Starlight and Atoms

I. StarlightA. Temperature and HeatB. The Origin of StarlightC. Two Radiation LawsD. The Color Index

II. AtomsA. A Model AtomB. Different Kinds of AtomsC. Electron Shells

III. The Interaction of Light and MatterA. The Excitation of AtomsB. The Formation of a Spectrum

Outline

IV. Stellar SpectraA. The Balmer ThermometerB. Spectral ClassificationC. The Composition of the StarsD. The Doppler EffectE. Calculating the Doppler VelocityF. The Shapes of Spectral Lines

Outline (continued)

The Amazing Power of Starlight

Just by analyzing the light received from a star, astronomers can retrieve information about a star’s

1. Total energy output

2. Surface temperature

3. Radius

4. Chemical composition

5. Velocity relative to Earth

6. Rotation period

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).

These colors tell us about the star’s

temperature.

Black Body Radiation (1)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 thermal spectrum called a black body spectrum.

A perfect black body emitter would not reflect any radiation. Thus the name “black body”.

Two Laws of Black Body Radiation

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).

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

L = A**T4

where = Stefan-Boltzmann constant A = surface area;

The Color Index (1)

B bandV band

The color of a star is measured by comparing its brightness in two different wavelength bands:

The blue (B) band and the visual (V) band.

We define B-band and V-band magnitudes just as we did before for total magnitudes (remember: a larger number indicates a fainter star).

The Color Index (2)

We define the Color Index

B – V(i.e., B magnitude – V magnitude).

The bluer a star appears, the smaller the color index B – V.

The hotter a star is, the smaller its color index B – V.

Light and MatterSpectra of stars are more complicated than pure blackbody spectra.

characteristic lines, called absorption lines.

To understand those lines, we need to understand atomic structure and the interactions between light and atoms.

Atomic Structure

• An atom consists of an atomic nucleus (protons and neutrons) and a cloud of electrons surrounding it.

• Almost all of the mass is contained in the nucleus, while almost all of the space is occupied by the electron cloud.

Atomic Density

If you could fill a teaspoon just with material as dense as the matter in an atomic nucleus, it would weigh ~ 2 billion tons!!

Different Kinds of Atoms• The kind of atom

depends on the number of protons in the nucleus.

Helium 4

Different numbers of neutrons ↔ different isotopes

• Most abundant: Hydrogen (H), with one proton (+ 1 electron).

• Next: Helium (He), with 2 protons (and 2 neutrons + 2 el.).

Electron Orbits• Electron orbits in the electron cloud are

restricted to very specific radii and energies.

r1, E1

r2, E2

r3, E3

• These characteristic electron energies are different for each individual element.

Atomic Transitions

• An electron can be kicked into a higher orbit when it absorbs a photon with exactly the right energy.

• All other photons pass by the atom unabsorbed.

Eph = E4 – E1

Eph = E3 – E1

(Remember that Eph = h*f)

Wrong energy

• The photon is absorbed, and

the electron is in an excited state.

Kirchhoff’s Laws of Radiation (1)1. A solid, liquid, or dense gas excited to emit

light will radiate at all wavelengths and thus produce a continuous spectrum.

Kirchhoff’s Laws of Radiation (2)2. A low-density gas excited to emit light will

do so at specific wavelengths and thus produce an emission spectrum.

Light excites electrons in atoms to higher energy states

Transition back to lower states emits light at specific frequencies

Kirchhoff’s Laws of Radiation (3)

3. If light comprising a continuous spectrum passes through a cool, low-density gas, the result will be an absorption spectrum.

Light excites electrons in atoms to higher energy states

Frequencies corresponding to the transition energies are absorbed from the continuous spectrum.

The Spectra of StarsInner, dense layers of a

star produce a continuous (blackbody) spectrum.

Cooler surface layers absorb light at specific frequencies.

=> Spectra of stars are absorption spectra.

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)

…

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 infer the composition of stars.

The Doppler Effect

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

The Doppler Effect (2)

The Doppler effect allows us to measure the source’s radial velocity.

vr

The Doppler Effect (3)Take 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.

Doppler BroadeningIn principle, line absorption should only affect a very unique wavelength.

Observer

Atoms in random thermal motion

vr

vr

Red shifted abs.

Blue shifted abs.

In reality, also slightly different wavelengths are absorbed.

↔ Lines have a finite width; we say:

they are broadened.

One reason for broadening: The Doppler effect!

Line BroadeningHigher Temperatures

Higher thermal velocities broader lines

Doppler Broadening is usually the most important broadening mechanism.

temperatureKelvin temperature scaleabsolute zerothermal energyelectronblack body radiationwavelength of maximum intensity (λmax)

color indexnucleusprotonneutronisotopeionizationionmoleculeCoulomb forcebinding energy

quantum mechanicspermitted orbitenergy levelexcited atomground statecontinuous spectrumabsorption spectrum (dark-line spectrum)

absorption lineemission spectrum (bright-line spectrum)

emission lineKirchhoff’s lawstransitionspectral class or typeDoppler effectblue shiftred shift

New Terms

1. In what ways is our model of an atom a scientific model? How can we use it when it is not a completely correct description of an atom?

Discussion Questions

Quiz Questions

1. Which of the following statements is true about the Celsius and Kelvin (Absolute) temperature scales?

a. Zero is at the same temperature on both scales.b. The size of one degree is the same on both scales.c. Zero degrees Celsius is the same temperature as -273 K.d. The size of one Celsius degree is 5/9 that of a Kelvin.e. The size of one Kelvin is 5/9 that of a Celsius degree.

Quiz Questions

2. The temperature of a gas is a measure of the

a. total amount of internal energy in the gas.b. amount of heat that flows out of the gas.c. total number of atoms in the gas.d. density of the gas.e. average motion of its atoms.

Quiz Questions

3. Which subatomic particle has a negative charge?

a. The electron.b. The proton.c. The neutron.d. Both a and b above.e. Both a and c above.

Quiz Questions

4. The wavelength of maximum intensity that is emitted by a black body is

a. proportional to temperature.b. inversely proportional to temperature.c. proportional to temperature to the fourth power.d. inversely proportional to temperature to the fourth power.e. Both a and c above.

Quiz Questions

5. Of the following, which color represents the lowest surface temperature star?

a. Yellow.b. Blue.c. Orange.d. Red.e. White.

Quiz Questions

6. The amount of electromagnetic energy radiated from every square meter of the surface of a blackbody each second is

a. proportional to temperature.b. inversely proportional to temperature.c. proportional to temperature to the fourth power.d. inversely proportional to temperature to the fourth power.e. Both a and c above.

Quiz Questions

7. The B - V color index of a star indicates its

a. density.b. total mass.c. radius.d. chemical composition.e. surface temperature.

Quiz Questions

8. If a star appears brighter through a B filter than it does through a V filter, its B - V color index is

a. negative.b. zero.c. positive.d. greater than or equal to zero.e. less than or equal to zero.

Quiz Questions

9. An atom that is ionized must have

a. more neutrons than protons.b. more protons than neutrons.c. more electrons than protons.d. more protons than electrons.e. Either c or d above.

Quiz Questions

10. Which of the following is true of an atomic nucleus?

a. It contains more than 99.9% of an atom’s mass.b. It contains all of an atom's positive charge.c. It contains no electrons.d. Both a and b above.e. All of the above.

Quiz Questions

11. At what energy level are the electrons in hydrogen gas at a temperature of 25,000 K?

a. Most are in energy level 1 (also known as the ground state).b. Most are in energy level 2.c. Most are in levels higher than energy level 2.d. Half are in energy level 1, and half are in level 2. e. None of the above.

Quiz Questions

12. What conditions produce a dark (absorption line) spectrum?

a. A hot solid, liquid, or high-density gas.b. A hot low-density gas.c. Light from a continuous spectrum source passing through a cooler low-density gas.d. Both a and b above.e. All of the above.

Quiz Questions

13. Where is the location of the cooler low-density gas that yields the dark (absorption) line stellar spectra that were studied by Annie Jump Cannon?

a. In the interior of the star.b. In the star's lower atmosphere.c. In Earth's atmosphere.d. Both a and b above.e. Both b and c above.

Quiz Questions

15. What does the presence of molecular bands in the spectrum of a star indicate?

a. The star has a low surface temperature.b. The star has a high surface temperature.c. The star is about to go supernova.d. The star is spectral type G.

Quiz Questions

16. Of the following spectral types, which one represents a star with the highest surface temperature?

a. Ab. Bc. Fd. Ke. G

Quiz Questions

17. All stars are composed of mostly hydrogen and helium, yet many stars have no lines for hydrogen or helium in their spectrum. What causes this apparent contradiction?

a. Spectral lines are created in the lower atmospheres of stars, and for many stars hydrogen and helium are hidden below the atmosphere.b. The upper layers of a star contain hot low-density gases that produce bright lines at precisely the same wavelengths as the dark lines, thus making them invisible.c. Hot hydrogen and helium gas in the interstellar medium produces bright lines to fill in the dark lines.d. The resolution of many spectrographs is too poor to show the extremely thin spectral lines for hydrogen and helium.e. The surface temperature is such that the electrons are not at the proper energy levels to produce spectral lines at visible wavelengths.

Quiz Questions

18. You research the star Sirius and find that its spectral lines are blue shifted. What does this tell you about Sirius?

a. Its surface temperature is higher than that of the Sun.b. It has a radial velocity that is away from us.c. It has a radial velocity that is toward us.

Quiz Questions

19. Suppose that you take the spectrum of several stars and identify the 656-nanometer line of hydrogen. You then measure against the reference spectrum on the same image and find that some of the 656-nm lines are shifted due to the Doppler Effect. Of the following shifted locations of this line, which one signals a star that is moving away from us at the highest speed?

a. Star A @ 655 nm.b. Star B @ 657 nm.c. Star C @ 658 nm.d. Star E @ 659 nm.e. Star D @ 654 nm.

Answers

1. b2. e3. a4. b5. d6. c7. e8. a9. e10. e

11. c12. c13. e14. c15. a16. b17. e18. c19. d