[Mesa-users] Stability Problems with use_other_energy

[José Lopes]

Hello Pablo,

Thank you for your help so far!

Still regarding the partial derivatives for the extra heating term: What if my heating term for a given zone k depends on the mass faction of a given element in that zone (so the heating term would depend on 's%xa(species,k)'). How can I obtain the partial derivative for the mass fraction? 

I have looked inside MESA in the hope of finding the partials for the mass fraction in the star_info structure, however, as far as I can see, this quantity is not being computed. Is it even possible to compute, say, the partial of 's%xa(2,k)’ with respect to lnr00, given that I can only access the array 's%xa(2,k)' from the star_info structure?

Thank you,

Cheers, 

José Vargas Lopes
PhD Student

CENTRA, Centre for Astrophysics and Gravitation
IST, University of Lisbon, Portugal
Ligado 16 de março de 2018 no 15:59:50, Pablo Marchant (pamarca at gmail.com) escreveu:

Hi Jose, as a toy example, consider a heating term that depends on the second derivative of density with mass (don't take it seriously, just an example):

eps_extra(k) = C*d^2 rho/ dm^2 = C*(rho(k-1)-2*rho(k)+rho(k+1))/(m(k-1)-m(k+1))

where C is a constant and the last part is just the finite difference expression of the derivative. Note that this uses the MESA definition where the surface of the star is at k=1. The partials need to provide information on how eps_extra changes when different properties change in this and neighboring cells. The meaning of the 00, m1 and p1 terms is as follows (the lnd in these terms means natural logarithm of density):

- d_extra_heat_dlndm1(k) is the partial derivative of extra_heat(k) with respect to ln(rho) at cell (k-1)
- d_extra_heat_dlnd00(k) is the partial derivative of extra_heat(k) with respect to ln(rho) at cell (k)
- d_extra_heat_dlndp1(k) is the partial derivative of extra_heat(k) with respect to ln(rho) at cell (k+1)

So, using that d/d(ln rho)=rho*d/d(rho), you can get expressions for the partial derivatives from the expression for eps_extra. For example:

d_extra_heat_dlndm1(k)= d(eps_extra(k))/d(ln rho(k-1)) = C*rho(k-1)/(m(k-1)-m(k+1))
d_extra_heat_dlnd00(k)= d(eps_extra(k))/d(ln rho(k)) = -2*C*rho(k)/(m(k-1)-m(k+1))
d_extra_heat_dlndp1(k)= d(eps_extra(k))/d(ln rho(k+1)) = C*rho(k+1)/(m(k-1)-m(k+1))

lnT and lnR for the other variables is, as you can guess, natural logarithm of the temperature and radial coordinates.

Hope this clears things.

Cheers

On Fri, Mar 16, 2018 at 10:40 AM, José Lopes <josevlopes at tecnico.ulisboa.pt> wrote:
Hello Pablo, 

As a follow-up to your e-mail:

After inspecting the other_energy_implicit.f90 and the required partial derivatives for the implicit energy computation, I would like to ask if you could identify the variables for the derivatives (e.g.: dlnr00, dlnrm1, dlndm1, etc.), or point me to a reference/file where that identification is explained, since I am having difficulties in understanding what each variable means.

Thank you,

José Vargas Lopes
PhD Student

CENTRA, Centre for Astrophysics and Gravitation
IST, University of Lisbon, Portugal

Ligado 16 de março de 2018 no 12:15:37, José Lopes (josevlopes at tecnico.ulisboa.pt) escreveu:

Hello Pablo,

Thank you very much for you suggestion!

I will change the implementation and report back once I have some results.

Cheers,

José Vargas Lopes
PhD Student

CENTRA, Centre for Astrophysics and Gravitation
IST, University of Lisbon, Portugal


No dia 16/03/2018, às 02:39, Pablo Marchant <pamarca at gmail.com> escreveu:

Hi Jose,

my guess is that your implementation needs to be done through the implicit other_energy option described in $MESA_DIR/star/other/other_energy_implicit.f90. other_energy is only called once at the beginning of the step (an explicit calculation), and this can induce large step-to-step variations. The implicit routines compute the energy through the Newton iterations and can prevent these large variations. One detail though is that you need to compute as well partial derivatives. You can see instructions for this in the source file I mentioned above.

Cheers

On Thu, Mar 15, 2018 at 9:24 PM, José Lopes via Mesa-users <mesa-users at lists.mesastar.org> wrote:
Dear MESA users,

I am developing an extension to MESA to include a Dark Matter Capture framework and interplay with the code. This is all done through the run_star_extras.f and the ‘use_other_energy’ hook. An extra energy contribution is computed for each step (this energy term depends on the stellar structure properties, such has the temperature profile and its second derivative w.r.t. the radius) and is injected as an extra heat term (it can be either positive or negative).

So far most results are consistent with what has already been studied for this phenomenology. The problems however start when the extra energy term grows to the same order of magnitude of either the nuclear energy or gravity energy terms. In these cases, the code shows an irregular oscillatory behavior, almost as if it is unable to converge to a stable solution. 

This oscillatory behavior can be seen in the plots attached to this e-mail (plot1 and plot2). There, you can see the nuclear (black), gravity (red) and extra (blue) energy terms in the first zone (r ~ 0) of the Star, as a function of Model Number. Plot1 shows a case where the extra energy term grows to a magnitude comparable to the nuclear energy term, and plot2 shows a similar situation for the gravity term. I also attach (plot3) a case where the extra energy term is smaller and thus the model is able to converge throughout the evolution, although a glitch can be seen in the gravity
energy term.

I have tried tuning some options in the controls inlist (such has time step control, variable control, mesh-refinement, etc.). However, so far, I have not been able to improve the stability of these models.

As anyone encountered a similar behavior? Is there any control option I should focus on to try and improve stability?

Thank you all,

José Vargas Lopes
PhD Student

CENTRA, Centre for Astrophysics and Gravitation
IST, University of Lisbon, Portugal

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--
Pablo Marchant Campos
M.Sc on Astrophysics, Universidad Católica de Chile
PhD on Astrophysics, Argelander-Institut für Astronomie, Universität Bonn



--
Pablo Marchant Campos
M.Sc on Astrophysics, Universidad Católica de Chile
PhD on Astrophysics, Argelander-Institut für Astronomie, Universität Bonn
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