A broken debris cascade as a possible source of hot dust emission in transitioning planet-forming disks

Open Access

Table C.1

All symbols used in this paper.

Symbol	Description	Value⁽¹⁾
Dust particles

s	particle size
s_min	size of the smallest particles	0.1 μm
s_b	size below which particles become bound to the gas	Eq. (7)
s_cc	size below which the collisional lifetime is longer than the damping timescale	Eq. (21)
s_pt	size of planetesimals provided to the system
m	mass of a particle	Eq. (4)
ρ_•	material density of dust and larger particles	1500 kg m⁻²
Ω_K	Kepler frequency	$\sqrt{G M_{} / R^{3}}$ $\[\sqrt{G M_ / R^3}\]$
υ_K	Kepler velocity	$\sqrt{G M_{} / R}$ $\[\sqrt{G M_ / R}\]$
ν	the relative velocity between particle relative to υ_K	η/4
σ_tot	total collisional cross-section of a particle	Eq. (18)
σ_g	geometric cross-section of a particle	Eq. (44)
ε	relative size of the smallest particle capable of destroying particle of a given size	0.043
ε₀		−πε^γ⁺¹/(γ + 1)
S	material strength/binding energy	200 J kg⁻¹
t_coll	collisional lifetime of a particle	Eq. (20)
z	height of a particle above the midplane

Size distributions

f	size distribution	f(s) = f₀ s^γ
f₀	size distribution scaling constant
γ	power-law value for size distributions
f_cc, f_0,cc	size distribution of particles in the collisional cascade	Eq. (35)
γ_cc	power-law value for steady-state collisional cascade	−3.5
f_int, f_0,int	size distribution of intermediate-size particles	Eq. (35)
f_b, f_0,b	size distribution of bound particles	Eq. (23)
f_frag, f_0,frag	size distribution of fragments resulting from the destruction of a larger particle	Eq. (26)
γ_f	power-law value for fragment size distribution	−3
ϕ_prod	production rate of particles	Eq. (28)

Dust cloud

R	distance of the dust cloud to the star	1 au
ΔR	width of the dust cloud measured along a line-of-sight from the star	0.1 au
η	fraction of the star surrounded by dust	0.3
τ_g	geometric optical depth of the cloud of dust	1
V	dust cloud volume	Eq. (49)

Gas & friction

∑_gas	gas surface density	1000 kg m⁻²
T_gas	gas temperature	300 K
μ_mol	mean molecular mass	2.3
ρ_gas	gas density	Eq. (51)
υ_th	thermal velocity of gas molecules	Eq. (2)
F_D	drag force	Eq. (1)
t_fric	friction time of a particle in gas	Eq. (5)
τ_fric	relative friction time of a particle in gas	Eq. (6)
t_settle	settling time of a particle	Eq. (12)

General

${\dot{M}}_{in}$ $\[\dot{M}_{\text {in }}\]$	mass flux of planetesimals into the system	Eq. (34)
M_*	mass of central star	1 M_⊙
G	gravitational constant	6.67 × 10⁻¹¹ N m² kg⁻²
k_B	Boltzmann constant	1.38 × 10⁻²³ J K⁻¹
m_p	proton mass	1.67 × 10⁻²⁷ kg

⁽¹⁾ For free parameters, the fiducial value is given. For secondary variables, the equation is given.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.