molecules and dust 1 april 2003 astronomy g9001 - spring 2003 prof. mordecai-mark mac low
TRANSCRIPT
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
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
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