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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 (Δ(n),δ(n)), respectively.

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