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Summary of Aarhus workshop

This document summarizes the results of the Aarhus workshop focusing on intrinsic numerical accuracy in stellar evolution modeling. It examines the computations of models using the ASTEC code with varying parameters such as mesh points and time steps. Key findings from several cases highlight the importance of these variations on the accuracy of the results. Additionally, the workshop compared the performance of different codes, including CESAM and CLES, in evaluating physical parameters and seismic oscillation frequencies. Insights into discrepancies in global quantities and evolutionary tracks between different models are also discussed.

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Summary of Aarhus workshop

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  1. Summary of Aarhus workshop Some selected results

  2. Intrinsic numerical accuracy • Compare models computed with a given code and given parameters • Vary number of meshpoints • Vary number of timesteps

  3. Case 1.1 0.9 M¯, Xc = 0.35 ASTEC 3He in equilibrium Test effect of no. of meshpoints: ( N = 1200) – (N = 600)

  4. Case 1.1 0.9 M¯, Xc = 0.35 ASTEC 3He in equilibrium Test effect of no. timesteps: ( Nt = 24) – (Nt = 13) (D ymax = 0.025) - (D ymax = 0.05)

  5. Case 1.3 1.2 M¯, Mc = 0.1 M¯ ASTEC 3He in equilibrium Test effect of no. of meshpoints: ( N = 600) – (N = 1200)

  6. Case 1.3 1.2 M¯, Mc = 0.1 M¯ ASTEC 3He in equilibrium Test effect of no. of meshpoints: ( N = 600) – (N = 1200)

  7. Case 1.3 1.2 M¯, Mc = 0.1 M¯ ASTEC 3He in equilibrium Test effect of no. timesteps: ( Nt = 277) – (Nt = 546) (D ymax = 0.05) - (D ymax = 0.025)

  8. Case 1.5 2.0 M¯, Xc = 0.01, Overshoot 0.15 Hp ASTEC 3He in equilibrium Test effect of no. of meshpoints: ( N = 600) – (N = 1200)

  9. Case 1.5 2.0 M¯, Xc = 0.01, Overshoot 0.15 Hp ASTEC 3He in equilibrium Test effect of no. of meshpoints: ( N = 600) – (N = 1200)

  10. Case 1.5 2.0 M¯, Xc = 0.01, Overshoot 0.15 Hp ASTEC 3He in equilibrium Test effect of no. of meshpoints: ( N = 600) – (N = 1200)

  11. Case 1.5 2.0 M¯, Xc = 0.01, Overshoot 0.15 Hp ASTEC 3He in equilibrium Test effect of no. of timesteps: ( Nt = 208) – (Nt = 402)

  12. Case 1.5 2.0 M¯, Xc = 0.01, Overshoot 0.15 Hp ASTEC 3He in equilibrium Test effect of no. of timesteps: ( Nt = 208) – (Nt = 402)

  13. Case 1.5 2.0 M¯, Xc = 0.01, Overshoot 0.15 Hp ASTEC 3He in equilibrium Test effect of no. of timesteps: ( Nt = 208) – (Nt = 402)

  14. Case 1.1 0.9 M¯, Xc = 0.35, TGEC Test effect of no. of timesteps: ( D t = 2000 yr) – (D t = 1800 yr) Continuous: d ln T Dotted: d ln p Dashed: d ln r Dot-dashed: d ln c2 3dot-dashed: d ln G1 Long-dashed: d ln L Thick continuous: d ln X

  15. Case 1.1 0.9 M¯, Xc = 0.35, TGEC Test effect of no. of timesteps: ( D t = 2000 yr) – (D t = 2200 yr) Continuous: d ln T Dotted: d ln p Dashed: d ln r Dot-dashed: d ln c2 3dot-dashed: d ln G1 Long-dashed: d ln L Thick continuous: d ln X

  16. Case 1.1 0.9 M¯, Xc = 0.35, TGEC Test effect of no. of timesteps: ( D t = 2000 yr) – (D t = 2200 yr) Continuous: d ln T Dotted: d ln p Dashed: d ln r Dot-dashed: d ln c2 3dot-dashed: d ln G1 Long-dashed: d ln L Thick continuous: d ln X

  17. Physics comparisons Evaluate physics (EOS, opacity, energy-generation rate, rate of composition change, …, at fixed T, r, Xi Examples: comparing CESAM and CLES with ASTEC, showing, e.g., ln(kASTEC(rCESAM, TCESAM, …)/kCESAM)

  18. CESAM, Case 1.1 Note: consistency problems in OPAL. See also Boothroyd & Sackman (2003; ApJ 583, 1004) In ASTEC implementation: Directly from OPAL: p, rad, d, a, G1 cp = cv + p d2/(r T a)

  19. CESAM, Case 1.1

  20. CESAM, Case 1.1

  21. CESAM, Case 1.1

  22. CLES, Case 1.1

  23. CLES, Case 1.1

  24. CLES, Case 1.1

  25. CLES, Case 1.1

  26. Main project: compare different codes • Evolution tracks • Global parameters for selected models • Detailed comparison of structure • Comparison of oscillation frequencies

  27. CLES and ASTEC Case 1.3 1.2 M¯ X0 = 0.73, Z0 = 0.01 MHeC = 0.1 M¯

  28. CLES and ASTEC Mc/M Case 1.3 1.2 M¯ X0 = 0.73, Z0 = 0.01 MHeC = 0.1 M¯ Xc

  29. CLES, CESAM and ASTEC Case 1.5n 2.0 M¯ X0 = 0.72, Z0 = 0.02 Xc = 0.01 No overshoot

  30. CLES, CESAM and ASTEC Case 1.5n 2.0 M¯ X0 = 0.72, Z0 = 0.02 Xc = 0.01 No overshoot

  31. CLES, CESAM and ASTEC Case 1.5n 2.0 M¯ X0 = 0.72, Z0 = 0.02 Xc = 0.01 Overshoot 0.15 Hp

  32. CLES, CESAM and ASTEC Case 1.5n 2.0 M¯ X0 = 0.72, Z0 = 0.02 Xc = 0.01 Overshoot 0.15 Hp

  33. Detailed model comparison • Global quantities • Differences at fixed m/M, plotted against m/M or r/R • Differences at fixed r/R might be more illustrative for effects on oscillations (but not used yet)

  34. Hydrogen abundance 0.9 M¯ X0 = 0.7 Z0 = 0.02 Xc = 0.35 X

  35. Case 1.1 0.9 M¯, Xc = 0.35 CLES – CESAM2

  36. Case 1.1 0.9 M¯, Xc = 0.35 CLES – CESAM2

  37. Case 1.1 0.9 M¯, Xc = 0.35 CLES – CESAM0

  38. Case 1.1 0.9 M¯, Xc = 0.35 CLES – CESAM0

  39. Case 1.1 0.9 M¯, Xc = 0.35 CESAM2 – CESAM0

  40. Case 1.1 0.9 M¯, Xc = 0.35 ASTEC – CESAM0

  41. Case 1.1 0.9 M¯, Xc = 0.35 ASTEC – CESAM0

  42. Case 1.1 0.9 M¯, Xc = 0.35 ASTEC – CESAM0

  43. Case 1.1 0.9 M¯, Xc = 0.35 STAROX – CESAM0

  44. Hydrogen abundance 1.2 M¯ X0 = 0.7 Z0 = 0.02 Xc = 0.69 X

  45. CLES – CESAM0 Case 1.2 1.2 M¯ X0 = 0.7 Z0 = 0.02 Xc = 0.69

  46. CLES – CESAM0 Case 1.2 1.2 M¯ X0 = 0.7 Z0 = 0.02 Xc = 0.69

  47. CLES – CESAM0 Case 1.2 1.2 M¯ X0 = 0.7 Z0 = 0.02 Xc = 0.69

  48. STAROX – CESAM0 Case 1.2 1.2 M¯ X0 = 0.7 Z0 = 0.02 Xc = 0.69

  49. STAROX – CESAM0 Case 1.2 1.2 M¯ X0 = 0.7 Z0 = 0.02 Xc = 0.69

  50. Hydrogen abundance 1.2 M¯ X0 = 0.73 Z0 = 0.01 MHeC/M = 0.1 X

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