Low-Temperature Gas-Phase &
Surface Reactions in Interstellar
Clouds
ERIC HERBST
DEPARTMENTS OF PHYSICS,
CHEMISTRY AND ASTRONOMY
THE OHIO STATE UNIVERSITY
Dense Interstellar Cloud Cores
10 K
10(4) cm-3
H2
dominant
Molecules seen in IR
absorption and radio
emission
sites of star
formation
Cosmic rays create weak plasma
Fractional ionization < 10(-7)
Cosmic Elemental Abundances
•
•
•
•
•
•
•
•
H =1
He = 6.3(-2)
O = 7.4(-4) 1.8(-4)
C = 4.0(-4) 7.3(-5)
N = 9.3(-5) 2.1(-5)
S = 2.6(-5) 8.0(-8)
Si = 3.5(-5) 8.0(-9)
Fe = 3.2(-5) 3.0(-9)
• Dust/gas = 1% by
mass
• Gas-phase
abundances of heavy
elements in clouds
reduced.
GAS PHASE INTERSTELLAR/CIRCUMSTELLAR MOLECULES - HIGH RESOLUTION (12/03)
_____________________________________________________________________________________________
H2
KCl
HNC
C3S
C5
HCO
NH3
CH3
H 3O +
CH
AlCl
CH4
CH3OH
CH+
AlF
HCO+
H2CO
SiH4
CH3SH
NH
PN
HOC+
H2CS
CH2NH
C2H4
OH
SiN
HN2+
HCCH
H2C3(lin)
CH3CN
C2
SiO
HNO
HCNH+
c-C3H2
CH3NC
CN
SiS
HCS+
H2CN
CH2CN
HC2CHO
CO
CO+
SO+
C3
C2O
CO2
C2S
AlNC
SiC2
SiCN
SO2
NaCN
OCS
MgNC
MgCN
N2O
C3H(lin)
c-C3H
NH2CN
CH2CO
NH2CHO
HC3NH+
HCCN
HCOOH
C4H2
H2C4(lin)
HNCO
SiC3
HOCO+
C4H
HNCS
C2CN
C3O
NaCN
HCCNC
HNCCC
C4Si
H2COH+
CSi
CP
H3+
CS
HF
NO
CH2
NS
SO
HCl
NaCl
H2O
H2S
C2H
HCN
NH2
HC2CN
C5H
C5N
CH3NH2
CH2CHOH
CH3CCH
CH3CHO
CH2CHCN
c-CH2OCH2
c-CH2SCH2
C6H
HC4CN
C7H, C6H2
C8H
HCOOCH3
CH3COOH
CH3C2CN
H2C6(lin)
C6H2
H2COHCHO
C2H5OH
(CH3)2O
C2H5CN
CH3C4H
HC6CN
(CH2OH)2
(CH3)2CO
CH3C4CN?
NH2CH2COOH?
HC8CN
c-C6H6
HC10CN
+ ISOTOPOMERS
Some Fractional Abundances in
TMC-1
•
•
•
•
•
•
CO
1(-4)
HCN 2(-8)
C4H
9(-8)
HCO+ 8(-9)
c-C3H2 1(-8)
HC9N 5(-10)
•
•
•
•
•
•
OH 2(-7)
NH3 2(-8)
HC3N 2(-8)
N2H+ 4(-10)
HNC 2(-8)
O2 < 8(-8)
Water, CO,
CO2
+ small grains
and PAH’s
Water ice = 10(-4) of
Gas density
H 2+ + e
Cosmic
ray
O
Efficient Low T GasPhaseReactions
1.
2.
3.
4.
5.
Ion-molecule reactions
Radiative association reactions
Dissociative recombination reactions
Radical-radical reactions
Radical-stable reactions
Ea = 0
Exothermic
In areas of star formation, reactions
with barriers occur.
Ion-Molecule Reactions


A BC D
• Experimental evidence down to a few K
• Rate coefficients explained by classical
“capture” models in most but not all
instances.
•
ion-non polar (Langevin case)

9
k L  2e
 2  10

cm3 s-1
Ion-mol. Rx. (cont)
• Ion-polar
kTS  kL [0.62  0.4767 x]
2
k
 k [1 
x]  10 7 cm 3 s 1
LD
L
1/ 2
D
1 / 2
x
T
2k BT
+ more complex state-specific models
Remaining Questions
1) Why are some reactions slow?

3

H  HD  H 2 D  H 2
2) Is there a quantum limit?
4
 2
k
2
(
2


1
)
sin


Radiative Association
A  B  AB  AB  h

*

k1
k ra 
k r  K (T )k r ; k r  10 2 s 1
k 1
K (T )  T
 ( rA  rB ) / 2
, size, bond engy
Few ion trap measurements by
Gerlich, Dunn down to 10 K
What is the 0 K limit?
What about competitive channels?
Dissociative Recombination Reactions

AB  e  A  B
Studied in storage rings down to “zero” relative
energy; products measured for approx.10 systems
k (T )  A(T / 300) n
7
n=0.5, 1.5
3 1
A  10 cm s
Some systems studied: H3+, HN2+,
HCNH+, H3O+, NH4+, CH5+ ,CnHm+
QUESTION
• How large must ions be before the
dominant process becomes radiative
recombination? “statistical trapping”
• Answer via statistical theories (RRKM):
20-30 atoms?????
Radical-radical Reactions
Detailed
capture
models
by Clary,
Troe
RADICAL-NEUTRAL RX (CONT)
CN + C2H2  HCCCN + H
YES
C + C2H2  C3H + H
CCH + HCN  HCCCN + H
Barrier cannot be
guessed!!
YES
NO
Attachment
e  A  A  h

If enough large molecules with
large electron affinities present,
electrons may not exist! Note no
competitive fragmentation
channels.
FORMATION OF GASEOUS
WATER
H2 + COSMIC RAYS  H2+ + e
Elemental
abundances:
C,O,N
=
10(-4);
C<O
Elemental abundances: C,O,N = 10(-4); C<O
H2+ + H2  H3+ + H
H3+ + O  OH+ + H2
OHn+ + H2  OHn+1+ + H
H3O+ + e  H2O + H; OH + 2H, etc
FORMATION OF HYDROCARBONS
H3+ + C  CH+ + H2
CHn+ + H2  CHn+1+ + H; n=1,2
CH3+ + H2  CH5+ + h
CH5+ + e  CH4 + H (5%)
 CH3 + 2H (70%)
CH5+ + CO  CH4 + HCO+
CURRENT GAS-PHASE MODEL NETWORKS
4,000 reactions; 10-20% "studied";
400 species through 13 atoms in size
elements: H, He, N, O, C, S, Si, Fe, Na, Mg, P, Cl
Solved kinetically; thermodynamics useless!
t=0; atoms except for H2
Latest network – osu.2003 – contains over 300 rapid
neutral-neutral reactions. Rate coefficients estimated by
Ian Smith and others for many of these. Verification
needed!!
GAS-PHASE MODELS OF DENSE CLOUD CORES
"SUCCESSES"
+
1. IONS ( H3 , HCO+, HC3NH+)
2. ISOMERS (HNC) & RADICALS (OH)
HCNH+ + e ----> HCN + H; HNC + H
3. ISOTOPIC FRACTIONATION

H3+ + HD <====> H2D+ + H2
4. UNSATURATED MOLECULES
A+ + H2 -------> No Reaction
5. ORDER-OF-MAGNITUDE AGREEMENT WITH AT BEST
80% OF MOLECULES
Chemistry imperfect!!
Nature of Solution for a homogeneous, timeindependent cloud
“early time if Orich”
fi
Small species (CO)
Large species (HC9N)
0.1
10
Time (Myr)
Nature of Solution for a homogeneous, timeindependent cloud
“early time if Orich”
fi
Found in
pre-stellar
cores
accretion
Small species (CO)
Large species (HC9N)
0.1
10
Time (Myr)
Low Temperature Surface Chemistry on
Amorphous Surfaces
• 1) Mechanisms (diffusive [LangmuirHinshelwood], Eley-Rideal, hot atom,
impurity site)
• 2) Dependence on size, mantle, fluffy
nature, energy parameters
• 3) Rate equations vs. stochastic
treatments
• 4) non-thermal desorption (cosmic rays)
Edes
Ediff
“physisorption”
(diffusion)
Desorption & Diffusion
k des ( s )   exp(  Edes / k BT )  0 *
1
for heavies
Desorption via evaporation and cosmic-ray heating.
khop (s )   exp( Ediff / kBT ); Ediff  0.30Edes
1
kdiff = khop/N; N is the number of binding sites
For H, tunneling can occur as well.
H diffuses the fastest and
dominates the chemistry.
TYPES OF SURFACE REACTIONS
REACTANTS: MAINLY MOBILE
ATOMS AND RADICALS
A +
H +
B 
H  H2
AB
association
X  XH (X = O, C, N, CO,
etc.)
WHICH CONVERTS
H +
O  OH  H2O
C  CH  CH2  CH3  CH4
N  NH  NH2  NH3
CO  HCO  H2CO  H3CO  CH3OH
X + Y  XY
(CO + O  CO2) ??????????
Experiments on cold surfaces
• Vidali et al. Formation of H2 on silicates, carbon, and
amorphous ice; LH mechanism characterized and
energies obtained; formation of CO2; energy partitioning
of hydrogen product (also UCL group)
• Ediff(H, olivine) = 287 K; Ediff(H, carbon) = 511 K
• But whole analysis of data has been questioned by
others, who feel that both tunneling and some
chemisorption sites are involved!!!!!
• Hiraoka et al. Formation of ices (CH4, H2O,NH3, H2CO)
• Watanabe et al. Formation of methanol
• Danish group formation of H2
MODELLING DIFFUSIVE
SURFACE CHEMISTRY
Rate Equations
dN ( H )
 k acc n( H )  k des N ( H )  K H  H N ( H ) N ( H )
dt
K H  H  k diff ( H )  k diff ( H )
The rate coefficient is obtained by
K A B  k hop N ( B ) / N
Method accurate if N>1
Biham et al. 2001
STOCHASTIC METHODS
Based on solution of master
equation, which is a kinetictype equation in which one
calculates not abundances but
probabilities that certain
numbers of species are
present. Can solve directly
(Hartquist, Biham) or via Monte
Carlo realization (Charnley).
MASTER EQUATION
dN ( H )
 k acc n( H )  k des N ( H )  K H  H N ( H ) N ( H )
dt
replaced when N(H) << 1 by a series of
coupled equations for Pn(H):
<N(H)> =
 n Pn(H)
dP0(H)/dt = ……….
Stochastic States
• Unfortunately, with more than one reactive
surface species, one must compute joint
probabilities P(n1 , n2 , n3...) so that
the computations require significant
computing power. It is necessary to
impose cutoffs on the ni and the total
number of surface species considered.
More simple fix: modified rate method
New Gas-Grain StochasticDeterministic Model
• Stantcheva & Herbst (2004)
• Gas-phase chemistry solved by
deterministic rate equations, while surface
chemistry solved by solution of master
equation. Some results quite different
from total deterministic approach.
RESULTS: surfaces
• From observations of grain mantles, the
dominant species in the ice are water, CO, CO2,
and occasionally methanol.
• The models at 10 K and a gas density of 10(4)
cm-3 are able to reproduce the high abundance
of water, seem to convert CO into methanol too
efficiently, and tend to underestimate the amount
of CO2. Results sensitive to density.
• The modified rate method reproduces the
master equation approach at 10 K, but the
normal rate method can be in error.
Results from Stantcheva & Herbst (2004)
CO
% Agreement in TMC-1
Gas-phase species
Roberts & Herbst 2002
Some Conclusions
• 1) Low-temperature chemistry in
interstellar clouds (both gas-phase and
surface) partially understood only.
• 2) Chemistry gives us many insights into
the current state and history of sources
• 3) More work on “cold chemistry” is
clearly needed to make our mirror into the
cosmos more transparent.