Transcript Dust / Molecules

Molecular Clouds
8 April 2003
Astronomy G9001 - Spring 2003
Prof. Mordecai-Mark Mac Low
Molecular Emission
• CO emission
–
–
–
–
–
Quickly becomes optically thick
Rare isotopes have lower optical depth: 13CO and C18O
More easily photodissociated than H2
Only traces H2 over limited column density
Reveals dynamics through Doppler shifts of lines
• Other molecules (NH3, H2S, H2O, OH…)
– Different critical densities for quenching of emission
– Can be hard to distinguish chemistry from dynamics
Dopita & Sutherland
Diffuse Matter, 2002
Chemistry
• In centers of molecular clouds, where CRs
dominate H2 ionization, chemistry driven by
H  H2  H  H
+
2
+
3
• Once H3+ is formed, it transfers protons
H  A  AH  H2
+
3
• For example
– with n < 100 cm-3:
+
H 3+  O  OH +  H 2
OH  H  OH  H
+
+
2
OH +2  H  OH 3+  H

OH  e  OH + 2H or OH 3+  C  H 2CO +  H
+
3

H 2CO  e  CO + 2H
+
– with n > 300 cm-3:
H  C  CH  H 2
+
3
+
CH +  H  CH 2+  H
CH +2  H  CH 3+  H
CH  e  CH + 2H or CH  O  H 2CO  H
H 2CO +  e   CO + 2H
• CH3+ can also react with C or N to form C2 or CN:
+
+
+
+
CH3  C  C2H 2 + H or CH3  N  HCN + 2H
+
3


+
3
+

C2 H + e  C2  2H
HCN + e  CN + H
• Other ways of making C2 include through ionmolecule reactions involving C+, followed by
charge-exchange or dissociative recombination
+
2
+
Grains
• Continuum emission
– Radiative transfer must be modeled to derive density structure
– Varying temperatures near heating sources (stars, shocks) also
complicate
• Absorption against background stars
– Optical has low dynamic range
– Near-IR better (NICE: Lada et al 1994, Cambresy et al 2002)
– Both require uniform background star field (eg MW disk)
• Reveal limitations of molecular emission line
measurements
Padoan, Cambrésy & Langer 2002
Extinction Map of Taurus
Structure of Clouds
• Density structure shows clumps and
filaments at all scales
– column density maps show fractal structure
– self-similar structure extends to largest scales
• Supersonic velocity dispersions seen
– line centroids also show strong dispersions
– velocity structure self-similar to largest scales
Bensch, Stutzki & Ossenkopf 2001
CfA: Heithausen & Thaddeus
1990
KOSMA: Bensch et al. 2001
IRAM: Falgarone et al.
1998
Molecular Cloud Kinematics
• Molecular line ratioes show cloud
temperatures to be of order 10 K, with
sound speeds ~0.2 km/s
• Line widths are much broader than thermal,
corresponding to random motions of order
1-10 km/s, or Mach numbers 5-50.
• Strong shocks should be produced, quickly
dissipating the kinetic energy.
Clump Finding
• Clumps identified in
position-velocity space
frequently used.
• Clump mass spectrum
dN

m
dm
with  1.3    1.9 for gas
and  1.9    2.5 for dust
(denser regions in position space)
• But only works for isolated
clumps!
Williams, de Geus & Blitz 1994
Superposition
Single
clumps in PV
space come
from multiple
regions. Only
truly isolated
clumps can
be reliably
measured
Ballesteros-Paredes & Mac Low 2002
Larson’s Laws
(or at least Suggestions)
• Larson (1981) suggested
R ; R


with α ~ -1 and β ~ 0.5
• Density law implies constant column density
– equipartition between KE & PE?
2  1
K
R
R
2

; 2 +1    3  0
 3
P
2GM 2GR
– lack of dynamic range in observations? More likely
(e.g. Kegel 1989, Scalo 1990, Ballesteros-Paredes &
Mac Low 2002)
• Velocity law appears to result from turbulence
Virial Theorem
• Eulerian virial theorem (McKee & Zweibel 1992):
moment of
inertia deriv
internal
energies
surface
terms
mag grav
inertia
flux
deriv
• Usually simplified by neglecting time-dependent
terms and kin, and taking homogeneous clouds:
1  GM 2
2
cs2 M  2 M 
Pext 
  4   4  3 3  3 
4 
R
R
R
R 
surface
term
grav
mag
internal
energies
• Pressure balance
PextV   c  
2
s
2
M
Boyle's Law
• Gravity balancing turbulence:
GM
3
2
2
2

 cs    M
R
3R
G
• External pressure and gravitational collapse
2
2
1  GM
cs M 
Pext 
  4  3 
4 
R
R 
– as R decreases, gravity becomes more important
• Balance gravity and magnetic field (both have
R-4 dependence)
12
1
M CR   
0.13
2
2
GM    


4 
12
4 R

G
 G 
– gravitational collapse occurs if M > MCR
• However, real interstellar clouds are not
isolated, but have substantial ram pressures
acting on them, so kin  0 and shapes change
(Ballesteros-Paredes et al 1999)
– ram pressure confinement may dominate
Masses
• Virial mass
– Derive…
• XCO
Magnetostatic Cores
(or not?)
• Observed dense cores suggested to be
magnetostatically supported
• Column density contrast through magnetostatic
cores insufficient to explain observed cores
(Nakano 1998)
• Millimeter maps of dense cores show that
roughly half have central protostars, while only
1 in 7 might be expected for magnetostatic
cores modulated by ambipolar diffusion
Magnetic Fields
• Near-IR polarization
– traces fields in surfaces of molecular clouds
– although clouds transparent in near-IR, dust grains
deep within less efficient at polarization
• Masers
– trace fields at very high densities n > 106 cm-3
• OH Zeeman measurements (Crutcher et al 1999)
M 
 

M 
2 
  CR
– suggests that fields (barely) insufficient to provide
magnetostatic support
Supersonic Motions
• In standard scenario, magnetic fields
converted shocks into linear Alfvén waves,
acting as a lossless spring that stores and
returns KE, maintaining supersonic motions.
• Computations of turbulence decay
demonstrate that non-linear MHD waves
interact strongly, dissipating energy quickly
(Mac Low et al. 1998, Stone et al. 1998)
• Observed motions must be more or less
continuously driven
Molecular Cloud Lifetimes
• Cloud lifetimes estimated by Blitz & Shu
(1980) to be around 30 Myr in Milky Way
– Locations downstream from spiral arms
– Stellar ages associated with GMCs
• Much shorter lifetimes of 5-10 Myr
proposed by Ballesteros-Paredes et al. (1999),
Fukui et al. (1998).
– Lack of 10 Myr old T Tauri stars
– Cluster ages vs. associated molecular gas
• Individual cloud lifetimes vs. ensemble
lifetime
Assignments
• Read Flash User’s Guide Chapters 5, 8, 9.1,
12, 15.2, and 18.2.1
• Read the review paper “Turbulence in
Molecular Clouds” by E. VázquezSemadeni, astro-ph/9701050
• I will release Exercise 6 as soon as I’m
convinced it works
Adaptive Mesh Refinement
• Original methods developed by Berger & Oliger
(1984) and Berger & Colella (1989) used subgrids
that were allowed to
– rotate with respect to axes
– merge with other subgrids
– have arbitrary shapes
• Very flexible and memory efficient, but complex
to program and hard to parallelize.
• Instead only refine fixed blocks (De Zeeuw &
Powell 1993, MacNiece et al 2000: PARAMESH)
Mesh
Refinement
• subdivision of
blocks, not zones
• quad-tree in 2D,
oct-tree in 3D
• blocks distributed
among processors
for load-balancing
• neighbors may
never differ by
more than one level
• top level only one
block (!)
Block Structure
PARAMESH User’s Guide
• Guard cells used for
interpolation,
boundary conditions
• Flash with PPM:
–
nxb = 8
– nguard = 4
• Blocks may be
declared “empty”
(eg to serve as
physical obstacles)
Load Balancing
• Peano-Hilbert space-filling
curve drawn through grid
blocks
• Gives “Morton-ordered” list
of blocks
• Blocks consecutively
assigned to processors from
Flash User’s Guide
list
• This increases chance of neighboring blocks
being on same processor
• Parent, leaf blocks get different weighting
• List divided among processors for load balance
Refinement Criterion
• Choice of refinement criterion depends strongly
on problem to be solved (this can be a black art!)
• Default Flash criterion is 2nd order error estimate
(Löhner 1987). In one dimension it is:
2
2
 u x
Ei 
u x i 1 2  u x i 1 2    2u x 2

ui 1  2ui  ui 1
ui 1  ui  ui  ui 1    ui 1  2 ui  ui 1 
4


10
• Setting
filters out small ripples
Other Refinement Criteria
• The Löhner error criterion picks out
discontinuities in the flow.
• Sometimes other things are more appropriate
– density enhancements
– high or low temperature regions
– regions with strong diffusion
• Any of these can be marked for refinement in
addition to or instead of regions with high E.
Interpolation Across Boundaries
• Flux must be conserved at boundaries between
different resolution blocks
• On Cartesian grid, add fluxes from fine grid
• Curvilinear grids also
require area factors
• Fine grid guard cells m
filled by interpolation
on coarse grid.
• Order of interpolation
must match order of
algorithm.
Prolongation
• Fine zones filled from coarse zones on refinement
• Interpolation must be same order as solution
• Care must be taken at boundaries to maintain
conservation
• Different order
interpolation
routines
available in
Flash.
Magnetic Fields
• Magnetic fields on AMR remains a problem
• Transfer of fluxes requires addition of edgecentered electric fields, which works
• Prolongation gives
div B errors
• Flash corrects using
Poisson solver
(inexact &
expensive)
• Balsara (2001)
proposes areaweighted solution.