Simulations of nonequilibrium processes in the Laboratory and in the Interstellar Medium

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• Simulations of non-equilibrium processes in the
  Laboratory and in the Interstellar Medium
• Ofer Biham
• The Hebrew University
• Azi Lipshtat
  Gian Vidali
• Itay Furman
  Valerio Pirronello
• Nadav Katz
  Joe Roser
• Hagai Perets
• Baruch Barzel
• 
  Israel Science
  Foundation
• 
  The Adler
  Foundation for Space Research
• 
  

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The Black Cloud Bernard 68
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Outline

• Introduction
• Observations
• Laboratory Experiments
• Modeling
• Astrophysical implications

• Rate equations
• Master equation

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Interstellar Clouds
Diffuse clouds
Dense clouds
Hydrogen Atoms
Hydrogen Molecules
Bare Dust Grains
Ice Coated Grains

• nH 10 - 100 cm-3
• ngrains 10-12 n
• Tgas 100 K
• Tgrains 10 20 K

104 cm-3 ngrains 10-12 n Tgas 10 20
K Tgrains 10 K
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Absorption Spectrum

• Diffuse Clouds
• Molecules detected H2, CO, OH, CS
• Dense Clouds
• Molecules detected H2 , CO, CO2, H20, HCN, H2CO,
  NH3, C2H2, CH4, CH3OH, HCOOH, OCSPAH..

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Interstellar Dust Grains

• Ejected from Red Giants and Super-novae
• Approximately 1 of the clouds mass
• Consist of amorphous silicates and carbon
  particles
• Broad size distribution in the range between 1nm
  100nm

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Molecular Hydrogen Recombination
Gas phase reaction - inefficient
More efficient channel - on dust grain surfaces
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The Role of Molecular Hydrogen

• The most abundant molecule in the universe
• Enables chemical reaction networks in the gas
  phase chemical complexity
• Molecules provide cooling during gravitational
  collapse enables star formation

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Rate of Recombination
R 0.5 nH vH s g ngrains
vH thermal velocity of H atoms in the gas s
cross section of the dust grains g
recombination efficiency
Gould and Salpeter (1963)
Hollenbach, Werner and Salpeter (1971)
g g(grain composition, surface morphology,
temperature, size, flux)
Laboratory experiments are needed
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Laboratory Experiments
Requirements samples (silicates,carbon,ice)
low temperatures vacuum low flux
long times efficient detection of
molecules
Sample temperature
Time
detector
Pirronello et al., ApJ 475, L69 (1997) Katz et
al., ApJ 522, 305 (1999)
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Temperature Programmed Desorption (TPD)
Experiment
Olivine sample
Irradiation times 0.55 (minutes) 0.2 0.07
Second order kinetics Thermal hopping no
tunneling
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Temperature Programmed Desorption (TPD)
Experiment
Olivine sample
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Rate Equation
atom concentration
hopping rate a? exp(-E0/kT)
desorption coefficient W? exp(-E1/kT)
flux
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TPD Experiment for Carbon
E044meV E157meV
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TPD Experiment for Ice
Low density ice porous material
E044.5 meV E152 meV
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H2 Formation Efficiency on Ice Under
Interstellar Conditions
Astrophysical Implications
Steady state conditions Gas temp. 25
K Density 20 atoms/cm3
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Grain Parameters
Size d 1 100 nm Adsorption site
density s 1 site/nm2 No. of sites on grain
Spd2s Flux density f 10-9 10-6 ML/sec Flux
FfS Number of H atoms on grain n?S Scanning
rate by H atoms A a/S
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Rate Equation ? Master Equation
For small grains under low flux the typical
population size of H atoms on a grain may go
down to n
1 Thus the rate equation (mean field
approximation) fails One needs to take into
account The discreteness of the H
atoms The fluctuations in the
populations of H atoms on grains Master
Equation for the probability distribution
P(n), n1,2,3,
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Master Equation

Flux
Desorption
Recombination
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H2 Formation Rate

• Green et al. AA 375 (2001)
• Biham Lipshtat, PRE 66 (2002)

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H2 Production Rate vs. Grain Size
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Grain Size Distribution
A broad power-law distribution
ngrain(d) d -3.5 for 5nm lt d lt 250 nm
Mathis et al. (1977) Therefore small grains
should be taken into account. Competing effects
smaller grains larger surface/volume
ratio however lower recombination
efficiency.
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Moment Equations

Lipshtat Biham, AA 400, 585 (2003)
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H2 in Photon Dominated Regions

• H2 molecules were detected in photon dominated
  regions (PDRs) where the grain temperature is
  around 40K
• This is in apparent contradiction with the
  experimental results
• Several explanations were proposed. One of them
  is based on the existence of chemisorption sites.
  It does not seem to apply in the relevant
  temperature range.

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Porous Grains
Porous grains may provide efficient
recombination even at grain temperatures around
40K.In the pores Atoms desorb and re-adsorb many
times.
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Rate Equations for Reaction Networks
HH?H2 OO?O2 HO?OH
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Master Equation for two Species
flux
desorption
HH?H2 OO?O2 HO?OH
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Deuteration Processes
Grain surface mechanism for enhanced formation
of HD and D2 molecules. The mechanism is based
On the longer residence time of D atoms on
grain Compared to H atoms May possibly apply to
more complex molecules such as NHD2 and ND3??
Lipshtat, Biham Herbst,MNRAS 348 (2004)
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Complex Reaction Networks
Number of equations increases Exponentially
with the number of reactive species
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Reaction Networks
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Solid lines master eq. Symbols
multi-plane Dashed lines rate eq.
The Multi-Plane Method
Solid lines master eq. Symbols
multi-plane Dashed lines rate eq.
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Summary

• Mobility of H atoms on grains is dominated by
  thermal diffusion not by tunneling
• Thus the recombination efficiency strongly
  depends on grain temperature, composition and
  surface morphology
• Experiments on silicates, carbon and ice show
  narrow temperature windows of high efficiency
  between 8-18K
• Recombination efficiency drops for very small
  grains the grain size distribution should be
  taken into account
• H2 observed in photon dominated regions (PDRs)
  where grain temperature is around 40K porous
  grains??
• The master equation suitable for gas-grain
  models of interstellar chemistry

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The Multi-Plane Method
Solid lines master eq. Symbols
multi-plane Dashed lines rate eq.