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Home , Luminosity, Solar constant, Solar luminosity

Extraterrestrial Life: Lecture #6 Liquid water is important because:

What are the requirements for the (or another planet) • solvent for organic molecules to be habitable? • allows transport of chemicals within cells • involved in many biologically important • liquid water on surface chemical reactions • atmosphere • plate tectonics / volcanism Other solvents (ammonia, methane etc) exist in liquid • magnetic field form on planets but are much less promising for life • … Normal atmospheric pressure: liquid water requires: 0o C (273K) < T < 100o C (373K)

…require planets with surface temperatures in this range ! Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008

What determines the Earth’s surface temperature? The flux of is the amount of energy that passes fraction of 2 incident radiation through unit area (1 m ) in one second is reflected Measured in units of / m2 incident Solar Solar flux declines with distance as 1 / d2: radiation L = remainder is 2 absorbed by 4"d the Earth and then reradiated …where d is the - planet distance and L is the total If the Earth is not heating up or cooling down, the total of the Sun (watts) of incoming and outgoing radiation must balance ! Are there other sources of energy for a planet?

Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008

Solar constant The fraction of the incident flux that is reflected is called is 3.9 x 1026 watts the albedo of the planet: 0 < A < 1 The fraction that is absorbed is (1-A) Earth-Sun distance is d = 1.5 x 1011 m (1 AU)

26 The albedo varies greatly depending 3.9 "10 watts on the surface terrain Solar flux = 2 4# " 1.5 "1011 m ( ) For the Earth, a global average 2 =1380 watts / m value is about A ~ 0.3

This is the Solar flux that would be measured above the How does A change as the Earth Earth’s atmosphere rotates? !

Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008

1 First consider the reflected component of How much energy is absorbed?

d P flux R2 (1 A) RE = " # E " $ 2 =1380 " # " (6.4 "106 ) " (1$ 0.3) watts Fraction of total Solar luminosity that is reflected is: =1.24 "1017 watts

flux " area of Earth as seen from Sun " A f = c.f. total world electricity consumption ~ 5 x 1012 watts solar luminosity 2 2 1380 watts / m " #RE " A ! = Note: total forcing due to greenhouse gases is about 3.9 "1026 watts 2 watts / m2 - i.e. a few tenths of a percent of the total 6 Earth radius is RE = 6.4 x 10 m Solar flux… this is why is a complex scientific problem ! f = 1.4 x 10-10 Seen from another , Earth is ~10 billion dimmer than the Sun Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008

The absorbed radiation is reradiated as thermal radiation, Thermal radiation emitted by the Earth is: mostly in the infra-red part of the spectrum 2 4 Pthermal = 4"RE #$T IR

As T increases, the peak area of the Earth’s power (watts / m2) emitted of thermal radiation moves surface in m2 by thermal radiation at a to shorter wavelengths, and ! temperature T the total emission increases 4 rapidly as ~T σ is a constant called the Stefan-Boltzmann constant, it equals 5.67 x 10-8 watts per m2 per K4 Sun: 6000K (visible) Earth: 300K (IR) Setting the emission equal to the energy absorbed from sunlight determines the equilibrium temperature of the Earth

Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008

Find that predict T ~ 260K - a bit too cold! But we have Habitable Zone ignored the influence of the atmosphere in blocking some of the outgoing radiation… Earth orbit

What does the surface temperature depend on: Define the habitable zone as the range of distances L(1# A) from the Sun for which a T 4 " d 2 planet can have liquid water on its surface • distance to the star Empirically: Venus is inside • luminosity of the star the habitable zone and Mars •! p roperties of the atmosphere and surface outside for the

But… calculating the exact boundaries is hard - depends upon the nature of the planet and its atmosphere

Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008

2 Additional complication: Solar luminosity changes with The continuously habitable zone is the range of radii (slowly)… Sun was less luminous in the past and for which liquid water is possible throughout a planet’s is slowly getting more luminous lifetime

Faint Sun problem: initial Solar luminosity is predicted Obviously narrower than the instantaneous habitable to be ~70% of the current luminosity… but no evidence zone - possibly much narrower… that temperature on the early Earth was much colder Means that whose luminosity changes relatively Thought to be an atmospheric effect quickly are unpromising hosts for life-bearing planets

Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008

What about planets on elliptical orbits that dip in and out of the habitable zone?

• surface temperature adjusts to the Solar forcing on a timescale << 1 year (e.g. seasons!) • temperature underground, or in the oceans, adjusts much more slowly • planets with non-circular orbits can’t be ruled out immediately

Extraterrestrial Life: Spring 2008

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