Pulsating variables

There are two types of pulsating stars, those where the pulsations are radial and are caused by ionisation and recombination of helium and hydrogen which causes shock waves which in turn move the star’s surface in and out; and non-radial pulsations, usually induced by rotation at high speeds. We are interested mainly in the longer period, radially pulsating objects which are suited to the equipment we can use to observe them—the eye, usually with a telescope and binoculars, CCD and DSLR cameras and now some of our members are turning to spectroscopy due to the development of low cost and dramatically improved detectors and software.

The stars where we operate projects are:

• Cepheids with periods from 10 days upward
• Long period, cool variable stars—Miras, semi-regular stars and irregular objects
• Delta Scuti stars, RR Lyrae (cluster Cepheids) and other short period stars

A few of our members make measures of other types — RV Tauri, Type 2 Cepheids, and other unclassified stars.

The Hertzsprung-Russell diagram, a plot of brightness against temperature, provides an immediate idea of how these stars relate to each other—see Wikipedia for an in depth background and explanation of this diagram. A typical H-R diagram appears below. There are two main ‘instability strips’ where the stars mentioned above are found. The Cepheid instability strip where the pulsations relate to doubly ionised helium—and a low temperature, poorly defined region in which the cool pulsators, LPVs, Miras and such, vary due to a cycle involving hydrogen.

Variable Stars in the Hertzsprung-Russell diagram

The diagram in Figure 1 plots absolute magnitude or luminosity against spectral class or temperature (decreasing to the right). As each step of 5 in magnitude is a factor of 100 the brightness range is billions of times. The temperature range is from about 40,000K to 1000K at which latter stage the star is only visible in the infra-red.

The helium instability strip goes from delta Scuti stars close to the main sequence to classical delta Cepheids in the supergiant area. A less well-defined hydrogen instability strip is also present in the cooler Mira, LPV and SR region.

Not all the variables shown here are pulsating – more detail about the others (binaries, cataclysmic variables, others) can be found elsewhere on this site.

Stars also show multiple frequencies or periods of variation and to understand why we need to understand a little elementary astrophysics.

Energy production and internal structure

Except for brown dwarfs and white dwarfs all stars are producing energy, mainly in the core, by nucleosynthesis or the fusing together of increasingly heavier elements. This begins with hydrogen, through helium and others until silicon is transmuted into iron. Fred Hoyle summarised this many years ago with his description of a seven layered star which was the final stage before the attempt to burn iron resulted in a catastrophic explosion which created the spectacular type II supernova in massive stars.

This energy makes its way to the surface where it has cooled from the tens or hundreds of millions of degrees in the core to between 2000K and 40000K. Three main processes are involved in this energy transfer—conduction, radiation and convection. Conduction is unimportant except in the case of degenerate stars such as white dwarfs where the density is sufficient for it to be effective. Radiative transfer requires high temperatures, otherwise convection is more effective and will be the dominant method.

So, energy in the inner regions of stars is transferred by radiation. This method of transfer can extend all the way to the surface with hotter stars. The changeover point is about spectral class F5 or a surface temperature of 6650K for main sequence stars. Cooler stars, such as our Sun with a temperature of ~5800K, thus have a convective envelope.

Apart from this there are interfaces between the various element layers with the least dense at the surface. Energy production can take place in these shells if the temperature is hot enough. This may be continuous or in isolated ‘flashes’. These interfaces are not rigidly defined but sufficient to affect the propagation of shock waves and hence the observed pulsations.

The most well-known pulsation method involves doubly ionised helium. This will occur in a radiative layer but only if the temperature and density are nicely balanced. Matter tends to be opaque to radiation and at these layers it depends critically on the number of particles. So let our layer fall a little toward the hotter central regions of the star. Helium will lose its second electron; thus the number of particles will increase. The layer becomes more opaque, offering greater resistance to energy flow, and is driven outward where it becomes cooler. The electrons recombine and radiation pressure is insufficient to keep it at this cooler level. It falls inward, becomes hotter, and the cycle repeats.

This process generates shock waves which travel in all directions in the star. The most important is that travelling outward. If conditions are right, it will reach the outer envelope and cause this to expand thus causing visible fluctuations in the brightness of the star. But luckily for us these shocks do not reach the outer layers of our star, the Sun, even though there are probably some being generated inside.

These shocks can also be reflected from the internal layers—10-day Cepheids show a double maximum which is probably such an effect. The pulsations may also occur in several overtones—beat Cepheids with periods of 2-5 days show frequencies of 1.0 and 0.71 of the fundamental mode.

Now let’s add another complication. All stars cooler than ~6650K have convective outer layers. These also affect the observed pulsations—but how is not really understood. What we do know is that the periods of Miras and cooler, long-period Cepheids oscillate between two extremes with an amplitude of 2-4% in period on a time of decades. Is this related to the convective envelope or is there some internal feature causing this?

Variable star astronomy seeks answers to these questions. Which is what Variable Stars South is all about. Follow the links in the diagram at the end of this section to see how you can participate in some of our interesting projects. But first two examples of using the observations.

What do the observations show?

The next two figures show two of the basic methods of both visualising what is happening and how this can be used.

Fig 2: A phased light curve

Phased light curves

Figure 2 shows a photoelectric light curve of the bright, naked eye Cepheid, l Carinae, as measured from the Auckland Observatory using a V filter, similar in response to the human eye. Its period is changing slightly but at that time it was best described by the light elements shown. In this case the epoch of minimum brightness is JD 2440725 which was 18 May, 1970, and the pulsation period was 35.548 days.

This can only be observed continuously from Antarctica in winter or a satellite so we need to ‘fold’ many nights’ measures to build up a composite picture of the light variations. This graph provides two markers—maximum and minimum— which can be used to look for evolutionary changes which cause the periods to vary.

Fig 3: O-C diagram of kappa PAVONIS

O-C diagrams

The graph in Figure 3 shows epochs of maximum of the naked eye, Type II Cepheid, kappa Pavonis from 31 December, 1871, to ~2000 AD. The observed epochs, O, JD—2400000, are plotted against the average mean period as calculated, C. Days late are positive, days early are negative.

Classifying variable stars

These are two of the more important ways of presenting observational data in the form of brightness at a particular date in an understandable manner. From here the analysis proceeds in a variety of ways to understanding what each star is doing and why. The pulsating variables are classified into various groups, as Figure 4 shows, but they are like people—all different and interesting in their own ways. So select a branch from the following graph and read a little more.

Fig 4: Variable star classification chart [Source: https://sites.google.com/site/uiaastrophysics/articles/stellar-astronomy/unit-18-star-clusters]

Projects for pulsating variables

VSS runs a number of projects related to pulsating variables, which are outlined below.