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

Chemistry• In centers of molecular clouds, where CRs

dominate H2 ionization, chemistry driven by

• Once H3+ is formed, it transfers protons

• For example– with n < 100 cm-3:

Dopita & SutherlandDiffuse Matter, 2002

+ +2 2 3H H H H

+ +3 2H H HA A

+ +3 2

+ +2

+ +2 3

+ +3 2

+2

H O OH H

OH H OH H

OH H OH H

OH C H CO H

H CO CO + 2He

+3OH OH + 2H or e

– with n > 300 cm-3:

• CH3+ can also react with C or N to form C2 or CN:

• Other ways of making C2 include through ion-molecule reactions involving C+, followed by charge-exchange or dissociative recombination

+ +3 2

+ +2

+ +2 3

+ +3 2

+2

H C CH H

CH H CH H

CH H CH H

CH O H CO H

H CO CO + 2He

+3CH CH + 2H or e

+ + + +3 2 2 3

+ +2 2 2

CH C C H + H or CH N HCN + 2H

C H + C 2H HCN + CN + He e

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

Extinction Map of TaurusP

adoa

n, C

ambr

ésy

& L

ange

r 20

02

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

CfA: Heithausen & Thaddeus1990

KOSMA: Bensch et al. 2001 IRAM: Falgarone et al.1998

Ben

sch,

Stu

tzki

& O

ssen

kopf

200

1

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

• But only works for isolated

clumps! Williams, de Geus & Blitz 1994

dNm

dm

with 1.3 1.9 for gas

and 1.9 2.5 for dust

(denser regions in position space)

Super-position

Ballesteros-Paredes & Mac Low 2002

Single clumps in PV space come from multiple regions. Only truly isolated clumps can be reliably measured

Larson’s Laws (or at least Suggestions)

• Larson (1981) suggested with α ~ -1 and β ~ 0.5

• Density law implies constant column density– equipartition between KE & PE?

– 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

; R R

2 12

3; 2 +1 3 0

2 2

K R R

P GM GR

Virial Theorem

• Eulerian virial theorem (McKee & Zweibel 1992):

• Usually simplified by neglecting time-dependent terms and kin, and taking homogeneous clouds:

moment of inertia deriv

internalenergies

surfaceterms

mag grav inertiafluxderiv

2 2 2 2

4 4 3 3

13

4s

ext

GM c M MP

R R R R

surface

term grav mag internalenergies

• Pressure balance

• Gravity balancing turbulence:

• External pressure and gravitational collapse

– as R decreases, gravity becomes more important

2 22 3

3 scGM

M RR G

2 2 Boyle's Lawext sP V c M

2 2

4 3

1

4s

ext

GM c MP

R R

• Balance gravity and magnetic field (both have R-4 dependence)

– 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

1 2

2 24 1 2

1 0.13

4CRM

GMR G G

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)

– suggests that fields (barely) insufficient to provide magnetostatic support

2CR

M M

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. Vázquez-Semadeni, 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

• 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)

PARAMESH User’s Guide

Load Balancing• Peano-Hilbert space-filling

curve drawn through grid blocks

• Gives “Morton-ordered” list of blocks

• Blocks consecutively assigned to processors from list

• This increases chance of neighboring blocks being on same processor

• Parent, leaf blocks get different weighting• List divided among processors for load balance

Flash User’s Guide

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:

• Setting filters out small ripples

2 2

2 2

1 2 1 2

1 1

1 1 1 1

2

2

i

i i

i i i

i i i i i i i

u xE

u x u x u x

u u u

u u u u u u u

410

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 edge-

centered electric fields, which works

• Prolongation gives div B errors

• Flash corrects using Poisson solver (inexact & expensive)

• Balsara (2001) proposes area-weighted solution.