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 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.

A + B = AB + h

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.

1

9-3

1.5 10 yr1 cmform

nt

UMIST rate database• Best compilation of gas phase astrochemical

rates currently at U Manchester (Le Teuff, Millar & Markwick 1999); available at http://www.rate99.co.uk

• 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

3 -1exp cm s300 K

Tk

T

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

Photodissociation

• 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

Lyman, Werner bands in range 912 to 1105 Å

Spitzer, PPISM

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

shock

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

• 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

• Mean extinction varies within, between galaxies

• Reddening ~1/λ in optical

• Bump due to small carbon grains

Dopita & Sutherland

2175 Å bump

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)

Optical Propertiesmax

min

2

Van de Hulst 1957

Draine 1988

( )

the extinction efficiency

while albedo is .

Mie theory ( ) or

discrete dipole array method ( )

used to compute

a

a

abs sca

sca abs

Qn a a da

Q Q Q

Q Q

Q

Dust Polarization

Mineralogy• 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.

PAHs

• 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)

Assignments

• Finish Exercises 4 and 5

• Read Ballesteros-Paredes, Hartmann, & Vázquez-Semadeni, 1999, ApJ, 527, 285

Gravity• 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

2

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

1, , 1, , 1 , , 1,2 2

2

1, 1, , 1 , 1 , ,

in two dimensions, Poisson's equation

can be differenced as

2 2

4

i j i j i j i j i j i ji j

i j i j i j i j i j i j

x x

x

Numerical Recipes

Fourier transform solution

11

0 0

11

0 0

discrete inverse Fourier transforms:

1 ˆ exp 2 exp 2

1ˆ exp 2 exp 2

substitute these expressions into our finite-difference eqn

ˆ

yx

yx

nn

jk mn x ym nx y

nn

jk mn x ym nx y

m

ijm n ikn nn n

ijm n ikn nn n

2

2

2 2 2 2ˆexp exp exp exp 4

this can be readily solved:

ˆˆ2 2

2 cos cos 2

The inverse transform then yields the solutio

n mnx x y y

mnmn

x y

im im in inx

n n n n

x

m n

n n

n

NumericalRecipes

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

1 22 2 2d x y z

Tree Methods

• 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

Volker, YoshidaWhite 2001

PPPM• 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

• 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

Sar

anit

i et a

l. 19

96

2 which goes to Poisson as tt

•Gauss-Seidel relaxation on multiple grids