Complex cyanides as chemical clocks in hot cores
AAstronomy & Astrophysics manuscript no. 32553˙corr˙2col c (cid:13)
ESO 2018April 10, 2018
Complex cyanides as chemical clocks in hot cores
V. Allen , , F. F. S. van der Tak , , , and C. Walsh Kapteyn Astronomical Institute, University of Groningen, the Netherlandse-mail: [email protected], [email protected] SRON, Groningen, the Netherlands School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT, UKReceived 2017; accepted 2017
ABSTRACT
Context.
In the high-mass star-forming region G35.20-0.74N, small scale ( ∼
800 AU) chemical segregation has been observed inwhich complex organic molecules containing the CN group are located in a small location (toward continuum peak B3) within anapparently coherently rotating structure.
Aims.
We aim to determine the physical origin of the large abundance di ff erence ( ∼ / dust temperature, and gas density. Methods.
We performed gas-grain astrochemical modeling experiments with exponentially increasing (coupled) gas and dust tem-perature rising from 10 to 500 K at constant H densities of 10 cm − , 10 cm − , and 10 cm − . We tested the e ff ect of varying theinitial ice composition, cosmic-ray ionization rate (1.3 × − s − , 1 × − s − , and 6 × − s − ), warm-up time (over 50, 200, and1000 kyr), and initial (10, 15, and 25 K) and final temperatures (300 and 500 K). Results.
Varying the initial ice compositions within the observed and expected ranges does not noticeably a ff ect the modeled abun-dances indicating that the chemical make-up of hot cores is determined in the warm-up stage. Complex cyanides vinyl and ethylcyanide (CH CHCN and C H CN, respectively) cannot be produced in abundances (versus H ) greater than 5 × − for CH CHCNand 2 × − for C H CN with a fast warm-up time (52 kyr), while the lower limit for the observed abundance of C H CN towardsource B3 is 3.4 × − . Complex cyanide abundances are reduced at higher initial temperatures and increased at higher cosmic-rayionization rates. Reaction-di ff usion competition is necessary to reproduce observed abundances of oxygen-bearing species in ourmodel. Conclusions.
Within the context of this model, reproducing the observed abundances toward G35.20-0.74 Core B3 requires a fastwarm-up at a high cosmic-ray ionization rate ( ∼ × − s − ) at a high gas density ( > cm − ). The abundances observed at theother positions in G35.20-0.74N also require a fast warm-up but allow lower gas densities ( ∼ cm − ) and cosmic-ray ionizationrates ( ∼ × − s − ). In general, we find that the abundance of ethyl cyanide in particular is maximized in models with a low initialtemperature, a high cosmic-ray ionization rate, a long warm-up time ( >
200 kyr), and a lower gas density (tested down to 10 cm − ).G35.20-0.74 source B3 only needs to be ∼ / B2 for the observed chemical di ff erence to be present, whichmaintains the possibility that G35.20-0.74 B contains a Keplerian disk. Key words. stars: massive – ISM: individual objects: G35.20-0.74N – astrochemistry – ISM : molecules
1. Introduction
In high-mass star formation, the hot molecular core (HMC) stageis marked by high abundances of complex organic molecules(COMs), molecular species containing at least six atoms includ-ing carbon and hydrogen (Herbst & van Dishoeck 2009), andemitting from a warm (100-500 K), dense (n H > cm − ), andcompact ( < years, as COMs are dissociated in the expandingHII region around a young high-mass star. As a short-lived stagewith specific physical parameters, the HMC is an ideal source forstudying the process of high-mass star formation and by tracingthe distribution of specific molecular species, we can learn moreabout the physical and chemical structure of these young objects.Chemical segregation has been observed in several di ff er-ent star-forming regions on scales from 1000-8000 AU, most famously in Orion KL where Blake et al. (1987) observed thatthe hot core has a much higher abundance of N-bearing speciesthan the compact ridge and surrounding sources. To explain this,Caselli et al. (1993) modeled shells of gas collapsing towardthe nearby object IRc2, which are halted and heated up show-ing di ff erent chemical compositions (see Feng et al. (2015) andCrockett et al. (2015) for recent work on Orion KL). A di ff erencein chemical composition has also been seen between W3(OH)and W3(H O) (Wyrowski et al. 1999) where the latter is a strongN-bearing source with various complex organics, but the formeronly contains a handful of O-bearing species. AFGL2591 VLA 3is another source (Jim´enez-Serra et al. 2012) where such chem-ical segregation has been observed on a scale of a few thousandAU, which was explained using models of concentric shells withdi ff erent temperatures and amounts of extinction.This paper follows our previous study (Allen et al. 2017) ofG35.20-0.74N (G35.20), a high-mass star-forming region con-taining several high-mass protostars at a distance of 2.19 kpcwith a bolometric luminosity of 3 . × L (cid:12) (S´anchez-Mongeet al. 2014). G35.20 was shown to be a strong Kepleriandisk candidate based on position-velocity diagrams for several a r X i v : . [ a s t r o - ph . GA ] A p r . Allen et al.: Complex cyanides as chemical clocks in hot cores Fig. 1.
Image of the 870 µ m continuum emission from Cycle0 ALMA observations of G35.20. The continuum peaks are la-beled in order of intensity (i.e., peak B1 has the highest and peakB3 the lowest continuum intensity). Contour levels are 0.03,0.042, 0.055, 0.067, 0.08, 0.10, 0.13, 0.18, and 0.23 Jy / beam ( σ = / beam). The pixel-sized colored squares denote eachof the spectral extraction points (from Allen et al. (2017)).species and the fit of the velocity field to a Keplerian disk model(S´anchez-Monge et al. 2013). In this source, we observed asegregation in Core B between complex N-bearing species, es-pecially cyanides (those containing the CN group), and otherCOMs on a scale of less than 1000 AU within an apparentlycoherent source presenting a potential signature of Keplerianrotation. Within Core B (shown in Figure 1) there is a higherabundance (generally 1-2 orders of magnitude) of almost all ob-served species to the southeast (at continuum peak B3), and ad-ditionally, the nitrogen-bearing species abundance drops quicklywhen proceeding to the northwest (to continuum peaks B1 andB2 about 1000 and 2000 AU from source B3, respectively)where most complex N-bearing species (especially those withthe CN group) are no longer detected. This is especially promi-nent in ethyl- and vinyl cyanide (C H CN and CH CHCN) andin vibrationally excited states and isotopologs of methyl cyanide(CH CN) and cyanoacetylene (HC N). We also model the ob-served abundances from Core A for comparision, as it is not partof the potential Core B disk system, but has a similar chemicalcomposition to source B3 with high abundances of cyanides andoxygen-bearing species.We expect G35.20 source B3 to be a high-mass source as ahigh kinetic temperature is observed toward peak B3 ( ∼
300 K)compared to peak B1 and peak B2 (160 and 120 K, respec-tively). Alongside this high temperature, the deuterium fractionis very high toward source B3 (13% for CH CN) implying thatit has only recently heated up, releasing deuterium enriched icesinto the gas phase. There is also a cluster of OH masers to-ward peak B3 (Hutawarakorn & Cohen 1999). At the outer ra-dius of this disk candidate, the rotation period is between 9700and 11100 years, which is fast enough that such a di ff erence inchemistry should not be present because of the mixing of gas. In this work, we use chemical modeling to investigate a causefor chemical segregation between complex cyanides and otherspecies related to age, temperature, warm-up time, or gas den-sity.
2. Chemical model
We used a large gas-grain chemical network (668 species, over8000 reactions) in which the gas-phase reactions are from theUMIST Database for Astrochemistry (McElroy et al. 2013)known as Rate12 , and the grain surface and gas-grain interac-tions are extracted from the Ohio State University (OSU) net-work (detailed description in Walsh et al. (2014)). Our networkincludes the following reaction types: two-body gas-phase re-actions, direct cosmic-ray ionization, cosmic-ray-induced pho-toreactions, photoreactions, cation-grain recombination, adsorp-tion onto grains, thermal desorption, photodesorption, grain-surface cosmic-ray-induced photoreactions, grain-surface pho-toreactions, two-body grain-surface reactions, and reactive des-orption.In this model, the thermal desorption rate depends onthe binding energy of the species (E bind , A ) and the num-ber density of that species on the grain surface ( n s (A)).If there are less than two monolayers, then the followingfirst order rate is used: f thermal , A = k evap , A n s (A) (Cuppenet al. 2017), where k evap , A = ν exp − E bind , A kT and ν is the char-acteristic attempt frequency. Once there are more than twomonolayers, then the following zeroth-order approximation: f thermal , A = k evap , A N act χ A N s σ g n grain , where N act is the number ofactive monolayers, χ A is the fractional abundance of species A,and N s σ g n grain is the number of available surface sites per unitvolume. Further details about this chemical code can be found inDrozdovskaya et al. (2014), Walsh et al. (2014), and Walsh et al.(2015). Reaction-di ff usion competition is included.The model considers a single embedded (A V =
10) pointsource at a constant gas density that is warming up over time.The relatively high extinction means that the only source of ion-ization and photodissociation in the model is cosmic rays. A lowcosmic-ray ionization rate of 1 . × − s − was used in thefiducial model. Higher cosmic-ray ionization rates are exploredin test cases ( § Table 1.
Initial ice composition vs. H O ice. The initial H abun-dance for all models is 50% of the total material. The H Oice abundances vs. the total composition are 5 × − for IC 1,5 × − for IC 3, and 10 − for IC 2, 4, and 5. Species IC 1 IC 2 IC 3 IC 4 IC 5CO (ice) 10% 5% 10% 8% 17%CO (ice) 10% 15% 10% 13% 23%NH (ice) 5% 2% 5% 15% 15%CH OH (ice) 5% 5% 5% 10% 4%HCOOH (ice) 10% 5% 10% 7% 1%CH (ice) 5% 1% 5% 1.5% 1.5%H CO (ice) 10% 2% 10% 3.5% 2% http: // /
2. Allen et al.: Complex cyanides as chemical clocks in hot cores CN CHCH CHCN C H CNCH OH Fig. 2.
Fractional abundance vs. H for one species with di ff erent initial conditions (ICs 1-5) for a gas density of 10 cm − and a fastwarm-up time of 50 kyr. Results are similar for other warm-up times and densities. We start a warm-up phase at the end of a theoretical collapsephase that results in a constant H density of n = , 10 , or10 cm − with enhanced ice abundances of several species (seeTable 1). The gas density of Core B is expected to be 10 -10 cm − and Core A is expected to have a density of 10 cm − fromS´anchez-Monge et al. (2014). The warm-up phases start with theinitial conditions (IC) outlined in Table 1 and the (coupled) gasand dust temperature increases from 10 to 500 K over 52 (fast),203 (medium), or 1000 (slow) kyr according to the equation T(t) = + κ t as based upon the methods in Viti et al. (2004), Garrod & Herbst (2006), and Garrod et al. (2008). The values of κ usedin this work to warm from 10-500 K in the prescribed times forthe fast, medium, and slow warm-ups are 1.96 × − , 1.2 × − , and 4.9 × − K / s , respectively.The initial ice abundances for IC 2, 4, and 5 are from ice ob-servations carried out by Gibb et al. (2004) of three high-massstar-forming regions, i.e., AFGL 2136, W33A, and NGC 7538IRS9, respectively. Initial conditions (IC) 1 and 3 are based ona lower limit of the water abundance of 10 − versus H and anupper limit of water abundance of 10 − versus H as suggestedin van Dishoeck (2004). Other molecular abundances in IC 1and 3 are then percentages of 5% (for NH , CH OH, and CH
3. Allen et al.: Complex cyanides as chemical clocks in hot cores
Fig. 3.
Abundances of simple species over time for a fast warm-up with a gas density of 10 cm − . Dashed lines show ice abundancesand solid lines show gas abundances.ice) or 10% (for CO, CO , HCOOH, and H CO ice) of water.The atomic gas abundances in our model are the result of sub-tracting the atoms that have gone into molecules from the typi-cal gas abundances found in the pristine model input.
Our ap-proach di ff ers from Garrod et al. (2008) in that their modelincludes a phase of initial collapse from di ff use cloud to densecore, thereby building up their ices in a model-dependentmanner. Our full gas and ice initial conditions are detailed inAppendix A. While we did not include molecular gas in our ini-tial abundances, the chemistry quickly converts the free atomsinto stable molecules (Figure 3). These gas-phase abundancesare within an order of magnitude of reported abundances in star-less and prestellar cores (Ruoskanen et al. 2011; Koumpia et al.2016; Vastel et al. 2016).
First, we tested the fiducial model ( § ff erent den-sities (based on the expected densities of our observed sources)at three di ff erent warm-up speeds based on expected gas warm-ing speed around low-, intermediate-, and high-mass stars (dis-cussed in § § ff usion competition( § § § § × − s − and 6 × − s − ( § Table 2.
Abundances vs. H across G35.20 from Allen et al.(2017). Species Source A Source B1 Source B2 Source B3CH OH 5.0 × − × − × − × − C H OH 3.0 × − × − × − × − CH CHO 1.1 × − × − × − × − CH OCHO 3.4 × − × − × − × − CH CN 3.0 × − × − × − × − CH CHCN 5.3 × − < × − < × − × − C H CN 6.4 × − < × − < × − × − HC N 5.1 × − × − × − × −
3. Results
We aim to constrain the time periods during which themodels reasonably reproduce the observed abundances withinobserved error limits (detailed in Table 2) of the follow-ing molecules: cyanides (CH CN, CH CHCN, C H CN),cyanoacetylene (HC N), methanol (CH OH), methyl formate(CH OCHO), acetaldehyde (CH CHO), and ethanol (C H OH).For a time period to be an acceptable fit, its duration must beless than half a disk rotation period ( < CHCN, C H CN), were not detected at con-tinuum peaks B1 and B2, giving an upper limit to their abun-dances of 1 × − with respect to H . Upper and lower limitsfor the XCLASS modeling results can be found in Appendix B.
4. Allen et al.: Complex cyanides as chemical clocks in hot cores
Fig. 4.
Fractional abundance for B3 fast warm-up (from 10-500 K) model at a density of 10 cm − for the time period 20000-35000yr with the fiducial model. Oxygen-bearing species are shown to the left and nitrogen bearing to the right. The y-axes have di ff erentscales. All species are shown in the key with color-coded dashed horizontal lines showing the observed abundances for B3. Thethinner dashed lines indicate the upper limit for HC N and the lower limit for C H CN, as they are the species that best constrainthe time span. The black ellipse highlights the di ff erence between the modeled abundance of C H CN and the lower limit of theobserved abundance. At the higher densities we tested, the model abundance of C H CN is lower.
Fig. 5.
Time periods for which the observed abundances of HC N, CH CN, CH CHCN, C H CN, CH OCHO, and CH H OH arereproduced. The purple ’X’ marks indicate that the abundance of C H CN is not reproduced for this source and gas density.
5. Allen et al.: Complex cyanides as chemical clocks in hot cores
B1/B2A
Fig. 6.
Best fit models of abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, andC H CN using IC 5. G35.20 B1 / B2 (top) is best fit by the fast model with a gas density of 10 cm − over a time period of 1.3kyr. G35.20 A (bottom) is also best fit by the fast model with a gas density of 10 cm − over a time period of 6.4 kyr. The line colorsfor A are the same as B1 / B2 as shown in the key. All species are shown in the key with color-coded dashed horizontal lines showingthe observed abundances for the source. The thinner dashed lines indicate the upper limit and lower limit species that best constrainthe time span. The time ranges in which all abundances can be reproduced within the errors reported in Appendix B are shaded. Wetruncate the x-axis scale to better highlight the chemistry changes over the temperature range at which the COMs are released fromthe ice mantles.We find little variation among the di ff erent starting condi-tions (see Figure 2), so in the following analysis we use the ini-tial ice composition of IC5 as NGC 7538 IRS9 has a similarbolometric luminosity and distance to G35.20 (4 × L (cid:12) and2.7 kpc for NGC 7538 IRS9 versus 3 × L (cid:12) and 2.2 kpc forG35.20). In our fiducial model, we begin with gas and dust at 10 K and theinitial ice and gas conditions of IC5, then warm the gas and dustat fast, medium, and slow speeds (detailed in §
6. Allen et al.: Complex cyanides as chemical clocks in hot cores
Table 3.
Time ranges (in kyr) that fit observed abundances using the fiducial model in the lower abundance sources, B1 / B2, thosefor the higher abundance source, B3, and the other hot core in this group, A. Corresponding temperatures are also shown (in K).Full details in Appendix A.
A B1 / B2 B3
Density Warm-up time Time range Temperature Time range Temperature Time range Temperature(cm − ) (kyr) (kyr) (K) (kyr) (K) (kyr) (K)10
52 21.6-28.5 93-158 20.0-25.0 81-123 C H CN 2 × too low10
52 22.1-28.5 97-158 22.0-23.3 96-107 C H CN 3 × too low10
52 C H CN 5 × too low 21.5-24.0 92-114 C H CN 10 × too low10
203 85.0-97.3 94-121 75.5-90.0 76-105 84.5-97.5 93-11610
203 86.0-105.0 96-139 85.5-91.0 95-107 87.0-115.0 98-16510
203 88.7-103.0 102-134 88.0-94.5 100-114 89.6-103.0 104-13410 Fig. 7.
Fractional abundance for B1-2 fast warm-up (from 10-500 K) model at a gas density of 10 cm − for the time period 5-50kyr without reaction-di ff usion competition. All species are color coded as in Figure 6 with horizontal lines showing the observedabundances for B1 / B2. The abundances of CH OH, CH OCHO, and C H OH are not reproduced.begin with the conditions of this fiducial model varying one pa-rameter. Time ranges and corresponding gas temperature rangesfor all fits are summarized in Table 3.Fast warm-up models can reproduce all of the abundancesobserved for peaks B1 / B2 and the C H CN abundance can bereproduced in core A for densities of n = and 10 cm − .The model C H CN abundance at peak B3 cannot be repro-duced by the fiducial model, although at a density of 10 cm − it is 1.4 × − lower (50%) than the minimum observed abun-dance (see Figure 4). This di ff erence is significantly largerthan the tolerance for the model (10 − ) and is therefore not afit. A summary of the time periods where the observed abun-dances of HC N, CH CN, CH CHCN, C H CN, CH OCHO,and CH H OH are reproduced in a fast warm-up for all sourcesand gas densities is shown in Figure 5.Medium-speed warm-up models can reproduce the C H CNabundance observed in source B3 at late times (after 97 kyr). Thetime period required to reproduce all observed abundances is >
13 kyr, which is longer than a disk rotation period. Abundancesin source B1 / B2 can be reproduced in a medium warm-up in ∼ = and10 cm − , although still very long ( >
40 kyr). For peaks B1 / B2the shortest time range is 40 kyr at n = cm − (tempera-ture range 96-113 K). The shortest time range for peak B3 is65 kyr, corresponding to a temperature range of 102-132 K at n = cm − . These time ranges are not reasonable, as the gas inthe disk would have made several revolutions during such a longperiod.The fiducial model fits peaks B1 / B2 and core A very well us-ing a fast warm-up. Abundances toward peaks B1 / B2 can evenbe reproduced within a time period of 1.3 kyr at a gas density of
7. Allen et al.: Complex cyanides as chemical clocks in hot cores cm − . Core A requires a longer time period of 6.4 kyr, butis still well fit at a gas density of 10 cm − with a fast warm-up. The best fit models for B1 / B2 and A are shown in Figure 6.The abundances of C H CN toward peak B3 cannot be repro-duced using a fast warm-up, but the shortest time period (13kyr) that reproduces all abundances is using a medium warm-up at a gas density of 10 cm − . This is too long kinematically(the disk rotational period is ∼
10 kyr), and we expect it to bea high-mass source with a fast warm-up time because it has ahigh luminosity, cluster of OH masers (Hutawarakorn & Cohen1999), and a high kinetic temperature ( ∼
300 K) together with ahigh deuterium fraction implying that it has recently heated upvery quickly (Allen et al. 2017). As our model does not use anyreactions with deuterium, we can only assume that the modelabundances may di ff er from those listed if these reactions wereincluded. For nearly all warm-up speeds and densities, the lower timerange is constrained by the HC N abundance in core A andsource B3 and by CH CN in B1 / B2. Where this is not the case,CH OCHO is the lower abundance constraint. The upper timerange is constrained by the C H CN abundance for source B3and core A in medium and slow warm-ups and by CH CHCN infast warm-ups, where source B3 cannot be reproduced becauseof the high C H CN abundance. The C H OH abundance pro-vides the upper time range constraint for sources B1 / B2 in mostcases, but the CH OCHO abundance provides the upper limit forthe fast warm-up at 10 cm − and the slow warm-up at 10 cm − and CH CHO is the upper constraining species for the mediumand slow warm-ups at 10 cm − .When investigating the time ranges for B1 / B2 observationsfor the abundances of the unobserved cyanides (CH CHCN andC H CN), we see that they are very low (between 10 − and10 − for all models). The abundances of these species increaserapidly in a short space of time. The most dramatic is C H CNwhich jumps up 2 orders of magnitude within 1000 years in thefast warm-up at n = cm − (a temperature change of ∼
10 K).
Reaction-di ff usion competition is a mechanism used in chemicalmodeling to allow grain surface reactions with energy barriersto proceed more easily. This mechanism compares the relativetimescales between the reaction of two species and their di ff u-sion to determine which process will occur (Cuppen et al. 2017).Because reaction-di ff usion competition may be overexpressedin a two-phase chemical model (gas and ice), we modeled atest case without it. In this case, key species such as CH OH,CH OCHO, and C H OH are underproduced by as much as 2orders of magnitude compared to the lower limit abundances forany of our observed sources. Figure 7 demonstrates one instancewhere all three of these species are underproduced for B1-2.More e ffi cient grain-surface chemistry facilitated by reaction-di ff usion competition is required to better match the observa-tions, which should be tested in more detailed three-phase chem-ical models. Fig. 8.
Comparing the fractional abundances for three constrain-ing species, CH OCHO (top), HC N (middle), and C H CN(bottom), using di ff erent initial temperatures (10 K in magenta,15 K in green, and 25 K in yellow) at a gas density of 10 cm − for a fast warm-up. The vertical lines show the time correspond-ing to a temperature of 100 K for each initial temperature. Theobserved abundances (horizontal lines) for G35.20 A are shownfor reference.
8. Allen et al.: Complex cyanides as chemical clocks in hot cores
It is plausible that for high-mass stars forming in a cluster, pos-sibly sequentially, an initial temperature of 10 K is an underes-timation (Tieftrunk et al. 1998). For this reason we also mod-eled the chemistry of dense gas warming up from 15 and 25 K.Looking at the changes in abundance for constraining species,CH OCHO, HC N, and C H CN, we see that increasing start-ing temperatures decrease the abundances of CH OCHO andC H CN but increase the abundance of HC N (see Figure 8).For C H CN, longer times at as a low temperature allows moreto form in the ice, to be later released into the gas phase.Because the warm-up is exponential, starting at 15 K ratherthan 10 K results in 6000 years less at a low temperature (and10000 for 25 K) for the fast warm-up. Since the formation pathto C H CN is mainly in the ice it appears that time at a low tem-perature is critical. This is demonstrated as well in the mediumand slow warm-ups in which high abundances of C H CN aremade as these models spend a very long time at low tempera-tures. The temperature range between 15 and 30 K is critical forgrain-surface reactions because the dust temperature determinesthe sticking e ffi ciency of volatile species (such as H, H , andCO). At higher temperatures hydrogenation pathways (such asthose that lead to C H CN) are less likely to occur.
To investigate the e ff ect of high temperature gas-phase chemistryon our final abundances in the fast warm-up, we modeled warm-ing up the dense gas to 300 K, then continued at that tempera-ture for an additional 40 kyr. As C H CN is the only species thatcannot be fit for source B3, we focus on the abundance of thisspecies produced at di ff erent densities with extra time to performgas-phase chemistry. In Figure 9, we see that the abundancesproduced after 300 K do not deviate from those when the gascontinues to warm to 500 K. In the extra time, abundances onlyincrease at the highest gas density and then by 36% ( ∼ × − ),which does not reproduce the observed minimum abundance. HCN has been observed in cometary ice (Mumma & Charnley2011; Le Roy et al. 2015) and is expected to occur in ices aroundprotostars but has not yet been detected (Boogert et al. 2015). Totest the e ff ect of including HCN in the ice, we modeled the fol-lowing three additional initial abundances of HCN ice: 0.1%,1%, and 10% versus H O. An abundance of 0.1% reflects theobserved abundance in cometary ice (0.08-0.5%), but the higherabundances were used to test if there was any increase in ourCN-bearing species using an unrealistic concentration of HCN.In Figure 10 we see that the constraining species are barely af-fected by this change in HCN abundance, while the HCN gasabundances are directly a ff ected. We conclude that HCN is notan important progenitor to any of the nitrogen-bearing speciesthat we are focusing on and for the range of physical conditionsexplored in this work. The fiducial model uses a low cosmic-ray ionization rate com-monly used in chemical modeling of 1.3 × − s − , which islow compared with more distant observed star-forming regions(Indriolo et al. 2015). We modeled the chemistry over time for Fig. 9.
Fractional abundances for C H CN comparing warmingup to 500 K with warming up to 300 K then continuing at aconstant temperature at densities of 10 cm − (top), 10 cm − (middle), and 10 cm − (bottom) for a fast warm-up. The ob-served abundance (horizontal lines) for G35.20 A is shown forreference.two higher cosmic-ray ionization rates, 1 × − s − and 6 × −
9. Allen et al.: Complex cyanides as chemical clocks in hot cores
Fig. 10.
Fractional abundances for nitrogen-bearing species with a gas density of 10 cm − and a fast warm-up. HCN gas (solidlines) and ice (dashed lines) abundances with the color key for all four panels (top left), HC N gas (top right), CH CN gas (bottomleft), and C H CN gas (bottom right) abundances over time are shown for four initial HCN ice abundances (0, 0.1, 1, and 10%).The observed abundances (horizontal lines) for G35.20 A are shown for reference.s − , to be comparable to the mean and uppermost values fromIndriolo et al. (2015). When comparing the changes in abun-dance for constraining species, CH CN, CH OCHO, HC N, andC H CN, we see that a higher cosmic-ray ionization rate in-creases their abundances, although after ∼
25 kyr the abun-dances for a cosmic-ray ionization rate of 6 × − s − dropsharply (see Figure 11). This sharp drop in our key species isdue to either a high abundance of H O + and HNCH + in the caseof CH CN, CH OCHO, and HC N, or dissociation by cosmicrays for C H CN. A cosmic-ray ionization rate of 1 × − s − presents a solution that fits the observed abundances in sourceB3 with a fast warm-up.The shortest time period that fits the observed abundancesin source B3 is 3.3 kyr in a fast warm-up with a cosmic-rayionization rate of 1 × − s − and a gas density of 10 cm − (Figure 12). The observed abundances of A and B1-2 are alsowell fit with a cosmic-ray ionization rate of 1 × − s − . A rateof 6 × − s − raises the modeled abundance of HC N such thatit no longer fits any of the observed abundances and so is not a vi-able solution for the model assumptions and parameters explored
10. Allen et al.: Complex cyanides as chemical clocks in hot cores
Fig. 11.
Comparing fractional abundances for four constraining species with di ff erent cosmic-ray ionization rates with a gas densityof 10 cm − for a fast warm-up. CH CN with the color key for all four panels (top left), HC N (top right), CH OCHO (bottom left),and C H CN gas (bottom right) abundances over time are shown for three cosmic-ray ionization rates (1.3 × − , 1 × − , and6 × − s − ). The observed abundances (horizontal lines) for G35.20 A are shown for reference.here. Table 4 summarizes the time ranges where the model abun-dances fit the observed abundances at a cosmic-ray ionizationrate of 1 × − s − , with corresponding temperatures. It is clearthat for the same H density and cosmic-ray ionization rate, thereis a small time overlap between sources B1 / B2 and source B3,and B3 is always a few thousand years older than B1 / B2.
We studied the reactions behind each of our eight focus speciesto determine whether they were formed mostly through ice pro-cessing and sublimation, through gas-phase formation followingthe sublimation of their precursors, or a mixture of both.CH OH, HC N, and C H CN are predominantly producedon the grain surfaces then sublimated with little to no gas-phaseproduction. Significant amounts of CH CN are produced on thegrain surface, but after sublimation gas-phase processes increase
11. Allen et al.: Complex cyanides as chemical clocks in hot cores
Fig. 12.
Fractional abundances for source B3 with a cosmic-ray ionization rate of 1 × − s − , a gas density of 10 cm − for a fastwarm-up. All species are shown in the key with color-coded dashed horizontal lines showing the observed abundances for sourceB3. The thinner dashed lines indicate the upper limit for HC N and the lower limit for C H CN, as they are the species that constrainthe time span. The best fit time period of 3.4 kyr is shaded. The colors are coded as in Figure 6.
Table 4.
Time ranges (in kyr) that are needed fit observed abun-dances in the lower abundance sources, B1 / B2, those for thehigher abundance source, B3, at a cosmic-ray ionization rate of1 × − s − in a fast warm up. Corresponding temperatures arealso shown (in K). B1 / B2 B3
Density Time range T gas
Time range T gas (cm − ) (kyr) (K) (kyr) (K)10 the abundance of CH CN gas to ∼ H OH is also produced predominantly in the ice,but gas processes double the maximum ice abundance.The ice and gas-phase abundances of CH CHO are unusualin that the ice abundance drops sharply around 63-70 K in thefast warm-up (at di ff erent densities). This appears to coincidewith an increase in CH OH and CH OCHO gas abundances.At this temperature in the model, grain surface CH CHO re-acts with CH OH to form either C H OH and HCO or CH andCH OHCHO in the ice, or it reacts with NH to form NH andCH CO in the ice as well. CH OHCHO is important in form-ing CH OH and CH OCHO on grain surfaces. The CH CHOgas abundance does not increase until the temperature reaches ∼
100 K. At that temperature, the main production pathway isthrough neutral-neutral reactions between CH OH and CH inthe gas phase. So despite the significant abundances of CH CHOthat are produced in the ice, very little of this sublimates into thegas phase. The CH CHO gas is mainly a product of CH OH andCH. CH OCHO is made abundantly in the ice, but reacts withOH in the ice to form COOCH and water ice by hydrogenabstraction. COOCH is hydrogenated in the ice and the re-sulting CH OCHO is released to the gas (H ( ice ) + COOCH ice ) = CH OCHO). This is the main mechanism for creatingCH OCHO in the gas rather than sublimation of CH OCHOfrom the ice or formation in the gas.CH CHCN is another species that can be made at low frac-tional abundances (10 − -10 − ) in the ice and gas. Ice phaseCH CHCN is dominantly produced through the dissociation ofC H CN by cosmic rays, whereas the gas-phase formation routeis the reaction of CN with either C H or CH CHCH . After atemperature of ∼
115 K, the CH CHCN in the ice is sublimatedand adds to the gas-phase abundance.
4. Discussion
The first interesting result is that our model abundances are al-most independent of initial ice conditions that we used, whichare constrained by the observations of Gibb et al. (2004) and the-oretical abundance ratios from van Dishoeck (2004). The rangeof ice abundances in our di ff erent IC sets is not large, but it isbased on real sources. The models suggest that the initial icecomposition is not crucial to modeling the chemical compositionof a later state, thereby showing that the warm-up stage deter-mines the composition of the hot core. It is possible that addingmolecular gas to the initial conditions would have an e ff ect onthe final abundances; however, such a parameter-space explo-ration of the initial gas composition requires a dedicated suiteof models and is beyond the scope of this work. This should becarried out in the future.
12. Allen et al.: Complex cyanides as chemical clocks in hot cores
The second interesting result is a much debated topic inchemical modeling (Cuppen et al. 2017): the importance ofapproximating reaction-di ff usion competition in rate equationbased models. In this work, in order to reproduce the lowerlimit abundances of the species that we focus on from G35.20,reaction-di ff usion competition is needed, otherwise oxygen-bearing complex organic species are underproduced by as muchas 2 orders of magnitude. Reaction-di ff usion competition hasalso been shown to be necessary in the work of Ruaud et al.(2016) and Qu´enard et al. (2018) among others, but it is im-portant to note that gas-phase reactions for complex organicmolecules in chemical networks have also been shown to be in-complete (Balucani et al. 2015).The modeled gas temperatures at which the abundances arereproduced are lower than the kinetic temperatures (300 K forsource B3, 285 K for core A, 160 K for source B1, 120 K forsource B2) determined in Allen et al. (2017). The gas temper-atures from our chemical model are 110-130 K for source B3,100-110 K for sources B1 / B2, and 100-130 K for core A. As wehave demonstrated that increasing the temperature and runningthe chemistry for longer does not significantly a ff ect the finalabundances, then the reproduction of the observed abundancesat lower temperatures is an advantage. In our fiducial model, the warm-up time is the most significantfactor in reproducing the abundances of the observed species.The high abundances of C H CN seen in source B3 cannot beproduced in a fast warm-up in our fiducial model. While rel-atively short time ranges can be found to reproduce the abun-dances seen in sources B1 / B2 in any of our models (with theshortest time range of 1.3 kyr from a fast model at 10 cm − ),those of source B3 can only be reproduced in medium or slowwarm-up models. These longer warm-up times imply a lowermass protostar. Observational evidence points to source B3 be-ing associated with a high-mass protostar: there are numerousmasers about its position and the kinetic temperature is high( ∼
300 K). On the other hand, a high deuterium fraction (13%)for CH CN (Allen et al. 2017) indicates that it was recently verycold and therefore needs a faster warm-up time.We reproduced the observed abundances in source B3 wellusing a cosmic-ray ionization rate a few times higher than inthe standard value (van der Tak & van Dishoeck 2000) for theinterstellar medium. A higher mean cosmic-ray ionization rateof 1.78 × − s − was found in observations by Indriolo et al.(2015) and our models seem to agree with this higher rate.Source B1 / B2 is also well reproduced within a 1.3 kyr time pe-riod using a cosmic-ray ionization rate of 1 × − s − , withoutthe abundances of the complex cyanides becoming too high.It is possible that adding gas-phase reactions formingC H CN to the network will make it possible to reproduce thehigher abundances seen in source B3 with the fiducial model,as the network currently contains no gas-phase reactions to pro-duce this species. Such reactions are not often tested in the lab-oratory as cyanides are dangerous to work with, but it would beextremely useful for labs to test these reactions in the future toimprove the chemical networks.
The Garrod models (Garrod & Herbst 2006; Garrod et al. 2008)and their predecessor models (Viti & Williams 1999) derive their warm-up times from the work of Bernasconi & Maeder (1996)(BM96 from here on). In BM96 work, the contraction times fordi ff erent masses of stars (from 0.8-60 M (cid:12) ) are determined un-der the assumption that the accretion rate is between 10 − and10 − M (cid:12) yr − . It has been reported more recently that mass ac-cretion rates can be as high as 10 − M (cid:12) yr − (Tan et al. 2014), al-though this may be episodic. Hosokawa & Omukai (2009) foundthat these high accretion rates led to pre-main sequence starswith larger-than-typical radii. Ram´ırez-Tannus et al. (2017) hasrecently reported observational evidence for this in M17. In anycase, our fast, medium, and slow warm-up times correspond to60, 15, and 6 M (cid:12) objects from the original BM96 paper, con-sidered to be very high, high, and intermediate mass sources.If we assume that the accretion rate of our objects is ten timeshigher and decrease the contraction times of the BM96 objectsaccordingly, that gives more reasonable stellar masses of 8, 4,and 1 M (cid:12) for the fast, medium, and slow warm ups, respec-tively. This is not a strictly accurate way of determining the re-lationship between mass at warm-up time, but it leads to muchmore reasonable masses and takes into account the observationaland theoretical work that has been carried out since BM96 waspublished.
5. Conclusions
The disagreement between the disk-like kinematics of the high-mass star-forming region in G35.20-0.74 B and its chemical seg-regation across its individual cores is not easily explained. Thehigh cyanide abundances observed toward peak B3 can be re-produced in a fast warm-up, but only with a higher cosmic-rayionization rate of 1 × − s − . The smallest time period requiredto reproduce the abundances in source B3 is 3.3 kyr at a gasdensity of 10 cm − . This is a reasonable cosmic-ray ionizationrate as evidenced by observations by Indriolo et al. (2015). Theabundances observed in the rest of the disk candidate (B1 / B2)can easily be reproduced with a fast warm-up at a gas densityof 10 cm − and a low rate of cosmic-ray ionization in a veryshort time period ( ∼ × − s − at a gasdensity of 10 cm − in 1.3 kyr.We find that the abundance of ethyl cyanide in particularis maximized in models with a low initial temperature, a highcosmic-ray ionization rate, a long warm-up time, or a lowergas density. The model is most sensitive to age in the contextof a warm-up model (therefore temperature), and to cosmic-rayionization rate. It is not sensitive to the initial ice composition(within observed ranges) and not strongly dependent on gas den-sity showing that the warm-up phase determines the composi-tion.If we assume that the cosmic-ray ionization rate is the samearound sources B1 / B2 and source B3 at 1 × − s − and thesources have a gas density of 10 cm − , then the age of sourcesB1 / B2 is 22.3-23.6 kyr while the age of source B3 is 22.7-26kyr. This indicates that both these sources began forming withina few thousand years and source B3 is 2000 years older. Basedon an outer disk rotation period between 9700 and 11100 years,this age di ff erence is physically possible. So we conclude thatthe detection of CH CHCN and C H CN can indicate a lowerlimit for the age of a hot core and a nondetection indicates anupper age limit. This can be useful when observing a potentialmultiple system at a lower resolution, where if CH CHCN orC H CN is detected toward one part of a source and undetectedin others, it indicates a young high-mass system with protostarsof di ff erent ages.
13. Allen et al.: Complex cyanides as chemical clocks in hot cores
We have covered a variety of star formation scenarios includ-ing a range of gas densities, regions with triggered star forma-tion (starting at temperatures above 10 K), regions with higherand lower cosmic-ray ionization rates, and a range of masses (viawarm-up speeds). With this coverage of parameter space we pro-pose that these model results can be used to interpret and predictobservations from a variety of embedded high-mass sources andintend to investigate other sources in the future. While we haveexplored the parameter space in these models comprehensivelyand noted the trends arising from this analysis, there is still muchwork to be carried out theoretically and experimentally to under-stand the gas and ice chemistry of cyanides. Without this work,our ability to study complex cyanide chemistry will remain hin-dered.
Acknowledgements.
We would like to thank our referee, Professor Serena Viti,for her constructive comments and quick reading. The PhD project of V. Allenis funded by the Netherlands Organisation for Scientific Research (NWO) andNetherlands Institute for Space Research (SRON). C. Walsh acknowledgesNWO (program 639.041.335) and the University of Leeds for financial support.
References
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14. Allen et al.: Complex cyanides as chemical clocks in hot cores
Appendix A: Initial conditions
Table A.1.
Full initial conditions (abundance of each species vs. total composition)
Species Initial conditions 1 Initial conditions 2 Initial conditions 3 Initial conditions 4 Initial conditions 5H (gas) 3.525 × − × − × − × − C (gas) 1.375 × − × − × − × − × − N (gas) 7.475 × − × − × − × − × − O (gas) 3.118 × − × − × − × − × − H O (ice) 5.0 × − × − × − × − × − CO (ice) 5.0 × − × − × − × − × − CO (ice) 5.0 × − × − × − × − × − NH (ice) 2.5 × − × − × − × − × − CH OH (ice) 2.5 × − × − × − × − × − HCOOH (ice) 5.0 × − × − × − × − × − CH (ice) 2.5 × − × − × − × − × − H CO (ice) 5.0 × − × − × − × − × − Notes.
It is assumed that all available atomic hydrogen is in the form of H . IC1 is based on a lower limit of the water abundance of 10 − vs. H and IC 3 is based on the upper limit of water abundance of 10 − vs. H . For IC 2, 4, and 5 the water ice abundance is set at 5 × − vs. H and theother ice abundances are calculated from percentages vs. water from observations of ice in star-forming regions (Gibb et al. 2004). IC2 is basedon AFGL 2136, IC4 on W33A, and IC5 on NGC7538 IRS9. Appendix B: Abundance ranges with errors
Table B.1.
Abundance range observed in Allen et al. (2017). Columns 2, 5, and 8 are the best fit abundances; 3, 6, and 9 are thelower limit to the abundances from error calculations; and 4, 7, and 10 are the upper limits to abundances. CH CHCN and C H CNwere not detected in B1 or B2 so their abundances are an upper limit.
A B1 / B2 B3Species Abundance Lower Upper Abundance Lower Upper Abundance Lower UpperCH OH × − × − × − × − × − × − × − × − × − C H OH × − × − × − × − × − × − × − × − × − CH CHO × − × − × − × − × − × − × − × − × − CH OCHO × − × − × − × − × − × − × − × − × − CH CN × − × − × − × − × − × − × − × − × − CH CHCN × − × − × − Upper limit 2 × − × − × − × − C H CN × − × − × − Upper limit 1 × − × − × − × − HC N × − × − × − × − × − × − × − × − × − Appendix C: Comparison with Garrod et al. (2008)
We compared our model without reaction-di ff usion competition to the well-known model in Garrod et al. (2008) and found sig-nificant di ff erences. At all warm-up speeds the di ff erence between our abundances and their reduced model is 1 to 4 orders ofmagnitude for more complex species, while the abundances of simpler species (H O, CO, NH , and CH ) are similar to those inGarrod et al. (2008). The model abundances from Garrod et al. (2008) cannot reproduce the observed abundances in G35.20 B3, asthe fractional abundances of C H OH, CH OCHO, and CH CHO are at least one order of magnitude too low. These authors did notreport abundances of CH CHCN or C H CN so that cannot be compared. There are some notable di ff erences between our modelresults and those of Garrod. The initial ice composition not the same, although we found that the initial ice composition does notstrongly a ff ect the final abundances. Without knowing their grain surface parameters, that cannot be compared. Garrod et. al alsoused a di ff erent gas network from us (UMIST versus OSU) and both networks have been updated significantly since 2008. Mostupdates to the networks involve updating the binding energies of surface species (Penteado et al. 2017). We also take further stepsin varying the cosmic-ray ionization rate and gas densities to investigate the e ff ect of these parameters on the chemical make-up ofour modeled sources. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s Appendix D: Time ranges
Tables and figures showing the time ranges that are required to reproduce observed abundances within errors.
Table D.1.
Approximate time period (in years) during which the modeled abundance range matches the observed abundance range for B3. The star symbol indicates that morethan one time range fits the observed abundance. The dagger symbol indicates that the observed abundance is not reached by the model (too low).
B3 n 10 n 10 n 10 Fast Medium Slow Fast Medium Slow Fast Medium Slow CH OH 22250-22300 86000-87000 420000-430000 22700-22800 88000-89000 439000 23200-23300 91000-91500 445000-450000C H OH 23400-23600 91000-91500 430000-440000 23800-24000 92800-93400 440000 24500-24700 95700-96000 455000CH CHO 22800-23800 85000-91500 405000-410000 24000-24800 86700-89000 (cid:63) (cid:63) CH OCHO † (cid:63) (cid:63) (cid:63) > (cid:63) (cid:63) CH CN > > > > > > > > > CHCN > > > H CN † † > † > N 21600-21800 84000-84500 400000-405000 22100-22300 86000-87000 418000-420000 22700-23000 89000-89600 430000-435000
Best time period fit no fit 84500-97500 375000-475000 no fit 87000-102000 420000-490000 no fit 89600-103000 435000-500000
Temperatures (K) N-C H CN HC N-C H CN CH OCHO-C H CN CH OCHO-CH CHCN HC N-C H CN HC N-C H CN HC N-CH CHCN HC N-C H CN HC N-C H CN Table D.2.
As Table D.1 for B1 / B2. Because vinyl and ethyl cyanide were not detected, the rows for CH CHCN and C H CN are the model abundances for the time period. Thestar symbol indicates that more than one time range fits the observed abundance. B1 / B2 n 10 n 10 n 10 Fast Medium Slow Fast Medium Slow Fast Medium Slow CH OH > > > > > > > > > H OH > > CHO 21700-23800 81500-91300 330000-410000 23000-24800 83000-95000 405000-425000 22600-29000 94500-97500 460000-480000CH OCHO > (cid:63) (cid:63) (cid:63) (cid:63) (cid:63) CH CN 19000-20000 74500-75500 360000-365000 22100-22200 85000-85500 407000-410000 22600-22900 87600-88000 418000-420000CH CHCN 10 − − − − − − − − − − − × − − × − × − C H CN 10 − − − × − − − − − − − − − − × − − HC N 20000-21800 79500-84000 365000-405000 21000-22300 82400-86800 400000-420000 21600-22900 84900-89500 410000-432000
Best time period fit
Temperatures (K) CN-CH OCHO CH CN-C H OH CH CN-C H OH CH OCHO-C H OH CH CN-C H OH CH CN-CH OCHO CH OCHO-C H OH CH CN-CH CHO CH CN-CH CHO . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s Table D.3.
As Table D.1 for A. The star symbol indicates that more than one time fits the observed abundance.
A n 10 n 10 n 10 Fast Medium Slow Fast Medium Slow Fast Medium Slow CH OH 21700-22300 84000-87000 415000-430000 22000-22800 86500-89000 423000-438000 22700-23200 88500-92000 438000-460000C H OH > (cid:63) > > CHO 13800-23400 52000-90000 260000-410000 22300-24500 81500-94300 395000-420000 22000-23500 83000-97000 450000-475000CH OCHO > (cid:63) (cid:63) (cid:63) (cid:63) (cid:63) CH CN 21300-23000 80000-87000 370000-410000 22400-23800 86000-89000 415000-425000 23000-24700 89000-92000 425000-435000CH CHCN > > > H CN > > > > N 21000-21600 81500-85000 380000-400000 21400-22100 83500-86000 405000-415000 22000-22700 86000-88700 418000-430000
Best time period fit
Temperatures (K) N CH CHCN HC N C H CN CH OCHO C H CN HC N C H CN HC N C H CN HC N C H CN CH OCHO CH CHCN HC N C H CN HC N C H CN A B3B1-2Fast n=10 Fig. D.1.
Abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, and C H CN using IC 5 with a density of 10 cm − and a fast warm-uptime of 50 kyr are shown for G35.20 A (left), B1 / B2 (middle), and B3 (right). The time period shown is only a part of the modeled time, from 18000-35000 yr. The time rangein which all abundances can be reproduced with an error of 1 order of magnitude are shaded in gray. The abundance of C H CN in B3 is not reproduced so a small black ellipseshows the gap between the lower abundance limit and the modeled abundance. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s A B3B1-2Fast n=10 Fig. D.2.
Abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, and C H CN using IC 5 with a density of 10 cm − and a fast warm-uptime of 50 kyr are shown for G35.20 A (left), B1 / B2 (middle), and B3 (right). The time period shown is only a part of the modeled time, from 18000-35000 yr. The time rangein which all abundances can be reproduced with an error of 1 order of magnitude are shaded in gray. The abundance of C H CN in B3 is not reproduced so a small black ellipseshows the gap between the lower abundance limit and the modeled abundance. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s A B3B1-2Fast n=10 Fig. D.3.
Abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, and C H CN using IC 5 with a density of 10 cm − and a fast warm-uptime of 50 kyr are shown for G35.20 A (left), B1 / B2 (middle), and B3 (right). The time period shown is only a part of the modeled time, from 18000-35000 yr. The time rangein which all abundances can be reproduced with an error of 1 order of magnitude are shaded in gray. The abundance of C H CN in A and B3 is not reproduced so a small blackellipse shows the gap between the lower abundance limit and the modeled abundance. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s A B3B1-2Medium n=10 Fig. D.4.
Abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, and C H CN using IC 5 with a density of 10 cm − and a mediumwarm-up time of 200 kyr are shown for G35.20 A (left), B1 / B2 (middle), and B3 (right). The time period shown is only a part of the modeled time, from 70-120 kyr for A andB3 and 30-105 kyr for B1 / B2. The time range in which all abundances can be reproduced with an error of 1 order of magnitude are shaded in gray. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s A B3B1-2Medium n=10 Fig. D.5.
Abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, and C H CN using IC 5 with a density of 10 cm − and a mediumwarm-up time of 200 kyr are shown for G35.20 A (left), B1 / B2 (middle), and B3 (right). The time period shown is only a part of the modeled time, from 70-120 kyr for A andB3 and 30-105 kyr for B1 / B2. The time range in which all abundances can be reproduced with an error of 1 order of magnitude are shaded in gray. The abundance of C H CNin B3 is not reproduced. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s A B3B1-2Medium n=10 Fig. D.6.
Abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, and C H CN using IC 5 with a density of 10 cm − and a mediumwarm-up time of 200 kyr are shown for G35.20 A (left), B1 / B2 (middle), and B3 (right). The time period shown is only a part of the modeled time, from 70-120 kyr for A andB3 and 30-105 kyr for B1 / B2. The time range in which all abundances can be reproduced with an error of 1 order of magnitude are shaded in gray. The abundance of C H CNin B3 is not reproduced. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s A B3B1-2 n7Slow
Fig. D.7.
Abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, and C H CN using IC 5 with a density of 10 cm − and a slow warm-uptime of 1 Myr are shown for G35.20 A (left), B1 / B2 (middle), and B3 (right). The time period shown is only a part of the modeled time, from 350-510 kyr. The time range inwhich all abundances can be reproduced with an error of 1 order of magnitude are shaded in gray. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s A B3B1-2 n8Slow
Fig. D.8.
Abundances vs. H for CH OH, C H OH, CH CHO, CH OCHO, HC N, CH CN, CH CHCN, and C H CN using IC 5 with a density of 10 cm − and a slow warm-uptime of 1 Myr are shown for G35.20 A (left), B1 / B2 (middle), and B3 (right). The time period shown is only a part of the modeled time, from 350-510 kyr. The time range inwhich all abundances can be reproduced with an error of 1 order of magnitude are shaded in gray. . A ll e n e t a l . : C o m p l e x c y a n i d e s a s c h e m i ca l c l o c k s i nho t c o r e s A B3B1-2 n9Slow
Fig. D.9.