# Intrinsic Variable Stars

Good day, folks. Fair word of warning: this is one of the longest posts we’ve done, at 2300 words (though there are lots of pictures). This is our second installment in our variable stars series, and today, we’ll be dealing with intrinsic variables. As we mentioned last week, intrinsic variables are the stars that change brightness because of processes that happen within them—internal factors.

So the first thing you need to know about intrinsic variable stars is that there are a lot of them. And I mean a lot. Within the group of intrinsic variable stars, there are three classes: pulsating, cataclysmic (or explosive), and eruptive. Within those three classes, there are further types for each one.

Pulsating types include Cepheids, RR Lyrae, RV Tauri, and long period variables, among others. Two of these types have further types—Cepheids split into Type I Classical and Type II W Virginis, and long-period variables split into Mira type and semiregular.

Cataclysmic types include supernovae, novae, dwarf novae, recurrent novae, symbiotic stars, and R Coronae Borealis.

Eruptive types include luminous blue variables, flare stars, supergiants, protostars, and Orion variables.

Very important features in identifying variable stars are their periods, population type, and of course, their light curves. The light curves for each kind of star are very distinctive, but there are a lot of them, so it may be a bit challenging at first to memorise all of them. To help you along, we’ve provided light curve examples for every kind of variable star we mention. The maximum luminosity is referred to as the maximum or maxima, and the minimum luminosity is referred to as the minimum or minima.

Now, we’ll walk through all of that information bit by bit, starting with pulsating types, by far the most common and most well known type. As we said last week, pulsating types are stars that actually change their size and brightness in a cycle. The length of one cycle is referred to as a period (and this is applicable to all variable stars). The periods of a pulsating star can range from a few seconds (ZZ Ceti stars) to years (long-period variables). The following table gives a good general view of the various pulsating variables and their period.

 Type Period Pop. Spectral Classes Long-Period Variables 100-700 days I, II Varying RV Tauri 20-100 days G, K Classical Cepheids 1-50 days I F to G/K W Virginis 12-45 days II F to G RR Lyrae 1.5-24 hours II A7 to F5 d Scuti 1-3 hours I b Cephei 3-7 hours I ZZ Ceti 100-1000 sec I

We’ll start with the most well-known kind of variable star: classical Cepheids. δ Cephei, the prototype of this class, was discovered by nineteen-year-old astronomer John Goodricke in 1784. Cepheids are very luminous and very large variables, at least 50 times the mass of the sun. The spectral classes of classical Cepheids generally change from F at a maximum value and a G or a K at a minimum value, typically fluctuating between a 0.5 and 2 magnitude. They have a very distinctive light curve as well—a very sharp rise in luminosity followed by a more gradual decline.

Light curves of Classical Cepheids. Credit: University of Arizona

As mentioned earlier, they are by far the most well known type of variable star—and on good grounds, too. They are extremely important to astronomy for several reasons. These stars can actually help measure distance in astronomy by a combination of the distance modulus and the period-luminosity relation. For now, we’ll only worry about the period-luminosity relation, because that’s what is really applicable to all these variable stars. Astronomers a long time ago discovered a whole bunch of Cepheids in the Small Magellanic Cloud, and realized that since all of the Cepheids were about the same distance away, then the difference between the absolute and the apparent magnitude had to be the same as well. This also led to a discovery that the length of the period was actually directly related to its luminosity, which—gasp—gave us the period-luminosity relation:

${ M }_{ (v) }=-2.81\log _{ 10 }{ { P }_{ d } } -1.43$

where M(v) is the absolute magnitude and Pd is the period in days. This equation actually proves that the longer the period of the star is, the brighter it is. Because of how bright Cepheids already are (being massive, pulsating, luminous stars), they allow astronomers to use them as standard candles of the universe, which can be used to determine distance. This method can measure much farther away than parallax can, as parallax can only measure distances up to 100 parsecs away.

There are a few other pulsating types, and we won’t go as much into detail about those. W Virginis stars (Type II Cepheids) are just like classical Cepheids, only slightly dimmer. Their period-luminosity relationship is exactly parallel to the classical Cepheid’s, and therefore, they also work as standard candles. However, because they are not as bright, we can’t use them to determine large distances. These stars are also much older than the classical Cepheid, being population II stars and therefore also rarer than classical Cepheids. Their spectral classes range from F to G.

Light curve of W Virginis. Credit: C. Hoffmeister / Strasbourg Astronomical Data Center

RR Lyrae stars are even older than the W Virginis stars. What is special about these stars is that they all have almost the exact same luminosities, so they too can be used for distance measurements in astronomy. They have a rather short period of up to a day, and range from 0.3 to 2 magnitudes. They are smaller than Cepheids, but they also have a well-defined period. RR Lyrae stars actually have several subtypes, based on the light curve of the star in question.

Light curve for an RR Lyrae star. Credit: Michael Richmond (RIT)

RV Tauri stars are yellow supergiants with an odd pulsation pattern. From the maximum, pulsates in an alternating pattern of shallow and then deep minimas. The period is measured from deep minima to deep minima. They vary from F to M and up to three magnitudes.

Light curve for an RV Tauri star. Credit: South Carolina State University/AAVSO LCG

δ Scuti stars are somewhat evolved F-class stars located closer to the centre of the H-R Diagram than most of the other variable stars. ZZ Ceti stars are actually pulsating white dwarfs—core remnants unstable enough to change and pulsate.

d Scuti-type light curve. Credit: Russian Astronomical Network

ZZ Ceti-type light curve. Credit: C. Hoffmeister / Strasbourg Astronomical Data Center

Long-period variables have, well, long periods, ranging from a few months to several years. They are AGB stars, which means that they are always quite large. The Mira-type long-period variable has a huge variation in brightness—up to ten magnitudes! The minimum variation in brightness is about 2.5 magnitudes. These pulsate regularly and have some outer layers in their atmospheres that get heated up and shocked when they pulsate.

Mira, in fact, was the first variable star discovered—in 1595, a young pastor who also happened to be an amateur astronomer began to observe ο Ceti, and found that over many months, it disappeared and then reappeared! He named this strange star Mira, “wonderful”.

The light curve of Mira, the prototype of Mira-type long-period variables. Credit: AAVSO LCG

Semi-regular variables are also long-period variables, but they have sporadically have periods of stability. The change in brightness is also much less—usually less than 2 magnitudes. Their light curves vary greatly because of the irregularity of their pulsations.

A semi-regular variable light curve. Credit: AFOEV / Kyoto University

On the H-R diagram, these pulsating stars are located on a special place called the instability strip, where—surprise—the stars are not stable and therefore pulsate. The exceptions to this are the long-period variables and the b Cephei stars. Long period variables are located to the right of the instability strip, while b Cephei stars are located to the left.

HR diagram showing location of pulsating variable stars. Credit: Case Western Reserve University

Of course, the next question we must go through is: why do stars pulsate? Most stars are stable in their respective phases of hydrostatic equilibrium, but sometimes, hydrostatic equilibrium isn’t reached. If the internal pressure of a star, which pushes outwards, is greater than the gravitational force, which pushes inwards, the outer layers of the star will expand. Once the star expands, the gravitational force is lessened somewhat, but the internal pressure drops very much, very fast. This means that when the star hits the point of hydrostatic equilibrium, it still has a lot of momentum—which means it carries the star past this point of hydrostatic equilibrium. When this happens, the force of gravity becomes greater than the internal pressure pushing outwards, so the star collapses inwards. When that happens, the internal pressure once again becomes greater than gravity, and everything happens all over again. It’s a vicious cycle, we know.

The physics of stellar pulsation are a bit painful to go through, so we’ll not deal with that too much. The most important thing you need to know about that is that pulsating stars, like sound, has fundamentals and overtones, and pulsates on these frequencies.

Next, we’ll go through cataclysmic variables. These are also called explosive variables, because they, well, explode. In fact, supernovae are a kind of cataclysmic variable. Yes, that’s right—a major stellar explosion that is a star’s death counts as a kind of variable star. No, I don’t know what’s wrong with astronomers’ brains either. As we have already discussed supernova (thank you, astroisstellar), I don’t feel the need to go any more in depth about these things. If you want to know more, please refer to our earlier post.

Generalized light curves for Type II SNe. Credit: Swinburne University of Technology

Another cataclysmic variable is the nova, which is actually a binary system comprised of a white dwarf and a companion star, usually a giant. The gravity of the white dwarf sucks—excuse me, accretes—matter from the companion star until it hits the Chandrasekhar Limit, at which point it triggers a thermonuclear reaction that blasts the shell off into space. This cycle repeats over and over again until there’s nothing left.

A light curve of a nova. Credit: NASA Goddard Space Flight Center / William T. Thompson

A recurring nova is exactly like a nova, only it has occurred at least two or more times and the period of its outburst is up to 200 days. There’s not much else special about it; it’s just a recurring nova.

Recurrent nova light curve. Credit: VSOLJ / Kyoto University

Dwarf novae are binary systems consisting of a white dwarf and a larger star. These stars are pretty dim, but have a sudden spurt of brightness over a few days with intervals of weeks or months. No one is exactly sure what causes these sudden increases in luminosity, but the most popular theory is the disk instability model, which states that the accretion disk of the white dwarf is thermodynamically unstable, which causes outbursts—but not explosions. Not much material is ejected when this happens, so it fits in with the rest of what happens.

Dwarf nova light curve (SS Cygni). Credit: AAVSO LCG

The next kind of cataclysmic star is the symbiotic nova. These are close binary systems comprising of a red giant and another hot star (be it a white dwarf, neutron star, or a main sequence star) in a cloud of dust and gas. A defining feature of these systems is that their periods are incredibly slow. It takes decades for them to go through one pulse. What happens with these stars is that the outer layers of the red giant is actually expelled due to stellar winds, and the hot companion star accretes this expelled matter. When there is enough matter, periodic explosions occur.

Light curve for symbiotic nova RR Telescopii (look at the dates along the bottom!). Credit: AAVSO LCG

Eruptive stars are much rarer—in fact, there is only one main type of these stars. These stars are called R Coronae Borealis stars, which are rare, luminous supergiants. Their “outburst” isn’t brightening, like every other intrinsic variable, but rather fading. For most of the time, they are at maximum brightness and even appear stable. Then suddenly, their brightness will decline by up to 9 magnitudes, and then slowly crawl back up to maximum luminosity over the course of a few months to a year.

R Coronae Borealis light curve. Credit: Wikipedia / AAVSO LCG

And whoo, we’re finally through! Of course, there are more types than the ones we’ve got listed here, but if you want to look at that, you might as well go to AAVSO’s 57-page document listing all the kinds of variable stars, listed here:

http://www.aavso.org/vsx/help/VariableStarTypeDesignationsInVSX.pdf

Nowadays, we’ve also got the GCVS, which is the General Catalogue of Variable Stars. It has about 46,000 catalogued variable stars from our own galaxy, 10,000 from outside our galaxy, and over 10,000 prospective ones. However, there are estimated to be millions simply in our own galaxy. We just haven’t gotten around to cataloguing all of them yet.

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TL;DR

There are a ton of variable intrinsic stars, and it is divided into three categories: pulsating, cataclysmic, and eruptive. There are many more subtypes within these stars. A common way to identify these stars is by using light curves. Pulsating stars are by far the most common and the most  studied, because of their uses as standard candles and pulsation periods, but cataclysmic and eruptive variable stars are quite…stellar…too.