MESA news
Hello and Happy New Year 2009!
One of my new year’s resolutions is to post more frequent updates about MESA—so here are a few recent highlights.
MESA numerics
MESA/mebdfi_95
MEBDFI_95 is an f95 library for solving stiff initial value problems with fully implicit systems of differential algebraic equations. The code is based on MEBDFI, backward differentiation formulas (BDF) as modified (M) and extended (E) by Jeff Cash, and then modified some more by him to handle fully implicit equations (I). So the name can be parsed as M-E-BDF-I, a modified extended backward difference formula scheme for stiff fully implicit initial value problems. It has automatic step-size selection and automatic order control up to 7th order.
MESA microphysics
Flexible net definitions and NACRE rates in MESA/net
The updated MESA/net module makes it easy to define new nets by specifying a desired set of isotopes and reactions. The rates now include most of the NACRE rates as well as the Caughlin & Fowler rates and others from Frank Timmes.
MESA/ionization
The new MESA/ionization module provides a routine based on Paquette et al. (1986) to estimate typical ionic charge as a function of local temperature, density, and free electrons per nucleon. (This was added along with the MESA/diffusion module described below.)
MESA evolution
semiconvection and salt finger instability in MESA/mlt
The new version of the MESA/mlt package includes support for semiconvection and salt finger instability based on Grossman and Taam (1996). It also has options both for computing the actual temperature gradient as a function of a given luminosity, and also for computing the convective luminosity given a specified actual temperature gradient. In both cases, partial derivatives are computed as well as basic results.
MESA/colors
The MESA/colors module implements a routine for calculating theoretical estimates of magnitudes and colors from Teff, L, M, and [Fe/H]. The color magnitude tables come from Lejeune, Cuisinier, and Buser (1998).
MESA/burn_and_mix
The updated MESA/burn_and_mix module now supports abundance evolution either by a sequence of substeps alternating burning and mixing or as a fully coupled set of equations simutaneously solving for the effects of both burning and mixing. Any of the high order implicit ODE solvers from MESA/num can be selected for use in either mode (in MESA/STAR, I’m currently using the ‘seulex’ solver which is an implicit extrapolation integrator of variable order with automatic step-size control and order selection).
MESA/diffusion
The new MESA/diffusion module handles gravitational settling and chemical and thermal diffusion. Radiative levitation is not currently supported. Burger’s equation is solved using a routine derived from Anne Thoul’s code. Approximate pressure ionization is based on Paquette et al. (as implemented in the MESA/ionization package). The element diffusion equation is solved using a semi-implicit, finite difference scheme described by Iben and MacDonald.
MESA/STAR
The MESA/STAR module continues to make progress. For example, the “standard solar model” now works reasonably well. With mixing length alpha tuned to 2.25 and with element diffusion turned on (it reduces the main sequence lifetime), when the model reaches the age of 4.4 Gyrs, it has reached L = 1.000 Lsun, R = 1.002 Rsun, and Teff = 5768.
My sample Roche-lobe overflow code can now get through the period minimum and take the donor down to 0.03Msun where it is dependent on the extended regions of the EOS based on D. Saumon, G. Chabrier, and H. M. Van Horn (1995). This is significant to me since it was EZ’s failure to handle such cases that got MESA started in the first place.
As a final example of the current state of MESA/STAR, last night while I slept, it cranked away on a 1 Msun ZAMS starting model (no diffusion this time, but with mass loss by Reimer’s and Blocker’s winds). When I checked this morning, it had died after 12107 steps (cause of death “bad value for pressure in eos” whatever that might mean; I’ll try to figure it out later today). But the good news is that it had survived the helium core flash, did a bunch of AGB shell flashes, lost a lot of mass to winds, and ended up as a 0.52 Msun C/O white dwarf with a tiny H/He envelope. Here’s the internal structure of a model near the end of the run: the x axis is log of mass exterior to the point, so you can see that the envelope is only about 10^-4 Msun at this time (pdf):
Here’s the H-R history of the run (the final large jump in luminosity and Teff happens in just a few steps before the run dies) (pdf):
Here’s the helium core flash followed by the progress of helium burning to the center (pdf):
And here are some AGB shell flashes during the period of rapid mass loss from Blocker wind (pdf):
Following the AGB flashes, the star cools uneventfully for the rest of the run (at least until it dies!).
There’s still lots of work to be done on stellar evolution in MESA—in particular, there are problems with convergence when attempting advanced burning that need to be fixed (at least I hope they can be fixed!). But there was lots of progress during 2008, and I’m equally hopeful for 2009.
Cheers, Bill
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Andreas Viklund