[Mesa-users] Energy conservation on the main sequence

[David Arnett]

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
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