WR Wolf Rayet stars

- Stars with broadband emission features of He I and He II as well as C II-C IV, 0 II-OIV, and N II-N V. They display irregular light changes with amplitudes up to 0".'l in V, which are probably caused by physical processes, in particular, by non-stable mass outflow from their atmosphere. GCVS

Wolf-Rayet (WR) stars, named after the French astronomers Charles Wolf and Georges Rayet, who discovered them in 1867, are as strange as the luminous blue variables. WR stars are luminous hot supergiants with temperatures comparable to those of normal O stars. However, they cannot actually be placed within this spectral class because of their eccentric spectra that display only emission lines and with little or no evidence of the most common of elements, hydrogen.

WR stars display luminosities that range between about 100,000 and a million times that of the Sun, at the limit or close to those of the LBVs. Considered rare -there are probably only a thousand or so within the Galaxy - they are at least more common than the LBVs. y2 Velorum, one of the sky's brighter stars, shining at 1™8, is a double star comprising an O-type giant and a Wolf-Rayet star. Also like the LBVs, the Wolf-Rayet stars are losing mass at high rates; a ten-thousandth to a hundred-thousandth or so of a solar mass per year and the dominant element is not hydrogen, but helium

Presently, there are approximately 20 Wolf-Rayet stars found within the GCVS. Two types exist: nitrogen-rich (WN) and carbon-rich (WC). WN stars do contain small amounts of hydrogen, although the normal ratio of hydrogen to helium is reversed. In normal stars, there is about 10 times as much hydrogen as helium, whereas in WNs, there is typically 3—10 times as much helium as hydrogen. While the elements carbon and oxygen are effectively absent, WNs contain up to 10 times as much nitrogen relative to helium, and much more relative to hydrogen.

Pulsating variables are stars showing periodic expansion and contraction of their surface layers. The pulsations may be radial or non-radial. A radially pulsating star remains spherical in shape, while in the case of non-radial pulsations the star's shape periodically deviates from a sphere, and even neighboring zones of its surface may have opposite pulsation phases.


Of all the variable stars, pulsating stars, especially the Mira (M) and semiregular (SR) stars, are probably the most observed by amateur astronomers. This claim is easily understood when you consider that well over 22,000 pulsating variable stars are cataloged within the GCVS and several million pulsating stars probably exist within the Milky Way. By any measure, this is quite a selection and would keep you busy for many lifetimes. As well as providing a large number from which to choose, many pulsating stars have large amplitudes making them an excellent choice for visual observation.

Keeping in mind that only several million pulsating stars are believed to exist among several hundred billion stars within our Galaxy, pulsation is believed to be a brief phenomenon for most stars. Apparently, because it is a relatively brief occurrence, stellar pulsation is an unusual phenomenon and is therefore, as with all rare objects, fascinating. Upon closer examination, the locations of many of the pulsating variables within the HR diagram are certainly interesting.

As explained earlier, the majority of stars spend a large percentage of their lives on the main sequence. However, the majority of pulsating stars occupy a narrow, nearly vertical instability strip on the right-hand side of the HR diagram. As stars located within the main sequence begin to evolve and move off the main sequence to the right, some will eventually enter this instability strip and begin to pulsate. Pulsation will also cease when they exit this instability strip. Remember, this is not the only instability strip found within the HR diagram; it just happens to be the largest. We will look at other instability strips later when we discuss the various types of pulsating variable stars. Of course, stellar evolutionary time-scales are too long to observe the beginning and end of a single star's pulsation; however, a few stars have been observed in the final phase of this interesting evolutionary stage.1

There are several types of pulsation. One type is known as radial pulsation, and results when the star pulses, as if breathing, expanding and contracting equally in all directions. Another type of pulsation, known as non-radial pulsation, will be discussed in a few moments.

Sound waves resonating within a star's interior cause pulsation. You can approximately estimate the pulsation duration for these stars by determining the time required for a sound wave to cross the diameter of a model star. However, one of the sources of error when doing this is unrealistic model parameters. Usually, the model star is developed with a known radius and a constant density. We know that it's unrealistic to assume that a star has a constant density but approximations such as this are necessary and they are the working tools of astrophysicists. If you're looking for a pencil and a calculator, let me warn you that the ability to compute the innumerable dynamic conditions exhibiting continual changes, both subtle and gross, within a star is beyond the computational power of today's most advanced computers. However, it can be shown that the pulsation period of a star is inversely proportional to the square root of its mean density. The period-mean density relation explains the decrease in the pulsation period when you move down the instability strip from the tenuous supergiant stars to

'Polaris (a UMi), a classical Cepheid variable, has shown a sharp reduction in its oscillation during recent years.

the very dense white dwarf stars.2 Think about this for a moment. Does sound travel faster in the atmosphere or, for example, underwater? Which is more dense? Of course, sound travels faster in the more dense water just as sound waves travel faster within the more dense stars. Fast traveling sound waves mean shorter periods.

Most of the classical Cepheids and W Virginis stars pulsate in what is called the fundamental mode. The long-period variables (LPVs) are probably also fundamental mode pulsating stars. In the fundamental mode, the gases of the star move in the same direction, inward or outward, at every point within the star. However, the RR Lyrae variables pulsate in either the fundamental or first overtone modes, with a few oscillating simultaneously in both. In the case of the first overtone, there is a single node between the center of the star and its surface defining the point at which gases move in opposite directions on either side of the node. The actual pulsation mode of the LPVs is the subject of considerable debate.

As briefly explained in the first chapter, when the core of a star is compressed, its temperature rises and thermonuclear energy increases. This energy-producing process, called the e (epsilon)-mechanism, is found deep within the core of a star. Perhaps this is where pulsation originates?

But no, this is not the case, as we'll see. When first studied, pulsation was believed to originate within the various layers of the star, located above the core, and so the e-mechanism was not considered to be the source of pulsation. Instead, Sir Arthur Eddington suggested that pulsating stars are thermodynamic heat engines. He believed that the stellar gases of the various layers within pulsating stars do work as they expand and contract. Accordingly, the net work performed by each layer during one cycle is the difference between the heat flowing into the gas and the heat leaving the gas. For maximum efficiency, the heat must enter the gas layer during the hottest part of the cycle and leave during the coolest part. In other words, the driving layers of a pulsating star must absorb heat at about the time of their maximum compression.

After much thought, Eddington suggested an unusual solution involving what he called a valve mechanism.

^Pulsating white dwarfs exhibit non-radial oscillations, and their periods are longer than predicted by the period-mean density relation.

He believed that if a layer deep within the star became more opaque upon compression, it could "dam up" the energy flowing toward the surface and as a result, this energy would push the upper layers of the star outward. As these layers were pushed outward, they became more transparent, allowing the trapped heat to escape. Once the heat escaped, the layer would fall back down to begin the cycle anew. In Eddington's own words, "To apply this method we must make the star more heat-tight when compressed than when expanded: in other words, the opacity must increase with compression."

Eddington's valve mechanism can successfully operate only within special layers of the star where the gases are partially ionized. In these partial ionization zones, part of the work done on the gases as they are compressed produces further ionization instead of raising the temperature of the gas. Ionization increases opacity, not temperature! The out-flowing energy is trapped by the ionization zones and the density of the zones increase.

As these layers are pushed outward by the increased pressure, their density begins to decrease and the ions begin to recombine and release energy. The temperature doesn't decrease much because the ions are recombining to release energy. The important thing is that the opacity of the layers decreases, with declining density during expansion. These layers of the star absorb heat during compression, are then pushed outward to release the heat during expansion, then fall back down again to begin another cycle. Astronomers refer to this opacity mechanism as the k (kappa-) mechanism.

In some cases, the surfaces layers of stars do not move uniformly in and out. Instead, they display a more complicated type of non-radial pulsation in which some regions of the star's surface expand while other areas contract. In this situation, non-radial pulsation, the sound waves can propagate not only radially but also horizontally and produce waves that travel around the star. These non-radial oscillations are called p-rnode oscillations because pressure is responsible for their compression and expansion.

For stars displaying non-radial pulsation, stellar material is not just moving in and then out, as if the star was breathing, but it is being sloshed back and forth. This sloshing of stellar gases produces another class of non-radial oscillations known as g-modes. The g-modes are produced by internal gravity waves. Because this sloshing cannot occur within stars displaying purely radial motion, there is no radial analog for the g-modes so they are found only within non-radial pulsating stars.

As you are beginning to understand, pulsation is complex and interesting and much can be learned from the study of pulsating stars. For example, the g-modes just mentioned involve the movement of stellar material deep within the star, while p-modes are confined near the stellar surface. Because they originate deep within the star, g-modes afford astronomers a probe into the very heart of a star. Just as important, the p-modes allow an inspection of the turbulent conditions within a star's surface layers. Of course, pulsation will tell much more than we've discussed here but this is just a beginning. With a basic understanding of pulsation, let's examine pulsating variable stars.

53 Persei stars are hot O- and B-type stars, usually classified as non-radial pulsating, with periods of less than a day. They are not officially recognized within the GCVS.

a Cygni stars are spectral type O through F, pulsating supergiant stars. These stars occasionally display variability that is typical of other classes of variable stars and as a result can be confused with other types.

The f) Cephei stars have in the past been called fi Canis Majoris stars and are normal early B-type giant stars with short periods lasting between two and seven hours. These stars occupy the fi Cephei instability strip, located in a small area in the upper right-hand region of the HR diagram.

BL Boo stars are also known as anomalous Cepheids because they do not obey the period-luminosity relation of either the classical Cepheids or the Cepheids found within globular clusters.

A variety of designations have been used for Cepheids in the past and you must be careful when consulting old literature. You'll find the luminosity class Ibll Cepheids of the characteristic spectral types F, G, or K; and the Type II Cepheids, known as W Virginis stars and in the past known as RRd stars. They are usually recognized as low-mass analogs to the classical Cepheids. Finally, you'll discover that the 8 Cepheids are also known as classical Cepheids or Type I Cepheids.

As a group, Cepheid variables are interesting variable stars but you must be attentive during your study of these stars. The light curve of a pulsating star will depend upon its mass, structure and chemical composition. When attempting to classify Cepheids, it can be difficult to distinguish between Type I (classical) Cepheids, anomalous (BL Boo) Cepheids, and Type II (W Vir) Cepheids. Patience and attention to detail during your observations will help you distinguish between these groups of stars.

S Scuti stars are low-amplitude, fast-pulsating stars of spectral type A to early F. These stars possess periods ranging from 30 minutes to eight hours. S Scuti stars have been known to pulsate with up to 23 different modes.

y Doradus stars are early F-type dwarf stars with short periods ranging from several tenths of a day to slightly more than a day. They became an official type within the GCVS in March 2000.

Slow irregular variables are generally poorly studied stars. Many of these stars are believed to be incorrectly classified and may actually be semiregular type variables. You will find two subtypes of slow irregular stars based on luminosity type (giants and supergiants).

X. Bootes stars are not listed within the GCVS but they are recognized as being metal-poor, Population I, A-type pulsating stars.

The Mira stars are a very popular group of variable star for amateur astronomers. They are also known as long period variables (LPVs) and are recognized as being late-type giants. Mira variables are known for large amplitudes, as much as 11 magnitudes.

Maia stars are predicted to exist but no true member of this group has ever been observed.

The mid-B variable stars were introduced in 1985 and are generally recognized to be B3-B8, luminosity class III—V stars with periods of approximately one to three days and amplitudes in the range of a few hundredths of a magnitude.

PV Telescopii stars are helium supergiants with periods less than a day and amplitudes in the range of a tenth of a magnitude.

RPHS variables, a new type of variable star that was officially recognized in 2001, are hot pulsating subdwarf stars previously known as EC 14026 stars.

RR Lyrae stars are fast radially pulsating A-F stars with amplitudes ranging from 0™2 to 2m, another group of stars well studied by amateur astronomers. There are three subtypes of RR Lyrae stars identified by the shapes of their light curves.

RV Tauri stars are radially pulsating supergiants, spectral class F-M, characterized by light curves having double waves with alternating primary and secondary minima. There are two subtypes of RV Tauri stars identified by their mean magnitude.

The semiregular (SR) variables are similar to the Mira variables differing in that they generally have smaller amplitudes and shorter periods. Exceptions occur and some SR variables have long periods and large amplitudes. There are five subtypes of SR variables distinguished by spectral type and luminosity class demonstrating different amplitudes, periodicity and luminosity classes.

SX Phoenicis stars resemble S Scuti variables but they display greater amplitudes.

UU Herculis stars are not recognized within the GCVS but are a possible transition phase between the asymptotic giant branch and the white dwarf evolutionary phases. UU Her, the prototype for this group of stars, seems to switch pulsation between fundamental and first overtone modes.

ZZ Ceti stars are non-radial pulsating white dwarfs with very fast periods and amplitudes reaching 0™2. There are three subtypes of ZZ Ceti stars distinguished by their various spectra. The GCVS classifications are listed in Table 4.1.

Observation Key

Bright stars ^ Small amplitudes ^^ Short periods <S> CCD or PEP

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