Free Access


Table 2:

Summary of the analytic recipe to obtain the impact radii $b_\sigma $ and approach velocities $v_{\rm a}$.

1. Calculate dimensionless parameters:
$\zeta _{\rm w}$ (headwind velocity) Eq. (15)  
  $\alpha_{\rm p}$ (planet size) Eq. (16)  
  ${\rm St} = t_{\rm s} \Omega$ (Stokes number) Eq. (12)  

2. Calculate impact radii:
$\tilde{b}_{\rm set}$ Eq. (27), Eq. (32)  
  $b_{\rm hyp}$ Eq. (28)  
  $b_{\rm 3b}$ Eq. (31)  

3. Determine regime:
${\rm St}<\min(1, 12/\zeta_{\rm w}^3)$   ${\rm St}>{\rm max}(\zeta _{\rm w}, 1)$
  Settling Hyperbolic Three body

4. Results
Impact radius (accretion), $b_\sigma $: ${\rm max}(\tilde{b}_{\rm set}, b_{\rm geo}$) ${\rm max}(\tilde{b}_{\rm set}, b_{\rm hyp})$ ${\rm max}(b_{\rm 3b}, b_{\rm geo})$
Approach velocity $v_{\rm a}$: $3b_\sigma/2 + \zeta_{\rm w}$ Eq. (29) 3.2
Approach radius $b_{\rm app}$: $b_\sigma $ $b_\sigma $ 2.5

Notes. Description of impact radii: $b_{\rm geo}$, geometrical impact radius ( $=\alpha_{\rm p}$); $b_{\rm set}$ impact radius in settling regime; $\tilde{b}_{\rm set}$, modified $b_{\rm set}$ (to cover the transition regime); $b_{\rm hyp}$ impact radius in the hyperbolic regime; $b_{\rm 3b}$ drag-enhanced impact radius for the 3-body regimes; $b_{\rm app}$, approach distance.

Source LaTeX | All tables | In the text

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.