4 'L 

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Silicon Chemistry in Interstellar Clouds 

William D. Langer 

AT&T Bell Laboratories and New York University 

A. E. Glassgold 

New York University 

Received May 26, 1989 

M&&v*d3d 

.1 

(NASA-CR-TB5862) SILXCOI CHEMISTBY IN N 89- 2 E4 ii 

32 P 

IIITEBSTELLAR CLOUDS (Bell Telephone Labs. ), CSCL 038 

Ooclas 

G3/90 0225005 
Abstract 

Interstellar Si0 was discovered shortly after CO but it has been detected 

mainly in high density and high temperature regions associated with outflow 

sources. We present a new model of interstellar silicon chemistry that explains the lack of Si0 detections in cold clouds and contains an exponential 

temperature dependence for the Si0 abundance. A key aspect of the model 

is the sensitivity of Si0 production by neutral silicon reactions to density and 

temperature, which arises from the dependence of the rate coefficients on the 

population of the excited fine structure levels of the silicon atom. This effect 

was originally pointed out in the context of neutral reactions of carbon and 

oxygen by Graff, who noted that the leading term in neutral atom-molecule 

interactions involves the quadrupole moment of the atom. Similar to the 

case of carbon, the requirement that Si has a quadrupole moment requires 

population of the J = 1 level, which lies lllK above the J = 0 ground 

state and has a critical density n, 2 106cm-3. The Si0 abundance then 

,cas;a temperature dependence proportional to exp(- 111/ 2') and a quadratic 

density dependence for n < n, . As part of the explanation of the the lack of 

Si0 detections at low temperatures and densities, our model also emphasizes 

the small efficiencies of the production routes and the correspondingly long 

times needed to reach equilibrium. Measurements of the abundance of SiO, 

in conjunction with theory, can provide information on the physical properties of interstellar clouds such as the abundances of oxygen bearing molecules 

and the depletion of interstellar silicon. 

Subject headings interstellar: abundances - interstellar: molecules - molecular processes 
I. INTRODUCTION 

Interstellar Si0 was detected at mm wavelengths (Wilson et al. 1971) 

shortly after the discovery of CO (Wilson, Jefferts, and Penzias 1970). Since 

then, CO has been observed to be the most widely distributed molecule 

other than H2 in the interstellar medium. In contrast, Si0 has been detected 

mainly in regions with high density and temperature associated with outflows 

from young stellar objects. Although silicon is likely to be strongly depleted 

on dust grains in dense clouds and Si0 requires a higher density to excite 

than CO, the almost complete lack of detections in quiescent regions cannot 

be understood solely in these terms. In this paper, we explain the lack of 

extensive Si0 detections in terms of the sensitivity of its production by neutral silicon reactions to density and temperature, an effect directly associated 

with the excitation of the atomic fine structure levels (Graff 1989). 

Interstellar silicon chemistry was first discussed in detail by Turner and 

Dalgarno (1977); other early work was carried out by Solomon and Klemperer 

(1971), Prasad and Huntress (1980) and Millar (1980). Silicon chemistry in 

shocks has been studied by Hartquist, Oppenheimer, and Dalgarno (1980) 

and more recently by Neufeld and Dalgarno (1989). Circumstellar silicon 

chemistry has been investigated by Scalo and Slavsky (1980) and Clegg et 

al. (1983). Recent theoretical and experimental studies of silicon reactions 

and new astronomical observations now provide the stimulation to develop 

further the interstellar chemistry of silicon. 

From radio observations it is apparent that the interstellar chemistry of 

silicon differs from that of carbon, oxygen, nitrogen, and sulfur. The elemental abundance of Si is twice that of S and only an order of magnitude 

less than C, N, or 0. Yet these species occur in many molecules in widely 

distributed interstellar molecular clouds whereas gas phase silicon is detected 

only as Si0 and SiS (Morris et al. 1975, Irvine et al. 1986) and then only in 

hot dense regions perturbed by star formation. (These two molecules are also 

observed in the circumstellar envelopes of highly evolved red giants; Sic and 

Sic2 have recently been detected in IRC +lo216 (Thaddeus, Cummins, and 

Linke 1984; Cernicharo et al. 1989)). To address the issue of the dependence 

of Si0 on temperature, Ziurys, Friberg, and Irvine (1989) searched for its 

J = 2 - 1 emission from both cold as well as hot molecular gas. Despite 

the fact that the observations of the colder regions were made down to very 

1 
low noise levels, Si0 was detected only in sources with kinetic temperatures 

greater than 30K. Because the dipole moment of Si0 (3.1 Debye) is much 

larger than that of CO, the Si0 emission arises from dense regions, typically 

with n(H2) 2 lo4 - lo6 ~m-~. Moreover, in the sample considered by Ziurys, 

Friberg, and Irvine (1989), all but one of the Si0 detections were made in 

or near outflows from young stellar objects and in the supernova remnant 

IC 443. To determine the abundance variation with temperature, Ziurys, 

Friberg, and Irvine (1989) compared the Si0 column densities with those of 

HCN, another molecule requiring high density excitation and found primarily in dense regions but not manifesting any strong temperature sensitivity. 

Over the temperature range from roughly 15 K to 200 K, they found that the 

relative abundance of Si0 varies roughly as exp(-90/ 2'). 

The observations of Ziurys, Friberg, and Irvine (1989) have prompted us 

to find a theoretical basis for a temperature depedent Si0 abundance. No 

such temperature sensitivity is known in interstellar carbon chemistry and 

eazlier silicon chemical models do not contain any strong temperature effects 

at low temperatures. However, recent theoretical work by Graff (1989) shows 

how the neutral reaction rates of carbon and oxygen atoms, which depend 

on the population, ordering, and spacing of the atomic fine structure levels, 

could have a strong temperature dependence. In the case of carbon, with a J 

= 0, symmetric, ground state, strong interactions with other neutral systems 

require significant population of the excited states, the first of which lies at 

23.6K above the ground state. The resultant temperature variation of the 

carbon chemistry may not be very pronounced because of the small energy 

level spacing relative to the kinetic temperature of clouds and also because of 

the dominance of many other chemical pathways. Oxygen, with opposite fine 

structure, does not show this behavior. However, silicon has the same finestructure ordering as carbon but with larger separations: the first level is at 

111 K and the second at 321 K. In this paper we propose that Si0 in shielded 

regions is formed mainly by neutral reactions of Si atoms in the J = 1 level 

with OH and 02. By applying Graff's ideas, we find that the interstellar 

Si0 abundance contains an exponential temperature dependence. We also 

find that the Si0 abundance is sensitive to density because the fine structure 

levels of Si are likely to be be sub-thermally populated at densities less than 

lo4 - 105cm-3. Our results explain the absence of Si0 detections in cold, 

dark clouds by Ziurys et al. Whether or not the the predicted temperature is 

2 
the same as reported by these authors is less certain because the conditions 

for the applicability of our model may not be satisfied for the sources they 

discussed. 

11. SILICON CHEMISTRY 

Although much basic laboratory and theoretical information on astrophysically interesting silicon compounds is lacking, we are in a better position 

than earlier investigators to evaluate the various reaction pathways. Some 

of the key neutral reactions were actually measured more than a decade ago 

(Husain and Norris 1978, Swearengen, Davies, and Niemcyzk 1978). Important recent progress includes the measurement of silicon ion-molecule reaction rates (e.g. Bohme, Wlodek, and Fox 1988) and the development of 

techniques for the extrapolation of room temperature rates to lower temperatures (e.g., Clary 1988, Graff 1989). Advances have also been made in the 

thermal-chemical data base. For example, the data for silicon hydrides (Curtiss and Pople 1988 and references therein) imply that all reactions of H1 with 

both neutral and charged mono-silicon hydrides with up to four H atoms are 

endothermic. Hence the first-stage species in the ion-molecule chemistry of 

silicon, SiH+ and SiHi, will not be hydrogenated further and may in fact be 

destroyed by molecular hydrogen. Even if they are not destroyed in this way, 

they provide relatively weak pathways to heavier silicon-bearing molecules, in 

contrast with interstellar carbon chemistry where hydrides provide efficient 

routes for the synthesis of CO and other molecules. 

The most important feature of our chemical model is the population dependence of the reaction rates of atomic silicon with the neutral species, OH 

and 02. Graff (1989) has recently investigated neutral atom reactions at very 

low temperatures, which are dominated by the long-range interaction of the 

atomic quadrupole with the dipole or quadrupole moment of the reactant 

radical or molecule. The low temperature behavior of these reaction rate 

coefficients is sensitive to the population of the ground state fine structure 

levels, which determines the atomic quadrupole moment. Graff illustrates 

the effect by comparing reactions of 0 and C atoms with the radicals OH 

and CH. Because these atoms have opposite fine-structure orderings (Table 

l), their low-temperature reaction rate coefficients are very different: oxygen will interact strongly 

weakly below 20K. Graff 

with neutral radicals and molecules and carbon 

suggests that the same principles apply to neii3 
actions of other atoms important in the interstellar medium and we list some 

of the relevant physical parameters in Table 1. We omit nitrogen because 

its (2~)~ 'S1l2 ground state has no fine structure. Because its quadrupole 

moment also vanishes, we speculate that N reacts the weakest of all the 

abundant heavy atoms unless other dynamical effects govern its low temperat ure reactivity. 

We extend Graff's ideas to the silicon atom reactions with radicals and 

molecules that are important in interstellar clouds. The fine structure level 

ordering of silicon is similar to carbon, but the spacing is larger: El0 = 111 K 

and ,321 = 321K (Table 1). Thus we expect these reaction rates to be 

proportional to e-(-lll/ 2") at low temperature. Carbon atom reactions 

will be governed by a similar population factor but, because of the smaller 

level spacing, significant effects can only be expected for cold clouds with 

T < 15K. The silicon atom reactions also depend on density because the 

fine structure level population in interstellar clouds may not be in thermal 

equilibrium. For the temperatures of interest here, T < 200K, the effects 

of the J = 2 level can be ignored and statistical equilibrium theory gives 

the following result for the the total steady state fractional population of the 

first excited level of Si 

Pl = 3 (n/[n( 1 + 3 ezp( -T1o/T) + n,]) ezp( -T1o/T) (1) 

where n, = Alo/c10 is the critical density for the J = 1 - 0 transition, 

assumed to be optically thin, A10 is the spontaneous decay probability, and 

cl0 is the collisional de-excitation rate coefficient for the J = 1 - 0 transition. 

Recent calculations of the de-excitation rate coefficient of the corresponding 

collisions of He atoms and H2 molecules with 0 atoms (Monteiro and Flower 

1986, Flower 1989) indicate that c10 < cm3s-l for T < 100K and 

clo << C~~,C~O. In the absence of similar calculations for Si, we use the 

results for 0 as a guide. If the H2 + Si rate coefficient c10 = lo-" cm3s-l for 

T < 100K, the critical density for the J = 1 - 0 transition is 8 x lo6 ~m-~. 

The corresponding critical density for the J = 2 - 1 transition would be 

at least 10 times smaller and might give interesting physical effects at low 

densities and T > 100K. 

Table 2 lists the key reactions in our model of the silicon chemistry of 

interstellar clouds. We assume that the clouds are well shielded from external stellar and interstellar ultraviolet radiation. We list the adopted rate 

4 
coefficients and give references to laboratory measurements if they exist. 

Otherwise we follow standard practice and conventional wisdom in estimating rate coefficents. If the rate coefficient depends on temperature, we give 

the exponent n if it follows a power law (in 2'") or indicate by "exp" that 

the rate has the exponential temperature dependence exp(-111/ T) associated 

with silicon atom reactions. For brevity we omit all endothermic reactions. 

They are unimportant for the low temperature regions under consideration 

here but they are crucial for shock and other high temperature chemistry. In 

the following paragraphs, we discuss the background for the several classes 

of reactions listed in Table 2. For ion-molecule reactions with neutrals with 

large dipole moments, we use n = -0.6, following the discussion of Clary 

(1988). 

Neutral Reactions 

We consider three neutral reactions in the synthesis of silicon molecules 

from Si and the most abundant oxygen species other than CO (for which the 

relevant reactions are endothermic). Although the reaction of Si with H2O 

is exothermic, we expect it to have a large enough activation energy to make 

it unimportant at low temperatures. The primary neutral reactions for the 

synthesis of Si0 are reactions 1 and 2 of Table 2, 

Si+OH -+ SiO+H 

Si+O2 + SiO+O 

Only the rate coefficient for reaction 2 has been measured and here the two 

room temperature experiments give very different results. Swearengen et 

al. (1978) suggest that the larger value, obtained with a flash photolysis 

technique is incorrect because of heating or the production of other reactive 

species. In this paper we adopt the smaller rate coefficient. Theoretical 

considerations support this choice. Because 02 does not have a permanent 

electric dipole moment, the leading term in the Si- 02 interaction is of the 

quadrupole-quadrupole type, which leads to a reduction in the Langevin rate 

coefficient by an order of magnitude (Graff 1989). Both reactions 1 and 2 will 

be reduced at low temperatures by the effects discussed above and expressed 

by equation (1). 

Applying the results of Graff (1989) to Si, we write the rate coefficients 

5 
for these reactions as 1 

L k = - 3 ki(o0)p1 

where ~(oo) (i = 1,2) is the value at high temperatures (relative 

fine-structure splitting). We have taken the fraction of the J = 1 

(2) 

to the 

states 

that contributes to the reaction to be 1/3 and we have ignored any residual 

interactions associated with the J = 1 - 0 state, again following Graff. Even 

with the smaller rate coefficient, reaction 2 is probably the dominant Si0 

production process because of the large abundance expected for 02 relative 

to OH. There is only one fairly weak route to Si02 (reaction 3, Si0 + OH) 

because the reaction of Si0 and 02 is endothermic. 

Cosmic Ray Induced Photodestruction 

Although neutral reactions occupy the central role in our chemical model, 

cosmic rays are also important. In addition to directly ionizing hydrogen and 

helium, they generate UV radiation by inelastic electron scattering from H2 

which photoionizes Si and dissociates silicon molecules (Prasad and Tarafdar 1983; Sternberg, Dalgarno, and Lepp 1987; Gredel, Lepp, and Dalgarno 

1987). The last group of authors finds that a cosmic ray ionization rate C 

(defined for H2) leads to destruction rates for interstellar molecules that are 

of order lo2 - lo3<, depending on the photodestruction cross section. We 

have made estimates for silicon species using the UV emission spectrum given 

by Gredel et al., which spans the range from 900- 1650 A. We have estimated 

the rate for Si, with ionization threshold at 1520 A, by scaling the result of 

Gredel et al. for C, using the Si photoionization cross section (Hudson, 1971) 

and taking the grain albedo as 0.5. The result, G,,, = 3 x s-l is 3 times 

larger than for C because the Si photoionization cross section matches better 

the strong UV emission by H2 near 1500 and 1250 A. If the albedo is taken 

to be 0.9, the rate would be 5 times larger. Our estimates for Si0 and Si02 

are much less certain because we know little more than the photodissociation 

thresholds of these species, 1510 and 2650 A, respectively. 

Ion- Molecule Reactions 

Pathways to Si0 formation can be initiated by radiative association of 

Si+ with Ha (reaction 8) and by the two exothermic reactions of Si+ with 

OH and HzO, (reactions 9 and 10 in Table 2). It is noteworthy that all 

of the measured ion-molecule reaction rates listed in Table 2 are an order 

6 
of magnitude less than the Langevin rate. Despite this fact, we ignore any 

possible activation energies as is customary in dealing with the low temperature behavior of ion-molecule reaction rates. Only an upper limit is reported 

for reaction 9 and it can be ignored. The thermal-chemical data needed to 

determine whether the reaction SiOi + H2 + Si02H+ + H (reaction 12) is 

exothermic is missing at this time. The corresponding reactions for COi and 

SO: do occur (Anicich and Huntress 1986). However, this point is not very 

important here because the production of SiOi is probably weak. 

The most important ions for destroying Si0 and Si02 are C+ and He+. 

We have introduced characteristic branching ratios for the various channels 

that arise when He+ destroys Si0 and Si02. Many reactions of He+ with 

other neutral molecules have been measured (Anicich and Huntress 1986) 

and serve as the basis for the following estimates. Because charge exchange 

is generally found to be weak (and frequently does not occur with oxides), 

we argue that these branchings are small (B3 and b4 < 0.1). Measurements 

for CO and NO, suggest that, for SiO, Si+ rather than O+ is favored (I32 N 1 

and I31 < 0.1). Similarly, data for C02 and SO2 suggest that the dominant 

branch for Si02 is SiO+ but that Si+ and O+ may be produced 20 % of the 

time. For numerical estimates, we adopt bl = 0.8, b2 = 0.1, b3 = 0.05, and 

b4 = 0.05 and B1 = 0.8, B2 = 0.2, and B3 = 0.1. 

Charge Exchange and Neutralization 

Charge exchange with neutral atoms is potentially an important destruction mechanism for Si+ but there is considerable uncertainty in the rate 

coefficients at the temperatures of interstellar clouds (e.g., see the review by 

Dalgarno 1988). We have followed the guidelines and estimates of PCquignot 

and Aldrovandi (1986) in assuming that Si+ charge exchanges rapidly with 

the following heavy atoms: Mg, Fe, Al, Ca, and Ni. Of course all of these 

elements are likely to be strongly depleted in grains, thereby reducing the 

effect. However, Si+ can be efficiently neutralized by the population of negatively charged solid particles and large molecules such as polycyclic aromatic 

hydrocarbons expected to exist in shielded interstellar clouds (e.g., see the 

review by Omont 1986). Without commiting ourselves to the exact identity 

of this component of the interstellar medium, we have included their neutralization of Si+ as reaction 28 in Table 2, denoting them by the symbol 

PM-. The relatively small abundance of such “particles” is offset by the 

7 
large cross section for neutralization, and this process is likely to dominate 

charge exchange with neutral atoms. 

111. CHEMICAL MODEL 

The production pathways for the chemistry discussed in $11 are represented schematically in Figure 1. The dominant pathways for the synthesis 

of Si0 and Si02 involve the reactions of Si with OH and 02 and Si+ with 

H2O. In this section, we derive approximate, analytic formulae which exhibit 

the dependence of the various silicon species abundances on temperature, 

density, and cosmic ray ionization rate. 

As mentioned in $11, the production of silicon hydrides is extremely inefficient. The SiH+ produced by proton transfer from H$ to Si does not 

react with H2 and most of it recombines to Si again. The only other significant route to SiH, radiative association (reaction 8) followed by dissociative 

recombination of SiHi, is also weak, as we will show below. Therefore we 

initially neglect the silicon hydrides and their ions because they are relatively 

unimportant as progenitors of Si0 and Si02, except at verylow temperatures. 

The SiO+ ion has negligible abundance because it reacts rapidly with H2 

(reaction 11) to form SiOH+. It is unlikely that SiOH+ interacts further with 

H2; instead it recombines to form SiO. Thus the interaction of Si+ with OH 

leads to the following ionic pathways to SiO: 

Si++OH -+ SiO++H 

SiO++H2 -, SiOH++H 

SiOH++e + SiO+H 

The corresponding neutral pathways are initiated by reactions 1 and 2. 

In the approximation of ignoring the silicon hydrides, we solve for the 

steady state silicon abundances using the three balance equations for Si+, 

SiO, and Si02 and the conservation condition for all gas phase silicon. The 

steady state equations for the fractional abundances of species X, z(X) = 

n(X)/n(H2), formed from species Y and 2 are written in the form 

Dz(X) = Pz(Y)z(Z) 

where D and P are appropriate destruction and production factors. The 

8 
balance equations are given below and the P’s and D’s are listed in Table 3: 

Dlz(Si+) = P4z(Si) + PEz(Si0) + Paz(Si02) 

DZz(Si0) = Plz(Si) + &(Si+) + P3z(Si02) 

(3) 

(4) 

Dsz(Si02) = &Z(Sio) (5) 

z(SiO2)/z(SiO) = P7/D3 (6) 

(7) 

(8) 

Solving these equations yields the following ratios among the silicon species: 

z(SiO)/z(Si) = [PI + P2P4/Dl]/A 

A = [D2 - P2Ps/D1] - [p7/D3][P3 + P2P6/D1] 

where 

IV. RESULTS 

We use the formulae derived in $111 to estimate the abundances of the 

silicon species as a function of the relevant astrophysical parameters. The 

essential nature of the temperature and density dependence can be most 

clearly understood by first assuming that Si02 and SiH can be neglected, 

which we later show to be a good approximation. The factor A in the 

denominator of equation (8) then reduces to A = D2 - P2PS/D1 and the 

second term can be neglected as long as z(H2O) < Consequently the 

SiO/Si abundance ratio can be written in a form where the contributions to 

molecule formation by neutral reactions with Si and ion reactions with Si+ 

occur additively: 

z(SiO)/z(Si) = Rfezp(-111/T) + Z (9) 

where 

R = P1(m)/D2 

(11) 

(12) 

1 

2 Z = P~P~/D~Dz - P2/D1 

f = n/[n(l+ 3ezp(-111/T)) + n,]. 

The factors R,Z, and f depend only weakly on temperature. The symbol 

Pl(m) is the production factor PI in Table 3 evaluated at 300 K. Taking into 

account the conservation condition for silicon yields 

z(SiO)/zs; = [Rfezp(-111/T) + Z]/[1+ Rfezp(-111/T) + Z] (13) 

9 
where zsi is the total abundance of all gas phase silicon species. This equation 

has an exponential temperature dependence for Tl < T < T2 if Rf is not 

very large and Z << 1. We can estimate TI and T2 by ignoring the term 

3ezp(-lll/T) in equation 12 and obtain 

T1 = lll/[Zn(Rf/Z)] (14) 

T2 = lll/[ln(Rf/(l+ Z))] (15) 

if Rf/(l + 2) > 1; otherwise 2'2 = 00. Substituting typical values of the parameters into R, f , and 2, expressing them in convenient units, and assuming 

that cl0 = 10-11cm3s-1, these quantities become 

R - 16ns [z(O2)-6 + O.lz(OH)-8]/C-17 

f N ns/(ns + 8.2) 

(16) 

(17) 

(18) 

Z - O.OO~~Z(H~O)-~/[Z(PM-)-~ T-O.' + 0.25 z(A)-~ + 0.005 z(HaO)-s] 

where we have introduced the notation, ns = n/lOs ~m-~, etc. 

According to equation 13 and the approximate forms for R, 2, and f, the 

abundance of Si0 is sensitive to the abundances of OH, 02 and H2O. At this 

time there is little observational information concerning the abundances of 

02, and H20 because of the extreme difficulty in observing the emission of 

these molecules from the ground. Indeed, the apportioning of oxygen among 

the various oxygen-bearing species in molecular clouds is widely considered to 

be one of the outstanding problems in interstellar chemistry. Radio' observations of OH (e.g., Crutcher 1979, Irvine et al. al. 1986) indicate a range from 

- lo-' for the OH abundance in clouds with densities n(H2) 5 lo4 ~m-~. 

Theory suggests that the OH abundance decreases with density (Langer and 

Graedel 1989) and we adopt an intermediate value for estimation purposes, 

%(OH) = 3 x lo-'. Emission from molecular oxygen has not yet been detected and the smallest upper limit, 402) < 5 x has been obtained 

with the isotopic variant, l60l8O, for the pOph cloud (Liszt and Vanden 

Bout 1985, Goldsmith et uZ. 1985). Here we adopt a slightly smaller value 

402) = 3 x representative of the results of chemical models. Radio observations of H2O (and its isotopic variants) involve transitions from highly 

excited states in hot, dense regions (n(H2) 2 lo4 ~m-~, T 2 lo2 K) and suggest that z(H2O) - A possible detection of infrared absorption from 

10 
the ground state of H2O leads to z(H20) 5 3 x - 2 x lo-' for the 

material along the line of sight towards Orion-BN (Knacke, Larson, and Noll 

1989). Because H2O can be expected to freeze out on grains at relatively high 

temperatures - 100K, we expect the H20 abundance to vary from region 

to region and, for estimation purposes, assume that it is in the range from 

The quantities Rf and 2 are the relative fractions of Si0 formed by 

neutral and ionic reaction pathways, respectively. One or the other must 

approach unity in order for a substantial fraction of silicon to be converted 

into molecules in steady state. It is important to note that Rf and 2 have 

different dependences on density: Rf - n2 for n < n, and 2 independent 

of n. In order to have efficient production of Si0 at high temperatures by 

neutral reactions, the density must be 2 5 x lo4 cm-3 for the choices made 

above for the abundances of oxygen-bearing molecules. The quantity 2 is a 

sensitive function of the H20 abundance and of the abundances of the species 

that neutralize Si+. Even for z(H20) as large as 2 is only - 0.01 for 

T = 100K. Because 2 is generally small, Si0 is produced efficiently by 

neutral reactions in warm, dense clouds, but the role of neutral reactions is 

significantly reduced in cool clouds by the Boltzmann factor, exp( -111/T). 

More specifically, equation (14) gives the condition that the temperature 

must satisfy in order for neutral reactions to dominate ionic reactions, i.e., 

T > TI, where TI is determined approximately from equation 14 using the 

quantity 

10-8 - 10-5. 

For example, if z(H2O) - z(02), then !Z"1 - 25K. Because H2O is expected 

to freeze out on grains at low temperatures, it is reasonable to expect that 

neutral reactions will continue to dominate production down to very low 

temperatures. Thus, if z(H2O) N O.lz(OZ), 2'1 is reduced to 15K. 

In Figure 2 we plot the solution to equation 13 for the ratio z(SiO)/zsi 

as a function of temperature (plotted as 1/T) for several values of Rf and 

2. As expected from the above discussion, the fractional Si0 abundance 

decreases approximately as exp(-lll/T) if Rf is not too large and 2 is 

small. In the case where Rf is large, the exponential decrease does not occur 

until low temperatures, e.g., it starts at T = 50K for Rf = 10. For 2 # 0, 

11 
the exponential decrease disappears at low temperatures and the solution 

goes over to a constant. In the case Rf = 1 and 2 = this changeover 

occurs below 20 K. However, we show below that time dependent effects 

become important at low temperatures and this leveling out probably does 

not occur. 

Although the contribution of SiH to Si0 production is usually small, it 

can become important at low temperatures because SiH can interact strongly 

with ground state oxygen atoms. The primary path for SiH formation is 

radiative association of Si+ with H2 (reaction 8) followed by recombination 

with electrons (reaction 24). It is destroyed primarily by 0 (reaction 4) as 

long as z(0) > Under these conditions the SiH abundance is given 

approximately by the following expression, 

z(SiH) - 5 x 10-3z(Si+)/z(0)-4. 

Because they are both proportional to the abundance of Si+, we can easily 

compare the efficiency of Si0 production by SiH with that of the ionic pathway involving Si+ and H2O (reaction 10). Production by SiH needs to be 

considered only if z(H2O) < 2 x lo-'. 

It is important to examine the time required to synthesize the silicon 

molecules. It is apparent from the above solutions that efficient conversion 

of silicon atoms into molecules only takes place at high densities. Thus little 

Si0 should be produced in the early, low density stages of cloud evolution 

when n < 104cm-3. This conclusion can be brought into clearer focus by 

considering the time for neutral reactions to produce SiO, which can be 

approximated by 

and can be written in convenient units as 

For T > 100K, the time required to achieve equilibrium is fairly long 

at low and intermediate densities, e.g., approximately 3 x lo7 yr for n = 

lo4 cm-3 and 402) = 3 x and z(0H) = 3 x lo-' and 3 x lo5 yr if 

12 
the density is increased to n = lo6 ~m-~. Densities greater than lo6 cm-3 

are required before the neutral reactions can produce Si0 in a time short 

compared to cloud evolutionary times but, even in this case, the clouds must 

be warm. The exponential increase of the chemical timescale suggests that, 

at low temperatures, where ions dominate its production, the abundance 

of Si0 will be very small. Consequently, we believe that it is unlikely that 

much Si0 is produced at low temperatures because, not only are the chemical 

pathways inefficient, but the time to produce near-equilibrium abundances 

is much longer than the lifetimes of the dense, cold regions of interstellar 

clouds. 

The effects of non-equilibrium chemistry are illustrated in Figure 3 where 

we show approximate time dependent solutions for z(SiO)/zs; as a function 

of temperature (plotted as 1/T) for Rf = 1 and for n = 5 x 104cme3, 

402) = 3 x We give solutions at times 

ranging from lo6 to los yr as well as the steady state solution for 2 = 0. 

For t < lo7 yr, the abundances are considerably depressed below the steady 

state solution at low temperatures (T < 25K). For the case 2 = 

(ionic chemistry included), we also present results at lo7 years and in steady 

state. Even though this steady state solution departs from an exponential 

(and becomes constant) below 20 - 25 K, the time dependent solution remains 

nearly exponential down to about 15K, although with a steeper slope than 

the function ezp(-lll/T). In the limit of T + 0, the ionic chemistry time 

scale becomes tehm = 3 x lo8 yr, independent of density, and probably 

longer than any relevant dynamical time scale. Figure 4 present additional 

illustrations of the theory for higher density regions without ionic reactions 

(2 = 0). For n = 106cm-3 (Fig. 4b), large Si0 abundances are achieved 

for temperatures down to 15K within - lo6 years. For times less than lo6 

years, the abundance has an exponential dependence on temperature. 

Finally, we can estimate the Si02 abundance in warm interstellar clouds 

of the type considered in our theory. From the equations in I11 we can write 

in convenient units 

and z(0H) = 3 x 

Significant amounts of Si02 can be produced in warm regions where Si0 

is abundant. Using the OH abundance adopted above, z(0H) - 3 x 

13 
we obtain SiO2/SiO ratios of order 0.5ns. Although Si02 is not directly 

observable by radio techniques, it might be possible to detect its protonated 

ion, HSiO;, which should have a large dipole moment. We estimate that 

HSiOt/SiO2 - 

V. SUMMARY 

We have developed a model of the gas phase silicon chemistry for shielded, 

quiescent interstellar clouds in which the Si0 abundance has a strong temperature dependence of the type suggested by Ziurys et al. In this theory, neutral 

reactions of Si with 02 and, perhaps, OH are mainly responsible for producing SiO. These reactions occur only for Si in excited fine structure levels and 

require relatively warm conditions, e.g., T 2 30K. Fairly high densities are 

also necessary to significantly populate the first excited fine structure level 

of Si, (n(H2) 2 lo6 ~m-~), in order to overcome its rapid spontaneous decay. 

Ion-molecule reactions are relatively unimportant in shielded regions in producing Si0 and, when they occur, proceed with such low efficiency that very 

long times are needed to achieve observationally significant values. According to our theory, the production rate of Si0 at low temperatures and low 

densities is so small that steady state abundances are unlikely to be achieved 

within cloud evolutionary times. 

In our model, the fraction of gas phase silicon in Si0 is sensitive to the 

density, the 02 and OH abundances, the total gas phase abundance of silicon, 

and the critical density for populating the J = 1 level of Si (see equations 13 

and 16-18). Consequently, in conjuction with observational determinations of 

the Si0 abundance, it should be possible to use our theory to determine, or at 

least constrain, presently poorly known physical parameters of appropriate 

interstellar clouds such as the depletion of silicon and the abundances of 

02 and H2O. For example, measurements of the Si0 abundance in warm, 

shielded regions could be used to determine the silicon depletion. In the high 

T limit 

Rf 

Rf+1 z(Si0) = zs; 

and, because Rf must be at least of order unity to produce Si0 efficiently, 

the Si0 abundance itself measures (to within a factor of a few) the gas phase 

abundance of silicon. Unfortunately, it is not yet possible to make a quantitative estimate along these lines because the observations discussed by Ziurys 

14 
et al. for warm regions refer to outflow sources or their environs. The abundance of Si0 in these sources is likely to have a significant contribution from 

the reaction of Si+ with H2O (equation lo). In this situation, an estimate 

of the Si0 abundance can be made in the context of a photodissociation 

region model (Tielens and Hollenbach et al., 1985) by assuming that Si0 is 

produced by reaction 10 and destroyed by UV radiation at a rate G(Si0): 

z(Si0) = Iclonz(Si+)z(H20)/G(SiO) 

The Si0 abundance now depends on the depletion factor for silicon, the 

strength of the radiation field, the density, the H2O abundance, and the 

photodestruction cross section of SiO. Entering reasonable values for these 

quantities leads to abundances of the same order given by Ziurys et al. for 

warm, outflow sources, although with considerable uncertainty because of 

the dependence on so many unknown parameters. 

Obtaining constraints for cold, dark clouds is more difficult because the 

chemistry is almost certainly time-dependent. The steady state expression 

for the Si0 abundance (equation 13) reduces to 

z(Si0) N Zzsi 

in the low temperature limit where ions contribute. Referring to equation 

18 for 2, we see the potential for obtaining a limit on the H20 abundance 

in cold, dark clouds using the upper limits to the Si0 abundance estimated 

by Ziurys et al. A low water abundance for cold, dark clouds is consistent 

with the expectation that H20 readily freezes out onto grains during the 

course of cloud evolution at low temperatures. However, the nondetection of 

Si0 in these clouds could also arise from severe depletion of silicon species 

onto grains or the long chemical time scale for the formation of Si0 or a 

combination of all these effects. 

In summary, our theory explains the failure of Ziurys et al. to detect 

Si0 in dark clouds in terms of the suppression of both the neutral and ionic 

chemistries, the former because of the low temperature and density and the 

latter by the freezing out of H20. The direct confirmation of the exponential 

temperature dependence associated with the excitation of the fine structure 

levels requires further observational studies of warm, shielded clouds. Despite 

the sensitivity of the theory to many presently unknown reaction rate coefficients and to the physical parameters and chemical abundances of interstellar 

15 
clouds, it does demonstrate the importance of neutral reactions for interstellar silicon chemistry. Our work also illustrates the significance of Graff’s ideas 

on the low temperature behavior of the rate coefficients for the reaction of 

atoms with molecules and radicals. In focusing in this paper on the most 

abundant silicon molecule, SiO, we have ignored several interesting problems 

in interstellar chemistry such as the synthesis of SiS and the abundance of 

the silicon carbides. We have also not attempted to treat the coupling between the silicon in the gas and solid phases other than to recognize that 

most of the silicon is incorporated in dust in dense clouds with depletion 

factor varying from cloud to cloud. These simplifications are justified by the 

current, preliminary nature of both the theoretical and observational aspects 

of interstellar silicon chemistry. 

Our theory suggest several directions for future research. In order to 

strengthen the basis of the theory, it would be extremely valuable to remeasure the fundamental neutral reaction, Si + 02 Si0 + 0, as a function of 

temperature at and below 300 K. Calculations of the collisional de-excitation 

rate of the Si fine structure levels by H2 would help quantify the density 

dependence of the chemistry. Measurements of the 02 and H2O abundances 

would permit interesting tests of the theory based on the close correlation 

between Si0 and the 02 and H2O abundances. More sensitive ground based 

observations of different types of interstellar clouds are required to establish 

the density and temperature dependence of the Si0 abundance. One of the 

goals of such observations should be to confirm the prediction of this paper 

that the Si0 abundance in dense, shielded clouds varies with temperature 

and density, primarily through the population of the excited fine structure 

levels. 

One of us (A.E.G) would like to acknowledge partial support of this research by a grant from NASA. The authors are grateful for helpful commments from Dennis Downes, Paul Goldsmith, Michel Guklin, Chris McKee, 

and Frank Shu. 

16 
1 

Table 1 

Fine Structure Energy Levels and Transition Probabilities 

Atom Eo/k El/k E2/k A10 A12 A21 A01 

~~ 

C 0 23.6 62.6 7.93 x 2.68 x 10-7 

0 325.9 228.1 0 8.95 x 10-5 1.70 x 10-5 

Si 0 111.0 321.1 8.25 x 4.20 x 10-5 

S 825.4 571.0 0 1.40 x 10-3 3.02 x 10-4 

a The units are K for energies and s-l for transition probabilities. 

17 
Table 2 

Silicon Chemical Reactions 

React ion Rate Constant a T-Dependence 

1. Si + OH -+ Si0 + H 

2. Si + 02 -+ Si0 + 0 

3. Si0 + OH -, Si02 + H 

4. SiH + 0 -+ Si0 + H 

5. CR UV + Si -+ Si+ + e 

6. CR UV + Si0 -+ Si + 0 

7. CR UV + Si02 -+ Si0 + 0 

8. Si+ + Hz + SiHt + hv 

9. Si+ + OH + SiO+ + H 

10. Si+ + H2O 3 SiOH+ + H 

11. SiO+ + H2 3 SiOH+ + H 

12. SiOt + H2 3 SiO2H+ + H 

13. H$ + Si -+ SiH+ + H2 

14. HCO+ + Si -+ SiH+ + CO 

18 

lO-'O exp 

9 x exP 

2.7 x 10-loc exp 

10-'0 

3 x 1044 d 

3 x 10-14d 

3 x 10-14d 

10-16 

5 10-11 e 

2.3 x 10-loe -0.6 

3 x 10-'0f 

2 x 10-l0 

10-9 

10-9 
15. H$ + Si0 -+ SiOH+ + H2 

16. HCO+ + Si0 -+ SiOH+ + CO 

17. He+ + Si0 -+ O+ + Si + He 

He+ + Si0 -+ 0 + Si+ + He 

He+ + Si0 -+ SiO+ + He 

18. He+ + Si02 -+ SiO+ + 0 + He 

He+ + Si02 -+ Si+ + 02 + He 

He+ + Si02 -+ O+ + Si0 + He 

He+ + Si02 -+ SiO; + He 

19. C+ + Si0 -+ CO + Si+ 

20. C+ + Si02 -+ CO + SiO+ 

21. Si+ + e -+ Si + hv 

22. SiOH+ + e +Si0 + H 

23. Si02H+ + e +Si02 + H 

24. SiH; + e +SiH + H 

25. H+ + Si0 -+ SiO+ + H 

26. H+ + Si02 -+ SiOt + H 

27. Si+ + A -+ A+ + H 

28. Si+ + PM- -+ Si + PM 

10-9 

10-9 

B~ x 10-9 

B2 x 

B3 x 

bl x 

b2 x 

b3 x 

b4 x lo-' 

10-9 

10-9 

8.7 x 10-l2g 

3.0 x 10-7 

3.0 x 10-7 

3.0 x 10-7 

10-l0 

1O-'O 

10-10 h 

2.4 x 10-8' 

-0.6 

-0.6 

-0.6 

-0.6 

-0.6 

-0.6 

-0.6 

-0.6 

-0.6 

-0.6 

-0.6 

-0.65 

-0.5 

-0.5 

-0.5 

-0.5 

19 
, 

a The units for cosmic ray induced UV photodestruction are s-'; the 

units for all other rate coefficients are cm3 s-'. The numerical values are for 

T = 300K. If the temperature dependence is a power law, the exponent is 

given in column 3; the symbol exp indicates the temperature dependence is 

exp(-lll/T). 

Measured by Swearengen et al. (1978). 

Measured by Husain and Norris et al. (1978). 

The rates for cosmic ray induced UV photodestruction are based on the 

work of Gredel, Lepp, and Dalgarno (1988). 

e Fahey et al. (1981) 

f Anicich and Huntress (1986). 

0 Pdquignot and Aldrovandi (1986). 

A stands for atoms that charge exchange rapidly with Si, such as Mg, 

Fe, Al, Ca, and Ni. The abundance of these atoms in dense clouds may be 

of the order of 

Omont (1986). 

20 
Table 3 

Coefficients P; and Di 

-~ 

Symbol Expression Order of Magnitude" 

D2 

D3 

A10 4320) 

gcruu (Si) 

kl8 %(He+) + gcruv(Si02) 

+ k20 .(C+) 

10- 

2 x 10-'0 

3 x 1049 

3 x 10-19 

3 x 10-19 

3 x 10-20 

3 x 10-18 

5 x 10-l6 

4 x 10- 

6 x lo-" 

a The order of magnitude estimates are based on the following parameters: 

.(a2) = los ~m-~, T = 100K and C = 

402) = 3 x z(OH) = 3 x z(A) = and z(PM-) = 

s-l; z(H20) = lov0, 

b gcruu Gcruu/n(H2)* 

21 
REFERENCES 

Anicich, V. G. and Huntress, W. T. 1986, Ap. J. Suppl., 62, 553. 

Bohme, D. K., Wlodek, S. and Fox, A.E. 1988, Rate Coefficients in 

Astrophysics, eds. T. J. Millar and D. A. Williams, 

(Kluwer, Dordrecht), p. 193. 

Cernicharo, J., Gottlieb, C. A., Guhlin, M., Thaddeus, P., and Vritlek, 

J. M. 1989, Ap. J. Letters in press. 

Clary, D. C. 1988, Rate Coefficients in Astrophysics, eds. T. J. 

Millar and D. A. Williams, (Kluwer/Dordrecht), p. 1. 

Clegg, R. E. S., van Ijzendoorn, L. J., and Allamandola, L. J. 1983, 

M.N.R.A.S., 203, 125. 

Crutcher, R. M. 1979 Ap. J., 234, 881. 

Curtiss, L. A. and Pople, J. A. 1988, Chem. Phys. Letts., 144, 38. 

Dalgarno, A. 1988, Physical Processes in Interstellar Clouds, eds. G. 

Morfill and M. S. Scholer (Reidel, Dordrecht). 

Fahey, et al. 1981, J. Chem. Phys., 75, 669. 

Flower, D. R., 1989, preprint. 

Goldsmith, P. F., Snell, R. L., Erickson, N. F., Dickman, R. L., Schloerb, 

F. P., and Irvine, W. M. 1985, Ap. J., 289, 613. 

Graff, M. M. 1989, Ap. J., 339, 239. 

Gredel, R., Dalgarno, A., and Lepp, S. 1987, Ap. J. Letters, 323, L137. 

Hartquist, T. W., Oppenheimer, M., and Dalgarno, A. 1980, Ap. J., 

310, 182. 

Hudson, R. D. 1971, Revs. Geophys. Sp. Phys., 9, 1. 

Husain, D. and Norris, P. E. 1978, J. Chem. SOC. Far. Trans. 11, 

71, 525. 

Irvine, W. M., Schloerb, Hjalmarson, A., and Herbst, E. 1985, Protostars 

and Planets 11, Eds. D. C. Black and Mathews, M. S. (Arizona), p. 579. 

22 
Knacke, R. F., Larson, H. P., and Noll, K. S. 1989, Ap. J. Letters, 

335, L27. 

Langer, W. D. and Graedel, T. E. 1988, Ap. J. Suppl., 69,241. 

Liszt, H. S. and Vanden Bout, P. A. 1985, Ap. J., 291, 178. 

Millar, T. J. 1980, Ap. Sp. Sci., 72, 509. 

Morris, M., Gilmore, W., Palmer, P., Turner, B. E., and Zuckerman, B. 

Ap. J. Letters, 199, L47. 

Monteiro and Flower 1987, M.N.R.A.S., 228, 101. 

Neufeld, D. A. and Dalgarno, A. 1989, Ap. J., 340, 369. 

Omont, A. 1986, Astr. Ap., 169, 159. 

Piquignot, D. and Aldrovandi, S. M. V. 1988 Astr. Ap., 161, 169. 

Prasad, S. S. and Tarafdar, S. P. 1983, Ap. J., 267, 603. 

Prasad, S. S. and Huntress, W. T. Jr., 1980, Ap. J. Suppl., 43, 1. 

Scalo, J. M. and Slavsky, D. B. 1980, Ap. J. Letters, 239, L73. 

Sternberg, A., Dalgarno, A. and Lepp, S. 1987, Ap. J., 320, 676. 

Solomon, P. M. and Klemperer, W. 1972, Ap. J., 178, 125. 

Swearengen, P. M., Davies, S. J., and Niemczyk, T. N. 1978, Chem. Phys. 

Letts., 55, 274. 

Turner, J. L. and Dalgarno, A. 1977, Ap. J., 213, 386. 

Tielens, A. G. G. M. and Hollenbach, D. J., 1985, Ap. J., 291, 722 

Wilson, R. W., Jefferts, K. B., and Penzias, A. A., 1970, Ap. J. Letters, 

161, L43. 

Wilson, R. W., Penzias, A. A., Jefferts, K. B., Kutner, M. L. and Thaddeus, 1971, Ap. J. Letters, 167, L97. 

Ziurys, L. M., Friberg, P., and Irvine, W. M. 1989, Ap. J., 343, 201. 

23 
FIGURE CAPTIONS 

Figure 1. Simplified schematic diagram of interstellar Si0 chemistry 

showing the principle production routes and the destruction of neutrals by 

cosmic ray produced UV radiation (signified by the label v). Ionic destruction has been omitted for simplicity. 

Figure 2. Fraction of silicon in the form of Si0 in steady state as a function 

of temperature (plotted as 1/ T along the lower axis and T along the upper). 

Three measures of the relative strength of the neutral production, Rf, are 

shown and two of the ion contribution, 2. A nearly exponential decrease 

of Si0 with decreasing T down to 15 K requires weak ion (2 _< and 

moderate neutral (Rf M 1) production, consistent with conditions expected 

in dense regions of interstellar clouds. 

Figure 3. Fraction of silicon in the form of Si0 as a function of temperature (plotted as 1/T along the lower axis and T on the upper scale) at different 

times for Rf = 1 and no ion contribution (2 = 0); n = 5 x lo4 ~m-~, z( 02) = 

3 x are shown 

for lo' yr and steady state. Below 30K, very long times are needed to approach equilibrium and, thus, even with contributions from ions, the solution 

looks like an exponential for T > 15K over times that are relatively long 

compared with cloud dynamical times. 

Figure 4. Similar to Figure 3 for (a) n = 2 x lo6 cm-3 (Rf N 20) and (b) 

n = 106cm-3 (Rf II 200). 

and =(OH) = 3 x lo-'. Results including ions (2 = 

24 
AUTHORS ADDRESSES 

A. E. Glassgold 

Department of Physics 

2 Washington Place 

New York University 

New York, NY 10003 

William D. Langer 

Princeton University 

PO Box451 

Princeton, NJ 08543 

25 
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