Helioseismic abundances with the new T-MHD Equation of State (EOS)

Dr. Regner Trampedach Research Scientist Space Science Institute, 4765 Walnut Street, Boulder, CO Dr. Regner Trampedach Research Scientist Space Science Institute, 4765 Walnut Street, Boulder, CO References References ●Barklem & Collet, 2016, A&A, 588, A96 Barklem & Collet, 2016, A&A, 588, A96 ●Buldgen Buldgen et al et al., 2024, A&A, 681, A57 ., 2024, A&A, 681, A57 ●Christensen-Dalsgaard, Christensen-Dalsgaard, et al. et al., 1996, Science, 272, 1286 , 1996, Science, 272, 1286 ●Di Mauro Di Mauro et al et al., 2002, A&A, 384, 666 ., 2002, A&A, 384, 666 ●Hummer & Mihalas 1988, ApJ, 331, 794 Hummer & Mihalas 1988, ApJ, 331, 794 ●Kramida Kramida et al et al., 2020, NIST Atomic Spectr, Database ., 2020, NIST Atomic Spectr, Database ●Potekhin, Chabrier & Gilles, 2002, Phys. Rev. E, 65, 036412 Potekhin, Chabrier & Gilles, 2002, Phys. Rev. E, 65, 036412 ●Trampedach Trampedach et al. et al. 2006, ApJ, 646, 560 2006, ApJ, 646, 560 ●Trampedach 2024, Sol. Phys., 300(1), #7 Trampedach 2024, Sol. Phys., 300(1), #7 T T-MHD EOS ingredients: -MHD EOS ingredients: ●Building on the Mihalas-Hummer-D Building on the Mihalas-Hummer-Dä äppen ppen EOS, Hummer & Mihalas (1988). EOS, Hummer & Mihalas (1988). ●191 molecules (Barklem & Collet, 2016), 191 molecules (Barklem & Collet, 2016), 129 diatomic, 35 ions. 129 diatomic, 35 ions. ●27 elements, with all 446 ionization stages, 27 elements, with all 446 ionization stages, and total of 135,029 explicitly treated excited and total of 135,029 explicitly treated excited levels ( levels (Kramida Kramida et al et al., 2020). ., 2020). ●Relativistic electrons. Relativistic electrons. ●Coulomb interactions ( Coulomb interactions (beyond beyond the Debyethe DebyeH Hückel approximation) valid up to the point ückel approximation) valid up to the point of crystallization. of crystallization. ●Quantum diffraction from Heisenberg’s Quantum diffraction from Heisenberg’s uncertainty and Quantum exchange from uncertainty and Quantum exchange from Pauli’s exclusion principle. Pauli’s exclusion principle. ●New micro-field distribution functions New micro-field distribution functions (responsible for pressure ionization) (responsible for pressure ionization) depending properly on plasma environment depending properly on plasma environment ( (Potekhin Potekhin et al et al., 2002). ., 2002). ●Abandoned hard-sphere approximation for Abandoned hard-sphere approximation for neutral atoms neutral atoms (which limited original MHD (which limited original MHD EOS to envelopes), and instead treat as EOS to envelopes), and instead treat as nuclear charges screened by bound electrons nuclear charges screened by bound electrons ⇒ ⇒ no excluded-volume effects at high density. no excluded-volume effects at high density. T T-MHD EOS ingredients: -MHD EOS ingredients: ●Building on the Mihalas-Hummer-D Building on the Mihalas-Hummer-Dä äppen ppen EOS, Hummer & Mihalas (1988). EOS, Hummer & Mihalas (1988). ●191 molecules (Barklem & Collet, 2016), 191 molecules (Barklem & Collet, 2016), 129 diatomic, 35 ions. 129 diatomic, 35 ions. ●27 elements, with all 446 ionization stages, 27 elements, with all 446 ionization stages, and total of 135,029 explicitly treated excited and total of 135,029 explicitly treated excited levels ( levels (Kramida Kramida et al et al., 2020). ., 2020). ●Relativistic electrons. Relativistic electrons. ●Coulomb interactions ( Coulomb interactions (beyond beyond the Debyethe DebyeH Hückel approximation) valid up to the point ückel approximation) valid up to the point of crystallization. of crystallization. ●Quantum diffraction from Heisenberg’s Quantum diffraction from Heisenberg’s uncertainty and Quantum exchange from uncertainty and Quantum exchange from Pauli’s exclusion principle. Pauli’s exclusion principle. ●New micro-field distribution functions New micro-field distribution functions (responsible for pressure ionization) (responsible for pressure ionization) depending properly on plasma environment depending properly on plasma environment ( (Potekhin Potekhin et al et al., 2002). ., 2002). ●Abandoned hard-sphere approximation for Abandoned hard-sphere approximation for neutral atoms neutral atoms (which limited original MHD (which limited original MHD EOS to envelopes), and instead treat as EOS to envelopes), and instead treat as nuclear charges screened by bound electrons nuclear charges screened by bound electrons ⇒ ⇒ no excluded-volume effects at high density. no excluded-volume effects at high density. Fig. 2: Adiabatic exponent, , computed for the temperature/density stratification of solar Model S by Christensen-Dalsgaard et al. (1996), for 9 different compositions: X={0.70, 0.75, 0.80} × Z={0.010, 0.015, 0.020} -pairs (black solid curves) with the T-MHD EOS. The light-blue curve shows the helioseismic inversion by Di Mauro et al. (2002), for logT<6.26, and with the width showing the uncertainty. The light-blue dashed curve (solid for logT>6.26) shows of the reference model. The inset to the right is zoomed in by a factor of 20, to show the effects of the 25 metals. Fig. 2: Adiabatic exponent, , computed for the temperature/density stratification of solar Model S by Christensen-Dalsgaard et al. (1996), for 9 different compositions: X={0.70, 0.75, 0.80} × Z={0.010, 0.015, 0.020} -pairs (black solid curves) with the T-MHD EOS. The light-blue curve shows the helioseismic inversion by Di Mauro et al. (2002), for logT<6.26, and with the width showing the uncertainty. The light-blue dashed curve (solid for logT>6.26) shows of the reference model. The inset to the right is zoomed in by a factor of 20, to show the effects of the 25 metals. Helioseismic abundances with the new Helioseismic abundances with the new T T-MHD -MHD Equation of State (EOS) Equation of State (EOS) Regner Trampedach Regner Trampedach1 1, , Werner D Werner Dä äppen ppen2,* 2,*, Maria Pia Di Mauro , Maria Pia Di Mauro3 3 (1) Space Science Inst., Boulder, CO; (2) Univ. of Southern California, L.A., CA; * (1) Space Science Inst., Boulder, CO; (2) Univ. of Southern California, L.A., CA; * Emeritus; (3) INAF-IAPS, Rome, Italy Emeritus; (3) INAF-IAPS, Rome, Italy Why helioseismic abundances? Why helioseismic abundances? ●Significant disagreements between different Significant disagreements between different spectroscopic spectroscopic solar solar abundances; abundances; low-/highlow-/highΖ Ζ . . ●Current solar models with lowCurrent solar models with lowΖ Ζ , disagree , disagree with helioseismology by 10-15 with helioseismology by 10-15σ σ! ! ●This is the solar abundance problem. This is the solar abundance problem. ●Helioseismic methods are orthogonal to Helioseismic methods are orthogonal to spectroscopic methods; independent from spectroscopic methods; independent from complicated atmosphere physics, or complicated atmosphere physics, or opacities - instead determined by EOS. opacities - instead determined by EOS. ●Individual elements are not within reach, Individual elements are not within reach, but He and but He and total total metallicity metallicity is possible now! is possible now! Why helioseismic abundances? Why helioseismic abundances? ●Significant disagreements between different Significant disagreements between different spectroscopic spectroscopic solar solar abundances; abundances; low-/highlow-/highΖ Ζ . . ●Current solar models with lowCurrent solar models with lowΖ Ζ , disagree , disagree with helioseismology by 10-15 with helioseismology by 10-15σ σ! ! ●This is the solar abundance problem. This is the solar abundance problem. ●Helioseismic methods are orthogonal to Helioseismic methods are orthogonal to spectroscopic methods; independent from spectroscopic methods; independent from complicated atmosphere physics, or complicated atmosphere physics, or opacities - instead determined by EOS. opacities - instead determined by EOS. ●Individual elements are not within reach, Individual elements are not within reach, but He and but He and total total metallicity metallicity is possible now! is possible now! Fig. 1 Fig. 1: The adiabatic exponent, , for the : The adiabatic exponent, , for the bottom part of the solar convection zone and to bottom part of the solar convection zone and to the core, showing hilly terrain of many the core, showing hilly terrain of many ionization zones. We use these features for ionization zones. We use these features for helioseismic inversions for the solar metallicity helioseismic inversions for the solar metallicity (Buldgen et al. 2024). The table is diagonal in (Buldgen et al. 2024). The table is diagonal in log logT T and log and logϱ, ϱ, and the drop towards the front and the drop towards the front shows the transition to the radiation dominated shows the transition to the radiation dominated regime, having = 4/3. regime, having = 4/3. Fig. 1 Fig. 1: The adiabatic exponent, , for the : The adiabatic exponent, , for the bottom part of the solar convection zone and to bottom part of the solar convection zone and to the core, showing hilly terrain of many the core, showing hilly terrain of many ionization zones. We use these features for ionization zones. We use these features for helioseismic inversions for the solar metallicity helioseismic inversions for the solar metallicity (Buldgen et al. 2024). The table is diagonal in (Buldgen et al. 2024). The table is diagonal in log logT T and log and logϱ, ϱ, and the drop towards the front and the drop towards the front shows the transition to the radiation dominated shows the transition to the radiation dominated regime, having = 4/3. regime, having = 4/3. Fig. 3: Helium abundance vs. metals-to-hydrogen ratio, from the (in color) between of a solar model and of the inversion, below, by Di Mauro et al. (2002), also shown in Fig.2. We also shown the ‘modern’, lowΖ Ζ abundance by Asplund et al. (2021) in yellow and the ‘classic’ abundances by Grevesse & Sauval (1998) in light blue. The location of the tables used in this work, are indicated with black ◊. The -minimum is indicated with the red +. Fig. 3: Helium abundance vs. metals-to-hydrogen ratio, from the (in color) between of a solar model and of the inversion, below, by Di Mauro et al. (2002), also shown in Fig.2. We also shown the ‘modern’, lowΖ Ζ abundance by Asplund et al. (2021) in yellow and the ‘classic’ abundances by Grevesse & Sauval (1998) in light blue. The location of the tables used in this work, are indicated with black ◊. The -minimum is indicated with the red +. Fig. 4: Same as Fig.2, but for the seismic solar model by Buldgen et al. (2024), and for the same 9 (X, Y) compositions. Temperature is not accessible to inversions, so we plot against pressure, which is. Only the inversion domain is included in this plot, in contrast to Fig.2. Fig. 4: Same as Fig.2, but for the seismic solar model by Buldgen et al. (2024), and for the same 9 (X, Y) compositions. Temperature is not accessible to inversions, so we plot against pressure, which is. Only the inversion domain is included in this plot, in contrast to Fig.2. He+ He++ H+ metals metals He+ He++ H+ metals metals Fig. 5: Same as Fig.3, but from the inversion by Buldgen et al. (2024), shown in Fig.4. Here we also show the modern, hiΖ Ζ abundance by Magg et al. (2021, not recommended, see attached) in green. The T-MHD EOS tables is the same set of 9 as used in Figs. 2-4. Fig. 5: Same as Fig.3, but from the inversion by Buldgen et al. (2024), shown in Fig.4. Here we also show the modern, hiΖ Ζ abundance by Magg et al. (2021, not recommended, see attached) in green. The T-MHD EOS tables is the same set of 9 as used in Figs. 2-4. Metal free Next steps 1.We need to account for the inversion kernels when comparing helioseismology with EOS. 2.Re EOS development, we need to solve a convergence problem caused by molecules. 3.Stay tuned! Next steps 1.We need to account for the inversion kernels when comparing helioseismology with EOS. 2.Re EOS development, we need to solve a convergence problem caused by molecules. 3.Stay tuned! Metal free Metal freeMetal free Fig. 11 of 2002 Note: The current Z values are entirely determined by the range of the solar stratification, for which we minimize the differences. Might be solved w/step 1, below.