[Mesa-users] Energy conservation on the main sequence

[RICHARD H D TOWNSEND]

HI Dave --

I've found out that MESA can in fact track the rest-mass change -- set use_mass_corrections = .true., and then look at the star_gravitational_mass variable in history data.

Regarding my original question: it's true that dE/dt should closely match L_nuc - L_surf. But a better  numerical treatment of energy conservation is required for this equality to be seen in calculations. Without wanting to give too much away, the MESA team hopes to make a new public release of the code sometime soon, which includes this better treatment (and gets the equality right).

cheers,

Rich

> On Feb 18, 2019, at 12:13 PM, David Arnett <wdarnett at gmail.com> wrote:
> 
> Hi Pablo, RICHARD,
> that is almost (~0.007 .neq. 0) right. There is a additional small correction (special relativity) for the rest mass change in the gravitational energy (the nuclear mass deficit). The MESA models, like almost all stellar evolution models, ignore this small change, but it is real. Helio-seismology should show a ~few% change in sound speed in inner 10% of solar core (He4 is lighter than 4 H nuclei), and could be used to measure the H consumed.
> 
> On Sun, Feb 17, 2019 at 2:20 PM Pablo Marchant via Mesa-users <mesa-users at lists.mesastar.org> wrote:
> Yes, I did this a while back and you need to account for the change in rest mass energy. Essentially you can get ~6.7e18 ergs per gram of burnt hydrogen. During the main sequence you're tapping into this rest mass energy, so if you don't include it explicitly you won't get energy balance right.
> 
> Playing with this I'm simply defining
> 
> E = internal_energy + gravitation_binding_energy + M*X*6.7e18
> 
> and defining the energy lost from the system as
> 
> L_lost = L_surf + L_neu
> 
> doing this in a MESA run I just checked that I get similar values for dE/dt (computed by comparing the value from step to step) and L_lost.
> 
> Cheers
> 
> On Sun, Feb 17, 2019 at 3:11 PM RICHARD H D TOWNSEND <townsend at astro.wisc.edu> wrote:
> I think L_neu has no effect on the energy budget because L_neu(surface) = L_neu(core).
> 
> So, total change in energy = (L_nuc + L_neu - L - L_neu)*dt = (L_nuc - L)*dt
> 
> However, could the discrepancy be due to changes in the stellar rest-mass energy?
> 
> cheers,
> 
> Rich
> 
> On Feb 17, 2019, at 2:24 PM, Pablo Marchant <pamarca at gmail.com> wrote:
> > 
> > Things do seem to match at the beginning, which I assume is the pre-MS. So I'm guessing you're missing something related to nuclear reactions. Maybe L_neu?
> > 
> > Easier to check with inlists at hand for sure.
> > 
> > Cheers
> > 
> > On Sun, Feb 17, 2019 at 2:21 PM Bill Paxton <paxton at kitp.ucsb.edu> wrote:
> > Hi Rich,
> > 
> > Please provide inlists etc so we can play along with you, starting by being able to reproduce your plots.
> > 
> > Thanks,
> > Bill
> > 
> > > On Feb 17, 2019, at 12:14 PM, RICHARD H D TOWNSEND via Mesa-users <mesa-users at lists.mesastar.org> wrote:
> > > 
> > > Hi folks --
> > > 
> > > I'm writing to ask about energy conservation on the main sequence, for a solar-mass star. I'm not yet sure whether this is more of a question about stellar evolution, or about MESA.
> > > 
> > > In the attached figure, I plot two quantities as a function of time:
> > > 
> > > tot_E_change -- the total energy change across each timestep
> > > total_energy_sources_and_sinks -- the total energy sources/sinks across each timestep
> > > 
> > > For this evolutionary stage, total_energy_sources_and_sinks is practically identical to (L_nuc - L)*dt, where L_nuc is the nuclear luminosity, L the surface luminosity, and dt the timestep.
> > > 
> > > My understanding is that the two quantities should align perfectly -- the net energy gain/loss is matched by a change in the star's total energy (which, according to the virial theorem, will result in an expansion/contraction). But that's clearly not what we see; while total_energy_sources_and_sinks is always positive (with the exception  of the ZAMS), the tot_E_change is initially negative and only becomes positive later on in the evolution.
> > > 
> > > I'm clearly missing something important, but I'm not sure what. So, can anyone help clarify what's going on?
> > > 
> > > cheers,
> > > 
> > > Rich
> > > 
> > > <energe-change.pdf>_______________________________________________
> > > mesa-users at lists.mesastar.org
> > > https://lists.mesastar.org/mailman/listinfo/mesa-users
> > > 
> > 
> > _______________________________________________
> > mesa-users at lists.mesastar.org
> > https://lists.mesastar.org/mailman/listinfo/mesa-users
> > 
> > 
> > 
> > -- 
> > Pablo Marchant Campos
> > M.Sc on Astrophysics, Universidad Católica de Chile
> > PhD on Astrophysics, Argelander-Institut für Astronomie, Universität Bonn
> 
> 
> 
> -- 
> Pablo Marchant Campos
> M.Sc on Astrophysics, Universidad Católica de Chile
> PhD on Astrophysics, Argelander-Institut für Astronomie, Universität Bonn
> _______________________________________________
> mesa-users at lists.mesastar.org
> https://lists.mesastar.org/mailman/listinfo/mesa-users
> 
> 
> 
> -- 
> David Arnett
> Regents Professor
> Steward Observatory
> University of Arizona
> 
> Facts are stubborn, but statistics are more pliable.  Mark Twain
> Facts do not cease to exist because they are ignored.  Aldous Huxley