[Mesa-users] Question about GR corrections for SMS

Sun Jul 26 13:01:18 EDT 2020

Hi Bill

I am trying to evolve a rapidly accreting supermassive primordial star. The
star starts at 10 Msun and accretes matter at 1 Msun / yr until the star
reaches ~450,000 Msun (no gr factors), 120,000 Msun (gr factors on) and ~
220,000-320,000 Msun with my other cgrav routine.

I am not familiar with how the corrections are produced. I’ve been told
they can be linearised in different ways, but from previous work in the
field with other codes such as Kepler and Geneva, they implemented gr
corrections to G in the same way I am trying. Also we think the terms in
Grel do not significantly effect G until the stars surpass 10^4 Msun and
that the between 1-3 x 10^5 Msun these corrections lead to strong collapse
features before the code stops with a min timestep error.

Initially I saw gr factors in Mesa and wasn’t sure what they were for but
for the case of supermassive stars they actually produce final masses in
the 10^5 Msun range. I was hoping to try implement the corrections from
Kepler and Geneva within other_cgrav to compare to gr factors in Mesa. What
was the intention for gr factors?

I will look further into where the gr corrections came from for
supermassive stars.

Thanks
Nick

On Sun, 26 Jul 2020 at 17:01, Bill Paxton <paxton at kitp.ucsb.edu> wrote:

> Hi Nick,
>
> As you know, mesa currently supports a simpler form of GR corrections:
>
>          !### use_gr_factors
>
>          ! GR corrections.  Currently just for pressure equation.
>          ! GR gravity factor = 1/sqrt(1-2Gm/(rc^2))
>
>       use_gr_factors = .false.
>
> You have changed of this term of the correction to 1/(1 - 2Gm/(rc^2)).
> You’ve approximated away the sqrt, but didn’t drop the factor of 2 as I
> would have expected.    Is that a bug?    Or do I have a bug in mesa?
>
> Also, I’ve been told that the other corrections you’ve included are not
> significant for situations expected in mesa (at least until we try to do
> neutron star interiors!).  Could you please provide numbers to show that in
> fact those extra terms are important for a plausible application in mesa
> (such as neutron star surface as opposed to interior) and that limiting the
> correction to the term GR gravity factor currently implemented in mesa
> would be significantly wrong.
>
> thanks,
> Bill
>
>
>
>
>
>
>
>
>
> On Jul 26, 2020, at 8:26 AM, Nicholas Herrington via Mesa-users <
> mesa-users at lists.mesastar.org> wrote:
>
> Hi
>
> I have transferred the corrections from the source code to the other_cgrav
> subroutine in the run_star_extras.f, as you suggested.
>
> When implementing the TOV corrections to G in the source code I added a
> few extra terms onto G = s% cgrav(k) to form G = s% cgrav(k)*Grel, where
> Grel is a function of the pressure, density, mass and radius. In my
> run_star extras.f I initially copied my Grel(P(k),rho(k),M(k),R(k)) into
> the subroutine other_cgrav, under s% cgrav(:) = standard_cgrav*Grel (where
> previously s% cgrav(:) = standard_cgrav). This did not work, so I presume I
> needed to iterate this throughout all the zones of the star. I have
> attached what I've got so far and from my tests and tweaks the results of
> this subroutine are close to what has been done before with this TOV
> implementation in other stellar evolution codes (final masses around 10^5
> Msun).
>
> I am still new to FORTRAN and my understanding of the loop I have made so
> far is that after each step of the code the loop evaluates G from 1 up to
> the current number of zones of the star, appends this to cgrav(:) as a list
> or array, which is then fed into the stellar equations? However I am not
> sure this is the case as each time I run the same star with same controls
> inlist, the final mass of the star changes significantly. With my source
> code implementation the star would consistently stop at ~110,000 Msun
> (accreting at 1 Msun/yr) when the timesteps drop significantly below the dt
> limit, which is expected for a supermassive star at this accretion rate.
> Additionally depending on the number of isotopes in the nuclear network the
> final mass changes significantly as well which wasn't previously the case
> with the source code changes. Other work with the TOV corrections to G in
> the KEPLER code show consistent final masses of ~200,000 Msun, which also
> leads me to believe I am doing something wrong in my subroutine.
>
> I would really appreciate any comments and feedback on whether the
> subroutine is computing Grel in the right way. Below is the TOV
> approximations to G I am looking to implement, <aepgpaknhdgjjhfh.png>
>
> Here is the subroutine I have created so far to try and compute this,
> <jflkhccofibpbple.png>
>
>
> ('real (dp) :: Mass, Rad, Pr, rho' were previously in the subroutine, but
> have been removed now please ignore them).
>
> I have attached the run_star_extras.f, inlist_1Mdot for the controls and
> images of Grel and the other_cgrav subroutine named 'TOV_cgrav'.
>
> Thanks
> Nick
> On 23/06/2020 16:06, Rob Farmer wrote:
>
> Hi
> Please keep all replies on mesa-users so others can learn and/or help.
>
> You should never need to alter the f90 source files (except your
> run_star_extras.f90). Mesa has the concept of "hooks" which can change the
> internal physics without needing to alter the mesa source code.
>
> In this case look at the routine in star/other/other_cgrav.f90. If you
> follow the instructions you can alter G however you want. This has the
> advantage that it ensures that all occurrences of G have your corrections
> applied.
>
> You can then call your routine again from your run_star_extras.f90 in the
> data_for_extra_profile_columns function to save the values to the profile
> file.
>
> Rob
>
>
> On Tue, 23 Jun 2020 at 16:55, Nicholas Herrington <
> Nicholas.Herrington at myport.ac.uk> wrote:
>
>> Hi Rob
>>
>> Sorry for the very late reply, I haven't been able to access my work
>> machine in a while. After coming back to it, I have not been able to
>> replicate the 10^6 Msun run in version 11701 (only 500-800x10^5). I spoke
>> to others in the field and they have said that without the GR corrections
>> these stars don't necessarily have to reach 10^6 Msun.
>>
>> Since the 12778 doesn't have post-Newtonian corrections to the G, I have
>> added the corrections to G within the subroutine associated to
>> 'use_gr_factors' (within the hydro_reconstruct.f90). Instead of 'G =
>> cgrav*gr_factors', I have added my own 'G = cgrav*Grel'. How can I output
>> Grel and G in my profiles or history.data? Also is there a better way for
>> me to correct G rather than changing the f90 files?
>>
>> Thanks
>> Nick
>>
>> On Fri, 15 May 2020 at 18:35, Rob Farmer <r.j.farmer at uva.nl> wrote:
>>
>>> Hi,
>>>
>>> >Is there anything along the lines of the TOV approximation? Was
>>> use_gr_factors intended for SMS?
>>>
>>> No only the changes to s% grav are implemented.
>>>
>>> > which is why I wonder if the new version has this.
>>>
>>> It is still there in 12778. But lots of other things will have changed
>>> between versions, which may be stopping the star from getting to 10^6msun
>>> (which is what i interpret your saying is the problem?). Or maybe you've
>>> stumbled on a bug, it would be helpful if you could make a small test case
>>> that shows this problem.
>>>
>>> Rob
>>>
>>>
>>>
>>> On Fri, 15 May 2020 at 18:59, Nicholas Herrington via Mesa-users <
>>> mesa-users at lists.mesastar.org> wrote:
>>>
>>>> Hi,
>>>>
>>>> I am evolving some supermassive primordial stars (SMS) with accretion
>>>> rates up to 1 Msun/yr. In the newest version of MESA is there general
>>>> relativistic correction to G for SMS. I have found the control
>>>> use_gr_factors with corrections to cgrav along the lines of
>>>> (1-2GM/rc^2)^-0.5. Is there anything along the lines of the TOV
>>>> approximation? Was use_gr_factors intended for SMS?
>>>>
>>>> I was running a SMS with version r11701 and with use_gr_factors off I
>>>> get results exceeding 10^6 Msun which is expected, but with version r12778
>>>> and the same inlist (use_gr_factors = .false.), the star reaches 10^5. This
>>>> is close to the final mass of the same star from other stellar evolution
>>>> codes with post-newtonian corrections to G, which is why I wonder if the
>>>> new version has this.
>>>>
>>>> Thanks
>>>> Nick
>>>>
>>> <run_star_extras.f><Grel.png><inlist_1Mdot.txt><runstarGrel.png>
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