Circumstellar Habitable Zone Limit

Functions
template<typename T >
T	EGXPhys::CircumstellarHabitableZoneLimit (const T starLuminosityInW, const T stellarFluxEffective)
	Calculates the Circumstellar Habitable Zone Limits, \(d_{CHZL}\) of a star. Also known as Habitable Zone Limits. More...
template<typename T >
T	EGXPhys::StellarFluxEffectiveSelsis (const T starEffectiveSurfaceTemperatureInK, const T sunEffectiveStellarFlux, const T aModelParameter, const T bModelParameter)
	Calculates the effective stellar flux, \((S_{eff})\) of a star using Selsis estimation. More...
template<typename T >
T	EGXPhys::StellarFluxEffectiveUnderwood (const T starEffectiveSurfaceTemperatureInK, const T sunEffectiveStellarFlux, const T aModelParameter, const T bModelParameter)
	Calculates the effective stellar flux \((S_{eff})\) using Underwood estimation. More...
template<typename T >
T	EGXPhys::CircumstellarHabitableZoneInnerBoundary (const T starEffectiveSurfaceTemperatureInK, const T starLuminosityInW)
	Calculates the inner boundary of the Habitable Zone of a solar system. More...
template<typename T >
T	EGXPhys::CircumstellarHabitableZoneOuterBoundary (const T starEffectiveSurfaceTemperatureInK, const T starLuminosityInW)
	Calculates Circumstellar Habitable Zone Outer Boundary \((r_o)\) of a star. More...
template<typename T >
T	EGXPhys::CircumstellarHabitableZoneDistance (const T distanceFromStar, const T CHZInnerBoundary, const T CHZOuterBoundary)
	Calculates Circumstellar Habitable Zone Distance \((CHZD)\) of a planet. Also known as Habitable Zone Distance. More...

Detailed Description

Todo:

Add more models for Seff. https://en.wikipedia.org/wiki/Circumstellar_habitable_zone lists way more models

Function Documentation

CircumstellarHabitableZoneDistance()

template<typename T >

T EGXPhys::CircumstellarHabitableZoneDistance	(	const T	distanceFromStar,
		const T	CHZInnerBoundary,
		const T	CHZOuterBoundary
	)

Calculates Circumstellar Habitable Zone Distance \((CHZD)\) of a planet. Also known as Habitable Zone Distance.

Circumstellar Habitable Zone is the orbital area around a star where in which a rocky planet, with the right atmosphere, can maintain liquid water at the surface of the planet. The HZ of an exoplanet is generally defined as the area (in terms of distance from its central star) See http://phl.upr.edu/library/notes/habitablezonesdistancehzdahabitabilitymetricforexoplanets and https://en.wikipedia.org/wiki/Circumstellar_habitable_zone

Equation from

Parameters

distanceFromStar	\(d\ (m)\) Distance of celestial object from the star in meters.
CHZOuterBoundary	\(r_{CHZ,Outer}\ (m)\) Radius of the outer boundary of the circumstellar habitable zone of the star in meters.
CHZInnerBoundary	\(r_{CHZ,Inner}\ (m)\) Radius of the inner boundary of the circumstellar habitable zone of the star in meters.

Returns

\(CHZD\)(HZU) circumstellar habitable zone distance, a habitability metric for planets. Between -1 and +1 HZU correspond to planets within the habitable zone.

See also

CircumstellarHabitableZoneInnerBoundary() for inner boundary of the circumstellar habitable zone.

CircumstellarHabitableZoneOuterBoundary() for outer boundary of the circumstellar habitable zone.

CircumstellarHabitableZoneLimit() to calculate outer and inner boundary using diffrent models.

CircumstellarHabitableZoneInnerBoundary()

template<typename T >

T EGXPhys::CircumstellarHabitableZoneInnerBoundary	(	const T	starEffectiveSurfaceTemperatureInK,
		const T	starLuminosityInW
	)

Calculates the inner boundary of the Habitable Zone of a solar system.

Habitable Zone is defined in astrophysics as the orbital area around a star where in which a rocky planet, with the right atmosphere, can maintain liquid water at the surface of the planet The HZ of an exoplanet is generally defined as the area (in terms of distance from its central star) See "Impacts of stellar evolution and dynamics on the habitable zone: The role of rotation and magnetic activity" https://doi.org/10.1051/0004-6361/201629034 Equation taken from http://phl.upr.edu/library/notes/habitablezonesdistancehzdahabitabilitymetricforexoplanets and

Parameters

starEffectiveSurfaceTemperatureInK	\(T_{eff}\ (K)\) Effective surface temperature of the star (black body) in kelvin. See https://en.wikipedia.org/wiki/Effective_temperature.
starLuminosityInW	\(L\ (W)\) Luminosity of the star in watts.

Returns

\(r_{inner}\ (AU)\) the inner boundary of the Habitable Zone.

See also

CircumstellarHabitableZoneDistance() for circumstellar habitable zone distance, a habitability metric for planets.

CircumstellarHabitableZoneOuterBoundary() for outer boundary of the circumstellar habitable zone.

CircumstellarHabitableZoneLimit() to calculate inner boundary using a diffrent model.

CircumstellarHabitableZoneLimit()

template<typename T >

T EGXPhys::CircumstellarHabitableZoneLimit	(	const T	starLuminosityInW,
		const T	stellarFluxEffective
	)

Calculates the Circumstellar Habitable Zone Limits, \(d_{CHZL}\) of a star. Also known as Habitable Zone Limits.

Circumstellar Habitable Zone Limit is used to calculations the inner and outer radius of the circumstellar habitable zone.

\[d_{CHZL}=1AU \sqrt{ \frac{L/L_\odot}{S_{eff}} }\]

See "Impacts of stellar evolution and dynamics on the habitable zone: The role of rotation and magnetic activity" (Gallet 2016) https://doi.org/10.1051/0004-6361/201629034

Equation taken from "Habitable Zones around Main Sequence Stars" http://dx.doi.org/10.1006/icar.1993.1010

Parameters

starLuminosityInW	\(L\ (W)\) Luminosity of the star in watts.
stellarFluxEffective	\(S_{eff}\)(dimensionless) Effective stellar flux. Estimation of the ratio of outgoing IR flux to incident IR flux of a planet with greenhouse effects folded in.

Returns

\(d_{CHZL}\)(AU) Circumstellar Habitable Zone Limit. Either the inner or outer radius of the circumstellar habitable zone.

See also

CircumstellarHabitableZoneDistance() for circumstellar habitable zone distance, a habitability metric for planets.

CircumstellarHabitableZoneInnerBoundary() for inner boundary of the circumstellar habitable zone.

CircumstellarHabitableZoneOuterBoundary() for outer boundary of the circumstellar habitable zone.

StellarFluxEffectiveKopparapu() for \(S_{eff}\) using Kopparapu's approximation.

StellarFluxEffectiveSelsis() for \(S_{eff}\) using Selsis's approximation.

StellarFluxEffectiveUnderwood() for \(S_{eff}\) using Underwood's approximation.

CircumstellarHabitableZoneOuterBoundary()

template<typename T >

T EGXPhys::CircumstellarHabitableZoneOuterBoundary	(	const T	starEffectiveSurfaceTemperatureInK,
		const T	starLuminosityInW
	)

Calculates Circumstellar Habitable Zone Outer Boundary \((r_o)\) of a star.

Parameters

starEffectiveSurfaceTemperatureInK	\(T_{eff}\ (K)\) Effective surface temperature of the star (black body) in kelvin. See https://en.wikipedia.org/wiki/Effective_temperature.
starLuminosityInW	\(L\ (W)\) Luminosity of the star in watts.

Returns

\(ESI_S\)(dimensionless) Surface Earth Similarity Index for a planet.

See also

CircumstellarHabitableZoneDistance() for circumstellar habitable zone distance, a habitability metric for planets.

CircumstellarHabitableZoneInnerBoundary() for inner boundary of the circumstellar habitable zone.

CircumstellarHabitableZoneLimit() to calculate outer boundary using a diffrent model.

StellarFluxEffectiveSelsis()

template<typename T >

T EGXPhys::StellarFluxEffectiveSelsis	(	const T	starEffectiveSurfaceTemperatureInK,
		const T	sunEffectiveStellarFlux,
		const T	aModelParameter,
		const T	bModelParameter
	)

Calculates the effective stellar flux, \((S_{eff})\) of a star using Selsis estimation.

Effective stellar flux is used in circumstellar habitable zone calculations.

\[S_{eff}= \frac{1}{(S_{eff\odot}+a(T_{eff}-5700)+b(T_{eff}-5700)^2)^2}\]

See "Impacts of stellar evolution and dynamics on the habitable zone: The role of rotation and magnetic activity" (Gallet 2016) https://doi.org/10.1051/0004-6361/201629034

Equation taken from "Habitable planets around the star Gl 581?" (Selsis 2007) https://doi.org/10.1051/0004-6361:20078091

Example inputs for model parameters (recent Venus - early Mars criteria):

\(S_{eff\odot,inner} = 0.72\), \(a_{inner} = 2.7619 \times 10^{-5}\), \(b_{inner} = 3.8095 \times 10^{-9}\)

\(S_{eff\odot,outer} = 1.77\), \(a_{outer} = 1.3786 \times 10^{-4}\), \(b_{outer} = 1.4286 \times 10^{-9}\)

Parameters

starEffectiveSurfaceTemperatureInK	\(T_{eff}\ (K)\) Effective surface temperature of the star (black body) in kelvin. See https://en.wikipedia.org/wiki/Effective_temperature.
sunEffectiveStellarFlux	\(S_{eff\odot}\)(dimensionless) Model parameter estimating the ratio of outgoing IR flux to incident IR flux of a planet with greenhouse effects folded in the presence of the sun.
aModelParameter	\(a\)(dimensionless) First order model fit parameter taking into account the change of star temperature from that of the Sun.
bModelParameter	\(b\)(dimensionless) Second order model fit parameter taking into account the change of star temperature from that of the Sun.

Returns

\(S_{eff}\)(dimensionless) Effective Stellar Flux. Approximation used in circumstellar habitable zone calculations.

See also

CircumstellarHabitableZoneDistance() for circumstellar habitable zone distance, a habitability metric for planets.

CircumstellarHabitableZoneInnerBoundary() for inner boundary of the circumstellar habitable zone.

CircumstellarHabitableZoneOuterBoundary() for outer boundary of the circumstellar habitable zone.

StellarFluxEffectiveUnderwood()

template<typename T >

T EGXPhys::StellarFluxEffectiveUnderwood	(	const T	starEffectiveSurfaceTemperatureInK,
		const T	sunEffectiveStellarFlux,
		const T	aModelParameter,
		const T	bModelParameter
	)

Calculates the effective stellar flux \((S_{eff})\) using Underwood estimation.

Effective stellar flux is used in circumstellar habitable zone calculations.

\[S_{eff}=S_{eff\odot}+aT_{eff}+bT^2_{eff}\]

See "Impacts of stellar evolution and dynamics on the habitable zone: The role of rotation and magnetic activity" (Underwood 2003) https://doi.org/10.1051/0004-6361/201629034

Equation taken from "The evolution of habitable zones during stellar lifetimes and implications on the search for extraterrestrial life" (Underwood 2003) https://doi.org/10.1017/S1473550404001715

Example inputs for model parameters (recent Venus - early Mars criteria):

\(S_{eff\odot,inner} = 1.786\), \(a_{inner} = 1.349 \times 10^{-4}\), \(b_{inner} = 2.286 \times 10^{-8}\)

\(S_{eff\odot,outer} = 0.2125\), \(a_{outer} = 1.371 \times 10^{-5}\), \(b_{outer} = 5.714 \times 10^{-9}\)

Parameters

starEffectiveSurfaceTemperatureInK	\(T_{eff}\ (K)\) Effective surface temperature of the star (black body) in kelvin. See https://en.wikipedia.org/wiki/Effective_temperature.
sunEffectiveStellarFlux	\(S_{eff\odot}\)(dimensionless) Model parameter representing the ratio of outgoing IR flux to incident IR flux with the effects of the greenhouse effect in the presence of the Sun.
aModelParameter	\(a\)(dimensionless) First order model fit parameter taking into account the change of star temperature from that of the Sun.
bModelParameter	\(b\)(dimensionless) Second order model fit parameter taking into account the change of star temperature from that of the Sun.

Returns

\(S_{eff}\)(dimensionless) Effective Stellar Flux. Approximation used in circumstellar habitable zone calculations.

See also

CircumstellarHabitableZoneDistance() for circumstellar habitable zone distance, a habitability metric for planets.

CircumstellarHabitableZoneInnerBoundary() for inner boundary of the circumstellar habitable zone.

CircumstellarHabitableZoneOuterBoundary() for outer boundary of the circumstellar habitable zone.