Open Access
Table A.2
Definitions of the relevant variables.
| Symbol | Equation | Definition |
|---|---|---|
| l | – | Level of fragmentation |
| Rl | – | Spatial scale at level l |
| Rstop | – | Spatial scale beyond which core fragmentation stops |
| i | – | Identifies a specific child within one parent when several fragments are produced on the same scale |
| Ml,i | 3 | Mass of the i–th child at level l |
| ⟨Ml⟩ | 7 | Average mass of all fragments at the level Rl |
| r | – | Scaling ratio between two successive levels |
| nl | – | Number of fragments produced at level l + 1 by one parent at level l |
| pl(nl) | – | Probability a parent at level l produces nl fragments at level l + 1 |
 |
1 | Expected number of fragments one parent at level l produces at the next level |
| ϵl | 6 | Mass efficiency with which fragments are formed from their parent at the previous level |
 |
– | Average mass efficiency with which the last fragmenting cores at Rstop turn into stars |
| q | – | Mass ratio between the more massive child and the less massive one within one siblinghood |
| ψl,i(nl, q) | 4 | Fraction of mass received by the i–th children from its parental reservoir ϵlMl |
| Γ(R, M) | 12 | Power-law index of a mass function in a ∂N/∂ log M representation at mass M and scale R |
| ϕ(M) | 5 | Spatial fragmentation rate |
 |
– | Derivative of the fragmentation rate with respect to the mass |
| ξ(M) | 6 | Spatial mass transfer rate |
 |
– | Derivative of the mass transfer rate with respect to the mass |
| ℰ(R) | – | Fragment formation mass efficiency between the cloud and the cores at scale R |
Notes. The ‘–’ character indicates the variable is not referenced in equations since it is introduced as a definition in the text.
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