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Molecules and Dust . 1 April 2003 Astronomy G9001 - Spring 2003 Prof. Mordecai-Mark Mac Low. Molecule Formation. Gas phase reactions must occur during collisions lasting < 10 -12 s Radiative association reactions: have rate coefficients of only 10 8 s -1

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molecules and dust

Molecules and Dust

1 April 2003

Astronomy G9001 - Spring 2003

Prof. Mordecai-Mark Mac Low

molecule formation
Molecule Formation
  • Gas phase reactions must occur during collisions lasting < 10-12 s
  • Radiative association reactions:
    • have rate coefficients of only 108 s-1
    • are faster if they involve at least one ion
  • Adsorption onto dust allows far longer contact times, so slower reactions can proceed. Dust is a catalyst.
h 2 formation
H2 Formation
  • Hollenbach & Salpeter (1971) computed H2 formation rate on dust to be
  • Molecule formation only proceeds quickly at high densities
  • Experimental results by Piranello et al. group show slower rates on graphite, olivine, but not on amorphous ice.
umist rate database
UMIST rate database
  • Best compilation of gas phase astrochemical rates currently at U Manchester (Le Teuff, Millar & Markwick 1999); available at
  • 12 elements, 396 species, and 4000 reactions, including T dependence. Also some photoionization and dissociation rates, and interactions with CRs.
  • Gives rates in the form
collisional dissociation
Collisional Dissociation
  • Electron collisions with molecules most important collisional dissociation mechanism
    • Collisional dissociation
    • Dissociative ionization
    • Dissociative recombination most likely

AB + e- A + B* + e-

AB + e-  A + B+ + 2e-

AB+ + e-  A + B


Lyman, Werner bands in

range 912 to 1105 Å

  • UV excitation followed by fluorescent dissociation
  • Self-shielding occurs in H2 when Lyman and Werner bands become optically thick
  • Similar physics controls CO dissociation, but lower abundance makes CO more fragile

Spitzer, PPISM

photodissociation regions
Photodissociation Regions
  • Shielded from H ionizing radiation, but exposed to lower energy UV and X-rays
  • Dust is dominant absorber
  • Contain nearly all atomic and molecular gas
  • Origin of much of IR from ISM
    • dust continuum
    • PAH features
    • fine structure lines

Hollenbach & Tielens 1999

dust formation
Dust formation
  • Stellar ejecta (time-dependent process)
    • giants and AGB stars
    • massive post-main-sequence stars
    • novae and supernovae
  • Composition of ejecta determine grains
    • Oxygen-rich ejecta make silicates
    • Carbon-rich ejecta make graphite and soot
  • Silicates must also form in cooler ISM
  • Ices freeze on in molecular cloud cores
grain destruction in shocks
Grain Destruction in Shocks
  • Thermal sputtering by ions
    • Most important if vs> 400 km s-1
    • Occurs over 105 yr for typical grains
    • Stopping time τstop~ (106 yr) a-5(nv500)-1
    • Only largest grains survive fast shocks
  • Grain-grain collisions lead to a-3.3 power law
    • Vaporization at high velocities
    • Spallation and fragmentation
      • Amorphous carbon at v > 75 km s-1
      • Silicates at v > 175 km s-1
    • Cratering at v > 2 km s-1
    • Coagulation
reddening curves
Reddening curves
  • Mean extinction varies within, between galaxies
  • Reddening ~1/λ in optical
  • Bump due to small carbon grains

2175 Å bump

Dopita & Sutherland

grain distribution
Grain distribution
  • Properties of reddening curve can be fit by a size distribution of grains n(a) ~ a-3.5(Mathis, Rumple, Nordsieck 1977) with composition
    • graphite
    • silicon carbide (SiC)
    • enstatite ([Fe,Mg]SiO3)
    • olivine ([Fe,Mg]2SiO4)
    • iron, magnetite (Fe3O4)
  • Wind density, velocity, imply grain mineralogy
  • If the wind is oxygen rich
    • fast, low density winds produce corundum (Al2O3), and perovskite (CaTiO3).
    • higher density allows forsterite (Mg2SiO4) and enstatite (MgSiO3) mantles
    • Iron reacts to form olivine (Fe2SiO4) and pyroxene (FeSiO3)
  • Narrow mid-IR features observed
  • Dust grains traced by isotopic anomalies to different stars.
  • Polycyclic aromatic hydrocarbons dominant species in carbon-rich winds.
  • Gradual transition from flat PAHs to spherical soot
  • 3-10 μm features prob. from mixture of PAHs

PAH formation in C-rich wind via H abstraction and acetylene

addition (Frenklach & Feigelson 1989)

  • Finish Exercises 4 and 5
  • Read Ballesteros-Paredes, Hartmann, & Vázquez-Semadeni, 1999, ApJ, 527, 285
  • Fixed (or at least pre-defined) potential from a background mass distribution not part of the computation
    • stars
    • dark matter
  • Self-consistent potential from the matter on the grid
    • requires solution of Poisson’s equation
poisson equation solutions
Poisson Equation Solutions
  • Poisson equation is solved subject to boundary conditions rather than initial conditions
  • Several typical methods used in astrophysics
    • uniform grid: Fourier transform (FFT)
    • particles:
      • direct summation (practical with hardware acceleration)
      • tree methods
      • particle-particle/particle-mesh (P3M)
    • non-uniform/refined grids: multigrid relaxation
finite differencing
Finite Differencing

Numerical Recipes

direct summation
Direct Summation
  • Simplest and most accurate method of deriving potential from a particle distribution.
  • Too bad its computational time grows as N2!
  • Normally only practical for small N < 100 or so
  • GRAPE project attacks with brute force by putting expensive part in silicon on a special purpose, massively parallel chip
tree methods
Tree Methods

Volker, Yoshida

White 2001

  • Tree is constructed with one pcle in each leaf
  • Every higher node has equivalent monopole, quadrupole moments
  • Potential computed by sum over nodes
  • Nodes opened if close enough that error > some ε
  • A grid covering all the particles is set up, with density in each zone interpolated from the particles in the zone.
  • The potential on the grid is solved by any method (eg FFT)
  • A local correction to the potential for each particle is then derived from direct summation of particles within its own grid cell
  • An adaptive mesh can be used for very clumpy density distributions
multigrid relaxation
Multigrid Relaxation

Saraniti et al. 1996

  • Gauss-Seidel relaxation
  • on multiple grids
  • Relaxation methods solve
  • Each “timestep” relaxes most strongly close to grid scale.
  • By averaging onto coarser grids, larger-scale parts of solution can be found