Reduction of ambient pressure and density

• Note that pressure needs to be reduced to minimize ambient energy density
• Density needs to be reduced to minimize ambient mass

Review of literature

• In the table below, "UG" stands for uniform grid, and "MM" for moving mesh
• Note: In Ohlmann+16a relaxation runs, the ambient density and pressure are much higher: 2e-10 g/cc and set to "roughly match the surface pressure of the star". He also says that the pressure gradient at the surface is not fully resolved, so the star expands a bit (leading to artificial motions in the ambient medium that do not affect the star) and then stabilizes during the relaxation run.

Possible strategies

1. Simply reduce ambient pressure and density.
   • This would cause pressure scale height at primary surface to decrease and it would no longer be resolved with standard resolution.
     • Since the standard resolution in the bulk of the envelope was chosen to resolve the pressure scale height at the surface, might as well reduce it (from envelope maxlevel = 4 to, e.g., envelope maxlevel = 3)
       • This seems to be the strategy of other groups, who seem to have low resolution in the envelope (except near the cores). Our resolution is probably still high by comparison.
     • Since the scale height will not be resolved, this will lead to artifacts (pressure waves owing to numerical diffusion)
       • This will lead to high temperature regions or steep pressure gradients in the ambient medium, leading to spurious motions that slow down the code
         • This can be averted to some extent by setting MinDensity, which is the floor density in the simulation
2. First perform a relaxation run, and then follow the method of #1 above (as done by Ohlmann)
   • This is done by some other groups.
   • This could help to eliminate spurious motions in the ambient medium that slow down the code
   • We have argued in Paper 1 that performing a relaxation run with velocity damping does not make a big difference to the evolution
   • It is computationally expensive
   • Grid effects become severe during the relaxation run since the primary is not moving with respect to the grid
     • For this reason our relaxation run was only half as long as that of Ohlmann+2016 (we did not include the phase without damping)
   • In Ohlmann+2016, the relaxation run is peformed with high ambient pressure (Ohlmann, private communication). This ambient pressure is then removed for the simulation. To implement this, we need a way to change the ambient pressure without changing the star.
3. That last point leads nicely into this 3rd option. Use our current simulations which resolve the pressure gradients at the surface, but at the appropriate time, when the secondary has already spiralled in (some time after first periastron passage), use the ambient tracer to reduce the ambient pressure and temperature
   • This can be done suddenly or gradually
   • Implementing it in the code seems to be straightforward
   • Total energy of the simulation would not be conserved
   • There can still be artificial effects of the ambient before this time.
     • If box is enlarged considerably then initial ambient mass will be very large
       • This may be harmless but one would have to justify it.
4. Give the primary a hydrostatic atmosphere, which transitions to a uniform ambient medium at some large radius
   • Explored in a previous blog post (Run 199) and again below
   • It fails catastrophically, for reasons that are still not clear

Performing the Runs

• Runs performed on Anvil using 16 nodes (2048 cores)
• No queue time!
• Total allocation on Anvil is 3,312,000 SUs = core-hours
• 16 nodes = 2048 cores
• We have already used 7% of the allocation for testing.
• Want to redo the ideal gas and tabular EOS runs (Runs 282 and 277 — it is not necessary to redo 283)
• If each simulation is 500 frames (as before) and each frame takes an average of 2.5 hours on 16 nodes, we have enough left for 1.2 simulations. So we may need to ask for a supplement.

Strategy #1 from above

• Frame rate kept same as Run 282 (2e4 s) (recall Run 282 lasted for 500 frames = 115 days)
• Simulations were run up to frame 2
• In table below, "eml" stands for envelope maxlevel for refinement of bulk of envelope (innermost 6Rsun is refined at maxlevel 5), "wt" stands for wall time, and "fr" stands for frame
• MinDensity is the density protection setting in physics.data
• The first run, Run002, is the same as Run282
• Runs started from scratch (lRestart=F)
• For each run, first image shows density rho, second shows pressure P in dyn/cm2, and P/rho. In Run027 (tabular EOS), the third image replaces P/rho by temperature T in K.

ID	iEOS	Lbox (cm)	eml	rho_amb (g/cc)	P_amb (dyn/cm2)	MinDensity (g/cc)	wt fr0 to 1 (h:m)	wt fr1 to 2 (h:m)	artifacts	images
002/282	0	8e13	4	1e-9	1e5	1e-10	1:20	1:55	~none
003	0	8e13	4	1e-10	1e4	1e-11	5:00	6:40	minor
005	0	8e13	4	1e-10	1e4	1e-15	6 days (estimated)		I killed it	N/A
004	0	8e13	3	1e-10	1e4	1e-11	1:05	1:20	minor
007	0	8e13	3	1e-11	1e3	1e-11	1:30	1:30	moderate
011	0	8e13	3	1e-11	1e3	1e-12	4:30	4:45	high
009	0	8e13	3	1e-11	1e2	1e-11	1:30	1:30	moderate
010	0	8e13	3	1e-12	1e2	1e-13	1.1 days (estimated)		I killed it	N/A
012	0	8e13	3	1e-12	1e2	1e-12	4:50	4:50	moderate
018	0	8e13	3	1e-12	1e1	1e-12	4:50	4:50	moderate
019	0	8e13	3	1e-13	1e0	1e-13	1.1 days (estimated)		I killed it
020	0	8e13	3	1e-11	1e1	1e-11	1:30	1:30	moderate
021	0	1.6e14	3	1e-11	1e1	1e-11	2:20	2:20	moderate
022	0	1.6e14	4	1e-11	1e1	1e-11	1:30	1:30	moderate
024	0	1.6e14	4	6.63e-12	1e1	6.63e-12	1:58	1:53	moderate
026	0	1.6e14	4	6.63e-12	1e-1	6.63e-12	1:48	1:45	moderate
027	6	1.6e14	4	6.63e-12	1e-1	6.63e-12	3:31	3:29	moderate

• Run time is principally determined by MinDensity (compare 007 and 011)
• Reducing the pressure does not greatly affect the run time (compare 012 and 018 or compare 007, 009 and 020)
• Reducing the pressure does not drastically change the level of artifacts present (compare 007 and 009)
• Increasing the box size while reducing the base resolution proportionately does not greatly affect the run time (compare 020 and 022)
• Ideal gas runs are faster than tabular EOS runs by a factor of 2 (compare 026 and 027)

Strategy #4 from above

I again tried to perform a run with an exponential hydrostatic atmosphere transitioning to a uniform ambient at large radius. This run is very similar to Run 199 of previous posts. There are severe artifacts.

ID	iEOS	Lbox (cm)	eml	rho_amb (g/cc)	P_amb (dyn/cm2)	MinDensity (g/cc)	wt fr0 to 1 (h:m)	wt fr1 to 2 (h:m)	artifacts	images
006	0	8e13	4	exp to uniform	exp to uniform	1e-16	1 month (estimated)		catastrophic

Strategy #3 from above

ID	iEOS	Lbox (cm)	eml	rho_amb (g/cc)	P_amb (dyn/cm2)	MinDensity (g/cc)	wt fr47 to 47.1 (h:m)	wt fr47.1 to 47.2 (h:m)	artifacts	images
016	0	8e13	4	1e-11	1e-11	1e-12	1:52	2:26	severe at ghost zones only

• Shock-like structure moving in from boundary at supersonic velocity
• Ambient not getting modified correctly in ghost zones?

Discussion

• Strategy #1 seems promising, but how much do artifacts affect the inspiral?
• Setting MinDensity equal to ambient density helps to speed up the simulation (apparently by avoiding very high temperatures)
• Smaller ambient density slows the code (why?). Good compromise is 6.63e-12 g/cc, which is 0.001x the lowest density in the initial primary star
• Wall time is very insensitive to changing the ambient pressure. But very low ambient pressure (1e-5 dyn/cm2) caused the code to crash. Good compromise is 1e-1 dyn/cm2.
• Wall time is insensitive to box size Lbox, provided base resolution delta_0 scales with Lbox. However, code crashed for Lbox=3.2e14 cm (do not know why). Also, grid effects are slightly amplified for a larger box (with coarser base resolution). A good compromise is Lbox=1.6e14 cm, which is 2x the box size of Runs 282 and 277. This will allow us to simulate up to 500 frames (115 days) with very little envelope material leaving the grid.

Conclusions

• For a reasonable wall time, sufficient ambient reduction and minimization of artifacts, parameter values of Run 026/027 seem optimal.
• Now need to test whether these runs reproduce the higher resolution runs (Runs 282/277) sufficiently accurately over the first ~40 days when effects of the ambient on envelope gas are still negligible.