Influence of galactic arm scale dynamics on the molecular composition of the cold and dense ISM III. Elemental depletion and shortcomings of the current physico-chemical models
V. Wakelam, W. Iqbal, J.-P. Melisse, P. Gratier, M. Ruaud, I. Bonnell
MMNRAS , 000–000 (2019) Preprint 24 July 2020 Compiled using MNRAS L A TEX style file v3.0
Influence of galactic arm scale dynamics on the molecular composition ofthe cold and dense ISM III. Elemental depletion and shortcomings of thecurrent physico-chemical models
V. Wakelam , W. Iqbal , J.-P., Melisse , P. Gratier , M. Ruaud , I. Bonnell (cid:63) Laboratoire d’astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France South-Western Institute for Astronomy Research (SWIFAR), Yunnan University (YNU), Kunming 650500, People’s Republic of China NASA Ames Research Center, Moffett Field, CA, USA Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, University of St. Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK
Accepted 2020 July 7. Received 2020 July 7; in original form 2020 January 14.
ABSTRACT
We present a study of the elemental depletion in the interstellar medium. We combined the results of a Galatic model describingthe gas physical conditions during the formation of dense cores with a full-gas-grain chemical model. During the transitionbetween diffuse and dense medium, the reservoirs of elements, initially atomic in the gas, are gradually depleted on dust grains(with a phase of neutralisation for those which are ions). This process becomes efficient when the density is larger than 100 cm − .If the dense material goes back into diffuse conditions, these elements are brought back in the gas-phase because of photo-dissociations of the molecules on the ices followed by thermal desorption from the grains. Nothing remains on the grains fordensities below 10 cm − or in the gas-phase in a molecular form. One exception is chlorine, which is efficiently converted at lowdensity. Our current gas-grain chemical model is not able to reproduce the depletion of atoms observed in the diffuse mediumexcept for Cl which gas abundance follows the observed one in medium with densities smaller than 10 cm − . This is an indicationthat crucial processes (involving maybe chemisorption and/or ice irradiation profoundly modifying the nature of the ices) aremissing. Key words:
Astrochemistry, ISM: atoms, ISM: abundances, ISM: evolution
After the Big Bang, the very first stars formed only from hydrogen (H)and helium (He). Heavier elements are formed later, either throughfusion inside stars or by neutron capture processes in supernovaeexplosion or neutron star mergers. At the end of the life of a star,some of the ejected atoms form refractory dust, others remain inthe gas phase. This material is included in the cycle of interstellarmatter: forming denser regions up to molecular clouds, newly starsand planetary systems, until the star dies and spreads its inner materialinto the diffuse interstellar medium (ISM) again. Within this cycle,chemical elements can be found in three phases: (a) in the gas-phase,(b) in the refractory grain cores, and (c) in the icy mantles of grains.The sum of abundance of the elements contained in all three phasesis called the cosmic elemental abundance. Cosmic abundances areassumed to represent some reference value and are measured in theatmosphere of stars (our Sun or other stars) (see for instance Sofiaet al. 1994; Asplund et al. 2009).In the diffuse medium, no icy mantles are expected to be present ongrains and so the measured abundances of gas-phase elements (whichare mostly in the ionized form except for O, N, and F) subtracted fromthese cosmic abundances should give the amount of each elementstored in the refractory cores, and so not available for any volatile (cid:63)
E-mail: [email protected] chemistry. Observations of gas-phase atomic lines towards differentlines of sight indicate that the depletion of the elements from thegas-phase increases with the density of the cloud, even when thedensity of the cloud remains too low to explain the depletion simplyby collisions with grains (Savage & Sembach 1996; Jenkins 2009).Silicon, for instance, has a cosmic elemental abundance of 3 . × − (compared to H, Asplund et al. 2009). The gas-phase abundance Si + measured in clouds with densities of about 10 − cm − is 2 × − and drops by a factor of ten at densities of 10 cm − . This observeddecrease of the atomic abundance in the gas-phase could be related toa more efficient neutralisation of the cations (since what is measuredis Si + ), but at such low densities, only dielectronic recombination orion-molecule reactions could really alter the balance of ion stages as itis the case for a small number of elements (Savage & Sembach 1996).Observations of atomic lines in diffuse clouds can only be done fordensities below 10 cm − because at higher density the atomic linesbecome optically thick. In dense molecular clouds (with densities ofa few 10 cm − ), SiO was not detected (upper limit of ∼ × − compared to H, Ziurys et al. 1989), indicating that the depletion ofsilicon continues at densities larger than 10 cm − .The mechanism of depletion can simply be understood as a matterof collision between gas-phase species and grains. At a density of10 cm − for a gas temperature of 100 K, the typical adsorption timeis about 10 yr, which is of the same order as the typical lifetimeof interstellar grains in the ISM (Draine 2009). At lower density, © 2019 The Authors a r X i v : . [ a s t r o - ph . GA ] J u l Wakelam et al. the adsorption timescale may be longer and turbulent mixing mayplay a role in driving dust from denser regions (Tielens 1998). Thechemistry associated with this depletion and the resulting species arestill a matter of debate (see for instance Tielens 1998; Whittet 2010).Whittet (2010) for instance debated on the depletion of oxygen at dif-ferent densities. Summing all the observed volatile phases of oxygenand the oxygen presumably contained in the refractory parts of thegrains, Whittet found that approximately 28% of the oxygen couldnot be accounted for, calling this fraction the unidentified depletedoxygen. This very specific problem of the elemental depletion in ten-uous regions (with densities below a few 10 cm − ) is particularlyimportant for the chemistry of dense regions such as star and plan-etary system forming regions. In fact, the fraction of the elementsavailable for phases (a - gas-phase) and (c - ice mantle), i.e. onlyphases that can be observed in star forming regions, is determined bywhat is depleted in phase (b - grain core), which is quite uncertain.Considering the uncertainties in the fraction of elements still avail-able, various values are used in astrochemical models and sometimeadjusted to reproduce observations.In this paper, we explore this problem coupling time dependentsimulations of the gas physical conditions following the transition be-tween diffuse and dense interstellar regions with a detailed gas-grainchemical model. In two previous papers, we have already analyzedtheses simulations to show 1) the chemical diversity of cold cores in-duced by the variety of physical histories experienced by the gas anddust forming such structures (Ruaud et al. 2018), and 2) the impactof these histories in the interstellar O abundance (Wakelam et al.2019). To simulate the chemistry during the formation of cold cores, weused the physical structure provided by the 3D SPH galactic modelfrom Bonnell et al. (2013). In these simulations the gas from thespiral arm is cold (T gas <
100 K) and n H ∼
100 cm − , whilst gasentering comprises warm gas (T gas < cm − . We then identified all the SPH particlesin a sphere of 0.5 pc around this maximum and retrieved the past and future history of these particles. The physical conditions of eachof the particles were used as input parameters at each time step ofthe Nautilus 3-phase gas-grain model (Ruaud et al. 2016). In total,we have approximately 3000 trajectories describing the physical andchemical evolution of parcels of material in a galactic arm goingfrom very diffuse conditions (below 0.1 cm − ) to dense ones (of afew 10 cm − ). The SPH model does not include self gravity sothe clouds are always dissipated after reaching the maximum peakdensity. This allows us to study the effect of cycles between denseand less dense ISM, which were suggested by Draine (2009) as anexplanation for elemental depletion. While exposing the results, wewill make a distinction between the first phase of the simulation (theincrease of the density with time up to a maximum value) and asecond phase which begins when the cloud starts to dissipate andthe density decreases again. More details on the methodology canbe found in Ruaud et al. (2018). Details on the chemical model andthe chemical parameters are in Wakelam et al. (2019). Analysis ofthe results of the physical model is done in Bonnell et al. (2013) andBonnell et al. (in prep). The cosmic-ray ionisation rate is kept constantto 10 − s − for simplicity. Determining the charge of the interstellargrains is complex and it depends on many parameters relative to thegrains themselves (size, nature etc) and on the physical properties ofthe environment (UV field, density, temperature) (Bel et al. 1989).To limit the computational time, the astrochemical model used inthese simulations assumes only one single grain size and the grainscan be either neutral or negatively charged. Only neutral gas-phasespecies are allowed to stick on the grains as the grains are supposedto be mostly negatively charged when the density is above 10 cm − (Bel et al. 1989). We do not take into account the possible stickingof ions on neutral grains. This means that we may overestimate thetimescale of depletion of atoms on the grains as it may occur earlierin the simulations. At the lowest densities however, the electronicrecombination of ionized atoms should be faster than the collisionwith grains.Table 1 lists the elemental abundances used in the model. Thesevalues correspond to abundances observed in the most diffuse regionsin Jenkins (2009) sample where they observed the smallest depletion(their F ∗ = 0). These values are smaller than the solar abundances asthe fraction of elements included in the refractory grains producedby stars has already disappeared. Two elements are not included inJenkins (2009) study: Na and F. For these two ones, we have usedthe solar abundance from Asplund et al. (2009). In our simulations, we obtain the chemical evolution for thousands ofparcel of material, each experiencing different physical conditions,that changes with time. It is not possible to describe the behavior ofthe species and the chemical processes at play for each of them aswe have a large spread of the chemical compositions as was shownin previous publications (Ruaud et al. 2018; Wakelam et al. 2019).We will then first show the examples for two selected trajectoriesand give more general statistical results considering all of them in asecond subsection.
To visualize the results, we first show in Figs. 1 and 2 the densityas a function of time for two selected trajectories and the associatedatomic gas-phase abundances as a function of density. These twotrajectories are the same as in Wakelam et al. (2019). The dust and
MNRAS , 000–000 (2019) lemental depletion Figure 1.
Density as a function of time for trajectory A (upper left panel) and gas-phase atomic abundances (X) as a function of density for the same trajectoryfor the rest of the figure. Symbols are just markers to help reading the time dependency of the figures. Blue and red parts of the lines represent the phase ofincreasing and decreasing density. gas temperatures as a function of of time for the two trajectoriesare shown in Appendix A. On the figures, we use markers to helpidentifying the initial and final times, as well as the peak density(at 4 . × yr for both). The time step of physical changes isgiven by the SPH model (2 . × yr). The maximum pic densityis then not much resolved representing only a few points. To testthe effect of this, we have doubled the number of temporal pointsby interpolating between two SPH points and run again the modelfor a few trajectories. The results are not changed significantly. Inthese two examples presented here, as in all the other trajectories,the evolution of the density is not linear, resulting in chaotic profileswhen looking at the abundance of the atoms as a function of density.The two trajectories do not have the same history of density resultingin a difference in the atomic abundances as a function of density. Thestarting density of A (0.7 cm − ) is smaller than for B (9 cm − ), the maximum density is 3 . × cm − for A while it is 9 . × cm − forB, and the final density is 125 cm − for A and 56 cm − for B. For bothtrajectories, except for Cl + , the atomic abundances are rather flat untilthe density reaches a few 10 or a few 10 cm − depending on thespecies. Then the abundances decrease before increasing again whenthe density decreases. All elements show a minimum at the densitypeak or just after. In the cases where the minimum abundances do notcoincide with the maximum density, the depletion timescale is longerthan the evolution of the density. The time scale for the species tocome back into the gas-phase depends on the physical conditions, i.e.different for each trajectory. The chaotic behavior of the results makesit difficult to describe generic results concerning the chemistry.For elements with complex chemistry, such as carbon, oxygen,nitrogen and sulphur, the elements can be spread over many differentspecies and these species will not be the same for all conditions MNRAS000
Density as a function of time for trajectory A (upper left panel) and gas-phase atomic abundances (X) as a function of density for the same trajectoryfor the rest of the figure. Symbols are just markers to help reading the time dependency of the figures. Blue and red parts of the lines represent the phase ofincreasing and decreasing density. gas temperatures as a function of of time for the two trajectoriesare shown in Appendix A. On the figures, we use markers to helpidentifying the initial and final times, as well as the peak density(at 4 . × yr for both). The time step of physical changes isgiven by the SPH model (2 . × yr). The maximum pic densityis then not much resolved representing only a few points. To testthe effect of this, we have doubled the number of temporal pointsby interpolating between two SPH points and run again the modelfor a few trajectories. The results are not changed significantly. Inthese two examples presented here, as in all the other trajectories,the evolution of the density is not linear, resulting in chaotic profileswhen looking at the abundance of the atoms as a function of density.The two trajectories do not have the same history of density resultingin a difference in the atomic abundances as a function of density. Thestarting density of A (0.7 cm − ) is smaller than for B (9 cm − ), the maximum density is 3 . × cm − for A while it is 9 . × cm − forB, and the final density is 125 cm − for A and 56 cm − for B. For bothtrajectories, except for Cl + , the atomic abundances are rather flat untilthe density reaches a few 10 or a few 10 cm − depending on thespecies. Then the abundances decrease before increasing again whenthe density decreases. All elements show a minimum at the densitypeak or just after. In the cases where the minimum abundances do notcoincide with the maximum density, the depletion timescale is longerthan the evolution of the density. The time scale for the species tocome back into the gas-phase depends on the physical conditions, i.e.different for each trajectory. The chaotic behavior of the results makesit difficult to describe generic results concerning the chemistry.For elements with complex chemistry, such as carbon, oxygen,nitrogen and sulphur, the elements can be spread over many differentspecies and these species will not be the same for all conditions MNRAS000 , 000–000 (2019)
Wakelam et al.
Figure 2.
Density as a function of time for trajectory B (upper left panel) and gas-phase atomic abundances (X) as a function of density for the same trajectoryfor the rest of the figure. Symbols are just markers to help reading the time dependency of the figures. Blue and red parts of the lines represent the phase ofincreasing and decreasing density. because it depends on the history (Ruaud et al. 2018). We show inFig. 3 the abundance of the main carriers of carbon as a functionof time for both trajectories. In trajectory A, between 2 . × and4 . × yr, C + dominates, but C and CO are also abundant. Duringthis time, in trajectory B, C and CO are much less abundant than in A,probably because the density is smaller. In A however, the increase ofthe density at 4 . × yr is faster than in B so that the C + abundancedrops faster while it remains high for a longer period of time in B. Atthe same time (when C + drops), gas-phase CO becomes the majorcarrier of carbon for approximately 2 × yr in trajectory A. Thenat about 4 . × yr, most of the carbon is locked into C H ice. Intrajectory B, at ∼ . × yr, most of the carbon is first in CO icefor a small amount of time and then in C H ice. In both models, C + becomes a reservoir again when the density decreases. Oxygen is lesscomplicated as atomic oxygen and water carry the majority of the element. The drop of gas-phase atomic oxygen happens later (after4 . × yr) in B while it happens at 4 . × yr in A. The nitrogengas-phase atomic abundance drops approximately at the same timeas for O. Later, NH and HCN ices carry most of the nitrogen but notwith the same amont and not at the same time for the two trajectories(see Fig. 4). For sulphur (Fig. 5), we also see a decrease of gas-phaseS + at the same time as O and N but S + and S alternatively share mostof the sulphur between 4 . × and 4 . × yr before forming HSand H S ices for trajectory A. This alternance of S + and S are notseen for trajectory B.For Fe, Mg, Na, and Si, which are initially ionic, the decrease inabundance is first due to the electronic recombination with electrons(this is in fact also the case for C and S). The neutral atoms are thendepleted on interstellar grains during collision, and hydrogenated.As such, FeH, MgH , NaH, and SiH ices are the main carriers of MNRAS , 000–000 (2019) lemental depletion A b un d a n c e Trajectory A
C+CCOKCOKC2H6 A b un d a n c e Trajectory B
C+CCOKCOKC2H6
Figure 3.
Abundances of the main carbon carriers as a function of time fortrajectories A (upper panel) and B (lower panel). K means species in the ices. A b un d a n c e Trajectory A
NN2KN2KNH3KHCN A b un d a n c e Trajectory B
NN2KN2KNH3KHCN
Figure 4.
Abundances of the main nitrogen carriers as a function of time fortrajectories A (upper panel) and B (lower panel). K means species in the ices. A b un d a n c e Trajectory A
S+SKHSKH2SKNS A b un d a n c e Trajectory B
S+SKHSKH2SKNS
Figure 5.
Abundances of the main sulphur carriers as a function of time fortrajectories A (upper panel) and B (lower panel). K means species in the ices. A b un d a n c e Trajectory A
Cl+ClKHClFe+KFeH A b un d a n c e Trajectory B
Cl+ClKHClFe+KFeH
Figure 6.
Abundances of the main chlorine and iron carriers as a function oftime for trajectories A (upper panel) and B (lower panel). K means species inthe ices. Note that the x axis is not the same as for Figs. 3, 4, and 5.MNRAS000
Abundances of the main chlorine and iron carriers as a function oftime for trajectories A (upper panel) and B (lower panel). K means species inthe ices. Note that the x axis is not the same as for Figs. 3, 4, and 5.MNRAS000 , 000–000 (2019)
Wakelam et al.
Figure 7.
Abundances as a function of density for phase 1 (left - (increasing phase of density)) and phase 2 (right - (decreasing phase of density)). The verticalline locates the 10 cm − density. The red lines show the depletion laws from Jenkins (2009).MNRAS , 000–000 (2019) lemental depletion Figure 8.
Same as figure 7. MNRAS000
Same as figure 7. MNRAS000 , 000–000 (2019)
Wakelam et al.
Figure 9.
Same as figure 7. these elements at high density. The case of iron is shown in Fig. 6. Fand P + react mostly with H to form HF and PH + . HF then depleteson the grains while PH + reacts with electrons to produce P (and PHbut PH gives P through the reactions PH + C + → PH + + C andPH + + e − → P + H). Atomic neutral phosphorus then depletes onthe grains and is hydrogenated into PH . HF and PH ices are themain carriers of fluorine and phosphorus at high density. Chlorineappears as an exception here because the Cl + gas-phase abundancedrops at much smaller density (see Fig. 6) as compared to the otherelements. This fast Cl + → Cl conversion is due to the combinedeffect of the electronic recombination of Cl + (Cl + + e − → Cl +h ν ) and the Cl + + H → HCl + + H reaction (followed by HCl + + H → H Cl + + H and H Cl + + e − → Cl + 2H). We checked this hypothesis by decreasing each and then both rate coefficients.The rate coefficient of the electronic recombination of Cl + , in ournetwork, is 1 . × − ( T / ) − . cm s − . This rate coefficient ismore than one order of magnitude larger than the typical electronicrecombination included in astrochemical databases. This ratecoefficient is indicated in the KIDA database (Wakelam et al. 2012)and comes from the 1991 version of UMIST (Millar et al. 1991).In the last UMIST version (2012) (McElroy et al. 2013), it hasbeen modified towards smaller values but without any reference.More laboratory work is required on this reaction. Decreasing http://kida.obs.u-bordeaux1.fr/ http://udfa.ajmarkwick.net/MNRAS , 000–000 (2019) lemental depletion Table 1.
Elemental abundances (with respect to the total hydrogen density)used in the simulations. The values are from Jenkins (2009) for a depletionfactor (F ∗ ) of zero except for Na and F for which we used the solar abundancesfrom Asplund et al. (2009).Atoms AbundanceHe 9 × − N 6 . × − O 5 . × − C 2 . × − S 1 . × − Si 2 . × − Fe 3 . × − Na 1 . × − Mg 2 . × − P 6 . × − Cl 5 . × − F 3 . × − the rate coefficient however does not significantly change the Cl + abundance as long as the Cl + + H → HCl + + H rate coefficientstays high (10 − cm − s − , Neufeld & Wolfire 2009). The twotrajectories show different results for Cl. As the density is initiallysmaller in A, the gas-phase abundance of Cl + is high for about2 . × yr while it is always low in B. Around 3 × yr, trajectoryB experiences a bump in density high enough to produce largeamounts of HCl ice but that is then dissociated and brought backinto the gas-phase as neutral Cl before the maximum density peakis achieved. At high density, HCl ices are the main carrier of chlorine.During the second phase, after the density peak, for the heavyelements with a simple chemistry (Mg, F, Fe, P, Si, Na, and Cl), thereservoirs stored on the grains are first dissociated on the surfacesas the density decreases. The atoms are then evaporated and ionized(except for fluorine). Photodesorption plays here a minor role. Ifthe efficiency of the process scales with the visual extinction, theyield is small (10 − ) and the same for all species (Ruaud et al.2016). Note that the fluorine atomic gas-phase abundance F in thetwo examples shown in Figs. 1 and 2 only represents 67% of theelemental abundance at the end of the simulation. The remainingfluorine is in the form of HF in the gas because of a rapid F + H → H + HF reaction. For smaller densities (as shown in Fig. 8), HFeventually dissociates and F becomes the main fluorine carrier again.
As time is a model dependent parameter, we plot the results as afunction of density in Figs. 7 to 9 for all trajectories. The abundancesduring the first phase (increasing density) are shown in the left andon the right for the second phase (decreasing density). Consideringall trajectories, we find similar behavior as previously shown. Formost elements, the decrease in the atomic abundances starts whenthe density is larger than ∼
10 cm − . Chlorine is an exception asits abundance decreases for some trajectories for densities below 0.1cm − . Some of the trajectories do not show any elemental depletionat high density, except for Cl + which is always depleted. This isbecause, within the full range of histories studied here, there arealways trajectories presenting fast increase of the density, whichinduces a delay in the molecular depletion. Chlorine again does notpresent this behavior because of its fast conversion to its neutral form in the gas-phase. For all elements, the abundances in phase2 (decreasing phase of density) are smaller at low density than inphase 1 (increasing phase of density), meaning that the depletionexperienced in the dense phase impacts the inventory of availablegas phase elements in phase 2. This effect is stronger for C + , Fe + ,Mg + , P + , Cl + and F. Later on, the gas abundances of Mg + , P + , F,Si + , Fe + , and Na + are equal to the initial abundances used in themodel when the density is smaller than 10 cm − .On Figs. 7 to 9, we have superimposed the elemental depletion lawsderived by Jenkins (2009) from atomic line observations in the diffuseinterstellar medium (up to 10 cm − . For carbon, oxygen and nitrogen,the observed elemental abundance is small and not in contradictionwith our predictions. For iron, magnesium, phosphorus, and silicon,the observed depletion is much stronger than predicted by the model.For chlorine, we do reproduce the observed depletion. In this paper, we studied the depletion of the elements during the tran-sition between the diffuse and dense interstellar medium by couplinga full gas-grain chemical model to results obtained from large scalehydrodynamics simulations of the interstellar medium at galacticscales. With this approach we could follow the evolution of inter-stellar matter over several millions of years and study the effect ofcycling between low density and high density phases on the deple-tion of elements such as C, O, N, S, Si, Fe, Na, Mg, P, Cl and F. Forall these elements, we find that the strength of their depletion is setby the balance between accretion/reactions at the surface and theirability to resist photoprocessing. Our main result is that all these el-ements, but Cl, recover their undepleted values when n H <
10 cm − and our model thus fails at reproducing depletion patterns derivedfrom observations of low density gas (Jenkins 2009).Chlorine is an exception and the depletion pattern of Cl + atn H <
10 cm − agrees well with the one derived by Jenkins (2009).Because of the fast electronic recombination of Cl + and its efficientreaction with H , Cl + disappears efficiently even at very low density.The fact that we are able to reproduce the chlorine observed depletionat very low density, may indicate that the electronic recombinationof other elements might be too low. Bryans et al. (2009) have testedthe impact of new more accurate estimates of the electronic recom-bination of He + , C + , O + , Na + , and Mg + for a variety of physicalconditions. According to their calculations, the largest difference be-tween the new rate coefficients and the ones typically listed in currentastrochemical databases was for for Mg + electronic recombination,which is 60% smaller at 10 K in the new estimates. Such differencesmay not impact our calculations. However, it could be worth deriv-ing parametrized rate coefficients from the original calculations toinclude them in astrochemical models. The authors also stated thatthere exists no reliable data for Si + , P + , S + , Cl + , and Fe + .Possible explanations for discrepancies observed at low densitiesmay also come from unaccounted processes in the current chemicalmodel. A first possibility comes from the single grain size approx-imation we make. For instance, a MRN size distribution extendeddown to a min ∼
10 Ådecreases the collision timescale between atomsand grains by a factor of ∼ ∼ yrs at n H ∼
10 cm − ).If we further take into account that a significant fraction of thesesmall grains (which dominate the surface area) would be negativelycharged, Coulomb focusing reduces this timescale to few 10 yrsmaking possible the in-situ depletion of some of the atomic cations(Weingartner & Draine 1999). The non-thermal desorption mecha- MNRAS000
10 cm − ).If we further take into account that a significant fraction of thesesmall grains (which dominate the surface area) would be negativelycharged, Coulomb focusing reduces this timescale to few 10 yrsmaking possible the in-situ depletion of some of the atomic cations(Weingartner & Draine 1999). The non-thermal desorption mecha- MNRAS000 , 000–000 (2019) Wakelam et al. nism (though cosmic-ray heating for instance) would however reducestrongly the depletion effect of the small grains (Cuppen et al. 2006).However, additional considerations such as the strength of theadsorption at the surface should also be explored. Even though en-hanced collision rates could facilitate the depletion process, a fractionof these elements must remain bound to the surface at very low den-sities (this is especially true for elements such as Mg, Fe, P and Si, forwhich significant depletion has been inferred at low densities). In thepresent study we assumed physisorption, for which typical bindingenergy vary between 10 and few 100 meV. Such low binding energieslead relatively fast thermal desorption timescale under diffuse cloudconditions. Indeed, we find that the combination of photoprocessingand thermal evaporation is efficient for clearing-out the grains surfacefrom any adsorbed atoms and molecules on timescales of few 10 yrsat n H ∼
10 cm − . The inclusion of chemisorption sites, characterizedby increased binding energies ( > . ACKNOWLEDGMENTS
DATA AVAILABILITY
The physical and chemical simulations and the nautilus gas-grainmodel are available upon request.
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APPENDIX A: DUST AND GAS-TEMPERATURES FORTRAJECTORIES A AND B
MNRAS , 000–000 (2019) lemental depletion Figure A1.
Gas and dust temperature as a function of time for trajectory A.
Figure A2.
Gas and dust temperature as a function of time for trajectory B.MNRAS000