[Mesa-users] Artificially inflating a star

Mon Mar 15 11:08:32 UTC 2021

Hi James --

I'm not sure if this is quite what you're after, but on the off chance it is useful:

The radius of a star can be regarded as a function of its entropy.  At fixed mass, if you increase the specific entropy a little, you'll increase the radius. You could do this in various ways (e.g., extra heating), but in some regimes, arguably the simplest approach is just to monkey around with the convective mixing length.  Of course this will have other effects, some of which are bound to be unphysical, but if you reallllly want to change the radius, it's at least a way of doing so in a fairly consistent way.

For example: I'm not sure if you're talking about fully-convective M-dwarfs or not, but for the sake of simplicity let's assume you are.  In that case, the bulk of the interior is probably going to be at some nearly-constant specific entropy (s_c, say); to change the radius appreciably, you need to change s_c. There is some entropy jump (Delta S, say) between the surface and the deep interior; in the context of a 1D model, the combination of the atmosphere plus the convection treatment (MLT) basically determines this, so if you change that treatment you will change Delta_S and hence s_c (and hence the radius).  E.g., for typical MLT in a regime where the convective flux doesn't change, the entropy jump is roughly proportional to the mixing length alpha^(-4/3).  That is, a lower alpha implies less efficient convection, a larger entropy gradient (at fixed total flux), and (typically, all else being equal) a larger radius.

Many attempts to explain the radius inflation problem can be viewed in this way -- for example, it's possible to construct a "magnetic" model (like those of MacDonald & Mullan and collaborators) by messing around with alpha, too, though to duplicate their model you generally need a depth-dependent mixing length.

If you decide to go down this route, you might find it helpful to look at some work led by Lewis Ireland (a former student of mine) from a couple of years ago (ApJ 2018, 856:132), which explicitly gives the relations between R, s, alpha, etc, and shows how to construct MLTs that mimic the "rotating" or "magnetic" effects proposed by various authors.

Hope that helps! Good luck with your project.

Best regards,

Matt

On Fri, Mar 12, 2021 at 10:09 AM James Wild via Mesa-users <mesa-users at lists.mesastar.org> wrote:
We've spent a week ruminating on this, and I'm not convinced it's quite what we're after. We are interested in trying to reproduce the observed donor_mass vs orbital period data in order to measure the required angular momentum loss (AML) rate. The end goal is an empirically measured AML rate for CVs below the gap.

Unless I've misunderstood, your approach would be analogous to adding extra AML - increasing the mass loss rate at a given donor mass. But this would have an inconsistent effect along the track. It would have no impact on the orbital period at which the CV came back into contact at the bottom of the gap, for example, since the stars in the gap are in equilibrium and not experiencing any mass loss.

Instead, we want to get the input stellar models as close to reality as possible. This way, when we adjust the AML rate to fit the observed data, we can be confident we are not adding extra AML to compensate for the tendency for the models to underpredict main sequence radii.

Ideally, we would tweak the models so that the MESA main-sequence radii are around 2-4% larger than now - see the attached plot, which shows the measured masses and radii of M-dwarfs from Parsons et al (2018), where we have shown the percentage discrepancy between measured radii and MESA main-sequence models with tau_100 boundary conditions.

[image.png]

I wonder if this might be done by introducing the effect of starspots into MESA somehow. For example, we might make our own boundary conditions table with a modified effective temperature, to account for the fact that starspots reduce the effective temperature from the pristine photospheric value. We are worried there are some subtle implications we haven't thought through, and wondered if anyone has any advice how to do this.

On Thu, 4 Mar 2021 at 01:46, Dean Townsley <Dean.M.Townsley at ua.edu> wrote:

Hi James,

While I think changing the size of the star that MESA produces is difficult, since that is determined by the physical state of the star, I think you can accomplish what you want in a different way.

The mass transfer rate between stars is usually determined by comparing the radius of the donor star (R_1) and the Roche Lobe radius (R_RL1).  A good example is equations 13 and just after in Paxton et al (2015).  I think you can accomplish what you want just by effectively changing how R_1 and R_RL are used to compute the mass transfer rate.  e.g. use f*R_1 where f is some inflation factor (like 1.02 for a 2% inflation), and/or something similar applied to R_RL1.

To implement this, I think you would want to implement your own subroutine to attach to the other_rlo_mdot() subroutine hook in your run_binary_extras.f90 and have use_other_rlo_mdot set to true.  You'll probably want to pattern your function after the actual rlo_mdot() subroutine that is in binary/private/binary_mdot.f90.  It looks like that implements what is described in Paxton et al. (2015).

This is somewhat like what is done in the run_binary_extras.f90 that is included with the Pala et al (2017) paper, but there it was done for the angular momentum loss rate using the other_jdot_mb() hook.  So it might be good to use the run_binary_extras.f90 there as an example of how to use one of these hooks.  There is also some documentation about using the _extras stuff on the mesa website I believe.

Hopefully that at least gets you started in the right direction.

Dean

On 3/3/21 2:00 AM, James Wild via Mesa-users wrote:
Hi,

I'm trying to simulate a full CV evolutionary track, based on the work by Paxton et.al. (2015)<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fui.adsabs.harvard.edu%2Fabs%2F2015ApJS..220...15P%2Fabstract&data=04%7C01%7Cdmtownsley%40ua.edu%7C41c84eab4da3415826b508d8de1a8c5c%7C2a00728ef0d040b4a4e8ce433f3fbca7%7C0%7C0%7C637503552909444457%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=WAwYiJ67P9KXi8420O4H1gC9CoywhxygwB8UwgvrCns%3D&reserved=0>, similar to this Pala (2017) paper<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Fui.adsabs.harvard.edu%2Fabs%2F2017MNRAS.466.2855P%2Fabstract&data=04%7C01%7Cdmtownsley%40ua.edu%7C41c84eab4da3415826b508d8de1a8c5c%7C2a00728ef0d040b4a4e8ce433f3fbca7%7C0%7C0%7C637503552909444457%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=ABYHYvrlf8PG5ZqV%2F2Kvqo5%2B3QEJpk4XBFE1dAKMGeU%3D&reserved=0>. Their inlists are provided on cococubed, so make for a good jumping off point. However, I'd like to make the empirical corrections that Knigge (2011)<https://nam11.safelinks.protection.outlook.com/?url=https%3A%2F%2Farxiv.org%2Fabs%2F1102.2440&data=04%7C01%7Cdmtownsley%40ua.edu%7C41c84eab4da3415826b508d8de1a8c5c%7C2a00728ef0d040b4a4e8ce433f3fbca7%7C0%7C0%7C637503552909454460%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=vl1vf2OT3uYJVoNwWgzcVwj65nN5y%2FwydaWaellSZVE%3D&reserved=0> make in their simulations, which includes modifying the radius of the M dwarf donor star by about 10% to account for both the generally underestimated radii of low mass main sequence stars, and the non-spherical geometry of the Roche Lobes

>From what I understand, the radius of a star in mesa is an observable quantity, calculated from other variables, rather than something that can be modified directly by the user, but I'm sure there will be some way to force the code to do this. I suspect that the non-spherical Roche geometry is already accounted for in the mass transfer code, but the underestimation of the main sequence radii can vary between 1-5%.

Unfortunately, I'm not familiar enough with the codebase to do this while being sure I'm not breaking anything important, what might the best approach be here?

Thanks for your time,
James Wild.

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