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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

Fourier transform solution
Fourier transform solution



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