Stellar Feedback Outflows

Class providing models of outflows driven by stellar feedback—the ejection of interstellar gas from galactic discs and spheroids by energy and momentum deposited by supernovae and stellar winds. Outflow rates (in \(\mathrm{M}_\odot\) Gyr\(^{-1}\)) are returned separately for ejective outflows (gas removed from the galaxy but retained in the halo) and expulsive outflows (gas expelled beyond the halo virial radius), as functions of the star formation rate and the energy input rate. These outflows regulate star formation and enrich the circumgalactic medium with metals.

Default implementation: stellarFeedbackOutflowsPowerLaw

Methods

outflowRate → void

Returns the outflow rates (both ejective and expulsive) due to stellar feedback in the given component in units of \(\mathrm{M}_\odot/\)Gyr.

  • class (nodeComponent), intent(inout) :: component

  • double precision , intent(in ) :: rateStarFormation , rateEnergyInput

  • double precision , intent( out) :: rateOutflowEjective, rateOutflowExpulsive

stellarFeedbackOutflowsCreasey2013

A stellar feedback outflow class which implements the model of Creasey et al. (2013). Specifically, the outflow rate is:

\[\dot{M}_\mathrm{outflow} = {\dot{E}_\mathrm{SN} \over E_\mathrm{SN} \dot{M}_\star} \int_0^\infty \beta_0 \Sigma_{g,1}^{-\mu}(r) f_\mathrm{g}^\nu(r) \dot{\Sigma}_\star(r) 2 \pi r \mathrm{d}r,\]

where \(\Sigma_{g,1}(r)\) is the surface density of gas in units of \(\mathrm{M}_\odot\) pc\(^{-2}\), \(f_\mathrm{g}(r)\) is the gas fraction, \(\dot{\Sigma}_\star(r)\) is the surface density of star formation rate, \(\dot{M}_\star\) is the total star formation rate in the disk, \(\dot{E}_\mathrm{SN}\) is the current energy input rate from supernovae, \(E_\mathrm{SN}\) is the total energy input per unit mass from a stellar population after infinite time, \(\beta_0=\)[beta0], \(\mu=\)[mu], and \(\nu=\)[nu].

Parameters

  • [mu] (real; default 1.15d0) — The parameter \(\mu\) appearing in the Creasey et al. (2013) model for supernovae feedback.

  • [nu] (real; default 0.16d0) — The parameter \(\nu\) appearing in the Creasey et al. (2013) model for supernovae feedback.

  • [beta0] (real; default 13.0d0) — The parameter \(\beta_0\) appearing in the Creasey et al. (2013) model for supernovae feedback.

stellarFeedbackOutflowsFixed

A stellar feedback outflow class in which the outflow rate is fixed. Specifically,

\[\dot{M}_\mathrm{outflow} = f_\mathrm{outflow} {\dot{E} \over E_\mathrm{canonical}},\]

where \(f_\mathrm{outflow}=\)[fraction] is the fraction of the star formation rate that goes into outflow, \(\dot{E}\) is the rate of energy input from stellar populations and \(E_\mathrm{canonical}\) is the total energy input by a canonical stellar population normalized to \(1 \mathrm{M}_\odot\) after infinite time.

Parameters

  • [fraction] (real; default 0.01d0) — The fixed fraction \(f_\mathrm{outflow}\) of the stellar energy input rate (normalized to a canonical \(1\,\mathrm{M}_\odot\) population) that drives gas outflows, setting the mass loading factor for stellar feedback in the galaxy.

stellarFeedbackOutflowsHaloScaling

A stellar feedback outflow model in which the mass outflow rate scales as a power law in the host halo virial velocity and cosmological expansion factor, providing a physically motivated mass-loading factor that increases in lower-mass halos.

Methods

  • tabulate — Tabulate the virial density contrast as a function of mass and time.

  • restoreTable — Restore a tabulated solution from file.

  • storeTable — Store a tabulated solution to file.

Parameters

  • [fraction] (real; default 0.01d0) — The normalization \(f\) of the outflow rate relative to the star formation rate at a reference halo velocity of 200 km/s and expansion factor of 1, setting the overall mass-loading amplitude of the halo-scaling feedback model.

  • [exponentVelocity] (real; default -2.0d0) — The exponent of virial velocity in the outflow rate in disks.

  • [exponentRedshift] (real; default 0.0d0) — The power-law exponent of the cosmological expansion factor \((1+z)\) in the halo-scaling outflow rate, allowing the mass-loading factor to evolve with redshift; a value of zero gives no redshift evolution.

stellarFeedbackOutflowsHaloScalingFormationHalo

A stellar feedback outflow model in which the mass outflow rate scales with the virial velocity and redshift of the galaxy’s formation halo (rather than the current host halo), giving feedback that reflects the initial potential well the galaxy formed in.

Parameters

  • [fraction] (real; default 0.01d0) — The normalization \(f\) of the outflow rate relative to the star formation rate, evaluated at the formation halo’s virial velocity of 200 km/s and expansion factor of 1, setting the overall mass-loading amplitude.

  • [exponentVelocity] (real; default -2.0d0) — The exponent of virial velocity in the outflow rate in disks.

  • [exponentRedshift] (real; default 0.0d0) — The power-law exponent of the cosmological expansion factor \((1+z)\) in the formation-halo outflow rate, allowing the mass-loading factor to evolve with the redshift of the formation halo; a value of zero gives no redshift evolution.

stellarFeedbackOutflowsMassLoadingLimit

A stellar feedback model which limits to a maximum mass-loading factor. The outflow rate will be

\[\dot{M}_\mathrm{out} = \mathrm{tanh} (\beta / \beta_\mathrm{max}) \beta_\mathrm{max} \dot{M}_\star,\]

where \(\dot{M}_\star\) is the star formation rate, \(\beta\) is the mass-loading factor of the decorated model, and \(\beta_\mathrm{max}=\)[factorMassLoadingMaximum] is the maximum mass loading factor.

Parameters

  • [factorMassLoadingMaximum] (real) — The maximum mass loading factor for outflows due to stellar feedback.

stellarFeedbackOutflowsPowerLaw

A stellar feedback outflow class in which the outflow rate is a power-law in circular velocity. Specifically the outflow rate is given by:

\[\dot{M}_\mathrm{outflow} = \left({V_\mathrm{outflow} \over V}\right)^{\alpha_\mathrm{outflow}} {\dot{E} \over E_\mathrm{canonical}},\]

where \(V_\mathrm{outflow}=\)[velocityCharacteristic] (in km/s) and \(\alpha_\mathrm{outflow}=\)[exponent] are input parameters, \(V\) is the characteristic velocity of the component, \(\dot{E}\) is the rate of energy input from stellar populations and \(E_\mathrm{canonical}\) is the total energy input by a canonical stellar population normalized to \(1 \mathrm{M}_\odot\) after infinite time.

(Default implementation)

Methods

  • tabulate — Tabulate the virial density contrast as a function of mass and time.

  • restoreTable — Restore a tabulated solution from file.

  • storeTable — Store a tabulated solution to file.

Parameters

  • [velocityCharacteristic] (real; default 250.0d0) — The velocity scale at which the SNe-driven outflow rate equals the star formation rate in disks.

  • [exponent] (real; default 3.5d0) — The velocity scaling of the SNe-driven outflow rate in disks.

stellarFeedbackOutflowsPowerLawRedshiftScaling

A power-law stellar feedback model in which the characteristic velocity scales as a power of \((1+z)\).

Parameters

  • [exponentRedshift] (real; default 0.0d0) — The redshift scaling of characteristic velocity for SNe-driven outflow rates in disks.

  • [velocityCharacteristic] (real; default 250.0d0) — The velocity scale at which the SNe-driven outflow rate equals the star formation rate in disks. (inherited from stellarFeedbackOutflowsPowerLaw)

  • [exponent] (real; default 3.5d0) — The velocity scaling of the SNe-driven outflow rate in disks. (inherited from stellarFeedbackOutflowsPowerLaw)

stellarFeedbackOutflowsRateLimit

A rate-limiting stellar feedback outflow model that wraps another outflow model and enforces a minimum outflow timescale (in units of the component dynamical time), preventing unphysically rapid ejection of gas from the galaxy.

Parameters

  • [timescaleOutflowFractionalMinimum] (real) — The minimum timescale (in units of the component dynamical time) for outflows due to stellar feedback.

stellarFeedbackOutflowsSummation

A stellar feedback outflow class that combines multiple outflow models by summing their ejective and expulsive outflow rates, allowing complex multi-component feedback prescriptions to be built from simpler models.

Methods

  • list — Return a list of all sub-components.

stellarFeedbackOutflowsSuperWind

A stellar feedback outflow class which implements a “superwind”. The outflow rate is given by:

\[\begin{split}\dot{M}_\mathrm{outflow} = \beta_\mathrm{superwind} {\dot{E} \over E_\mathrm{canonical}} \left\{ \begin{array}{ll} \left( V_\mathrm{superwind}/V\right)^2 & \hbox{ if } V > V_\mathrm{superwind} \\ 1 & \hbox{ otherwise,} \end{array} \right.\end{split}\]

where \(V_\mathrm{superwind}=\)[velocityCharacteristic] (in km/s) and \(\beta_\mathrm{superwind}=\)[massLoading] are input parameters, \(V\) is the characteristic velocity of the component, \(\dot{E}\) is the rate of energy input from stellar populations and \(E_\mathrm{canonical}\) is the total energy input by a canonical stellar population normalized to \(1 \mathrm{M}_\odot\) after infinite time.

Parameters

  • [velocityCharacteristic] (real; default 200.0d0) — The velocity scale at which the SNe-driven superwind outflow rate transitions to a constant.

  • [massLoading] (real; default 2.0d0) — The mass-loading parameter \(\beta_\mathrm{superwind}\) of the superwind outflow model, giving the outflow rate per unit stellar energy input normalized to a canonical \(1\,\mathrm{M}_\odot\) stellar population; larger values drive more gas out of the galaxy.

stellarFeedbackOutflowsVlctyMxSclng

A stellar feedback outflow model in which the mass outflow rate scales as a power law in the peak (maximum) circular velocity of the dark matter halo profile and the cosmological expansion factor, providing stronger feedback in lower-mass halos with lower peak velocities.

Methods

  • calculationReset — Reset memoized calculations.

Parameters

  • [fraction] (real; default 0.01d0) — The normalization \(f\) of the outflow rate relative to the star formation rate, evaluated at the reference peak circular velocity of 200 km/s and expansion factor of 1, setting the overall amplitude of the feedback-driven outflow.

  • [exponentVelocity] (real; default -2.0d0) — The exponent of velocity in the cooling timescale for low mass halos in the velocity maximum scaling scaling cooling rate model.

  • [exponentRedshift] (real; default 0.0d0) — The exponent of \((1+z)\) in the cooling timescale for low mass halos in the velocity maximum scaling scaling cooling rate model.

stellarFeedbackOutflowsZero

A stellar feedback outflow model that produces zero outflow rate, used to disable stellar feedback-driven gas ejection while still satisfying the interface requirements of the stellar feedback outflows class.