[Mesa-users] "Mirror star nuggets" in MESA with modified gravity and heating rate

[Franco Cabral]

Hey Jeremy,

Thanks for your reply. I basically want to add an external gravitational potential that is set by a "mirror star" core density of around 150 g/cm^3. Since I'm dealing with objects that have much lower densities, this means that this potential is around 10^10 times stronger than the self gravity. And so one way I thought this could be consistently implemented is through other_cgrav by making G dependent on the radius and enclosed mass.

I will give your time-dependent G suggestion a try and see where I can go from there.

Sincerely,
Franco Cabral
________________________________
From: Jeremy Sakstein <sakstein at hawaii.edu>
Sent: Thursday, January 9, 2025 3:25 PM
To: Franco Cabral <franco.cabral at mail.utoronto.ca>
Cc: mesa-users at lists.mesastar.org <mesa-users at lists.mesastar.org>
Subject: Re: [Mesa-users] "Mirror star nuggets" in MESA with modified gravity and heating rate

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Hi Franco,

I would have thought that a combination of other_cgrav and other_energy_implict would be enough for what you are trying to simulate.

What values of G are you using?

My experience with scaling G by a factor >1.5 is that these types of errors occur. My solution is to increase it slowly from standard_cgrav to your required value over some time-scale T where T is chosen to be long enough to allow convergence but shorter than the timescale of the physics you are interested in.

An example that I have used in the past is G(t) = G0 (1 + a[1-Exp(-t/T)]) where G0 is standard_cgrav, a is whatever scaling factor you want to apply, and t is star_age. This ensures that G=G0 at times shorter than T but G=G0(1+alpha) by the time the star has reached the phase you are interested in.

Cheers,

Jeremy

On Sun, Jan 5, 2025 at 2:26 PM Franco Cabral via Mesa-users <mesa-users at lists.mesastar.org<mailto:mesa-users at lists.mesastar.org>> wrote:
Dear all,

I am reaching out for advice on an issue I am encountering while trying to model optically thick "mirror star nuggets" in MESA (version 24.03.1) as part of a dark matter study. These nuggets are intended to represent compact objects with around the following specifications:

  1.
Mass: 10^20 g
  2.
Radius: 10^9 cm
  3.
Heating Rate: 10^10 erg/g/s (implemented via extra_power_source in the inlist), driven by suppressed interactions with dark matter.
  4.
Modified gravity: Gravitational acceleration set by a mirror star core density of around 150 g/cm^3.

I have modified create_initial_model.f90 to change the local gravity definition there and its associated differential equations. With these changes, MESA is able to converge on an initial model with specified mass and radius. However, once this initial model is passed to the main MESA solver, it encounters tolerance and convergence errors in the first simulation step.

Here are my attempts so far in changing the gravity which have been unsuccessful:

  1.
Modifying MESA's global m_grav definition in star_utils.f90.
  2.
Using the other_cgrav hook.
  3.
Using the other_momentum_implicit hook.

I suspect that the nugget is evolving too rapidly from its initial model. Adjusting certain tolerance switches may help, but I’m unsure which ones are most relevant or if the issue lies elsewhere. I would greatly appreciate any advice on this matter.

I am attaching a GitHub link with my code changes and a sample run output using the other_cgrav hook to show the errors.

https://github.com/MESAHub/mesa/compare/main...fmcabral123:mesa:main<https://urldefense.com/v3/__Https://github.com/MESAHub/mesa/compare/main...fmcabral123:mesa:main__;!!PvDODwlR4mBZyAb0!RyMJojKiPqrEenO8JWmYKvVhJQq-AESDNilmRuqMqRfNSGxUEgM_8pLXegWmj8aAQ7oPnxFKY4l1IH2s6EmHgMrcAbY$>

Sincerely,
Franco Cabral
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--
Jeremy Sakstein (He/Him/His)
Assistant Professor of Theoretical Physics
Department of Physics & Astronomy
University of Hawaiʻi at Mānoa
Watanabe Hall
2505 Correa Road
Honolulu, HI, 96822, USA
http://www.jeremysakstein.com<http://www.jeremysakstein.com/>
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