[mesa-users] The mass and radius of the Sun
adamjermyn at gmail.com
Wed Jan 27 11:18:36 EST 2016
Are you also changing the mixing length parameter? That can have an impact on things like the convective boundary location...
> On Jan 27, 2016, at 3:38 PM, Warrick Ball <wball at astro.physik.uni-goettingen.de> wrote:
> Hi MESAlians,
> This is a note on some fine-tuning of my solar calibrations that I thought might be of community interest. And I'm hoping there might be some input from list subscribers who've been calibrating solar models for longer than I have!
> To put this in context, MESA's test suite solar calibration makes use of all sorts of information to calibrate a solar model. I wanted to do an accurate "classical" solar calibration instead, where one varies the Sun's initial metallicity, initial helium abundance, and mixing length parameter to match its luminosity, radius and surface metallicity, at the Sun's measured age (4.61 Gyr in MESA) and mass. But as an extra constraint, I wanted the final model to match low-order, low-degree solar oscillation data about as well as the infamous Model S. This isn't a strict requirement, but basically I wanted it to look okay to the eye.
> The first attached inlists (for MESA star and star/astero) was my naive attempt at doing this, some time ago. I've also attached one of the best-fit models in FGONG format, and a plot of the frequency differences from ADIPLS between this model and low-degree BiSON data [1,2]. As you can see, there is a slight offset in the low-frequency modes. (The growing systematic difference with frequency is the infamous surface effect.) This low-frequency discrepancy always bugged me, so I was inspired to return to it about 6 weeks ago. I decided to take a look at the values being used for Model S' calibration and my own, and some interesting differences start to appear...
> First, what is the mass of the Sun? The mass of Model S is 1.989e33 g, and MESA's constants module has Msun = msol = 1.9892e33 g. What we really know precisely is the product G*Msun, the "standard gravitational parameter", to quite impressive precision:
> G*Msun = 1.32712440018(9) e26 cm^3/s^2
> Okay, so what's G*Msun in MESA?
> G*Msun(MESA) = 6.67428e-8 * 1.9892e33 = 1.32765e26
> So my first change to the constants was to set my solar mass so that G*M is its measured value. This demands M/Msun(MESA) ~= 0.999606.
> Second, what's the radius of the Sun? The radius of Model S is 6.9599e10 cm, whereas MESA's constant module has 6.9598e10 cm. Not a big difference. I glanced through the reference in the MESA papers (and code)  and references therein, but my cursory glance didn't turn up where MESA's value actually came from. With some more digging, I came across a paper by Haberreiter, Schmutz & Kosovichev  in which they discuss the difference between the seismic solar radius and photospheric (for want of a better name) radius. Based on some detailed atmospheric modelling, specifically close to the limb of the Sun, they conclude that the photospheric value must be corrected to match the seismic value, which is what should then be used for stellar models. Consulting their table, they suggest a corrected solar radius of 6.95568e10 cm, which is what I plugged into my solar calibration.
> The second inlist has these changes made. Again, I've also attached the FGONG file and a plot showing the frequency differences. As you can see, they now basically match, at least to the extent that I desired.
> Is this the end? Of course not! For a start, there's a chance I happen to have cherry-picked appropriate values that solve my problem. Though I'm pretty set on the solar mass, I'm still not perfectly satisfied with how to choose the solar radius. I also haven't really mentioned the solar luminosity yet. (For the time being, I'm using the recently-defined nominal solar luminosity of 3.828e33 erg/s.) But most of all, my convection zone boundary isn't quite in the right place: it's at 0.719 Rsun, rather than the helioseismic value of 0.713 ± 0.001 Rsun. So I'll have a closer look at that later.
> Hope that was interesting to someone!
>  http://adsabs.harvard.edu/abs/2009MNRAS.396L.100B
>  http://adsabs.harvard.edu/abs/2014MNRAS.441.3009D
>  http://adsabs.harvard.edu/abs/2005ApJ...618.1049B
>  http://adsabs.harvard.edu/abs/2008ApJ...675L..53H
> Warrick Ball
> Postdoc, Institut für Astrophysik Göttingen
> wball at astro.physik.uni-goettingen.de
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