Molecular freeze-out as a tracer of the thermal and dynamical evolution of pre- and protostellar cores

0.23 MB·English

by  J. K. Jorgensen

Astronomy&Astrophysicsmanuscriptno.ms2092 February2,2008
(DOI:willbeinsertedbyhandlater)
Molecular freeze-out as a tracer of the thermal and dynamical
evolution of pre- and protostellar cores
J.K.Jørgensen1⋆,F.L.Scho¨ier2,andE.F.vanDishoeck1
1 LeidenObservatory,P.O.Box9513,NL-2300RALeiden,TheNetherlands
5 2 StockholmObservatory,AlbaNova,SE-10691Stockholm,Sweden
0
0
Received¡date¿/Accepted¡date¿
2

n
Abstract.Radiativetransfermodelsofmulti-transitionobservationsareusedtodeterminemolecularabundancesasfunctions
a
ofpositioninpre-andprotostellarcores.Thedatarequirea“drop”abundanceprofilewithradius,withhighabundancesinthe
J
outermostregionsprobedbylowexcitation3mmlines,andmuchlowerabundancesatintermediatezonesprobedbyhigher
8
frequencylines.TheresultsareillustratedbydetailedanalysisofCOandHCO+ linesforasubset ofobjects.Wepropose a
2
scenario in which the molecules are frozen out in a region of the envelope where the temperature is low enough (. 40 K)

to prevent immediate desorption, but where the density is high enough (>104–105 cm−3) that the freeze-out timescales are
1
v shorterthanthelifetimeofthecore.Thesizeofthefreeze-outzoneistherebyarecordofthethermalanddynamicalevolution
3 of the cores. Fitsto CO data for asample of 16 objects indicate that the size of the freeze-out zone decreases significantly
2 between Class 0 and I objects, explaining the variations in, for example, CO abundances with envelope masses. However,
6 thecorrespondingtimescalesare105±0.5 years,withnosignificantdifferencebetweenClass0andIobjects.Thesetimescales
1 suggestthatthedensepre-stellarphasewithheavydepletionslastsonlyashorttime,oforder105yr,inagreementwithrecent
0 chemical-dynamicalmodels.
5
0
Keywords.stars:formation,ISM:molecules,ISM:abundances,astrochemistry
/
h
p
-
o 1. Introduction emissionshowsthatthecharacteristictemperaturescanriseto
r a few hundredK in the innermostregions(e.g.,Shirleyetal.,
t The environments of the youngest pre- and protostellar ob-
s 2002; Jørgensenetal., 2002). Still, significant depletions are
a jects are characterized by large amounts of cold gas and
observedalsointhesestages,e.g.,forCO,indicatingthatasub-
v: dust. The chemistry in these early stages is affected to a stantial fraction of the envelopematerial remains at low tem-
Xi largedegreebyfreeze-outofmoleculesontodustgrains(e.g., peratures(e.g.,Blakeetal.,1995;Ceccarellietal.,2001).Ina
Bergin&Langer, 1997) and is closely related to the thermal
large survey of pre- and protostellar objects, Jørgensenetal.
r evolutionof the cores. An importantquestion is how the pre-
a (2002, 2004b) found a strong correlation between the abun-
and protostellar stages are linked and what their respective dancesofCO(andrelatedspeciessuchasHCO+)andenvelope
timescales are. In the pre-stellar stages the thermalbalance is
mass.
dominatedbytheexternalradiationfield,which,exceptinspe-
cial cases, does not heat the material to temperatures higher Thetimescalesforfreeze-outandevaporationdependsen-
than≈15K(e.g.,Evansetal.,2001).Atsuchlowtemperatures sitively on density and temperature. The availability of accu-
mostmoleculesgraduallyfreezeout,withveryshorttimescales ratephysicalstructuresfromdustcontinuumdatathusprovides
in the innermost dense regions and increasing timescales to- an opportunity to constrain the timescales independently us-
wardtheexteriorwheretheymaybecomelongerthantheage ing only chemistry. Currently, the ages of pre- and protostel-
ofthecore(e.g.,Casellietal.,1999). lar objects are determined almost exclusively from statistics,
In the protostellar stages, in contrast, the thermal balance such as the number counts of cores with and without asso-
is dominated by the heating from the central newly formed ciated far-infrared (IRAS) sources (e.g., Lee&Myers, 1999;
protostar,introducinga steep temperaturegradienttowardthe Jessop&Ward-Thompson,2000),resultinginalargespreadin
corecenter.Radiativetransfermodelingofthedustcontinuum pre-stellaragesfrom∼105toafew×106yr.Oursemi-empirical
procedure for constraining the chemistry and its assumptions
aresummarizedinFig.1ofDotyetal.(2004),andconsistsin
Sendoffprintrequeststo:JesK.Jørgensen
⋆ Present address: Harvard-Smithsonian Center for Astrophysics, the simplest case of fitting a constant abundance to the data,
60GardenSt.MS42,Cambridge,MA02138,USA as used in Jørgensenetal. (2002, 2004b). In those papers, it
Correspondenceto:[email protected] wasalsorealizedthatconstantabundancemodelsprovidepoor
2 J.K.Jørgensenetal.:Molecularfreeze-outasatracerofthethermalanddynamicalevolutionofpre-andprotostellarcores
fits to the lowest excitation lines of species such as CO and
HCO+, leading to the proposalof a “drop” abundanceprofile
withaspecificfreeze-outregionoverpartoftheenvelope.Such
“drop”profileswerealsofoundtobestreproducetheinterfer-
ometerdataof H CO in two sources(Scho¨ieretal., 2004). In
2
this paper, we further explore and quantify the “drop” abun-
danceprofilesforthe fullsetof 16 objectsandrelate the size
andlocationofthedepletionzonestopre-andprotostellarevo-
lution.Thissemi-empiricalstudyformsanimportantcomple-
ment to fullchemo-hydrodynamicalmodels which follow the
chemistryintimeasthemattercollapsestoformacentralstar
(e.g.,Rawlingsetal.,1992;Leeetal.,2004).
2. Model
Themainassumptioninouranalysisisthatthechemicalstruc-
Fig.1. Comparison between CO desorption and freeze-out
turein theprotostellarstagesiscontrolledbythermaldesorp-
timescales as functions of temperature and density. The solid
tion processes. Althoughother non-thermalprocessessuch as
line indicates the desorption timescale while the dotted and
cosmic-ray induced desorption play a role for weakly-bound
dashed lines indicate the (density and temperature depen-
specieslikeCO, theycannotpreventfreeze-outinthedensest
dent) freeze-out timescales for TMR1 and N1333-I2, respec-
and coldest gas (e.g., Shenetal., 2004). Similarly, photodes-
tively. Depletion occurs where the curves for the freeze-out
orptioncankeepmoleculesoffthegrains,butthisonlyinvolves
timescale intersect the dark colored region, in this example
the outermost regions up to an A ≈ 2 (Berginetal., 1995).
V for an assumed age of 105 years (dash-dotted line). Freeze-
These effects are expected to be secondary to the abundance outtimescalescorrespondingtoH densitiesof1×105,1×106
2
structureresultingfromthefreeze-outandthermalevaporation and1×107cm−3forNGC1333-IRAS2and1×104,1×105and
ofCO.Finally,outflowsandshocksmaybeimportantinregu- 1×106 cm−3 for TMR1 have been indicated by the filled and
latingtheabundancestructures,butthenarrowline-widthsfor
opencircles,respectively.
optically thin species such as C18O and H13CO+ suggest that
they probe predominantly the quiescent bulk envelope mate-
rial.Ouranalysisfocussesonthechemistryintheouterenve-
a first-orderformulationwith a pre-exponentialfactor of 1013
lopeon500–10,000AUscales,anddoesnotconsidertheaddi-
but this is notexpectedto change ourmain conclusionssince
tionalabundancejumpsintheinnermostregion(<100AU)at
theexponentstaysthesameanddominatesthetemperaturebe-
T >100Kwhereallicesevaporate.
havior.
FollowingRodgers&Charnley(2003),thethermaldesorp-
tionrateξandthefreeze-outrateλcanbewrittenas: Fig. 1 shows the desorption and freeze-out timescales of
CO, definedas1/ξ(M)and1/λ(M),respectively,asfunctions
ξ(M) ∝ exp −Eb(M) (1) ofdepthfortwoprotostarsfromthesampleofJørgensenetal.
kT ! (2002),NGC1333-IRAS2andTMR1.Theseobjectsareclassi-
d
T 0.5 fiedasClass0andI,andhavesignificantlydifferentenvelope
λ(M) =4.55×10−18 g nH [s−1] (2) masses of 1.7 and 0.12 M⊙, respectively. Their temperatures
m(M)!
and densities have been constrained from submillimeter con-
where T and T are the dust and gas temperatures, respec- tinuumdataandvarystronglywithradius.Figure1showsthat
d g
tively, m(M) the molecular weight, and n the total hydrogen freeze-out can – for a given age – only occur for a restricted
H
density.E (M)isthebindingenergyofthemoleculedepending regionofdensityandtemperatureintheenvelope.Athightem-
b
ontheice mantlecomposition,forwhichweadoptthe values peraturesT >Tevthemoleculeevaporateswhereasatlowden-
tabulatedbyAikawaetal.(1997)(Eb=960KforCO).TheCO sities n < nde the freeze-outtimescale is too long.Due to the
desorptiontemperaturesof30Korhigherinferredfromtheob- exponentialdependenceinEq.(1),thethermaldesorptionpro-
servationaldata(Jørgensenetal.,2002)suggestthatnotallCO ceeds very rapidly as soon as the temperature is higher than
isboundinapureCOicematrixbutthatatleastsomeofitisin Tev. In contrast, the freeze-out timescale varies more slowly
amixturewithH Owherethebindingenergymayincreaseto with depth in the envelope,due to the inverse dependenceon
2
≈1200K(Collingsetal.,2003).Thepre-exponentialfactorin density.
Eq.(1)dependsonwhether“zeroth”or“first”orderdesorption Inordertoquantifythisscenario,a“drop”abundancestruc-
kineticsareconsidered.Inastrochemicalmodelsfirst-orderki- tureisintroducedasatrialprofile,withadepletedabundance
neticsarecommonlyused,whichisappropriateforthedesorp- X whereT ≤ T andn ≥ n ,andanundepletedabundance
D ev de
tionof(sub-)monolayerquantitiesofanadsorbatefromasolid X where T ≥ T or n ≤ n . Whereas T is in principle
0 ev de ev
surface. For a thick layer of pure CO, a zeroeth-orderformu- awell-definedquantitydependingprimarilyontheicemantle
lation of the desorptionprocess is more appropriate,however properties, n depends on the lifetime of the core compared
de
(seediscussioninCollingsetal.,2003).Ourcalculationsadopt tothedepletiontimescale(inducedinthepre-andprotostellar
J.K.Jørgensenetal.:Molecularfreeze-outasatracerofthethermalanddynamicalevolutionofpre-andprotostellarcores 3
stages)andthedynamicalevolutionofthecoreatearlierstages,
includingreplenishmentof undepletedmaterialthroughinfall
from larger radii. This may move undepleted envelope mate-
rialtosmallerradii,orhigherdensities,increasingthederived
valueofn .Ontheotherhand,withinthestandardinside-out
de
collapsemodel(Shu,1977)theinfallradiifortheseveryearly
stagesare so smallthatthebulkof theenvelopeisnotyetin-
falling,includingthematerialnearthedepletionradiuswhere
n=n .
de
For this discussion we only assume step functions
at T and n , which are thus free parameters together
ev de
with X and X . With these assumptions the full Monte
0 D
Carlo line radiative transfer is performed as described in
Jørgensenetal.(2002)andScho¨ieretal.(2002)usingthecode
of Hogerheijde&vanderTak (2000). We adopt the molec-
Fig.2. Comparison between the density (black) and CO
ular data summarized in the Leiden Atomic and Molecular
abundance profiles (grey) from Bacmannetal. (2002) (dot-
Database (Scho¨ieretal., 2005)1. Single-dish data on CO and
ted lines), Tafallaetal. (2002) (solid lines), Leeetal. (2003)
HCO+ takenfromJørgensenetal.(2002,2004b)arefittedini-
and this paper (dashed lines) for the pre-stellar core L1544.
tially for four objects at different stages of evolution, leaving
Thedashed-dottedlineindicatestheconstantabundancefrom
all4parametersfreeinthemodelingoftheCOdata.Theabun-
Jørgensenetal. (2002). The freeze-out radius at which a sig-
dance of HCO+ is expectedto reflect the freeze-outof CO as
nificantdropintheCO abundanceoccursin thestep-function
illustrated by chemical models (e.g., Bergin&Langer, 1997;
model of Leeetal. (2003) is indicated by the vertical arrow.
Leeetal.,2004),buttheHCO+ lineshavehighercriticalden-
Theopenandsolidstarsindicatethevaluesofn (Tafallaetal.,
0
sities and therefore provide an independent probe. Leeetal.
2002)andn (thiswork),respectively.Seetextfordetails.
de
modeled the chemical and physical evolution of a collapsing
core through its pre- and protostellar stages and found simi-
lar “dropprofiles” for the CO abundancesand closely related profile types and find that a step function with a characteris-
species.FortheHCO+fits,T andn arethereforetakenfrom tic density marked with the vertical arrow in Fig. 2 provides
ev de
the fits to the CO data, givinglow valuesof the χ2-estimator. thebestfit.Bacmannetal.(2002)deriveonlyanaverageabun-
Withn constrainedfromfitstotheobservedCOlines,Eq.(2) dancetowardthecenterofthecorewithadensityprofilewitha
de
thengivesthedepletiontimescalet = 1/λfora sourcewith lessdenseinnerflattenedregion,andthereforedonotgivecon-
de
agiventemperatureanddensityprofile.Subsequently,theCO straintsonnde.Takingthisdifferenceintheunderlyingdensity
datafortheentiresampleof16sourceshavebeenfitted,keep- profilesintoaccounttheiraverage(orconstant)COabundance
ingonlyX andn asfreeparameters. of7×10−6isingoodagreementwiththeconstantabundanceof
D de
The pre-stellar cores require a special discussion because 5×10−6forL1544derivedbyJørgensenetal.(2002).
they do not have a central source of heating so that there is
onlyasinglefreeze-outradiusRdecorrespondingtodensitynde. 3. Results
The precise value of n depends in this case on the adopted
de
physical structure and abundance profile. As an example of The best fit parameters to the CO and HCO+ data for the 4
the uncertainties, ourbest-fit modelsfor L1544are compared sources are listed in Table 1 and illustrated in Fig. 4–5. For
withotherrecentworkbyBacmannetal.(2002),Tafallaetal. the class I object, TMR1, the data are found to be consistent
(2002) and Leeetal. (2003) in Fig. 2, which shows the best with a model without a depletion zone. For CO, X0 is found
fitphysicalstructurestogetherwiththederivedCOabundance to be 2.7×10−4 consistent with the direct measurementof the
structures. There are some differences in the adopted under- CO abundancerelative to H2 by Lacyetal. (1994) in a warm
lying density profiles and derived parameters. For example, cloudinwhichCOisnotfrozenout.Thisisalsotheexpected
Tafallaetal.(2002)useanexponentiallydecreasingCOabun- valuebasedontheresultsofJørgensenetal.(2002)whofound
dancestructuretowardthecenterX(r)= X exp(−n(r)/n )with amaximumconstantCOabundanceof∼2×10−4.VanderTak
0 0
n = 5.5 × 104 cm−3. The origin of the difference between etal.(2000)foundasimilarmaximumconstantabundancefor
0
their n and the lower n of 1.5 × 104 cm−3 derived using asampleofhigh-massYSOs.Inthecontextofthedropabun-
0 de
step functionsofthe CO abundance(Leeetal., 2003, this pa- dance model presented in this paper, this constant abundance
per) stems from (i) the slightly lower density profile derived appliestosourcessuchasTMR1,wherethedropregionisso
by Evansetal. (2001) and used by Leeetal. and in this pa- small that the abundance profile can be assumed to be essen-
per;(ii)thehigher(undepleted)COabundanceintheouterre- tiallyconstant.
gionofthecorefromLeeetal.andthispaper,and(iii)thefact Fortheclass0objects,incontrast,theconstantabundances
thatCOdisappearscompletelyinthemodelsofTafallaetal.at foundbyJørgensenetal.(2002) areaboutan orderofmagni-
radii less than ∼ 5000 AU. Leeetal. test differentabundance tudelower,indicatingthattheregionofCOdepletion(thedrop
zone)islargefortheseobjects.Thesearealsotheobjectswhere
1 http://www.strw.leidenuniv.nl/∼moldata theintensitiesofthelowexcitationJ =1−0transitionsareun-
4 J.K.Jørgensenetal.:Molecularfreeze-outasatracerofthethermalanddynamicalevolutionofpre-andprotostellarcores
Table1.BestfitparametersforCOandHCO+linesforthepro-
tostarsN1333-I2,L723,TMR1andthepre-stellarcoreL1544.
N1333-I2 L723 TMR1 L1544
T [K] & 35 40 ... ...
ev
n [104cm−3] 7 4 ... 1.5
de
CO:
X [10−4] 2.7 2.7 2.7 2.7
0
X [10−4] <0.14 0.14 ... 0.02
D
χ2/N 4.4/7 2.4/6 0.75/6 4.2/4
HCO+:
X [10−8] 1.8 <2.0 2.7b –
0
X [10−8] 0.26 0.35 ... –
D
χ2/N 4.1/5 1.8/3 2.1b/2 –
t [105yrs]a 2 3 .1c 8
de
Fig.3.Fitted C18O line-profilesforNGC1333-IRAS2.Upper
Notes: The abundances have been derived from observations of the
panels:constantfractionalabundance[12CO]of2.4×10−5from
optically thin isotopic species, C18O, C17O and H13CO+ assum-
Jørgensenetal. (2002). Lower panel: best fit drop abundance
ing the standard isotopic ratios adopted in Jørgensenetal. (2004b).
aDepletiontimescalecorresponding tothederivednde usingEq.(2). modelwithX0 =2.7×10−4andXD =1.4×10−5fromthispa-
bModelincludingexcitationthroughcollisionswithelectronsatden- per. The calibrationaluncertaintyfor each observed spectrum
sities≤3×104cm−3.c1σlimitassumingT of35K. isabout20%.
ev
derestimatedunlessthedropabundancestructureisintroduced. 2.7×10−4andtheevaporationtemperatureTevat35Ktoreduce
Thisisclearly illustratedin Fig.3 whichshowsthe bestfitto the numberof free parameters.We stress thatuncertaintiesin
the C18O lines for NGC 1333-IRAS2 with a constant abun- theunderlyingphysicalmodelsuchasduetotheuncertaindust
dancemodelfromJørgensenetal. (2002) andthe dropmodel properties(see discussion in Jørgensenetal., 2002) and other
fromthispaper.AsimilarplotillustratingthefitsforL723can factorsmay resultin systematic uncertaintiesbyfactorsof2–
befoundinFig.7ofJørgensenetal.(2004b).Fig.4illustrates 3inthederivedabsoluteabundancesandvaluesofnde andtde
theconfidencelevelsforthevariousparametersforNGC1333- (see also aboveexampleon L1544).However,the conclusion
IRAS2.ItisseenthatT onlyhasalowerlimitandX onlyan thatadropabundanceprofileprovidesamuchbetterfitthana
ev D
upperlimit:forT higherthan35–40Ktheinnermostregion constant abundance profile is not affected by these uncertain-
ev
with high CO abundanceshas a very low filling factor in the ties. Also, sinceallsourcesare analyzedin thesame way,the
single-dish beam and therefore only contributes a small frac- relativevaluesandinferredtrendsshouldbemorereliable.
tiontothebeam-averagedcolumndensities.Thebestfitvalue The fitted nde and XD, together with the χ2 value and
ofX0isagain2.5–3×10−4. derived tde are given in Table 2. For each source, all lines
ForallsourceslistedinTable1exceptTMR1,X isfound could be well fitted (χ2 ≤ 2) using depletion densities
D red
tobetypicallyanorderofmagnitudelowerthanX0forbothCO nde =1×104–6×105 cm−3 (105±0.4 cm−3) correspondingto de-
andHCO+.TheCOevaporationtemperaturesT areallfound pletiontimescalesof2×104–8×105years(105±0.5years).No
ev
to be ≥ 35 K, consistent with the results of Jørgensenetal. significantdifferencein timescales between Class 0 and I ob-
(2002),whereasthevaluesofX arealloforder2–3×10−4with jectsisfound.Fortheobjectswiththeleastmassiveenvelopes
0
a10–20%statisticaluncertainty. (M . 0.1 M⊙)wherephotodesorptioncouldbecomeanissue,
The derived CO abundance profile depends somewhat on thederivedtdeisalowerlimittotheactualdepletiontimescale.
the adopted outer radius and any contribution from the sur- In general, however, the depletion radius is located further in
rounding cloud to the lowest excitation lines. However, the theenvelopethantheradiuswhereAV =2forourobjects.
samedropabundanceprofilesarealso necessaryto reproduce
higherangularresolutioninterferometerdata,wherecontribu-
4. Discussion
tions from the larger scale cloud are resolved out, as well as
to model transitions with higher critical densities of H CO Thefactthatthedropabundanceprofilesprovidebetterfitsthan
2
and HCO+ which are not excited in the surrounding cloud constantabundanceprofilesforallsourcesandmoleculesstud-
(Scho¨ieretal.,2004;Jørgensen,2004,andTable1). iedshowsthatthisstructureprovidesagoodrepresentationof
Given the success of these models, the C18O and C17O the dominant chemistry in protostellar envelopes, with other
linesfortheentiresampleofJørgensenetal.(2002)havebeen chemical effects being of secondary importance. To illustrate
fitted to infer the CO abundance structure and the depletion the dependence on envelope mass, Fig. 6 compares the radii
time scales. Based on the results for the above 4 sources, it correspondingto T and n for varyingenvelopemasses for
ev de
seemsreasonabletotaketheundepletedabundanceX0fixedat a (typical) 3 L⊙ centralsource. For an objectwith a large en-
J.K.Jørgensenetal.:Molecularfreeze-outasatracerofthethermalanddynamicalevolutionofpre-andprotostellarcores 5
Table2.Valuesofn andX constrainedfromtheCOlinesfor
d D
eachindividualsourceinthesample,togetherwiththetotalχ2,
numberoffittedlinesandderivedt .
de
Source n X χ2/N t
de D de
[cm−3] [yr]
L1448-I2 4.8×105 3.0×10−7 4.2/4 3×104
L1448-C 6.0×104 2.0×10−5 10.7/7 2×105
N1333-I2 7.0×104 1.4×10−5 4.4/7 2×105
N1333-I4A 6.0×105 2.0×10−7 11.2/7 2×104
N1333-I4B 1.7×105 4.3×10−6 9.5/7 7×104
L1527 1.4×105 2.7×10−5 9.2/7 1×105
VLA1623a – – – –
L483b 1.5×105 5.0×10−6 1.5/3 9×104
L723 4.0×104 1.4×10−5 2.4/6 3×105
L1157 <2.3×105 – – >5×104
CB244 1.3×105 1.6×10−5 3.8/5 1×105
L1489 7.0×104 1.0×10−5 8.1/6 1×105
Fig.4. χ2 confidence plots for fits to the CO lines toward TMR1 &1.0×105 – 0.75/6 .8×104
NGC 1333-IRAS2. In each plot the grey area marks the 1σ L1544 1.5×104 1.6×10−6 4.2/4 8×105
confidenceregionandthesubsequentlinecontoursthe2σ,3σ L1689B &1.0×104 .5×10−5 0.16/3 .1×106
and4σconfidenceregions. IRAS16293c 1.0×105 – – 1×105
aFor VLA1623 the 1–0 line observations are significantly underes-
timated even for a high constant abundance. This likely reflects the
denseridgeofmaterialinwhichthissourceislocated,whichalsoaf-
fectsthehigherexcitationlines(seealsodiscussioninJørgensenetal.,
2002). bFrom fits to single-dish and interferometric C18O obser-
vations (Jørgensen, 2004). cFrom fits to H CO interferometer data
2
(Scho¨ieretal., 2004). The CO isotopic lines for IRAS 16293-2422
areconsistentwithaconstantabundancethroughouttheenvelopebut
donotruleoutadropinabundance.
Fig.5.AsFig.4butforTMR1(left)andL1544(right).Inthe
leftpanelthedashedregionindicatesconstantabundancemod-
els (i.e., models where the radius corresponding to n is lo-
de
catedclosertothecentralsourcethantheradiuscorresponding
toT ).
ev
velope mass like NGC 1333-IRAS2 (1.7 M⊙), the depletion
zone is a few thousand AU, a substantial fraction of the en-
tire envelope. For an object with a small envelope mass like
TMR1(0.1 M⊙),the freeze-outradiusmovesinwardsandthe
sizeofthedepletedregionbecomesvanishinglysmall.Thisin-
dicatesthatthetrendofincreasing(constant)abundanceswith
decreasing envelope mass for these species (Jørgensenetal.,
2002,2004b)reflectsthesizeofthedepletionregion.
Based on the above fits, we propose a chemical structure Fig.6. Characteristic radii as functions of envelope mass for
of the outer envelopesas shown schematically in Fig. 7. The a 3 L⊙ protostar using the models of Jørgensenetal. (2002).
main differencebetween the pre- and protostellarcores is the Ann ∝ r−1.5 envelopedensityprofilewasassumedwithinner
innersource of heatingin the protostarsthatcauses CO to be andouterradiiof25and15000AU, respectively.Thedashed
evaporatedratherthan depletedtoward the source center. The line indicate the radius where T = 35 K and the solid and
ev
maindifferencebetweentheClass0andIobjectsisthesizeof dotted lines the radii where the depletion timescales are 104
thedepletionzone. and 105 years, respectively. The dashed-dotted line indicates
Is this chemical structure also an evolutionary indicator? thedifferencebetweenthedepletionandevaporationradii(i.e.,
Due to progressive dispersion of the envelope by outflows size of the depletion zone) for a depletion timescale of 105
and mass accretion, an intially massive envelope like that of years.
NGC1333-IRAS2shouldeventuallygothrougha phasewith
6 J.K.Jørgensenetal.:Molecularfreeze-outasatracerofthethermalanddynamicalevolutionofpre-andprotostellarcores
luminosity embeddedinfrared sourcesdue to the limited sen-
sitivtyofIRAS(see,e.g.,Youngetal.,2004)andthusleadto
overestimatesofthetimescales.Furtherunbiasedsurveys,e.g.,
with the Spitzer Space Telescope, may shed further light into
thisissue.
Torefinetheproposedmodels,itwillbenecessarytocou-
plemodelsforthedynamicalandradialchemicalevolutionas
done by Leeetal. (2004) to fully address the use of n as a
de
tracerofage.Itisinterestingtonotethatourderivedempirical
dropabundancestructureagreeswellwiththesedetailedmod-
els,notonlyqualitativelybutalsoquantitatively.AstheirFig.6
shows,thetimescalesoverwhichtheheavydepletionoccursin
thepre-andprotostellarstagesisonlyoforder105years.
Another important consequence of the “drop” chemical
structureisthatitaffectsthetracersofinfallinprotostostellar
envelopes.Since the dynamicalstructure of protostellar cores
isofteninferredfromfitsoflineprofilesofmoleculessuchas
HCO+ (e.g., Gregersenetal., 1997), knowledge about the ra-
dialchemicalstructureisimportantfordetaileddescriptionsof
theinfallingenvelope.Forexample,thelocationofthecollapse
radiusintheinside-outcollapsemodelfortheenvelopearound
NGC 1333-IRAS2 (Jørgensenetal., 2004a) is at ≈ 1000 AU
Fig.7.Proposedchemicalstructureforlow-masspre-andpro- whichisinthemiddleofthedropzonewherethetemperature
tostellar objects. The left column gives the temperature and is≈ 25K.Theexact“infall”lineprofilewillthereforedepend
density as functions of radius (black solid and grey dashed critically not only on the velocity field but also the presence
lines, respectively) for three archetypical low-mass pre- and andlocationoftheouterpre-depletion(n < nde)zoneandthe
protostellarobjects: L1544(pre-stellar core),N1333-I2(class amountofdepletion.
0,Menv >0.5M⊙protostar)andTMR1(classI,Menv <0.5M⊙
protostar). The black dotted lines indicate the derived abun-
Acknowledgements. The authors thank Ted Bergin, Jeong-Eun Lee
dance structures. The right column gives the depletion signa- and NealEvansfor useful discussions. Theresearch ofJKJismade
tureforeachclassofobjectwith,goingfromtheoutsidetothe possiblethroughaNOVAnetwork2Ph.D.stipend,FLSacknowledges
inside,thedarkgreyindicatingtheregionwherethedensityis supportfromtheSwedishResearchCouncil.Astrochemistryresearch
toolowfordepletion(n< n ),theblackindicatingtheregion inLeidenissupportedbyaNWOSpinozagrant.
de
where the moleculesdeplete and the light grey indicating the
regionwheretheyevaporate(T >T ).
ev
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