Unit 5 – Creating and Understanding Spectra

ASTR 101Prof. Dave Hanes

The Full Spectrum

Question: What objects emit light?

Naive Answer: lamps, fires, sun, stars….

Correct Answer: all objects emit light of some sort! But only those that are hot enough emit visible light.

The Interest of Other Wavelengths

Anticipating Later Discussions

Astronomers use all wavelengths, but not just to study familiar objects in alternative ways.

It is because certain objects can be detected

and studied only at these other wavelengths.

Astronomical Examples

Dense clouds of cool gas (the birthplace of stars) give off light at infrared and radio wavelengths (low energies).

The hot gas surrounding massive stars gives off copious quantities of energetic ultraviolet light.

Very dense objects (black holes, neutron stars) can give rise to the emission of X-rays.

One Complication:

Not All Wavelengths Reach the Ground

Hence telescopes on mountain-tops in balloons and high-flying aircraft in orbiting satellites (like the Hubble Space

Telescope)

Consider Visible Light First

Why? Because: it’s the most familiar; and it’s all we could use until the mid-

1900’s

How can we analyze the spectrum – that is, the distribution of emitted energies – of a source of light?

Light Refracts (changes direction when changing

media)

Why Does Light Refract?

Fundamentally, it is because it moves at different speeds in different media.

(It moves fastest of allin vacuum. In water, however, it slows to about 75% of c.)

The Result(note the ‘wavefronts’)

Some Light Also Reflects from Surfaces

Different Colours are Slowed to Different Degrees:

Light Can Thus be Dispersed

Newton Again

Opticks – his famous book

Studied rainbows, sunlight, etc -- Rather foolishly in some respects

Rainbows – Nature’s Spectrum

Newton’s Laboratory

Newton’s Prismatic Studies

Newton’s Profound Discovery

Light can be broken up and reconstituted.White light = the summed effect of light of all

colours.

http://www.youtube.com/watch?v=b3NXsgjPSQo

Basic Questions

First, consider one glowing object. What determines:

The amount of light it emits, and the distribution of colours?

Second, compare two glowing objects. How and why might they differ?

One Irrelevant Factor

Apparent brightness tells us nothing fundamental. Even a very bright object will look faint if it’s far away. (The inverse-square law.)

Solution

We will consider the light emitted by some fixed area (say, one square centimeter) of a radiating body, and see how that changes if we adjust something like the temperature or composition.

We also ignore any reflected light, concentrating only on the light emitted by the object itself.

One Further RestrictionFor now, we focus our attention on dense bodies, where the atoms are in close proximity and interacting. (This includes the hotplate on the left – and also stars.)

Later we will return to the question of very diffuse gases, where the particles are well separated and interacting less. Needless to say, such circumstances are common in astronomy, in clouds of gas in space!

Digression: What Temperatures?

Physicists use temperatures expressed in Kelvins. These are the same size as centigrade degrees, but start from absolute zero (the coldest temperature there is, -273o C).

“Room temperature” (20 C) is thus about 290K; “body temperature” is about 300K. The Sun’s surface is about 6000K.

An Amazing Discovery

All dense bodies emit radiant energy in exactly the same way, with only the temperature determining the amount and spectral distribution of the light. The nature of the material itself is irrelevant.

e.g. heat a lump of carbon and a lump of iron to the same temperature. They will ‘glow’ in exactly the same way.

We call such objects “thermal radiators”

The ‘Glow’ Depends on Temperature

A hotter body has more internal energy than a cool one. (Remember the meaning of temperature!) It is perhaps not surprising, then, that:

hotter bodies emit more energy per square centimeter than cooler bodies; and

the ‘average’ light given off by a hotter body is more energetic (that is, bluer) than that given off by a cooler body.

Hence the Poker…

At room temperature, the poker glows at infrared wavelengths (so does your body!)

In the fire, it can get red-hot In a very hot blacksmith’s fire, it can glow

white-hot

Human Bodies and Stars

Notice that the curves all have the same form – only the temperatures are different.

A hotter object emits more light at all wavelengths (colours) than a cooler body, but there is also a shift to shorter (bluer, more energetic) wavelengths.

Thermal Radiators[refer back to the previous figure]

Let’s be a little more specific. Remember that we are talking about the energy emitted by every square centimeter of the object (not the total). Look back at the previous figure, and note:

Your (cool) body, at 300K, glows in the infrared (that is, at long wavelengths). Of course you emit no visible light!

A hotter star, like Betelgeuse, at 3000K gives off lots more light, predominantly infrared and red light.

The sun, at 6000K, gives off even more, with a peak in the yellow light.

A very hot star, at 15000K, emits even more, with lots of blue and energetic ultraviolet light.

The Colours of the Stars!

Hot stars look blue in pictures (and perhaps even to the eye if they are bright enough to stimulate the colour receptors).

Cool stars look red (e.g. Betelgeuse and Antares)

A Warning!

Mars also looks red to the eye, but that is simply reflected sunlight. The colour tells us about the materials on the surface of Mars – the rusty-red minerals. That planet’s actual emissions are in the infrared because of its modest temperature. Likewise, your blue jeans aren’t super-hot!

A Numerical Detail

The light emitted per square centimeter depends on “temperature to the fourth power” - that is, T4 (= T x T x T xT)

So one object twice as hot as another produces 2x2x2x2 = 16 times as much light per square centimeter

Meet Betelgeuse(top left)

Glowing Feebly

Betelgeuse is more than 600 light-years away, about 70 times the distance of Sirius. So it must be emitting lots of light to show up so conspicuously. In fact, its total light ouput has to be about 10,000 times as much as the Sun!

Problem: as indicated by its red colour, Betelguese is quite cool. As a result, its surface is glowing relatively feebly.

How, then, can it be putting out such a prodigious amount of light?

The Amazing Reality: a Giant Star

Since it gives off so little light per

square centimeter, this means

that Betelgeuse must be huge,

with an enormous surface area.

It is a RED GIANT star, bigenough to swallow up muchof the Solar System.

(Our Sun will become a red giant

at the end of its life, swallowing

up Mercury and Venus!)

The Sizes of Planets – and Stars

We easily determine the sizes of planets in the Solar System because we can resolve them: see “how big they look”.

That’s not the case for stars, which appear as dots of light. Given their temperatures, however, we can consider the total light they emit, and deduce their sizes – as we just did for Betelgeuse. Stars come in varied sizes.

http://www.astro.queensu.ca/~hanes/ASTR101-Fall2015/ANIMS/StarSize.mp4

(By the way, stellar diameters can also be worked out in binary stars by analyzing how the brightness changes when one star passes in front of the other, blocking a fraction of the light.)

Sirius – and its Faint Companion

Here is the bright star Sirius. (The ‘spikes’ are artifacts caused by struts in the telescope. Stars are round!)

Note the very faint companion to the lower left. It orbits Sirius, so is at the same distance from us. It is the same colour, so is just as hot. So why does it look so faint?

Sirius B: a Dwarf Star

We apply the same reasoning, in reverse: for this very hot object to be so faint, it must have a very small surface area to emit light.

Sirius B is the size of the Earth! It’s a white dwarf star.

The Implication: New Physics!

The orbit of Sirius and its companion reveals (by Newton’s laws) that the white dwarf is as massive as the Sun. But it is tiny, so it must be a million times as dense as water! One cubic centimeter of it (a sugar cube) contains about a tonne of material.

There is nothing on Earth like this. New physics is required – and we know all this simply because we can determine the colour, brightness and distance of that star.