[Mesa-users] Inconsistency between Omega/Omega_crit reported by MESA and that computed with Paxton et al. (2019) equations
Pablo Marchant
pamarca at gmail.com
Mon Jul 13 14:43:53 EDT 2020
Hi Larry,
thanks for reporting this, I'll give it a check in the following days. One
thing you have to be aware of is that omega (by which I mean the little
omega used in Paxton+ 2019 and not the angular frequency) is computed
explicitly at the beginning of the step, we are not implicitly solving its
value in a consistent way inside the newton solver as the structure of the
star changes. The other detail to be aware of is that angular momentum
mixing is done separate from the structure of the star. I believe a
combination of these two things should be related to the variation you see
in reported values.
A simple test I'd ask you to do to confirm this is to see if the large
variation holds if you use a very small timestep, which you can do with
max_timestep. In this case the explicit calculation of omega should not
matter, and you should find near consistent values. If you keep finding a
large discrepancy in omega from step to step while the entire structure of
the star and its rotation remain static, then there's likely a deeper issue.
In any case, these subtleties should be better documented in the future.
Cheers
On Mon, Jul 13, 2020 at 8:21 PM Larry Molnar <lmolnar at calvin.edu> wrote:
> I am running the latest MESA based on the revisions described in Paxton et
> al. (2019): MESA R12778, SDK 20.3.2, on a Linux operating system.
>
>
>
> I am interested in rotation of main sequence stars with intermediate mass,
> so I ran a case with 1.0 Msun and default (solar) abundances with several
> initial values of the frequency ratio omega := Omega_Psi/Omega_crit [p. 28
> of Paxton et al. (2019)]. I attach the inlist used and copy the first few
> lines of output from profile39.data (at which age = 6.79 Gy).
>
>
>
> The run completed fine and the results largely look sensible. The left
> side of Equation 39 of section 4 of Paxton et al. (2019) contains j_rot,
> m_Psi, and r_Psi, the quantities needed to determine omega for a given zone
> (and hence the quantities r_e and i_rot which are found on the right side
> of the equation). As a consistency check I computed both sides separately
> for a number of zones and found significant disagreement (up to several
> percent, depending on the zone). So I used Equation B30 to implicitly find
> the value of omega that is consistent (and the values for other things like
> r_e, r_p, etc.). I found a slightly larger value of omega that was
> consistent with everything. Using this revised omega, I checked separately
> and found the profile values of Omega_Psi, r_e, r_p, and i_rot are all
> consistent with the left side of Eqn. 39 while omega, v_rot, and Omega_crit
> are not. I repeated this for different zones and for two initial values of
> omega (0.3 and 0.4). I find the omega reported by the profile is
> approximately equal to the following function of the omega from the
> equation: omega_Eqn*(1 – 0.25*omega_Eqn^2).
>
>
>
> For the example below, omega of zone 1 is reported to be 0.32961 when it
> should be 0.33906, a difference of 2.8%.
>
>
>
> In summary, the correct omega ratio seems to be computed and used for some
> things (like r_e, r_p, i_rot, Omega_Psi), but something else is being
> reported (and being used to compute v_rot and Omega_crit).
>
>
>
> Prof. Larry Molnar
>
> Department of Physics and Astronomy
>
> Calvin University
>
> 1734 Knollcrest Circle SE
>
> Grand Rapids, MI 49546-4403 USA
>
>
>
> E-mail: lmolnar at calvin.edu
>
> Phone: 616-526-6341
>
>
>
> Profile39.data: first three zones plus header
>
>
>
>
> 1
> 2
> 3
> 4
> 5 6
> 7
> 8
> 9
> 10
> 11 12
> 13
> 14
> 15
> 16
> 17 18
> 19
> 20
> 21
> 22
> 23
> 24
> 25
> 26
> 27
> 28
> 29
> 30 31
> 32
> 33
> 34
> 35
> 36 37
> 38
> 39
> 40
> 41
> 42 43
> 44
> 45
> 46
> 47
> 48
> 49
> 50
> 51 52
>
> model_number
> num_zones
> initial_mass
> initial_z
> star_age time_step
> Teff
> photosphere_L
> photosphere_r
> center_eta
> center_h1 center_he3
> center_he4
> center_c12
> center_n14
> center_o16
> center_ne20
> star_mass
> star_mdot
> star_mass_h1
> star_mass_he3
> star_mass_he4
> star_mass_c12
> star_mass_n14
> star_mass_o16
> star_mass_ne20
> he_core_mass
> c_core_mass
> o_core_mass
> si_core_mass fe_core_mass
> neutron_rich_core_mass
> tau10_mass
> tau10_radius
> tau100_mass
> tau100_radius dynamic_time
> kh_timescale
> nuc_timescale
> power_nuc_burn
> power_h_burn
> power_he_burn
> power_neu
> burn_min1
> burn_min2
> time_seconds
> version_number
> compiler build
> MESA_SDK_version
> math_backend date
>
> 840
> 788 1.0000000000000000E+000
> 2.0000000000000000E-002
> 6.7862319465169029E+009
> 1.0974467458049601E+008
> 5.6913137780955512E+003
> 1.1106458896908029E+000
> 1.0854793927473201E+000
> -1.4234108223730109E+000
> 1.7892625342288088E-001
> 1.2875481967828730E-006
> 8.0076368174195711E-001
> 3.0901329101104673E-005
> 6.8050315038511392E-003
> 7.2830595800253044E-003
> 2.0994604783340942E-003
> 1.0000000000000000E+000
> 0.0000000000000000E+000
> 6.4251076451589306E-001
> 9.1978547547992594E-004
> 3.3638630678708026E-001
> 2.3204305753635767E-003
> 2.3422350540312545E-003
> 9.3306927181358093E-003
> 2.0994604783340300E-003
> 0.0000000000000000E+000
> 0.0000000000000000E+000 0.0000000000000000E+000
> 0.0000000000000000E+000
> 0.0000000000000000E+000
> 0.0000000000000000E+000
> 9.9999999986641774E-001
> 1.0852251060789109E+000
> 9.9999999977220166E-001
> 1.0850847080353851E+000
> 1.1323115727543849E+004
> 1.9470734833037574E+007
> 9.0037698719471607E+009
> 1.1106109430736193E+000
> 1.1106109430736197E+000
> 1.9379726463585424E-041
> 3.1117358618271040E-002
> 5.0000000000000000E+001
> 1.0000000000000000E+003
> 2.1416092559439270E+017
> "12778"
> "gfortran" "9.2.0"
> "x86_64-linux-20.3.2"
> "CRMATH" "20200707"
>
>
>
>
> 1 2
> 3
> 4
> 5
> 6
> 7 8
> 9
> 10
> 11
> 12
> 13 14
> 15
> 16
> 17
> 18
> 19
> 20
> 21
> 22 23
>
> zone
> mass
> logR logT
> logRho
> logP x_mass_fraction_H
> y_mass_fraction_He
> z_mass_fraction_metals x
> luminosity
> conv_L_div_L
> omega log_omega
> log_J_inside i_rot
> j_rot
> v_rot r_polar
> r_equatorial
> r_e_div_r_p omega_crit
> omega_div_omega_crit
>
> 1
> 1.0000000000000000E+000
> 3.5621583017451837E-002
> 3.7553873899760544E+000
> -6.8226384760895904E+000
> 4.7364521258960668E+000
> 6.9837283051018251E-001
> 2.8162185819852292E-001
> 2.0005311291294570E-002
> 6.9837283051018251E-001
> 1.1106458896908029E+000 0.0000000000000000E+000
> 1.8289678787990470E-004
> -3.7377939217421856E+000
> 5.0141558734190070E+001
> 4.0452322195411635E+021
> 7.3985997918237632E+017
> 1.3817339257946193E+002
> 1.0466378035378214E+000
> 1.1061445120438380E+000
> 1.0568551110086730E+000
> 5.5489221113985861E-004 3.2960777644400241E-001
>
> 2
> 9.9999999999949996E-001
> 3.5621053101314769E-002
> 3.7558294668053462E+000
> -6.8198510069919314E+000
> 4.7396826558142946E+000
> 6.9837283051018251E-001
> 2.8162185819852292E-001
> 2.0005311291294570E-002
> 6.9837283051018251E-001
> 1.1106458896908031E+000
> 0.0000000000000000E+000
> 1.8289678787990470E-004 -3.7377939217421856E+000
> 5.0141558734187761E+001
> 4.0452210785591907E+021
> 7.3985794153255962E+017
> 1.3817322398356947E+002
> 1.0466367126293932E+000
> 1.1061430561848453E+000
> 1.0568548215798377E+000
> 5.5489322674071766E-004 3.2960717317489624E-001
>
> 3
> 9.9999999999862488E-001
> 3.5620131676504144E-002
> 3.7563968080601273E+000
> -6.8163424224394999E+000
> 4.7437598235062506E+000
> 6.9837283051018240E-001
> 2.8162185819852292E-001
> 2.0005311291294681E-002
> 6.9837283051018240E-001
> 1.1106458896908031E+000
> 0.0000000000000000E+000
> 1.8289678787990470E-004
> -3.7377939217421856E+000
> 5.0141558734183725E+001 4.0452026442495694E+021
> 7.3985456995654310E+017
> 1.3817293082741162E+002
> 1.0466346781989255E+000
> 1.1061406031617111E+000
> 1.0568545321517389E+000
> 5.5489490448713092E-004 3.2960617659473646E-001
>
>
>
>
>
>
> _______________________________________________
> 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
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