Table 1.

Parameters used in the test models and simulations.

Model nameDescriptionValues
sc1aSpherical cavity with radius r0 and placed at z = ±r0; min(tcool/tff) ≈12r0 = 10 kpc
sc2ar0 = 20 kpc
sc3ar0 = 40 kpc
cc1aConical cavity with half-opening angle θcav and height hcav; min(tcool/tff) ≈12hcav = 10 kpc, θcav = 30°
cc2ahcav = 20 kpc, θcav = 30°
cc3ahcav = 20 kpc, θcav = 45°, θview = 45°
bh1amin(tcool/tff) ≈12, no cavity, with black hole|$M_{\rm bh} = 10^{10} \rm M_\odot$|
bh2a|$M_{\rm bh} = 10^{12} \rm M_\odot$|
cc1bConical cavity with min(tcool/tff) =5hcav = 20 kpc, θcav = 30°
cc2bhcav = 20 kpc, θcav = 30°, θview = 45°
cc3bhcav = 50 kpc, θcav = 45°
cc4bhcav = 50 kpc, θcav = 45°, θview = 45°
cc5bhcav = 50 kpc, θcav = 45°, θview = 0°
cc6bSame as cc4b but the conical cavity is replaced by gas with T = 7 keV. This gas follows the HSE pressure profilehcav = 20 kpc, θcav = 45°, θview = 45°
dscbDisplaced spherical cavity with min(tcool/tff) =5r0 = 10 kpc, z0 = 15 kpc
flrA floor in the tcool/tff placed at the centrefloor (tcool/tff) =10
pr1a3D geometry with perturbation, min(tcool/tff) ≈12|$({\Delta \rho }/{\rho })|_{\rm max} = 0.01$|
pr2a|$({\Delta \rho }/{\rho })|_{\rm max} = 0.1$|
simt0Simulation data, min(tcool/tff) ≊9.9t = 0 Myr
simt1000Simulation data, min(tcool/tff) ≊11t = 1000 Myr
simt1000th0Simulation data, min(tcool/tff) ≊11t = 1000 Myr, θview = 0°
simt170Simulation data, min(tcool/tff) ≊2.4t = 170 Myr
simt840Simulation data, min(tcool/tff) ≊3.08t = 840 Myr
simt1910Simulation data, min(tcool/tff) ≊3.05t = 1910 Myr
Model nameDescriptionValues
sc1aSpherical cavity with radius r0 and placed at z = ±r0; min(tcool/tff) ≈12r0 = 10 kpc
sc2ar0 = 20 kpc
sc3ar0 = 40 kpc
cc1aConical cavity with half-opening angle θcav and height hcav; min(tcool/tff) ≈12hcav = 10 kpc, θcav = 30°
cc2ahcav = 20 kpc, θcav = 30°
cc3ahcav = 20 kpc, θcav = 45°, θview = 45°
bh1amin(tcool/tff) ≈12, no cavity, with black hole|$M_{\rm bh} = 10^{10} \rm M_\odot$|
bh2a|$M_{\rm bh} = 10^{12} \rm M_\odot$|
cc1bConical cavity with min(tcool/tff) =5hcav = 20 kpc, θcav = 30°
cc2bhcav = 20 kpc, θcav = 30°, θview = 45°
cc3bhcav = 50 kpc, θcav = 45°
cc4bhcav = 50 kpc, θcav = 45°, θview = 45°
cc5bhcav = 50 kpc, θcav = 45°, θview = 0°
cc6bSame as cc4b but the conical cavity is replaced by gas with T = 7 keV. This gas follows the HSE pressure profilehcav = 20 kpc, θcav = 45°, θview = 45°
dscbDisplaced spherical cavity with min(tcool/tff) =5r0 = 10 kpc, z0 = 15 kpc
flrA floor in the tcool/tff placed at the centrefloor (tcool/tff) =10
pr1a3D geometry with perturbation, min(tcool/tff) ≈12|$({\Delta \rho }/{\rho })|_{\rm max} = 0.01$|
pr2a|$({\Delta \rho }/{\rho })|_{\rm max} = 0.1$|
simt0Simulation data, min(tcool/tff) ≊9.9t = 0 Myr
simt1000Simulation data, min(tcool/tff) ≊11t = 1000 Myr
simt1000th0Simulation data, min(tcool/tff) ≊11t = 1000 Myr, θview = 0°
simt170Simulation data, min(tcool/tff) ≊2.4t = 170 Myr
simt840Simulation data, min(tcool/tff) ≊3.08t = 840 Myr
simt1910Simulation data, min(tcool/tff) ≊3.05t = 1910 Myr

Notes. The first two letters of each model name (except for ‘flr’ and ‘simt’ models) indicate the geometry of the model while the last letter indicates the min(tcool/tff) of that model (e.g. ‘a’ implies min(tcool/tff) =12 and ‘b’ implies min(tcool/tff) =5). Unless otherwise mentioned, the viewing angle, θview = 90° (i.e. edge on) by default.

Table 1.

Parameters used in the test models and simulations.

Model nameDescriptionValues
sc1aSpherical cavity with radius r0 and placed at z = ±r0; min(tcool/tff) ≈12r0 = 10 kpc
sc2ar0 = 20 kpc
sc3ar0 = 40 kpc
cc1aConical cavity with half-opening angle θcav and height hcav; min(tcool/tff) ≈12hcav = 10 kpc, θcav = 30°
cc2ahcav = 20 kpc, θcav = 30°
cc3ahcav = 20 kpc, θcav = 45°, θview = 45°
bh1amin(tcool/tff) ≈12, no cavity, with black hole|$M_{\rm bh} = 10^{10} \rm M_\odot$|
bh2a|$M_{\rm bh} = 10^{12} \rm M_\odot$|
cc1bConical cavity with min(tcool/tff) =5hcav = 20 kpc, θcav = 30°
cc2bhcav = 20 kpc, θcav = 30°, θview = 45°
cc3bhcav = 50 kpc, θcav = 45°
cc4bhcav = 50 kpc, θcav = 45°, θview = 45°
cc5bhcav = 50 kpc, θcav = 45°, θview = 0°
cc6bSame as cc4b but the conical cavity is replaced by gas with T = 7 keV. This gas follows the HSE pressure profilehcav = 20 kpc, θcav = 45°, θview = 45°
dscbDisplaced spherical cavity with min(tcool/tff) =5r0 = 10 kpc, z0 = 15 kpc
flrA floor in the tcool/tff placed at the centrefloor (tcool/tff) =10
pr1a3D geometry with perturbation, min(tcool/tff) ≈12|$({\Delta \rho }/{\rho })|_{\rm max} = 0.01$|
pr2a|$({\Delta \rho }/{\rho })|_{\rm max} = 0.1$|
simt0Simulation data, min(tcool/tff) ≊9.9t = 0 Myr
simt1000Simulation data, min(tcool/tff) ≊11t = 1000 Myr
simt1000th0Simulation data, min(tcool/tff) ≊11t = 1000 Myr, θview = 0°
simt170Simulation data, min(tcool/tff) ≊2.4t = 170 Myr
simt840Simulation data, min(tcool/tff) ≊3.08t = 840 Myr
simt1910Simulation data, min(tcool/tff) ≊3.05t = 1910 Myr
Model nameDescriptionValues
sc1aSpherical cavity with radius r0 and placed at z = ±r0; min(tcool/tff) ≈12r0 = 10 kpc
sc2ar0 = 20 kpc
sc3ar0 = 40 kpc
cc1aConical cavity with half-opening angle θcav and height hcav; min(tcool/tff) ≈12hcav = 10 kpc, θcav = 30°
cc2ahcav = 20 kpc, θcav = 30°
cc3ahcav = 20 kpc, θcav = 45°, θview = 45°
bh1amin(tcool/tff) ≈12, no cavity, with black hole|$M_{\rm bh} = 10^{10} \rm M_\odot$|
bh2a|$M_{\rm bh} = 10^{12} \rm M_\odot$|
cc1bConical cavity with min(tcool/tff) =5hcav = 20 kpc, θcav = 30°
cc2bhcav = 20 kpc, θcav = 30°, θview = 45°
cc3bhcav = 50 kpc, θcav = 45°
cc4bhcav = 50 kpc, θcav = 45°, θview = 45°
cc5bhcav = 50 kpc, θcav = 45°, θview = 0°
cc6bSame as cc4b but the conical cavity is replaced by gas with T = 7 keV. This gas follows the HSE pressure profilehcav = 20 kpc, θcav = 45°, θview = 45°
dscbDisplaced spherical cavity with min(tcool/tff) =5r0 = 10 kpc, z0 = 15 kpc
flrA floor in the tcool/tff placed at the centrefloor (tcool/tff) =10
pr1a3D geometry with perturbation, min(tcool/tff) ≈12|$({\Delta \rho }/{\rho })|_{\rm max} = 0.01$|
pr2a|$({\Delta \rho }/{\rho })|_{\rm max} = 0.1$|
simt0Simulation data, min(tcool/tff) ≊9.9t = 0 Myr
simt1000Simulation data, min(tcool/tff) ≊11t = 1000 Myr
simt1000th0Simulation data, min(tcool/tff) ≊11t = 1000 Myr, θview = 0°
simt170Simulation data, min(tcool/tff) ≊2.4t = 170 Myr
simt840Simulation data, min(tcool/tff) ≊3.08t = 840 Myr
simt1910Simulation data, min(tcool/tff) ≊3.05t = 1910 Myr

Notes. The first two letters of each model name (except for ‘flr’ and ‘simt’ models) indicate the geometry of the model while the last letter indicates the min(tcool/tff) of that model (e.g. ‘a’ implies min(tcool/tff) =12 and ‘b’ implies min(tcool/tff) =5). Unless otherwise mentioned, the viewing angle, θview = 90° (i.e. edge on) by default.

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