Table 1
Numerical results for our grid of disk models.
Parm. | Ref. | ω-dep. | ɡ-dep. | pmax-dep. | χ-dep | α-dep. | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ω ɡ pmax χ α | ωr=0.5 ɡr = 0.5 pr = 0.5 χr=32.5° αr = 10° | 0.20 ɡr pr χr αr | 0.80 ɡr pr χr αr | ωr 0.00 pr χr αr | ωr 0.25 pr χr αr | ωr 0.75 pr χr αr | ωr ɡr 0.20 χr αr | ωr ɡr 0.80 χr αr | ωr ɡr pr 12.5° αr | ωr ɡr pr 57.5° αr | ωr ɡr pr 82.5° αr | ωr ɡr pr χr 5° | ωr ɡr pr χr 15° | ωr ɡr pr χr 20° | |
para ![]() |
i | ||||||||||||||
7.5 | 2.89 | 0.82 | 7.87 | 4.03 | 3.81 | 1.50 | 2.92 | 2.85 | 3.30 | 1.82 | 0.41 | 1.36 | 4.62 | 6.65 | |
32.5 | 2.89 | 0.84 | 7.48 | 3.69 | 3.52 | 1.68 | 2.90 | 2.87 | 3.79 | 1.25 | 0.73 | 1.35 | 4.66 | 6.71 | |
57.5 | 1.66 | 0.48 | 4.36 | 2.58 | 2.18 | 0.93 | 1.66 | 1.66 | 4.62 | 0.98 | 0.89 | 0.78 | 2.66 | 3.82 | |
77.5 | 0.90 | 0.24 | 2.66 | 2.25 | 1.51 | 0.38 | 0.89 | 0.91 | 2.06 | 0.86 | 0.80 | 0.46 | 1.08 | 0.87 | |
![]() |
7.5 | 0.90 | 0.34 | 1.52 | 1.36 | 1.27 | 0.44 | 0.36 | 1.45 | 1.22 | 0.53 | 0.13 | 0.42 | 1.43 | 2.02 |
32.5 | 0.69 | 0.26 | 1.17 | 1.00 | 0.92 | 0.36 | 0.28 | 1.12 | 1.04 | 0.31 | 0.10 | 0.33 | 1.10 | 1.56 | |
57.5 | 0.33 | 0.12 | 0.58 | 0.56 | 0.47 | 0.17 | 0.13 | 0.54 | 0.75 | 0.13 | 0.06 | 0.15 | 0.54 | 0.78 | |
77.5 | 0.11 | 0.04 | 0.21 | 0.26 | 0.18 | 0.05 | 0.04 | 0.18 | 0.38 | 0.05 | 0.04 | 0.06 | 0.14 | 0.13 | |
![]() |
7.5 | 0.147 | 0.145 | 0.148 | 0.170 | 0.155 | 0.143 | 0.144 | 0.147 | 0.140 | 0.160 | 0.272 | 0.145 | 0.150 | 0.152 |
32.5 | 0.086 | 0.081 | 0.092 | 0.151 | 0.110 | 0.076 | 0.085 | 0.087 | 0.067 | 0.147 | 0.431 | 0.079 | 0.094 | 0.104 | |
57.5 | 0.035 | 0.036 | 0.034 | 0.070 | 0.046 | 0.034 | 0.034 | 0.036 | 0.015 | 0.101 | 0.190 | 0.028 | 0.043 | 0.051 | |
77.5 | −0.005 | 0.005 | 0.025 | 0.001 | −0.008 | 0.004 | −0.005 | −0.004 | −0.003 | 0.016 | 0.030 | −0.011 | 0 | 0.018 | |
![]() |
7.5 | 0.152 | 0.153 | 0.154 | 0.170 | 0.160 | 0.148 | 0.154 | 0.152 | 0.146 | 0.162 | 0.252 | 0.149 | 0.154 | 0.156 |
32.5 | 0.135 | 0.128 | 0.142 | 0.201 | 0.163 | 0.119 | 0.133 | 0.135 | 0.111 | 0.211 | 0.234 | 0.126 | 0.144 | 0.152 | |
57.5 | 0.153 | 0.141 | 0.171 | 0.222 | 0.182 | 0.136 | 0.154 | 0.154 | 0.083 | 0.273 | 0.161 | 0.134 | 0.173 | 0.195 | |
77.5 | 0.265 | 0.245 | 0.295 | 0.290 | 0.271 | 0.263 | 0.265 | 0.267 | 0.089 | 0.351 | 0.163 | 0.223 | 0.306 | 0.373 | |
![]() |
7.5 | 0.161 | 0.160 | 0.162 | 0.162 | 0.163 | 0.162 | 0.160 | 0.162 | 0.161 | 0.164 | 0.175 | 0.162 | 0.162 | 0.162 |
32.5 | 0.213 | 0.212 | 0.217 | 0.219 | 0.223 | 0.204 | 0.215 | 0.213 | 0.205 | 0.248 | 0.193 | 0.212 | 0.214 | 0.214 | |
57.5 | 0.375 | 0.375 | 0.371 | 0.341 | 0.368 | 0.367 | 0.375 | 0.373 | 0.329 | 0.298 | 0.322 | 0.379 | 0.366 | 0.356 | |
77.5 | 0.422 | 0.424 | 0.420 | 0.404 | 0.421 | 0.414 | 0.422 | 0.421 | 0.478 | 0.348 | 0.402 | 0.441 | 0.382 | 0.303 | |
![]() |
7.5 | 0.166 | 0.167 | 0.165 | 0.149 | 0.159 | 0.170 | 0.167 | 0.165 | 0.170 | 0.154 | 0.063 | 0.167 | 0.164 | 0.162 |
32.5 | 0.177 | 0.183 | 0.168 | 0.109 | 0.147 | 0.193 | 0.177 | 0.177 | 0.201 | 0.095 | 0.001 | 0.187 | 0.168 | 0.159 | |
57.5 | 0.079 | 0.090 | 0.066 | 0.033 | 0.055 | 0.102 | 0.082 | 0.080 | 0.176 | 0.003 | 0.002 | 0.096 | 0.065 | 0.052 | |
77.5 | −0.002 | −0.002 | −0.003 | −0.003 | −0.002 | −0.002 | −0.002 | −0.002 | 0.020 | −0.002 | 0.004 | −0.003 | 0 | 0 | |
![]() |
7.5 | 0.168 | 0.168 | 0.163 | 0.141 | 0.156 | 0.170 | 0.170 | 0.165 | 0.173 | 0.149 | 0.020 | 0.169 | 0.163 | 0.160 |
32.5 | 0.135 | 0.144 | 0.125 | 0.062 | 0.096 | 0.166 | 0.137 | 0.136 | 0.167 | 0.017 | 0 | 0.144 | 0.126 | 0.117 | |
57.5 | 0.007 | 0.008 | 0.006 | 0.001 | 0.002 | 0.013 | 0.006 | 0.007 | 0.069 | 0 | 0 | 0.009 | 0.005 | 0.004 | |
77.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
〈pφ〉 | 7.5 | 0.31 | 0.41 | 0.19 | 0.34 | 0.33 | 0.29 | 0.12 | 0.51 | 0.37 | 0.29 | 0.33 | 0.31 | 0.31 | 0.31 |
32.5 | 0.24 | 0.31 | 0.16 | 0.27 | 0.26 | 0.21 | 0.10 | 0.39 | 0.27 | 0.25 | 0.14 | 0.24 | 0.24 | 0.23 | |
57.5 | 0.20 | 0.26 | 0.13 | 0.22 | 0.22 | 0.18 | 0.08 | 0.32 | 0.16 | 0.14 | 0.07 | 0.20 | 0.20 | 0.21 | |
77.5 | 0.12 | 0.16 | 0.08 | 0.12 | 0.12 | 0.12 | 0.05 | 0.20 | 0.18 | 0.06 | 0.05 | 0.12 | 0.13 | 0.15 | |
〈pQ〉 | 7.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.01 | 0 | 0.01 | 0.02 | 0 | 0 | 0 |
32.5 | 0.05 | 0.06 | 0.03 | 0.06 | 0.06 | 0.04 | 0.02 | 0.08 | 0.05 | 0.08 | −0.01 | 0.05 | 0.05 | 0.05 | |
57.5 | 0.14 | 0.18 | 0.09 | 0.13 | 0.15 | 0.12 | 0.06 | 0.23 | 0.09 | 0.07 | 0.03 | 0.14 | 0.14 | 0.13 | |
77.5 | 0.10 | 0.14 | 0.07 | 0.09 | 0.10 | 0.10 | 0.04 | 0.17 | 0.18 | 0.04 | 0.04 | 0.11 | 0.10 | 0.09 | |
max( pφ) | 7.5 | 0.35 | 0.49 | 0.22 | 0.37 | 0.37 | 0.35 | 0.16 | 0.55 | 0.49 | 0.34 | 0.43 | 0.34 | 0.37 | 0.38 |
32.5 | 0.32 | 0.44 | 0.21 | 0.36 | 0.35 | 0.32 | 0.14 | 0.53 | 0.42 | 0.30 | 0.35 | 0.32 | 0.34 | 0.36 | |
57.5 | 0.32 | 0.43 | 0.22 | 0.37 | 0.35 | 0.30 | 0.13 | 0.52 | 0.40 | 0.31 | 0.27 | 0.32 | 0.33 | 0.35 | |
77.5 | 0.33 | 0.42 | 0.23 | 0.38 | 0.37 | 0.29 | 0.13 | 0.53 | 0.40 | 0.26 | 0.21 | 0.33 | 0.34 | 0.36 | |
I180/I000 | 7.5 | 1.23 | 1.29 | 1.14 | 0.96 | 1.09 | 1.39 | 1.23 | 1.23 | 1.37 | 0.98 | 0.08 | 1.22 | 1.24 | 1.26 |
32.5 | 1.93 | 2.37 | 1.37 | 0.65 | 1.13 | 3.20 | 1.93 | 1.95 | 3.00 | 0.16 | 0 | 1.91 | 1.98 | 2.04 | |
57.5 | 0.29 | 0.44 | 0.16 | 0.04 | 0.11 | 0.75 | 0.29 | 0.29 | 6.11 | 0 | 0 | 0.32 | 0.27 | 0.26 | |
77.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.97 | 0 | 0 | 0 | 0 | 0 |
Notes. Results are given for the reference model for i = 7.5°, 32.5°, 57.5°, and 77.5°, and models that deviate for one of the following parameters: scattering albedo ω, asymmetry ɡ, maximum scattering polarization pmax, wall slope χ, and angular wall height a. Numerical uncertainties for the calculated model results are at a level of about one or two units for the last digit of the given values.
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