Global Average Temperatures of Planetary Surfaces and the

Global Average Temperatures of Planetary Surfaces and the “Habitable Zone” Astrobiology Workshop June 27, 2006

Habitability What Might Make a Planet or Moon “Habitable”? § IF • • • § IF § life on Earth is a reliable guide, life requires Carbon Chemistry Energy Source to Sustain Metabolism Liquid Water! – Or some other good liquid medium for carbon chemistry (but water seems best) liquid water really is essential, then • temperatures (and pressures) must permit liquid water to exist So we are led to ask: • What determines planet temperatures?

Planet Temperatures 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 Light • Outflow of Internal Heat • Impacts • Latent Heats of Surface or Atmosphere Constituents Which of these usually dominates the Global Average Temperature Tsurf after a fewx 108 years? • Starlight!

Planet Temperatures Basic Principles for Global Average T’s § § Equilibrium • Input of Energy per second to the surface equals the Output of Energy per second Factors affecting Input? Input • Luminosity of the star • Distance from the star • Reflectivity (Albedo) of the surface and/or atmosphere – The fraction of the starlight that is scattered or reflected by the surface without being absorbed

Planet Temperatures Basic Principles for Global Average T’s § § What is the principal mechanism that cools the surface of a planet? • Radiation by the surface because it is hot! Factors affecting Output? Output • Temperature of the surface – At typical temperatures of planetary surfaces, they radiate in the infrared – Energy/sec. as temperature • Insulation of the surface by a blanket of atmosphere that blocks the infrared – The Greenhouse Effect

The Planet Temperature Calculator What is It? § § The PTC is a Web-based tool that calculates the Global Average Temperature Tsurf assuming • Energy Input Rate = Energy Output Rate Parameters you provide to the calculator: • Mass of the star Luminosity of the star • Distance of the planet from the star • The Albedo of the planet • The 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

The Planet Temperature Calculator

Calculating Tsurf with No Atmosphere Tsurf Calculation § § Equilibrium says • Star Energy/sec. In = Planet Energy/sec. Out Input Energy/sec. from starlight depends on • Luminosity L = light energy emitted per sec. • Distance D = distance of object from star • Energy/meter 2/sec. at the object L 4 D 2 • Energy/sec. hitting an object of Radius R L 4 D R 2 x 4 D 2

Calculating Tsurf with No Atmosphere § § Input Energy/sec. absorbed by the object • Albedo A = fraction of light energy scattered or reflected by object • Fraction absorbed is 1 -A Input Energy/sec. from star that is absorbed (I-A) R 2 x L 4 D 2

Calculating Tsurf with No Atmosphere § Energy/meter 2/sec. emitted by a hot object at Temperature T (Stefan-Boltzmann Law) is T 4 § § Output Infrared Energy/sec. from the object • Assume uniform surface temperature Tsurf 4 R 2 x Tsurf 4 Set Input = Output and solve for Tsurf 1/4 Tsurf = [(1 -A)L] 2( )1/4 D 1/2

Calculating Tsurf with an Atmosphere Greenhouse Effect § § § The Greenhouse Effect occurs for gases that are • Transparent to visible light but • Opaque to infrared light Examples of Greenhouse Gases: • H 2 O, CO 2, CH 4, Freon The surface then has to reach a higher Tsurf to force an equilibrium flux of infrared light back up through the atmosphere.

Calculating Tsurf with an Atmosphere Greenhouse Effect § The change in Tsurf is greater when the “mean free path” path for infrared photons is smaller, which depends on the amount of greenhouse gas in the atmosphere. • Roughly one extra Tsurf 4 for each mean free path through the atmosphere • For large amounts of greenhouse gas, if you double the column density of greenhouse gas, then Tsurf increases by 21/4 times

Luminosities of Stars? § What about L? For Main Sequence Stars, Stars which burn hydrogen to helium in their centers, it is approximately true that L = L (M/M )3 § In this formula, M refers to the star’s mass and the subscript refers the solar value.

The Habitable Zone for Earth-Like Planets § § Simple Definition of the Habitable Zone: • Range of distances from a Star for Tsurf is such that the surface water of an Earth-like planet (or moon) would not either – Freeze or – Boil Questions for Activities & Discussions: • What is the Habitable Zone for the Sun and for your star? • What would happen to Earth if we moved it to the edges of the HZ? HZ What do Venus and Mars suggest about the edges of the HZ? HZ • Where was the Sun’s Habitable Zone in the past? Where will it be in the future?