Download Time-dependent evaporation of icy mantles in hot cores

Mon. Not. R. Astron. Soc. 305, 755±762 (1999)
Time-dependent evaporation of icy mantles in hot cores
Serena Viti* and David A. Williams
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT
Accepted 1999 January 5. Received 1998 December 22; in original form 1998 July 31
A B S T R AC T
Hot cores are rich in saturated molecules that are believed to arise from the evaporation of
molecular ices on dust grains. It is usually assumed that the ices are evaporated instantaneously
when a nearby star is switched on. We have developed a new model in which the grain
temperature rises over a time-scale determined by the switch-on time of the star. This time-scale
is likely to be comparable to the lifetime of the hot cores. In consequence, evaporation of
different species occurs at different epochs, leading to chemical differentiation in time and space
within the hot core. By computing qualitative models of hot cores, we show that observations
of hot cores may be able to constrain the rise time of hot stars to the main sequence.
Key words: stars: evolution ± stars: formation ± ISM: abundances ± ISM: clouds ± dust,
extinction ± ISM: molecules.
1
INTRODUCTION
Hot cores are small (,10 2 ±,10 1 pc), dense ($ 107 H2 cm 3 ),
relatively warm ($ 102 K), optically thick (Av $ 102 mag) and
transient (#105 yr) cores of gas found in the vicinity (#0:1 pc) of
newly formed massive stars. They have a rich chemistry that is
distinct from that found in quiescent, lower density (,103 ±
,105 cm 3 ) and cool (,10 K) molecular clouds which are the
sites of low-mass star formation. Hot cores may differ signi®cantly in
their chemical composition from one another. Since their discovery
some two decades ago they have been studied intensively, both
observationally and theoretically (see, e.g., reviews by Millar 1993
and Walmsley & Schilke 1993). The cores are believed to be the
remnants of the cloud that collapsed in the process of formation of the
massive star. Therefore they enable us to sample the pre-stellar
material; from these studies we may be able to infer conditions in
the natal cloud, prior to or during the collapse. These implications for
star formation have ensured an intense study of hot cores in recent
years (cf. Millar, Macdonald & Gibb 1997, hereafter MMG).
Hot cores are found to contain some molecular species with
abundances relative to H2 that are unusually high compared to the
values found in quiescent molecular clouds. These anomalies
include small saturated molecules such as NH3 and H2 O, and also
large organics such as methyl formate HCOOCH3 and dimethyl
ether (CH3 )2 O. The origin of these anomalies is believed to arise
from the evaporation stimulated by the nearby star of ice mantles
frozen-out on to the dust grains during the cloud collapse. Since the
freeze-out time-scale is short compared to the chemical time-scale,
material freezing-out includes reactive species that may undergo
further processing on the ice. For example, atomic N can be
converted to NH3 , and large organics may arise from a more drastic
processing of the molecular ice. Models of hot cores in which a
*E-mail: [email protected]
q 1999 RAS
collapse phase including chemistry and freeze-out is followed by a
static warm phase in which evaporation and gas-phase chemistry
occur have had considerable success in explaining their chemical
richness (see, e.g., Brown, Charnley & Millar 1988; Caselli,
Hasegawa & Herbst 1993; Charnley 1997; MMG; Cesaroni et al.
1998 and Hatchell et al. 1998). These studies may differ in the
emphasis given to the chemistry in pre- and post-stellar phases. For
example, Millar & Hatchell (1998) determine the composition of
the ice guided by observations of cosmic ice, rather than as a
consequence of freeze-out.
In all the studies so far, it has been assumed that the removal of the
ices and injection of that material into the gas phase occurs effectively
instantaneously. If the evaporation is driven by the stellar radiation
®eld, then the grain temperature must rise rapidly from around 10 K
(in the molecular cloud) to around 200 K (in the hot core). At the
higher temperature, evaporation of the ices is very rapid indeed.
This approximation has always been adopted since contraction
occurs so quickly for high-mass stars that hydrogen starts burning
while the new-born star is still well embedded in the parent cloud
which is probably still collapsing (Hanson 1998). By de®nition, the
star is a `zero-age' main-sequence (ZAMS) star when it reaches its
minimum radius, its maximum mass (for single-star evolution) and
its hottest effective temperature (Hanson 1998). However, the
contraction time (tc ), the time after which hydrogen starts burning
and the star reaches the ZAMS, is not well known for hot stars, and
certainly its dependence on the initial mass of the star has not yet
been de®ned. It may, however, be that tc is long enough that the
assumption of instantaneous temperature rise is inappropriate. If the
rise in the stellar intensity is too slow to be considered instantaneous, then this also applies to the grain temperature. If this is the
case, then different species will be evaporated at different times. If the
time-scale (tc ) over which this occurs is comparable to the lifetime of
the core (against, e.g., disruption by winds or shocks), then the
chemical composition of the hot core must also be time-dependent.
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S. Viti and D. A. Williams
There are several consequences that follow from the assumption
of instantaneous temperature rise.
(i) There is no connection between the contraction time and the
intensity of the radiation of the star. However, the intensity of the IR
radiation must increase with time before it stabilizes as the
contraction ®nishes.
(ii) It treats the core as a point source. Although cores are small in
size, the extinction towards the centre of the core is very high. The
radiation will certainly affect the edge of the core differently from
the centre of the core. Therefore a point-source treatment might not
be appropriate.
(iii) The actual distance of the core from the star becomes
irrelevant. Observationally it is very dif®cult to estimate where
the core is with respect to the star. `Observing' hot cores means
detecting particular key molecules such as NH3 and CO. If their
abundances change according to the intensity of the radiation, then
the distance of the core to the star becomes relevant.
(iv) Hot cores all have the same general characteristics regardless
of their ages. This may not be supported by the observations
(Cesaroni, Walmsley & Churchwell 1992; Cesaroni et al. 1998).
Conversely, there are potential advantages in dropping the
assumption of instantaneous temperature rise. If the evaporation
is time-dependent, species-dependent and temperature-dependent,
we may be able to constrain the age and the distance of the core±star
system. Each species will evaporate at different rates determined by
the grain temperature. This may lead to selective effects in the
chemistry. A complete chemical model of hot molecular cores
could therefore constrain the contraction times of hot stars.
In this exploratory paper we follow some of the consequences of
relaxing the condition of instantaneous temperature rise. Bernasconi & Maeder (1996, hereafter BM96) computed evolutionary
models for stars with masses up to 120 M( . They calculated the
epoch where a contracting protostar starts burning hydrogen by
using one of the numerous criteria accepted as a de®nition of a
ZAMS, the last minimum total radius (see Table 1). The contraction
time-scales they ®nd are large enough for important chemistry to
occur before the star starts burning hydrogen. Therefore, by relaxing the assumption of instantaneous temperature rise, we can
explore the signi®cant changes to the chemistry during the contraction and after the star reaches the main sequence.
In this paper we investigate what happens if we allow the grains
to reach temperatures of the order of 200 K at three different epochs
(corresponding to the BM96 contraction times). We ®nd that the
chemistry developed by the individual models differs so that the
assumption of instantaneous temperature rise is inappropriate. We
Table 1. Extract from table 2
in BM96. Contraction times,
tc (in units of 106 yr), for
stars
with
metallicity
Z ˆ 0:020.
Initial mass
M(
60
25
15
9
5
tc
106 yr
0.0282
0.0708
0.117
0.288
1.15
describe the model in Section 2 and the results in Section 3, and give
a discussion in Section 4.
2
THE MODEL
Our model follows the chemical evolution of a modi®ed free-fall
collapsing cloud (Rawlings et al. 1992) in the process of forming a
hot massive star. Once the cloud has collapsed, the chemical
evolution of a remnant core situated in the vicinity of the `newly
born' massive hot star is explored. The original molecular cloud is
assumed to have an initial and ®nal density of respectively 104
H2 cm 3 and 107 H2 cm 3 , and an initial and ®nal visual extinction
at the centre of the core of respectively 1.2 and 620 mag. The cosmic
ray ionization rate used is 1:2 ´ 10 17 s 1 . We note, however, that
the chemistry is likely to be sensitive to this parameter (Hatchell et
al. 1998). The core is represented by a uniform slab subdivided into
50 shells represented by 50 depth points of increasing visual
extinction from the edge of the core towards the centre. During
collapse, dust grains accrete gas-phase species. tfo , the freeze-out
time-scale for accretion of gas on to the surfaces of dust grains,
depends on the gas-to-dust ratio. For unit ef®ciency,
tfo ˆ 3 ´ 109 yr / n, where n is the number density of H nuclei
per cm3 . For details of the collapsing cloud models see Rawlings
et al. (1992) and Ruf¯e et al. (1997).
2.1
The chemistry
We have included 119 gas-phase species and 39 surface species
interacting in 1728 chemical reactions. All the molecules so far
detected in hot cores (see table 5 in Millar & Hatchell 1998) have
been included in the chemistry. Before the collapse starts, the gasphase environment is purely atomic, apart from hydrogen that is
assumed initially to be all H2 . The initial gas-phase elemental
abundances are given in Table 2. We have adopted similar initial
elemental abundances as in Taylor & Williams (1996) and Taylor,
Morata & Williams (1996), apart from our carbon and oxygen
initial abundances which have been chosen to approach the ®nal
depleted abundances of CO used as initial conditions by MMG
(note that very small changes in the initial elemental abundances of C and O can cause large differences in the ®nal
depleted abundances of H2 O and CO). We start our chemical
computation from a pure gas-phase chemistry, and allow freezeout to occur during the collapse phase. The mantle composition
is therefore determined self-consistently with the gas-phase
chemistry.
In the collapse phase we let the chemistry develop for , 1 Myr.
During this time all the species that can freeze-out on to grains will
have done so. At any time-step, the abundance Y of each species will
be determined by an equation representing formation, destruction
Table 2. Total initial gasphase elemental abundances
used in all the models.
H
He
O
C
N
S
Mg
1.0
0.14
7.0 ´ 10
1.0 ´ 10
6.9 ´ 10
1.3 ´ 10
1.0 ´ 10
5
4
5
5
7
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Evaporation of icy mantles in hot cores
757
Figure 1. Fractional abundances with respect to hydrogen as a function of visual extinction for selected species. Top left: model (a) at 9000 yr; top centre:
model (c) at 9000 yr; top right: model (c) at 20 000 yr. Bottom left: model (a) at 20 000 yr; bottom centre: model (c) at 20 000 yr; bottom right: model (c) at 50 000
yr. The top panels illustrate the behaviours for weakly bound species, while the lower panels refer to strongly bound species (note the different scales for each
panel).
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758
S. Viti and D. A. Williams
and freeze-out:
Y…X†t ˆ Y…X†t
1
‡ Y…X†form
t
Y…X†destr
t
Y…X†freeze
:
t
…1†
We do not explicitly include any surface chemistry, but we allow (i)
hydrogenation of species once depleted on to grains, and (ii)
conversion of a fraction of CO into methanol (CH3 OH). After 1
Myr we reset the time, `switch on' the star, either instantaneously or
over a period of time, tc . We then follow the chemical evolution of
the hot core from this initial state. The distance of the core from the
star is taken to be ro , 3´1016 cm. Once the star is born, the core
will be affected by the radiation of the star, and the depleted species
will start evaporating.
(b) Tdust ˆ 200 K after tc ˆ 2:8 ´ 104 yr, corresponding to a
60-M( star;
(c) Tdust ˆ 200 K after tc ˆ 7:0 ´ 104 yr, corresponding to
25-M( star, and
(d) Tdust ˆ 200 K after tc ˆ 1:1 ´ 105 yr, corresponding to
15-M( star.
Temperature dependence on space and time were found using
equation (3). In all the models the chemistry is followed for
1 Myr to investigate the destruction times of each species, although
such long times may be unrealistic: hot cores have lifetimes limited
by their energetic environments; stellar winds, heating and shocks
will erode the core in a time probably shorter than 1 Myr.
2.2 The evaporation treatment
Our model differs from earlier hot-core models in its treatment of
evaporation from the dust grains. In the earlier models, all the
species evaporate together and instantaneously. We investigate a
time-dependent evaporation model by adopting the rate for direct
thermal evaporation (e.g. Bergin, Langer & Goldsmith 1995):
Kev ˆ no ´ e
Eb =Tdust
:
…2†
According to equation (2), the evaporation rate, Kev , for each
species depends on its binding energy to the surface (Eb ), on the
temperature of the grains (Tdust ) and on the fundamental frequency
for vibrations perpendicular to the surface (no ). We adopt the
binding energies compiled by Aikawa et al. (1997), who combined
experimental binding energies (Sandford & Allamandola 1993),
where known, with computed binding energies from Hasegawa &
Herbst (1993). The fundamental frequencies are taken from
Hasegawa, Herbst & Leung (1992), and they are of the order of
1012 ±1013 s 1 . Equation (2) shows that Kev behaves almost like a
step function in temperature. For each species it is either close to
zero, or extremely high with a strong dependence on the dust
temperatures. If the grains are instantaneously heated up to
,200 K everywhere in the core as soon as the star is born, then
instantaneous evaporation would indeed occur. However, if there is
a temperature gradient in position and in time, then the chemical
evolution of each species may develop differently.
The temperature of the dust grains in the core is a function of
radiation, distance from the star, grain size and visual extinction.
Rowan-Robinson (1980) derived an expression for the temperature
distribution dependent on depth, which we have ®tted with an
exponential expression and have extended to include a linear
dependence on time:
Tdust …t; r† ˆ Tdust;0 ´ t=tc ´ …r=ro †
0:4
;
…3†
where Tdust …t; r† is the dust temperature, Tdust;0 represents the
maximum temperature of the dust grains; r represents the distance
between a depth point and the star, and ro is the distance of the edge
of the core from the star. We assume that at the densities found in hot
cores the gas temperature is equal to the dust temperature.
3
R E S U LT S
We have investigated the chemical evolution of a core of 0.01 pc in
diameter, of number density 107 H2 cm 3 , and at a distance of 0.01
pc from the star. We have taken the contraction times from BM96 as
the epochs at which the temperature of the edge of the core
reaches 200 K, and we have examined the gas-phase chemistry in
the hot-core phase for the following cases:
(a) Tdust ˆ 200 K instantaneously (as soon as the star is born);
3.1
Chemical abundances as a function of depth and time
Fig. 1 shows the chemical abundances of some selected species as a
function of depth at different epochs for two models: (a) and (c). We
group the species so that their binding energies are similar, and
therefore they evaporate at roughly the same time, for timedependent evaporation models. For model (a) we show each set
of species at only one time, since for this model the depth
dependence will be constant with time. Av increases from 3.35 to
620 mag from the edge to the centre. At both epochs and for both
models, at very low extinction, all the species, apart from CO
(which self-shield), are destroyed by photodissociation.
In general, for model (a), at both epochs, the dependence of the
species abundances with depth is constant. This is consistent with
an instantaneous rise of the temperature and with the idea that it
takes over 104 yr for the core to be altered chemically (Millar &
Hatchell 1998). Note, however, that even in model (a) there is a
change in abundance with depth. This re¯ects the frozen species at
the end of the collapse phase and not the chemical composition of
the gas after the star is born; most of the time during the slow
collapse (, 1 Myr), the density and therefore the visual extinction
throughout the core is very low (the initial Av is unity). Therefore
photodissociation is effective, leading to a differentiation in the
chemical evolution of all the species at each visual extinction. Since
freeze-out turns on very rapidly, the abundances in the ices (and the
initial abundances in the hot core) re¯ect these chemical variations.
We have tested this effect by reducing the radiation ®eld to
negligible amounts during the collapse phase, and we ®nd that
not only the ®nal frozen abundance of every species is constant with
depth, but also their amounts are changed drastically: for example,
if there is no photodissociation, all the available carbon and most of
the oxygen will be locked in CO which, at the end of the collapse,
would be three orders of magnitude larger than it is in the calculations presented in Fig. 1.
The top-centre, top-right, bottom-centre and bottom-right plots
in Fig. 1 show the depth dependence of selected species for model
(c) at different epochs. In the central plots, the species are still
evaporating, and the increasing visual extinction with depth leads to
a chemical differentiation for early times. In the right-hand plots,
the selected species have mostly evaporated, and the depth dependence is more similar to model (a). Note how in model (c)
abundances ratios change drastically with time, e.g. the NH3 /CO
or the H2 S/SO2 ratio. This is obviously due to the relaxation of an
instantaneous temperature rise: for example, NH3 has a higher
binding energy than CO, and in young cores it will not have
completely evaporated. This implies that, since both species are
observable, NH3 /CO could be used as a tool for differentiating old
and young hot cores and their position with respect to the hot star.
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Evaporation of icy mantles in hot cores
In general, the change in abundances with visual extinction is
much more pronounced in models where a time-dependent temperature rise is assumed. Some species seem to vary in abundance
by more than several orders of magnitude with Av . This suggests
that more detailed models, including spatial variations, will be
required to make comparisons with observations.
3.2 Chemical evolution at the centre of the core
Figs 2 to 5 show some examples of the results of our computations
of the fractional abundances (with respect to hydrogen) of some
species at the centre of the core (i.e., corresponding to Av ˆ 620
mag in Fig. 1) as a function of time. Note that the the time-axis scale
varies from plot to plot. In general, we ®nd that the four models (a,
b, c and d) differ signi®cantly for the ®rst 60 000 years. For models
(b), (c) and (d) Tdust needs to reach at least 80 K, for all the species to
have evaporated. The case (a) is the instantaneous temperature rise
case; the fractional abundances rise immediately to their hot-core
values and persist for at least 104 yr without signi®cant change for
most of the species. Cases (b)±(d) show a rise of the fractional
abundances from low values to the plateau hot-core values, the
transition period moving to later times from (b) to (d); however, in
any particular case, different species rise to the plateau at different
times. For example, in case (b) CO, CH4 and H2 O arrive at their
plateau values at 4, 5 and 160 thousand years, while in case (d) the
corresponding times are 17, 20 and 600 thousand years. The
differences between these times are comparable with the supposed
age of the hot core, and therefore they are chemically signi®cant.
For example, if ± say ± ablation of a hot core limits its existence to
759
10 thousand years, then in case (b) the core would be destroyed
before the H2 O abundance had risen to its plateau value. The
interesting feature of our results is the rise in abundances from
low values to the plateau values. In the next ®ve subsections we will
look at some species in more detail.
3.2.1 Ions
We ®nd that the species that differ most in their chemical evolution
between the instantaneous temperature rise case and the timedependent ones are the ions (see Figs 2 and 3). In fact, in model
(a) all the ions have low fractional abundances already after the ®rst
1000 years, probably due to very early reactions with carbonbearing species and mainly with water to form H3 O‡ , H2 O‡ and
CO. In the time-dependent models, ions will survive for a longer
time. In fact, H2 O has a very high binding energy, and therefore it
realistically will not evaporate until late stages, allowing ions such
‡
‡
as H‡
3 , H and HCO to survive longer and ignite a series of
reactions that do not occur in the model (a). The ions start
decreasing and reaching model (a) values when H2 O starts evaporating signi®cantly (cf. Figs 2 and 3).
3.2.2 Carbon- and oxygen-bearing species
Some selected carbon- and oxygen-bearing species are shown in
Fig. 2. In model (a) the relative fractional abundances among
carbon-bearing species are constant during much of the life of the
hot core and CH4 is always about one order of magnitude larger than
CO, while in models (b), (c) and (d), during the contraction time,
Figure 2. Fractional abundance of some carbon- and oxygen-bearing species as a function of time for (a) instantaneous evaporation model; (b) time-dependent
evaporation model with tc ˆ 28 000 yr; (c) time-dependent evaporation model with tc ˆ 70 000 yr; (d) time-dependent evaporation model with tc ˆ 110 000 yr.
The x-axis scale varies according to the model, so that the portion of the plot shown is where the species evaporate.
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S. Viti and D. A. Williams
Figure 3. Fractional abundance of some ions and some nitrogen-bearing species as a function of time for (a) instantaneous evaporation model; (b) timedependent evaporation model with tc ˆ 28 000 yr; (c) time-dependent evaporation model with tc ˆ 70 000 yr; (d) time-dependent evaporation model with
tc ˆ 110 000 yr.
CH4 and CO are of the same order. We ®nd a `depression' for O2
which occurs in all four cases, but at different epochs. This
`depression' is caused by reactions with sulphur liberated by H2 S
to form SO2 . If the instantaneous temperature rise assumption is
relaxed, the network destroying O2 and H2 S to form other sulphurbearing species could be used as an indicator of the age of the core
and of the rise time of the star.
In all the three time-dependent cases we ®nd `dips' followed
by `rises' in the fractional abundances of HCO (although the
abundances are probably undetectable). The sudden rises of some
species such as HCO are caused by reactions involving ions, created
by He‡ [which is assumed not to freeze-out, and may attain high
values in the pre-stellar phase (Hartquist & Williams 1989)].
Reactions of C‡ created in this way with H2 O released from the
grains may feed the HCO/HCO‡ network. The recovery of HCO
occurs at the H2 O evaporation time. In models (b), (c) and (d) the
abundance of HCO‡ becomes as low as in model (a) only after at
least 40 000 yr. This is consistent with the behaviour of other ions.
Although it is not a directly observable effect, note also that, due to
its slow release, the ratios of H2 O with other species vary
signi®cantly with time in models (b), (c) and (d).
3.2.3 Nitrogen-bearing species
The fractional abundances of some nitrogen-bearing species are
plotted in Fig. 3. Their temporal abundances seem to vary quite
signi®cantly according to the contraction time chosen. In model (a),
NH2 has a lower (but increasing) abundance with respect to NH3
until late times (, 250 000 yr) when their abundances are similar. In
models (b), (c) and (d) the abundances of the two species are very
similar while they are both evaporating; NH3 then increases faster
than NH2 and has a larger abundance for 170 000 yr (model d) to
235 000 yr (model b). NH2 and NH3 are also interesting because in
cases (b), (c) and (d), after having partly evaporated from grains,
they suffer a dip in their abundances and a sudden rise again to
levels slightly higher than in the instantaneous case. Again, this
behaviour is caused mainly by reactions with ions such as HCO‡
and CH‡
5 . The abundance of NH3 in model (a) or in models (b), (c)
and (d) after the evaporation is completed is reasonably consistent
with MMG models and observations (Cesaroni et al. 1992).
N2 has a lower binding energy with respect to NH2 and
NH3 and therefore in the time-dependent evaporation models it
will have a larger abundance with respect to the other two
nitrogen-bearing species for a period of time depending on the
contraction time. In model (a) N2 abundance is always lower than
NH3 .
3.2.4 Sulphur-bearing species
Fig. 4 shows the chemical evolution of some sulphur-bearing
species. In all the four models H2 S is slowly destroyed to form
other sulphur-bearing molecules. This is consistent with existing
models (Charnley 1997; Hatchell et al. 1998) However, we ®nd that
the destruction of H2 S occurs at much later times than in previous
models, although our results are reasonably consistent with those of
Hatchell et al. for the lowest cosmic ray ionization rate case. This is
again due to the different approach in estimating the initial
abundances prior to the birth of the star; in fact, in our models
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Evaporation of icy mantles in hot cores
761
Figure 4. Fractional abundance of some sulphur-bearing species as a function of time for (a) instantaneous evaporation model; (b) time-dependent evaporation
model with tc ˆ 28 000 yr; (c) time-dependent evaporation model with tc ˆ 70 000 yr; (d) time-dependent evaporation model with tc ˆ 110 000 yr.
H2 S is more than an order of magnitude larger when the star is born
than in the Hatchell et al. model.
In models (b), (c) and (d), during the evaporating phase most of
the sulphur-bearing species have similar abundances. These
models therefore predict that in young cores S, SO, SO2 , CS
and H2 CS are similarly abundant, and they differentiate only at a
late stage of the life of the core in accordance with the destruction
of H2 S. In models (b), (c) and (d) we ®nd a `dip' in the abundance
of S at different epochs according to the contraction time [for
example, for model (c) it occurs at 40 000 yr]. This is caused
mainly by reactions of atomic sulphur with CH3 whose abundance
is higher in models (b), (c) and (d) than in model (a) due to its
enhancement by CH‡
5 . In model (a) these reactions do not occur
because of the early destruction of CH‡
5 . Note also that in the
time-dependent evaporation models the abundance of H2 S is
closer to other sulphur-bearing species for longer times than in
model (a).
3.2.5 Large organic molecules
Large species such as CH3 OH, C2 H5 OH and HCOOCH3 have been
observed in hot cores with abundances enhanced by factors of
, 103 ±105 over those in cold clouds. We have included these
species in our models by assuming that the ®rst one is formed on
the grain from a fraction of CO, and the last two in gas-phase
chemistry during the collapse. We found them very sensitive to
changes in the evaporation treatment, since they evaporate
relatively late in the core evolution. This makes them potentially
good indicators of age, since they should not be present in
signi®cant amounts in very young cores.
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In model (a), H2 CO, CH3 OH and HCN are similarly abundant
(,10 8 ±5´10 7 ). In models (b), (c) and (d), CH3 OH, due to its
high binding energy and therefore slow evaporation, is much less
abundant than the other species for a period of time depending on
the contraction time. A species of particular interest is CH2 CO: in
case (a) its abundance is of the order of 10 17 , while in (b), (c) and
(d) it increases with time, reaching abundances of the order of
10 13 . One possible explanation for such a chemical difference can
be found by again invoking ions: CH2 CO is destroyed by reactions
with He‡ . As previously discussed, if an instantaneous temperature
rise is assumed, ions have a very short lifetime as they quickly react
with many species, including CH2 CO. In models (b), (c) and (d),
CH2 CO evaporates quite late, allowing the ions to be `used up' by
other species.
4
CONCLUSIONS
We have extended existing chemical models of hot cores by
introducing a more realistic treatment of the evaporation of
icy mantles formed in star-forming regions, allowing for a ®nite
(rather than zero) `switch on' time for the hot star. We have shown
that the changes in the chemical evolution of every species by
introducing time-dependent evaporation models are likely to be
important.
We have modelled the chemical evolution of a hot core near a hot
star and applied a temperature gradient for the dust grains, where the
maximum temperature of the dust was reached at some variable
contraction time constrained by recent evolutionary models of hot
massive stars. We found that the ®rst 60 000 years after the birth of the
star differ signi®cantly among models with different contraction times.
762
S. Viti and D. A. Williams
Figure 5. Fractional abundance of some large species as a function of time for (a) instantaneous evaporation model; (b) time-dependent evaporation model with
tc ˆ 28 000 yr; (c) time-dependent evaporation model with tc ˆ 70 000 yr; (d) time-dependent evaporation model with tc ˆ 110 000 yr.
Although 60 000 years is a very short time in astronomical terms, it
becomes relevant when dealing with potentially short-lived cores.
We identi®ed some key species where the selective effects are
strong. In particular, ions deeply affect the chemistry of other
species such as CO, HCO and CH2 CO in the time-dependent
evaporation models.
The selective effects caused by a time-dependent evaporation can
be used to address at least two issues: (i) the age of the core [the use
of the chemistry to estimate hot cores ages has been proposed and
investigated before (Helmich et al., 1994; Charnley 1997; Hatchell
et al. 1998)], and (ii) the rise time (contraction time) of hot massive
stars.
AC K N O W L E D G M E N T S
SV acknowledges the ®nancial support of PPARC. We thank Drs J.
M. C. Rawlings and D. P. Ruf¯e for useful discussions. We are also
grateful to the referee for helpful comments on an earlier version of
this paper.
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q 1999 RAS, MNRAS 305, 755±762