Cosmic ray sputtering yield of interstellar ice mantles: CO and CO2 ice thickness dependence
E. Dartois, M. Chabot, T. Id Barkach, H. Rothard, P. Boduch, B. Augé, A.N. Agnihotri
CCosmic ray sputtering yield of interstellar ice mantles:CO and CO ice thickness dependence. E. Dartois , M. Chabot , T. Id Barkach , H. Rothard , P. Boduch B. Augé A.N.Agnihotri Institut des Sciences Moléculaires d’Orsay, CNRS, Université Paris-Saclay, Bât 520, Rue André Rivière, 91405 Orsay, Francee-mail: [email protected] Laboratoire de physique des deux infinis Irène Joliot-Curie, CNRS-IN2P3, Université Paris-Saclay, 91405 Orsay, France Centre de Recherche sur les Ions, les Matériaux et la Photonique, CIMAP-CIRIL-GANIL, Normandie Université, ENSICAEN,UNICAEN, CEA, CNRS, F-14000 Caen, France Institut de planétologie et d’astrophysique de Grenoble, CNRS, Université Grenoble Alpes, 38000 Grenoble, France Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi, 110016, Indiakeywords: Astrochemistry, cosmic rays, molecular processes, lines and bands, interstellar ice mantles, solid state: volatile
To appear in Astronomy & Astrophysics
Abstract
Cosmic-ray-induced sputtering is one of the important desorp-tion mechanisms at work in astrophysical environments. Thechemical evolution observed in high-density regions, from denseclouds to protoplanetary disks, and the release of species con-densed on dust grains, is one key parameter to be taken into ac-count in interpretations of both observations and models. Thisstudy is part of an ongoing systematic experimental determina-tion of the parameters to consider in astrophysical cosmic raysputtering. As was already done for water ice, we investigatedthe sputtering yield as a function of ice mantle thickness for thetwo next most abundant species of ice mantles, carbon monoxideand carbon dioxide, which were exposed to several ion beams toexplore the dependence with deposited energy. These ice sput-tering yields are constant for thick films. It decreases rapidly forthin ice films when reaching the impinging ion sputtering des-orption depth. An ice mantle thickness dependence constraintcan be implemented in the astrophysical modelling of the sput-tering process, in particular close to the onset of ice mantle for-mation at low visual extinctions.
1. Introduction
In the dense and cold zones of the interstellar medium, dustgrains are covered with volatile solids (the ice mantles), whichare relatively protected from ambient radiation fields outside thecloud. However, cosmic radiation consisting of high-energy par-ticles penetrates deeply into these clouds and induces complexchemistry through its direct interaction (radiolysis), or indirectinteraction (production of a secondary vacuum ultraviolet-VUV-background radiation field by interaction with the gas, mainlymolecular hydrogen) with dust grains. These cold and denseregions should in theory be considered as gas phase chemical’dead zones’ on time scales above the condensation (freeze-out)time of the whole gas phase on cold dust grains. The obser-vation of a great diversity of species in the gas phase in thesedense clouds thus implies the presence of mechanisms, not onlyof physico-chemical evolution, but also of desorption of the con-densed species. Among these mechanisms are invoked chemicaldesorption (e. g. Yamamoto et al. 2019; Oba et al. 2018; Wake-lam et al. 2017; Minissale et al. 2016a,b; Garrod et al. 2007),photodesorption by secondary VUV photons or X-rays (Westleyet al. 1995; Öberg et al. 2009; Muñoz Caro et al. 2010; Öberg et al. 2011; Fayolle et al. 2011, 2013; Muñoz Caro et al. 2016;Cruz-Diaz et al. 2016, 2018; Fillion et al. 2014; Dupuy et al.2017; Bertin et al. 2012, 2016; Dupuy et al. 2018), excursionsin grain temperature (e.g. Bron et al. 2014), and sputtering in theelectronic interaction regime by cosmic radiation (e.g. SeperueloDuarte et al. 2009; Dartois et al. 2013; Boduch et al. 2015; Dar-tois et al. 2015; Mejía et al. 2015; Rothard et al. 2017, and refer-ences therein). Once the e ffi ciencies of these di ff erent processeshave been quantitatively evaluated in the laboratory for a largenumber of systems, it is then possible to understand, throughmodelling, their absolute and relative impact on the chemistry ofthe interstellar medium.The work presented in this paper is a continuation of a system-atic study of the interstellar ice sputtering by cosmic radiationsimulated in the laboratory. Of particular interest is the e ff ectof the finite size of the interstellar ice mantle on the sputteringe ffi ciency, which has been studied for H O (Dartois et al. 2018),in the context here of two of the other major ice mantle com-ponents, CO and CO . In §2, the experiments of irradiation byaccelerated heavy ions is described. The model of evolution ofthe ices under the e ff ect of this bombardment is described in §3.The fitting of the obtained data for CO and CO ices is presentedin §4, leading to the determination of the finite sputtering depthfor the considered ions. We then discuss the dependence of thesputtering depth on the stopping power and provide constraintsfor astrophysical models on the sputtering e ff ective yield includ-ing finite size e ff ects.
2. Experiments
Swift ion irradiation experiments were performed at the heavy-ion accelerator Grand Accélérateur National d’Ions Lourds(GANIL; Caen, France) . Heavy ion projectiles were deliveredon the IRRSUD beam line . The IGLIAS (Irradiation de GLacesd’Intérêt AStrophysique) facility, a vacuum chamber (10 − mbarunder our experimental conditions) holding an infrared transmit-ting substrate that was cryocooled down to about 9 K, is coupledto the beam line. The ice films were produced by placing a coldwindow substrate in front of a deposition line. Carbon monoxide Part of the equipment used in this work has been financed by theFrench INSU-CNRS program“Physique et Chimie du Milieu Interstel-laire” (PCMI). http: // a r X i v : . [ a s t r o - ph . GA ] F e b able 1. Experiments and results. N , ρ, and thickness are the ice film initial column density, density, and thickness, respectively. σ des is theradiolysis destruction cross section. Y ∞ s and N d are the semi-infinite sputtering yield and sputtering depth origin of the species within the modelused in this work, in a column density equivalent. l d is the depth in monolayers converted from N d . σ s is the e ff ective sputtering cross-section.r s / r d is the ratio of the e ff ective sputtering radius over the radiolysis destruction radius (deduced from the radiolysis destruction cross-section).Species T N ρ a Thickness σ des Y ∞ s N d Depth l d σ s r s / r d K 10 cm − g / cm µ m nm × cm − layers nm H + at 100 keV; S e =
46 eV / CO molecules / cm (Raut & Baragiola 2013) CO
25 50 1.1 0.33 - 1.5 ± × − + . − . Ca + at 38.4 MeV ; S e = / CO molecules / cm (this work) CO ± ± ± ±
69 26.8 . . CO ± ± ± ±
108 10.7 . . CO Ni + at 33 MeV ; S e = / CO molecules / cm (this work) CO ± ± ± ±
119 37.4 . . CO ± ± ± ±
126 24.1 . . CO CO Ni + at 46 MeV ; S e = / C O molecules / cm (Seperuelo Duarte et al. 2009) C O ± ±
31 15.7 ± ±
200 50.0 . Xe + at 630 MeV ; S e = / CO molecules / cm (Mejía et al. 2015) CO
30 6.8 1.17 0.042 Y thins / Y ∞ s ≈ . + . − . . b + − + − - - Ca + at 38.4 MeV ; S e = / CO molecules / cm (this work) CO ± ± ± ±
79 18.2 . . CO CO CO Ni + at 33 MeV ; S e = / CO molecules / cm (this work) CO ± ±
22 15.1 ± ±
149 49.9 . . CO Ni + at 50 MeV ; S e = / CO molecules / cm (Seperuelo Duarte et al. 2010) CO ± ±
13 19.8 ± ±
58 42.0 . . CO a The density (g / cm ) considered for the ice thickness and the determination of the number of molecular layers are given for CO for the di ff erent temperatures following Satorre et al. (2008), and taken as 0.8 g / cm for CO (e.g. Loe ffl er et al. 2005; Bouilloud, etal. 2015). b Ratio of thin-to-thick yields. The yield value for infinite thickness is obtained from the fit of the other data with a powerlaw for the considered stopping power. See text for details.or carbon dioxide films were condensed at 9 K on the window,from the vapour phase, and kept at this temperature during theirradiations. Details of the experimental setup are given in Augéet al. (2018). The ion flux, set between 10 and 10 ions / cm / sis monitored online using the current measured on the beam en-trance slits defining the aperture. The irradiation is performedat normal incidence, whereas the infrared transmittance spectraare recorded simultaneously at 12 o of incidence. A sweepingdevice allows for uniform and homogeneous ion irradiation overthe target surface. The relation between the current at di ff erent slit apertures and the flux is calibrated before the experiments us-ing a Faraday cup inserted in front of the sample chamber. Thethin ice films deposited allow the ion beam to pass through thefilm with an almost constant energy loss per unit path length. ABruker FTIR spectrometer (Vertex 70v) with a spectral resolu-tion of 1 cm − was used to monitor the infrared film transmit-tance. The evolution of the infrared spectra was recorded as afunction of the ion fluence. The projectiles used were Ca + at 38.4 MeV and Ni + at 33 MeV with an electronic stoppingpower, calculated using the SRIM package (Ziegler et al. 2010) Fluence (cm -2 )10 C o l u m n den s i t y ( c m - ) CO CO
0N (cm -2 )02•10 - d N / d F Ca
0N (cm -2 )05.0•10 Y i e l d
875 438 0Monolayers
Fig. 1.
Left panel: CO column density evolution measured with the anti-symmetric stretching mode ( ν ) spectra as a function of Ca + ionfluence for CO ice films deposited with di ff erent initial thicknesses (shown with di ff erent colours) measured at 9 K. The radiolytically producedCO is also shown. Middle panel: Experimentally measured di ff erential evolution -dN / dF as a function of column density, to be compared toEquation 1. Fits of the equation to the data are shown as long-dashed lines (in black for the thickest film and orange for the intermediate thicknessone) for the two thickest films, as well as fits not taking into account the finite depth of sputtering (dashed lines). No fit is attempted for thethinnest film. Right panel: Sputtering yield evolution as a function of column density; over-plotted are the infinite thickness yield (dashed lines)and adjusted exponential decay (long-dashed lines). See text for details. The experiments are summarised in Table 1. Fluence (cm -2 )10 C o l u m n den s i t y ( c m - ) CO CO
0N (cm -2 )05.0•10 - d N / d F Ni
0N (cm -2 )01•10 Y i e l d Fig. 2.
Left panel: CO column density evolution measured with the anti-symmetric stretching mode ( ν ) spectra as a function of Ni + ionfluence for CO ice films deposited with di ff erent initial thicknesses (shown with di ff erent colours) measured at 9 K. The radiolytically producedCO is also shown. Middle panel: Experimentally measured di ff erential evolution -dN / dF as a function of column density, to be compared toEquation 1. Fits of the equation to the data are shown as dashed lines for the two thickest films, as well as fits not taking into account the finitedepth of sputtering (straight lines). Right panel: Sputtering yield evolution as a function of column density; over-plotted are the infinite thicknessyield (dashed lines) and adjusted exponential decay (long-dashed lines). See text for details. The experiments are summarised in Table 1. for CO ice of S e = . / CO molecules / cm andS e = . / CO molecules / cm , respectively. We alsomade use of additional experiments already presented in Seperu-elo Duarte et al. (2009) for C O using a 46 MeV Ni + pro-jectile, a measurement on a CO very thin film irradiated with a630 MeV Xe + presented in Mejía et al. (2015), and a low-energy 100 keV proton irradiation experiment on CO from Raut& Baragiola (2013). For CO ice with projectiles of Ca + at38.4 MeV, the S e = . / CO molecules / cm , and for Ni + at 33 MeV, the S e = . / CO molecules / cm .We also made use of additional experiments already presented inSeperuelo Duarte et al. (2010) for CO using a 50 MeV Ni + projectile, and a low-energy 9 keV proton irradiation experimentfrom Schou & Pedrys (2001).
3. Model
As discussed previously when modelling the evolution of wa-ter ice mantles (Dartois et al. 2015) and in the modelling of asputtering crater in the N ice case of Dartois et al. (2020), thecolumn density evolution of the ice molecules submitted to ionirradiation can be described, to first order and as a function ofion fluence (F) by a di ff erential equation:dN / dF = − σ des N − Y ∞ s (cid:18) − e − NNd (cid:19) × f . (1)N is the CO or CO column density. σ des is the ice e ff ective ra-diolysis destruction cross-section (cm ). Y ∞ s is the semi-infinite(thick film) sputtering contribution in the electronic regime tothe evolution of the ice column density, multiplied, to first or-der, by the relative concentration (f) of carbon monoxide orcarbon dioxide molecules with respect to the total number of .5•10
0N (cm -2 )05.0•10 - d N / d F Ni Fluence (cm -2 )10 C o l u m n den s i t y ( c m - ) C O C O
0N (cm -2 )02•10 Y i e l d Fig. 3.
Left panel: C O ice experimental column densities for ion irradiation experiment (beam of Ni + at 46 MeV) discussed in SeperueloDuarte et al. (2009). Middle panel: − dN / dF calculated from the recorded data. The blue circles represent the data used in the fit, whereas the skyblue points are discarded as they represent the phase transition of the ice observed at the early irradiation stage (low fluence). The long, dashedorange line corresponds to the best-fit models using equation 1, and the dashed orange line to what would be expected from thick film behaviour.The dotted green line represents the fit using previously determined values from Seperuelo Duarte et al. (2009). Right panel: Sputtering yieldevolution and fitted contribution as a function of column density. Fluence (cm -2 )10 C o l u m n den s i t y ( c m - ) COCO
0N (cm -2 )02•10 - d N / d F Ca
0N (cm -2 )01•10 Y i e l d Fig. 4.
Left panel: CO column density evolution at 9K as a function of at 33 MeV Ni + ion fluence for CO ice films deposited with di ff erentinitial thickness (di ff erent colours). The radiolytically produced CO is shown. Middle panel: Experimentally measured di ff erential evolution-dN / dF as a function of column density. The fit of Equation 1 to the data for the thickest film is shown (long black dashed line), as well as a fit nottaking into account the finite depth of sputtering (straight dashed line). Right panel: Sputtering yield evolution and fitted contribution as a functionof column density. molecules and radicals in the ice film. f can be evaluated tofirst order by f X = N X / (N CO + N CO ) with X = CO or CO, ne-glecting the presence of radicals, carbon suboxides, and O . Inthe case of CO , one of the main products formed by irradiationis CO, and reaches about 20% of the ice at the top of its con-centration. When the ice film is thin (column density N (cid:46) N d ;N d being the semi-infinite ’sputtering depth’), the removal ofmolecules by sputtering follows a direct impact model, that is, allthe molecules within the sputtering area defined by a sputtering’e ff ective’ cylinder are removed from the surface. The apparentsputtering yield, as a function of thickness, is modelled to firstorder to estimate the corresponding sputtering depth by an expo-nential decay, leading to the 1 − e ( − N / N d ) correcting factor appliedto Y ∞ s . A schematic view of such a simplified cylinder approxi-mation is shown in Fig.1 of Dartois et al. (2018). The sputtering cylinder is defined by a radius r s (defining an e ff ective sputter-ing cross section σ s ) and a height d (related to the measuredsputtering depth). These parameters, reported in Table. 1, arecalculated from the measurement of N d and Y ∞ s . These parame-ters also give access to the more or less prominent elongation ofthe sputtering cylinder, which is species- and deposited-energy-dependent. To monitor this elongation within the cylinder ap-proximation one can calculate the so-called aspect-ratio param-eter (height-to-diameter ratio of the cylinder in the semi-infiniteice film case). This model is a simplification. The reformationof the main species via the destruction of the daughter speciesis, for example, neglected as a second-order e ff ect. The shape ofthe sputtering crater also influences the exact parametrisation, asshown in Dartois et al. (2020). An evolved model may be builtwhen more precise data is acquired. Nevertheless, N d is an e ffi - Fluence (cm -2 )10 C o l u m n den s i t y ( c m - ) COCO
0N (cm -2 )05.0•10 - d N / d F Ni
0N (cm -2 )02•10 Y i e l d Fig. 5.
Left panel: CO column density evolution at 9K as a function of at 33 MeV Ni + ion fluence for CO ice films deposited with di ff erentinitial thickness (di ff erent colours). The radiolytically produced CO is shown. Middle panel: Experimentally measured di ff erential evolution-dN / dF as a function of column density. The fit of Equation 1 to the data for the thickest film is shown (long black dashed line), as well as a fitnot taking into account the finite depth of sputtering (straight dashed line ). Right panel: Sputtering yield evolution and fitted contribution as afunction of column density. Fluence (cm -2 )10 C o l u m n den s i t y ( c m - ) COCO
0N (cm -2 )05.0•10 - d N / d F Ni
0N (cm -2 )02•10 Y i e l d Fig. 6.
Left: CO column density evolution at 9K as a function of fluence for 50 MeV Ni + ion irradiation experiments (the blue one isdiscussed in Seperuelo Duarte et al. 2009) for ice films with di ff erent initial thicknesses (di ff erent colours). Radiolytically produced CO is shown.Middle panel: Experimentally measured di ff erential evolution -dN / dF as a function of column density. The fit of Equation 1 to the data for thethickest film is shown (long black dashed line), as well as a fit not taking into account the finite depth of sputtering (black dashed line). Rightpanel: Sputtering yield evolution and fitted contribution as a function of column density. cient single parameter useful in estimating the sputtering depthin a column density equivalent.The column densities of the molecules are followed experimen-tally in the infrared via the integral of the optical depth ( τ ¯ ν )of a vibrational mode, taken over the band frequency range.The band strength value (A, in cm / molecule) for a vibrationalmode has to be considered. In the case of the CO ν modenear 2342 cm − , we adopted 7.6 × − cm / molecule (Bouil-loud, et al. 2015; Gerakines et al. 1995; D’Hendecourt & Al-lamandola 1986), although some measurements tend towardsa higher value ( ∼ × − cm / molecule Gerakines & Hudson2015). For the CO ν mode near 2342 cm − , we adopted1.1 × − cm / molecule (Bouilloud, et al. 2015; Gerakines et al.1995). The results are anchored to these adopted values andshould be modified, if another reference value is favoured. Fitsof Equation 1 are shown in the middle panels of Figs. 1-6. Best parameters were retrieved with an amoeba method minimisationto find the minimum chi-square estimate on the model function.Only the experiments thick enough to sample the infinite thick-ness sputtering yield can be used. The fitted output parameters,namely σ des , Y infS , and N d , are reported in Table 1, with the un-certainties being estimated at two times the reduced chi-squarevalue obtained in the minimisation.
4. Results and discussion
The evolution of the infrared spectra upon ion irradiation showsthree stages that are much better understood when the data areplotted showing dN / dF as a function of the column density,rather than the column density as a function of the fluence, evolv-ng over several decades. We clearly see in Figs. 1-6 that the evo-lution of dN / dF departs from the ideal model of Equation 1, inparticular at low fluence. At the beginning of irradiation, the icefilm is restructuring with the first ions impinging the freshly de-posited ice film. Therefore the molecular environment and phaseis modified and / or compacted. The oscillator strength of themeasured transitions in the infrared and / or the refractive indexof the ice are slightly changing. As a consequence, the apparentdN / dF evolution is rapid. At the considered stopping powers forthe ions, this is stabilised after a fluence of a few 10 ions / cm ,and the observed behaviour of dN / dF better follows the expec-tation of the model. This early phase of the irradiation cannot besafely used to monitor the column density variations as both themolecule column density and the infrared band strength vary,leading to unpredictable changes, and they are discarded fromthe fits used to extract the model parameters (in the figures theyare represented by light colours in the dN / dF plots). Includingthese points in the fit leads to a misestimation of the radioly-sis destruction cross-section. In the second evolution stage, thefilm can be considered semi-infinite with respect to the sputter-ing and dN / dF evolves as a slope combining the radiolysis of thebulk and semi-infinite sputtering. In the later phase, the film be-comes thin with respect to the sputtering’s semi-infinite sputter-ing depth (N d ) of individual ions. dN / dF decreases accordinglywith a linear and exponentially convolved behaviour.In each experimental session, CO and CO films with sev-eral starting thicknesses (summarised in Table 1) were irradiated.This was done to estimate the reproducibility of the results, andalso to check that the behaviour of the experimental results, par-ticularly when reaching the thin film conditions, does not dependon the initial thickness. This can be seen in the middle panels ofFigs. 1-6, in which the dN / dF evolution is the same regardlessof the initial film thickness within experimental uncertainties. Itis important to state that it means that in these experiments theradiolysis (e.g. production of CO for CO films) does not accu-mulate enough to significantly a ff ect the thin film’s behaviouralevolution. We reanalysed the data from Seperuelo Duarte et al. (2009) ona C O ice film exposed to Ni + ions at 46 MeV. This isshown in Fig.3. The right panel shows − dN / dF as a functionof the column density, with the previous fit with the parametersfrom Seperuelo Duarte et al. (2009) shown via a green dashedline, and the reanalysis with our current model via orangedashed lines. Our model includes an exponential decay at lowcolumn densities (long dashed orange lines). The dashed orange(straight) line shows what would be expected from thick filmsputtering. As discussed above, the first points at low fluence,below about 10 ions / cm were discarded from our fit, as theydo not follow the theoretical expected − dN / dF behaviour.Mejía et al. (2015) reported a strong decrease of the sputteringyield for thin CO films exposed to Xe + ions at 630MeV. Using the adjusted expected experimental yields forsemi-infinite thick films, extrapolated to the stopping power ofthis experiment (S e = / CO molecules / cm ), acrude estimate of the sputtering depth can be made. The thinfilm had a column density of N thin = . × cm − , and theyreport a measured sputtering yield of Y thins ≈ . + . − . × . Thesputtering yield at the same value of electronic stopping powerfor a semi-infinite thick ice film can be estimated from the thick film quadratic dependence, and we estimate it to be of the orderof Y ∞ s ≈ . × . From Y thins = Y ∞ s × (1 − e − N thin / N d ), one canestimate N d ≈ − N thin / ln(1 − Y s / Y ∞ s ) ≈ . + . − . × cm − .To provide another point at low stopping power (S e = / CO molecules / cm ), we also include the sputteringof CO films induced by 100 keV H + at 25K from Raut &Baragiola (2013). In this experiment, the authors measured ayield Y ∞ s ≈ ±
5. They did not measure the depth N d . We canfix a range of variation by assuming upper and lower boundslimiting cases. For the lower bound, all sputtered molecules areassumed to come from the first layer. For the upper bound, theycome from a depth thick as the yield. The mean value is taken asthe cube root of the yield in monolayers, that is, a homogeneous3D sputtering volume with no preferential extension along anyaxis. Assuming a density of 1.1 g / cm at 25K (Satorre et al.2008) for the ice thickness and number of molecular layers, thisleads to N d ≈ . + . . × cm − , providing an anchor point atlow stopping power. To provide another point at low stopping power (S e =
14 eV / CO molecules / cm ), we also included the sputtering of CO filminduced by 9 keV H + at 25K from Schou & Pedrys (2001). Inthis experiment, the authors measured a yield Y ∞ s ≈ .
4. Weagain fixed its range of variation by assuming that all sputteredmolecules come from the first layer for the lower bound, from adepth as thick as the yield for the upper bound, and the mean asthe cube root of the yield in monolayers. Assuming a density of0.8 g / cm at 10K (Loe ffl er et al. 2005; Bouilloud, et al. 2015) forthe ice thickness and the determination of the number of molec-ular layers, this leads to N d ≈ . + . × cm − , providing ananchor point at low stopping power.In this reanalysis of these previous literature data, CO andCO ice film temperatures are slightly higher than the one usedin our experiments. The sputtering yield has been shown to betemperature-dependent, in particular in the case of H O ice (e.g.Baragiola et al. 2003), with a higher yield when the temperatureincreases, Y = Y + Y exp ( − Ea / kT) ), with an activation energyEa that is related to the binding energy of the ice under consid-eration. For water ice it becomes significant above around 90K.We thus expect that for CO ice, in the 9-30K range consideredhere, the sputtering yield should be fairly constant. In the caseof CO, the measured sputtering yield might be slightly higherthan expected at the same temperature as the one we used in ourmeasurements. However, as discussed above, the error bar set byour lack of knowledge on the corresponding sputtering depth forCO covers more than one order of magnitude, and we considerit most probably includes this uncertainty. The depth of sputtering obtained from the fit with the model ofEquation 1, along with the parameters of the fit, are reportedin Table 1. Only the su ffi ciently thick films are fitted, as asu ffi cient number of points in the linear part of the curve isneeded to retrieve the cross-section and the depth of sputteringsimultaneously. The corresponding equivalent column densitydepth N d is reported in Fig. 7 for CO , and Fig. 8 for COas a function of the stopping power. The best fit to the dataas a function of the stopping power is S . ± . and S . ± .
00 1000 10000
100 1000 10000 eV / 10 CO molecules/cm N D ( c m ) M ono l a y e r s +
38 MeV Ca
33 MeV Ni
46 MeV Ni
630 MeV Xe Fig. 7.
Evolution of sputtering depth N d as a function of the stoppingpower for CO ice. The colour code for the points is the same as inTable 1. The best fit is given by N d = . ± . × S . ± . . See text fordetails.
10 100 1000 10000
10 100 1000 10000 eV / 10 CO molecules/cm N D ( c m ) M ono l a y e r s +
38 MeV Ca
50 MeV Ni
33 MeV Ni Fig. 8.
Evolution of sputtering depth N d as a function of the stoppingpower for CO ice. The colour code for the points is the same as inTable 1. The best fit is given by N d = . ± . × S . ± . . See text fordetails. for CO and CO, respectively, that is, close to linear with thestopping power. Experiments and thermal spike models of theion-track-induced phase transformation in insulators predict adependence of the radius r of the phase change cross-sectionevolving as r ∼ √ S e , where S e = dE / dx is the deposited energyper unit path length (e.g. Lang et al. 2015; Toulemonde et al.2000; Szenes 1997), with a threshold in S the to be determined.The measured semi-infinite (thick film) sputtering yield for ices(i.e. corresponding to the total volume) generally scales as thesquare of the ion electronic stopping power (Y ∞ s ∝ S , Rothardet al. 2017; Dartois et al. 2015; Mejía et al. 2015; Boduchet al. 2015). In the electronic sputtering regime consideredin the present experiments, and as expected from the abovecited dependences, it makes sense that the sputtering depthapproximatively scales linearly with the stopping power and the aspect ratio scales with the square root of the stopping power.An estimate of a sputtering cross-section can be inferredfrom our measurements with σ s ≈ V / d, where V is the volumeoccupied by Y ∞ s molecules and d the depth of sputtering. σ s ≈ Y ∞ s / l d / ml, where ml is the number of CO or CO molecules / cm in a monolayer (about 6 . × / cm and 5 . × / cm , respec-tively, with the adopted ice densities). As is shown in Table 1, thesputtering radius r s would therefore be about 1.26 to 2.12 timeslarger than the radiolysis destruction radius r d in the case of theCO ice, and 2.03 to 2.36 for CO in the considered energy range( ∼ / u). The net radiolysis is the combined e ff ect of thedirect primary excitations and ionisations, the core of the energydeposition by the ion, and the so-called delta rays (energetic sec-ondary electrons) travelling at much larger distances from thecore; that is, several hundreds of nanometres at the consideredenergies in this work (e.g. Mozunder et al. 1968; Magee & Chat-terjee 1980; Katz et al. 1990; Moribayashi 2014; Awad & Abu-Shady 2020). The e ff ective radiolysis track radius that we calcu-late is lower than the sputtering one, which points towards a largefraction of the energy deposited in the core of the track. The scat-ter on the ratio of these radii is due to the lack of more precisedata. It nevertheless allows to put a rough constraint on the es-timate of N d in the absence of additional depth measurements,with N d (cid:46) Y ∞ s /σ d . If the r s / r d ratio is high, a large amount ofspecies come from the thermal sublimation of an ice spot less af-fected by radiolysis, and the fraction of ejected intact moleculesis higher. The aspect ratio corresponding to these experimentsevolves between about ten and twenty for CO and CO, whereasfor water ice at a stopping power of S e ≈ . × eV / H O molecules / cm , we show that it is closer to one (Dartois etal. 2018). The depth of sputtering is much larger for CO andCO than for H O at the same energy deposition, not only be-cause their sublimation rate is higher, but also because they donot form OH bonds. For complex organic molecules embeddedin ice mantles dominated by a CO or CO ice matrix, with thelack of OH bonding and the sputtering for trace species beingdriven by that of the matrix (in the astrophysical context), theco-desorption of complex organic molecules present in low pro-portions with respect to CO / CO cannot only be more e ffi cient,but will thus arise from deeper layers. If we integrate the sputtering yield over the distribution of galac-tic cosmic rays (GCR), the depth dependence of the yield canbe parametrised in astrophysical models to provide an e ff ectiveyield. Assuming the quadratic behaviour observed for many ices(e.g. Rothard et al. 2017; Dartois et al. 2015; Mejía et al. 2015;Boduch et al. 2015),Y ∞ s (S e ) = Y S , (2)where Y is a pre-factor. S e = (dE / dx) e is the stopping power inthe electronic regime. For Se in units of eV / molecules / cm ,we used Y = . × − for CO, 8 . × − for CO , and5 . × − for H O. The thickness-dependent sputtering yieldin the electronic regime can be parametrised with the followingprescription:Y s (N ice , S e ) = Y S × (cid:18) − e − NiceNd(Se) (cid:19) . (3)N ice is the ice column density, and N d (S e ) is the sputtering depthin column density equivalent, as determined in the previous sec-ion. The e ff ective sputtering rate by cosmic rays can be cal-culated by integrating over their distribution in abundance andenergies:Y e ff e (N ice ) = × π (cid:88) Z (cid:90) ∞ E min Y s [N ice , S e (E , Z)] dN CR dE (E , Z)dE , (4)where Y e ff e (N ice ) is the e ff ective sputtering rate for agiven ice mantle thickness corresponding to a column den-sity of N ice (or equivalently a number of monolayers), dN CR dE (E , Z)[particles . cm − . s − . sr − / (MeV / u)] is the di ff erentialflux of the cosmic ray element of atomic number Z, with a cut-o ff in energy E min set at 100 eV. Moving the cuto ff from 10 eVto 1 keV does not change the results significantly. The di ff eren-tial flux for di ff erent Z follows the GCR observed relative abun-dances from Wang et al. (2002; H, He), de Nolfo et al. (2006;Li, Be), George et al. (2009; > Be), as explained in more detailin Dartois et al. (2013). The integration is performed up to Z = e is calculated using the SRIM code (Ziegler etal. 2010) as a function of atomic number Z and specific energyE (in MeV per nucleon). For the di ff erential Galactic cosmicray flux, we adopted the functional form given by Webber &Yushak (1983) for primary cosmic ray spectra using the leakybox model, also described in Shen et al. (2004):dNdE (E , Z) = C E . (E + E ) , (5)where C is a normalisation constant ( = . × , Shen et al.2004) and E a parameter influencing the low-energy componentof the distribution. Under such parametrisation, the high-energydi ff erential flux dependence goes asymptotically to a − . ζ ) corresponding to the same distributioncan be calculated, and it gives an observable comparisonwith astrophysical observations in various environments. Theionisation rates for E = / u correspondto ζ = . × − s − , 5 . × − s − , and 2 . × − s − ,respectively. To show the dependence as a function of thenumber of layers, we set the value of C (E ≈ / u) so thatthe ionisation rate corresponds to ζ = × − s − , a typicalvalue for the ionisation measured in dense clouds (Geballe &Oka 2010; Indriolo & McCall 2012; Neufeld, & Wolfire 2017;Oka et al. 2019).The best fit to the thickness-dependent e ff ective sputteringyield, integrated over the GCR distribution corresponding to ζ = × − s − , can be adjusted with the following functional:Y e ff e (n layers ) ≈ α × (cid:18) − e − (cid:16) nlayers β (cid:17) γ (cid:19) , (6)with α ∼ β ∼ γ ∼ α ∼ β ∼ γ ∼ , and α ∼ β ∼ γ ∼ O (plot-ted in brown, red, and blue in Fig.9, respectively).The typical thickness of ice mantles estimated from astro-nomical observations varies from a few to several hundreds ofmonolayers in dense clouds (Boogert et al. 2015 and referencestherein). In the dust particle size distribution, there might besigns of unusually large grain sizes or aggregates forming big-ger particles, which is supported by the observations of scatter-ing excess in spectral features or core shine e ff ect (e.g. Jones etal. 2016; Steinacker et al. 2015; Dartois 2006). The ice man-tle growth, and thus thickness, is, to first order, independent of Y ee ff CO CO H O Fig. 9.
Thickness-dependent e ff ective sputtering yields (circles) in theelectronic regime calculated for CO and CO , for ζ = × − s − ,using the thickness dependence with stopping power derived in this ar-ticle. The water ice behaviour is included for comparison, calculatedusing the single anchor point from Dartois et al. (2018). The functionalEquation 6 fitted to the data is shown in dashed lines for each species.The typical absolute scale error bars are over-plotted. the grain radius, but dependent on the temperature and density.In gas and grain astrochemical models, ice mantle thicknessesevolve with local conditions and time (e.g. Ruaud et al. 2016;Pauly & Garrod 2016). As the semi-infinite sputtering yield limitis reached rapidly with water ice, its e ff ective sputtering, exceptat the border of clouds, should not vary significantly from thebulk, whereas for carbon dioxide and carbon monoxide, sputter-ing yield variations are expected when looking at the sputteringyield evolution displayed in Fig. 9.To calculate the sputtering rates for di ff erent ionisation rates,we varied the E parameter in Equation 5. It leads to a propor-tionality between the ionisation and sputtering rates (as in, e.g.Dartois et al. 2015; Faure et al. 2019). By doing so, one assumesthat the energy spectra of all CR species are identical. For a CRspectrum with low energy particles impacting thick clouds con-taining the ice mantles, the stopping powers (di ff erent for eachspecies) are di ff erentially shaping the spectra during the propa-gation within the cloud (see Fig. 3 in Chabot 2016). To derivean estimate of the expected variations with respect to the simpleproportionality between sputtering and ionisation rates, we prop-agated di ff erent initial CR spectra through clouds, as explainedin Chabot (2016). We then calculated the ionisation rates andcorresponding sputtering rates. In the worst case, the propor-tionality approximation overestimates the complete calculationby a factor 2. It occurs in the very dense parts of clouds (Av > ζ > × − s − ). Itis worth mentioning that magnetic fields may also a ff ect such aproportionality between ionisation and sputtering rates. Indeed,proton and heavy particles do not have the same magnetic rigid-ity nor Larmor radius.
5. Conclusions
We measured the swift, heavy ion-induced CO and CO ice sput-tering yield at ∼
10 K, and its dependence on the ice thickness.hese measurements allow us to constrain the sputtering depthprobed by the incident ion. Within the context of an ’e ff ective’sputtering cylindrical shape to describe the sputtered moleculevolume, the aspect ratio (height-to-diameter ratio of the cylinderin the semi-infinite ice film case) is higher than one, for the ionstopping powers considered in this study. The ejected moleculesare arising from deeper layers than would be the case for a purewater ice mantle at the same deposited energies. The measureddepth of desorption N d scales with the ion electronic stoppingpower as ∝ S e . ± . (S e , deposited energy per unit path length)and ∝ S e . ± . , for CO and CO, respectively. We thus exper-imentally measured a behaviour in agreement with what is ex-pected from studies with swift heavy ions on insulators, as thephase transformations show a dependence of the radius r of thecross-sections evolving as r ∼ √ S e , and the ice’s total sputteringyields are generally proportional to the square of S e .Following the trend measured, the depth of desorptionevolves almost linearly with S e , and the aspect ratio dependencewill thus scale as S α e , with α ∼ Acknowledgements.
This work was supported by the Programme National’Physique et Chimie du Milieu Interstellaire’ (PCMI) of CNRS / INSU withINC / INP co-funded by CEA and CNES, and benefited from the facility devel-oped during the ANR IGLIAS project, grant ANR-13-BS05- 0004, of the FrenchAgence Nationale de la Recherche. Experiments performed at GANIL. We thankT. Madi, T. Been, J.-M. Ramillon, F. Ropars and P. Voivenel for their invalu-able technical assistance. A.N. Agnihotri acknowledges funding from INSERM-INCA (Grant BIORAD) and Région Normandie fonds Européen de développe-ment régional-FEDER Programmation 2014-2020.
References
Augé, B., Been, T., Boduch, P., et al. 2018, Review of Scientific Instruments, 89,075105Awad, E. M., & Abu-Shady, M. 2020, Nuclear Instruments and Methods inPhysics Research B, 462, 1Baragiola, R. A., Vidal, R. A., Svendsen, W., et al. 2003, Nuclear Instru-ments and Methods in Physics Research B, 209, 294. doi:10.1016 / S0168-583X(02)02052-9Bertin, M., Fayolle, E. C., Romanzin, C., et al. 2012, Physical Chemistry Chem-ical Physics (Incorporating Faraday Transactions), 14, 9929Bertin, M., Romanzin, C., Doronin, M., et al. 2016, ApJ, 817, L12Boduch, P., Dartois, E., de Barros, A. L. F., et al. 2015, Journal of Physics Con-ference Series, 629, 012008Boogert, A. C. A., Gerakines, P. A., & Whittet, D. C. B. 2015, ARA&A, 53, 541Bouilloud, M., Fray, N., Bénilan, Y., et al. 2015, MNRAS, 451, 2145.Bron, E., Le Bourlot, J., & Le Petit, F. 2014, A&A, 569, A100Chabot, M. 2016, A&A, 585, A15Cruz-Diaz, G. A., Martín-Doménech, R., Muñoz Caro, G. M., & Chen, Y.-J.2016, A&A, 592, A68Cruz-Diaz, G. A., Martín-Doménech, R., Moreno, E., Muñoz Caro, G. M., &Chen, Y.-J. 2018, MNRAS, 474, 3080Dartois, E. 2006, A&A, 445, 959Dartois, E., Ding, J. J., de Barros, A. L. F., et al. 2013, A&A, 557, A97Dartois, E., Augé, B., Rothard, H., et al. 2015, Nuclear Instruments and Methodsin Physics Research B, 365, 472Dartois, E., Chabot, M., Id Barkach, T., et al. 2018, A&A, 618, A173Dartois, E., Chabot, M., Id Barkach, T., et al. 2020, Nuclear Instruments andMethods in Physics Research B, 485, 13. doi:10.1016 / j.nimb.2020.10.008Dupuy, R., Bertin, M., Féraud, G., et al. 2017, A&A, 603, A61Dupuy, R., Bertin, M., Féraud, G., et al. 2018, Nature Astronomy, 2, 796Faure, A., Hily-Blant, P., Rist, C., et al. 2019, MNRAS, 487, 3392Fayolle, E. C., Bertin, M., Romanzin, C., et al. 2011, ApJ, 739, L36Fayolle, E. C., Bertin, M., Romanzin, C., et al. 2013, A&A, 556, A122 Fillion, J.-H., Fayolle, E. C., Michaut, X., et al. 2014, Faraday Discussions, 168,533Garrod, R. T., Wakelam, V., & Herbst, E. 2007, A&A, 467, 1103Geballe, T. R., & Oka, T. 2010, ApJ, 709, L70George, J. S., Lave, K. A., Wiedenbeck, M. E., et al. 2009, ApJ, 698, 1666Gerakines, P. A., Schutte, W. A., Greenberg, J. M., & van Dishoeck, E. F. 1995,A&A, 296, 810Gerakines, P. A. & Hudson, R. L. 2015, ApJ, 808, L40.D’Hendecourt, L. B., & Allamandola, L. J. 1986, A&AS, 64, 453Indriolo, N., & McCall, B. J. 2012, ApJ, 745, 91Jones, A. P., Köhler, M., Ysard, N., et al. 2016, A&A, 588, A43Katz, R., Loh K. S., Baling, L., Huang, G.-R. 1990, Radiation E ff ects and De-fects in Solids, 114, 1-2, 15Lang, M., Devanathan, R., Toulemonde, M., & Trautmann, C. 2015, CurrentOpinion in Solid State and Materials Science, 19, 39Loe ffl er, M. J., Baratta, G. A., Palumbo, M. E., et al. 2005, A&A, 435, 587Magee, J. L., & Chatterjee, A. 1980, J. Phys. Chem., 84, 3529.Mejía, C., Bender, M., Severin, D., et al. 2015, Nuclear Instruments and Methodsin Physics Research B, 365, 477Minissale, M., Moudens, A., Baouche, S., et al. 2016, MNRAS, 458, 2953Minissale, M., Dulieu, F., Cazaux, S., et al. 2016, A&A, 585, A24Moribayashi, K. 2014, Radiation Physics and Chemistry, 96, 211Mozumder, A., Chatterjee, A., Magee, J.L., Radiation Chemistry, AmericanChemical Society, 27Muñoz Caro, G. M., Jiménez-Escobar, A., Martín-Gago, J. Á., et al. 2010, A&A,522, A108Muñoz Caro, G. M., Chen, Y.-J., Aparicio, S., et al. 2016, A&A, 589, A19Neufeld, D. A., & Wolfire, M. G. 2017, ApJ, 845, 163de Nolfo, G. A., Moskalenko, I. V., Binns, W. R., et al. 2006, Advances in SpaceResearch, 38, 1558Oba, Y., Tomaru, T., Lamberts, T., et al. 2018, Nature Astronomy, 2, 228Öberg, K. I., Linnartz, H., Visser, R., & van Dishoeck, E. F. 2009, ApJ, 693,1209Öberg, K. I., Boogert, A. C. A., Pontoppidan, K. M., et al. 2011, ApJ, 740, 109Oka, T., Geballe, T. R., Goto, M., et al. 2019, ApJ, 883, 54Pauly, T. & Garrod, R. T. 2016, ApJ, 817, 146Raut, U., & Baragiola, R. A. 2013, ApJ, 772, 53Rothard, H., Domaracka, A., Boduch, P., et al. 2017, Journal of Physics BAtomic Molecular Physics, 50, 062001Ruaud, M., Wakelam, V., & Hersant, F. 2016, MNRAS, 459, 3756Satorre, M. Á., Domingo, M., Millán, C., et al. 2008, Planet. Space Sci., 56,1748Schou, J., & Pedrys, R. 2001, J. Geophys. Res., 106, 33309Seperuelo Duarte, E., Boduch, P., Rothard, H., et al. 2009, A&A, 502, 599Seperuelo Duarte, E., Domaracka, A., Boduch, P., et al. 2010, A&A, 512, A71Shen, C. J., Greenberg, J. M., Schutte, W. A., & van Dishoeck, E. F. 2004, A&A,415, 203Steinacker, J., Andersen, M., Thi, W.-F., et al. 2015, A&A, 582, A70Szenes, G. 1997, Nuclear Instruments and Methods in Physics Research B, 122,530Toulemonde, M., Dufour, C., Meftah, A., & Paumier, E. 2000, Nuclear Instru-ments and Methods in Physics Research B, 166, 903Wakelam, V., Loison, J.-C., Mereau, R., et al. 2017, Molecular Astrophysics, 6,22Wang, J. Z., Seo, E. S., Anraku, K., et al. 2002, ApJ, 564, 244Webber, W. R., & Yushak, S. M. 1983, ApJ, 275, 391Westley, M. S., Baragiola, R. A., Johnson, R. E., & Baratta, G. A. 1995, Nature,373, 405Yamamoto, T., Miura, H., & Shalabiea, O. M. 2019, MNRAS, 490, 709Ziegler, J. F., Ziegler, M. D., & Biersack, J. P. 2010, Nuclear Instruments andMethods in Physics Research B, 268, 1818 Appendix A: Infrared spectra from the experiments
The baseline-corrected infrared optical depth spectra in the CO ν antisymmetric stretching mode and CO ν stretching moderegion for the experiments reported in this work are displayedhere for the di ff erent initial films’ thicknesses considered.
500 2400 2300 2200 2100Wavenumber (cm -1 )0123 O p t i c a l dep t h CO ν CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.1.
Infrared spectra for first CO ice experiment with Ca + at 38.4 MeV ions. The inserted colour code gives the correspondingirradiation fluence. -1 )0.00.51.01.52.02.5 O p t i c a l dep t h CO ν CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.2.
Infrared spectra for second CO ice experiment with Ca + at 38.4 MeV ions. -1 )0.00.20.40.60.8 O p t i c a l dep t h CO ν CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.3.
Infrared spectra for third CO ice experiment with Ca + at38.4 MeV ions. -1 )02468 O p t i c a l dep t h CO ν CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.4.
Infrared spectra for first CO ice experiment with Ni + at33 MeV ions. We note that the spectra are saturated at the beginning ofthe experiment. These spectra were discarded from the analysis.
500 2400 2300 2200Wavenumber (cm -1 )0.00.51.01.52.02.5 O p t i c a l dep t h CO ν CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.5.
Infrared spectra for second CO ice experiment with Ni + at 33 MeV ions. -1 )0.00.51.01.52.0 O p t i c a l dep t h CO ν CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.6.
Infrared spectra for third CO ice experiment with Ni + at33 MeV ions. -1 )0.00.20.40.60.8 O p t i c a l dep t h CO ν CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.7.
Infrared spectra for fourth CO ice experiment with Ni + at 33 MeV ions. -1 )0.00.51.01.52.0 O p t i c a l dep t h C O ν C O ν C O ν Fig. A.8.
Infrared spectra for C O ice experiments with Ni + at46 MeV ions.
400 2300 2200 2100Wavenumber (cm -1 )0.00.51.01.52.02.53.0 O p t i c a l dep t h CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.9.
Infrared spectra for first CO ice experiment with Ca + at38.4 MeV ions. -1 )0.00.51.01.5 O p t i c a l dep t h CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.10.
Infrared spectra for second CO ice experiment with Ca + at 38.4 MeV ions. -1 )0.00.20.40.6 O p t i c a l dep t h CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.11.
Infrared spectra for third CO ice experiment with Ca + at38.4 MeV ions. -1 )0.00.20.40.6 O p t i c a l dep t h CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.12.
Infrared spectra for fourth CO ice experiment with Ca + at 38.4 MeV ions.
400 2300 2200 2100Wavenumber (cm -1 )012345 O p t i c a l dep t h CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.13.
Infrared spectra for first CO ice experiment with Ni + at33 MeV ions. We note that the spectra are saturated at the beginning ofthe experiment. These spectra were discarded from the analysis. -1 )0.00.51.01.5 O p t i c a l dep t h CO ν CO ν F l uen c e ( i on s / c m x ) Fig. A.14.
Infrared spectra for second CO ice experiment with Ni ++