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
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