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? 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 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?)

Sadly, Life isn’t That Simple 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 super-bright 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: 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.