global average temperatures of planetary surfaces and the “habitable zone”

Global Average Temperatures of Planetary Surfaces and the

“Habitable Zone”

Global Average Temperatures of Planetary Surfaces and the

“Habitable Zone”

Astrobiology WorkshopJune 27, 2006

Astrobiology WorkshopJune 27, 2006

HabitabilityHabitabilityHabitabilityHabitability

What What MightMight Make a Planet or Moon Make a Planet or Moon “Habitable”?“Habitable”? IFIF life on EarthEarth is a reliable guide, life

requires• Carbon ChemistryCarbon Chemistry• Energy Source to Sustain MetabolismEnergy Source to Sustain Metabolism• Liquid Water!Liquid Water!

– Or some other good liquid medium for carbon chemistry (but water seems best)

IFIF liquid water really is essential, then• temperaturestemperatures (and pressures) must permit

liquid water to exist So we are led to ask:

• What determines planet temperatures?What determines planet temperatures?

Planet TemperaturesPlanet TemperaturesPlanet TemperaturesPlanet Temperatures

What Heats Surfaces of Moons & Planets?What Heats Surfaces of Moons & Planets? What are the sources of heat for the surfaces of

a solid (or liquid) body in a planetary system?• Starlight and Planet LightStarlight and Planet Light• Outflow of Internal HeatOutflow of Internal Heat• ImpactsImpacts• Latent Heats of Surface or Atmosphere Latent Heats of Surface or Atmosphere

ConstituentsConstituents Which of these usually dominates the Global Global

Average Temperature TAverage Temperature Tsurfsurf after a fewfewxx101088 years?• Starlight!Starlight!


Basic Principles for Global Average T’sBasic Principles for Global Average T’s EquilibriumEquilibrium

• InputInput of Energy per second to the surface equals the OutputOutput of Energy per second

Factors affecting InputInput?• Luminosity Luminosity of the star• Distance Distance from the star• Reflectivity (Albedo) Reflectivity (Albedo) of the surface

and/or atmosphere– The fraction of the starlight that is scattered

or reflected by the surface without being absorbed


Basic Principles for Global Average T’sBasic Principles for Global Average T’s What is the principal mechanism that cools the

surface of a planet?• RadiationRadiation by the surface because it is hot!

Factors affecting OutputOutput?• Temperature Temperature of the surface

– At typical temperatures of planetary surfaces, they radiate in the infraredinfrared

– Energy/sec. as temperature• Insulation of the surface by a blanket of

atmosphere that blocks the infraredinfrared– The Greenhouse EffectThe Greenhouse Effect

The Planet Temperature The Planet Temperature CalculatorCalculator


What is It?What is It? The PTC is a Web-based tool that calculates the

Global Average Temperature TGlobal Average Temperature Tsurfsurf assuming

• Energy InputInput Rate = Energy OutputOutput Rate Parameters you provide to the calculator:

• Mass Mass of the star LuminosityLuminosity of the star• Distance Distance of the planet from the star• The Albedo Albedo of the planet• The Greenhouse Factor Greenhouse Factor relative to Earth

– This is a measure of the column density of Greenhouse gases in the atmosphere relative to the same quantity on Earth

Calculating TCalculating Tsurfsurf with with No AtmosphereNo Atmosphere

Calculating TCalculating Tsurfsurf with with No AtmosphereNo Atmosphere

TTsurfsurf Calculation Calculation Equilibrium says

• Star Energy/sec. Energy/sec. InIn = = Planet Planet Energy/sec. Energy/sec. OutOut InputInput Energy/sec. from starlight depends on

• Luminosity L = Luminosity L = light energy emitted per sec.• Distance D = Distance D = distance of object from star• Energy/meterEnergy/meter22/sec. /sec. at the object

• Energy/sec. Energy/sec. hitting an object of Radius RRadius R

L L 44DD22

L L 44DD22RR22xx

Calculating TCalculating Tsurfsurf with withNo AtmosphereNo Atmosphere


InputInput Energy/sec. absorbed by the object• Albedo A = Albedo A = fraction of light energy scattered

or reflected by object• Fraction absorbed is 1-A1-A

InputInput Energy/sec. from star that is absorbed

L L 44DD22(I-A)(I-A)RR22xx



Energy/meter2/sec. emitted by a hot object at Temperature T Temperature T (Stefan-Boltzmann Law) is

OutputOutput InfraredInfrared Energy/sec. from the object

• Assume uniform surface temperature TTsurfsurf

Set Input Input == Output Output and solve for TTsurfsurf

[(1-A)L][(1-A)L]1/41/4

2(2())1/41/4DD1/21/2

TT44

44RR22xxTTsurfsurf44

TTsurfsurf = =

Calculating TCalculating Tsurfsurf withwithan Atmospherean Atmosphere


Greenhouse EffectGreenhouse Effect

The Greenhouse Effect Greenhouse Effect occurs for gases that are• Transparent to visiblevisible light but• Opaque to infraredinfrared light

Examples of Greenhouse Gases:

• H2O, CO2, CH4, Freon

The surface then has to reach a higher TTsurfsurf to force an equilibrium flux of infraredinfrared light back up through the atmosphere.



Greenhouse Effect Greenhouse Effect

The change in TTsurfsurf is greater when the “mean mean free pathfree path” for infraredinfrared photons is smaller, which depends on the amount of greenhouse gas in the atmosphere.• Roughly one extra TTsurfsurf

4 4 for each mean free path through the atmosphere

• For large amounts of greenhouse gas, if you double the column densitycolumn density of greenhouse gas, then TTsurfsurf increases by 221/41/4 times

Luminosities of Stars?Luminosities of Stars?Luminosities of Stars?Luminosities of Stars?

What about LL? For Main Sequence StarsMain Sequence Stars, which burn hydrogen to helium in their centers, it is approximately true that

In this formula, MM refers to the star’s mass and the subscript refers the solar value.

L = LL = L (M/M (M/M))33

The Habitable ZoneThe Habitable Zonefor Earth-Like Planetsfor Earth-Like PlanetsThe Habitable ZoneThe Habitable Zone

for Earth-Like Planetsfor Earth-Like Planets

Simple Definition of the Habitable Zone:Habitable Zone:• Range of distances from a Star for TTsurfsurf is such

that the surfacesurface water of an Earth-likeEarth-like planet (or moon) would not either

– FreezeFreeze or– BoilBoil

Questions for Activities & Discussions:Questions for Activities & Discussions:• What is the Habitable ZoneHabitable Zone for the Sun and

for your star?• What would happen to EarthEarth if we moved it to

the edges of the HZHZ? What do VenusVenus and MarsMars suggest about the edges of the HZHZ?

• Where was the Sun’s Habitable ZoneHabitable Zone in the past? Where will it be in the future?

global average temperatures of planetary surfaces and the “habitable zone”

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