# Update CEE energy budget project

## New Work

**Energy of bound and unbounded mass**- Unbounded Mass

- Bounded Mass

**Mach number and speed of sound at particles**- gas speed of sound

- gas Mach number

- particle Mach number in gas

**In orbit bound and unbounded mass**- area we plot

https://www.pas.rochester.edu/~yishengtu/CEE_gp_meeting_08272018/D143_orbit_movie.gif

- energy of gas inside orbit

- Unbounded mass of gas inside orbit

**Energy movie**- kinetic energy

https://www.pas.rochester.edu/~yishengtu/CEE_gp_meeting_08272018/Ekin_D200.gif

- some frames

70:

71:

72:

73:

74:

75:

## Next Step

- Comparing between reduced resolution data and high resolution dat
- re-simulate, without changing softening radius, around frame 73 to understand the blast wave at frame 73

3.1 Using first few frames to determine how stable the star is https://www.pas.rochester.edu/~yishengtu/CEE_gp_meeting_08272018/First_few_frames_comparison_08272018.pdf OR 3.2 run another simulation for several dynamical time scale to ensure result.

- cooperate with Luke to prepare for paper

# Radiation pressure calculation

## Current calculation

Here I'm attempting to add the effects of ablation (more energy is absorbed by the layers being blown off than is required to unbind them), as well as the nonzero width of the bound torus (the gas at the inner edge of the torus will be more tightly bound than the gas at the orbital distance).

See these movies for some physical intuition. Note the steady state reached by the first - I've approximated this as two nested parabolas for the calculation.

## Other approaches

Ruth's 2009 paper shows that radiation pressure alone would be insufficient to produce the mass loss rate determined by observations. Since this calculation is concerned primarily with ablation of the planet itself, and assumes a priori that radiation pressure can accelerate planetary hydrogen to the orbital velocity, I'm not sure it's relevant to our current situation.

Shaikhislamov et al. used the reconstructed Lyman-^{14} phot/cm^{2}/s to calculate the pressure applied to the planetary wind: barye, which is about 2 orders of magnitude less than the pressure from their stellar wind (so they argue it's appropriate to neglect). Our torus is supported by a thermal pressure of ~8x10^{-7} barye, and a ram pressure (in the x direction) of ~10^{-11} barye (so insignificant compared to the thermal pressure).

# PNe and updates 08/27

## PNe simulation

x-z density profile at 6010.9, 6150, 6196.43, 6250 days.

http://www.pas.rochester.edu/~yzou5/PNe_simulation_movies/Old_movies/High_momentum_Day6250_rho_y-slice.gif

- ran simulation to 6250 days (250 days after quiescent phase), no self-gravity
- next: adjust refinement region

## Recombination

- still working on the equations

# Ionization transfer

To solve the ionization equations with scattering, you would want to use a diffusion equation. Something like

Now the equations are non-linear - so one has to iterate towards convergence. I found a good write-up of the method necessary in a paper on Enzo-RT (where they also use FLD for ionizing radiation transport).

# Radiation pressure initial steady-state status

Slowly-ramping (full flux around frame 80)

Quickly-ramping (full flux around frame 20)

As a reminder, here are the parameters for the planet:

Simulation domain: 20 R_p cube (0.0146 AU)

rho_p = 1.625d-15 g/cm^{3}

T_p = 3000 K (not really important as long as wind gets hotter - T_wind should be >5300 K for this planet)

M_p = 0.73 MJ

R_p = 1.529 RJ

a = 65 R_p = 0.0475 AU

M_s = 1.23 MS (for tidal forces)

F_UV = 2d13 phot/cm^{2}/s (Sun-like for orbital radius)

F_Ly-alpha = 4.1d14 phot/cm^{2}/s, 4.1d15 phot/cm^{2}/s, 4.1d13 phot/cm^{2}/s (HD209458b flux, 10x, 1/10x - would it be better to do 5x and 1/5x?)
(ramping up in approximately 1.5 CT, or 1/6 orbit)

# pnStudy: conical wind with wedge tip

## Add a wedge tip to test if it solves the "piston/knots" issue along the y-axis

- The wedge tip is added using a wedge angle and tangent line to the edge to original conical wind launching region (circle in the testing example). The new launching region is now the circle + a wedge with the Info%q as the values of initial ambient at the area. The wedge area is marked as red in the following picture

30 deg vs 15 deg vs 10 deg |

- Compare the result with(left panel)/without Wedge tip (wedge angle = 15 deg)

150 yr | no wedge tip; 15 deg wedge tip |

- Conclusion: seems making things worse..