Constraints on PDS 70 b and c from the dust continuum emission of the circumplanetary discs considering in situ dust evolution

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Volume 687 (July 2024)

A&A, 687 (2024) A166

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Table 1

Parameters.

Description	Symbol	Value	Reference
General

Dust-to-gas mass ratio of gas inflow	x	0.0001, 0.001, 0.01	−
Strength of turbulence in CPD	α	10⁻⁵, 10⁻³	−
Mass fraction of helium in gas	Y	0.27	−
Heat of water sublimation	$L_{H_{2} O}$ $\[L_{\mathrm{H}_2 \mathrm{O}}\]$	6070 K	Bauer et al. (1997)
Constant of water vapour pressure	$A_{H_{2} O}$ $\[A_{\mathrm{H}_2 \mathrm{O}}\]$	30.86	Bauer et al. (1997)
Icy dust fragmentation speed	υ_ice	50 m s⁻¹	Wada et al. (2013)
Rocky dust fragmentation speed	υ_rock	5 m s⁻¹	Wada et al. (2013)
Icy dust internal density	ρ_int,ice	1.4 g cm⁻³	−
Rocky dust internal density	ρ_int,rock	3.0 g cm⁻³	−
Size (radius) of dust in gas inflow	R_d,0	1 μm	Bae et al. (2019)
Minimum size (radius) of dust particles	a_min	0.1 μm	−
(Minus) power-low index of SFD of dust	^q	3.5	−
Real part of refractive index	n	2.298	Birnstiel et al. (2018)
Imaginary part of refractive index	k	0.02146	Birnstiel et al. (2018)
Dust internal density (for opacity calc.)	ρ_{int opa}	1. 675 g cm⁻³	Birnstiel et al. (2018)
Global radiation efficiency of gas accretion	η_eff	0.95	Marleau et al. (2019)
Dynamo region to surface mean magnetic field ratio	f_surf	3.5	Christensen et al. (2009)
Ratio of ohmic to total dissipation	f_ohm	1	Christensen et al. (2009)
Constant of proportionality (for magnetic field calc.)	c	0.63	Christensen et al. (2009)
Efficiency factor (for magnetic field calc.)	F	1	Christensen et al. (2009)
Aspect ratio of CPD (for magnetic field calc.)	h_asp	0.1	Christensen et al. (2009)

PDS 70 system

Host star mass	M_star	0.76 M_⊙	Müller et al. (2018)
Distance from Earth	d	113.43 pc	Gaia Collaboration (2018)
Inclination of CPDs (same with PPD)	i	51.7^°	Keppler et al. (2019)

PDS 70 b

Planet mass	M_p	(0.5–20) M_J	−
Gas accretion rate	${\dot{M}}_{g, p l}$ $\[\dot{M}_{\mathrm{g}, \mathrm{pl}}\]$	(10⁻⁹−10^−6.5) M_J yr⁻¹	−
Semimajor axis	a_pl	20.6 au	Haffert et al. (2019)
Radius	R_pl	2.0 R_J	Wang et al. (2021)
Effective temperature	T_pl,eff	1392 K	Wang et al. (2021)
Temperature of PPD	T_irr,PPD	51 K	Law et al. (2024)

PDS 70 c

Planet mass	M_p	(0.5–20) M_J	−
Gas accretion rate	${\dot{M}}_{g, p l}$ $\[\dot{M}_{\mathrm{g}, \mathrm{pl}}\]$	(10⁻⁹−10^−6.5) M_J yr⁻¹	−
Semimajor axis	a_pl	34.5 au	Haffert et al. (2019)
Radius	R_pl	2.0 R_J	Wang et al. (2021)
Effective temperature	T_pl,eff	1051 K	Wang et al. (2021)
Temperature of PPD	T_irr,PPD	32 K	Law et al. (2024)

Notes. The four varied quantities are in boldface.

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