[mesa-users] Rapidly accreting metal-free protostars

[Bill Paxton]

Hi Warrick,

On Oct 18, 2013, at 7:13 AM, Warrick Ball wrote:

> I tried to follow the recent discussion about accretion and, if I understand correctly, I shouldn't get too hopeful because the results are only really reliable as long as Mdot*dt < dm(surf). i.e. the while the mass accreted in a timestep is less than the mass in the outermost shell. 

NO!  The good news is that with the scheme we came up with finally by combining the Sugimoto&Nomoto Eulerian formulation of the Lagrantian time derivative with the Townsley&Bildsten formula for the spatial part of that split time derivative, we are not limited by Mdot*dt < dm(surf).

We haven't heard from Dean yet, so there may still be issues to resolve, but I'm hopeful that we can now safely do much longer timesteps during accretion.   At least that should be true for moderate to low accretion rates.  For high rates, the time part of the Eulerian formulation can dominate over the spatial part, and then we're back to 1st order convergence in time, so to get adequate convergence, you might have to take small timesteps.

> And before I discuss the output, I acknowledge that there are a few differences between my MESA input and the Hosokawa et al. models. Notably, the surface boundary condition is different: Hosokawa et al. implemented a shock boundary condition and also solve for the structure of the material falling onto the protostar.

I don't think it makes sense to use any sort of photospheric boundary condition when you have such high mdot.   You may need to follow Hosokawa et al. by doing a separate calculation to determine the boundary conditions at the surface of the mesa model -- i.e., compute the temperature and pressure at the outer boundary of the mesa model and use that in place of the boundary condition from the mesa/atm module.  

The new release of MESA actually has a new control for an extra pressure at the surface.  You might play around with this as a start,.
     
      ! extra gas pressure at surface -- added to surface pressure from atm
         surface_extra_Pgas = 0d0 ! in ergs/cm^3
         
If you need more control that you get with that, the next thing to try is the "other_atm" hook.  That lets you write a replacement routine for the standard atm boundary calculation.  Your routine is called with M, R, L at the surface of the mesa model, and you return Teff along with lnT and lnP at the surface of the model.   In your case of an extremely high accretion rate Teff may not be very meaningful, but you can do whatever "shocking" calculation you want to come up with lnT and lnP as surface boundary conditions.

Please keep us informed!   You are pushing into unexplored areas for using mesa.  I'll do what I can to help. ;p

Cheers,
Bill


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