Issue |
A&A
Volume 508, Number 1, December II 2009
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|
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Page(s) | 275 - 287 | |
Section | Interstellar and circumstellar matter | |
DOI | https://doi.org/10.1051/0004-6361/200913119 | |
Published online | 21 October 2009 |
A&A 508, 275-287 (2009)
Microscopic simulation of methanol and formaldehyde ice formation in cold dense cores
H. M. Cuppen1 - E. F. van Dishoeck1,2 - E. Herbst3 - A. G. G. M. Tielens1
1 - Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
2 - Max-Planck-Institut für Extraterrestrische Physik, Giessenbachstrasse 1, 85748 Garching, Germany
3 -
Departments of Physics, Astronomy, and Chemistry, The Ohio State University, Columbus, OH 43210, USA
Received 14 August 2009 / Accepted 15 October 2009
Abstract
Context. Methanol and its precursor formaldehyde are among
the most studied organic molecules in the interstellar medium and are
abundant in the gaseous and solid phases. We recently developed a model
to simulate CO hydrogenation via H atoms on interstellar ice surfaces,
the most important interstellar route to H2CO and CH3OH, under laboratory conditions.
Aims. We extend this model to simulate the formation of both
organic species under interstellar conditions, including freeze-out
from the gas and hydrogenation on surfaces. Our aim is to compare
calculated abundance ratios with observed values and with the results
of prior models.
Methods. Our model utilises the continuous-time, random-walk
Monte Carlo method, which - unlike other approaches - is able to
simulate microscopic grain-surface chemistry over the long timescales
in interstellar space, including the layering of ices during
freeze-out.
Results. Simulations under different conditions, including density and temperature, have been performed. We find that H2CO and CH3OH
form efficiently in cold dense cores or the cold outer envelopes of
young stellar objects. The grain mantle is found to have a layered
structure with CH3OH on top. The species CO and H2CO
are found to exist predominantly in the lower layers of ice mantles
where they are not available for hydrogenation at late times. This
finding is in contrast with previous gas-grain models, which do not
take into account the layering of the ice. Some of our results can be
reproduced by a simple quasi-steady-state analytical model that focuses
on the outer layer.
Conclusions. Observational solid H2CO/CH3OH and CO/CH3OH
abundance ratios in the outer envelopes of an assortment of young
stellar objects agree reasonably well with our model results, which
also suggest that the large range in CH3OH/H2O
observed abundance ratios is due to variations in the evolutionary
stages. Finally, we conclude that the limited chemical network used
here for surface reactions apparently does not alter the overall
conclusions.
Key words: astrochemistry - methods: numerical - molecular processes - ISM: molecules - ISM: clouds
1 Introduction
Methanol and its precursor formaldehyde are among the most studied organic molecules in the interstellar medium (ISM). Both species have been observed in the gas phase and as constituents of ice mantles. Whereas gas-phase detections of both molecules have been numerous, (e.g., Jørgensen et al. 2005; Maret et al. 2004,2005; Schöier et al. 2004; van der Tak et al. 2000) and methanol is a well-known constituent of the ice (Allamandola et al. 1992; Dartois et al. 1999; Herbst & van Dishoeck 2009), there are only a few secure solid-state detections of H2CO. These detections occur mostly in high-mass young stellar sources such as W33A, GL2136, and GL 989, and often only upper limits are given (Boogert et al. 2008; Gibb et al. 2004). For example, Pontoppidan et al. (2004) found an upper limit for the H2CO ice abundance in the outer envelope of the low-mass young stellar source Serpens SMM 4 of 5% with respect to water ice. CH3OH ice has a much higher abundance of 28% with respect to water in this source, resulting in an H2CO/CH3OH ice ratio of less than 0.18. Typically, in sources where both species have been detected, the observed H2CO/CH3OH ratio is still smaller than unity, with values ranging from 0.09 to 0.5. Sub-millimetre observations of the gas in seven massive hot-cores show a similar trend: Bisschop et al. (2007) found a constant ratio of gas phase H2CO/CH3OH between 0.13 and 0.28.
In this paper, we aim to develop a model that explains these
observed abundances and abundance ratios and to study the
implications for the conditions in regions where they are
found. Following Tielens & Hagen (1982) and Charnley et al. (1992) and
supported by numerous laboratory studies on hydrogenation of CO
(Fuchs et al. 2009; Hiraoka et al. 2002; Watanabe & Kouchi 2002), we assume that
methanol and formaldehyde are formed from hydrogenation of CO on
grain surfaces. Observations have revealed that CO is present in
three distinct components in interstellar ices: non-polar (pure) CO,
CO mixed with CO2 and CO as a trace in polar ice
(Chiar et al. 1998; Pontoppidan et al. 2008; Tielens et al. 1991). Here, we
exclusively focus on methanol formation during the
condensation/formation of the non-polar CO component. This component
is thought to be formed when the cloud density increases and the
gaseous atomic H/CO ratio decreases (Tielens & Hagen 1982), and thus
occurs at a later stage or deeper in the cloud than the water ice
formation. This is consistent with the higher observed extinction
threshold for CO ice formation compared with that of H2O (Whittet et al. 2001). In the highest density regions (>few
cm-3), the
timescales for collisions of CO with the grains become so short that
most of the gaseous CO is removed from the gas. This so-called
``catastrophic'' CO freeze-out has been observed directly through
infrared ice-mapping observations (Pontoppidan 2006) and
indirectly through the lack of gas-phase CO (and other molecules) from
the densest parts of the core, e.g., L1544, B68
(Bergin et al. 2002; Caselli et al. 1999), as well as the accompanying rise in
H2D+ and the deuterated molecules. In such high density regions, the
bulk of the CO ice is in the pure form.
For this pure CO-ice component, we can thus be assured that CO is the main
reaction partner of accreted hydrogen and hence all the relevant
reactions have been studied experimentally. For the other CO ice
environments, competition with other reactions clearly plays an
important role, in particular hydrogenation of atomic oxygen to water.
We briefly comment on this competition in Sect. 5 but leave the formation
of methanol and formaldehyde in these other interstellar ice
environments to a future paper.
The formation route of methanol ice by hydrogenation of solid CO studied in
the laboratory consists of the following steps:
where the reactions involving CO and H2CO possess small activation energy barriers. The experiments all show that for a range of temperatures and H-fluences (time


The models presented in this paper differ from previous models on the formation of interstellar methanol ice in that they include details of the surface structure of CO and utilise parameters obtained to reproduce experiments in the laboratory setting (Fuchs et al. 2009). In this manner, a set of energy barriers for the different processes on the surface - diffusion, desorption and reaction - was obtained, which can now be used in an interstellar environment. Unlike the master equation (Stantcheva et al. 2002), rate equation (Ruffle & Herbst 2000), and macroscopic Monte Carlo (Ruffle & Herbst 2000) studies of methanol formation, the continuous-time, random-walk (CTRW) Monte Carlo technique accounts for the layering of the CO. This layering is crucial, because the constant addition of fresh CO tends to protect the underlying layers from hydrogenation and limits the time available for reaction. Moreover, our current approach is different from previous CTRW-Monte Carlo simulations on this system (Chang et al. 2007), both because we use newly determined barriers, and because we account for the actual crystal structure of CO ice, instead of utilising a simple cubic structure. On the other hand, the previous study of Chang et al. (2007) coupled the gas-phase chemistry with grain-surface chemistry and used a larger grain surface reaction network.
The paper is organised in the following way. The next section describes the Monte Carlo method and introduces the input parameters of the model and their origin. Section 3 presents the model results for interstellar conditions covering the same temperature regime as in the experiments (12.0-16.5 K) (Fuchs et al. 2009). The focus of the discussion is on how the abundances depend on various parameters, especially the gas-to-dust ratio, and on the ice structure and layering. Section 3.4 extends the model to lower temperatures of 8 and 10 K, which are more appropriate for cold dense cores. In Sect. 4 the model results are compared to a rate equation model using similar input parameters and conditions, an analytical steady-state model, other prior grain surface models, and observations. Section 5 discusses the effect of the limited chemical network on the results by introducing more reactions.
2 Monte Carlo method
The CTRW method has been described previously (see, e.g., Chang et al. 2005).
A detailed overview of the Monte Carlo program and its input parameters can be found in Fuchs et al. (2009).
In brief, the technique simulates a sequence of processes that can
occur on a grain surface, which is modelled as a lattice with the
number of lattice sites determined by the size of the grain and the
site density for the adsorbate CO. The order of this sequence is
determined by means of a random number generator in combination with
the rates for the different processes. These processes include
deposition onto the surface, hopping from one lattice site to a nearest
neighbour, desorption of the surface species, and reactions between two
species. We assume that the (first-order) rate coefficients (s-1) for hopping and desorption are thermally activated according to the formula
where



Table 1:
Reaction rate coefficients,
,
and activation energy barriers for CO + H and H2CO + H for different temperatures.
The desorption, or binding, energy for an adsorbate
depends on an energy parameter E.
To understand the role of this parameter, let us first consider a CO
molecule either in the ice or adsorbing onto the surface. The CO
molecule is assumed to lie or stick in a configuration close to the -CO structure (Vegard 1930).
In this configuration, each CO molecule has up to 14 neighbours to
which hopping can occur, four in the same layer, four one layer above
and below and one two layers above and below. The binding energy
is determined by the additive energy contributions of the occupied neighbouring sites. The contributions are
2E for the layers below and, if applicable, E
for the neighbours in the same layer (lateral bonds) or in upper
layers. An alternative treatment for sites below the particle is to add
a single overall contribution for longer range interactions from the
ice layer. In this way, the added long range contribution is roughly
the same for all species of the same kind, regardless of their very
local environment. However, if a very porous structure forms, the lower
neighbouring sites are most likely not all occupied and the added long
range contribution is less, reflecting the ``real'' long range
contribution. As an example, if a CO molecule lands on top of a CO
layer in a multi-layered CO ice, its binding energy is
,
while if it lies in a deeply embedded layer in the ice, its binding energy is the full
.
From ab-initio calculations (Andersson, in prep.) the parameter
for CO is 63 K, so that the binding energy of a CO adsorbate
onto CO ice is 630 K. Experimentally a desorption energy of
CO from a CO surface was determined to be
K, which corresponds to 13-14
.
For atomic hydrogen,
was calculated to be 32 K onto CO ice (Andersson, in prep.). For H2 a value of
K is used, slightly higher than for H as expected from calculations of Hornekær et al. (2005) for H2 and Al-Halabi & van Dishoeck (2007) for H atoms. If lattice sites are occupied by heavier species than CO (mainly CH3OH)
the total binding energy of an H or CO, and the structure are assumed
not to change. If lattice sites are occupied by H atoms rather than CO,
the lower value of
is used for those relevant sites, so that the total binding energy for
a specific CO is an expression containing both the parameters for CO
and for H. For atomic H, the van der Waals interaction with
another atomic H in an adjoining site is rather small, i.e.,
.
The energy parameters
for H2CO and CH3OH and the intermediates, HCO and H3CO,
are chosen such that these species neither desorb nor diffuse (see
below) from the grain at the temperatures studied. All adopted values
for E are summarised in Table 2.
Table 2: The energy parameter E for the different species.
The same parameter E is used to help determine the hopping barrier from
site i to an empty adjacent site, j. If sites i and j have the same binding energy, then the barrier for hopping is given by the equation
where





If the binding sites i and j have different binding
energies, we add a second term to the formula for the hopping barrier
in order to have the forward and backward rates obey detailed balance.
The overall expression then becomes
where

Thus, each species can in principle undergo up to 15 processes:
thermal desorption and hopping to one of the up to 14 neighbouring
sites, or, if sites are occupied, reaction with the species in that
site. Reactions without activation energy (e.g., H + HCO
H2CO)
occur with 100% efficiency, whereas for reactions with barriers, we
must simulate the competition between the efficiency of reaction and
that of hopping out of the adjacent lattice sites. Some of these
processes can be forbidden. Bulk species are, for instance, not allowed
to desorb and not all species react with each other. The rate
coefficients of all these processes are determined using Eq. (2) and the barriers as discussed above. In this way, diffusion and reaction are automatically treated competitively.
In addition to reactions occurring via the Langmuir-Hinshelwood mechanism, which happen as a result of diffusion into adjacent sites, the program includes reactions occurring via the Eley-Rideal mechanism, in which a gas-phase species lands atop a surface species and reacts with it. The barriers for reactions are assumed to be independent of mechanism. In the diffusive case, however, if two reactants do not tunnel under or cross over the activation energy barrier, they have multiple additional opportunities until they diffuse away from one another. In the Eley-Rideal case, we allow only one opportunity. For example, an H atom landing directly atop a CO molecule gets one chance to overcome the reaction barrier and react. If the reaction does not proceed, the H atom can then hop further to find another reactant.
Deposition onto a surface site occurs with a rate coefficient
according to
![]() |
(5) |
where



![]() |
(6) |
with







3 Results
3.1 Ice abundances as functions of time
In order to follow the build up of CO, H2CO, and CH3OH
in the ice mantle, simulations at different temperatures and densities
were carried out. All simulations commence with the same initial bare
surfaces consisting of lattices with
sites and some simple surface steps (similar to Surface c in Cuppen & Herbst 2005).
The choice of the initial surface (either silicates or amorphous
carbon) was found to be unimportant after the build-up of a few
monolayers of ice. To start the simulation on a bare surface, the
energy parameters used were chosen to be the same as for the
CO surface.
All results were converted to grains with a standard size of 0.1
m.
The simulation surface is a square flat surface. The spherical,
continuous nature of a grains is mimicked by periodic boundary
conditions.
The size of the simulated surface has been found to be in the regime
where no size effects are observed (Chang et al. 2005); this regime is associated with surface abundances of reactive species such as H larger than one per grain. For H2
formation, a size dependence is observed, since for smaller grains the
average surface density of atomic hydrogen is much smaller than one
(accretion limit), but because of the stronger sticking of CO and H2CO with respect to H atoms, the size dependence is probably only important for higher temperatures where CO and H2CO start to desorb.
Figure 1 shows the evolution of the three dominant ice species as a function of time for
cm-3,
and four different temperatures: 12.0, 13.5, 15.0, and 16.5 K.
These temperatures are the same as used in the experiments in Fuchs et al. (2009). The abundances are plotted in terms of 1015 molecules per cm-2,
which is equivalent to species per lattice site. The plotted curves are
the combined results of several independent simulations using different
initial seeds, e.g., initial settings of the random number generator.
Simulations were added until the evolution did not significantly
change. Initial gas phase abundances of
and
were assumed; these correspond to observed (CO) (Lacy et al. 1994) and calculated (H) fractional abundances for cold dense cores of a density of
cm-3. The abundance of atomic H is mainly determined by the ration between the cosmic-ray destruction rate of H2 and the formation rate of H2 which leads to
1 cm-3 independent of the density (Duley & Williams 1984). Goldsmith & Li (2005) showed observationally that the H-atom abundance is higher than 1 cm-3 and we therefore use a higher H abundance of 10 cm-3
for our high density case which will be discussed below. The gas-phase
abundance of CO is allowed to deplete as CO accretes onto grains while
the gas-phase abundance of H remains constant. The solid line
indicates the combined ice build-up of the three species together; in 105 yr, at most 10 monolayers of ice are produced at the value of
used.
From the graphs, a difference in this total build-up for the higher
temperatures is immediately clear. Whereas the ice thickness grows
linearly for 12.0 and 13.5 K, a clear non-linear behaviour as well
as a drop in the total coverage can be observed at 15.0 and
especially 16.5 K. This is due to the binding energy of CO.
The residence time of an adsorbed CO molecule is 0.3 yr on a flat
grain at 16.5 K. This time will increase once the CO molecules can
stick together and form small islands, because the binding within the
islands is stronger than for individual molecules. With the CO
gas-phase concentration of 1 cm-3,
the arrival time of new CO molecules onto a grain is of similar
order as the residence time on a bare surface, so that the CO molecules
do not have the opportunity to meet and stick together to form small
islands, which is an efficient mechanism for growth. Figure 2 shows similar time evolution curves for a density of
cm-3, leading to a ten times higher flux, and indeed here there is a greater ice build-up at 16.5 K.
![]() |
Figure 1:
CO, H2CO, and CH3OH build-up as a function of time for a density of
|
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In general, the production of H2CO and CH3OH decreases with increasing temperature for both densities. This dependence is in agreement with the laboratory experiments of the hydrogenation of a CO ice by Fuchs et al. (2009). There the initial production rate was observed to be higher for low temperature whereas the final yield at the end of the experiments peaked at 15.0 K due to an increase of the penetration depth of H-atoms into the CO ice with temperature. In the co-deposition simulations presented in this paper, the penetration depth has less impact on the formation of H2CO and CH3OH since a fresh supply of CO is constantly deposited and the formation rate is therefore more comparable to the rate at the start of the experiments when a pure CO ice is exposed to atomic hydrogen. In this condition, it is the shortened grain lifetime of H atoms at the higher temperatures that reduces the rate of methanol formation from CO. The rate for reaction changes only minimally with increasing temperature.
The pure CO build-up here peaks at 13.5 K for both densities as can be clearly seen in Figs. 1 and 2
by comparing the dash-dotted curves. This quantity is influenced by two
effects with opposite temperature dependence: the desorption of CO
molecules (see above), which increases with increasing temperature, and
the conversion of CO into H2CO, which decreases with
increasing temperature because of the lessened ability of H atoms to
remain on grains long enough to react. Nevertheless, for most
conditions, CH3OH dominates the ice layer at late times and exhibits a very steep formation curve. CO and H2CO
on the other hand start with a high abundance at early times and
increase much more slowly, even reaching a steady-state level on some
occasions. The steady-state can be clearly seen for T=12.0 and 13.5 K for
cm-3 and T=16.5 K for
cm-3. For lower atomic H abundances,
1 cm-3, the H2CO and CH3OH formation is expected to occur at later times, since similar n(H)/n(CO) ratios will occur at later times.
![]() |
Figure 2:
Similar to Fig. 1 for
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3.2 Dust-to-gas number ratio
The dust-to-gas number ratio determines the rate of the gas phase
depletion and the maximum ice thickness that can be achieved before
depletion of gaseous CO, which is roughly 50 ML for
and 100 ML for
as is discussed in the next section.
Figure 3 shows the temporal evolution of CO, H2CO and CH3OH for 12.0 and 16.5 K with a reduced dust-to-gas ratio of
.
Densities of
and 105 cm-3 are used. Panel (a) can be compared with the 12.0 K panel in Fig. 1a, panel (b) with the 16.5 K panel in Fig. 1 and panels (c) and (d) with the 12.0 and 16.5 K panels in Fig. 2, respectively. It is apparent that only Fig. 3c is significantly different from its analogs.
For the lower density cases (
cm-3), substantial depletion of gaseous CO has not started yet after
yr,
resulting in roughly the same gas-phase composition throughout the
simulation for both dust-to-gas ratios. This is generally not true for
the higher density models. At 16.5 K, however, the build-up of ice
layers is hampered by the desorption of CO back into the gas phase,
again resulting in very similar accretion rates for the two dust-to-gas
cases. At lower temperatures, however, the accretion rate for CO is
greater for the lower dust-to-gas case. The main difference between
Figs. 2a (12.0 K) and 3c is indeed that the levelling off to constant values for CO and H2CO occurs at later times and thicker ice layers for
.
![]() |
Figure 3:
CO, H2CO, and CH3OH build-up as a function of time for
|
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3.3 Ice structure
In addition to the overall surface abundance as a function of time, the
Monte Carlo approach allows us to obtain more detailed information
concerning the layering of the ice. Figure 4 plots the fraction per monolayer of the main ice components CO, H2CO and CH3OH at a time of
yr
for 12.0 K (a, b, d)) and 15.0 K (c). The abscissa is the
number of the monolayer starting from the bare surface as zero
indicated by ``grain boundary'' in the figure. The label ``gas phase
boundary'' indicates the top layer of the ice mantle, which faces the
gas phase. Despite differences in dust-to-gas ratios and other
parameters in the panels (see caption), the plot clearly shows that
there is a gradient in the ice composition. At the onset of the CO
freeze-out, a fraction of the layers remains in the form of CO and the H2CO is not fully hydrogenated to CH3OH. While the gas phase CO slowly depletes, the
ratio becomes more favourable for the complete hydrogenation of CO. For example, in the
yr of the simulation, the gas phase CO abundance drops from 10 cm-3 to 0.2 cm-3 for 12.0 K,
cm-3 and
.
The right panels show the ice composition for slower CO depletion (
). Panel (d) has additionally an altered initial abundance of
.
Note that the horizontal scale for the right panels differs from that for the left panels. For
the change to pure CH3OH layers occurs over more layers than for
.
If panels (a) and (b) were plotted as a function of the fraction of the
total ice thickness instead of the absolute ice thickness, very similar
graphs would be obtained. The final overall H2CO/CH3OH
ratio after freeze-out is therefore independent of the exact
dust-to-gas ratio. Comparison of panels (a) and (c) confirms that the
rate and efficiency of the conversion of CO into methanol is determined
by the temperature while comparison of panels (b) and (d) shows that
the rate and efficiency are also determined by the
ratio. A closer look at panel (d) compared with panel (b) shows that the lower
ratio leads to larger H2CO
and CO fractions for the lower monolayers and that the conversion to
pure methanol layers occurs only at higher layers, which are formed at
later times.
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Figure 4:
Fractional abundance of the three main ice components as a function of monolayer after
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Figure 5 paints a
schematic picture of a grain mantle. At the onset of CO freeze-out, the
flux of CO molecules accreting onto the grain is large, larger than the
part of H atom flux that is available for hydrogenation of CO, and, as
a consequence, the mantle will be rich in CO with H2CO and CH3OH as minor components. As the
ratio in the gas phase increases, more and more CO and H2CO is converted into CH3OH and the outer layers of the mantle become more CH3OH
rich.
Note that the astronomically observed solid abundances are sums over
the entire grain mantle, although different ice components can be
distinguished through the line profiles.
![]() |
Figure 5: Schematic picture of the growth of the ice mantle during CO freeze-out. For coloured figures, see the online version. |
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Figure 6:
Cross section of the ice mantle after
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Actual simulated grain mantle cross sections for individual runs are plotted in Fig. 6.
Here unoccupied sites are indicated in black, light gray on the bottom of the figures represents the bare grain, while H and H2 are represented by white. All other mantle species, CO, HCO, H2CO, H3CO, and CH3OH, have different gray scale levels according to their degree of hydrogenation; i.e., CH3OH is darkest, whereas CO is represented by the lightest gray. The four panels correspond to the resulting icy mantle after
yr under the same conditions as in Fig. 2.
The grain temperatures are 12.0, 13.5, 15.0 and 16.5 K from
top to bottom. The zigzagging pattern at the grain mantle surface
reflects the zigzagging structure of
-CO. The panels show clearly the gradient in CO, H2CO and CH3OH
across the grain with the top layers containing the more saturated
species. Furthermore, it shows that the lower temperature grains
contain more CH3OH. The grain mantle at 16.5 K is much
thinner due to the desorption of CO at this temperature. Finally, some
small pores can be observed in the mantles; these appear to form during
hydrogenation where two species recombine to one, which takes up less
space. It appears that at late times, when the flux is low, either CO
or CH3OH has some time to rearrange and fill most of these vacancies.
3.4 Methanol formation at 8 and 10 K
The results presented above all concern the formation of methanol in
the temperature regime between 12.0 and 16.5 K. These temperatures
are more representative for the outer regions of protostellar
envelopes. In cold dense cores, the temperature is most likely lower.
Figure 7
presents simulation results for 8 and 10 K. The model is extended
to temperatures outside the regime studied in the laboratory, by
assuming that the reaction rates (
in Table 1)
do not change with temperature, since they are dominated by tunnelling,
whereas all other processes are thermally activated. The results in
Fig. 7 clearly show that
formaldehyde and methanol are still efficiently formed at these
temperatures. Simulations with much lower reaction rates for H+CO and
H+H2CO, thermally activated using barriers of 390 and 415 K, respectively, still result in the formation of both H2CO and CH3OH, although with much lower abundances as indicated by the thin lines in Fig. 7.
The abundance of formaldehyde is much larger in this case, since it is
not efficiently converted into methanol. However, the rates at higher
temperature suggest tunneling to be important and the abundances are
therefore probably better represented by the thick curves.
![]() |
Figure 7:
CO, H2CO, and CH3OH build-up as a function of time for a density of
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4 Comparison with other models and observations
This section compares the results of our Monte Carlo simulations with different models and with observations of H2CO and CH3OH abundances. In particular, our results are compared with a similar model with similar input parameters using a standard rate equation technique (see, e.g., Ruffle & Herbst 2000) and with different models of various degrees of chemical and astrophysical complexity that are reported in the literature. Finally, the simulations are compared with a steady-state model proposed by Charnley et al. (1997) that we have adjusted to take the changing CO gas-phase abundance into account.
4.1 Comparison with rate equations
Figure 8 plots the results for a rate equation model (see, e.g., Ruffle & Herbst 2000)
with the same chemical and physical processes as used in our Monte
Carlo approach. Besides the difference in mathematical techniques, the
rate equation method uses single hopping and desorption rates rather
than rates that depend on the local structure. We expect the diffusion
to be dominated by hopping between sites of the same type which results
in a diffusion energy of
(see Eq. (4))
and the desorption dominated by strong binding sites (three horizontal
neighbours), since diffusion will allow the particles to move to these
sites where they remain attached. The competition between reactions
with activation energy barriers and hopping and desorption is treated
by dividing the rate coefficient for reaction by the total rate
including diffusion and desorption, as discussed in detail by Herbst & Millar (2008). The panels in Fig. 8 can be compared with those in Fig. 2, which are determined with the Monte Carlo approach.
![]() |
Figure 8: Similar to Fig. 2 but using rate equations instead of Monte Carlo simulations. |
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In comparison with the Monte Carlo results, two trends become immediately apparent in the rate equation results: (1) there is a clear drop in the CO and H2CO abundances at late times and (2) the difference in the initial CH3OH formation (<103 yr) increases with surface temperature. The drop in the surface abundance of CO and H2CO at late times is due to the mean field character of the rate equation technique. It treats all molecules of the same species in the same way, regardless of their position in the ice layers. CO ice that resides at the lower layers of the ice can in the standard implementation of the rate equation technique still react with impinging hydrogen atoms, whereas in reality this reaction will not proceed unless H atoms can penetrate into the porous ice. Figure 4 shows that indeed most of the CO and H2CO is buried deep into the ice. In the Monte Carlo simulations, the hydrogenation reactions will therefore be hampered by the deficiency of gas phase CO at late times whereas the rate equations continue hydrogenating the CO and H2CO that have been formed at early times. In general, the effect of a changing gas phase composition is limited to the top layers of the ice. For this reason, layering should be taken into account when modelling the grain surface chemistry. The three-phase model introduced by Hasegawa & Herbst (1993) is a first attempt to implement this effect into a rate equation model.
The second effect is probably due to the difference in the treatment of diffusion and desorption between the two methods. The agreement in the total ice thickness indeed becomes less if lower desorption barriers are used. Due to the implementation of the competition for reaction in the rate equation approach, the choice of the diffusion barrier has very little effect on the final results. This can be understood by realising that faster diffusion will lead to more encounters between diffusers and the more stationary reacting species but that the residence time in the vicinity of the stationary reactant is reduced. The site dependent rates in the Monte Carlo code result in longer residence times at some sites and shorter residence times at other sites, favouring reactions, especially at higher temperatures, as first discovered for the formation of H2 (Cuppen & Herbst 2005). In addition to the two effects, it can also been seen that with the rate equation approach, the ice cannot even develop to 1 monolayer at 16.5 K, presumably because the CO growth mechanism of forming islands is not accounted for.
4.2 Comparison with other surface models
A variety of different models concerning the formation of
formaldehyde and methanol via surface reactions from CO have been
reported in the literature. Figure 9 (top) shows fractional methanol and formaldehyde abundances with respect to
as functions of the product of time and density (
)
for a number of these models. This product is roughly proportional to
the total fluence, the number of reaction species that reaches the
grain surface, and can therefore serve as a measure to help compare
models with different densities.
The solid lines indicate the methanol and the dashed lines the
formaldehyde abundances obtained in the present paper (Figs. 1, 2, and 7).
Only the data at 8.0, 12.0 and 16.5 K are plotted since the 12.0
and 16.5 K data represent the extreme values and 8.0 K is
closed to cold core conditions. The
and 105 cm-3
data overlap nicely indicating that the formation rate of methanol and
that of formaldehyde are directly dependent on the fluence and that the
flux difference of one order of magnitude does not introduce additional
scaling effects.
![]() |
Figure 9:
Comparison of the present simulation data with values obtained by different models (see legend) as a function of time |
Open with DEXTER |
The symbols represent the fractional abundances of both species obtained from a selection of different studies. Open symbols represent H2CO whereas filled symbols represent CH3OH. Given the large differences in parameters, and assorted methods of calculation among the various studies, large variance in results can be expected. The diamonds show results by Ruffle & Herbst (2000), who used a large reaction network of both gas phase reactions and grain surface reactions. Both chemistries were treated using rate equations for four different scenarios defined by slow and fast diffusion rates combined with atomic and molecular initial conditions. The circles represent master equation results from Stantcheva et al. (2002). Here for a wide range of densities (103, 104, 105 cm-3) the gas-grain chemistry for a limited set of surface reactions is obtained. Five additional reactions with respect to the surface network of the present paper were included, leading to the formation of H2O, CO2 and O2. No gas phase chemistry was considered. The two triangles are obtained from Garrod et al. (2006), who followed both the gas and grain chemistry during the collapse and heat-up phase of hot cores using a rate equation approach. The points used here are in the early times of the collapse when the density is still close to the initial density. Again a full network was used, comparable to Ruffle & Herbst (2000), but with intermediate diffusion rates. In all three models (Garrod et al. 2006; Ruffle & Herbst 2000; Stantcheva et al. 2002) the barrier crossing of surface reactions with activation energy was treated simply by multiplying the meeting rates of reactive species by the probability of crossing the activation energy barrier. Unlike our rate equation approach (see above), surface reactions with barriers were not treated to be in competition with other processes like diffusion (Herbst & Millar 2008). This neglect magnifies the differences obtained between low and high diffusion rates. Furthermore, these three models do not capture the layered structure of the ice mantle but allow all species to react with each other, regardless of their position. This assumption can become a problem once multiple layers start to build up, as shown in the previous section.
The squares in Fig. 9 represent data from Chang et al. (2007) obtained by a similar Monte Carlo method to that used in the present paper (Chang et al. 2005),
which includes both the layering effect as well as the competition of
the reaction barriers. The surface chemistry is coupled to the gas
phase chemistry and the surface chemistry network is very similar to
one used by Stantcheva et al. (2002). The square symbols represent results for
cm-3 and a surface temperature of 10 and 15 K. The main difference between the method by Chang et al. (2007)
and the present simulations is that our Monte Carlo algorithm is
optimised to reproduce laboratory experiments and it includes important
features of the CO + H system that were revealed through this
optimisation.
In general, Fig. 9
shows a large spread which reflects the different levels of complexity
among the different methods. Most of the obtained abundances of H2CO and CH3OH lie between our 12.0 and 16.5 K results and follow roughly the same trend that H2CO dominates at early times and CH3OH at late times. It appears that the slow diffusion results underestimate the formation of both molecules and the CH3OH/H2CO
ratio, as compared to our model that is parameterized by experiments.
Our 8.0 K data lie on the high end of the results, probably for
two reasons. Our
is relatively high throughout the entire simulation, although it should be comparable to the intermediate abundance of Stantcheva et al. (2002), and our limited network might overproduce H2CO and CH3OH instead of forming H2O and CO2
for instance. Our simulations are however geared towards conditions
where most of the atomic oxygen is locked up in CO, and H and CO are
indeed the most important reactants on the surface.
The bottom panel of Fig. 9 shows the H2CO/CH3OH ratio for the low temperature models (<20 K) presented in the top panel. It is immediately evident from this plot that there is a spread in this quantity for the different models, even within the same paper. The difference in the H2CO/CH3OH ratio for our 8.0, 12.0 and 16.5 K is much smaller compared with the spread found in other models. This spread is due to different assumptions in the modelling method and differences in methodology. In a few instances, the spread is due to different physical conditions such as temperature (as in our data) and density. In general, the largest differences with our results come from models with a low diffusion rate that do not consider the competition between reaction and diffusion.
4.3 Comparison with analytical model
Charnley et al. (1997) derived an analytical steady-state rate equation approach to predict the CO/CH3OH and H2CO/CH3OH surface abundance ratios as functions of
,
the relative H-to-CO flux ratio, and
, the ratio of the probabilities for single CO and H2CO
molecules to react with an H atom; i.e., the ratio of the rate
coefficients. The exact derivation of these expressions is given in
Appendix A. Each value for
and
results in a unique combination of both abundance ratios. When Charnley et al. (1997) was published,
was unknown. Now, we can use Table 1
to obtain this quantity for different temperatures, so as to compare
this steady state rate equation approach with the more realistic Monte
Carlo simulations.
![]() |
Figure 10:
CO/CH3OH versus H2CO/CH3OH ice abundance. The top panel compares results as obtained by the Monte Carlo simulations (open symbols) and Eqs. (A.6)-(A.8) (solid lines). The filled circles represent a simulation at 12.0 K that includes an O-atom flux. The bottom panel
indicates the Monte Carlo results by solid lines. The triangles
indicate ratios from ice observations where the numbers refer to the
methanol content in the ice with respect to H2O (see text). The quantity
|
Open with DEXTER |
The top panel of Fig. 10 plots the n(CO)/n(CH3OH) abundance ratio versus the n(H2CO)/n(CH3OH)
abundance for the Monte Carlo simulations (open symbols except for
16.5 K) and for the steady-state model (lines). For each
temperature,
is indicated as obtained from Table 1.
The Monte Carlo curves follow the abundance ratios in time; i.e., they
start from a relatively high CO gas-phase abundance which is partially
converted into formaldehyde and methanol, so that the general direction
is right to left. Likewise, the general direction is from top to bottom
since formaldehyde is generally converted into methanol.
The steady-state model by Charnley et al. (1997) plots curves for varying
.
Since
increases gradually during the course of our simulations, both
approaches can be compared in a relative straightforward way although
the simulations have also other sources of time dependence.
The time it takes for the top layer of the grain mantle to reach steady
state is short as compared to the change in
.
Figure 10 (top) includes the steady-state model lines for values of
that correspond to the values in the simulations. We would like to emphasise that the lines by Charnley et al. (1997) represent
/
and
/
,
where
indicates the steady-state coverage of species X in the top layer,
whereas the abundances in the Monte Carlo simulations are for the
entire grain mantle. At first sight, very good agreement is obtained
between the simulation results and the analytical model, especially
considering the requirement for steady state in the latter, which is
not fulfilled in the Monte Carlo simulations. However, it must be
remembered that in the absence of a third dimension to the plot,
is a hidden parameter, and the agreement for
between the two methods for the same points on the figure is not good. Indeed, the same results in Fig. 10
are obtained for a 5-20 times lower H/CO flux in the steady-state
model as compared with the simulations. In the simulations, a
significant portion of the H atoms are ``lost'' to H2 formation and desorption. Both processes are not included in the model by Charnley et al. (1997).
The smaller symbols in the right top corner are the result of
simulations with a different starting H abundance, chosen such that the
flux of CO molecules is 10 times higher than the H atom flux,
e.g.,
is 0.1 at the start of the simulation. The absolute abundances of H and
CO have little influence on the obtained ratios. These independent
simulations continue nicely on the analytical curve. As Keane (2001) shows, the introduction of more competing hydrogenation reactions leads to different curves. Section 5 addresses this point in more detail.
One purpose behind a plot like Fig. 10 is to visualise whether H atoms are more likely to react with CO or H2CO. The laboratory results indicate that for low temperature (12.0 K) CO + H is dominant whereas H2CO hydrogenation becomes the preferred channel for higher temperatures (16.5 K). The plot shows that, even though the
agreement is not very good, the agreement for
is very nice.
The curves in Fig. 10 (top) are for one value of
and varying
,
which can be compared with the simulations at a single temperature. The
steady-state model and Monte Carlo simulation results for the same
value of
trace the same unique lines in the n(CO)/n(CH3OH) versus n(H2CO)/n(CH3OH) plot.
Since
decreases with temperature, plotting observational H2CO/CH3OH versus CO/CH3OH ratios could give a good temperature and evolutionary indication between sources.
The main conclusions that can be drawn from these comparisons are that the surface chemistry of the top layer can at each point in time be very well approximated by quasi-steady state conditions, since the time to reach a quasi-steady state is smaller than the change in flux, and that the majority of the hydrogen atoms do not react but leave the surface by desorption. This means that the conversion rate of CO and H2CO into more saturated species is overestimated by the model of Charnley et al. (1997). Table 3 lists the steady-state conversion fractions of CO into H2CO and CH3OH as a function of temperature and H/CO gas phase abundance ratio obtained from the Monte Carlo simulations. The calculated fractions include the effect of desorption of atomic hydrogen and the competition of the CO hydrogenation reactions with the formation of H2, which is not included in the analytical model.
These conversion fractions clearly show that CO is very efficiently converted into H2CO and CH3OH. Naturally, the exact numbers depend on many assumptions regarding for instance the values of E,
and the reaction barriers. The parameter E is central in determining the desorption temperature of the species and an increase in E
will therefore result in an appreciable H-atom abundance at higher
temperature increasing the hydrogenation regime with a few degrees. The
diffusion parameter
,
on the other hand, will have a stronger effect at low temperature.
Finally, a change in the reaction barriers will lead to a slightly
different H2CO/CH3OH ratio.
Table 3: Conversion fraction of CO into H2CO and CH3OH as a function of T and H/CO.
4.4 Comparison with observations
A comparison between the simulation results presented in this paper and
observations is most straightforward with IR ice data. As long as the
ice is not processed too severely, either by UV photons, which can
break down formaldehyde and methanol, or by heating, which can
sublimate CO, the IR data represents the most direct comparison with
our simulations (see Sect. 5
below). Ideal conditions are most likely found in cold dense cores or
the outer cold envelopes of YSO's. Since it is difficult to use
absolute column densities for the comparison, the same ratios are used
as in Fig. 10. CO is usually present on grains in different mixtures: pure CO, polar CO and CO mixed with CO2 (Pontoppidan et al. 2008). Laboratory spectra of CO mixed with either H2O or CH3OH show similar changes in the 4.7 m CO feature, broadening and redshifting (Bisschop 2007; Bottinelli et al. in prep; Bouwman et al. 2007). The polar CO component at 2139 cm-1, normally ascribed to CO in a water-rich ice, can therefore also be due to a methanol-rich mixture. A CO:CH3OH=1:1 mixture is already sufficient to shift the band to the observed range. Thus, to obtain the observed CO/CH3OH
ratio for comparison with our models, we use both the pure CO component
and the polar CO component to account for the maximum amount of CO
mixed with the formed CH3OH ice. The triangles in the bottom panel of Fig. 10 represent ratios obtained from ISO data for the YSO's AFGL 989, AFGL 2136, W33A, AFGL 7009S, and NGC 7538 IRS9 (Gibb et al. 2004) and VLT-ISAAC data for the Class 0 source Serpens SMM 4 (Pontoppidan et al. 2004). Arrows indicate upper limits. As with the earlier data, Spitzer spectra of sources near SMM4 by Boogert et al. (2008) resulted only in upper limits for H2CO. They found formaldehyde to contribute perhaps 10-35% of their C1 component, which cannot be assigned to a single species. Gibb et al. (2004) used a feature equivalent to the C1 component to obtain their reported H2CO abundances. Both the H2CO abundances by Gibb et al. (2004) and the H2CO part of the C1 components by Boogert et al. (2008) vary minimally with respect to water ice and are typically 6%. The range in H2CO/CH3OH
abundances is therefore mainly due to methanol.
The abundance ratios for the six sources nicely overlap with the
simulation data (solid lines). The good agreement with the CO/CH3OH ratio could however be deceiving if part of the CO ice has already desorbed.
Solid methanol abundances are found to vary substantially with respect to water ice, ranging from upper limits of a few percent to more than 30% (Boogert et al. 2008; Dartois et al. 1999; Pontoppidan et al. 2003). In Fig. 10, these percentages are indicated for the six sources compared here, spanning a range of more than an order of magnitude, assuming that, as discussed above, H2CO ice does not vary much in abundance. A reason for this large range could lie in the differing evolutionary stages of the sources. If most of the water ice is formed first before the catastrophic freeze-out of CO, from which methanol is formed, the methanol over water ratio will increase in time. The temporal evolution of the simulated abundance ratios proceeds from the top-right corner to the bottom-left corner of the figure, and the increase in methanol abundances for the six sources appears to follow this trend, suggesting that indeed the large spread in methanol observations can simply be due to a difference in evolutionary stage of the outer envelope. Unfortunately, solid H2CO has only been detected in a handful of sources and the same holds for clear upper limits for this molecule.
An alternative observational test could be to perform CO, H2CO, and CH3OH gas phase observations in very cold and dense cores, where all three species are frozen-out onto the grains. Since most molecules have similar non-thermal desorption rates (Öberg et al. 2009a,b), one would expect the trace amounts in the gas phase to be representative of the ice layer composition (Öberg et al. 2009c). The problem with this technique is that not all observed gas-phase CO may result from CO ice evaporation and that gas-phase reactions can contribute to H2CO as well. As shown in Fig. 12 of Fuchs et al. (2009), the current model can reproduce the observed H2CO/CH3OH ratios in high-mass hot cores where the majority of the observed gas-phase molecules are likely evaporated ice species.
By ignoring the formation of water ice, our model predicts that CH3OH
is mainly present on the grain mantles in the pure form or mixed with
CO, and that it is not in a water-rich phase. Unfortunately, the ice
composition has very little effect on the 9.75 m band profile of CH3OH,
which is usually used to determine its abundance, neither in peak shape
nor position. The feature only becomes red-shifted when water ice is
dominant, >90% (Bottinelli et al. in prep.; Skinner et al. 1992). Similarly, the 3.54
m CH3OH feature can be used to constrain the CH3OH ice environment (Dartois et al. 1999; Pontoppidan et al. 2003; Thi et al. 2006). All of these studies generally conclude that at least a fraction of the CH3OH ice is in a water-poor, CH3OH-rich environment but additional laboratory data on CH3OH mixtures with CO are needed to quantify this.
5 Impact of competing reactions
The Monte Carlo simulations reported in the previous sections all involve hydrogenation of pure CO ice. The reason for this is two fold. First, one aim of this study is to model CO freeze-out in the centre of cold cloud cores (Pontoppidan et al. 2008; Pontoppidan 2006) where most of the gas is in molecular form and H2 and CO are the dominant species. In these centres, most of the elemental oxygen is in the form of CO or frozen out into grains in form of H2O.
Table 4: Surface reactions in the H, O and CO system.
To study the effect of competing reactions, however, simulations that
include oxygen atoms have been performed as well. These simulations use
a reaction network that is similar to that reported by Chang et al. (2007), leading to the formation of O2, H2O, and CO2. In addition, H2CO and H3CO can be destroyed by reaction with OH, leading to the formation of water (see Table 4).
All new species are assumed to bind very strongly and have only minimal
diffusion. Eley-Rideal reactions are again allowed. The gas-phase
abundances of CO and O are both assumed to be
.
Figure 10
contains results for the simulation at 12.0 K using filled
circles. From this figure, two things are immediately clear: the time
dependence of the CO/CH3OH and H2CO/CH3OH
ratios is minimal in the simulation and the filled circles overlap
nicely with the analogous simulations that do not include the extra
reactions. Keane (2001) presents a similar
graph obtained with a full gas-grain network using macroscopic Monte
Carlo simulations. Their curves obtained for the full network are less
steep than for the analytical expressions that are based on a limited
network, since a considerable fraction of the hydrogen atoms reacts
with other grain species. This is in contrast with our simulations that
include H2O and CO2 as competing mechanisms. The origin of this discrepancy is unclear.
Another type of competing reaction would be the destruction of methanol
by photodissociation. The photofragments could then react to synthesise
more complex molecules. In dense cloud conditions, photodissociation
mainly occurs via cosmic ray induced photons, with a typical flux of
photons cm-2 s-1 (Cecchi-Pestellini & Aiello 1992). Using a photodissociation cross section of
cm2 (Öberg et al. 2009d; Gerakines et al. 1996), 5 % of the methanol molecules has been photodissociated in
years. Most of these molecules are dissociated to simpler species like CO, HCO, CH3, CH3O, and H2CO
and can be hydrogenated to methanol again. Gas-phase H atoms can
hydrogenate the radicals in top layers of the ice, whereas H atoms that
are produced through photodissociation can react with the fragments
deep in the ice. We therefore expect only a minor change in the grain
abundances due to photodissociation as long as the grains remain cold.
Higher temperatures allow the radicals to diffuse rapidly enough to
form large molecules such as methyl formate and dimethyl ether (Öberg et al. 2009d; Garrod et al. 2008).
6 Conclusions
The surface formation of CH3OH and H2CO from precursor CO has been simulated using the continuous-time, random-walk Monte Carlo method. The formation of both species was found to be very efficient under certain conditions and to depend mainly on grain temperature and the gas phase abundance ratio of H and CO. During the freeze-out of CO onto the grain, this ratio changes, favouring the more complete hydrogenation of CO to CH3OH. The more unsaturated species remain locked in the lower layers of the ice mantle. Due to the layering of the ice, changes in the gas phase abundance can only affect the top layers of the grain, which is important to take into account when modelling grain surface chemistry. The detailed Monte Carlo method used can be compared with a variety of other approaches. Of these, perhaps the most successful is a quasi-steady-state rate equation approach (Charnley et al. 1997) that focuses on the outermost layer of the grain only.
The model results can be compared with observations through plots of the CO/CH3OH and H2CO/CH3OH abundance ratios. A very good agreement is obtained for the outer envelopes of a number of YSO's, with temperatures in the range 12.0-16.5 K. Moreover, the comparison allows us to trace the temporal evolution between different sources. Our results suggest that the difference in CH3OH abundances with respect to water are mostly due to differences in temporal evolution where the younger sources have not yet had sufficient time to build up much methanol.
AcknowledgementsH. C. is supported by the Netherlands Organization for Scientific Research (NWO) and the Leiden Observatory. E. H. thanks the National Science Foundation (US) and NASA for support of his research programs in astrochemistry and astrobiology. We would like to thank Lars Kristensen, Karin Öberg, and Harold Linnartz for stimulating discussions.
Appendix A: CO hydrogenation in steady state conditions
This appendix presents a derivation of the steady state model proposed by Charnley et al. (1997).
When the flux of hydrogen atoms to the surface is lower than the flux
of CO molecules, the assumption can be made that every hydrogenation
atom either reacts with CO or with H2CO. The probabilities of reaction are denoted by
and
,
respectively. They are determined by the likelihood of barrier crossing once an H atom is in the vicinity of the CO or H2CO,
and
,
and the fractional coverage of these species over the outermost surface layer,
and
according to the equations
and
The change in CO coverage with time is then
Here the first term accounts for the increase by the incoming CO flux,


and
From Eqs. (A.4) and (A.5),

with
![]() |
(A.7) |
and furthermore
From Eqs. (A.3) and (A.4) and using Eqs. (A.1), (A.2), we obtain that
![]() |
(A.9) |
where
![]() |
(A.10) |
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All Tables
Table 1:
Reaction rate coefficients,
,
and activation energy barriers for CO + H and H2CO + H for different temperatures.
Table 2: The energy parameter E for the different species.
Table 3: Conversion fraction of CO into H2CO and CH3OH as a function of T and H/CO.
Table 4: Surface reactions in the H, O and CO system.
All Figures
![]() |
Figure 1:
CO, H2CO, and CH3OH build-up as a function of time for a density of
|
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Similar to Fig. 1 for
|
Open with DEXTER | |
In the text |
![]() |
Figure 3:
CO, H2CO, and CH3OH build-up as a function of time for
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Fractional abundance of the three main ice components as a function of monolayer after
|
Open with DEXTER | |
In the text |
![]() |
Figure 5: Schematic picture of the growth of the ice mantle during CO freeze-out. For coloured figures, see the online version. |
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Cross section of the ice mantle after
|
Open with DEXTER | |
In the text |
![]() |
Figure 7:
CO, H2CO, and CH3OH build-up as a function of time for a density of
|
Open with DEXTER | |
In the text |
![]() |
Figure 8: Similar to Fig. 2 but using rate equations instead of Monte Carlo simulations. |
Open with DEXTER | |
In the text |
![]() |
Figure 9:
Comparison of the present simulation data with values obtained by different models (see legend) as a function of time |
Open with DEXTER | |
In the text |
![]() |
Figure 10:
CO/CH3OH versus H2CO/CH3OH ice abundance. The top panel compares results as obtained by the Monte Carlo simulations (open symbols) and Eqs. (A.6)-(A.8) (solid lines). The filled circles represent a simulation at 12.0 K that includes an O-atom flux. The bottom panel
indicates the Monte Carlo results by solid lines. The triangles
indicate ratios from ice observations where the numbers refer to the
methanol content in the ice with respect to H2O (see text). The quantity
|
Open with DEXTER | |
In the text |
Copyright ESO 2009
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