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Table B.1
Derivative matrix
| Parameters | ||||||
| Constraints | lnτ | lnα | lnℳ | lnY0 | lnZ/X0 | lndov |
|
|
||||||
| lnTeff | –6.57 | 4.61 | –5.96 | –1.62 | –2.41 | 1.53 |
| lnL/L⊙ | 35.67 | –0.51 | 332.56 | 147.39 | –34.42 | –2.77 |
| lnΔ0 | –463.07 | 158.08 | –2534.54 | –1210.27 | 208.50 | 65.19 |
| lnδ01 | 7.17 | –13.33 | 74.67 | 34.40 | –8.97 | –15.73 |
| lnZ/X ⋆ | 0.0 | 0.0 | 0.0 | 0.0 | 14.42 | 0.0 |
| lnΔ0(15) | –83.57 | 27.36 | –444.42 | –211.62 | 35.40 | 11.16 |
| lnΔ0(16) | –118.91 | 30.68 | –592.85 | –283.15 | 44.88 | 17.41 |
| lnΔ0(17) | –145.03 | 33.61 | –698.05 | –333.54 | 52.14 | 22.19 |
| lnΔ0(18) | –217.07 | 45.70 | –1013.67 | –486.53 | 70.42 | 31.06 |
| lnΔ0(19) | –78.81 | 37.32 | –509.87 | –243.52 | 47.44 | 10.59 |
| lnΔ0(20) | –47.95 | 21.74 | –291.07 | –140.00 | 26.05 | 5.94 |
| lnΔ0(21) | –37.96 | 16.65 | –228.98 | –110.12 | 20.22 | 4.89 |
| lnΔ0(22) | –23.94 | 10.37 | –144.96 | –69.18 | 13.09 | 3.44 |
| lnΔ0(23) | –28.44 | 8.03 | –141.67 | –67.69 | 10.73 | 4.04 |
| lnΔ0(24) | –49.36 | 14.60 | –259.59 | –123.46 | 20.58 | 7.61 |
| lnΔ0(25) | –87.62 | 25.13 | –450.42 | –214.64 | 35.63 | 13.43 |
| lnΔ0(26) | –105.98 | 29.51 | –530.19 | –254.34 | 40.02 | 15.27 |
| lnΔ0(27) | –55.40 | 21.96 | –329.12 | –157.42 | 28.95 | 8.54 |
| lnΔ1(15) | –31.08 | 8.14 | –153.13 | –73.15 | 11.22 | 4.49 |
| lnΔ1(16) | –44.22 | 12.12 | –225.93 | –107.65 | 17.72 | 6.85 |
| lnΔ1(17) | –73.60 | 14.50 | –335.01 | –160.39 | 22.91 | 11.16 |
| lnΔ1(18) | –80.55 | 25.79 | –438.57 | –209.65 | 35.19 | 11.37 |
| lnΔ1(19) | –84.56 | 45.03 | –568.25 | –271.55 | 54.20 | 11.05 |
| lnΔ1(20) | –52.70 | 22.33 | –308.09 | –148.26 | 26.37 | 6.49 |
| lnΔ1(21) | –48.31 | 23.36 | –309.54 | –147.80 | 28.53 | 6.54 |
| lnΔ1(22) | –55.56 | 19.42 | –302.12 | –143.94 | 24.88 | 7.72 |
| lnΔ1(23) | –50.74 | 13.91 | –254.42 | –121.11 | 18.99 | 7.15 |
| lnΔ1(24) | –49.28 | 15.31 | –266.17 | –126.20 | 21.69 | 7.42 |
| lnΔ1(25) | –70.73 | 18.65 | –347.23 | –165.91 | 25.81 | 9.70 |
| lnΔ1(26) | –42.79 | 14.49 | –236.48 | –113.15 | 19.30 | 5.92 |
| lnΔ1(27) | –31.40 | 12.95 | –187.74 | –89.64 | 16.63 | 4.27 |
| lnΔ2(14) | –25.16 | 8.91 | –138.01 | –65.57 | 11.25 | 3.36 |
| lnΔ2(15) | –38.56 | 9.99 | –191.95 | –91.64 | 14.39 | 5.65 |
| lnΔ2(16) | –53.30 | 12.94 | –260.44 | –124.31 | 19.68 | 8.20 |
| lnΔ2(17) | –132.65 | 27.38 | –614.31 | –294.68 | 42.11 | 19.12 |
| lnΔ2(18) | –51.35 | 23.84 | –329.16 | –157.09 | 30.24 | 6.93 |
| lnΔ2(19) | –21.35 | 10.06 | –132.17 | –63.48 | 11.94 | 2.64 |
| lnΔ2(20) | –20.67 | 9.11 | –124.57 | –59.88 | 10.93 | 2.61 |
| lnΔ2(21) | –19.99 | 8.96 | –123.16 | –58.72 | 11.19 | 2.82 |
| lnΔ2(22) | –23.82 | 6.89 | –119.60 | –57.09 | 9.10 | 3.31 |
| lnΔ2(23) | –26.86 | 7.92 | –140.96 | –66.99 | 11.08 | 4.02 |
| lnΔ2(24) | –28.62 | 8.32 | –148.37 | –70.61 | 11.77 | 4.29 |
| lnΔ2(25) | –41.26 | 11.37 | –205.63 | –98.56 | 15.40 | 5.73 |
| lnΔ2(26) | –19.77 | 7.79 | –117.41 | –56.12 | 10.27 | 2.92 |
| lnδ01(15) | 2.45 | –0.45 | 9.09 | 5.01 | –1.13 | –1.67 |
| lnδ01(16) | 0.94 | –0.31 | 3.87 | 2.08 | –0.48 | –0.70 |
| lnδ01(17) | 1.27 | –0.44 | 5.30 | 2.82 | –0.54 | –0.94 |
| lnδ01(18) | 1.19 | –3.77 | 22.42 | 11.28 | –3.81 | –3.33 |
| lnδ01(19) | 12.89 | –6.05 | 57.70 | 29.26 | –5.34 | –9.86 |
| lnδ01(20) | 4.49 | –3.52 | 28.93 | 14.07 | –3.08 | –4.93 |
| lnδ01(21) | 105.94 | –129.88 | 893.65 | 413.04 | –105.15 | –159.17 |
| lnδ01(22) | –2.43 | 1.53 | –11.88 | –5.39 | 0.75 | 2.44 |
| lnδ01(23) | 1.09 | 7.32 | –32.05 | –12.97 | 4.23 | 7.09 |
| lnδ01(24) | 0.77 | 2.88 | –8.54 | –2.85 | 0.97 | 2.49 |
| lnδ01(25) | 10.23 | 11.10 | –6.05 | 3.64 | –0.20 | 7.12 |
| lnδ01(26) | 2.00 | 0.84 | 1.78 | 1.48 | 0.11 | 0.15 |
| lnδ01(27) | 1.69 | 0.45 | 4.22 | 2.65 | –0.43 | –0.15 |
Notes. Logarithmic derivatives of various properties of the computed reference model of HD 49933 with respect to the model parameters. The mean and individual separations have been defined (Δ0,δ01) and (Δℓ(n),δℓ(n)), respectively.
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