[Mesa-users] Missing energy generation in MESA output?

[Jason Wright]

Hi, all.  Me again teaching stellar structure with MESA.

One set of our assignments is to test the precision of MESA in computing
the equations of stellar structure.  This is a good way for the students to
practice coding up physics and exploring which physics matters where in the
Sun.  We are using a solar-mass ZAMS star of solar metallicity as our
example (from Ed Brown's excellent notes).

We find that the 1st 3 equations of stellar structure are obeyed extremely
well, but we are struggling with the luminosity equation.

Δl/Δm = ε_nuc - T

(Eq. 11 of the first MESA instrument paper).

*Problem 1:*

We get reasonably good agreement for most of the star, but in the outermost
cells (m/M > 0.999) there is a big divergence between these quantities.  In
the atmosphere of the star, Δl/Δm actually goes *very slightly* negative,
but the reported ε_grav (calculated as -T ds/dt) is still positive there.

I'm guessing the answer is that I'm not calculating T ds/dt properly.  I'm
using the delta_entropy profile output, and log_dt from the history file
for that timestep.  Perhaps these do not correspond exactly, or that is not
the quantity used in determining Δl/Δm?

(I do see there is an advertised eps_grav parameter in MESA, but it is set
to zero everywhere, which is why I'm using T ds/dt.  Is there a way to get
that output to "turn on"?)

Below:  comparison of the finite difference of Δl/Δm (red, dashed line is
negative) and energy generation terms reported by MESA.

[Core is on the left, atmosphere on the right.    The logit_10 function
"counts nines" near m/M~1 (so 0.9999 is 4) and "counts zeros" near m~0 (so
0.0001 is -4).  ]
["eps" here is "net_energy", which does not have the precision to show
values below 1 erg/s/g]


[image: Screenshot 2025-02-24 at 1.12.43 PM.png]


*Problem 2:*

Another mismatch is more subtle, but suggests I'm missing physics.

It's hard to see in the above plot, but the discrepancy actually stars at
about m/M=0.5 (logit_10(m/M)=0).  If I integrate up (ε_nuc - T ds/dt)dm to
compute luminosity and compare it to the actual luminosity, I get about a
0.1% discrepancy with a strange shape.This shape shares some qualities /
features of both eps_nuc and eps_grav, but not exactly.

[image: Screenshot 2025-02-24 at 1.18.56 PM.png]
Any ideas what's going on?  Am I misunderstanding something about neutrino
losses?

Happy to share my code if it helps.



-- 
                                                -
---------------
Jason T Wright
Professor of Astronomy and Astrophysics
Director, Penn State Extraterrestrial Intelligence Center
he/him/his
*https://sites.psu.edu/astrowright/ <https://sites.psu.edu/astrowright/>*
*https://bsky.app/profile/astrowright.bsky.social
<https://bsky.app/profile/astrowright.bsky.social>*
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.mesastar.org/pipermail/mesa-users/attachments/20250227/dba8bdf4/attachment.htm>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Screenshot 2025-02-24 at 1.12.43?PM.png
Type: image/png
Size: 170808 bytes
Desc: not available
URL: <https://lists.mesastar.org/pipermail/mesa-users/attachments/20250227/dba8bdf4/attachment.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: Screenshot 2025-02-24 at 1.18.56?PM.png
Type: image/png
Size: 261110 bytes
Desc: not available
URL: <https://lists.mesastar.org/pipermail/mesa-users/attachments/20250227/dba8bdf4/attachment-0001.png>