MESA Summer School 2018: Lecture 1

Table of Contents

Part 0: Overview

This guide was written as part of the 2018 MESA summer school. It is an introduction to MESA, with a particular focus on using run_star_extras.f. It assumes you are using r10398 of MESA.

If you're new to Fortran, we prepared a short document with some examples. Don't let yourself get hung up by the Fortran; quickly ask your classmates and the TAs for help!

There is a version of this document available with solutions. The git repository hosting this document contains the full source code used in each task, which you can see by looking at the appropriately named tag (i.e. part2-task2).

Part 1: Running and controlling MESA

If you've used MESA before, much of this should be familiar.

Part 1a: Getting started

Each time you want to start a MESA project, you should make a new copy of the star/work directory. 

cp -r $MESA_DIR/star/work lecture1

In this case, we have prepared and provided a work directory for you. Download, unpack, and enter this work directory. 

unzip lecture1.zip
cd lecture1

Task 1: Compile and run the provided work directory

This directory evolves a solar mass star from the middle of the main sequence to hydrogen exhaustion. Confirm that you can compile and run it. A window with a few plots should appear. Familiarize yourself with the terminal output.

You can receive valuable MESA bonus points by restarting your run from a saved photo.

Answer
./clean
./mk
./rn
Bonus Answer

During your run, lines line 

save photos/x010 for model 10

were output to the terminal. These photos are MESA restart files.

To restart, use the re script and specify the name of the photo. 

./re x010

Part 1b: Using inlists

MESA/star has three inlist sections. Each section contains the options for a different aspect of MESA.

star_job
options for the program that evolves the star
controls
options for the MESA star module
pgstar
options for on-screen plotting

The distinction between star_job and controls can be a little subtle. We won't discuss pgstar in this lecture, but Frank will later this morning.

star_job contains options that answer questions like:

  • how should MESA obtain the initial model?
  • are there any changes MESA should make to the initial model?
  • what microphysics data should MESA read?
  • where should MESA store its output?

controls contains options that answer questions like:

  • when should MESA stop evolving the model?
  • which angular momentum transport processes should MESA consider?
  • what numerical tolerances should MESA's solvers use?

MESA's many inlist options are documented in the files

They are roughly sorted into groups of related options. When you're searching for an option, see if it seems to match any of the section headings and then look there first. If that fails, try searching for some key words.

Note that inlists can point to other inlists. This can be useful for keeping things organized. In the lecture1 directory, inlist points MESA to inlist_project and inlist_pgstar.

Task 2: Read the documentation

Use the documentation to learn about the stopping condition that we are using (xa_central_lower_limit and xa_central_lower_limit_species). Look near this option to see some of the other mass fraction based stopping conditions that are available.

You can receive valuable MESA bonus points by reporting problems or shortcomings in the documentation.

Answer

Look at the version of controls.defaults on the web or included in MESA. Note that the main webpage has the documentation for the latest release. You should consult the documentation appropriate to your version of MESA. Either use the online documentation archive or should consult the defaults files included in your version of MESA.

The documentation for xa_central_lower_limit and xa_central_lower_limit_species says:

Lower limits on central mass fractions. Stop when central abundance drops below this limit. Can have up to num_xa_central_limits of these (see star_def.inc for value). xa_central_lower_limit_species contains an isotope name as defined in chem_def.f. xa_central_lower_limit contains the lower limit value.

Nearby you will find similar controls with upper/lower limits on average and surface mass fractions.

Bonus Answer

Use the email link given at the top of the documentation webpages. (This is a long-term assignment.)

Part 1c: Controlling output

MESA already knows how to output a tremendous amount of information. The two key file types are history files, which store the value of scalar quantities (e.g. mass, luminosity) at different timesteps and profile files which store the value of spatially varying quantities (e.g. density, pressure) at a single timestep.

The contents of MESA's output files is not directly controlled via inlists. The default output is set by the files 

$MESA_DIR/star/defaults/history_columns.list
$MESA_DIR/star/defaults/profile_columns.list

In order to customize the output, you copy these files to your work directory. 

cp $MESA_DIR/star/defaults/history_columns.list .
cp $MESA_DIR/star/defaults/profile_columns.list .

Then, open up history_columns.list or profile_columns.list in a text editor and comment/uncomment any lines to add/remove the columns of interest ('!' is the comment character.)

You can use run_star_extras.f to define your own history and/or profile columns. We will discuss this later today.

Task 3: Add some output

Look at LOGS/history.data and LOGS/profile1.data to see what information is included by default. In our later exercises, we will be setting the variable extra_heat, which is an additional specific heating rate defined at each cell in the star. Add this quantity to the output. Run MESA and confirm that the column you want is there (its value should be zero).

You can receive valuable MESA bonus points by including the total amount of extra heat being added to the star in your output.

Answer

Uncomment the following lines in profile_columns.list 

extra_heat

and then run MESA 

./rn
Bonus Answer

Uncomment the following lines in history_columns.list 

extra_L

Part 2: Using run_star_extras.f

To activate run_star_extras.f, navigate to the lecture1/src directory and open run_star_extras.f in your text editor of choice. The stock version of run_star_extras.f is quite boring. It "includes" another file which holds the default set of routines. 

include 'standard_run_star_extras.inc'

The routines defined in the included file are the ones we will want to customize. Because we want these modifications to apply only to this working copy of MESA, and not to MESA as a whole, we want to replace this include statement with the contents of the included file.

Delete the aforementioned include line and insert the contents of $MESA_DIR/include/standard_run_star_extras.inc. (The command to insert the contents of a file in emacs is C-x i <filename>, vim :r <filename>, or you can just copy and paste.)

Before we make any changes, we should check that the code compiles. 

cd ..
./mk

If it doesn't compile, double check that you cleanly inserted the file and removed the include line.

The two most important things that one needs to know in order to use run_star_extras.f effectively are (1) the control flow of a MESA run and (2) the contents of the star_info structure.

The different run_star_extras.f routines get called at different points during MESA execution. Here is a high-level overview of a MESA run, written in Fortran-ish pseudocode. 

subroutine run1_star(...)

   ! star is initialized here

   ! before evolve loop calls:
   !   extras_controls
   !   extras_startup
   call before_evolve_loop(...)

   ! evolve one step per loop
   evolve_loop: do while(continue_evolve_loop)

      call before_step_loop(...)

      ! after before_step_loop call to:
      !   extras_start_step

      step_loop: do ! may need to repeat this loop

         if (stop_is_requested(s)) then
            continue_evolve_loop = .false.
            result = terminate
            exit
         end if

         result = star_evolve_step(...)
         if (result == keep_going) result = star_check_model(...)
         if (result == keep_going) result = extras_check_model(...)
         if (result == keep_going) result = star_pick_next_timestep(...)
         if (result == keep_going) exit step_loop

         ! redo, retry, or backup must be done inside the step_loop

         if (result == redo) then
            result = star_prepare_to_redo(...)
         end if
         if (result == retry) then
            result = star_prepare_to_retry(...)
         end if
         if (result == backup) then
            result = star_do1_backup(...)
            just_did_backup = .true.
         else
            just_did_backup = .false.
         end if
         if (result == terminate) then
            continue_evolve_loop = .false.
            exit step_loop
         end if

      end do step_loop

      ! once we get here, the only options are keep_going or terminate.

      ! after_step_loop calls:
      !   extras_finish_step
      call after_step_loop(...)

      if (result /= keep_going) then
         exit evolve_loop
      end if

      ! write out data
      !
      ! do_saves calls:
      !   how_many_extra_history_header_items
      !   data_for_extra_history_header_items
      !   how_many_extra_history_columns
      !   data_for_extra_history_columns
      !   how_many_extra_profile_header_items
      !   data_for_extra_profile_header_items
      !   how_many_extra_profile_columns
      !   data_for_extra_profile_columns
      call do_saves(...)

   end do evolve_loop

   ! after_evolve_loop calls:
   !   extras_after_evolve
   call after_evolve_loop(...)

end subroutine run1_star

In even more distilled terms, here is a flowchart summarizing this.

flowchart.png

The heart of MESA is the grey "take step" box, which contains all of the machinery by which MESA evaluates and solves the equations of stellar structure.

The star_info structure contains all the information about the star that is being evolved. By convention, the variable name s is used throughout run_star_extras.f to refer to this structure. In Fortran, the percent (%) operator is used to access the components of the structure. (So you can read s% x = 3 in the same way that you would read s.x = 3 in C.)

The star_info structure contains the stellar model itself (i.e., zoning information, thermodynamic profile, composition profile). These components are listed in the file $MESA_DIR/star/public/star_data.inc. In addition, star_info contains the values for the parameters that you set in your controls inlist (i.e., initial_mass, xa_central_lower_limit). Recall that the list of controls is located in $MESA_DIR/star/defaults/controls.defaults.

There is one set of controls that will prove useful time and time again when using run_star_extras.f and that is x_ctrl, x_integer_ctrl, and x_logical_ctrl. These are arrays (of length 100 by default) of double precision, integer, and boolean values. You can set the elements in your inlists 

&controls
  x_ctrl(1) = 3.14
  x_ctrl(2) = 2.78
  x_integer_ctrl(1) = 42
  x_logical_ctrl(1) = .true.
/ ! end of controls inlist

and access them later on as part of the star structure (i.e., s% x_ctrl(1), etc.).

Part 2a: Monitoring your models

Task 0 (Example): Add a stopping condition

If you assume that the Earth is a perfect blackbody, its equilibrium temperature is given by

\begin{equation*} T_\oplus = T_\odot \left(\frac{R_\odot}{2\,\rm AU}\right)^{1/2} \end{equation*}

Suppose the stellar model we're evolving represents the Sun and I want to stop my calculation when the Earth would reach a given temperature. A look through controls.defaults seems to indicate that such a condition doesn't already exist. How do I do this?

First, look at how the routines in run_star_extras.f fit into a MESA run. To decide whether to stop, I want to check the value of the Earth's temperature after each step. Thus, I want the subroutine that is called after each step, which is extras_finish_step.

Now, I need to figure out how to access information about the conditions at the stellar photosphere. I open up star/public/star_data.inc and start looking around. If I search for the word photosphere, I can find what I'm looking for photosphere_r and Teff.

MESA uses cgs units unless otherwise noted. The most common non-cgs units are solar units. MESA defines its constants in $MESA_DIR/const/public/const_def.f. Since the run_star_extras module includes the line use const_def, we will be able to access these values. Using the built in constants lets us make sure we're using exactly the same definitions as MESA. The constant with the value of the solar radius (in cm) is named Rsun. Note the other constants that are defined. 

! returns either keep_going or terminate.
! note: cannot request retry or backup; extras_check_model can do that.
integer function extras_finish_step(id, id_extra)
   integer, intent(in) :: id, id_extra
   integer :: ierr
   type (star_info), pointer :: s
   real(dp) :: Tearth
   ierr = 0
   call star_ptr(id, s, ierr)
   if (ierr /= 0) return
   extras_finish_step = keep_going
   call store_extra_info(s)

   ! calculate blackbody temperature of earth
   Tearth = s% Teff * sqrt(s% photosphere_r * Rsun / (2.0 * AU))
   write(*,*) "Tearth =", Tearth

   ! stop if it exceeds 300 K
   if (Tearth > 300) extras_finish_step = terminate

   ! to save a profile,
      ! s% need_to_save_profiles_now = .true.
   ! to update the star log,
      ! s% need_to_update_history_now = .true.

   ! see extras_check_model for information about custom termination codes
   ! by default, indicate where (in the code) MESA terminated
   if (extras_finish_step == terminate) s% termination_code = t_extras_finish_step
end function extras_finish_step

Now, recompile your working directory 

./mk

You will need to do this step each and every time you edit run_star_extras.f. (You will not need to do this when you edit only inlist files.)

Now start the model again from the beginning 

./rn

This run should halt around step 21.

Task 1: Allow the user to specify a temperature

Stop when the temperature of Earth exceeds a given value. Allow the user to specify this value in the inlist. A good value to specify is 330K, as it should take your model about 100 steps to reach this value.

Edit your inlist_project and comment out the central hydrogen abundance stopping condition that was included. We won't use it again.

You can receive valuable MESA bonus points if your routine stops when the temperature of the Earth is within one part in a million of the specified temperature. For its built-in stopping conditions, MESA provides the ability to control the absolute and/or relative error between the model and the specified stopping target. You can look at these controls, when_to_stop_rtol and when_to_stop_atol, for inspiration on how to do this.

Answer

Modify the termination condition in extras_finish_step to be 

! stop if it exceeds a user-specified temperature (in K)
if (Tearth > s% x_ctrl(1)) extras_finish_step = terminate

and then specify x_ctrl in your inlist 

! stop when Tearth > this value
  x_ctrl(1) = 330
Bonus Answer

The basic code stops at the first timestep where the Earth temperature exceeds the threshold. In order to stop very near the threshold, we can ask MESA to "redo" any step that causes us to exceed the threshold by an amount greater than some tolerance.

This gives us the opportunity to use extras_check_model. If the temperature is greater than the target temperature by more than our threshold, we reject the step and redo it with half of the previous timestep.

We define a few variables 

real(dp) :: T, dT, delta
real(dp), parameter :: epsilon = 1d-6

and then the logic itself straightforward 

T = s% Teff * sqrt(s% photosphere_r * Rsun / (2.0 * AU))
dT = T - s% x_ctrl(1)
delta = dT / s% x_ctrl(1)

if (delta > 0) then
   if (delta > epsilon) then
      extras_check_model = redo
      s% dt = 0.5d0 * s% dt
   endif
endif

You could also do this with retry instead of redo. In a retry, MESA will do the step again with the timestep scaled down by timestep_factor_for_retries and then not allow any timestep increases for retry_hold steps afterwards.

Part 2b: Changing input physics

MESA provides hooks to override or modify many of its built-in routines. (These routines mostly affect things that occur within "take step" box of the flowchart.) These are referred to as "other" routines. There are two main steps needed to take advantage of this functionality: (1) writing the other routine and (2) instructing MESA to use this routine.

Navigate to $MESA_DIR/star/other, where you will see a set of files named with the pattern other_*.f. In general, find the one corresponding to the physics (or numerics) that you want to alter. Two that we will use are other_energy.f and other_mlt.f. Open one up and read through it. Many of the files contain comments and examples.

Note that we do not want to directly edit these files. Instead we want to copy the template routine into our copy of run_star_extras.f and then further modify it there. The template routines are usually named either null_other_* or default_other_*.

In this example, we will focus on other_energy.f. Open up this file. Copy the subroutine default_other_energy and paste it into your run_star_extras.f. It should be at the same "level" as the other subroutines in that file (that is, contained within the run_star_extras module.). 

subroutine default_other_energy(id, ierr)
  use const_def, only: Rsun
  integer, intent(in) :: id
  integer, intent(out) :: ierr
  type (star_info), pointer :: s
  integer :: k
  ierr = 0
  call star_ptr(id, s, ierr)
  if (ierr /= 0) return
  s% extra_heat(:) = s% extra_power_source
  return
  ! here is an example of calculating extra_heat for each cell.
  do k = 1, s% nz
     if (s% r(k) > 0.7*Rsun .and. s% r(k) < 0.9*Rsun) then
        s% extra_heat(k) = 1d3*exp(-10*(s% r(k) - 0.8*Rsun)**2)
     end if
  end do
end subroutine default_other_energy

The variable s% extra_heat is an additional specific (per mass) heating rate that will be included. Note that this routine already does something; default_other_energy is responsible for making the extra_power_source control work. Go ahead and remove that bit, the existing example (kudos if you spot the error), and rename it to lecture1_other_energy.

In Fortran, you can write expressions that operate on the whole array at once (like s% extra_heat(:) = s% extra_power_source). However, it is often simplest to explicitly set the value of extra_heat (or some other array) one value at a time, by using a loop. While we're looking code with a loop, it is a good time to mention that in MESA, the outermost zone is at k=1 and the innermost zone is at k=s% nz. 

subroutine lecture1_other_energy(id, ierr)
  integer, intent(in) :: id
  integer, intent(out) :: ierr
  type (star_info), pointer :: s
  integer :: k
  ierr = 0
  call star_ptr(id, s, ierr)
  if (ierr /= 0) return

  ! calculate extra_heat for each cell
  do k = 1, s% nz
     s% extra_heat(k) = 0
  end do

end subroutine lecture1_other_energy

If you read the comments in other_energy.f (and you should), you can see that the file tells us how to have MESA use our other_* routine. Perform these steps (hint: you will need to edit both your run_star_extras.f and your inlists).

Task 2: Add an extra energy source in the core of the star

Use the other_energy routine to add a heating term

\begin{equation*} \texttt{extra_heat} = L_{\mathrm{extra}} \frac{1}{\Delta M} \exp\left(-\frac{M_r}{\Delta M}\right) \end{equation*}

where \(M_r\) is the enclosed mass. Good values are \(\Delta M = 0.05 M_\odot\) and \(L_{\mathrm{extra}} = 0.1 L_\odot\).

The lower left panel in the PGSTAR plots displays the value of s% extra_heat, so you should be able to easily check if it looks OK.

You can receive valuable MESA bonus points if your routine allows for user-specified values of \(\Delta M\) and \(L_{\mathrm{extra}}\).

Answer

First, edit the controls section of your inlist to set the appropriate use_other_* flag to .true. . In our example, this means adding the line 

use_other_energy = .true.

Second, edit the extras_controls routine in run_star_extras.f to point s% other_energy at the routine you want to be executed. 

subroutine extras_controls(s, ierr)
   type (star_info), pointer :: s
   integer, intent(out) :: ierr
   ierr = 0

   ! this is the place to set any procedure pointers you want to change
   ! e.g., other_wind, other_mixing, other_energy  (see star_data.inc)
   s% other_energy => lecture1_other_energy

   ...

end subroutine extras_controls

Failure to do perform both of these is the most common problem people encounter when using the other_* hooks. 

subroutine lecture1_other_energy(id, ierr)
  integer, intent(in) :: id
  integer, intent(out) :: ierr
  type (star_info), pointer :: s
  integer :: k
  real(dp) :: L_extra, dM, Mr
  ierr = 0
  call star_ptr(id, s, ierr)
  if (ierr /= 0) return

  ! allow user-specified values  
  L_extra = s% x_ctrl(2) * Lsun
  dM = s% x_ctrl(3) * Msun

  do k = 1, s% nz
     ! m(k) is the enclosed mass at the outer cell edge
     ! so the mass coordinate at the middle of the cell is 
     Mr = s% m(k) - 0.5 * s% dm(k)

     s% extra_heat(k) = L_extra * exp(-Mr/dM)/dM
  end do

  ! output rate at which energy is added
  write(*,*) "Added ", dot_product(s% extra_heat(1:s%nz), s% dm(1:s%nz))/Lsun, &
       s% x_ctrl(2)

end subroutine lecture1_other_energy

Part 2c: Analyzing your models

It is often useful to do some of your analysis in run_star_extras. At runtime, you have access to more information about the star than will be in the history and profile columns. Additionally, by allowing you to only record the final quantities of interest, this can help make your MESA output smaller and your subsequent analysis easier. (This is particularly useful if you are running large sets of MESA models.)

Task 3: Compare the extra heating to nuclear heating

Calculate the local ratio of your extra heating rate to the nuclear energy generation rate (eps_nuc) and add this quantity your MESA output.

You can receive valuable MESA bonus points by adding this quantity to the existing PGSTAR plot window.

Answer

First, indicate that you will add an extra profile column by editing the function 

integer function how_many_extra_profile_columns(id, id_extra)
   ...
   how_many_extra_profile_columns = 1
end function how_many_extra_profile_columns

The subroutine data_for_extra_profile_columns already has access to the star_info pointer, so you can make use of any of the quantities defined in $MESA_DIR/star/public/star_data.inc. This includes s% eps_nuc and the s% extra_heat you defined earlier.

The desired ratio can then be calculated in each zone. 

subroutine data_for_extra_profile_columns(id, id_extra, n, nz, names, vals, ierr)
   use star_def, only: star_info, maxlen_profile_column_name
   use const_def, only: dp
   integer, intent(in) :: id, id_extra, n, nz
   character (len=maxlen_profile_column_name) :: names(n)
   real(dp) :: vals(nz,n)
   integer, intent(out) :: ierr
   type (star_info), pointer :: s
   integer :: k
   ierr = 0
   call star_ptr(id, s, ierr)
   if (ierr /= 0) return

   !note: do NOT add the extra names to profile_columns.list
   ! the profile_columns.list is only for the built-in profile column options.
   ! it must not include the new column names you are adding here.

   names(1) = 'eps_ratio'
   do k = 1, nz
     vals(k,1) = s% extra_heat(k)/s% eps_nuc(k)
   end do

end subroutine data_for_extra_profile_columns
Bonus Answer

The extra profile column acts just like an included profile column. It can easily be included the PGSTAR plot by adding 

Profile_Panels1_other_yaxis_name(1) = 'eps_ratio'

to inlist_pgstar. (The inlist was already set up to display this nicely.) There are infinitely many ways to plot things with PGSTAR; we'll learn more about it in Frank's lecture.

Part 2d: Changing controls

Recall that star_info contains the values for the parameters that you set in your controls inlist. That also means that you can set the value of these parameters by modifying the star_info structure. Since run_star_extras gives us hooks to access to the star_info at each step, that means we can modify parameters as the run proceeds. This often saves us the hassle of stopping, saving a model, editing the inlist, and restarting.

Task 4: Turn on other_energy at central hydrogen exhaustion

Instead of having the other energy routine always on, activate it only after central hydrogen exhaustion has occurred.

Answer

In order to activate the other_energy routine, we add the following line to extras_finish_step 

! activate other_energy after central hydrogen depletion
if (s% center_h1 < 0.01 ) s% use_other_energy = .true.

So after the end of the first step where the central hydrogen abundance falls below 0.01, the extra heating will occur.

Author: Josiah Schwab and Héctor Martínez-Rodríguez

Created: 2018-08-08 Wed 08:56

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