Aggregate magnetic quantities for the unscaled |$B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| and scaled |$5B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| magnetic fields considered in this work. The ‘Case’ column gives the star’s case name, which is prepended by ‘5 ×’ for models in the |$5B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| series. An identifying symbol as in Table 1 for models in the |$B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| series and in the shape of a star for models in the |$5B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| series is also provided for each model, and used throughout this paper. In the following columns |Br| and max |Br| are the mean and maximal unsigned radial magnetic surface field strength, calculated from the magnetograms in Fig. 1. |$|\boldsymbol{B}|$| is the average surface magnetic field strength of the final, steady-state wind models in Fig. 2. |$\Phi = 4\pi R_{\mathchoice{}{}{\scriptscriptstyle }{}\bigstar }^2 |B_r|$| is the unsigned magnetic flux at the stellar surface. The ‘dip.’, ‘quad.’ ‘oct.’, and ‘16 + ’ columns give the proportion of magnetic energy associated with, respectively, the dipolar (ℓ = 1), quadrupolar (ℓ = 2), octupolar (ℓ = 3), and higher order (ℓ ≥ 4) degrees of the spherical harmonics coefficients αℓm in equation (1). The ℓ0.90 and ℓ0.99 columns give the magnetogram degree for which 90 per cent and 99 per cent of the magnetic energy is contained in spherical harmonics of degree less than or equal to ℓ.
Case . | |Br| . | max |Br| . | |$|\boldsymbol{B}|$| . | Φ . | Dip. . | Quad. . | Oct. . | 16 + . | ℓ.90 . | ℓ.99 . |
---|---|---|---|---|---|---|---|---|---|---|
. | G . | G . | G . | Wb . | per cent . | per cent . | per cent . | per cent . | . | . |
![]() | 51.4 | 221.9 | 73.9 | 2.8 × 1016 | 68.7 | 8.4 | 9.5 | 13.5 | 4 | 9 |
![]() | 9.9 | 45.1 | 14.4 | 1.4 × 1016 | 24.7 | 14.8 | 20.4 | 40.1 | 6 | 9 |
![]() | 17.0 | 105.1 | 25.1 | 1.1 × 1016 | 10.4 | 9.0 | 20.4 | 60.2 | 6 | 8 |
![]() | 94.2 | 536.4 | 136.9 | 3.5 × 1016 | 43.8 | 4.5 | 3.7 | 48.0 | 12 | 15 |
![]() | 15.3 | 41.7 | 21.5 | 5.4 × 1015 | 76.3 | 19.5 | 3.2 | 1.0 | 2 | 4 |
![]() | 10.1 | 29.9 | 13.8 | 3.9 × 1015 | 82.6 | 11.2 | 2.5 | 3.8 | 2 | 5 |
![]() | 58.6 | 222.0 | 82.5 | 2.6 × 1016 | 83.7 | 1.8 | 3.6 | 10.8 | 4 | 7 |
![]() | 88.6 | 588.6 | 131.3 | 2.4 × 1016 | 36.0 | 8.4 | 7.4 | 48.3 | 10 | 15 |
![]() | 70.7 | 448.4 | 100.8 | 2.7 × 1016 | 43.5 | 7.6 | 5.7 | 43.2 | 8 | 12 |
![]() | 18.7 | 59.3 | 27.7 | 5.6 × 1015 | 38.1 | 30.0 | 21.3 | 10.7 | 4 | 6 |
![]() | 48.5 | 128.3 | 67.9 | 2.4 × 1016 | 85.6 | 4.5 | 2.6 | 7.3 | 2 | 6 |
![]() | 32.8 | 163.7 | 47.5 | 1.9 × 1016 | 57.8 | 21.4 | 8.0 | 12.9 | 4 | 6 |
![]() | 33.4 | 135.5 | 47.3 | 1.8 × 1016 | 56.3 | 7.6 | 8.6 | 27.5 | 6 | 10 |
![]() | 30.1 | 137.0 | 43.5 | 3.5 × 1016 | 61.0 | 8.4 | 10.7 | 19.9 | 5 | 6 |
![]() | 64.9 | 404.0 | 94.1 | 2.3 × 1016 | 53.3 | 12.6 | 13.6 | 20.5 | 4 | 7 |
![]() | 257.0 | 1109.4 | 370.2 | 1.4 × 1017 | 68.8 | 8.3 | 9.5 | 13.4 | 4 | 9 |
![]() | 49.6 | 225.5 | 72.0 | 7.1 × 1016 | 25.0 | 14.7 | 20.4 | 39.9 | 6 | 9 |
![]() | 85.1 | 525.3 | 126.0 | 5.7 × 1016 | 10.6 | 9.0 | 20.4 | 60.1 | 6 | 8 |
![]() | 470.7 | 2681.9 | 685.6 | 1.8 × 1017 | 43.9 | 4.5 | 3.7 | 47.9 | 12 | 15 |
![]() | 76.3 | 208.4 | 107.7 | 2.7 × 1016 | 76.4 | 19.4 | 3.2 | 1.0 | 2 | 4 |
![]() | 50.3 | 149.3 | 69.2 | 2.0 × 1016 | 82.7 | 11.1 | 2.5 | 3.7 | 2 | 5 |
![]() | 293.2 | 1110.2 | 413.6 | 1.3 × 1017 | 83.8 | 1.8 | 3.6 | 10.8 | 4 | 7 |
![]() | 442.9 | 2942.8 | 657.2 | 1.2 × 1017 | 36.1 | 8.3 | 7.4 | 48.2 | 10 | 15 |
![]() | 353.3 | 2241.9 | 504.9 | 1.3 × 1017 | 43.6 | 7.6 | 5.7 | 43.2 | 8 | 12 |
![]() | 93.6 | 296.6 | 138.7 | 2.8 × 1016 | 38.3 | 29.9 | 21.2 | 10.6 | 4 | 6 |
![]() | 242.4 | 641.5 | 340.6 | 1.2 × 1017 | 85.7 | 4.5 | 2.6 | 7.3 | 2 | 6 |
![]() | 163.8 | 818.4 | 238.2 | 9.3 × 1016 | 57.9 | 21.4 | 7.9 | 12.8 | 4 | 6 |
![]() | 167.2 | 677.5 | 237.3 | 8.9 × 1016 | 56.5 | 7.5 | 8.6 | 27.4 | 6 | 10 |
![]() | 150.3 | 685.1 | 218.0 | 1.8 × 1017 | 61.2 | 8.4 | 10.7 | 19.8 | 5 | 6 |
![]() | 324.7 | 2019.9 | 471.3 | 1.1 × 1017 | 53.3 | 12.6 | 13.6 | 20.5 | 4 | 7 |
Case . | |Br| . | max |Br| . | |$|\boldsymbol{B}|$| . | Φ . | Dip. . | Quad. . | Oct. . | 16 + . | ℓ.90 . | ℓ.99 . |
---|---|---|---|---|---|---|---|---|---|---|
. | G . | G . | G . | Wb . | per cent . | per cent . | per cent . | per cent . | . | . |
![]() | 51.4 | 221.9 | 73.9 | 2.8 × 1016 | 68.7 | 8.4 | 9.5 | 13.5 | 4 | 9 |
![]() | 9.9 | 45.1 | 14.4 | 1.4 × 1016 | 24.7 | 14.8 | 20.4 | 40.1 | 6 | 9 |
![]() | 17.0 | 105.1 | 25.1 | 1.1 × 1016 | 10.4 | 9.0 | 20.4 | 60.2 | 6 | 8 |
![]() | 94.2 | 536.4 | 136.9 | 3.5 × 1016 | 43.8 | 4.5 | 3.7 | 48.0 | 12 | 15 |
![]() | 15.3 | 41.7 | 21.5 | 5.4 × 1015 | 76.3 | 19.5 | 3.2 | 1.0 | 2 | 4 |
![]() | 10.1 | 29.9 | 13.8 | 3.9 × 1015 | 82.6 | 11.2 | 2.5 | 3.8 | 2 | 5 |
![]() | 58.6 | 222.0 | 82.5 | 2.6 × 1016 | 83.7 | 1.8 | 3.6 | 10.8 | 4 | 7 |
![]() | 88.6 | 588.6 | 131.3 | 2.4 × 1016 | 36.0 | 8.4 | 7.4 | 48.3 | 10 | 15 |
![]() | 70.7 | 448.4 | 100.8 | 2.7 × 1016 | 43.5 | 7.6 | 5.7 | 43.2 | 8 | 12 |
![]() | 18.7 | 59.3 | 27.7 | 5.6 × 1015 | 38.1 | 30.0 | 21.3 | 10.7 | 4 | 6 |
![]() | 48.5 | 128.3 | 67.9 | 2.4 × 1016 | 85.6 | 4.5 | 2.6 | 7.3 | 2 | 6 |
![]() | 32.8 | 163.7 | 47.5 | 1.9 × 1016 | 57.8 | 21.4 | 8.0 | 12.9 | 4 | 6 |
![]() | 33.4 | 135.5 | 47.3 | 1.8 × 1016 | 56.3 | 7.6 | 8.6 | 27.5 | 6 | 10 |
![]() | 30.1 | 137.0 | 43.5 | 3.5 × 1016 | 61.0 | 8.4 | 10.7 | 19.9 | 5 | 6 |
![]() | 64.9 | 404.0 | 94.1 | 2.3 × 1016 | 53.3 | 12.6 | 13.6 | 20.5 | 4 | 7 |
![]() | 257.0 | 1109.4 | 370.2 | 1.4 × 1017 | 68.8 | 8.3 | 9.5 | 13.4 | 4 | 9 |
![]() | 49.6 | 225.5 | 72.0 | 7.1 × 1016 | 25.0 | 14.7 | 20.4 | 39.9 | 6 | 9 |
![]() | 85.1 | 525.3 | 126.0 | 5.7 × 1016 | 10.6 | 9.0 | 20.4 | 60.1 | 6 | 8 |
![]() | 470.7 | 2681.9 | 685.6 | 1.8 × 1017 | 43.9 | 4.5 | 3.7 | 47.9 | 12 | 15 |
![]() | 76.3 | 208.4 | 107.7 | 2.7 × 1016 | 76.4 | 19.4 | 3.2 | 1.0 | 2 | 4 |
![]() | 50.3 | 149.3 | 69.2 | 2.0 × 1016 | 82.7 | 11.1 | 2.5 | 3.7 | 2 | 5 |
![]() | 293.2 | 1110.2 | 413.6 | 1.3 × 1017 | 83.8 | 1.8 | 3.6 | 10.8 | 4 | 7 |
![]() | 442.9 | 2942.8 | 657.2 | 1.2 × 1017 | 36.1 | 8.3 | 7.4 | 48.2 | 10 | 15 |
![]() | 353.3 | 2241.9 | 504.9 | 1.3 × 1017 | 43.6 | 7.6 | 5.7 | 43.2 | 8 | 12 |
![]() | 93.6 | 296.6 | 138.7 | 2.8 × 1016 | 38.3 | 29.9 | 21.2 | 10.6 | 4 | 6 |
![]() | 242.4 | 641.5 | 340.6 | 1.2 × 1017 | 85.7 | 4.5 | 2.6 | 7.3 | 2 | 6 |
![]() | 163.8 | 818.4 | 238.2 | 9.3 × 1016 | 57.9 | 21.4 | 7.9 | 12.8 | 4 | 6 |
![]() | 167.2 | 677.5 | 237.3 | 8.9 × 1016 | 56.5 | 7.5 | 8.6 | 27.4 | 6 | 10 |
![]() | 150.3 | 685.1 | 218.0 | 1.8 × 1017 | 61.2 | 8.4 | 10.7 | 19.8 | 5 | 6 |
![]() | 324.7 | 2019.9 | 471.3 | 1.1 × 1017 | 53.3 | 12.6 | 13.6 | 20.5 | 4 | 7 |
Aggregate magnetic quantities for the unscaled |$B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| and scaled |$5B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| magnetic fields considered in this work. The ‘Case’ column gives the star’s case name, which is prepended by ‘5 ×’ for models in the |$5B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| series. An identifying symbol as in Table 1 for models in the |$B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| series and in the shape of a star for models in the |$5B_{\mathchoice{}{}{\scriptscriptstyle }{}\mathrm{ZDI}}$| series is also provided for each model, and used throughout this paper. In the following columns |Br| and max |Br| are the mean and maximal unsigned radial magnetic surface field strength, calculated from the magnetograms in Fig. 1. |$|\boldsymbol{B}|$| is the average surface magnetic field strength of the final, steady-state wind models in Fig. 2. |$\Phi = 4\pi R_{\mathchoice{}{}{\scriptscriptstyle }{}\bigstar }^2 |B_r|$| is the unsigned magnetic flux at the stellar surface. The ‘dip.’, ‘quad.’ ‘oct.’, and ‘16 + ’ columns give the proportion of magnetic energy associated with, respectively, the dipolar (ℓ = 1), quadrupolar (ℓ = 2), octupolar (ℓ = 3), and higher order (ℓ ≥ 4) degrees of the spherical harmonics coefficients αℓm in equation (1). The ℓ0.90 and ℓ0.99 columns give the magnetogram degree for which 90 per cent and 99 per cent of the magnetic energy is contained in spherical harmonics of degree less than or equal to ℓ.
Case . | |Br| . | max |Br| . | |$|\boldsymbol{B}|$| . | Φ . | Dip. . | Quad. . | Oct. . | 16 + . | ℓ.90 . | ℓ.99 . |
---|---|---|---|---|---|---|---|---|---|---|
. | G . | G . | G . | Wb . | per cent . | per cent . | per cent . | per cent . | . | . |
![]() | 51.4 | 221.9 | 73.9 | 2.8 × 1016 | 68.7 | 8.4 | 9.5 | 13.5 | 4 | 9 |
![]() | 9.9 | 45.1 | 14.4 | 1.4 × 1016 | 24.7 | 14.8 | 20.4 | 40.1 | 6 | 9 |
![]() | 17.0 | 105.1 | 25.1 | 1.1 × 1016 | 10.4 | 9.0 | 20.4 | 60.2 | 6 | 8 |
![]() | 94.2 | 536.4 | 136.9 | 3.5 × 1016 | 43.8 | 4.5 | 3.7 | 48.0 | 12 | 15 |
![]() | 15.3 | 41.7 | 21.5 | 5.4 × 1015 | 76.3 | 19.5 | 3.2 | 1.0 | 2 | 4 |
![]() | 10.1 | 29.9 | 13.8 | 3.9 × 1015 | 82.6 | 11.2 | 2.5 | 3.8 | 2 | 5 |
![]() | 58.6 | 222.0 | 82.5 | 2.6 × 1016 | 83.7 | 1.8 | 3.6 | 10.8 | 4 | 7 |
![]() | 88.6 | 588.6 | 131.3 | 2.4 × 1016 | 36.0 | 8.4 | 7.4 | 48.3 | 10 | 15 |
![]() | 70.7 | 448.4 | 100.8 | 2.7 × 1016 | 43.5 | 7.6 | 5.7 | 43.2 | 8 | 12 |
![]() | 18.7 | 59.3 | 27.7 | 5.6 × 1015 | 38.1 | 30.0 | 21.3 | 10.7 | 4 | 6 |
![]() | 48.5 | 128.3 | 67.9 | 2.4 × 1016 | 85.6 | 4.5 | 2.6 | 7.3 | 2 | 6 |
![]() | 32.8 | 163.7 | 47.5 | 1.9 × 1016 | 57.8 | 21.4 | 8.0 | 12.9 | 4 | 6 |
![]() | 33.4 | 135.5 | 47.3 | 1.8 × 1016 | 56.3 | 7.6 | 8.6 | 27.5 | 6 | 10 |
![]() | 30.1 | 137.0 | 43.5 | 3.5 × 1016 | 61.0 | 8.4 | 10.7 | 19.9 | 5 | 6 |
![]() | 64.9 | 404.0 | 94.1 | 2.3 × 1016 | 53.3 | 12.6 | 13.6 | 20.5 | 4 | 7 |
![]() | 257.0 | 1109.4 | 370.2 | 1.4 × 1017 | 68.8 | 8.3 | 9.5 | 13.4 | 4 | 9 |
![]() | 49.6 | 225.5 | 72.0 | 7.1 × 1016 | 25.0 | 14.7 | 20.4 | 39.9 | 6 | 9 |
![]() | 85.1 | 525.3 | 126.0 | 5.7 × 1016 | 10.6 | 9.0 | 20.4 | 60.1 | 6 | 8 |
![]() | 470.7 | 2681.9 | 685.6 | 1.8 × 1017 | 43.9 | 4.5 | 3.7 | 47.9 | 12 | 15 |
![]() | 76.3 | 208.4 | 107.7 | 2.7 × 1016 | 76.4 | 19.4 | 3.2 | 1.0 | 2 | 4 |
![]() | 50.3 | 149.3 | 69.2 | 2.0 × 1016 | 82.7 | 11.1 | 2.5 | 3.7 | 2 | 5 |
![]() | 293.2 | 1110.2 | 413.6 | 1.3 × 1017 | 83.8 | 1.8 | 3.6 | 10.8 | 4 | 7 |
![]() | 442.9 | 2942.8 | 657.2 | 1.2 × 1017 | 36.1 | 8.3 | 7.4 | 48.2 | 10 | 15 |
![]() | 353.3 | 2241.9 | 504.9 | 1.3 × 1017 | 43.6 | 7.6 | 5.7 | 43.2 | 8 | 12 |
![]() | 93.6 | 296.6 | 138.7 | 2.8 × 1016 | 38.3 | 29.9 | 21.2 | 10.6 | 4 | 6 |
![]() | 242.4 | 641.5 | 340.6 | 1.2 × 1017 | 85.7 | 4.5 | 2.6 | 7.3 | 2 | 6 |
![]() | 163.8 | 818.4 | 238.2 | 9.3 × 1016 | 57.9 | 21.4 | 7.9 | 12.8 | 4 | 6 |
![]() | 167.2 | 677.5 | 237.3 | 8.9 × 1016 | 56.5 | 7.5 | 8.6 | 27.4 | 6 | 10 |
![]() | 150.3 | 685.1 | 218.0 | 1.8 × 1017 | 61.2 | 8.4 | 10.7 | 19.8 | 5 | 6 |
![]() | 324.7 | 2019.9 | 471.3 | 1.1 × 1017 | 53.3 | 12.6 | 13.6 | 20.5 | 4 | 7 |
Case . | |Br| . | max |Br| . | |$|\boldsymbol{B}|$| . | Φ . | Dip. . | Quad. . | Oct. . | 16 + . | ℓ.90 . | ℓ.99 . |
---|---|---|---|---|---|---|---|---|---|---|
. | G . | G . | G . | Wb . | per cent . | per cent . | per cent . | per cent . | . | . |
![]() | 51.4 | 221.9 | 73.9 | 2.8 × 1016 | 68.7 | 8.4 | 9.5 | 13.5 | 4 | 9 |
![]() | 9.9 | 45.1 | 14.4 | 1.4 × 1016 | 24.7 | 14.8 | 20.4 | 40.1 | 6 | 9 |
![]() | 17.0 | 105.1 | 25.1 | 1.1 × 1016 | 10.4 | 9.0 | 20.4 | 60.2 | 6 | 8 |
![]() | 94.2 | 536.4 | 136.9 | 3.5 × 1016 | 43.8 | 4.5 | 3.7 | 48.0 | 12 | 15 |
![]() | 15.3 | 41.7 | 21.5 | 5.4 × 1015 | 76.3 | 19.5 | 3.2 | 1.0 | 2 | 4 |
![]() | 10.1 | 29.9 | 13.8 | 3.9 × 1015 | 82.6 | 11.2 | 2.5 | 3.8 | 2 | 5 |
![]() | 58.6 | 222.0 | 82.5 | 2.6 × 1016 | 83.7 | 1.8 | 3.6 | 10.8 | 4 | 7 |
![]() | 88.6 | 588.6 | 131.3 | 2.4 × 1016 | 36.0 | 8.4 | 7.4 | 48.3 | 10 | 15 |
![]() | 70.7 | 448.4 | 100.8 | 2.7 × 1016 | 43.5 | 7.6 | 5.7 | 43.2 | 8 | 12 |
![]() | 18.7 | 59.3 | 27.7 | 5.6 × 1015 | 38.1 | 30.0 | 21.3 | 10.7 | 4 | 6 |
![]() | 48.5 | 128.3 | 67.9 | 2.4 × 1016 | 85.6 | 4.5 | 2.6 | 7.3 | 2 | 6 |
![]() | 32.8 | 163.7 | 47.5 | 1.9 × 1016 | 57.8 | 21.4 | 8.0 | 12.9 | 4 | 6 |
![]() | 33.4 | 135.5 | 47.3 | 1.8 × 1016 | 56.3 | 7.6 | 8.6 | 27.5 | 6 | 10 |
![]() | 30.1 | 137.0 | 43.5 | 3.5 × 1016 | 61.0 | 8.4 | 10.7 | 19.9 | 5 | 6 |
![]() | 64.9 | 404.0 | 94.1 | 2.3 × 1016 | 53.3 | 12.6 | 13.6 | 20.5 | 4 | 7 |
![]() | 257.0 | 1109.4 | 370.2 | 1.4 × 1017 | 68.8 | 8.3 | 9.5 | 13.4 | 4 | 9 |
![]() | 49.6 | 225.5 | 72.0 | 7.1 × 1016 | 25.0 | 14.7 | 20.4 | 39.9 | 6 | 9 |
![]() | 85.1 | 525.3 | 126.0 | 5.7 × 1016 | 10.6 | 9.0 | 20.4 | 60.1 | 6 | 8 |
![]() | 470.7 | 2681.9 | 685.6 | 1.8 × 1017 | 43.9 | 4.5 | 3.7 | 47.9 | 12 | 15 |
![]() | 76.3 | 208.4 | 107.7 | 2.7 × 1016 | 76.4 | 19.4 | 3.2 | 1.0 | 2 | 4 |
![]() | 50.3 | 149.3 | 69.2 | 2.0 × 1016 | 82.7 | 11.1 | 2.5 | 3.7 | 2 | 5 |
![]() | 293.2 | 1110.2 | 413.6 | 1.3 × 1017 | 83.8 | 1.8 | 3.6 | 10.8 | 4 | 7 |
![]() | 442.9 | 2942.8 | 657.2 | 1.2 × 1017 | 36.1 | 8.3 | 7.4 | 48.2 | 10 | 15 |
![]() | 353.3 | 2241.9 | 504.9 | 1.3 × 1017 | 43.6 | 7.6 | 5.7 | 43.2 | 8 | 12 |
![]() | 93.6 | 296.6 | 138.7 | 2.8 × 1016 | 38.3 | 29.9 | 21.2 | 10.6 | 4 | 6 |
![]() | 242.4 | 641.5 | 340.6 | 1.2 × 1017 | 85.7 | 4.5 | 2.6 | 7.3 | 2 | 6 |
![]() | 163.8 | 818.4 | 238.2 | 9.3 × 1016 | 57.9 | 21.4 | 7.9 | 12.8 | 4 | 6 |
![]() | 167.2 | 677.5 | 237.3 | 8.9 × 1016 | 56.5 | 7.5 | 8.6 | 27.4 | 6 | 10 |
![]() | 150.3 | 685.1 | 218.0 | 1.8 × 1017 | 61.2 | 8.4 | 10.7 | 19.8 | 5 | 6 |
![]() | 324.7 | 2019.9 | 471.3 | 1.1 × 1017 | 53.3 | 12.6 | 13.6 | 20.5 | 4 | 7 |
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