The Role of Ambipolar Di ff usion in GMC Collisions Duncan Christie - - PowerPoint PPT Presentation

The Role of Ambipolar Diffusion in GMC Collisions

Duncan Christie Department of Astronomy, University of Virginia

Jonathan Tan

University of Virginia Chalmers University of Technology

Benjamin Wu

National Astronomical Observatory of Japan

Cloud Collisions

Introductory Rambling about Cloud Collisions Ambipolar Diffusion and the Resistivity Model Simulation Results Summary Outline Why? Cloud collisions provide a mechanism to quickly assemble large amounts of gas.
 
 If they occur frequently enough, they may play a role in determining the star formation rate.

Cloud Collisions and Mergers

Tasker & Tan (2009) performed simulations of GMC formation and evolution in disks with flat rotation curves, and found a typical cloud undergoes a merger or collision every 1/5 of an

• rbital time.

Li+ (2017) found collisions and mergers to be even more frequent, occurring on the order of every 0.1 to 0.2 of an

• rbital time.

Dobbs+ (2014) found very frequent collision and mergers within their simulations (1 every 1/15 of an orbit for simulations with a spiral potential); however, it is unclear how many of these are the more violent collisions envisioned The estimates for the collision rates requires that the clouds be sufficiently long-lived (i.e., bound, and not disrupted by internal star formation). None of these simulations contain contain feedback/star formation which could shorten cloud lifetimes.

Σ

Tasker & Tan (2009) Li et al. (2017) Dobbs et al. (2014)

Cloud Collisions: Observations

Identifying potential interacting clouds is difficult, and is primarily done by looking for bridge features in PV and PPV diagrams. e.g., Fujita et al. (2017), Furukawa et al. (2009), Fukui+ (2014) Bisbas+ (2017) has argued that CII 158μm emission may contain bridge features as the source is the cloud edges/ ambient medium. This is useful as CO lines may not always show indication of the collision. Thomas has a poster here describing this work. The clouds Westerlund 2 and RGC3603 both have stellar clusters associated with them, supporting the idea that cloud collisions may be involved in the cluster formation process

W51A, Fujita et al. (2017) Fukui et al. (2014)

Modeling Cloud Collisions

0.60 Myr

z [pc] x [pc] x [pc]

Chen & Ostriker (2014)

Although not exactly colliding clouds, can local
 simulation of part of a collision, specifically the initial interface between the clouds (with appropriate pre-shock conditions). Colliding Flows Global Simulations of Colliding Clouds

Shima et al. (2017) Balfour et al. (2017)

The other option is to model two entire clouds colliding. You’re modeling larger scales, requiring larger simulations.
 
 The parameter space to be investigated is quite large, with different possibilities for the cloud masses, impact parameter, magnetic fields, etc. We opt to investigate the case of two colliding giant molecular clouds of equal mass.

GMC COLLISIONS AS TRIGGERS OF STAR FORMATION

A Never Ending Series of Papers GMC Collisions as Triggers of Star Formation. I. Parameter Space Exploration with 2D Simulations

Benjamin Wu, Sven Van Loo, Jonathan C. Tan, Simon Bruderer

GMC Collisions as Triggers of Star Formation. II. 3D Turbulent, Magnetized Simulations

Benjamin Wu, Jonathan C. Tan, Fumitaka Nakamura, Sven Van Loo, Duncan Christie, David Collins

GMC Collisions as Triggers of Star Formation. III. Density and Magnetically Regulated Star Formation

Benjamin Wu, Jonathan C. Tan, Duncan Christie, Fumitaka Nakamura, Sven Van Loo, David Collins

GMC Collisions As Triggers of Star Formation. IV. The Role of Ambipolar Diffusion

Duncan Christie, Benjamin Wu, Jonathan C. Tan

GMC Collisions as Triggers of Star Formation. V. Observational Signatures

Thomas G. Bisbas, Kei E. I. Tanaka, Jonathan C. Tan, Benjamin Wu, Fumitaka Nakamura

GMC Collisions as Triggers of Star Formation. VI. Collision-Induced Turbulence

Benjamin Wu, Jonathan C. Tan, Fumitaka Nakamura, Duncan Christie, Qi Li

2D Investigation of Collisions 3D Investigation of Collisions Star Particle Formation Prescriptions Ambipolar Diffusion Synthetic Observations Internal Turbulence

Initial Conditions and Parameter Study

To study the role of ambipolar diffusion, ideal MHD and non-ideal MHD runs with

• therwise identical parameters.

v = +5 km/s v = -5 km/s

2 p c

nH = 100 cm-3 M=1.1x105 M☉ B=10 uG Numerical Parameters 1283 pc3 box with a top grid of resolution 1283 4 levels of refinement, resolving the Jeans length by 8 zones Smallest grid: Δx = 0.0625 pc Physical Parameters Cloud Mass-to-flux ratio: 3.8 Cloud mass: 9.3 x 104 Msun Cloud turbulence with Ms = 23

Chemistry

• Chemical model developed in Wu+ (2015) including 31 chemical species
• Using PyPDR and CLOUDY, equilibrium chemical abundances are calculated for each value
• f gas density and temperature.
• UV shielding effects included by assuming AV = f(nH)
• This is used to calculate heating and cooling rates for the gas.

Equilibrium Temperature Curve Limitations

• The model doesn’t allow for non-equilibrium chemistry.
• UV plays an important role in determining where molecules can form. The fixed prescription

for AV precludes variability in where this transition occurs.

Actual Simulation Result

Chemistry

• Chemical model developed in Wu+ (2015) including 31 chemical species
• Using PyPDR and CLOUDY, equilibrium chemical abundances are calculated for each value
• f gas density and temperature.
• UV shielding effects included by assuming AV = f(nH)
• This is used to calculate heating and cooling rates for the gas.

Chemical Abundances at Equilibrium Temperature

(Only most important ions and neutrals shown)

Limitations

• The model doesn’t allow for non-equilibrium chemistry.
• UV plays an important role in determining where molecules can form. The fixed prescription

for AV precludes variability in where this transition occurs.

Collision Evolution: The Movie

The fiducial 10μG colliding case with ambipolar diffusion. Non-Colliding Non-Colliding

• Slower collisions (5 km/s) develop more slowly, with a less high density gas

and a more extended morphology.

• Faster collisions (20 km/s) result in more localized, denser objects which

develop more quickly. Higher temperatures are observed around the shocked regions.

Qualitative Results from Ideal Simulations

A large parameter study using this setup was performed in Wu+ (2016) in the ideal MHD limit. Collision Speed Field Orientation

• For fields parallel to the collision axis (𝜾=0°), gas can easily move along the

field lines, resulting in faster collapse and

• A Perpendicular field (𝜾=90°) results in a build up of magnetic pressure,

slowing collapse.

Including Ambipolar Diffusion

• The induction equation deviates from ideal MHD through the inclusion of

ambipolar diffusion terms on the right hand side:

• The 2nd order Li MHD solver in the publicly available ENZO code has been

modified to include ambipolar diffusion as an explicit update. This puts a strict requirement on the timestep:
 
 


tAD ∝ ∆x2

ηAD

∂B ∂t − r × (v × B) = −cr × (ηADj⊥)

• Adding ambipolar diffusion (ion-neutral drift) in the strong coupling limit. At the

densities investigated, the Ohmic and Hall terms can be ignored due to the small resistivities.

⇣

∂eρ ∂t

⌘

AD = c2ηAD 16π2 |r ⇥ B|2

• Include resistive heating

Ambipolar Diffusion Resistivity

• We calculate the ambipolar diffusion resistivity in the standard manner for

weakly-ionized gases.

• The UV field and the transition from atomic ions to molecular ions limits the

resistivity at low density

• At high density, the resistivity agrees well with results from fixed

temperature, single ion models for the resistivity

Limitations

• No dust grains. They don’t become the 


charge carrier until at least nH = 107 cm-3, but
 they do allow for freeze-out which alters the gas
 chemistry (e.g., Tassis+ 2012).

• No heavier atomic ions such as Na+, Mg+, etc.

H2 with HCO+, H3+ and H3O+ H2 with C+ and H+ H with H+

B=10μG

Ambipolar Diffusion Resistivity

• We calculate the ambipolar diffusion resistivity in the standard manner for

weakly-ionized gases.

• The UV field and the transition from atomic ions to molecular ions limits the

resistivity at low density

• At high density, the resistivity agrees well with results from fixed

temperature, single ion models for the resistivity

Limitations

• No dust grains. They don’t become the


charge carrier until at least nH = 107 cm-3, but
 they do allow for freeze-out which alters the gas
 chemistry (e.g., Tassis+ 2012).

• No heavier atomic ions such as Na+, Mg+, etc.

H2 with HCO+, H3+ and H3O+ H2 with C+ and H+ H with H+

B=10μG

ni ∝ n1/2

n

η ∝ (αρiρn)−1

New Simulations: End States

Since the ideal MHD runs are so similar to the AD runs on the largest scales, they have been omitted.

Colliding Non-Colliding 10μG 30μG

Non-Ideal MHD Ideal MHD

The Case of Colliding Clouds with B=30μG

The only scenario to show visually distinguishable differences was the strong field colliding case. 
 
 The non-ideal case shows increased fragmentation and higher surface densities.

Distribution of Gas Densities

Colliding Non-Colliding

Gas Heating Due To Resistivity

Drag between the ions and neutrals provides an additional source of gas heating. 
 
 Where or no this produces significant effect has been debated with the results depending primarily on the cosmic ray ionization rate 𝜂CR. Padoan+ 2000,2012, Li+ 2012 Only noticeable deviations between the ideal MHD and AD runs are seen in the colliding

• simulations. Deviations in temperature begin around the local peak in resistivity.

Density-Weighted Gas Temperature

B-⍴ Relation

The scaling of the magnetic field with density is assumed to take the form

B ∝ ρκ

κ is poorly constrained observationally, but is expected to be in the range 0.47 - 0.67 e.g, Crutcher+ (1999), Crutcher (2012)
 
 We get a shallower relation with κ ~ 0.4 for all simulations.

Why?

• Gas accretion along the field lines increases


density without increasing the field

• In the case of flattened objects and cooling gas


the exponent should be less than 0.5 .

• Resolution effects. Higher resolution runs will


be able to pin this down more.

Histogram of Relative Orientations

The histogram of relative orientations is a measure of the relative orientation of the magnetic field relative to the local density gradient (Soler+ 2013, also discussed in his talk earlier.)
 
 We looked at the HRO along each line of sight for the colliding simulations. We do not see significant deviations between the ideal and non-ideal runs. X Y Z

High(er) Resolution Simulations

Mass Function at 2 Myrs

• Rerun the simulations at a higher resolution (Δx = 0.015625 pc) to improve the

model.

• Using the astrodendro package to extract cores in projection.

High(er) Resolution Simulations

• Rerun the simulations at a higher resolution (Δx = 0.015625 pc) to improve the

model.

• Using the astrodendro package to extract cores in projection.

Mass Function at 2 Myrs 3 Myrs 4 Myrs

High(er) Resolution Simulations

• Rerun the simulations at a higher resolution (Δx = 0.015625 pc) to improve the

model.

• Using the astrodendro package to extract cores in projection.

Mass Function at 2 Myrs Warning: Take this with a grain of salt! The simulations which are run to 4 Myrs are low resolution, violate the Truelove condition, and lack feedback/star formation which could arrest accretion of gas onto cores (which continues as the clouds are colliding).

Simulated Observations

Simulation Synthetic Obs (at 5 kpc) Graduate student Cheng Yu (Poster 10) has been observing sites of massive star

• formation. He recently (the last few days) processed the 10μG simulation data to

see how the observed structure changed.

Summary and Conclusion

Developed a resistivity model that covers the transition from atomic ions to molecular ions, resulting in deviations from power law behavior for η Simulated colliding and non-colliding clouds, using both ideal and non-ideal
 MHD, for both strong and weak field cases. No evidence for changes in large-scale structure, but in cases of stronger fields ambipolar diffusion can accelerate the collapse.

Ongoing and Future Work

Higher resolution simulations to test convergence and to better resolve clump- like/core-like structures.
 
 Introduce stars/sinks and feedback to more accurately regulate star formation.