Lecture 7:Lecture 7: The Physics of Light, part 2

Astronomy 111

SpectraSpectra

“Twinkle, twinkle, little star,little star, How I wonder what you are ”what you are.

ASTR111 Lecture 7

Every type of atom, ion, and molecule has a unique spectrummolecule has a unique spectrum

Ion: an atom with electrons addedIon: an atom with electrons added (negative ion) or taken away (positive ion)ion).

Molecule: two or more atoms bonded together.

The spectrum of each atom, ion, and molecule is a distinctiveand molecule is a distinctive “fingerprint”.

The more li t dcomplicated

the atom, ion thor the

molecule, the lmore complex

the spectrum.electron

tneutron

proton

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F i i b ti li kFrom emission or absorption lines, we know:1) which elements are present;2) whether they are ionized;3) whether they are in molecules3) whether they are in molecules.

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emission spectrum of the Carina Nebula

Kirchoff’s Laws of SpectroscopySpectroscopy

1) A hot solid or hot, dense gas produces a continuous spectrum.a continuous spectrum.

2) A hot, low-density gas produces an i i li temission-line spectrum.

3) A continuous spectrum source viewed through a cool, low-density gas produces an absorption-line spectrum.

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p p p

Continuum

Source Cloud

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A hot, low density cloud of gas produces an emission line spectrumproduces an emission line spectrum

Light is emitted only at wavelengths corresponding to energy differences co espo d g to e e gy d e e cesbetween permitted electron orbits.

Results: an emission line spectrumResults: an emission line spectrum.

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Hydrogen emission spectrum

The Carina Neb laThe Carina Nebula

A cloud of hot, low density gas aboutdensity gas about 7000 light years away.y

Its reddish color comes from the 656.3 nm emission

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line of hydrogen.

A cool, transparent gas produces an absorption line spectruman absorption line spectrum

C id ld l d it l d fConsider a cold, low density cloud of hydrogen in front of a hot blackbody.

Light is absorbed only at wavelengths corresponding to energy differences between permitted electron orbits.

Result: an absorption line spectrum.p p

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Absorption spectra can tell us about extrasolar planetsabout extrasolar planets

• A planet’s atmosphere is a cold, low density cloud of gas illuminated by a y g ybackground source (its star)

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The most abundant elements in the Universe are hydrogen and heliumUniverse are hydrogen and helium

It is fairly easy to determine whichelements are present in a star.p

It is much harder to determine how muchof each element is presentof each element is present.

Strength of emission and absorption lines depends on temperature as well as ondepends on temperature as well as on the element’s abundance.

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Abundance of elements i th S ’ t hin the Sun’s atmosphere:

Hydrogen (H): 75%Helium (He): 23%Helium (He): 23%

Everything else: 2%

As discovered in 1920’s, other stars areAs discovered in 1920 s, other stars are mostly hydrogen and helium, too.

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C ili PCecilia Payne-Gaposchkin (1900-1979) was a British-1979) was a British-American astronomer. She left England in 1922. gIn 1925, she became the first ever Ph.D. in astronomy from Harvard. Her thesis established that hydrogen was thethat hydrogen was the overwhelming constituent of the stars.

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of the stars.

Temperature ScaleTemperature Scale

I h i d t thIn physics and astronomy, we use the Kelvin scale, which has a zero at b l tabsolute zero.

Kelvin = Celsius + 273Water boils: 373 KelvinWater boils: 373 KelvinWater freezes: 273 KelvinAb l t 0 K l i

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Absolute zero: 0 Kelvin

An object is hot when the atoms of which it is made are in rapid random motionmade are in rapid random motion.

The temperature is a measure of the average speed of the atomsspeed of the atoms.

Random motions stop at absolute zerotemperaturetemperature.

A hot, opaque object produces a continuous blackbody spectrum of light

The universe is full of light of all different wavelengths. How is light made?

One way to make objects emit light is to y j gheat them up.

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Blackbody RadiationBlackbody Radiation

A Blackbody is an object that absorbs all lightA Blackbody is an object that absorbs all light.• Absorbs at all wavelengths• Characterized by its Temperature• Characterized by its Temperature

It is also the perfect radiator:E it t ll l th ( ti• Emits at all wavelengths (continuous spectrum)

• Total Energy emitted depends on• Total Energy emitted depends on Temperature

• Peak wavelength also depends on

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• Peak wavelength also depends on Temperature

Wien’s Law

W l th f i i i

Wien s Law

Wavelength of maximum emission is inversely related to temperature

nm 000,900,2

emissionmaximumofhwavelengt

max

T

Kelvins)(in re temperatuemissionmaximumofh wavelengtmax

T

Stefan-Boltzmann LawStefan-Boltzmann Law

E itt d d bEnergy emitted per second per area by a blackbody with Temperature (T):

i B lt ' t t ( b )E T4=

is Boltzmann's constant (a number).

In Words:In Words:“Hotter objects are Brighter at All

Wavelengths”

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a e e gt s

Blackbody curves:Blackbody curves:

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Solar spectrum:Solar spectrum:

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Taking theTaking the temperature of stars

Betelgeuse: a greddish star (cooler).( )

Rigel: a bluish star (hotter)

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star (hotter).

Stellar spectra inStellar spectra in order from the hottest

(top) to coolest (bottom).( )

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Inverse-Square Law of Brightness

Luminosity is not the same B i ht !

Brightness

as Brightness !

Luminosity is how much light leaves a source (it does not depend on your location)depend on your location).

Brightness is how much light arrives at a particular location (it depends on how

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location (it depends on how far away you are).

Doppler shiftDoppler shift

• Light can experience a Doppler shiftLight can experience a Doppler shift much like the change in frequency of a train whistle as it passes an observertrain whistle as it passes an observer

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Th f D l hiftThe reason for Doppler shifts:

Wave crests are bunched up ahead of the

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Wave crests are bunched up ahead of the light source, stretched out behind.

The Doppler effect in lightThe Doppler effect in light

Amount of Shift depends upon the emittedAmount of Shift depends upon the emitted wavelength (em) and the relative speed v:

• If the motion is away from observerWavelength gets longer = REDSHIFTWavelength gets longer = REDSHIFT

If th ti i t d th b• If the motion is towards the observerWavelength gets shorter = BLUESHIFT

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If a light source is moving toward you, the wavelength is shorter (called a “blueshift”)wavelength is shorter (called a blueshift ).

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If a light source is moving away from you, the wavelength is longer (called a “redshift”).

The radial velocity of an object is found from its Doppler shiftfound from its Doppler shift

R di l l it h f t bj t iRadial velocity = how fast an object is moving toward you or away from you.

If a wave source moves toward you or f th l th i

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away from you, the wavelength is changed.

Size of Doppler shift is proportional to radial velocityproportional to radial velocity

cvr

shift h wavelengtobserved 0

c

ifl idi lmovingnot is source ifh wavelengt0

light ofspeed sourcemovingofvelocity radial

cvr

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gp

Example:p

t3656 light with absorbsHydrogen

λat line absorptionstar with a observe But we

nanometers36560 .λ

nm 10.nanometers2656

.Δλ.λ

v0

r

c

km/sec 000,300 nm3656nm 1.0 v r

0

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km/sec 46vnm3.656

r

Way to Measure SpeedsWay to Measure Speeds

Observe the wavelength (obs) of a source with a known emitted wavelength (em)g ( em)

The difference is directly proportional to the speed of the source v:the speed of the source, v:

v

cv)( ememobs

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c