Cepheid Variable Stars - PowerPoint Presentation

Slide1

Cepheid Variable StarsSlide2

Cepheids

Very late in their lives, massive stars can pass briefly through a stage in which they are

unstable.

During this stage, their outerparts oscillate (‘pulsate’) in and out, like a beating heart,for reasons we understand.The name Cepheid comes from the fact that the first such starwas found in the constellation Cepheus.Slide3

The Evolutionary State of

Cepheids

[they are massive

stars nearing the ends of their lives] Slide4

How

Cepheids

Behave

[regular, periodic change in brightness] Slide5

Quite Distinctive

Behaviour

These stars vary in “sawtooth” fashion. They get bright fairly quickly, then fade away more slowly.Slide6

Why

Does the Brightness Change?

There are

actually two reasons:the stars change in size (different radiating area); and their temperatures vary as they pulsateBoth these effects are important.As the Cepheids pump in and out, like a ‘beating heart,’ they change by perhaps 10% in diameterThe periods range from a few days to several hundred days (but any given Cepheid has a fixed, well-defined period). Slide7

Cepheids

Really Do

Pulsate!The spectrum shows a changing Doppler shift. The surface of the star rises towards us -- and then later falls away!Slide8

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 livesSo when we look at a field of stars, only a very few will be Cepheids, and they will probably be quite remote.Slide9

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.Slide10

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 distancesThey also draw attention to themselves by varying conspicuously:in a sense, they ‘wink’ at us, as if to catch our attention!Slide11

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 changesby ~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.)Slide12

Meet Henrietta Leavitt

She was directed

by Harlow

Shapley to study Cepheid variable stars, with one clever proviso: – she was to look at a richsample of Cepheids that are all at the same distance. How???Slide13

Her

Target

Shapley

asked Henrietta to work on the stars in the Magellanic Clouds – the LMC in particular. Slide14

Close

Neighbours

The ‘

Magellanic Clouds’ (Large and Small) are satellites of the Milky Way, visible in Southern skiesSlide15

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).Slide16

The

LMC

Irregular in appearance: no spiral structure

Slide17

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.Slide18

A Rich Harvest

There are more

than 1000 known

Cepheids in each of the LMC and the SMC!The positions ofsome of them areplotted here.Slide19

Henrietta

’

s

Careful ApproachShe 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)Slide20

For Example:

average

brightnessSlide21

What Might We Find?

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.Slide22

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 inverse-square law.]

It

wouldn

’

t matter what sort of Cepheid she found! (Long-period? Short-period? If they

’

re all

exactly alike

, who cares?) Slide23

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.. Slide24

Here is Henrietta

Leavitt

’

s Original Data- just 24 Cepheids! Slide25

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.Slide26

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.Slide27

Of Course, Henrietta Leavitt

Considered ALL the

Cepheids

Slide28

The Leavitt Law

B

righter

Cepheids pulsate more slowly than the fainter ones! [In this representation, brightnesses are shown relative to the Sun.]Slide29

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 cousinsSlide30

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 super-bright Cepheid (with a long period) or a somewhat less luminous one (with a short period) (continued…)Slide31

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!Slide32

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 Cepheidsin one of the mysterious spiral nebulae! That will accomplish two things: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.