfromboththenearandfarsidesreachestheobserver. which might eventually be accessible to resolved observa−tions
The atomic fine-structure lines of [CI] and [CII] emerge withtheGREATinstrumentonboardSOFIA.
mainlyfromthe outerdisk atradii 150 300AU. Owingto
∼ −
thehigherabundanceofthosespeciesintheupperatmosphere,
combinedwiththelowcriticaldensity( 103cm 3)andlowup-
perlevelenergyofthe[CI]and[CII]l∼ines,thes−elinesemerge J =3−2
fromregionshigherinthediskthanthelow-J linesofCO.The J =10−9
oxygen[OI]lineshaveconsiderablyhighercriticaldensitiesof y 1 J =16−15
t∼hu1s05n−ot1e0x6ccitmed−3inantdhealosuotehrigdhiesrkuapnpderthleevleilneeneemrgiisessi.oTnhceoymaeres ensit J =30−29
t
n
fromregionswithin 50 210AU.Sincethislineisoptically I
∼ − d
thick,mostoftheemissionisfromthenearsideofthedisk. ze 0.5
ali
m
r
3.5.COlineprofile o
N
ThepredictedshapesoftheCOJ =3 2,J =10 9,J =16 15
0
− − −
andJ =30 29linesareshowninFigure7.ForCO J =3 2,
− −
theprofileisgivenfortheAPEXbeam,whilethehigher-Jlines
arecalculatedfortheHerschelbeam.TheHIFIheterodynespec- −15 −10 −5 0 5 10 15
trometer onboard Herschel (deGraauwetal. 2010) can spec- Velocity(kms−1)
trally resolve lines down to < 0.1 km s 1 and covers the fre-
−
quency range of CO J = 5 4 up to CO J = 16 15. For Fig.7.PredictedlineshapesfortheCOJ =10 9,J =16 15,
− − andJ =30 29inthebeamofHerschel.TheC−OJ =3 2−line
− −
1 Measuredbythe75%contributionradiigiveninFigure6andTable predictedforAPEX isshowntogetherwith theobservationsof
2. Panic´etal.(2010).
8
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
Fig.6.Contributionfunctiontothelineformation.Thediskisviewedfromthetopandthecontributionfunctionisnormalizedto
thepeak.Total(line+dust)opacitiesofτ =1atthelinecenterareindicatedbyablackline,anddustopacitiesofτ =0.1
linecenter dust
bygraylines.Theredarrowsindicatetheradiifromwhich75%oftheemissionemerges,eitherinsideoroutside.Thethindashed
lineindicates z/r =0.15,0.2,and0.25.
| |
The modeled CO J = 3 2 line agrees well in terms of the main emission found in Section 3.4. We note that the CO
−
widthwiththespectraobservedbyPanic´etal.(2010).Aslight J = 30 29 line is broader than expected from the projected
−
asymmetryin the observedspectra witha strongerblue-shifted Kepler velocity at the inner rim. This is due to thermal broad-
peakishowevernotreproducedbythemodel.Panic´etal.(2010) ening of the line, correspondingto more than 1 km s 1 for the
−
attributed the asymmetry to an asymmetric temperature struc- gas temperatures of a few 1000 K reached in the inner, upper
ture that might be due to a warped inner disk (Quillen 2006). atmosphere.
Modeling these asymmetries is beyond the scope of this study WeconcludethatthewidthoftheCOlinesisaninteresting
and would requiretighterobservationalconstraintson the den- indicatoroftheradialoriginoftheemissionandthusaprobe/test
sitystructureofthedisk. of the temperaturestructure. With currentfacilities, lines up to
The CO J = 16 15 and J = 30 29 lines are predicted CO J =16 15canbespectrallyresolved,allowingustostudy
to be considerably b−roader than those−of CO J = 3 2 and regions wit−hin radii of a few tens of AU as suggested by our
J = 10 9. While CO J = 3 2 and J = 10 9 bo−th have results.
a width−of 5 km s 1, CO J−= 16 15 and−J = 30 29
−
have widths∼of 9 km s 1 and 12 k−m s 1. This can be−un-
∼ − ∼ − 4. Results:Dependenceonparameters
derstoodbased on the originof those lines from regionscloser
to the star. For the assumed Keplerian velocity field around a This section presents the results of a parameterstudy. We vary
2.5 M star,theprojectedvelocityalongthesemi-majoraxisis different input parameters of the model, such as the size of
vproj =⊙sin(i)√M G/r = 31.5rA−U1/2 kms−1.Foragivenvelocity the disk or the amount of gas in the disk in order to under-
v intheobserv∗edspectra,r correspondstothemaximumra- stand the dependence of the line fluxes on those parameters.
proj
diusfromwhichthelinephotonscanemerge.Forthehalfwidth Understandingthesedependenceswillhelpustointerpretobser-
of the CO lines discussed here (2.5, 4, and 6 km s 1) we get vationaltrendsandalsotoquantifytherobustnessoftheresults,
−
r = 160, 50,and 27 AU, roughlycorrespondingto the radiiof giventhatlargeuncertaintiesenterthemodeling(Section5.5).
9
Brudereretal.:ThewarmgasatmosphereoftheHD100546disk
4.1.Varyingsize,gas/dustratio,andcarbonabundance considerablepartoftheemissionoriginatesfromwithin220AU
(Section3.4).
Keyparametersforthegasmodelingarethetotalamountofgas As expected, the fine-structure lines of [OI] for gas/dust
and the size of the disk. In this section, we vary the outer ra- = 20donotchangewiththeamountofcarboninthegas.They
diusofthegasdisktobeeither200or400AUandassumethat
howeverslightly scale with the outer radiusby aboutthe same
gas/dust = 20 or 100. A disk outer radius of r = 400 AU
out factorasthelow-JlinesofCO.Thiscanbeunderstoodbythese
and gas/dust = 20 (= 100) yields a gas mass of 8 10 4 M
− linesemergingfromwithinaboutthesameradialregion,asdis-
(4 10 3 M ). For an outer radius of r = 200 A×U, the ga⊙s
− out cussedinSection3.4.
ma×ssis4 1⊙0 4 M (2 10 3 M ),thusafactoroftwolower
− − The[CI]and[CII]linesdependonboththeouterradiusand
thanforr× =400A⊙U. × ⊙
out theamountofcarboninthegasphasebysimilaramounts.This
Theouterradiusofthediskisdifficulttodetermine,asdis- istheresultofbothlinesbeingopticallythinandemergingfrom
cussedinMuldersetal.(2011).ForHD100546,scatteredlight approximatelythesameregion.Thelinefluxesindeedscalewith
hasbeendetected outto 1000AU (Ardilaetal. 2007), butit the amountof carbonin the atmosphere,while they changeby
∼
remainsunclearwhetherthis emission originatesfromthe disk aboutafactoroffourwithradius.
or a diffuse remnantenvelope.Thus, the disk might be signifi- Themodelswith gas/dust= 100,shown in the lower panel
cantlysmaller.Modelingthelow-JCOlines,Panic´etal.(2010) ofFigure8,exhibitverysimilardependencesontheouterradius
constrainedthesizeofthegasdisktobe 400AUandthegas andamountofcarboninthegasphase.Howdothelineschange
mass to be 10−3 M . Muldersetal. (2011∼) employed an expo- withthe largeramountofgasintheatmosphere?Theoptically
nentialcutoffinsur⊙facedensityoutside350AU.Inotherdisks, thinhigh-JlinesofCOapproximatelyscalewiththeamountof
Hughesetal.(2008)foundthatCOJ =3 2canbemoreclearly gas. However,since the thermalbalanceis also affected by the
−
explainedwhensuchaexponentialcutoffisused.Here,weuse higherdensity,leadingtoslightlyhighertemperatures,thelines
a sharpcutoffatrout = 400AU (Panic´etal. 2010),butwe also increase by more than a factor of five. As expected, the low-J
consideradiskwitharadiusofonly200AU(Pantinetal.2000). lines scale by a smaller factor, owing to optical depth effects.
The gas/dustratio is assumed to be either an ISM value of The[OI]fluxesapproximatelyscalewithgasmass.Thecarbon
100oralowervalue,aspreviouslysuggestedbyChapillonetal. fine-structurelinesscalebyasmallerfactor,asthehigherdensity
(2010)toexplainthenon-detectionof[CI]370µmand609µm movestheC+/COtransitionupintheatmosphereresultingina
linestowardsthe HerbigAe star CQ Tau. We adoptgas/dust= smallerincreaseinthecolumndensity.
20,whichissimilartotheirchoice.Asmentionedbefore,these Thelineratio[CI]/[CII]isaboutafactoroftwolowerforthe
gas/dustratios only refer to the populationof small grainsand highergas/dustratio.Thisisduetodifferentbranchingratiosin
arethusupperlimits. theC+destruction.TheradiativeassociationofC+withH leads
2
The carbonbudgetofthe gasdependsonthe elementalde- toCH+,while grainsurfacereactionsofC+ with hydrogenated
2
pletion on dust grains. The warm ISM shows signs of little or PAHs (PAH:H) leads to CH+. Following a chain of reactions
nodepletionofoxygenandwethusassumethatalloxygennot withH andelectronrecombinations,CH+ andCH+ leadtoCH
2 2
locked up in silicates is in the gas phase. We note that oxygen andCH .Forhigherdensities,CHandCH areturnedintoCO
2 2
mayfreeze-outas moleculesontothe dustgrains,e.g.as water rather than being photodissociated (see Tielens&Hollenbach
ice,butthishappensonlyinthecoldshieldedregionsofthedisk 1985). This only slightly shifts the CO transition, thus affects
(seeSection3.1).Carbon,however,maybedepletedbyaconsid- theCOfluxesonlyslightly,butdoesaffectthe[CI]lines.
erablefractionbylockingitupinrefractorymaterial.Wechose Thereissomedegeneracybetweenmodelshavingmoregas
acarbonabundanceofδ 0.1,correspondingtoanabundance (gas/dust=100)butlesscarbon(δ =0.1)andmodelswithless
C C
of2.4 10 5relativetohy∼drogen2.Inthisway,wecanstudythe gas(gas/dust=20)andmorecarbon(δ =0.5),sincetheyhave
− C
×
degeneracybetweenhavingahighergas/dustratioof100com- the same amount of carbon in the atmosphere. These models
paredto20andalowercarbongasphaseabundanceofδ =0.1 withthesameouterradiusagreemorecloselythanaboutafac-
C
comparedtoδ 0.5.Forgas/dust= 100,wealsorunmodels toroftwointhelow-J tomid-JlinesofCOand[CII](seealso
C
∼
withδ =0.05. Figure9,modelswithR =5.5).Thehigh-JlinesofCOexhibit
C V
InFigure8,weshowtheintegratedlinefluxesforthemod- largerchanges.Asdiscussedbefore,neutralcarbonchangesby
elswithdifferentradii,gas/dustratios,andcarbonabundancesin aboutafactorofthree.
thegas,asinFigure5.Wefirstdiscussthemodelswithgas/dust
=20shownintheupperpanelofthefigure.Thelow-Jandhigh-
4.2.Varyingthedustopacity
J linesofCOhavedifferentbehaviors.Asexpected,thehigh-J
linesdonotdependontheouterradiusofthedisksincetheradi- The dustopacitiesat UV wavelengthsare anotherkeyparame-
ationemergesfromtheinnerdisk.Theopticallythinhigh-Jlines terofthegas,astheycontrolthepenetrationofthehigh-energy
howeverscalewiththeamountofcarboninthegas.Wenotethat photonsintothediskatmosphere.Thisaffectsboththechemistry
thisisalreadytrueformid-J linesthataremarginallyoptically andthermalbalance,forexamplebymeansofthephotodissoci-
thick.Theopticallythicklow-Jlinesdependlessontheamount ation/ionization of molecules or the photoelectric effect on the
ofcarbon,withachangebetweenthemodelofthesameradius dust grains. The opacity at short wavelengths is dominated by
ofaboutafactoroftwo.Wenotethattheseopticallythicklines VSGsandPAHs.
maystilldependontheabundance,sincee.g.thelinewingsmay Observationally,thesizeofthesmallestgrainsisdifficultto
remainthin.Thelow-J linesalsodependontheouterradiusof determine.ForHD100546,indicationsofgrainprocessingand
thedisk.Changingtheradiusfrom200AUto400AUincreases largerminimumgrainsizes were foundbyArdilaetal. (2007).
the area of the disk by about a factor of four. The low-J lines Bouwmanetal.(2003)suggestedthatthesizedistributionsvary
howeveronlychangebyaboutafactoroftwo.Thisisbecausea withradii,employingapopulationofsmallergrainsintheinner
40 AU and larger grains in the outer disk. Using such a grain
2 δ isdefinedasthefractionofcarboninthegas-phase(SeeSection distribution,Benistyetal.(2010)fittheSEDusingsilicatedust
C
3) grainsandasurfacelayerof0.05 1µmgrainsat13 50AUand
− −
10