Download Unit 5 – Creating and Understanding Spectra

Unit 5 – Creating and Understanding
Spectra
ASTR 101
Prof. 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
n  on mountain-tops
n  in balloons and high-flying aircraft
n  in orbiting satellites (like the Hubble Space Telescope)
Consider Visible Light First
Why? Because:
n  it’s the most familiar; and
n  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 all
in 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
n  the distribution of colours?
n 
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 Restriction
For 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:
n 
n 
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…
n 
n 
n 
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:
n 
n 
n 
n 
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, big
enough to swallow up much
of 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.