Assigned Reading

• Today’s assigned reading is:– Finish Chapter 7

Reminder: e.m. Radiation generally contains bundles of waves of different

wavelengths (colors)The strength of each color in a given bundle of e.m. radiation, i.e. the intensity of the light at each wavelength, is called the spectrum

Here is an example of optical (visible) light:

Blackbody Radiation (a.k.a. Thermal Radiation)

– Every object with a temperature greater than absolute zero emits blackbody radiation.

– Hotter objects emit more total radiation per unit surface area.

– Hotter objects emit photons with a higher average energy.

Reminder: Blackbody Radiation, i.e. a continuum of wavelengths with a characteristic distribution of strengths

Hotter B.B. emitters “emit” more total radiation per unit area.However, a big cold object can emit the same or more energy

(depending on how big it is) than a small, hotter one

Cold Hot

Stefan-Boltzmann Law:

Emitted power per square meter = σ T4

σ = 5.7 x 10-8 W/(m2K4)

Total emitted power: E = 4 R2 σ T4

An Object’s Spectrum

Encoded in an object’s spectrumis information about the emitter/absorber. This is how we learn what the Universeis made of!

Stars come in different colors

Color and Temperature

Orion

Betelgeuse

Rigel

Stars appear in different colors,

from blue (like Rigel)

via green / yellow (like our sun)

to red (like Betelgeuse).

If the spectra of stars are black bodies, then these colors tell us about the star’s temperature.

The spectrum of a star: nearly a Black Body

The light from a star is usually concentrated in a rather narrow range of wavelengths.

The spectrum of a star’s light is approximately a black body spectrum.

In fact, the spectrum of a star at the photosphere, before the light passes through the atmosphere of the star, is a nearly PERFECT black body one

The Spectra of StarsThe inner, dense layers of a

star do produce a continuous (blackbody)

spectrum.

Cooler surface layers absorb light at specific frequencies.

The atmosphere also absorbes light at other specific frequencies

=> Spectra of stars are B.B.absorption spectra.

The Spectrum of a star (the Sun)

There are similar absorption lines in the other regions of the electromagnetic spectrum. Each line exactly corresponds to chemical elements in the stars.

Again, remember the two Laws of Black Body Radiation. I

1. The hotter an object is, the more energy it emits:

L = 4 R2*T4

where

= Stefan-Boltzmann constant

L = Energy =

= Energy given off in the form of radiation, per unit time [J/s];

More area, more energy

Again, remember the two Laws of Black Body Radiation. II

2. The peak of the black body spectrum shifts towards shorter wavelengths when the temperature increases.

Wien’s displacement law:

max ≈ 3,000,000 nm / TK

(where TK is the temperature in Kelvin)

Stellar Spectra

The spectra of stars also contain characteristic absorption lines.

With what we have learned about atomic structure, we can now understand how those lines are formed.

Analyzing Absorption Spectra• Each element produces a specific set of absorption

(and emission) lines.

By far the most abundant elements in the Universe

• Comparing the relative strengths of these sets of lines, we can study the composition of gases.

Lines of HydrogenMost prominent lines in many astronomical objects: Balmer lines of hydrogen

The Balmer Linesn = 1

n = 2

n = 4

n = 5n = 3

H H H

The only hydrogen lines in the visible wavelength range

Transitions from 2nd to higher levels of hydrogen

2nd to 3rd level = H (Balmer alpha line)2nd to 4th level = H (Balmer beta line)

…

Observations of the H-Alpha LineEmission nebula, dominated by the red H line

Absorption Spectrum Dominated by Balmer Lines

Modern spectra are usually recorded digitally and

represented as plots of intensity vs. wavelength

The Balmer ThermometerBalmer line strength is sensitive to temperature:

Almost all hydrogen atoms in the ground state (electrons in

the n = 1 orbit) => few transitions from n = 2 => weak

Balmer lines

Most hydrogen atoms are ionized => weak Balmer

lines

Measuring the Temperatures of Stars

Comparing line strengths, we can measure a star’s surface temperature!

Spectral Classification of Stars (1)

Tem

pera

ture

Different types of stars show different characteristic sets of absorption lines.

Spectral Classification of Stars (2)

Mnemonics to remember the spectral sequence:

Oh Oh Only

Be Boy, Bad

A An Astronomers

Fine F Forget

Girl/Guy Grade Generally

Kiss Kills Known

Me Me Mnemonics

Stellar Spectra

OB

A

F

GKM

Surface tem

perature

The Composition of StarsFrom the relative strength of absorption lines (carefully accounting for their temperature dependence), one can derive the chemical composition of stars.

The Doppler Effect:another key information contained in

spectrum• The frequency of light (or of sound) of a

source in motion relative to an observer has frequency altered by an amount that depends on its speed relative to the observer.

• In other words, speed changes the perceived wavelength of a source (color for light; pitch for sound)

• Listen to a moving fire truck…• … or take a look at the police car to see how

this works.

The Doppler Effect (1)The light of a moving source is blue/red shifted by

/0 = vr/c

0 = actual wavelength

emitted by the source

Wavelength change due to

Doppler effect

vr = radial velocity

Blue Shift (to higher frequencies)

Red Shift (to lower frequencies)

vr

Sound waves always travel at the speed of sound – just like light

always travels at the speed of light, independent of the speed of the

source of sound or light.

The Doppler Effect (2)The Doppler effect allows us to measure the component

of the source’s velocity along our line of sight.

This component is called radial velocity, vr.

Doppler Effect

The first crest travels out in circle from the original position of the plane

At a later time, a second crest is emitted from the planes new position,but the old crest keeps moving out in a circle from the planes original position

The same thing happens again at a later time

Longer wavelength (more red)

Shorter wavelength (more blue)

In general …

• The “native” frequency at which an object is emitting is called the rest frequency.

• You will see/hear frequencies higher than the rest frequency from objects moving towards you.

• You will see/hear frequencies lower than the rest frequency from objects moving away from you.

• This is true with sound waves, as well as with light waves and any other type of waves

Spectra tell us about the motion of sources

The Doppler Effect (2)

Example:

The Doppler EffectTake of the H (Balmer alpha) line:

0 = 656 nmAssume, we observe a star’s spectrum with the H line at = 658 nm. Then,

= 2 nm.

We find = 0.003 = 3*10-3

Thus,

vr/c = 0.003, or

vr = 0.003*300,000 km/s = 900 km/s.The line is red shifted, so the star is receding from us with a radial velocity of 900 km/s.

Two identical stars are moving towards the Earth. Two identical stars are moving towards the Earth. Star A’s emission lines are observed to be at Star A’s emission lines are observed to be at visible wavelengths. The same emission lines visible wavelengths. The same emission lines for Star B are observed to be at ultraviolet for Star B are observed to be at ultraviolet wavelengths. From these observations you wavelengths. From these observations you conclude that: conclude that:

Both stars are moving away from the EarthBoth stars are moving away from the Earth Star A is moving towards the Earth faster than Star A is moving towards the Earth faster than

Star BStar B Star B is moving towards the Earth faster than Star B is moving towards the Earth faster than

Star AStar A Star B is moving away from the Earth while Star B is moving away from the Earth while

Star A is moving towards the Earth.Star A is moving towards the Earth.

The Doppler shift• An object shining red light with =656.3 nm

is moving at V=5,000,000 m/s toward you. What is the color of the light that you see?

• V/c = (- 0)/0

• 5x106/3x108 = 1.67x10-2 = (- 0)/0

0 = x (1+1.67x10-2) = 667.3 nm

Two otherwise identical stars are rotating at Two otherwise identical stars are rotating at different rates. Star A is rotating slower different rates. Star A is rotating slower than Star B. How do Star A’s spectral than Star B. How do Star A’s spectral lines appear with respect to Star B’s lines appear with respect to Star B’s lines? lines?

Star A’s lines are narrower than Star B’s Star A’s lines are narrower than Star B’s lines.lines.

Star B’s lines are narrower than Star A’s Star B’s lines are narrower than Star A’s lines.lines.There is no difference in the lines of the There is no difference in the lines of the two stars.two stars.Star A’s lines are stronger than Star B’s Star A’s lines are stronger than Star B’s lines.lines.