Differentiating formation models with new dynamical masses for the PDS 70 protoplanets

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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)
a_b (au)	LogUniform(1, 100)	${19.8}_{- 0.6 (- 1.1)}^{+ 0.6 (+ 1.1)}$ $19.8_{ - 0.6( - 1.1)}^{ + 0.6( + 1.1)}$	${20.6}_{- 0.5 (- 1.1)}^{+ 0.5 (+ 1.1)}$ $20.6_{ - 0.5( - 1.1)}^{ + 0.5( + 1.1)}$	${21.1}_{- 0.8 (- 1.0)}^{+ 0.4 (+ 0.210)}$ $21.1_{ - 0.8( - 1.0)}^{ + 0.4( + 0.210)}$
e_b	Uniform(0, 1)	${0.207}_{- 0.041 (- 0.080)}^{+ 0.041 + 0.085)}$ $0.207_{ - 0.041( - 0.080)}^{ + 0.041 + 0.085)}$	${0.183}_{- 0.04 (- 0.09)}^{+ 0.05 + 0.09}$ $0.183_{ - 0.04( - 0.09)}^{ + 0.05 + 0.09}$	${0.131}_{- 0.037 (- 0.048)}^{+ 0.035 + 0.069)}$ $0.131_{ - 0.037( - 0.048)}^{ + 0.035 + 0.069)}$
i_b (deg)	sin(i)	${131.7}_{- 1.8 (- 3.4)}^{+ 1.9 (+ 3.9)}$ $131.7_{ - 1.8( - 3.4)}^{ + 1.9( + 3.9)}$	${130.8}_{- 1.7 (- 3.4)}^{+ 1.7 (+ 3.5)}$ $130.8_{ - 1.7( - 3.4)}^{ + 1.7( + 3.5)}$	${128.7}_{- 1.2 (- 3.7)}^{+ 1.9 (+ 3.4)}$ $128.7_{ - 1.2( - 3.7)}^{ + 1.9( + 3.4)}$
ω_b (deg)	Uniform(0, 360)	$191_{- 5 (- 10)}^{+ 6 (+ 16)}$ $191_{ - 5( - 10)}^{ + 6( + 16)}$	$194_{- 6 (- 15)}^{+ 5 (+ 11)}$ $194_{ - 6( - 15)}^{ + 5( + 11)}$	${191.4}_{- 3.6 (- 5.1)}^{+ 2.7 (+ 4.9)}$ $191.4_{ - 3.6( - 5.1)}^{ + 2.7( + 4.9)}$
Ω_b (deg)	Uniform(0, 360)	${175.7}_{- 3.3 (- 6.1)}^{+ 4.4 (+ 9.6)}$ $175.7_{ - 3.3( - 6.1)}^{ + 4.4( + 9.6)}$	${177.9}_{- 3.7 (- 7.6)}^{+ 4.4 (+ 9.1770)}$ $177.9_{ - 3.7( - 7.6)}^{+ 4.4( + 9.1770)}$	${174.3}_{- 2.9 (- 3.8)}^{+ 3.4 (+ 8.1740)}$ $174.3_{ - 2.9( - 3.8)}^{+ 3.4( + 8.1740)}$
τ_b	Uniform(0, 1)	${0.366}_{- 0.018 (- 0.034)}^{+ 0.021 (+ 0.041)}$ $0.366_{ - 0.018( - 0.034)}^{+ 0.021( + 0.041)}$	${0.365}_{- 0.017 (- 0.034)}^{+ 0.022 (+ 0.043)}$ $0.365_{ - 0.017( - 0.034)}^{+ 0.022( + 0.043)}$	${0.387}_{- 0.024 (- 0.039)}^{+ 0.008 (+ 0.010)}$ $0.387_{ - 0.024( - 0.039)}^{+ 0.008( + 0.010)}$

a_b (au)	LogUniform(1, 100)	${32.5}_{- 0.9 (- 1.9)}^{+ 0.9 (+ 1.320)}$ $32.5_{ - 0.9( - 1.9)}^{+ 0.9( + 1.320)}$	${34.6}_{- 1.0 (- 2.3)}^{+ 0.9 (+ 1.340)}$ $34.6_{ - 1.0( - 2.3)}^{+ 0.9( + 1.340)}$	${35.3}_{- 0.9 (- 2.2)}^{+ 0.8 (+ 1.350)}$ $35.3_{ - 0.9( - 2.2)}^{+ 0.8( + 1.350)}$
e_b	Uniform(0, 1)	${0.062}_{- 0.014 (- 0.028)}^{+ 0.019 (+ 0.039)}$ $0.062_{ - 0.014( - 0.028)}^{+ 0.019( + 0.039)}$	${0.036}_{- 0.010 (- 0.021)}^{+ 0.014 (+ 0.028)}$ $0.036_{ - 0.010( - 0.021)}^{+ 0.014( + 0.028)}$	${0.033}_{- 0.008 (- 0.017)}^{+ 0.011 (+ 0.016)}$ $0.033_{ - 0.008( - 0.017)}^{+ 0.011( + 0.016)}$
i_b (deg)	sin(i)	${130.5}_{- 1.1 (- 2.0)}^{+ 1.2 (+ 2.1300)}$ $130.5_{ - 1.1( - 2.0)}^{+ 1.2( + 2.1300)}$	${129.1}_{- 1.0 (- 1.8)}^{+ 1.2 (+ 2.1290)}$ $129.1_{ - 1.0( - 1.8)}^{+ 1.2( + 2.1290)}$	${128.5}_{- 0.7 (- 0.8)}^{+ 1.4 (+ 2.1280)}$ $128.5_{ - 0.7( - 0.8)}^{+ 1.4( + 2.1280)}$
ω_b (deg)	Uniform(0, 360)	$94_{- 18 (- 30)}^{+ 8 (+ 14)}$ $94_{ - 18( - 30)}^{ + 8( + 14)}$	$66_{- 10 (- 21)}^{+ 12 (+ 38)}$ $66_{ - 10( - 21)}^{ + 12( + 38)}$	$63_{- 13 (- 21)}^{+ 19 (+ 23)}$ $63_{ - 13( - 21)}^{ + 19( + 23)}$
Ω_b (deg)	Uniform(0, 360)	${155.3}_{- 2.3 (- 5.0)}^{+ 2.0 (+ 3.1550)}$ $155.3_{ - 2.3( - 5.0)}^{+ 2.0( + 3.1550)}$	${158.8}_{- 2.3 (- 6.0)}^{+ 1.6 (+ 3.1580)}$ $158.8_{ - 2.3( - 6.0)}^{+ 1.6( + 3.1580)}$	${159.8}_{- 0.8 (- 2.9)}^{+ 1.0 (+ 2.1590)}$ $159.8_{ - 0.8( - 2.9)}^{+ 1.0( + 2.1590)}$
τ_b	Uniform(0, 1)	${0.585}_{- 0.055 (- 0.097)}^{+ 0.026 (+ 0.047)}$ $0.585_{ - 0.055( - 0.097)}^{+ 0.026( + 0.047)}$	${0.49}_{- 0.03 (- 0.06)}^{+ 0.04 (+ 0.013)}$ $0.49_{ - 0.03( - 0.06)}^{+ 0.04( + 0.013)}$	${0.482}_{- 0.051 (- 0.066)}^{+ 0.049 (+ 0.063)}$ $0.482_{ - 0.051( - 0.066)}^{+ 0.049( + 0.063)}$

a_b (au)	LogUniform(1, 100)	${12.9}_{- 1.6 (- 2.9)}^{+ 1.6 (+ 3.120)}$ $12.9_{ - 1.6( - 2.9)}^{+ 1.6( + 3.120)}$	${10.7}_{- 1.3 (- 2.3)}^{+ 1.5 (+ 2.100)}$ $10.7_{ - 1.3( - 2.3)}^{+ 1.5( + 2.100)}$	${10.7}_{- 1.1 (- 2.3)}^{+ 2.1 (+ 2.100)}$ $10.7_{ - 1.1( - 2.3)}^{+ 2.1( + 2.100)}$
e_b	Uniform(0, 1)	${0.21}_{- 0.10 (- 0.18)}^{+ 0.12 (+ 0.24)}$ $0.21_{ - 0.10( - 0.18)}^{+ 0.12( + 0.24)}$	${0.27}_{- 0.15 (- 0.25)}^{+ 0.15 (+ 0.29)}$ $0.27_{ - 0.15( - 0.25)}^{+ 0.15( + 0.29)}$	${0.25}_{- 0.23 (- 0.25)}^{+ 0.13 (+ 0.30)}$ $0.25_{ - 0.23( - 0.25)}^{+ 0.13( + 0.30)}$
i_b (deg)	sin(i)	$136_{- 5 (- 10)}^{+ 5 (+ 11)}$ $136_{ - 5( - 10)}^{ + 5( + 11)}$	$153_{- 12 (- 21)}^{+ 13 (+ 22)}$ $153_{ - 12( - 21)}^{ + 13( + 22)}$	$151_{- 8 (- 23)}^{+ 6 (+ 18)}$ $151_{ - 8( - 23)}^{ + 6( + 18)}$
ω_b (deg)	Uniform(0, 360)	$80_{- 30 (- 60)}^{+ 150 (+ 220)}$ $80_{ - 30( - 60)}^{ + 150( + 220)}$	$80_{- 60 (- 80)}^{+ 110 (+ 220)}$ $80_{ - 60( - 80)}^{ + 110( + 220)}$	$29_{- 17 (- 26)}^{+ 24 (+ 51)}$ $29_{ - 17( - 26)}^{ + 24( + 51)}$
Ω_b (deg)	Uniform(0, 360)	$161_{- 18 (- 37)}^{+ 12 (+ 25)}$ $161_{ - 18( - 37)}^{ + 12( + 25)}$	$190_{- 50 (- 130)}^{+ 130 (+ 160)}$ $190_{ - 50( - 130)}^{ + 130( + 160)}$	$144_{- 10 (- 22)}^{+ 21 (+ 38)}$ $144_{ - 10( - 22)}^{ + 21( + 38)}$
τ_b	Uniform(0, 1)	${0.58}_{- 0.40 (- 0.54)}^{+ 0.12 (+ 0.21)}$ $0.58_{ - 0.40( - 0.54)}^{+ 0.12( + 0.21)}$	${0.47}_{- 0.09 (- 0.20)}^{+ 0.09 (+ 0.18)}$ $0.47_{ - 0.09( - 0.20)}^{+ 0.09( + 0.18)}$	${0.55}_{- 0.08 (- 0.15)}^{+ 0.04 (+ 0.09)}$ $0.55_{ - 0.08( - 0.15)}^{+ 0.04( + 0.09)}$

Parallax (mas)	𝒩(8.8975, 0.0191)	${8.872}_{- 0.031 (- 0.058)}^{+ 0.025 (+ 0.80)}$ $8.872_{ - 0.031( - 0.058)}^{+ 0.025( + 0.80)}$	${8.881}_{- 0.025 (- 0.058)}^{+ 0.024 (+ 0.80)}$ $8.881_{ - 0.025( - 0.058)}^{+ 0.024( + 0.80)}$	${8.882}_{- 0.021 (- 0.025)}^{+ 0.018 (+ 0.80)}$ $8.882_{ - 0.021( - 0.025)}^{+ 0.018( + 0.80)}$
M_b (M_jup)	Uniform(0, 30)	$10_{- 5 (- 9)}^{+ 9 (+ 18)}$ $10_{ - 5( - 9)}^{ + 9( + 18)}$	$5_{- 3 (- 4)}^{+ 4 (+ 11)}$ $5_{ - 3( - 4)}^{ + 4( + 11)}$	${0.7}_{- 0.5 (- 0.7)}^{+ 1.7 (+ 4.46)}$ $0.7_{ - 0.5( - 0.7)}^{+ 1.7( + 4.46)}$
Mc (M_jup)	Uniform(0, 30)	$9_{- 5 (- 8)}^{+ 7 (18)}$ $9_{ - 5( - 8)}^{ + 7(18)}$	$8_{- 5 (- 7)}^{+ 8 (+ 18)}$ $8_{ - 5( - 7)}^{ + 8( + 18)}$	${2.4}_{- 1.3 (- 2.2)}^{+ 4.3 (+ 5.20)}$ $2.4_{ - 1.3( - 2.2)}^{+ 4.3( + 5.20)}$
M_d (M_jup)	Uniform(0, 30)	$8_{- 6 (- 8)}^{+ 7 (+ 16)}$ $8_{ - 6( - 8)}^{ + 7( + 16)}$	$9_{- 7 (- 9)}^{+ 9 (+ 18)}$ $9_{ - 7( - 9)}^{ + 9( + 18)}$	${0.4}_{- 0.3 (- 0.4)}^{+ 1.5 (+ 1.00)}$ $0.4_{ - 0.3( - 0.4)}^{+ 1.5( + 1.00)}$
M_* (M_⊙)	𝒩(0.88,0.09)	${0.960}_{- 0.031 (- 0.063)}^{+ 0.032 (+ 0.065)}$ $0.960_{ - 0.031( - 0.063)}^{+ 0.032( + 0.065)}$	${0.953}_{- 0.033 (- 0.064)}^{+ 0.031 (0.062)}$ $0.953_{ - 0.033( - 0.064)}^{ + 0.031(0.062)}$	${0.965}_{- 0.025 (- 0.088)}^{+ 0.041 (+ 0.068)}$ $0.965_{ - 0.025( - 0.088)}^{+ 0.041( + 0.068)}$

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