[Mesa-users] wd_diffusion doesn't work?

Tue Oct 3 20:44:20 EDT 2017

Hi Michael,

Fascinating question. I’m not sure I can give you a definitive answer here, but I’ll do my best.

The MESA defaults aren’t really meant to resolve timescales for sedimentation away from the photosphere in a model like yours. For a star with no surface convection like yours, I believe the timescale given in that paper is the time it takes for metals to sediment past the photosphere and disappear from where an observer might see them. This timescale is often very fast, but the metals don’t have to go very far to be buried deeper than the photosphere. On the other hand, the MESA defaults bundle many zones near the surface together to make the boundary conditions better for diffusion, so that the photosphere can be contained in an effectively larger cell that reaches much deeper for purposes of diffusion.

         !### diffusion_min_dq_at_surface

         ! treat at least this much at surface as a single cell for purposes of diffusion

      diffusion_min_dq_at_surface = 1d-9

         !### diffusion_min_T_at_surface

         ! treat cells cells at surface with T < this as a single cell for purposes of diffusion
         ! default should be large enough to ensure hydrogen ionization

      diffusion_min_T_at_surface = 1d4

      	 !### diffusion_min_dq_ratio_at_surface

         ! combine cells at surface until have total mass >= this factor times the next cell below them
         ! this helps with surface boundary condition for diffusion by putting large cell at surface

      diffusion_min_dq_ratio_at_surface = 10

It’s pretty clear from the pgstar window that you sent that this is at least part of what’s going on, since the abundances are constant for logxm < -9. You could try changing those controls to resolve things better near the photosphere, but I can’t promise the solver will be happy with this.

Also, when you’re looking very close to the surface of a star, be aware that there’s a control that will set a global maximum on diffusion velocities. For white dwarfs with high surface gravity, this might artificially restrict diffusion velocities that really should be pretty fast near the surface.

         !### diffusion_v_max

         ! Max velocity (cm/sec).
         ! We can get extremely large velocities in the extreme outer envelope
         ! that cause problems numerically without really effecting the results,
         ! so we allow a max for the velocities that should help the numerics
         ! without changing the results.
         ! Note: change `diffusion_v_max` to at least 1d-2 when using radiative levitation.

      diffusion_v_max = 1d-3

Finally, your model is still very hot, so perhaps radiative levitation might be playing a role in slowing things down? I don’t believe that effect is included in the calculations that you linked to. Have you tried doing this same run without including radiative levitation?

Cheers,
Evan

> On Oct 3, 2017, at 11:21 AM, Zhang, Zhaoxi M. (Michael) <mz at astro.caltech.edu> wrote:
> 
> Hi Evan,
> 
> Thanks for your help!  I was trying to analyze diffusion in white dwarves, and didn't realize that wd_diffusion is completely inappropriate for this.
> 
> Following the release notes, I made a new inlist that uses OPAL opacities, setsdiffusion_use_cgs_solver = .true., and enables radiative acceleration.  I used it on the 0.604_from_2.3_z2m2.mod model that came pre-packaged with MESA, and found that it takes around 200,000 years for a noticeable amount of heavy elements to settle out of the atmosphere.  This is far longer than what I would expect, and far longer than the diffusion timescales I've seen in papers (e.g. https://arxiv.org/pdf/0903.1499.pdf <https://arxiv.org/pdf/0903.1499.pdf>)
> 
> I'm not sure if I'm doing something wrong, but the inlist (attached) is very simple.  Any help is appreciated!
> 
> 
> Michael 
> 
> From: Mesa-users <mesa-users-bounces at lists.mesastar.org <mailto:mesa-users-bounces at lists.mesastar.org>> on behalf of Evan Bauer <ebauer at physics.ucsb.edu <mailto:ebauer at physics.ucsb.edu>>
> Sent: Monday, October 2, 2017 11:59:50 AM
> To: Zhang, Zhaoxi M. (Michael)
> Cc: mesa-users at lists.mesastar.org <mailto:mesa-users at lists.mesastar.org>
> Subject: Re: [Mesa-users] wd_diffusion doesn't work?
>  
> Hi Michael,
> 
> Short answer: yes, this is expected behavior. You’re right to call attention to this sort of thing, but I wouldn’t worry about this particular test right now.
> 
> Long answer: this test case is out of date. It isn’t meant to test diffusion timescales, but conditions for diffusive equilibrium, so the length of timesteps shouldn’t be relevant for the physics being tested. It starts from a model that is already near diffusive equilibrium, and then runs for long enough (a few Gyr) that many diffusion timescales should have occurred in the atmosphere and H/He should have achieved diffusive equilibrium. It then tests against an analytic expression for H/He abundance profiles in diffusive equilibrium. See figure 23 in the second instrument paper for more details.
> 
> All of this is out of date because the wd_diffusion routines assume ideal gas for diffusion, as do the analytics that they test against. They agree very nicely, but the ideal gas EOS is not the correct thing to use in a WD, so this test isn’t very useful.
> 
> If you want to do diffusion in a WD, I strongly recommend going through the release notes for 9793: https://sourceforge.net/p/mesa/mailman/message/35869775/ <https://sourceforge.net/p/mesa/mailman/message/35869775/>
> mesa / Mailing Lists - SourceForge <https://sourceforge.net/p/mesa/mailman/message/35869775/>
> sourceforge.net <http://sourceforge.net/>
> Hello MESA Users, We are happy to announce a new MESA public release version: 9793. Release notes below. Cheers, Evan (on behalf of Pablo, Rich, Josiah, Rob, Aaron ...
> 
> If you still have convergence issues after that, let me know and I can send more suggestions.
> 
> Cheers,
> Evan
> 
> 
>> On Oct 2, 2017, at 11:42 AM, Zhang, Zhaoxi M. (Michael) <mz at astro.caltech.edu <mailto:mz at astro.caltech.edu>> wrote:
>> 
>> Hello everyone,
>> 
>> In MESA 10000, I ran wd_diffusion in the test suites.  It worked, but its timesteps were almost 100 million years, which I thought was far higher than the diffusion timescale.    So I decreased the timesteps to see how the elements diffuse initially:
>> 
>> max_years_for_timestep = 1d3
>> 
>> and the test stopped working.  It struggles to converge, and fails with:
>> 
>> stopping because of problems dt < min_timestep_limit
>> terminated evolution: cannot find acceptable model
>> 
>> Is it expected behaviour for this test to fail due to smaller timesteps?  Why would having a smaller timestep create convergence problems?
>> 
>> 
>> Cheers,
>> 
>> Michael
> 
> <inlist><grid8_000190.png>

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