# Update 11/30/2015 - Eddie

- I've applied to several jobs now, but need to do more.

- Working on rewrites for paper. Plan on finishing it by the end of this week.

- MHD version of 3D pulsed jets was having some restart issues, but I fixed it. Below is an image from a run with an initially purely toroidal field with beta = 1, with 64 cells per jet radius. This run (6 out of 120 frames) took 3 hours on 576 cores. The current standard output estimates that the run will take about 3 weeks to finish. Perhaps it's a better idea to do a longer run at a lower resolution (32 cells per jet radius) before continuing with this production-level run. I just don't want to waste time and resources if there turns out to be some difficult-to-explain-weirdness in the jet at later times.

# Prescription for making line projections from Planetary Sims

The prescription of Bourrier et al is to calculate (at each pixel) the average optical depth for range of velocity bins with spacing (or frequency bins with size , so that

So we have

and

Now to get the line profile in terms of velocities, we can start with the line profile in terms of frequencies:

and realizing that this is a distribution, we can use

where

so

and

to get

Putting this all together we have…

Now if we bin the column densities into velocity bins, we have

and

and we have

or

where

Now

is of order 20 km/s and is 76 m/s… so if , then the integral may as well go to infinity and we have

and for

(wave arms in air for a bit)

so we have

Or at least that's how I get agreement with their equation 11…

So were I to implement this approach, I would create projections (integrations along LOS) of

where

where Saha equation - or balancing radiative recombination with direct ionization… They give very different answers for the ionization fraction at the planet wind temp.

corresponds to the bin that the LOS cell velocity lies within and is the ionization fraction computing using either the## Remaining questions

- How to chose the ionization fraction? - Need to balance photo ionization with radiative recombination
- We should use thermal broadening (which dominates over natural broadening)..
- Binning particle velocities before convolution seems numerically expedient - but binning errors are orders larger than convolution corrections…?
- Why not just numerically approximate integral of line profile - and calculate contributions to each absorption bin for each cell.

## Thermal broadening

It should be more accurate to calculate the LOS velocity and the thermally broadened line profile, and then calculate the contribution of that profile to each bin in frequency space. The thermal broadening profile is just a Gaussian, so using the error function we can calculate the contribution to each bin…

Now without thermal broadening, we have

however, with thermal broadening, we have

where

which gives us

Now the integral over

is a convolution with a lorentz and gaussian profile - which gives a Voight profile… however, the thermal broadening is much larger than the natural broadening, so we can approximate the natural broadening as a delta function…

which gives

or upon integrating the exponential, we get

So for each frequency bin, we can create a LOS integration of a corresponding integrated opacity

where

is the number density of neutral Hydrogen## Photoionization

Also need to update code to include photoionization rates as well as direct ionization and radiative recombination…

Photoionization rate can be calculated from

We can approximate

where

and

and we can calculate the luminosity from Planck's law integrated over the area and solid angle…

where

and

Putting this all together, we get

Now assuming a temperature of

, this gives

where

and a photoionization time scale (at the .047 AU) of .0435 yr

Here is the same plot as before, but included are the equilibrium ionization fraction as a function of temperature for material at the orbital separation and with densities of 1e7 and 1e9 particles/cm^{3
}

Now in Bourrier et al, they leave the photoionization rate a free parameter and adjust it between .5, 1, and 5 times the solar value.

They quote the ionizing flux at the solar minimum from

which cite

http://www.aanda.org/articles/aa/pdf/2008/43/aa8810-07.pdf

which have a photoionization rate at 1 AU of 1e-7/s or 115 days. At .047 AU this would be 6 hours which is close to the 8 hours shown in Bourrier et al.

This would imply a photoionizing rate of

currently I am using 3.5808d19

# meeting update

I am building a ticket on RadFeedback from sink particles as I go along with this development: https://astrobear.pas.rochester.edu/trac/ticket/442

Been in touch with Federrath and learned a bit more about how Disperse works, wrote this up here: http://astrobear.pas.rochester.edu/trac/wiki/u/erica/Amira

Am building a talk for my qual and am modifying the paper draft to be given as my qual report

Working on buildig feedback routines for radiation transfer — going to modify the bondiaccretion routine to do this, am close to understanding what the routines are doing there.

# Update 11/16/2015 - Eddie

- working on edits for 3D bow shock interactions paper

- applying to jobs

- still trying to figure out waviness in 3D precessing jets
- Things I have tried so far:
- primitive limiters instead of characteristic
- lower CFL
- outflow object inside lower z boundary
- velocity fade in radial direction
- no pulses
- H viscosity
- apply diffusion
- smaller precession angle

- Noticed some potentially odd things:
- jet boundary looks tilted in first frame, likely due to precession in magnitude of the velocity in z-directio
- the magnitudes of the velocity in every direction x, y, z seem to be precessing. I don't think this is what we want. I think vz should be constant in time (except for the pulsations of course), and vx and vy should change but in a way such that at any given time they are constant throughout the outflow object. In the current implementation, there appears to be a phi dependence on magnitude.

- Things I have tried so far:

# 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.

# Update 11/09/2015 - Eddie

- Made image from HH 2 for my 3D clumpy paper. This is to compare with the multi-clump simulation since both show a shock "sheet".

- We wanted to do another comparison figure with HH 34 to show lateral motion, but this is looking a bit trickier than I thought it would be because the .fits images are not aligned with each other. Waiting to hear back from Pat to see if there is an easy way to deal with this.

- Having issues with Grass and with my account on the Rice machine, so I don't have all of the data from some of my new 3D pulsed jet runs. Below are images from a 0 deg precession and a 1 deg precession run. I have simulation data for a run with increased refinement around the outflow object, and a run where the outflow object is inside the bottom domain boundary; I just can't get to the data right now. Below is an image comparing runs with 0, 1, and 3 deg precession from left to right respectively.

- Lastly, I worked on my CV and I've been busy for the past few days applying for some national lab jobs.

# M2-9

Model Description:

where

, , and are varibles.The jet is bipolar jet and has open angle of only

so the solid angle is only . I calculate with given , and .The outflow density of the jet is

.The base grid is

and I added 3 levels of AMR. AGB star has radius of 4 AU and 1.4 solar mass (as in the paper by Garcia-Arredondo and Frank 2004) and the companion has 0.6 solar mass and radius of 2 AU.This is the case of strong jet, which is,

where

, so which is just the escape velocity of the AGB star.Below is the weak jet case.

where

, so unchanged.# observational diagnostics: Ly alpha absorption

A recipe for Ly alpha profiles by Bourrier and Lecavalier des Etangs 2013 can be found here in their section 2.4.1 http://adsabs.harvard.edu/abs/2013A%26A...557A.124B

# Colliding Flows draft

My edits of the paper draft are done as far as I can go right now. I stopped at the spectra section which is the weakest section of the paper and is not yet telling a coherent story. I fixed one of the spectra plots it looks better. Not sure where to go with the spectra section at this point, whether I should take the time to improve this section now or not. I still need to add a discussion section to the paper as well.

I'm almost inclined to take the spectra section out of the paper entirely.. Thoughts?

# Update 11/02/2015 - Eddie

Using ds9 and gimp to generate a couple of figures for my 3D clumpy paper that will show an HST image and a simulation image side-by-side. Below is an example:

### 3D Jets

I've tried several things, and I still see the waves in all cases:

- For some reason, the exact Riemann solver does not work well. Code stops early due to nan in flux.
- Added velocity fade from 0 to Rjet. This is not a precession fade, just a velocity magnitude fade.
- Turned off characteristic limiters, use primitive limiters instead.
- Turned on ApplyDiffusion.
- Lowered target CFL from 0.3 to 0.1.
- Turned off pulsations.

Below is an image from the run with no pulses:

# Planetary Wind and Mass Loss Rate for HD209458b

## 1. AstroBEAR code and Set-up

In this study we use the AstroBEAR code (Cunningham et al 2009) to perform 3D hydrodynamic and magnetohydrodynamic numerical simulations and model the "Hot Jupiter" HD209458b ( Ballister et al 2007). AstroBEAR is a fully parallelized AMR MHD multi-physics code which currently includes modules for the treatment of self-gravity, ionization dynamics, chemistry, heat conduction, viscosity, resistivity and radiation transport via flux-limited diffusion. For our simulations we use a polytropic equations of state (the polytropic index

In this part we only focus on the planetary wind (hydrodynamic) for HD209458b without considering the star and stellar wind. We present the simulation results of planetary wind launching using the AstroBEAR code and calculate the mass loss rate of the planet using the density and velocity from the simulation data.

## 2. Parameters and Initial Conditions

The mass for H209458b is SouthWorth et al 2010). We use for the temperature of the planet.

where is the Jupiter mass (Wang et al 2002) and the radius is where is the Jupiter radius (

measures the strength of the planetary wind. For this , a Parker-type thermally driven hydrodynamic wind is expected.As a comparason, the sun with its corona has .

We use

as the initial density for the planet atmosphere. For the initial temperature, we use two set-ups: 1) set the outer boundary of the planet with temperature (without temperature profile or spherically-launching wind) and 2) set the outer boundary of the planet with azimuthally variable temperature where is the sub solar point and (with temperature profile). For the 2nd case, we use similar initial set up to that of Stone & Progra (2009). We summarize the parameters we use for HD209458b are shown in Table 1.
Table 1. Parameters for HD209458b

## 3. Resolutions

In our simulations the planet is considered as an internal boundary and the physical quantities are fixed during the simulation. Our computational domain consists a cube of size

with resolution for the base grid and totally -level of AMR is used. This makes the finest resolution up to zones per .## 4. Planetary Wind Results and Mass Loss Rate

In Figure 1, we show the 3D simulation results for both without-temperature-profile and with-temperature-profile cases. For the without-temperature-profile case (top panels in Fig.1), we can see the planet temperature launches a spherical thermal wind and Mach=1 contour is approximately spherical or circle in 2D cross section. While for the with-temperature-profile case (bottom panels in Fig. 1), there's flow across from the dayside to the nightside and the Mach=1 contour shows there's a weak shock between two sides.

in color | |

in gray |

Fig. 1 Steady state planetary wind solution of cross section in the xy-plane for simulations without (top) and with the temperature profile. Flow and density are shown on the left and thermal structure and M=1 contours are shown on the right. The small circle at the center shows the radius of the planet.

The mass loss rate can be calculated by integrating

With the planet temperature

, we can also analytically solve the problem in 1D with Parker's wind solution (Parker 1958). The mass loss rate with Parker's wind solution gives . The estimated mass loss rate for H209458b can be found in Table 2.Methods | Mass Loss Rate |

3D Simulation Without Temperature Profile | |

3D Simulation With Temperature Profile | |

Analytic Parker wind Solution |

Table 2. Estimated Mass Loss Rate for HD209458b

## 5. References

Ballister, G., King, D., & Herbert, 2007, Nature, 445, 511

Cunningham A., Frank, A., Varniere, P., Mitran, S., Jones, T. W., 2009, ApJS, 182, 519

Southworth, J. 2010, MNRAS, 408, 1689

Wang, J. & Ford, E. B., 2011, MNRAS, 418, 1822

Parker,E.N. (1958) ApJ, vol. 128, pp.664-676