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

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Table 3

Orbital parameters fit to astrometry of PDS 70 b and c only.

Quantity	Prior	Coplanar	Stable	Stable (incl. N-body)
a_b (au)	LogUniform(1, 100)	${20.1}_{- 0.7 (- 1.4)}^{+ 0.7 (+ 1.5)}$ $20.1_{ - 0.7( - 1.4)}^{ + 0.7( + 1.5)}$	${20.8}_{- 0.7 (- 1.4)}^{+ 0.6 (+ 1.3)}$ $20.8_{ - 0.7( - 1.4)}^{ + 0.6( + 1.3)}$	${20.7}_{- 0.5 (- 1.2)}^{+ 0.6 (+ 1.4)}$ $20.7_{ - 0.5( - 1.2)}^{ + 0.6( + 1.4)}$
e_b	Uniform(0, 1)	${0.21}_{- 0.05 (- 0.10)}^{+ 0.05 (+ 0.10)}$ $0.21_{ - 0.05( - 0.10)}^{ + 0.05( + 0.10)}$	${0.18}_{- 0.05 (- 0.09)}^{+ 0.05 (+ 0.12)}$ $0.18_{ - 0.05( - 0.09)}^{ + 0.05( + 0.12)}$	${0.16}_{- 0.04 (- 0.01)}^{+ 0.05 (+ 0.12)}$ $0.16_{ - 0.04( - 0.01)}^{ + 0.05( + 0.12)}$
i_b (deg)	sin(i)	${130.7}_{- 1.9 (- 3.7)}^{+ 1.9 (+ 3.8)}$ $130.7_{ - 1.9( - 3.7)}^{ + 1.9( + 3.8)}$	${130.3}_{- 1.8 (- 3.4)}^{+ 1.8 (+ 3.9)}$ $130.3_{ - 1.8( - 3.4)}^{ + 1.8( + 3.9)}$	${130.6}_{- 1.6 (- 3.2)}^{+ 1.6 (+ 3.5)}$ $130.6_{ - 1.6( - 3.2)}^{+ 1.6( + 3.5)}$
ω_b (deg)	Uniform(0, 360)	$197_{- 8 (- 19)}^{+ 8 (+ 14)}$ $197_{ - 8( - 19)}^{+ 8( + 14)}$	$193_{- 10 (- 22)}^{+ 9 (+ 16)}$ $193_{ - 10( - 22)}^{+ 9( + 16)}$	$190_{- 13 (- 28)}^{+ 10 (+ 16)}$ $190_{ - 13( - 28)}^{+ 10( + 16)}$
Ω_b (deg)	Uniform(0, 360)	${178.2}_{- 4.1 (- 8.0)}^{+ 4.5 (+ 9.1)}$ $178.2_{ - 4.1( - 8.0)}^{ + 4.5( + 9.1)}$	$179_{- 4 (- 8)}^{+ 5 (+ 11)}$ $179_{ - 4( - 8)}^{+ 5( + 11)}$	$176_{- 4 (- 8)}^{+ 5 (+ 12)}$ $176_{ - 4( - 8)}^{+ 5( + 12)}$
τ_b	Uniform(0, 1)	${0.373}_{- 0.021 (- 0.040)}^{+ 0.024 (+ 0.047)}$ $0.373_{ - 0.021( - 0.040)}^{+ 0.024( + 0.047)}$	${0.360}_{- 0.023 (- 0.045)}^{+ 0.027 (+ 0.051)}$ $0.360_{ - 0.023( - 0.045)}^{+ 0.027( + 0.051)}$	${0.355}_{- 0.025 (- 0.049)}^{+ 0.028 (+ 0.055)}$ $0.355_{ - 0.025( - 0.049)}^{+ 0.028( + 0.055)}$

a_b (au)	LogUniform(1, 100)	${31.9}_{- 1.0 (- 2.0)}^{+ 0.9 (+ 1.8)}$ $31.9_{ - 1.0( - 2.0)}^{+ 0.9( + 1.8)}$	${33.3}_{- 1.0 (- 2.2)}^{+ 1.1 (+ 2.0)}$ $33.3_{ - 1.0( - 2.2)}^{+ 1.1( + 2.0)}$	${33.9}_{- 1.1 (- 2.1)}^{+ 1.0 (+ 1.7)}$ $33.9_{ - 1.1( - 2.1)}^{+ 1.0( + 1.7)}$
e_b	Uniform(0, 1)	${0.065}_{- 0.015 (- 0.029)}^{+ 0.017 (+ 0.036)}$ $0.065_{ - 0.015( - 0.029)}^{+ 0.017( + 0.036)}$	${0.046}_{- 0.013 (- 0.027)}^{+ 0.014 (+ 0.032)}$ $0.046_{ - 0.013( - 0.027)}^{+ 0.014( + 0.032)}$	${0.042}_{- 0.013 (- 0.030)}^{+ 0.014 (+ 0.027)}$ $0.042_{ - 0.013( - 0.030)}^{+ 0.014( + 0.027)}$
i_b (deg)	sin(i)	${131.5}_{- 1.1 (- 2.2)}^{+ 1.2 (+ 2.5)}$ $131.5_{ - 1.1( - 2.2)}^{+ 1.2( + 2.5)}$	${130.4}_{- 1.2 (- 2.2)}^{+ 1.3 (+ 2.8)}$ $130.4_{ - 1.2( - 2.2)}^{+ 1.3( + 2.8)}$	${129.8}_{- 1.0 (- 1.9)}^{+ 1.3 (+ 2.7)}$ $129.8_{ - 1.0( - 1.9)}^{+ 1.3( + 2.7)}$
ω_b (deg)	Uniform(0, 360)	$89_{- 10 (- 24)}^{+ 9 (+ 21)}$ $89_{ - 10( - 24)}^{ + 9( + 21)}$	$77_{- 11 (- 22)}^{+ 11 (+ 33)}$ $77_{ - 11( - 22)}^{ + 11( + 33)}$	$77_{- 13 (- 25)}^{+ 12 (+ 28)}$ $77_{ - 13( - 25)}^{ + 12( + 28)}$
Ω_b (deg)	Uniform(0, 360)	${154.9}_{- 2.6 (- 5.8)}^{+ 2.1 (+ 4.0)}$ $154.9_{ - 2.6( - 5.8)}^{+ 2.1( + 4.0)}$	${157.5}_{- 2.2 (- 5.8)}^{+ 1.8 (+ 3.3)}$ $157.5_{ - 2.2( - 5.8)}^{+ 1.8( + 3.3)}$	${158.0}_{- 2.0 (- 3.8)}^{+ 1.7 (+ 3.1)}$ $158.0_{ - 2.0( - 3.8)}^{+ 1.7( + 3.1)}$
τ_b	Uniform(0, 1)	${0.572}_{- 0.035 (- 0.078)}^{+ 0.030 (+ 0.068)}$ $0.572_{ - 0.035( - 0.078)}^{+ 0.030( + 0.068)}$	${0.52}_{- 0.03 (- 0.07)}^{+ 0.04 (+ 0.11)}$ $0.52_{ - 0.03( - 0.07)}^{+ 0.04( + 0.11)}$	${0.521}_{- 0.038 (- 0.070)}^{+ 0.038 (+ 0.085)}$ $0.521_{ - 0.038( - 0.070)}^{+ 0.038( + 0.085)}$

Parallax (mas)	𝒩 (8.8975, 0.0191)	${8.880}_{- 0.024 (- 0.051)}^{+ 0.024 (+ 0.48)}$ $8.880_{ - 0.024( - 0.051)}^{+ 0.024( + 0.48)}$	${8.881}_{- 0.023 (- 0.046)}^{+ 0.25 (+ 0.048)}$ $8.881_{ - 0.023( - 0.046)}^{ + 0.25( + 0.048)}$	${8.878}_{- 0.023 (- 0.046)}^{+ 0.026 (+ 0.050)}$ $8.878_{ - 0.023( - 0.046)}^{ + 0.026( + 0.050)}$
M_b (M_jup)	Uniform(0, 30)	$10_{- 7 (- 10)}^{+ 10 (+ 18)}$ $10_{ - 7( - 10)}^{+ 10( + 18)}$	$6_{- 4 (- 6)}^{+ 6 (+ 18)}$ $6_{ - 4( - 6)}^{ + 6( + 18)}$	${1.4}_{- 1.0 (- 1.3)}^{+ 2.1 (+ 4.10)}$ $1.4_{ - 1.0( - 1.3)}^{+ 2.1( + 4.10)}$
Mc (M_jup)	Uniform(0, 30)	$9_{- 6 (- 9)}^{+ 8 (+ 18)}$ $9_{ - 6( - 9)}^{ + 8( + 18)}$	$9_{- 6 (- 8)}^{+ 9 (+ 19)}$ $9_{ - 6( - 8)}^{ + 9( + 19)}$	${6.4}_{- 3.7 (- 5.7)}^{+ 4.3 (+ 8.60)}$ $6.4_{ - 3.7( - 5.7)}^{+ 4.3( + 8.60)}$
M_* (M_⊙)	𝒩 (0.88, 0.09)	${0.967}_{- 0.030 (- 0.060)}^{+ 0.033 (+ 0.067)}$ $0.967_{ - 0.030( - 0.060)}^{+ 0.033( + 0.067)}$	${0.954}_{- 0.031 (- 0.063)}^{+ 0.032 (+ 0.070)}$ $0.954_{ - 0.031( - 0.063)}^{+ 0.032( + 0.070)}$	${0.952}_{- 0.028 (- 0.063)}^{+ 0.032 (+ 0.065)}$ $0.952_{ - 0.028( - 0.063)}^{+ 0.032( + 0.065)}$

Notes. The third column shows the results of the fit using the Gaussian prior on the mutual inclination (see Eq. (2)), while the final two columns show the results of the fit using Eq. (1) as a prior, before and after the N-body analysis. For each parameter the median value of the posterior is listed, with subscripts and superscripts listing the 68% and 95% CIs (with the 95% CIs in parentheses).

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