| Observables . | |
|---|---|
| Rs | Observed radius of the forward shock along the major axis |
| Rc | Observed radius of the contact discontinuity along the major axis |
| M | Mach number of the forward shock |
| z∥/x⊥ | Observed aspect ratio of the forward shock |
| nt | Total number density of the ambient medium at r = Rs |
| ρa | Mass density of the ambient medium at r = Rs |
| Pa | Pressure of the ambient medium at r = Rs |
| α | Power-law index of the ambient density profile |
| Model parameters | |
| E | Total energy injected by the jet |
| tage | Age of the system |
| tb | Duration of jet activity |
| θ0 | Opening angle of the injected jet |
| Lj | One-sided jet luminosity, i.e. Lj = E/2tb |
| Evolutionary time-scales | |
| tsp | Time for the forward shock to become spherical |
| tbuoy | Time-scale for buoyancy to pull the bubbles apart |
| tE | Time when the outflow reaches pressure equilibrium with the ambient medium |
| Properties of the outflow upon choking | |
| Rch | Radius at which the jet is choked |
| tch | Time at which the jet is choked |
| ζ | Dimensionless ratio of Rch/Rs |
| η | Dimensionless ratio of tch/tage |
| ρch | Density of the ambient medium at Rch |
| βh | Velocity of the jet head upon choking |
| βc | Velocity of the cocoon shock upon choking |
| βh/βc | Estimate for the aspect ratio of the forward shock upon choking |
| Σh | Surface area of the jet head upon choking |
| θh | Angle subtended by the jet head upon choking |
| Vfs,ch | Volume enclosed by the forward shock upon choking |
| Pc,ch | Pressure in the cocoon upon choking |
| Λ(Rch) | Parameter determining susceptibility to the magnetic kink instability |
| Observables . | |
|---|---|
| Rs | Observed radius of the forward shock along the major axis |
| Rc | Observed radius of the contact discontinuity along the major axis |
| M | Mach number of the forward shock |
| z∥/x⊥ | Observed aspect ratio of the forward shock |
| nt | Total number density of the ambient medium at r = Rs |
| ρa | Mass density of the ambient medium at r = Rs |
| Pa | Pressure of the ambient medium at r = Rs |
| α | Power-law index of the ambient density profile |
| Model parameters | |
| E | Total energy injected by the jet |
| tage | Age of the system |
| tb | Duration of jet activity |
| θ0 | Opening angle of the injected jet |
| Lj | One-sided jet luminosity, i.e. Lj = E/2tb |
| Evolutionary time-scales | |
| tsp | Time for the forward shock to become spherical |
| tbuoy | Time-scale for buoyancy to pull the bubbles apart |
| tE | Time when the outflow reaches pressure equilibrium with the ambient medium |
| Properties of the outflow upon choking | |
| Rch | Radius at which the jet is choked |
| tch | Time at which the jet is choked |
| ζ | Dimensionless ratio of Rch/Rs |
| η | Dimensionless ratio of tch/tage |
| ρch | Density of the ambient medium at Rch |
| βh | Velocity of the jet head upon choking |
| βc | Velocity of the cocoon shock upon choking |
| βh/βc | Estimate for the aspect ratio of the forward shock upon choking |
| Σh | Surface area of the jet head upon choking |
| θh | Angle subtended by the jet head upon choking |
| Vfs,ch | Volume enclosed by the forward shock upon choking |
| Pc,ch | Pressure in the cocoon upon choking |
| Λ(Rch) | Parameter determining susceptibility to the magnetic kink instability |
| Observables . | |
|---|---|
| Rs | Observed radius of the forward shock along the major axis |
| Rc | Observed radius of the contact discontinuity along the major axis |
| M | Mach number of the forward shock |
| z∥/x⊥ | Observed aspect ratio of the forward shock |
| nt | Total number density of the ambient medium at r = Rs |
| ρa | Mass density of the ambient medium at r = Rs |
| Pa | Pressure of the ambient medium at r = Rs |
| α | Power-law index of the ambient density profile |
| Model parameters | |
| E | Total energy injected by the jet |
| tage | Age of the system |
| tb | Duration of jet activity |
| θ0 | Opening angle of the injected jet |
| Lj | One-sided jet luminosity, i.e. Lj = E/2tb |
| Evolutionary time-scales | |
| tsp | Time for the forward shock to become spherical |
| tbuoy | Time-scale for buoyancy to pull the bubbles apart |
| tE | Time when the outflow reaches pressure equilibrium with the ambient medium |
| Properties of the outflow upon choking | |
| Rch | Radius at which the jet is choked |
| tch | Time at which the jet is choked |
| ζ | Dimensionless ratio of Rch/Rs |
| η | Dimensionless ratio of tch/tage |
| ρch | Density of the ambient medium at Rch |
| βh | Velocity of the jet head upon choking |
| βc | Velocity of the cocoon shock upon choking |
| βh/βc | Estimate for the aspect ratio of the forward shock upon choking |
| Σh | Surface area of the jet head upon choking |
| θh | Angle subtended by the jet head upon choking |
| Vfs,ch | Volume enclosed by the forward shock upon choking |
| Pc,ch | Pressure in the cocoon upon choking |
| Λ(Rch) | Parameter determining susceptibility to the magnetic kink instability |
| Observables . | |
|---|---|
| Rs | Observed radius of the forward shock along the major axis |
| Rc | Observed radius of the contact discontinuity along the major axis |
| M | Mach number of the forward shock |
| z∥/x⊥ | Observed aspect ratio of the forward shock |
| nt | Total number density of the ambient medium at r = Rs |
| ρa | Mass density of the ambient medium at r = Rs |
| Pa | Pressure of the ambient medium at r = Rs |
| α | Power-law index of the ambient density profile |
| Model parameters | |
| E | Total energy injected by the jet |
| tage | Age of the system |
| tb | Duration of jet activity |
| θ0 | Opening angle of the injected jet |
| Lj | One-sided jet luminosity, i.e. Lj = E/2tb |
| Evolutionary time-scales | |
| tsp | Time for the forward shock to become spherical |
| tbuoy | Time-scale for buoyancy to pull the bubbles apart |
| tE | Time when the outflow reaches pressure equilibrium with the ambient medium |
| Properties of the outflow upon choking | |
| Rch | Radius at which the jet is choked |
| tch | Time at which the jet is choked |
| ζ | Dimensionless ratio of Rch/Rs |
| η | Dimensionless ratio of tch/tage |
| ρch | Density of the ambient medium at Rch |
| βh | Velocity of the jet head upon choking |
| βc | Velocity of the cocoon shock upon choking |
| βh/βc | Estimate for the aspect ratio of the forward shock upon choking |
| Σh | Surface area of the jet head upon choking |
| θh | Angle subtended by the jet head upon choking |
| Vfs,ch | Volume enclosed by the forward shock upon choking |
| Pc,ch | Pressure in the cocoon upon choking |
| Λ(Rch) | Parameter determining susceptibility to the magnetic kink instability |
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