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Cepheid Variable Stars
Cepheids
Very late in their lives, massive stars can pass briefly
through a stage in which they are unstable.
During this stage, their outer
parts oscillate (‘pulsate’) in
and out, like a beating heart,
for reasons we understand.
The name Cepheid comes from
the fact that the first such star
was found in the constellation
Cepheus.
The Evolutionary State of Cepheids
[they are massive stars nearing the ends of their lives]
How Cepheids Behave
[regular, periodic change in brightness]
Quite Distinctive Behaviour
These stars vary in “sawtooth” fashion. They get
bright fairly quickly, then fade away more slowly.
Why Does the Brightness Change?
There are actually two reasons:
 the stars change in size (different radiating area); and
 their temperatures vary as they pulsate
Both these effects are important.
As the Cepheids pump in and out, like a ‘beating heart,’
they change by perhaps 10% in diameter
The periods range from a few days to several hundred days
(but any given Cepheid has a fixed, well-defined period).
Cepheids
Really Do
Pulsate!
The spectrum
shows a changing
Doppler shift.
The surface of the
star rises towards
us -- and then later
falls away!
Cepheids are Rare! But Why?
Consider a big galaxy, full of stars. How many Cepheids will it
contain? Not many, because:

massive stars are uncommon (there are many more lower mass
stars);

massive stars are also relatively short-lived; and

such stars become Cepheids only for a very small fraction of their
already quite short lives
So when we look at a field of stars, only a very few will be
Cepheids, and they will probably be quite remote.
This Presents a Chellenge
We’d like to intercompare a lot of Cepheids, to work out
their general characteristics and behaviour.
Most interestingly, exactly how bright is a typical Cepheid
star? That requires determining its distance.
But the rarity of Cepheids means that even the closest
ones are too far away for parallax measurements, and
they are often often seen behind lots of gas and dust.
Consequently, it’s hard to determine their distances and
true brightnesses.
On the Positive Side…
Cepheids act the way they do way late in life, when they
have become bright supergiants – so they are easily
seen at great distances
They also draw attention to
themselves by varying
conspicuously:
in a sense, they ‘wink’ at us,
as if to catch our attention!
In the Milky Way
About 500 Cepheids are well-studied.
The very closest is Polaris,
the North Star! (Yes, it’s a
Variable star!) It changes
by ~10% in brightness, with
a period of about 4 days -not readily noticeable.
(Some Cepheids vary by a factor
of 2 or more in brightness.)
Meet Henrietta Leavitt
She was directed by Harlow
Shapley to study Cepheid
variable stars, with one
clever proviso:
– she was to look at a rich
sample of Cepheids that are
all at the same distance.
How???
Her Target
Shapley asked Henrietta to work on the stars in the
Magellanic Clouds – the LMC in particular.
Close Neighbours
The ‘Magellanic Clouds’ (Large and Small) are
satellites of the Milky Way, visible in Southern skies
What Are They?
In Shapley’s day, the LMC and SMC were
considered as two isolated offshoots of the
Milky Way, different from the spiral nebulae.
We now realize that they are ‘dwarf’
galaxies in their own right (but not spirals).
The LMC
Irregular in appearance: no spiral structure
Why Does this Help?
All the stars in the LMC look rather faint because it is
150,000 light-years away! (Still, this is less than 10% of
the distance to the Andromeda nebula, M31.)
But in the LMC, the member stars are at a common
distance, so any differences are meaningful and real.
In other words, if one star looks brighter than another, it
really is. We can safely intercompare the member stars.
A Rich Harvest
There are more
than 1000 known
Cepheids in each
of the LMC and
the SMC!
The positions of
some of them are
plotted here.
Henrietta’s Careful Approach
She took many photographs of the Clouds, night after
night, month after month, and year after year.
She intercompared the photographs to find all the variable
stars.
She worked out the period for each one (the time taken for
a complete cycle from brightfaintbright)
She work out the apparent brightness of each one (suitably
averaged over the cycle of variability)
For Example:
average
brightness
What Might We Find?
1.
1.
1.
It could be that the Cepheids in the LMC are all exactly the
same in apparent brightness, regardless of the periods. This
would tell us that all Cepheids are equally bright intrinsically.
(That would be very helpful!)
On the other hand, the Cepheids might have a variety of
brightnesses that are completely random, utterly unrelated
to the periods. (That would be very unhelpful!)
Finally the brightness might be related to the period in some
way that we can interpret and put to use.
Case 1: Suppose Henrietta Found
That They Were All Identical
…then life becomes very simple!
Suppose, for example, that Henrietta later found a Cepheid in a
more remote nebula (like M31, the Andromeda nebula)
It would look much fainter than the ones she has been observing
in the nearby LMC. This tells us the relative distance. [For
example, if it looks 100x fainter, it must be 10x as far away, by the inversesquare law.]
It wouldn’t matter what sort of Cepheid she found! (Long-period?
Short-period? If they’re all exactly alike, who cares?)
Sadly, Life isn’t That Simple!
The Cepheids aren’t all made by the same ‘cookie cutter’!
Real Cepheids actually
span a considerable
range in intrinsic
brightness.
Some are ultra-luminous,
others less so.
Here is Henrietta Leavitt’s
Original Data
- just 24 Cepheids!
Consider a Couple of Her Stars
1. The brightest Cepheid in the table varies over magnitudes ranging
from 11.2 (at maximum luminosity) to 12.1 (at the faintest), with an
‘average’ of ~ 11.65. Its period is 127 days (more than four months).
Note, by the way, that this star is ~5 magnitudes (a factor of 100)
fainter than the dimmest star that we can see with the unaided eye.
Telescopes are needed!
2. The faintest Cepheid in the table ranges from 15.1 to 16.3, with an
average of ~15.7. Its period is just 1.88 days.
The Important Clue
The first star is ~4 mag brighter than the
second one, corresponding to a factor of
almost 40 in luminosity.
It also has a much longer period.
Of Course, Henrietta Leavitt
Considered ALL the Cepheids
The Leavitt Law
Brighter Cepheids pulsate more slowly than the
fainter ones!
[In this representation, brightnesses are shown relative to the Sun.]
To Visualize This
Compare the slow, steady heartbeat of a blue whale [8-10
times a minute] to the rapid-fire heartbeat of a tiny
hummingbird [around 1000 per minute]
Picture the biggest, brightest Cepheids pulsating much
more slowly than their smaller, fainter cousins
How Do We Apply This?
Step 1: discover a Cepheid in a remote nebula, by
noticing its variability in a series of separate images.
Step 2: carefully determine its Period, by making many
repeated observations over a span of time. (This
might take years!)
Step 3: from the Period, decide whether it is a superbright Cepheid (with a long period) or a somewhat
less luminous one (with a short period)
(continued…)
Determine the Distance
Step 4: If the Cepheid is a super-bright one (long-period),
but looks really faint, the nebula that it is in must be
very far away.
Conversely, if the Cepheid is less luminous (short-period),
its parent nebula must be quite a bit closer (or else we
wouldn’t even see the Cepheid).
Such reasoning can be quantified and made precise.
It’s not just hand-waving remarks. We can derive actual
distances!
One Remaining Problem…
Henrietta Leavitt has given us the
tools, by studying the two Magellanic
Clouds. But to complete the exercise,
you still have to find some Cepheids
in one of the mysterious spiral nebulae!
That will accomplish two things:
1.
2.
It will prove that the nebulae contain stars. (‘Planets in
formation’ don’t vary like Cepheids do!)
It will allow us to determine the distance to that nebula, and
thus the size of the nebula.