Instability Strip
Cepheid variables
Cepheid variables are important because one extremely useful fact is that there is a relationship between their period and luminosity. This is very useful as from the luminosity, we can calculate the distance to the star (how to do so is covered in the next section).
Using these cepheids, astronomers were able to get a rough idea of the size of our milky way, and estimate the distance the Andromeda Galaxy (and thereby proving that it is a galaxy and not a nebula in the first place).
Note
Cepheid variables are named after Delta Cephei (in the constellation Cepheus). It is not to be confused with Beta Cepheids, another type of variable star named after Beta Cephei.
Examples of Cepheids include: Eta Aquilae, Zeta Geminorum, Beta Doradus, Polaris, and of course, Delta Cephei.
Explanation
Doubly ionized helium (helium whose atoms are missing both electrons, i.e. He2+) is more opaque than singly ionized helium (He+).
The more helium is heated, the more ionized it become, as temperatures become high enough to strip more electrons from the nucleus.
At the dimmest part of a Cepheid's cycle, the ionized gas in the outer layers of the star is opaque, and so is heated by the star's radiation, and due to the increased temperature, begins to expand. As it expands, it cools, and so becomes less ionized and therefore more transparent, allowing the radiation to escape. Then the expansion stops, and reverses due to the star's gravitational attraction. The process then repeats.
Note
There are many types of Cepheids. The original and most common type are called classical cepheids, but there are also Type II Cepheids, which are more metal-poor, and lower in mass. (They can be further divided into subclasses depending on their period: BL Herculis, W Virginis and RV Tauri). They have a different period-luminosity relationship compared to classical cepheids are general dimmer and hence less useful.
There even more types of cepheids like Anomalous Cepheids (higher luminosities than expected) and Double-mode cepheids (pulsating in more than one mode at the same time), but those are still rarer.
RR Lyrae variables
RR Lyrae variables are periodic variable stars, commonly found in globular clusters. They are pulsating horizontal branch stars of spectral class A or F, with a mass of around half the Sun's.
They are thought to have shed mass during the red-giant branch phase, and were once stars of similar or slightly less mass than the Sun, around 0.8 solar masses.
The absolute magnitudes of the RR Lyrae stars are about \(M_V = 0.6 \pm 0.3\). They are all of roughly the same age and mass, and thus represent the same evolutionary phase, where helium is just beginning to burn in the core. Since the absolute magnitudes of the RR Lyrae variables are known, they can be used to determine distances to the globular clusters.
Although RR Lyrae variables do not follow a strict period-luminosity relationship at visual wavelengths, they do in the infrared K band.
They pulse using the same \(\kappa\)-mechanism as cepheids, although RR Lyrae variables are much more metal-poor.
RR Lyrae variables are typically found in a particular area of the Hertzsprung-Russell Diagram called the "horizontal branch", and further described as the "RR Lyrae gap" since most of the stars in that area are RR Lyraes.
Delta Scuti variables
Delta Scuti (\(\delta\) Sct) variables are similar to Cepheids but much fainter and with much shorter periods. They exhibit radial and non-radial luminosity pulsations (i.e. The star as a whole can pulsate, but individual regions can also pulsate too) They often show many superimposed periods, which combine to form an extremely complex light curve. Despite this, there is also a period-luminosity relationship.
Examples of Delta Scuti variables includes Seginus (Gamma Boötis), Epsilon Cephei, Caph (Beta Cassiopeiae), Polaris Australis (Sigma Octanis, the southern pole star), and of course, Delta Scuti.
Vega is also a suspected delta scuti variable.
Outside the Instability strip
There are other stars outside the instability strip as well, like Mira variables and Beta cepheids.
Mira variables
Mira variables are stars massive enough that they have undergone helium fusion in their cores but are less than two solar masses, However, they can be thousands of times more luminous than the Sun due to their very large distended envelopes. They are pulsating due to the entire star expanding and contracting. This produces a change in temperature along with radius, both of which factors cause the variation in luminosity. The pulsation depends on the mass and radius of the star and there is a well-defined relationship between period and luminosity (and colour).
The amplitude of the light variations is typically about 6 magnitudes in the visual region. The effective temperature of the Mira variables is only about 2000 K. Thus 95 % of their radiation is in the infrared, which means that a very small change in temperature can cause a very large change in visual brightness