[mesa-users] eps_grav_integral and Base of RGB

Bill Paxton paxton at kitp.ucsb.edu
Mon Jan 19 13:58:03 EST 2015

On Jan 19, 2015, at 9:52 AM, Michael Medford wrote:

> Hello everyone,
> One of the history columns listed under Integrated Power is eps_grav_integral (in Lsun units). I have uncommented this variable and have been playing around with it in my models, but cannot quite understand what it represents. I thought it would be the gravitational energy released due to contraction, but comparing this value to the time derivative of gravity yielded very different results. I also considered that eps was often a variable for per mass units, but this variable is listed as Lsun units.
> What does eps_grav_integral calculate? And is there a place in the code to dig through to figure out the definitions for those variables listed without comments?

Hi Michael,

I'm working on adding hydrodynamics to mesa/star and as part of that effort I've been digging into details of energy balance in the code.  And that has given rise to a bunch of not-yet-documented options for output in profiles and histories.   You are of course welcome to use anything that looks interesting.   Just understand that some of these (most?) will just go away in future releases if I decide they aren't particularly useful.

As you know 'eps_grav' shows up as a term in some formulations of the energy equation. see Kippenhahn&Weigert, eqn 4.27 for example.
it has units erg/g/s.   The "integral" of eps_grav by mass gives erg/s, the same as L, hence the (dubious?) units of Lsun.

To find details like this in the code, I do something like the following:

cd mesa/star/private
grep eps_grav_integral *
history.f90:            case(h_eps_grav_integral)
star_history_def.f90:      integer, parameter :: h_eps_grav_integral = h_log_abs_Lgrav + 1 
star_history_def.f90:      integer, parameter :: h_log_extra_L = h_eps_grav_integral + 1 
star_history_def.f90:         history_column_name(h_eps_grav_integral) = 'eps_grav_integral' 

In history.f90 we find
               val = dot_product(s% dm(1:nz), s% eps_grav(1:nz))/Lsun

[While I was writing this, Rob beat me with the same response -- good job Rob!]

> Also, I am attempting to investigate the properties of stellar core boundaries across stars of 10-80 solar masses, specifically at the base of RGB.

excellent --- please make sure you have good spatial resolution for the core boundary.
to check this, look at profile plots of logdq (if you don't know what that is, find out!).
You need much better resolution around the boundary than you do in other parts of the model,
so you don't want to crank up the resolution uniformly by using mesh_delta_coeff.
instead you might try doing something like this  ---  and be sure to look at plots of logdq to see how the resolution is changing near the convective boundary.

      min_dq = 1d-8
      max_surface_cell_dq = 1d-8
      max_center_cell_dq = 1d-8
      ! for extra resolution near convective boundaries

      xtra_dist_a_u_rzb = 2
      xtra_coef_a_u_rzb = 1d-4
      xtra_dist_b_u_rzb = 2
      xtra_coef_b_u_rzb = 1d-4
      xtra_dist_a_l_rzb = 2
      xtra_coef_a_l_rzb = 1d-4
      xtra_dist_b_l_rzb = 2
      xtra_coef_b_l_rzb = 1d-4

      xtra_coef_czb_full_on = 1
      xtra_coef_czb_full_off = 1
      xtra_dist_a_u_hb_czb = 2
      xtra_coef_a_u_hb_czb = 1d-4
      xtra_dist_b_u_hb_czb = 2
      xtra_coef_b_u_hb_czb = 1d-4
      xtra_dist_a_l_hb_czb = 2
      xtra_coef_a_l_hb_czb = 1d-4
      xtra_dist_b_l_hb_czb = 2
      xtra_coef_b_l_hb_czb = 1d-4
      xtra_dist_a_u_sczb = 2
      xtra_coef_a_u_sczb = 1d-4
      xtra_dist_b_u_sczb = 2
      xtra_coef_b_u_sczb = 1d-4
      xtra_dist_a_l_sczb = 2
      xtra_coef_a_l_sczb = 1d-4
      xtra_dist_b_l_sczb = 2
      xtra_coef_b_l_sczb = 1d-4


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