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Table 4

Orbital parameters fit to the astrometry of PDS 70 b, c, and the candidate d.

Quantity Prior Coplanar Stable Stable (incl. N-body)
ab (au) LogUniform(1, 100) 19.80.6(1.1)+0.6(+1.1)$19.8_{ - 0.6( - 1.1)}^{ + 0.6( + 1.1)}$ 20.60.5(1.1)+0.5(+1.1)$20.6_{ - 0.5( - 1.1)}^{ + 0.5( + 1.1)}$ 21.10.8(1.0)+0.4(+0.210)$21.1_{ - 0.8( - 1.0)}^{ + 0.4( + 0.210)}$
eb Uniform(0, 1) 0.2070.041(0.080)+0.041+0.085)$0.207_{ - 0.041( - 0.080)}^{ + 0.041 + 0.085)}$ 0.1830.04(0.09)+0.05+0.09$0.183_{ - 0.04( - 0.09)}^{ + 0.05 + 0.09}$ 0.1310.037(0.048)+0.035+0.069)$0.131_{ - 0.037( - 0.048)}^{ + 0.035 + 0.069)}$
ib (deg) sin(i) 131.71.8(3.4)+1.9(+3.9)$131.7_{ - 1.8( - 3.4)}^{ + 1.9( + 3.9)}$ 130.81.7(3.4)+1.7(+3.5)$130.8_{ - 1.7( - 3.4)}^{ + 1.7( + 3.5)}$ 128.71.2(3.7)+1.9(+3.4)$128.7_{ - 1.2( - 3.7)}^{ + 1.9( + 3.4)}$
ωb (deg) Uniform(0, 360) 1915(10)+6(+16)$191_{ - 5( - 10)}^{ + 6( + 16)}$ 1946(15)+5(+11)$194_{ - 6( - 15)}^{ + 5( + 11)}$ 191.43.6(5.1)+2.7(+4.9)$191.4_{ - 3.6( - 5.1)}^{ + 2.7( + 4.9)}$
Ωb (deg) Uniform(0, 360) 175.73.3(6.1)+4.4(+9.6)$175.7_{ - 3.3( - 6.1)}^{ + 4.4( + 9.6)}$ 177.93.7(7.6)+4.4(+9.1770)$177.9_{ - 3.7( - 7.6)}^{+ 4.4( + 9.1770)}$ 174.32.9(3.8)+3.4(+8.1740)$174.3_{ - 2.9( - 3.8)}^{+ 3.4( + 8.1740)}$
τb Uniform(0, 1) 0.3660.018(0.034)+0.021(+0.041)$0.366_{ - 0.018( - 0.034)}^{+ 0.021( + 0.041)}$ 0.3650.017(0.034)+0.022(+0.043)$0.365_{ - 0.017( - 0.034)}^{+ 0.022( + 0.043)}$ 0.3870.024(0.039)+0.008(+0.010)$0.387_{ - 0.024( - 0.039)}^{+ 0.008( + 0.010)}$

ab (au) LogUniform(1, 100) 32.50.9(1.9)+0.9(+1.320)$32.5_{ - 0.9( - 1.9)}^{+ 0.9( + 1.320)}$ 34.61.0(2.3)+0.9(+1.340)$34.6_{ - 1.0( - 2.3)}^{+ 0.9( + 1.340)}$ 35.30.9(2.2)+0.8(+1.350)$35.3_{ - 0.9( - 2.2)}^{+ 0.8( + 1.350)}$
eb Uniform(0, 1) 0.0620.014(0.028)+0.019(+0.039)$0.062_{ - 0.014( - 0.028)}^{+ 0.019( + 0.039)}$ 0.0360.010(0.021)+0.014(+0.028)$0.036_{ - 0.010( - 0.021)}^{+ 0.014( + 0.028)}$ 0.0330.008(0.017)+0.011(+0.016)$0.033_{ - 0.008( - 0.017)}^{+ 0.011( + 0.016)}$
ib (deg) sin(i) 130.51.1(2.0)+1.2(+2.1300)$130.5_{ - 1.1( - 2.0)}^{+ 1.2( + 2.1300)}$ 129.11.0(1.8)+1.2(+2.1290)$129.1_{ - 1.0( - 1.8)}^{+ 1.2( + 2.1290)}$ 128.50.7(0.8)+1.4(+2.1280)$128.5_{ - 0.7( - 0.8)}^{+ 1.4( + 2.1280)}$
ωb (deg) Uniform(0, 360) 9418(30)+8(+14)$94_{ - 18( - 30)}^{ + 8( + 14)}$ 6610(21)+12(+38)$66_{ - 10( - 21)}^{ + 12( + 38)}$ 6313(21)+19(+23)$63_{ - 13( - 21)}^{ + 19( + 23)}$
Ωb (deg) Uniform(0, 360) 155.32.3(5.0)+2.0(+3.1550)$155.3_{ - 2.3( - 5.0)}^{+ 2.0( + 3.1550)}$ 158.82.3(6.0)+1.6(+3.1580)$158.8_{ - 2.3( - 6.0)}^{+ 1.6( + 3.1580)}$ 159.80.8(2.9)+1.0(+2.1590)$159.8_{ - 0.8( - 2.9)}^{+ 1.0( + 2.1590)}$
τb Uniform(0, 1) 0.5850.055(0.097)+0.026(+0.047)$0.585_{ - 0.055( - 0.097)}^{+ 0.026( + 0.047)}$ 0.490.03(0.06)+0.04(+0.013)$0.49_{ - 0.03( - 0.06)}^{+ 0.04( + 0.013)}$ 0.4820.051(0.066)+0.049(+0.063)$0.482_{ - 0.051( - 0.066)}^{+ 0.049( + 0.063)}$

ab (au) LogUniform(1, 100) 12.91.6(2.9)+1.6(+3.120)$12.9_{ - 1.6( - 2.9)}^{+ 1.6( + 3.120)}$ 10.71.3(2.3)+1.5(+2.100)$10.7_{ - 1.3( - 2.3)}^{+ 1.5( + 2.100)}$ 10.71.1(2.3)+2.1(+2.100)$10.7_{ - 1.1( - 2.3)}^{+ 2.1( + 2.100)}$
eb Uniform(0, 1) 0.210.10(0.18)+0.12(+0.24)$0.21_{ - 0.10( - 0.18)}^{+ 0.12( + 0.24)}$ 0.270.15(0.25)+0.15(+0.29)$0.27_{ - 0.15( - 0.25)}^{+ 0.15( + 0.29)}$ 0.250.23(0.25)+0.13(+0.30)$0.25_{ - 0.23( - 0.25)}^{+ 0.13( + 0.30)}$
ib (deg) sin(i) 1365(10)+5(+11)$136_{ - 5( - 10)}^{ + 5( + 11)}$ 15312(21)+13(+22)$153_{ - 12( - 21)}^{ + 13( + 22)}$ 1518(23)+6(+18)$151_{ - 8( - 23)}^{ + 6( + 18)}$
ωb (deg) Uniform(0, 360) 8030(60)+150(+220)$80_{ - 30( - 60)}^{ + 150( + 220)}$ 8060(80)+110(+220)$80_{ - 60( - 80)}^{ + 110( + 220)}$ 2917(26)+24(+51)$29_{ - 17( - 26)}^{ + 24( + 51)}$
Ωb (deg) Uniform(0, 360) 16118(37)+12(+25)$161_{ - 18( - 37)}^{ + 12( + 25)}$ 19050(130)+130(+160)$190_{ - 50( - 130)}^{ + 130( + 160)}$ 14410(22)+21(+38)$144_{ - 10( - 22)}^{ + 21( + 38)}$
τb Uniform(0, 1) 0.580.40(0.54)+0.12(+0.21)$0.58_{ - 0.40( - 0.54)}^{+ 0.12( + 0.21)}$ 0.470.09(0.20)+0.09(+0.18)$0.47_{ - 0.09( - 0.20)}^{+ 0.09( + 0.18)}$ 0.550.08(0.15)+0.04(+0.09)$0.55_{ - 0.08( - 0.15)}^{+ 0.04( + 0.09)}$

Parallax (mas) 𝒩(8.8975, 0.0191) 8.8720.031(0.058)+0.025(+0.80)$8.872_{ - 0.031( - 0.058)}^{+ 0.025( + 0.80)}$ 8.8810.025(0.058)+0.024(+0.80)$8.881_{ - 0.025( - 0.058)}^{+ 0.024( + 0.80)}$ 8.8820.021(0.025)+0.018(+0.80)$8.882_{ - 0.021( - 0.025)}^{+ 0.018( + 0.80)}$
Mb (Mjup) Uniform(0, 30) 105(9)+9(+18)$10_{ - 5( - 9)}^{ + 9( + 18)}$ 53(4)+4(+11)$5_{ - 3( - 4)}^{ + 4( + 11)}$ 0.70.5(0.7)+1.7(+4.46)$0.7_{ - 0.5( - 0.7)}^{+ 1.7( + 4.46)}$
Mc (Mjup) Uniform(0, 30) 95(8)+7(18)$9_{ - 5( - 8)}^{ + 7(18)}$ 85(7)+8(+18)$8_{ - 5( - 7)}^{ + 8( + 18)}$ 2.41.3(2.2)+4.3(+5.20)$2.4_{ - 1.3( - 2.2)}^{+ 4.3( + 5.20)}$
Md (Mjup) Uniform(0, 30) 86(8)+7(+16)$8_{ - 6( - 8)}^{ + 7( + 16)}$ 97(9)+9(+18)$9_{ - 7( - 9)}^{ + 9( + 18)}$ 0.40.3(0.4)+1.5(+1.00)$0.4_{ - 0.3( - 0.4)}^{+ 1.5( + 1.00)}$
M* (M) 𝒩(0.88,0.09) 0.9600.031(0.063)+0.032(+0.065)$0.960_{ - 0.031( - 0.063)}^{+ 0.032( + 0.065)}$ 0.9530.033(0.064)+0.031(0.062)$0.953_{ - 0.033( - 0.064)}^{ + 0.031(0.062)}$ 0.9650.025(0.088)+0.041(+0.068)$0.965_{ - 0.025( - 0.088)}^{+ 0.041( + 0.068)}$

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