Learn some diagnostics associated with detecting radiation.

• Kirchhoff's laws

Heat and Energy Transfer

Learn about blackbody emission.

• Properties
• Wien's law
• Stephan-Boltzmann law

Energy Flux

Luminosity

• These are three laws, know as Kirchhoff's laws, that govern the spectrum we see from objects.
• They allows us to interpret the spectra we observe.

1. A hot solid, liquid or gas at high pressure has a continuous spectrum.

There is energy at all wavelengths.

2. A gas at low pressure and high temperature will produce emission lines.

There is energy only at specific wavelengths.

3. A gas at low pressure in front of a hot continuum causes absorption lines.

Dark lines appear on the continuum.

As illustrated below, Kirchhoff's laws refer to three types of spectra: continuum, emission line, and absorption line.

Thus when we see a spectrum we can tell what type of source we are seeing.

• All objects radiate and receive energy.
• In everyday life, we call this heat.
• The hotter an object, the more energy it will give off.
• An object hotter than its surroundings will give off more energy than it receives
• With no internal heat (energy) source, it will cool down.

There are three ways to transport or move energy from one location to another:

• Conduction:
• particles share energy with neighbors
• Convection:
• bulk mixing of particles, e.g. turbulence
• Radiation:
• photons carry the energy

• An object in thermal equilibrium emits energy at all wavelengths.
• resulting in a continuous spectrum
• We call this thermal radiation.

• A black object or blackbody absorbs all light which hits it.
• This blackbody also emits thermal radiation. e.g. photons!
• Like a glowing poker just out of the fire.
• The amount of energy emitted (per unit area) depends only on the temperature of the blackbody.

• In 1900 Max Planck characterized the light coming from a blackbody.
• The equation that predicts the radiation of a blackbody at different temperatures is known as Planck's Law.

Note that the peak shifts with temperature.

• The peak emission from the blackbody moves to shorter wavelengths as the temperature increases (Wien's law).
• The hotter the blackbody the more energy emitted per unit area at all wavelengths.
• bigger objects emit more radiation

The wavelength of the maximum emission of a blackbody is given by:

Some sources of radiation and the wavelength of their peak emission are given below.

Consequences of Wien's Law

Hot objects look blue.

Cold objects look red.

The radiated energy increases very rapidly with increasing temperature.

where s = 5.7x10^-8 W m^-2 K^-4.

For instance, when T doubles the power increases 16 times: 2⁴ = 2 x 2 x 2 x 2 = 16. Likewise if T triples the power increases by 81 times.

The Energy flux, F, is the power per unit area radiated from an object.

The units are energy, area and time.

Total power radiated from an object.

For a sphere (like stars), the area is given by: Area = 4pR² (m²)

So the luminosity, L, is:

You can see the dependencies on radius and temperature.

Examples:

• Doubling the radius increases the luminosity by a factor of 4.
• Doubling the temperature increases the luminosity by a factor of 16.

Suppose I observe with my telescope two stars, C and D, that form a binary star pair.

• Star C has a spectral peak at 3500 A (0.35 mm, deep violet)
• Star D has a spectral peak at 7000 A (0.70 mm, deep red)

What are the temperatures of the stars?

By Wien's law

Thus we have for star C,

and for star D

If both stars are equally bright (which means in this case they have equal luminosities since the stars are part of a pair the same distance away), what are the relative sizes of stars C and D?

Now we have

So that stars C is 4 times smaller than star D.