# Bondi Flow/Accretion Subgrid Model Questions

** The equations for Bondi flow admit 4 classes of solution only two of which are physical**

- A solution with u(r) = 0 at r = infinity. (AB'C' in Bondi 1954 Fig 2)

- A solution with u(r) = 0 at r = 0. (A'BC in Bondi 1954 Fig 2)

Note both are of type ii in Bondi's formulation.

From first principles we expect the global solution (not just what happens in the kernel to be solution 1. We have a spherically collapsing cloud which has

.That solution however must be matched as cleanly as possible with what happenes within the kernel (whose radius is

) with the kernel values being given asSo the question becomes are we expecting that within the kernel we may switch from solution type 1 to solution type 2?

Physically this can only occur if a shock has formed at the "surface" of the accreator which has then expanded such that

.So given the values of velocity and location, we can calcualte x0 and y0, which give us lambda and lambda_c. This then divides the x0-y0 space into super/subsonic and super/subcritical regions.

- In the yellow region, you can integrate inward (or outward) without ever becoming subsonic.
- In the cyan region you can integrate inward (or outward) without ever becoming supersonic.
- In the left supercritical region,s you should be ok - as you should be able to integrate inward - though not outward
- The right supercritical region presents a problem - as the integral inward will diverge. It is these regions which have no steady state solution and require something like the 'shock assumption'

And for reference, here's the same figure ignoring Gamma

Not the line dividing sub/super critical follows x0^{2}*y0*z0=lambda=lambda_c - as z0 = 1 by definition.

And here's the same plot but for a range of

.# Exo-civilization Planetary Feedback Equation Derivation

# Exo-civilization Planetary Feedback Equation Derivation

## Begin with most general form.

We begin with three coupled equations for the interaction between a exo-civilization population , a resource and which they draw energy from ® and the state of the planetary environment (E).

In the equations above generally B is used as "birth" terms that increase the variable and D is used for "death" terms that decrease the variable (though the meaning depends on the case). Each terms may have dependencies on the other variables - the "phase space" variables (N,R,E) - and other parameters/constraints.

In the above,

is the population natural birth rate.

is the population death rate.

is the additional population birth rate gained from extraction/consumption of resource .

is the extraction/consumption rate of resource due to activity of .

is the modification of extraction/consumption rate of resource due to changes in planetary environmental state .

is measure of capacity of planetary environment to return to an pre-civilization equilibrium state . is the forcing of the planetary environment from pre-civilization equilibrium state due to non-resource based population activity.

is the forcing of the planetary environment from pre-civilization equilibrium state due to resource based population activity.

## Choosing forms for the terms.

All alpha terms represent either growth rates or measures of the effect of variable

on variable ..

where the death rate is now dependent on an environmentally dependent carrying capacity K(E).

where

is a measure of the additional birth rate gained from extraction/consumption of resource R and is the per captia extraction/consumption rate of resource R

where

is the critical environmental state beyond which resource extraction is no longer possible.

Finally for the carrying capacity we choose,

# Exo-civilization Planetary Feedback Equations

Our final equations are,

# Estimating Timescales for Radiation Diffusion

So this is an execerise in thinking dimensionally and in order of magnitudes.

Consider the equation for radiation energy conservation ignoring a bunch of terms that should be of lower order

The second term on the right hand side tells us about the diffusion of radiation and the right hand term tells us about coupling with matter.

Lets consider the diffusion term to get an estimate of the timescale,

We do this terms of dimensions (L = length, T= time etc). Radiation energy density E is, for example

So the diffusion term reads

which has units of energy of time as would be expected. To get a timescale for radiative diffusion

we can write things in terms of the scales of the problem and

or

Note

drops out here
Now we just have to find values of the Rosseland opacity relevant to something like a dusty in falling protostellar envelope. I am seeing the Rosseland opacity being given in units of cm^{2/g which means we will need to multiply by a density scale in the above expression i.e.
}

where

is the value we get from tables and is our density scale.Here is a paper I found that gives some useful opacity information

http://www.aanda.org/articles/aa/full/2003/41/aa3802/aa3802.right.html

Check out this table from the paper

# List of Key Simulation Papers for Planet Winds

Matsakos et al 2015 http://adsabs.harvard.edu/abs/2015A%26A...578A...6M

Tripathi 2016 http://adsabs.harvard.edu/abs/2015ApJ...808..173T

Frank et al 2015 http://adsabs.harvard.edu/abs/2015IAUS..314..237F

Stugaret 2015 http://adsabs.harvard.edu/abs/2015ApJ...815..111S

Christie http://adsabs.harvard.edu/abs/2016arXiv160105302C

Schnieter 2016 http://adsabs.harvard.edu/abs/2016MNRAS.457.1666S

Scnieter 2007 http://adsabs.harvard.edu/abs/2007ApJ...671L..57S

Bourrier 2013 http://adsabs.harvard.edu/abs/2013A%26A...557A.124B

Cohen 2009 http://adsabs.harvard.edu/abs/2009ApJ...704L..85C

Cohen 2010 http://adsabs.harvard.edu/abs/2011ApJ...733...67C

# Paper on Exo-Planet Transits with Bowshock

Here is a paper suggested by Ian with results (and some details) on modeling transits when a bow shock from a stellar wind interacting with a planetary magnetosphere is present.

# Clumpy Simulation Figure Set

The big question now is what figures to make/show. Below are my suggestions.

1) We need an initial figure set for a single 2 clump run which illustrates the basic kinds of phenomena we are seeing. I suggest this should include

a) A column density "movie" figure showing the simulation at 3 (or 4) times. b) An [SII]+Ha intensity "movie" figure with same frame times as a) c) A single (blow up) frame of the [SII]+Ha with arrows/labels for features we want to explore in text

2) An initial figure set for a single 3 clump run which builds off 1)

a) A column density "movie" figure showing the simulation at 3 (or 4) times. b) An [SII]+Ha intensity "movie" figure with same frame times as a)

3) Seperation Comparison

a) no need for "movies" here just the best example(s) illustrating how seperation effects things. Only need [SII]+Ha.

4) Velocty Comparision

a) (same as above) Perhaps we make sure we are using different simulations for each of these comparisons so that in the end we are not repeating showing the same sim.

5) Orientation comparison

a) (same as above)

6) 10 clump run.

a) A single column density frame b) A movie of 3 (or 4) [SII]+Ha intensity images at a single orientation/inclination

# Adam's Edits of Erica's paper

My edits

# Erica's paper notes

Some feedback on Erica's paper

# Must Read Planetary Wind Paper.

A recent paper used PLUTO to carry forward full MHD orbital dynamics of planetary winds interacting with a stellar wind.

This paper is exactly where we want to be going. So for Jonathan, Baowei and I reviewing this in detail is a must. The authors are Matsakos, Uribe & Königl

# A reduced grid space for Planetary Wind Runs

The stand-off distance for the stellar wind/planetary wind R_so can be computed simply by balancing the ram pressure

Thus we have

Thus dropping the stellar wind density by 10 should increase the stand-off distance by ~ 3.

Also lets keep keep v_s the same and change the T_s to modify the Mach number

Here are the runs I think we should focus on

# | lambda | Solar Wind Mach # | |

1 | 1.01 | 0.8 | 10^{-5
} |

2 | 1.01 | 5.0 | 10-5 |

3 | 1.3 | 0.8 | 10^{-5
} |

4 | 1.3 | 5.0 | 10-5 |

# Grid of Runs for Planetary Wind Problem

Lets begin with all runs having

** Hot Jupiter **

** Stellar Wind **

km/s

Other parameters.

Resolution: 60 zone/planet radius

Allow planetary wind to fill grid for 2 of its own crossing times ( L_grid/V_pw(max) ) then turn on stellar wind and let it run for 10 crossing times ( L_grid/V_s )

# | lambda | Solar Wind Mach # | |

1 | 1.01 | 0.8 | 10^{-4
} |

2 | 1.01 | 0.8 | 10-4 |

3 | 1.3 | 0.8 | 10^{-4
} |

4 | 1.3 | 0.8 | 10-4 |

5 | 1.01 | 5.0 | 10^{-4
} |

6 | 1.01 | 5.0 | 10-4 |

7 | 1.01 | 5.0 | 10^{-6
} |

8 | 1.01 | 5.0 | 10-3 |

9 | 1.3 | 5.0 | 10^{-4
} |

10 | 1.01 | 0.8 | 10-3 |

# Some Planetary Wind Tests

Results of some \gamma = 5/3 runs.

Test Run A: standard. 200x400. 1 level of refinement. Tmax = 1.0

Test Run B: standard. 100x200. 0 level of refinement. Tmax = 1.0

- seeing weird behavior?

Test Run C: standard. 100x200. 0 level of refinement. Tmax = 4.9; 50 frames

- seeing weird behavior.
- Wind does not expand uniformly

attachment:C_0404015_rho.gif

Test Run D: standard. 100x200. 1 level of refinement. Tmax = 4.9; 50 frames

- no change from C

attachment:D_0404015_rho.gif

Test Run E: standard. 200x400. 1 level of refinement. Tmax = 4.9; 50 frames

- no change from C, just better resolution
- is it the \gamma=5/3 or something about timing? Almost looks like the wind is turning off.

attachment:E_040415_Full.gif

Test Run F: standard. 200x400. 1 level of refinement. Tmax = 4.9; 50 frames

- \gamma=1.01

# Binary Star Fall Back Disk Variable Set

Here are variables which go into the HAFBAD problem (Highly Abstracted Fall Back Disk)

**Stars**

Primary Mass (solar masses):

Binary Mass ratio:

Orbital Separation:

**Outflow in the form of a brief Shell**

Velocity of Shell (< escape velocity but >> sound speed:

Density of Shell:

Temperature of Shell (with sound speed constraint:

Rotation of Shell:

Duration of shell ejection

**Simulation
**

Resolution defined in terms of injection radius R_0:

# Planet Wind/Stellar Wind Cooling Times

So we have been seeing lots of cool instabilities in the simulations of the planet wind/stellar wind interactions. So far all these sims have been run as isothermal with

This means we expect cooling to play and important role for both the shocked planetary wind (pw) and shocked stellar wind (sw). I wanted to check these assumptions and so I did a brief calculation.

We are taking about Hot Jupiter's here so the orbital radius is small

## Stellar Wind

At that radius the stellar wind is still acceleration and is likely subsonic (M<1). That means no shock. If I assume its a solar type star with a corona the parameters are likely

and using

gives me a number density of

To get a cooling time scale I just use

and I approximate the cooling rate

Putting in #s I get

To see if the wind actually cools I need a dynamical time to compare it to which I chose to be the time crossing time of the shocked flow past the planet (I use Jupiter's radius for the planet and assume the interaction happens at 10 R_j)

This gives me

Thus

and the stellar wind will not cool.

## Planetary Wind

For the planetary wind shock things look a bit better but not too much.

# My First Movie

This is density
[
[Image(movie10019.png,width=300)]]

This is contours of velocity and energy

# One T rad-transfer vs not

# 11.19 LLE Meeting Results

Adam,

Three people have expressed some interest in AstroBEAR: Riccardo, Radha and Suxing. The main issue is whether anybody would have time to work with a new code. That might be influenced by the level of support that you can supply and if we can find a student willing to work on these problems.

Riccardo would want to try a variation of the problem that you were originally looking at (presumably with a corrected treatment of the boundary conditions). Apparently no additional physics modules would be required. His comments were:

I am interested in this code if I can find at least one problem that is very well defined, doesn't require upgrades to the code and for which our codes cannot provide an answer. I think I may have found it, 3D ablative RT in a slab with gravity. That could tell us if there is a major differentce in 3D multimode ablative RT with respect to 2D. It uses the same input I already gave to Adam years ago.

Radha and Suxing might be interested to use AstroBEAR to look at other problems that would require developing some additional physics modules. A description of these is in the attachment.

Possible physics issues that can be addressed with AstroBEAR Nov 9, 2012

- B. Radha and S. X. Hu

Problem classes fall under either short wavelength studies or 3D studies. Problems requiring some form of laser energy deposition, such as study of imprint or evolution of target defects are not listed below.

- Short wavelength mixing at plastic (CH) gas (deuterium or deuterium/tritium etc.) interfaces for different Atwood numbers and materials with different atomic numbers, during the deceleration phase of implosion and hot-spot formation.

Physics issue: How significant is the classical interface for determining target performance (fusion yields)? Physics needed:

- Implicit heat conduction – Can we get away with explicit if we limit time steps (probably not)
- Multigroup diffusive radiation transport – Radiation plays an important role in setting up the density profile and the growth of Rayleigh –Taylor at the related unstable interface influences the growth at the material interface.

Scope:

- This problem is not accessible by HYDRA.
- While radiation is not critical to initial studies, they need to be added eventually to realistically model plastic shell implosions.
- How do we know that numerical noise is not overwhelming the problem?

- 3D assembly of hotspot

Physics issue: How does 3D physics influence the assembly of the hotspot in cryogenic DT-implosions? Physics needed:

- Implicit heat conduction – Can we get away with explicit if we limit time steps (probably not)
- Alpha transport

Scope:

- This problem can be tackled by HYDRA though the effort at Livermore seems to be more toward modeling the integrated implosions as opposed to trying to understand the basis of the physics.
- Where will the computational resources come from?

- The effect of magnetic fields in implosions (3D problem)

Physics issue: Do magnetic fields influence heat conduction in the compressed core – particularly for Polar Drive implosions where we see significant variations in the symmetry of the hot spot in OMEGA implosions.

Physics needed:

- Implicit heat conduction – Can we get away with explicit if we limit time steps (probably not)
- Self-generated magnetic fields.
- Effect of magnetic fields on heat conduction coefficients.

Scope:

- This problem is likely unique to LLE and Polar Drive.
- Where will the computational resources come from?

- Studying the magnetic field reconnection in laboratory astrophysics NLUF experiments on OMEGA (this could be a possible application in not-so-near future)

Physics issue: How magnetic field reconnection starts and how magnetic energy is released as kinetic energy of particles?

Physics needed:

- Self-generated and/or external B-field evolution
- Multigroup diffusive radiation transport

Scope:

- This is one of the grand challenges in astrophysics and is unrelated to ICF. It belongs to the basic science category. However, it may relate to LLE through reconnection experiments being conducted on EP.
- The 3D nature might be crucial.

# Nice Series of CFD notes

http://www.its.caltech.edu/~appelo/ae232/lecture1.pdf

You have to change the lecture # to step through the series

# Agenda for Today

Discussion of Senior Programmer Applicants.

Conferences.

Oral Examinations.

Research Discussion.

# Meeting tonight at 6 pm

Agenda

Plan meeting schedule for semester

Questions for senior programmer

Research review

# Agenda 4 today

Schedule of meetings for semester

Schedule for this week

Research review

# Meetings this week

1) Monday 4 pm: The usual research review 2) Tuesday 4pm: A special new users group meeting where WE ALL are new users and will do a general code review. Jonathan will present an overview of the AMR methodology and the current code capabilities and we will then run through an overview of what the code can can not do. 3) Thursday morning: (Optional for Most except but Eddie and Jason should attend if possible): We will be running experiments at the LLE on Wednesday and on thursday morning there will be a meeting to review the shots and more importantly discuss future directions. More details will follow

# Thoughts on Collapse Papers

Just reading over the Foster & Chevalier

http://adsabs.harvard.edu/abs/1993ApJ...416..303F

The collapse of a Bonner-Ebert Sphere appears fairly complex with solutions approaching the Larson-Penston (1969!) solution or the Shu 1977 solutions or the Hunter 1977 solutions depending on intiial conditions in the BE sphere.

# Cooling Method Paper

Here is a link to the paper we discussed about a new method for cooling

http://adsabs.harvard.edu/abs/2009ApJS..181..391T

And here is a link from the guy who told me about it Allard Jan van Marle on AMR and cooling

# Agenda Items

I am hoping that folks will start to get their stuff on the Wiki by sunday night (post with general description of results for that week) so I can check them out and have an idea for setting agenda's.