CO2 infrared emission as a diagnostic of planet-forming regions of disks

2.6 MB·

by  Arthur Bosman

Astronomy&Astrophysicsmanuscriptno.Bosman_CO2_2017_01-26 (cid:13)cESO2017
January30,2017
CO infrared emission as a diagnostic
2
of planet-forming regions of disks
ArthurD.Bosman1,SimonBruderer2,andEwineF.vanDishoeck1,2
1 LeidenObservatory,LeidenUniversity,POBox9513,2300RALeiden,TheNetherlands
e-mail:[email protected]
2 Max-Planck-InsitutfürExtraterrestrischePhysik,Gießenbachstrasse1,85748Garching,Germany
January30,2017
7 ABSTRACT
1
0 Context.Theinfraredro-vibrationalemissionlinesfromorganicmoleculesintheinnerregionsofprotoplanetarydisksareunique
2 probesofthephysicalandchemicalstructureofplanetformingregionsandtheprocessesthatshapethem.Theseobservedlinesare
mostlyinterpretedwithlocalthermalequilibrium(LTE)slabmodelsatasingletemperature.
n
Aims. The non-LTE excitation effects of carbon dioxide (CO ) are studied in a full disk model to evaluate: (i) what the emitting
a 2
J regionsofthedifferentCO2 ro-vibrationalbandsare;(ii)howtheCO2 abundancecanbebesttracedusingCO2 ro-vibrationallines
usingfutureJWSTdataand;(iii)whattheexcitationandabundancestellusabouttheinnerdiskphysicsandchemistry.CO isa
7 2
majoricecomponentanditsabundancecanpotentiallytestmodelswithmigratingicypebblesacrosstheiceline.
2
Methods.Afullnon-LTECO excitationmodelhasbeenbuiltstartingfromexperimentalandtheoreticalmoleculardata.Thechar-
2
acteristics of the model are tested using non-LTE slab models. Subsequently the CO line formation has been modelled using a
] 2
R two-dimensionaldiskmodelrepresentativeofT-TauridiskswhereCO2isdetectedinthemid-infraredbytheSpitzerSpaceTelescope.
Results. TheCO gasthatemitsinthe15µmand4.5µmregionsofthespectrumisnotinLTEandarisesintheupperlayersof
S 2
disks,pumpedbyinfraredradiation.Thev 15µmfeatureisdominatedbyopticallythickemissionformostofthemodelsthatfit
2
h. the observations and increases linearly with source luminosity. Its narrowness compared with that of other molecules stems from
p a combination of the low rotational excitation temperature (∼ 250 K) and the inherently narrower feature for CO2. The inferred
- CO2 abundances derived for observed disks range from 3×10−9 to 1×10−7 with respect to total gas density for typical gas/dust
o ratiosof1000,similartoearlierLTEdiskestimates.Line-to-continuumratiosarelow,oforderafew%,stressingtheneedforhigh
r signal-to-noise(S/N >300)observationsforindividuallinedetections.
t
s Conclusions. The inferred CO abundances are much lower than those found in interstellar ices (∼ 10−5), indicating a reset of
2
a the chemistry by high temperature reactions in the inner disk. JWST-MIRI with its higher spectral resolving power will allow a
[ muchmoreaccurateretrievalofabundancesfromindividual P−andR−branchlines,togetherwiththe 13CO Q-branchat15µm.
2
1 The 13CO2 Q-branchisparticularlysensitivetopossibleenhancementsofCO2 duetosublimationofmigratingicypebblesatthe
v iceline(s).ProspectsforJWST-NIRSpecarediscussedaswell.
0
Keywords. Protoplanetarydisks–molecularprocesses–astrochemistry–radiativetransfer–line:formation
4
0
8
01. Introduction some molecules such as H O and HCN have reaction barriers
2
. in their formation pathways that make it difficult to produce
1Mostobservedexo-planetsorbitclosetotheirparentstar(fora
the molecule in high abundances at temperatures below a few
0reviewsee:Udry&Santos2007;Winn&Fabrycky2015).The
hundred Kelvin. As soon as the temperature is high enough to
7
atmospheres of these close-in planets show a large diversity in
overcomethesebarriers,formationisfastandtheybecomema-
1
molecular composition (Madhusudhan et al. 2014) which must
: jorreservoirsofoxygenandnitrogen.Aninterestingexampleis
vbesetduringplanetformationandthusberepresentativeofthe
formed by the main oxygen bearing molecules, H O and CO :
inatalprotoplanetarydisk.Understandingthechemistryofthein- 2 2
X thegasphaseformationofboththesemoleculesincludestheOH
ner,planet-formingregionsofcircumstellardisksaroundyoung radical.Attemperaturesbelow∼200KtheformationofCO is
arstars will thus give us another important piece of the puzzle of faster,leadingtohighgasphaseabundances,upto∼ 10−6 w2ith
planetformation.PrimemoleculesforsuchstudiesareH O,CO,
2 respectto(w.r.t.)totalgasdensity,inregionswhereCO isnot
CO andCH whicharethemajoroxygen-andcarbon-bearing 2
2 4 frozen out. When the temperature is high enough, H O forma-
speciesthatsettheoverallC/Oratio(Öbergetal.2011). 2
tion will push most of the gas phase oxygen into H O and the
2
The chemistry in the inner disk, i.e., its inner few AU, dif- CO abundance drops to ∼ 10−8 (Agúndez et al. 2008; Walsh
fersfromthatintheouterdisk.ItlieswithintheH OandCO 2
2 2 et al. 2014, 2015). Such chemical transitions can have strong
icelinessoallicyplanetesimalsaresublimated.Thelargerange
implicationsfortheatmosphericcontentofgasgiantsformedin
oftemperatures(100–1500K)anddensities(1010−1016 cm−3)
these regions if most of their atmosphere is accreted from the
thenmakesforadiversechemistryacrosstheinnerdiskregion
surroundinggas.
(see e.g. Willacy et al. 1998; Markwick et al. 2002; Agúndez
etal.2008;Henning&Semenov2013;Walshetal.2015).The Amajorquestionistowhatextenttheinnerdiskabundances
driving cause for this diversity is high temperature chemistry: indeed reflect high temperature chemistry or whether continu-
Articlenumber,page1of22
A&Aproofs:manuscriptno.Bosman_CO2_2017_01-26
ously migrating and sublimating icy planetesimals and pebbles disk parameters affect the H O emission. Mandell et al. (2012)
2
attheicelinesreplenishthediskatmospheres(Stevenson&Lu- comparedaLTEdiskmodelanalysisusingRADLITEwithslab
nine1988;Ciesla&Cuzzi2006).Interstellaricesareknownto modelsandconcludedthat,whileinferredabundanceratioswere
berichinCO ,withtypicalabudancesof25%w.r.t.H Oice,or similarwithfactorsofafew,therecouldbeordersofmagnitude
2 2
about10−5 w.r.t.totalgasdensity(deGraauwetal.1996;Gibb differences in absolute abundances depending on the assumed
etal.2004;Berginetal.2005;Pontoppidanetal.2008;Boogert emittingareainslabmodels(seealsodiscussioninSalyketal.
etal.2015).CometaryicesshowsimilarlyhighCO /H Oabun- 2011b). Thi et al. (2013) concluded that the CO infrared emis-
2 2
danceratios(Mumma&Charnley2011;LeRoyetal.2015).Of sion from disks around Herbig stars was rotationally cool and
all molecules with high ice abundances, CO shows the largest vibrationallyhotduetoacombinationofinfraredandultraviolet
2
contrast between interstellar ice and high temperature chem- (UV)pumpingfields(seealsoBrownetal.2013).Brudereretal.
istryabundances,andcouldthereforebeagooddiagnosticofits (2015) modelled the non-LTE excitation and emission of HCN
chemistry.Pontoppidan&Blevins(2014)arguebasedonSpitzer concludingthattheemittingareaformid-infraredlinescanbe10
SpaceTelescopedatathatCO isnotinheritedfromtheinterstel- timeslargerindisksthantheassumedemittingareainslabmod-
2
larmediumbutisresetbychemistryintheinnerdisk.However, elsduetoinfraredpumping.OurstudyofCO isalongsimilar
2
that analysis used a Local Thermodynamic Equilibrium (LTE) linesasthatforHCN.
CO excitation model coupled with a disk model and did not As CO cannot be observed through rotational transitions
2 2
investigate the potential of future instruments, which could be in the far-infrared and submillimeter, because of the lack of a
moresensitivetoacontributionfromsublimatingplanetesimals. permanent dipole moment, it must be observed through its vi-
Here we re-consider the retrieval of CO abundances in the in- brationaltransitionsatnear-andmid-infraredwavelengths.The
2
nerregionsofprotoplanetarydisksusingafullnon-LTEexcita- CO inourownatmospheremakesitimpossibletodetectthese
2
tionandradiativetransferdiskmodel,withaforwardlooktothe CO linesfromastronomicalsourcesfromtheground,andeven
new opportunities offered by the James Webb Space Telescope atal2titudesof13kmwithSOFIA.ThismeansthatCO hastobe
2
(JWST). observedfromspace.CO hasbeenobservedbySpitzerinpro-
2
The detection of infrared vibrational bands seen from CO , toplanetarydisksthroughitsv Q-branchat15µmwheremany
2 2
C H andHCN,togetherwithhighenergyrotationallinesofOH individual Q−band lines combine into a single broad Q-branch
2 2
andH O,wasoneofthemajordiscoveriesoftheSpitzerSpace feature at low spectral resolution (Lahuis et al. 2006; Carr &
2
Telescope (e.g. Lahuis et al. 2006; Carr & Najita 2008; Salyk Najita 2008). These gaseous CO lines have first been detected
2
etal.2008,2011b;Pascuccietal.2009;Pontoppidanetal.2010; inhighmassprotostarsandshockswiththeInfraredSpaceOb-
Carr & Najita 2011; Najita et al. 2011; Pascucci et al. 2013). servatory (ISO, e.g., van Dishoeck et al. 1996; Boonman et al.
These data cover wavelengths in the 10–35 µm range at low 2003a,b).CO alsohasastrongbandaround4.3µmduetothe
spectralresolvingpowerofλ/∆λ=600.Complementaryground- v asymmetric2stretchmode.ThismodehashighEinsteinAco-
3
basedinfraredspectroscopyofmoleculessuchasCO,OH,H O, efficientsandthusshouldthusbeeasilyobservable,buthasnot
2
CH , C H and HCN also exists at shorter wavelengths in the beenseenfromCO gastowardsprotoplanetarydisksorproto-
4 2 2 2
3–5 µm range (e.g. Najita et al. 2003; Gibb et al. 2007; Salyk stars,incontrastwiththecorrespondingfeatureinCO ice(van
2
etal.2008,2011a;Fedeleetal.2011;Mandelletal.2012;Gibb Dishoecketal.1996).
&Horne2013;Brownetal.2013).Thehighspectralresolving
The CO v Q-branch profile is slightly narrower than that
powerofR = 25000−105 forinstrumentslikeKeck/NIRSPEC 2 2
of C H and HCN observed at similar wavelengths. These re-
and VLT/CRIRES have resolved the line profiles and have re- 2 2
sultssuggestthatCO isabsent(orstronglyunder-represented)
vealed interesting kinematical phenomena, such as disk winds 2
intheinner,hottestregionsofthedisk.FulldiskLTEmodeling
in the inner disk regions (Pontoppidan et al. 2008, 2011; Bast
ofRNO90byPontoppidan&Blevins(2014)usingRADLITE
et al. 2011; Brown et al. 2013). Further advances are expected
showedthattheobservationsofthisdiskfavouralowCO abun-
with VLT/CRIRES+ as well as through modelling of current 2
dance(10−4 w.r.t.H O,≈10−8 w.r.t.totalgasdensity).Theslab
datawithmoredetailedphysicalmodels. 2
models by Salyk et al. (2011b) indicate smaller differences be-
Protoplanetarydiskshaveacomplexphysicalstructure(see
tweentheCO andH Oabundances,althoughCO isstillfound
Armitage2011,forareview)andputtingallphysics,frommag- 2 2 2
tobe2to3ordersofmagnitudelowerinabundance.
neticallyinducedturbulencetofullradiativetransfer,intoasin-
glemodelisnotfeasible.Thismeansthatsimplificationshaveto To properly analyse CO2 emission from disks, a full non-
bemade.DuringtheSpitzerera,themodelsusedtoexplainthe LTE excitation model of the CO2 ro-vibrational levels has to
observationswereusuallyLTEexcitationslabmodelsatasingle be made, using molecular data from experiments and detailed
temperature.With2DphysicalmodelssuchasRADLITE(Pon- quantumcalculations.Thismodelcanthenbeusedtoperforma
toppidanetal.2009)andwithfull2Dphysical-chemicalmodels simpleslabmodelstudytoseeunderwhichconditionsnon-LTE
such as Dust and Lines (DALI, Bruderer et al. 2012; Bruderer effects may be important. These same slab model tests are also
2013) or Protoplanetary Disk Model (ProDiMo, Woitke et al. usedtochecktheinfluencesoftheassumptionsmadeinsetting
2009)itisnowpossibletofullytakeintoaccountthelargerange up the ro-vibrational excitation model. Such CO2 models have
oftemperaturesanddensitiesaswellasthenon-localexcitation been developed in the past for evolved AGB stars (Cami et al.
effects.Forexample,ithasbeenshownthatitisimportanttoin- 2000; González-Alfonso & Cernicharo 1999, e.g.,) and shocks
cluderadiativepumpingintroducedbyhot(500−1500K)ther- (e.g.,Boonmanetal.2003b),butnotappliedtodisks.
maldustemissionofregionsjustbehindtheinnerrim.Thishas Our CO excitation model is coupled with a full protoplan-
2
beendoneforH ObyMeijerinketal.(2009)whoconcludedthat etarydiskmodelcomputedwithDALItoinvestigatetheimpor-
2
to explain the mid-infrared water lines observed with Spitzer, tanceofnon-LTEexcitation,infraredpumpinganddustopacity
waterislocatedintheinner∼1AUinaregionwherethelocal ontheemissionspectra.Inaddition,theeffectsofvaryingsome
gas-to-dustratiois1–2ordersofmagnitudehigherthanthein- key disk parameters such as source luminosity and gas/dust ra-
terstellar medium (ISM) value. Antonellini et al. (2015, 2016) tiosonlinefluxesandline-to-continuumratiosareinvestigated.
performed a protoplanetary disk parameter study to see how Finally, Spitzer data for a set of T-Tauri disks are analysed to
Articlenumber,page2of22
A.D.Bosmanetal.:CO infraredemissionasadiagnostic ofplanet-formingregionsofdisks
2
manetal.2013).Linesdenotethetransitionsthataredipoleal-
lowed. Colours denote the part of the spectrum where features
4 6µm
3000 8−12µm willshowup.ThiscolourcodingisthesameasinFig.2where
011 1(1) 1−2 20µm amodelCO2spectrumispresented.
−
4000 CO is a linear molecule with a 1Σ+ ground state. It has a
2 g
symmetric,v ,andanasymmetric,v ,stretchingmode(bothof
1 3
2500 J = 80 theΣtype)andadoublydegeneratebendingmode,v (Πtype)
2
J = 78
withanangularmomentum,l.Avibrationalstateisdenotedby
000 1(1) these quantum numbers as: v vlv . The vibrational constant of
111 0(1) 1 2 3
033 0(1) 3000 the symmetric stretch mode is very close to twice that of the
) 2000 bendingmode.Duetothisresonance,stateswiththesamevalue
1m− 111 0(2) K) for2v1+v2 andthesameangularmomentummix.Thismixing
( leads to multiple vibrational levels that have different energies
c y
( g in a process known as Fermi splitting. The Fermi split levels
rgy 1500 022 0(1) 100 0(1) 2000ner have the same notation as the unmixed state with the highest
ne 100 0(2) E symmetricstretchquantumnumber,v1andnumberedinorderof
E decreasing energy.1 This leads to the vibrational state notation
of: v vlv (n) where n is the numbering of the levels. This full
1000 1 2 3
designation is used in Fig. 1. For the rest of the paper we will
dropthe(n)forthelevelswherethereisonlyonevariant.
011 0(1) 1000 ThenumberofvibrationalstatesintheHITRANdatabaseis
500 muchlargerthanthesetofstatesusedhere.Notallofthevibra-
tional states are needed to model CO in a protoplanetary disk
2
becausesomethehigherenergylevelscanhardlybeexcited,ei-
ther collisionally or with radiation, so they should not have an
0 J = 0 v vlv (n)=000 0(1) 0 impactontheemittedlineradiation.Weadoptthesamelevelsas
1 2 3
used for AGB stars in González-Alfonso & Cernicharo (1999)
andaddtothissetthe0330vibrationallevel.
Fig.1. VibrationalenergylevelsoftheCO molecule(right)together
2
with the rotational ladder of the ground state (left). Note that for the
groundstatetherotationalladderincreaseswith∆J=2.Linesconnect-
2.2. Rotationalladders
ingthevibrationallevelsdenotethestrongestabsorptionandemission
pathways.Thecolourindicatesthewavelengthrangeofthetransition:
blue,4–6µm,green,8–12µmandred,12–20µm(spectruminFig.2). The rotational ladder of the ground state is given in Fig. 1. All
MoreinformationontherotationalladdersisgiveninSec.2.2. statesupto J=80ineachvibrationalstateareincluded;thisro-
tationallevelcorrespondstoanenergyofapproximately3700K
(2550 cm−1) above the vibrational state energy. The rotational
derive the CO abundance structure using parametrized abun- structureofCO ismorecomplexthanthatofalineardiatomic
2 2
dances. likeCO.ThisisduetothefullysymmetricwavefunctionofCO
2
JWST will allow a big leap forward in the observing capa- inthegroundelectronicstate.ThismeansthatallstatesofCO
2
bilities at near- and mid-infrared wavelengths, where the inner needtobefullysymmetrictosatisfyBose-Einsteinstatistics.As
planet-forming regions of disks emit most of their lines. The aresult,notallrotationalquantumnumbers J existinallofthe
spectrometersonboardJWST,NIRSPECandMIRI(Riekeetal. vibrationalstates:somevibrationalstatesmissalloddoralleven
2015) with their higher spectral resolving power (R ≈ 3000) J levels.TherearealsoadditionalselectionsontheWangparity
compared to Spitzer (R = 600) will not only separate many of the states (e,f). For the ground vibrational state this means
blended lines (Pontoppidan et al. 2010) but also boost line-to- that only the rotational states with even J numbers are present
continuum ratios allowing detection of individual P, Q and R- andthattheparityofthesestatesisfixedtoe.
branch lines thus giving new information on the physics and
TherotationalstructureissummarizedinTable1.Thestates
chemistryoftheinnerdisk.Herewesimulatetheemissionspec- with v = v = 0 all have the same rotational structure as the
traofCO andits13CO isotopologuefromaprotoplanetarydisk 2 3
2 2 ground vibrational state. The 0110(1) state has both even and
atJWST resolution.Weinvestigatewhichoftheselinesaremost odd J levels starting at J = 1. The even J levels have f parity,
usefulforabundancedeterminationsatdifferentdiskheightsand
while the odd J levels have e parity. In general for levels with
pointouttheimportanceofdetectingthe13CO2feature.Wealso v (cid:44) 0 and v = 0, the rotational ladder starts at J = v with
investigate which features could signify high CO abundances 2 3 2
2 anevenparity,withtheparityalternatingintherotationalladder
aroundtheCO2icelineduetosublimatingplanetesimals. withincreasing J.Forv (cid:44)0andv =0,onlyodd Jlevelsexist
3 2
if v is odd, whereas only even J levels exist if v is even. All
3 3
levels have an e parity. For v (cid:44) 0 and v (cid:44) 0, the rotational
2. ModellingCO2 emission ladderisthesameasforthev22(cid:44)0andv3 =3 0caseifv3iseven,
whereastheparitiesrelativetothiscaseareswitchedifv isodd.
2.1. Vibrationalstates 3
Thestructureofamolecularemissionspectrumdependsonthe
vibrational level energies and transitions between these levels 1 Forexample:Fermisplittingofthetheoretical0200and1000levels
that can be mediated by photons. Fig. 1 shows the vibrational leadstotwolevelsdenotedas1000(1)and1000(2)wheretheformerhas
energyleveldiagramforCO fromtheHITRANdatabase(Roth- thehigherenergy.
2
Articlenumber,page3of22
A&Aproofs:manuscriptno.Bosman_CO2_2017_01-26
Table1. Therotationalstructureofthevibrationallevelsincludedin 2010;Neufeld2012).Duetothelackofdipolemoment,thecrit-
themodel.
ical density for rotational transitions of CO is expected to be
2
verylow(n <104)cm−3andthustheexactcollisionalrateco-
Vibrationallevel lowestJ Jlevelsandparity crit
efficientsarenotimportantforthehigherdensityenvironments
0000(1) 0 evenJ,e
considered here. A method similar to Faure & Josselin (2008);
0110(1) 1 evenJ, f;oddJ,e
Thietal.(2013);Brudereretal.(2015)isusedtocreatethefull
0220(1) 2 evenJ,e;oddJ, f state-to-state collisional rate coefficient matrix. The method is
1000(1,2) 0 evenJ,e
describedinAppendixA.
0330(1) 3 evenJ, f;oddJ,e
1110(1,2) 1 evenJ, f;oddJ,e
0001(1) 1 oddJ,e 2.4. CO spectra
2
0111(1) 1 evenJ,e;oddJ, f
Fig. 2 presents a slab model spectrum of CO computed using
2
the RADEX program (van der Tak et al. 2007). A density of
1016 cm−3 was used to ensure close to LTE populations of all
2.3. Transitionsbetweenstates levels. A column density of 1016 cm−2 was adopted, close to
theobservedvaluederivedbySalyketal.(2011b),withatem-
Tobeabletoproperlymodeltheemissionofinfraredlinesfrom
protoplanetary disks non-LTE effects need to be taken into ac- perature of 750 K and linewidth of 1 km s−1. The transitions
are labelled at the approximate location of their Q-branch. The
count. The population of each level is determined by the bal-
spectrum shows that, due to the Fermi splitting of the bending
ance of the transition rates, both radiative and collisional. The
radiativetransitionratesaresetbytheEinsteincoefficientsand and stretching modes, the 15 µm feature is very broad stretch-
the ambient radiation field. Einstein coefficients for CO have ing from slightly shorter than 12 µm to slightly longer than 20
2 µm for the absorption in the Earth atmosphere. For astronomi-
beenwellstudied,bothinthelaboratoryandindetailedquantum
cal sources, the lines between 14 and 16 µm are more realistic
chemical calculations (see e.g. Rothman et al. 2009; Jacquinet-
targets.
Husson et al. 2011; Rothman et al. 2013; Tashkun et al. 2015,
andreferencestherein).Thesearecollectedinseveraldatabases Two main emission features are seen in the spectrum. The
forCO energylevelsandEinsteincoefficientssuchastheCar- strong feature around 4.3 µm is caused by the radiative decay
bon Di2oxide Spectroscopic Database (CDSD) (Tashkun et al. of the 0001 vibration level to the vibrational ground state. As a
2015) and as part of large molecular databases such as HI- Σ−Σ transition this feature does not have a Q−branch, but the
TRAN (Rothman et al. 2013) and GEISA (Jacquinet-Husson R and P branches are the brightest features in the spectrum in
etal.2011).Herethe 12CO and 13CO datafromtheHITRAN LTEat750K.Thesecondstrongfeatureisat15µm.Thisemis-
databaseareused.Itshould2benotedtha2tthedifferencesbetween sioniscausedbytheradiativedecayofthe0110vibrationalstate
thethreedatabasesaresmallforthelinesconsideredhere,within intothegroundstate.Italsocontainssmallcontributionsofthe
afew%inlineintensityandlessthan1%forthelinepositions. 0220 → 0110 and 0330 → 0220 transitions. This feature does
The HITRAN database gives the energies of the ro- have a Q−branch which has been observed both in absorption
vibrationallevelsabovethegroundstateandtheEinstein Aco- (Lahuisetal.2006)andemission(Carr&Najita2008;Pontop-
efficients of transitions between them. Only transitions above pidan et al. 2010). The CO2 Q−branch is found to be narrow
a certain intensity at 296 K are included in the databases. The comparedtotheotherQ−branchesofHCNandC2H2 measured
weakestlinesincludedinthelinelistare13ordersofmagnitude inthesamesources.
weaker than the strongest lines. With expected temperatures in The narrowness is partly due to the fact that the CO
2
theinnerregionsofdisksrangingfrom100–1000K,noimpor- Q−branch is intrinsically narrower than the same feature for
tantlinesshouldbemissedduetothisintensitycut.Inthefinal, HCN. This has to do with the change in the rotational constant
narroweddownsetofstatesalltransitionsthataredipoleallowed betweenthegroundandexcitedvibrationalstates.Acomparison
areaccountedfor. between Q−branchprofilesforCO andHCNfortwooptically
2
Collisional rate coefficients between vibrational states are thin LTE models is presented in Fig. 3. The lighter HCN has a
collected from literature sources. The measured rate of the re- fullwidthhalfmaximum(FWHM)thatisabout50%largerthan
laxationofthe0110tothe0000statebycollisionswithH from thatofCO .Thedifferenceintheobservedwidthofthefeature
2 2
Allen et al. (1980) is used. Vibrational relaxation of the 0001 isgenerallylarger(Salyketal.2011b):theHCNfeatureistyp-
ically twice as wide as the CO feature. Thus the inferred tem-
state due to collisions with H is taken from Nevdakh et al. 2
2 perature from the CO Q−branch from the observations is low
(2003).ForthetransitionsbetweentheFermisplitlevelstherate 2
comparedtothetemperatureinferredfromtheHCNfeature.The
byJacobsetal.(1975)forcollisionsbetweenCO withCO is
2 2 intrinsically narrower CO Q−branch amplifies the difference,
usedwithascalingforthedecreasedmeanmolecularmass.Al- 2
makingitmorestriking.
though data used here supersede those in Taylor & Bitterman
(1969),thatpaperdoesgiveasensefortheuncertaintiesofthe
experiments. The different experiments in Taylor & Bitterman
2.5. Dependenceonkinetictemperature,densityand
(1969) usually agree within a factor of two and the numbers
radiationfield
used here from Allen et al. (1980) and Nevdakh et al. (2003)
fall within the spread for their respective transitions. It is thus Theexcitationof,andthelineemissionfrom,amoleculedepend
expected that the accuracy of the individual collisional rate co- strongly on the environment of the molecule, especially the ki-
efficientsisbetterthanafactoroftwo. netictemperature,radiationfieldandcollisionalpartnerdensity.
Noliteratureinformationisavailableforpurerotationaltran- In Fig. 4 slab model spectra of CO for different physical pa-
2
sitions induced by collisions of CO with other molecules. We rametersarecompared.Thedependenceontheradiationfieldis
2
therefore adopt the CO rotational collisional rate coefficients modelled by including a blackbody field of 750 K diluted with
from the LAMDA database (Schöier et al. 2005; Yang et al. a factor W: (cid:104)J (cid:105) = WB (T ) with T = 750 K. When test-
ν ν rad rad
Articlenumber,page4of22
A.D.Bosmanetal.:CO infraredemissionasadiagnostic ofplanet-formingregionsofdisks
2
21 sr)−− 102 000 1−000 0 0(1)0(1) 000(1) 0(1) 0(1)
m 2 1 0 1 2
c 101 0201 − 01 02
−− ) − −
1 1
− )) ( ) )
s 11 0 2 2
g 0(0( 1 0( 0(
y (er 100 0(2) 0(1) 111010 01 010 111
sit 00 00
n 1 1
te 10-1 1− 1−
n
d i 000 000
e
t
a
r 10-2
g
e
t
n 4.0 4.2 4.4 4.6 4.8 5.0 5.2 10 12 14 16 18 20
I
wavelength [µm]
Fig.2. CO slabmodelspectrumcalculatedwithRADEX(vanderTaketal.2007),eachlineinthespectrumisplottedseparately.Slabmodel
2
parametersare:density,1016cm−3;columndensityofCO ,1016cm−2;kinetictemperature,750Kandlinewidth,1kms−1.Forthesedensities,the
2
levelpopulationsareclosetolocalthermalequilibrium(LTE).SpectrumandlabelcolorcorrespondtothecolorsinFig.1
In the absence of a pumping radiation field, collisions are
1.0
needed to populate the higher energy levels. With enough col-
CO v 14.99 µm lisions, the excitation temperature becomes equal to the kinetic
2 2
temperature.Thedensityatwhichtheexcitationtemperatureof
HCN v 14.05 µm
0.8 2 a level reaches the kinetic temperature depends on the critical
density: n = A /K for a two-level system, where A is the
c ul ul ul
EinsteinAcoefficientfromlevelutolevellandK isthecolli-
ux sionalratecoefficientbetweentheselevels.Fordeunlsitiesbelow
Fl 0.6 the critical density the radiative decay is much faster than the

d collisionalexcitationandde-excitation.Thismeansthattheline
e
z intensityscalesasn/n .Abovethecriticaldensitycollisionalex-
ali citationandde-excitatcionarefast:theintensityisthennolonger
m 0.4
dependentonthedensity.Thecriticaldensityofthe15µmband
r
No iscloseto1012 cm−3,sothereislittlechangeinthisbandwhen
increasingthedensityabovethisvalue.However,whendecreas-
ingthedensitybelowthecriticalvaluethisresultsintheastrong
0.2
reductionofthebandstrength.Thecriticaldensityofthe4.3µm
featureiscloseto1015cm−3sobelowthisthelinesareordersof
magnitudeweakerthanwouldbeexpectedfromLTE.
0.0 Addingaradiationfieldhasasignificantimpactonboththe
0.25 0.20 0.15 0.10 0.05 0.00 0.05 4.3 and 15 µm features. The radiation of a black body of 750
Difference from Q(1) (µm) Kpeaksaround3.8µmsothe4.3µm/15µmfluxratiointhese
casesislargerthanthefluxratiowithoutradiationfieldforden-
sitiesbelowthecriticaldensityofthe4.3µmlines.Anotherdif-
Fig.3. v2 Q-branchprofileofCO2 andHCNatatemperatureof400 ferencebetweenthecollisionallyexcitedandradiativelyexcited
K.Fluxisplottedasfunctionoftheoffsetfromthelowestenergyline
states is that in the latter case vibrational levels that cannot be
(wavelengthgiveninthelegend).Thelinesareconvolvedtoaresolving
directly excited from the ground state by photons, such as the
powerR=600appropriateforSpitzerdata.Thefullwidthhalfmaximum
1000(1)and1000(2)levels,arebarelypopulatedatall.
(FWHM)forCO andHCNare0.4and0.6µmrespectively.
2
3. CO emissionfromaprotoplanetarydisk
ingtheeffectsofthekinetictemperatureanddensity,noincident 2
radiationfieldisincluded(W =0). Toproperlyprobethechemistryintheinnerdiskfrominfrared
Fig.4showsthatataconstantdensityof1012 cm−3 the4.3 lineemissiononeneedstogobeyondslabmodelswiththeirin-
µm band is orders of magnitude weaker than the 15 µm band. herent degeneracies. A protoplanetary disk model such as that
The 15 µm band increases in strength and also in width, with used here includes more realistic geometries and contains a
increasing temperature as higher J levels of the CO v vibra- broadrangeofphysicalconditionsconstrainedbyobservational
2 2
tionalmodecanbecollisionallyexcited.Especiallythespectrum data. Information can be gained on the location and extent of
at 1000 K shows additional Q branches from transitions origi- the emitting CO region as well as the nature of the excitation
2
nating from the higher energy 1000(1) and 1000(2) vibrational process.Bycomparingwithobservationaldata,molecularabun-
levelsat14and16µm. dancescanbeinferredasfunctionoflocation.Acriticalaspect
Articlenumber,page5of22
A&Aproofs:manuscriptno.Bosman_CO2_2017_01-26
3.1. Modelsetup
1.8
DetailsofthefullDALImodelandbenchmarktestsarereported
7 Temperature (1012 cm−3) in Bruderer et al. (2012) and Bruderer (2013). Here we use the
1000 K samepartsofDALIasinBrudereretal.(2015).Themodelstarts
1.6 with the input of a dust and gas surface density structure. The
gas and dust structures are parametrized with a surface density
6 profile
)
1 750 K
− 1.4
2m sr− 5 250 K Σ(R)=Σc(cid:32)RRc(cid:33)−γexp−(cid:32)RRc(cid:33)2−γ (1)
1.2
c andverticaldistribution
Density (750 K)
1rg s− 4 1015 cm−3 1.0 ρ(R,Θ)= √2Σπ(RRh)(R)exp−12(cid:32)π/h2(R−)Θ(cid:33)2, (2)
e
( withthescaleheightangleh(R) = h (R/R )ψ.Thevaluesofthe
y c c
t parametersfortheAS205(N)diskaretakenfromAndrewsetal.
i
ns 1012 cm−3 0.8 (2009)whofittedboththeSEDandsubmillimeterimagessimul-
3
e taneously.Astheinferredstructureofthediskisstronglydepen-
nt 109 cm−3 dentonthedustopacitiesandsizedistribution,thesamevalues
I
d 0.6 from Andrews et al. (2009) are used. They are summarized in
e Table 2 and the gas density structure is shown in Fig. 5, panel
t
ra 2 Rad. field (750 K, 109 cm−3) a.ThecentralstarisaT-TauristarwithexcessUVduetoaccre-
g tion.Alltheaccretionluminosityisassumedtobereleasedatthe
te 0.4 stellar surface as a 104 K blackbody. The density and tempera-
n W = 0.3
I tureprofilearetypicalforastronglyflareddiskasusedhere.The
temperature,radiationfieldandCO excitationstructurecanbe
1 2
0.2 foundintheappendix,Fig.C.1.
In setting up the model special care was taken at the inner
W = 0.1
rim,whereopticalandUVphotonsareabsorbedbythedustover
W = 0.01 averyshortphysicalpath.Toproperlygetthetemperaturestruc-
0 0.0
tureofthediskdirectlyaftertheinnerrim,highresolutioninthe
4.04.24.44.64.85.0 13 14 15 16 17
radial direction is needed. Varying the radial width of the first
Wavelength [µm]
cellsshowedthatthetemperaturestructureonlyconvergeswhen
thecellwidthofthefirsthandfulofcellsissmallerthanthemean
freepathoftheUVphotons.
Fig.4. CO slabmodelspectraformultiplekinetictemperatures,densi-
2 Themodelduststructureisirradiatedbythestarandthein-
tiesandradiationfields.ForallthecasestheCO columndensityiskept
2 terstellarradiationfield.AMonte-Carloradiativetransfermod-
at1016 cm−2 andtheintrinsiclinewidthissetto1kms−1.Thespectra
areoffsetforclarity.AllspectraarecalculatedwithRADEX(vander ule calculates the dust temperature and the local radiation field
Taketal.2007). atallpositionsthroughoutthedisk.Thegastemperatureisthen
assumedtobeequaltothedusttemperature.Thisisnottruefor
theupperandouterpartsofthedisk.FortheregionswereCO is
2
of the models is the infrared continuum radiation field, which abundantinourmodelsthedifferencebetweendusttemperature
hastobecalculatedaccuratelythroughoutthedisk.Thismeans and gas temperature computed by self-consistently calculating
thatdetailedwavelengthdependentdustopacitiesneedtobein- thechemistryandcoolingislessthan5%.Theexcitationmod-
cludedanddusttemperatureshavetobecalculatedonaveryfine ule calculates the CO level populations, using a 1+1D escape
grid,sincethepumpingradiationcanoriginateinadifferentpart probablitythatinclude2sthecontinuumradiationduetothedust
ofthediskthanthelines,e.g.,thenear-infraredforclosetothe (Appendix A.2 in Bruderer 2013). Finally the synthetic spectra
inner rim. The dust is also important in absorbing some of the are derived using the ray tracing module, which solves the ra-
lineflux,effectivelyhidingpartsofthediskfromourview. diative transfer equation along rays through the disk. The ray
Inthissection,theCO spectraaremodelledusingtheDALI tracing module as presented in Bruderer et al. (2012) is used
2
(Dust and Lines) code (Bruderer et al. 2012; Bruderer 2013). as well as a newly developed ray-tracing module that is pre-
The focus is on emission from the 15 µm lines that have been sented in Appendix B which is orders of magnitude faster, but
observedwithSpitzerandwillbeobservablewithJWST-MIRI. afewpercentlessaccurate.Intheray-tracingmoduleathermal
Trendsintheshapeofthev Q−branchandtheratiosoflinesin broadeningandturbulentbroadeningwithFWHM∼0.2kms−1
2
theP−andR−branchesareinvestigatedandpredictionsarepre- isused,whichmeansthatthermalbroadeningdominatesabove
sented.Firstthemodelanditsparametersareintroducedandthe ∼40K.ThegasisinKeplerianrotationaroundthestar.Thisap-
results of one particular model are used as illustration. Finally proachissimilartoMeijerinketal.(2009)andThietal.(2013)
theeffectsofvariousparametersontheresultinglinefluxesare for H O and CO respectively. However Thi et al. (2013) used
2
shown,inparticularsourceluminosityandgas/dustratio.Asin achemicalnetworktodeterminetheabundances,whereashere
Brudereretal.(2015),themodelisbasedonthesourceAS205 onlyparametricabundancestructuresareusedtoavoidtheadded
(N)butshouldberepresentativeofatypicalT-Tauridisk. complexityanduncertaintiesofthechemicalnetwork.
Articlenumber,page6of22
A.D.Bosmanetal.:CO infraredemissionasadiagnostic ofplanet-formingregionsofdisks
2
Table2. AdoptedstandardmodelparametersfortheAS205(N)star
plusdisk.
0001R(7) 4.25 µm
Parameter Value
Star 10-16
Mass M [M ] 1.0
(cid:63) (cid:12) )
Luminosity L(cid:63)[L(cid:12)] 4.0 2−
Effectivetemperature Teff [K] 4250 m 10-17
Accretionluminosity L [L ] 3.3 W
accr (cid:12) (
Accretiontemperature Taccr [K] 10000 x
u
DDiisskkMass(g/d =100) M [M ] 0.029 Fl 10-18 g/d=100 xin=1×10−8
Surfacedensityindex γ disk (cid:12) 0.9 g/d=1000 xin=1×10−7
CInhnaerrarcatedriiussticradius RRcin[[AAUU]] 04.169 10-19 g/d=10000 xin=1×10−6
Scaleheightindex ψ 0.11
Scaleheightangle h [rad] 0.18 10-14 14.8 - 15.0 µm
c
Dustpropertiesa
Size a[µm] 0.005–1000
Sizedistribution dn/da∝a−3.5 2)− 10-15
m
Composition ISM

Gas-to-dustratio 100 (W 10-16
Distance d[pc] 125 x Observations
Inclination i[◦] 20 u
Fl
10-17
Notes.(a) DustpropertiesarethesameasthoseusedinAndrewsetal.
(2009) and Bruderer et al. (2015). Dust composition is taken from
Draine&Lee(1984)andWeingartner&Draine(2001). 10-18
10-9 10-8 10-7 10-6
Outer CO abundance
TheadoptedCO abundanceiseitheraconstantabundance 2
2
orajumpabundanceprofile.Theabundancethroughoutthepa-
per is defined as the fractional abundance w.r.t n = n(H) + Fig.6. LinefluxesasfunctionsofouterCO abundancesformodels
H 2
2mna(gH,2w).hTichheiisnnaeprprroegxiiomnatieslydetfihneerdegbiyonTw>he2r0e0thKeatrnadnsAfVorm>a2- pwainthelcsohnoswtasntthdeusfltumxaosfst(hge/Rdg(a7s))lainndevfraormyinthgegfausn/dduasmteranttiaolsa.sTyhmemupetpreicr
stretch band at 4.3 µm. The lower panel shows the flux contained in
tionofOHintoH OisfasterthanthereactionofOHwithCO
2 the 15 µm Q-branch feature. The grey region denotes the full range
to form CO . The outer region is the region of the disk with
2 inCO fluxesfromthedisksthatarereportedinSalyketal.(2011b),
T < 200 K or A < 2 mag, where the CO abundance is ex- 2
V 2 scaledtothedistanceofAS205(N).The15µmfeaturecontainsthe
pAeVct<ed0t.o5pmeaakg.aNsopChoOt2odisisassoscuimateiodntoisbeexppreecsteendttionrbeegivoenrysweffiith- pflruixmafrroilmyomnutlhtieploeutQer−CbrOancahbeusnwdaitnhce∆avn2d=th1e.tTothaelgC/Od2rafltiuoxadnedpdenodess
2
cientinthisregion.Thephysicalextentoftheseregionsisshown notstronglydependontheinnerCO abundances.Onlyforverylow
2
inpanelbofFig.5. outerCO abundancesistheeffectoftheinnerabundanceontheline
2
As shown by Meijerink et al. (2009) and Bruderer et al. fluxesvisible.Thefluxesformodelswithg/ddustaregiveninFig.D.1.
(2015), the gas-to-dust ("G/D") ratio is very important for the
resultinglinefluxesasthedustphotospherecanhidealargepor-
tionofthepotentiallyemittingCO .Herethegas-to-dustratiois emitting region is between 100 and 500 K and the CO exci-
2 2
changedintwoways,byincreasingtheamountofgas,orbyde- tation temperature ranges from 100–300 K (see Fig. C.1). The
creasingtheamountofdust.Whenthegasmassisincreasedand densityislowerthanthecriticaldensityatanypointintheemit-
thus the dust mass kept at the standard value of 2.9×10−4M , tingarea.
(cid:12)
this is denoted by g/dgas. If the dust mass is decreased and the PaneldofFig.5showsthecontributionforthev31→0R(7)
gasmasskeptat0.029M(cid:12)thisisdenotedbyg/ddust. linewiththesamelinesandcontoursaspanelc.Thecriticalden-
sityforthislineisveryhigh,∼ 1015 cm−3.Thismeansthatex-
ceptfortheinner1AUnearthemid-plane,thelevelpopulation
3.2. Modelresults
of the v level is dominated by the interaction of the molecule
3
PanelcofFig.5presentsthecontributionfunctionforoneofthe withthesurroundingradiationfield.Theemittingareaofthev3
15µmlines,thev 1 → 0 Q(6)line.Thecontributionfunction 1 → 0 R(7) line is smaller compared to that of the line at 15
2
showstherelative,azimuthallyintegratedcontributiontotheto- µm. The emitting area stretches from close the the sublimation
tal integrated line flux. Contours show the areas in which 25% radiusupto∼ 10AU.Theexcitationtemperaturesforthisline
and 75% of the emission is located. Panel c also includes the arealsohigher,rangingfrom300–1000Kintheemittingregion
τ=1surfaceforthecontinuum(blue)duetothedust,theτ=1 (seeFig.C.1).
surface for the v 1 → 0 Q(6) line (red) and surface where the In Fig. 6 the total flux for the 0001−0000R(7) line at 4.25
2
densityisequaltothecriticaldensity.Theareaofthediskcon- µm and the 15 µm feature integrated from 14.8 to 15.0 µm are
tributing significantly to the emission is large, an annulus from presentedasfunctionsofx ,fordifferentgas-to-dustratiosand
out
approximately 0.7 to 30 AU. The dust temperature in the CO different x . The 15 µm flux shows an increase in flux for in-
2 in
Articlenumber,page7of22
A&Aproofs:manuscriptno.Bosman_CO2_2017_01-26
a.) ngas (cm−3) b.) CO2 abundance
1016
1.0
0.8 1014 AV<0.5CO2 iceline Fig. 5. Overview of one of the DALI mod-
z/r00..46 11001102 ATV<<2020 o Kr Retul(sr7es)ha0on0wd0i1enmgliintthetiesn.dgTirshekegsmitoronudscetfulorsreht,ohawebunQnh(d6aa)sn0ac1eg1sa0tsr-autnocd--
dust ratio, g/d = 1000 and a constant CO
0.2 108 xin xout abundanceof1g0as−7 withrespecttoH.Thepan2-
0.0 106 els show: (a) gas density structure; (b) abun-
dancestructureusedmodels:x andx arethe
c.) 0110Q(6) Line contribution d.) 0001R(7) Line contribution CO abundances in the inner ainnd outoeurt region
2
respectively,thegreyregionispartoftheouter
1.0 regionanddenotestheregionaroundtheCO
2
icelinewhereplanetesimalsareassumedtova-
0.8 τline=1 τline=1 porize. The abundance in this region is varied
/r0.6 inthemodelsinSec.4.2;(c)linecontribution
z τ =1 τ =1 functionoftheQ(6)0110lineat15µm,thecon-
0.4 dust dust
toursshowtheareasinwhich25%and75%of
0.2 thetotalfluxisemitted;(d)contributionfunc-
n=ncrit n=ncrit tionfortheR(7)0001lineat4.3µm.Panelsc
0.0 anddhavetheτ=1surfaceofdust(blue)and
10-1 100 101 102 10-1 100 101 102 line(red)andthen=n surface(black)over-
r (AU) r (AU) crit
plottedfortherelevantline.
creasingtotalCO abundanceandgas-to-dustratioandsodoes The grey band in Fig. 6 and Fig. D.1 shows the range of
2
thelinefluxofthe4.25µmlineformostoftheparameterspace. fluxesobservedforprotoplanetarydisksscaledtoacommondis-
Thetotalfluxneverscaleslinearlywithabundance,duetodiffer- tance of 125 pc (Salyk et al. 2011b). This figure immediately
entopacityeffects.Thedustisopticallythickatinfraredwave- shows that low CO abundances, x < 3 × 10−7, are needed
2 out
lengthsupto 100AU,sotherewillalwaysbeareservoirofgas to be consistent with the observations. Some disks have lower
thatwillbehiddenbythedust.Thelinesthemselvesarestrong fluxesthangivenbythelowestabundancemodel,whichcanbe
(havelargeEinsteinAcoefficients)andthenaturallinewidthis duetootherparameters.Amorecompletecomparisonbetween
relatively small (0.2 km s−1 FWHM). As a result the line cen- modelandobservationsismadeinSec.4.1.
ters of transitions with low J values quickly become optically
In AppendixE acomparison ismade betweenthe fluxes of
thick. Therefore, if the abundance, and thus the column, in the
models with CO in LTE and models for which the excitation
upper layers of the disk is high, the line no longer probes the of CO is calcula2ted from the rate coefficients and the Einstein
innerregions. This canbeseen inFig. 6asthe fluxesfor mod- A coeffi2 cients. The line fluxes differ by a factor of about three
elswithdifferentxinconvergewithincreasingxout.Convergence betweenthemodels,similartothedifferencesfoundbyBruderer
happensatlower x forhighergas-to-dustratios.Theinnerre-
out etal.(2015)(theirFig.6)forthecaseofHCN.
gionisquicklyinvisiblethroughthe4.25µmlinewithincreasing
gas-to-dustratios:foragas-to-dustratioof10000,thereisaless
than50%differenceinfluxesbetweenthemodelswithdifferent 3.2.1. Thev bandemissionprofile
2
innerabundances,evenforthelowestouterabundances.Thisis
notseensostronglyinthe15µmfeatureasitalsoincludeshigh Fig. 7 shows the v Q-branch profile at 15 µm for a variety of
2
Jlineswhicharestrongerinthehotterinnerregionsandarenot models.Alllineshavebeenconvolvedtotheresolvingpowerof
as optically thickas the low J lines. There is nosignificant de- JWST-MIRI at that wavelength (R = 2200, Rieke et al. 2015;
pendenceofthefluxontheinnerabundanceofCO iftheouter Wellsetal.2015)withthreebinsperresolutionelement.Panel
2
abundanceis> 3×10−7 andthegastodustratioishigherthan a shows the results from a simple LTE slab model at different
1000.Inthesemodelsthe15µmfeaturetracespartoftheinner temperatures whereas panels b and c presents the same feature
1AUbutonlytheupperlayers. from the DALI models. Panel b contains models with different
gas-to-dust ratios and abundances (assuming x = x ) scaled
in out
Differentwaysofmodellingthegas-to-dustratiohaslittleef- so g/d × x is constant. It shows that gas-to-dust ratio and
CO
2
fectontheresultingfluxes.Fig.6showsthefluxesforaconstant abundancearedegenerate.Itisexpectedthatthesemodelsshow
dustmassandincreasinggasmassforincreasingthegas-to-dust similarspectra,asthetotalamountofCO abovethedustphoto-
2
ratio,whereasFig.D.1inAppendixDshowsthefluxesforde- sphereisequalforallmodels.Thelackofanysignificantdiffer-
creasing dust mass for a constant gas mass. The differences in enceshowsthatcollisionalexcitationofthevibrationallyexcited
fluxes are very small for models with the same gas/dust ratio stateisinsignificantcomparedtoradiativepumping.Panelcof
timesCO abundance,irrespectiveofthetotalgasmass:fluxes Fig.7showstheeffectofdifferentinnerabundancesonthepro-
2
agree within 10% for most of the models. This reflects the fact file.Forthehighestinnerabundanceshown,1×10−6,anincrease
that the underlying emitting columns of CO are similar above intheshorterwavelengthfluxcanbeseen,butthedifferencesare
2
thedustτ = 1surface.Onlythetemperatureoftheemittinggas farsmallerthanthedifferencesbetweentheLTEmodels.Panel
changes: higher temperatures for gas that is emitting higher up d shows models with similar abundances, but with increasing
in a high gas mass disk and lower temperatures for gas that is g/d .Thefluxinthe15µmfeatureincreaseswithg/d for
dust dust
emittingdeeperintothediskinalowdustmassdisk. thesemodelsascanbeseeninFig.D.1.Thisispartlyduetothe
Articlenumber,page8of22
A.D.Bosmanetal.:CO infraredemissionasadiagnostic ofplanet-formingregionsofdisks
2
a.) Thin LTE models b.) Constant column models c.) Different x models d.) Different g/d models
1.2 1.2 1.2 in 1.2
1.0 T=100 K 1.0 xCO2=3×10−9 1.0 xin=3×10−9 1.0 g/d=100
d Flux0.8 TT==360000 KK d Flux0.8 xxCCOO22==33××1100−−87 d Flux0.8 xxiinn==33××1100−−87 d Flux0.8 gg//dddduusstt==110000000
e0.6 e0.6 e0.6 e0.6
z z z z
ali ali ali ali
m0.4 m0.4 m0.4 m0.4
or or or or
N0.2 N0.2 N0.2 N0.2
0.0 0.0 0.0 0.0
14.85 14.90 14.95 15.00 14.85 14.90 14.95 15.00 14.85 14.90 14.95 15.00 14.85 14.90 14.95 15.00
Wavelength [µm] Wavelength [µm] Wavelength [µm] Wavelength [µm]
Fig.7. Q-branchprofilesofdifferentmodelsshownatJWST-MIRIresolvingpower.Allfluxesarenormalizedtothemaximumofthefeature.In
theleftpanelLTEpointmodelswithatemperatureof200K(cyan),400K(red)and800K(blue)areshown.Panelb.showsDALIdiskmodels
withaconstantabundanceprofileforwhichtheproductofabundancetimesgas-to-dustratioisconstant.Allthesemodelshaveverysimilartotal
fluxes.Themodelsshownareg/d =100,x =3×10−7inred;g/d =1000,x =3×10−8inblueandg/d =10000,x =3×10−9in
gas CO gas CO gas CO
cyan.Thespectraarevirtuallyindistinguishable2.Panelc.showsDALIdiskmodelswit2hajumpabundanceprofile,ag/d =10002,anouterCO
dust 2
abundanceof3×10−8 andaninnerabundanceof3×10−7 (red),3×10−8 (blue),3×10−9 (cyan).Themodelwiththehighestinnerabundance
shows a profile that is slightly broader than those of the other two. Panel d. shows DALI disk models with the same, constant abundance of
x =3×10−8,butwithdifferentg/d ratios.RemovingdustfromtheupperlayersofthediskpreferentiallybooststhehighJlinesinthetail
CO dust
ofth2efeatureasemissionfromthedenseandhotinnerregionsofthediskislessoccultedbydust.
wideningofthefeatureascanbeseeninPaneldwhichiscaused 800Karegiveninthefigure.Itcanbeseenthatthemodelsdo
by the removal of dust. Due to the lower dust photosphere it is not show strong differences below J = 20, where emission is
now possible for a larger part of the inner region to contribute dominatedbyopticallythicklines.Towardhigher J,themodel
tothisemission.Theinnerregionishotterandthusemitsmore withx =10−6startstodiffermoreandmorefromtheothertwo
in
towardhighJlinescausingtheQ−branchtowiden. models.Themodelswithx =10−7andx =10−8staywithina
in in
Fitting of LTE models to DALI model spectra in Fig. 7b-d factorof2ofeachotheruptoJ =80wherethemoleculemodel
resultsininferredtemperaturesof300–600K.Onlythemodels ends.
withastrongtail(bluelinesin7band7d)needtemperaturesof Models with similar absolute abundances of CO2 (constant
600Kforagoodfit,theothermodelsarewellrepresentedwith g/d × xCO ) but different g/dgas ratios are nearly identical: the
∼300K.Forcomparison,theactualtemperatureintheemitting widthofth2eQ-branchandtheshapesoftheP−andR−branches
layersis150–350K(Fig.C.1),illustratingthattheopticallythin aresetbythegastemperaturestructure.Thistemperaturestruc-
model overestimates the inferred temperatures. The proper in- tureisthesameformodelswithdifferentg/dgasratiosasitisset
clusion of optical depth effects for the lower-J lines lowers the bytheduststructure.Thetemperatureis,however,afunctionof
inferredtemperatures.Thismeansthatcarehastobetakenwhen g/ddust, but those temperature differences are not large enough
interpretingatemperaturefromtheCO profile.Awidefeature for measurable effects. From this it also follows that the exact
canbeduetohighopticaldepthsorhig2hrotationaltemperature collisionalratecoefficientsarenotimportant:Thedensityislow
ofthegas. enoughthattheradiationfieldcansettheexcitationofthevibra-
tionallevels.Atthesametimethedensityisstillhighenoughto
AbroaderlookattheCO spectrumisthusneeded.Theleft
2 be higher than the critical density for the rotational transitions,
panel of Fig. 8 shows the P, Q and R−branches of the vibra-
settingtherotationalexcitationtemperatureequaltothegaski-
tional bending mode transition at R = 2200, for models with
netictemperature.
different inner CO abundances and the same outer abundance
2 Thebranchshapesareafunctionofg/d atconstantabso-
of10−7.TheshapefortheR−andP−branchesisflatterforlow dust
luteabundance.Apartfromthetotalfluxwhichisslightlyhigher
to mid-J and slightly more extended at high J in the spectrum
athigherg/d (Fig.D.1),thespectraarealsobroader(Paneld.
from the model with an inner CO abundance of 10−6 than the dust
2 Fig.7).Thisisbecausethehotterinnerregionsarelessocculted
otherspectra.Thepeaksat14.4µmand15.6µmareduetothe
bydustforhigherg/d ratios.Thishottergashasmoreemis-
Q−branches from the transitions between 1110(1) → 1001(1) dust
sioncomingfromhighJlines,boostingthetailoftheQ−branch.
and1110(2)→1001(2)respectively.Theseareoverlappingwith To quantify the effects of different abundance profiles, line
lines from the bending fundamental P and R branches. For the
ratioscanalsobeinformative.Thelinesarechosensotheyare
constantandlowinnerCO abundances,10−7 and10−8 respec-
2 freefromwateremission(seeAppendixF).Thetoptwopanels
tivelyR−andP−branchshapesaresimilar,withmodelsdiffering ofFig.9showsthelineratiosforlinesinthe0110(1)→0000(1)
onlyinabsoluteflux.DecreasingtheinnerCO abundancefrom
2 15µmband:R(37):R(7)andP(15): P(51).TheR(7)andP(15)
10−8tolowervalueshasnoeffectofthelinestrengths. linescomefromlevelswithenergiesclosetothelowestenergy
TherightpanelofFig.8showsBoltzmannplotsofthespec- level in the vibrational state (energy difference is less than 140
tra on the left. The number of molecules in the upper state in- K). These levels are thus easily populated and the lines com-
ferredfromthefluxisgivenasafunctionoftheupperstateen- ingfromtheselevelsarequicklyopticallythick.TheR(37)and
ergy. The number of molecules in the upper state is given by: P(51)linescomefromlevelswithrotationalenergiesatleast750
N =4πd2F/(A hν g ),withdthedistancetotheobject,Fthe K above the ground vibrational energy. These lines need high
u ul ul u
integrated line flux, g the statistical weight of the upper level kinetic/rotational temperatures to show up strongly and need
u
and A and ν the Einstein A coefficient and the frequency of higher columns of CO at prevailing temperatures to become
ul ul 2
thetransition.Fromslopeoflog(N )vsE arotationaltemper- optically thick. From Fig. 9 a few things become clear. First,
u up
ature can be determined. The expected slopes for 400, 600 and forveryhighouterabundances,itisverydifficulttodistinguish
Articlenumber,page9of22
A&Aproofs:manuscriptno.Bosman_CO2_2017_01-26
1041
y
1.0 1.5 J xin=10−6 xin=10−6
0.8 Peak: xxiinn==1100−−78 1040 400 K xxiinn==1100−−78
600 K
800 K
)
x (Jy0.6 uN1039
u
Fl
0.4
1038
0.2
1037 J=20 J=40 J=60
0.0
14.0 14.5 15.0 15.5 16.0
0 1000 2000 3000 4000 5000
Wavelength (µm)
Upper level energy (K)
Fig.8. Left:FulldiskspectraatJWST-MIRIresolvingpower(R=2200)forthreediskmodelswithdifferentinnerCO abundances.Theouter
2
CO abundanceis10−7withg/d =1000.Themodelswithaninnerabundanceof10−8and10−7arehardtodistinguish,withverysimilarPand
2 gas
R−branchshapes.Thespectrumofthemodelwithhighinnerabundancesof10−6areflatterintheregionfrom14.6to14.9µmandthewingsare
alsomoreextendedleadingtohigherhightomidJlineratios.Right:Numberofmoleculesintheupperstateasfunctionoftheupperlevelenergy
inferredfromthespectraontheleft(Boltzmannplot).Inversetrianglesdenotethenumberofmoleculesinferredfrom P-branchlines,squares
fromQ-branchlinesandcirclesfromR-branchlines.VerticaldashedlinesshowtheupperlevelenergiesoftheJ =20,40,60,v2=1levels.the
blackdotted,dashedandsolidlinesshowtheexpectedslopeforarotationalexcitationtemperatureof400,600and800Krespectively.Thenear
verticalasymptotenearupperlevelenergiesof1000K(thev = 1rotationalgroundstateenergyisduetotheregionswithlargeopticaldepths
2
thatdominatetheemissionfromtheselevels.FromaroundJ =20thecurveflattenssomewhatandbetweenJ =20andJ =40thecurveiswell
approximatedbythetheoreticalcurveforemissionfroma400Kgas.Athigher J levels,themodelwiththehighestinnerabundancestartsto
deviatefromtheothertwomodelsasinneranddeeperregionbecomemoreimportantforthetotallineemission.AboveJ=60themodelsinwith
aninnerabundanceof10−8and10−7arewellapproximatewitha600Kgas,whilethehigherinnerabundancemodelisbetterapproximatedwith
a800Kgas.
betweendifferentinnerabundancesbasedonthepresentedline highestinnerabundances.Thetotalfluxinthe 13CO Q-branch
2
ratio.Second,modelswithhighouterabundancesarenearlyde- showsastrongerdependenceontheinnerCO abundancethan
2
generatewithmodelsthathavealowouterabundanceandahigh the 12CO Q-branch.AhotreservoirofCO stronglyshowsup
2 2
innerabundance.Ameasureoftheopticaldepthwillsolvethis. as an extended tail of the 13CO Q-branch between 15.38 and
In the more intermediate regimes the line ratios presented here 2
15.40µm.
oraBoltzmannplotwillsupplementtheinformationneededto
distinguish between a cold, optically thick CO reservoir and a
2
hot,moreopticallythinCO2 reservoirthatwouldbedegenerate 3.2.3. Emissionfromthev3 band
injustQ−branchfitting.
The v band around 4.25 µm is a strong emission band in the
3
diskmodels,containingalargertotalfluxthanthev band.Even
3.2.2. 13CO v band 2
2 2 so,the4.3µmbandofgaseousCO hasnotbeenseeninobser-
2
vationsofISOwiththeShortWaveSpectrometer(SWS)toward
Aneasiermethodtobreakthesedegeneraciesistousethe13CO
2 highmassprotostarsincontrastwith15µmbandthathasbeen
isotopologue. 13CO is approximately 68 times less abundant
2 seen towards these sources in absorption (van Dishoeck et al.
compared to 12CO , using a standard local interstellar medium 1996; Boonman et al. 2003a). This may be largely due to the
2
value(Wilson&Rood1994;Milametal.2005).Thismeansthat strong solid CO 4.2 µm ice feature obscuring the gas-phase
2
theisotopologueismuchlesslikelytobeopticallythickandthus lines for the case of protostars, but for disks this should not be
13CO :12CO lineratioscanbeusedasameasureoftheoptical alimitation.Fig.11showsthespectrumofgaseousCO inthe
2 2 2
depth, adding the needed information to lift the degeneracies. v bandaround4.3µmatJWST-NIRSpecresolvingpower.The
3
The bottom panel of Fig. 9 shows the ratio between the flux in resolvingpower ofNIRSpecis takento beR = 3000,which is
the13CO2v2 Q-branchandthe12CO2v2 P(25)line. notenoughtofullyseparatethelinesfromeachother.TheCO2
Asthe Q−branchfor 13CO islessopticallythick,itisalso emissionthusshowsupasanextendedband.
2
moresensitivetotheabundancestructure.The Q−branch,situ- ThebandshapesinFig.11areverysimilar.Thelargestdif-
ated at 15.42 µm, partially overlaps with the P(23) line of the ferenceisthestrengthofthe4.2µmdiscontinuity,whichisprob-
more abundant isotopologue so both isotopologues need to be ablyanartefactofthemodelasonlyafinitenumberof J levels
modelledtoproperlyaccountthethecontributionoftheselines. aretakenintoaccount.Thetotalfluxoverthewholefeaturedoes
Fig. 10 shows the same models as in Fig. 8 but now with the dependontheinnerabundance,butthedifferenceisoftheorder
13CO emissioninthicklines.The 13CO Q-branchispredicted of ∼ 10% for 2 orders of magnitude change of the inner abun-
2 2
tobeapproximatelyasstrongasthenearby 12CO linesforthe dance.
2
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