Transcript The HR Diagram Interpreted (PowerPoint version)

The HR Diagram Interpreted:
Properties of Stars
Why These Names?
“Main Sequence” is
a ‘no-brainer.’
But why Red
Why White
Giant?
Dwarf?
Remember the Radiation Laws
[See ASTR 101]
Consider two glowing objects
of exactly the same size.
The luminosity flowing out
depends on the 4th power
of the temperature (= T4),
with T measured upwards
from ‘absolute zero.’
So one object twice as hot as another identical one emits
24 = 2x2x2x2 = 16 times as much energy.
In Other Words...
All other things being equal,
hot bodies shine more brightly than
cooler bodies.
But Can a Cool Body
Outshine a Hot Body?
Yes, it can – but only if it has a huge surface area, every
square centimeter of which will contribute a little bit.
Consider Betelgeuse
The Sun, a G star, is about twice the temperature of
Betelgeuse, an M star. If they were the same size, the
Sun would be 16x as bright!
But Betelgeuse is 10,000 times as bright overall. This tells
us that it must have 160,000 times as much surface
area!
This means that it must be 400x as big across. In other
words, if we replaced the Sun with Betelgeuse, the Earth
would be inside it! It is truly a red (cool) giant.
The Size
of Betelgeuse
Another Giant,
Drawn to Scale
Notice that we do not measure these sizes directly: essentially all
the stars appear as unresolved points of light. But knowing
their intrinsic luminosities (how much total energy they emit)
and their surface temperatures tells us their sizes right away!
(The study of eclipsing binary stars allows us to check and
confirm these determinations independently.)
Comparing Sizes in Astronomy
From Small to Huge
Visit
http://apod.nasa.gov/apod/ap130606.html
from the “Astronomy Picture of the Day” website
Note also the various colours, indicative of different
temperatures. [This montage starts with the moon and
planets, the visible colours of which are determined by
reflected sunlight: they are so cool that they ‘glow’ in
the infrared. The beautiful blue planet Earth is not at a
temperature of 20,000 K!]
So Much For the Red Giants:
We Can Turn this Argument Around
Let’s imagine a very hot object that is extremely
faint. How can this be?
Answer: it must be very small, with a limited
surface area to radiate its heat and light.
Reconsider the
HR Diagram
Notice the hot but faint ‘white dwarfs’ - twice as
hot as the Sun, but less than 1% as bright!
One Nearby Example:
the Companion of Sirius
As hot as Sirius itself, but very faint.
So it must be small: a “white dwarf”
Indeed, ‘Sirius B’ is Earth-sized!
You may say “so what?” – perhaps you expected there to
be very small stars.
But further analysis reveals something amazing.
This is a True Binary Star
Sirius and its companion orbit each other
Notice how they orbit their
common center of mass, once
every ~50 years.
[The light of Sirius A has been suppressed in this
series of images so that B shows up clearly]
When We Apply Newton’s Laws…
…we discover that Sirius B is just as massive as
the sun. But we know it is somewhat smaller
than the Earth (to explain its limited brightness)
A simple calculation then
reveals that ‘Sirius B’ is
one million times
as dense as water
- a tonne per cubic cm
There is nothing on Earth like this. This is ‘new physics.’
Sizes Shown Schematically
(but not to correct scale: the ‘supergiants’ are really huge!)
Some Specific Stars
with radii shown (compared to the Sun)
The Ranges are Worth Noting
Stars range, roughly,
from 3000 K (cool, red) to 30,000 K (hot, giving off
lots of ultraviolet light!) in surface temperature
from 1% of the sun’s diameter to 1000 times
its size
from a thousandth of the sun’s brightness to
a million times as bright
A Peek Forward in Time:
Our Fate

As noted, if Betelgeuse were put down where
the sun is, the Earth would be inside it.
As we will come to learn in this course:


The sun’s eventual fate is to pass through a
stage in which it will swell to red giant
proportions
But it will eventually end up as a white dwarf!
Q: What is an ‘Average’ Star?
We have to be careful about what we mean by
“average.”
Suppose you earned these first-year marks, in ten
courses: 50, 50, 50, 50, 50, 50, 50, 60, 75, 100
Is the “average” mark 75 because it is exactly in
the middle of the range?
I think not!
Is the Sun an ‘Average’ Star?
It is (roughly) in the middle of the range, so it
is certainly not unusual. But is it average?
Analogy: is a human being an average-sized living
creature? We are in the ‘mid-range’, between blue
whales and bacteria, giraffes and mice,…
But there are many more bacteria and ants than people
and whales!
Relative Numbers of Stars
How many stars are there of various kinds? (The
brightest supergiant stars, for example, catch
the eye. But are they rare, or commonplace?)
Remember my informal‘law of nature’: for every
big thing, there are lots of little things.
The same sort of ‘law’ applies in astronomy:
super-bright stars are rare, but there are lots of
little faint ones.
The HR Diagram with Populations
For every bright blue “O” star, there are more than a
million faint red dwarfs low on the main sequence.
So: The Truly ‘Average’ Star
… is an undistinguished low-luminosity star, fainter and
cooler than the sun. The Sun is ‘mid-range’ in its
properties, and technically “above average” in size and
mass – but it’s not a superstar.
The Most Influential Stars
The stars that we notice in the night sky, however, are the
biggest, brightest ones – not at all ‘average!’
As we will learn later, such stars have also had the greatest
role to play in the history of our galaxy and the universe,
indeed making our very existence possible!
So such stars are not only prominent but also influential.