Lecture 12

ASTR 111 – Section 002

Measurements in Astronomy

• In astronomy, we need to make

remote and indirect

measurements – Think of an example of a remote and indirect measurement from everyday life

Using Light

• Light has many properties that we can use to learn about what happens far away • Light interacts with matter in a special way

• Only photons with special wavelengths will interact with atom • How will this affect what a person will see at point X?

• When is the atom “hotter”?

X

Why is UV light usually blamed for skin cancer? What is special about it compared to other light sources?

A prism bends photons more or less depending on their

wavelength

Cloud of Gas

A prism bends photons more or less depending on their

wavelength

Cloud of Gas

What will the spectrum look like here?

Emission line spectrum

Continuous Spectrum

• A blackbody emits photons with many energies (wavelengths) – a

continuous spectrum

What will the spectrum look like here?

Absorption Spectrum

Absorption vs. Emission

• What type of spectrum is produced when the light emitted from a hot, dense object passes through a prism?

• What type of spectrum is produced when the light emitted directly from a cloud of gas passes through a prism?

• Describe the source of light and the path the light must take to produce an absorption spectrum • There are dark lines in the absorption spectrum that represent missing light. What happened to this light that is missing in the absorption line spectrum?

From Lecture Tutorials for Introductory Astronomy, page 61.

Each chemical element produces its own unique set of spectral lines

• Stars like our Sun have low-density, gaseous atmospheres surrounding their hot, dense cores. If you were looking at the spectra of light coming from the Sun (or any star), which of the three types of spectra would be observed?

• If a star existed that was only a hot dense core and did not have a low-density atmosphere surrounding it, what type of spectrum would you expect this particular star to give off?

• Two students are looking at a brightly lit full Moon, illuminated by reflected light from the Sun. Consider the following discussion between two students about what the spectrum of moonlight would look like: – I think moonlight is just reflected sunlight, so we will see the Sun’s absorption line spectrum.

– I disagree, an absorption spectrum has to come from a hot, dense object. Since thie Moon is not a hot, dense object, it can’t give off an absorption line spectrum.

Do you agree or disagree with either or both of these students? Explain your reasoning.

• Imagine that your are looking at two different spectra of the Sun. Spectrum #1 is obtained using a telescope that is in a high orbit far above Earth’s atmosphere. Spectrum #2 is obtained using a telescope located on the surface of Earth. Label each spectrum below as either Spectrum #1 or Spectrum #2.

Would this make sense?

This dark line was removed

Energy and electromagnetic radiation

Planck’s law relates the energy of a photon to its frequency or wavelength

E



hc

l

E

= energy of a photon

h

= Planck’s constant

c

= speed of light l = wavelength of light The value of the constant

h

in this equation, called

Planck’s constant,

experiments to be has been shown in laboratory

h

= 6.625 x 10 –34 J s

• Which electromagnetic wave has a higher energy: one with f=10 cycles per second or f=1 cycles per second?

Three Temperature Scales

Color and Temperature

An

opaque

object emits electromagnetic radiation according to its temperature

Blue: Hot or Not?

http://www.straightdope.com/mailbag/mhotflame.html

Blackbody Definition

• Does not reflect incoming radiation, only absorbs • Emits radiation, depending on temperature • Temperature and emitted radiation intensity follow a

special

relationship One way of creating a blackbody Photon enters If hole is very small, what is probability that it exits?

Wien’s law and the Stefan-Boltzmann law are useful tools for analyzing glowing objects like stars • A blackbody is a hypothetical object that is a perfect absorber of electromagnetic radiation at all wavelengths • Stars closely approximate the behavior of blackbodies, as do other hot, dense objects

• Blackbodies do not always appear black!

–The sun is close to being a “perfect” blackbody –Blackbodies appear black only if their temperature very low

Special

Relationship

For Intensity, think photons/second on a small area Wavelength

Question

• Why is photon/second similar to energy/second? How are they related?

Watt? Energy Flux?

Flux

Flux is a measure of how much “stuff” crosses a small patch in a given amount of time. Can have flux of green photons, red photons, etc.

Blackbodies and Astronomy

Blackbody Laws

• Stefan-Boltzmann Law – relates energy output of a blackbody to its temperature • Wein’s law – relates peak wavelength output by a blackbody to its temperature

Special Relationship

For Intensity, think photons/second on a small area Wavelength

Stefan-Boltzmann Law

• A blackbody radiates electromagnetic waves with a total energy flux

F

directly proportional to the fourth power of the Kelvin temperature

T

of the object:

F

~

T

4

Special Relationship

Stefan-Boltzmann Law tells us that if we add up the energy from all wavelengths, then the total energy Flux F ~

T

4 Wavelength

Special Relationship

Wien’s law tells us that l

max

depends on temperature l max 1 ~

T

Max intensity at l

max

l

max

Wavelength

Special Relationship

Sketch this curve for larger and smaller T Wavelength

Wavelength of peak decreases as temperature increases At high wavelengths, intensity goes to zero Overall amplitude increases with Temperature As wavelength goes to zero, intensity goes to zero

Color and Temperature

What would this object look like at these three temperatures?

Why does it glow white before

blue?

• Can this figure help us explain?

• Can this figure help us explain?

Near this temperature, this special combination of intensities is what we call white. Also, the real curve is a little flatter near the peak

The Sun does not emit radiation with intensities that exactly follow the blackbody curve

So, what color is the sun in space?

Left side is white Right side is (should be) a little “pinker” • http://casa.colorado.edu/~ajsh/colour/Tspectrum.html

If blue light has higher energy, and energy is proportional to temperature, why are my cold spots blue?

1 0 5 4 3 2 A B C

• Which curve represents an ideal blackbody?

– Curve A – Curve B – Curve C

• If the object in Figure 1 were increased in temperature, what would happen to curves A, B, and C?

• Curve C is more jagged. The locations where the curve C is small correspond to – Spectral lines of a blackbody – Spectral lines of atmospheric molecules – Instrumentation error – Diffraction lines – Spectral lines of the lens used to the light into colors

• What is the intensity of curve B at 550 nm?

– Impossible to tell; 550 nm is not shown in this figure – Nearest 0.2

– Nearest 0.1

– Nearest 0.05

– Nearest 0.0

• Venus has no atmosphere. If you measure the spectrum from its surface, – Curves B and C would not change – Curve C would look more like A – Curve C would look more like B – Curve B would look more like A – Curve B would look more like C

• White light is composed of – Equal intensities of all colors of the rainbow – Unequal intensities of all colors of the rainbow – Equal number of photons of all colors of the rainbow – Unequal number of photons of all colors of the rainbow – Equal numbers of red, green, and blue photons

• Does a blackbody have color?

– Yes, and they all appear the color of the sun – No, you cannot see a blackbody – Yes, but its depends on its temperature – Maybe, it depends on if it is an ideal blackbody

• Why is the best reason for putting a telescope in orbit? – Closer to stars – Better view of celestial sphere – The speed of light is higher in space – Less atmospheric interference – Cost