26 Classification of Variable Stars

Mohd Altaf Sofi

Learning Outcomes

After studying this module, you shall be able to

• Learn a few basic rules of classification of variable stars.
• Know that how to recognise a particular group of variable stars having very high luminosity
• Learn the concept involved in the classification of type I and Type II Cepheid variable stars.
• Know that (i) the observation of the classical cepheid variable stars are the best large scale distance indicators, (ii) the binary stars and variable stars are altogether different as per star classification, (iii) the basic criteria for classification is the variation in the output radiation from variable stars.

1. INTRODUCTION

Observations reveal that the luminosity changes that take place in a variable star are due to the changes in its internal physical mechanism. Such stars are therefore known as intrinsic variables. There are stars whose luminosity variations are only apparent and are caused by the obscuration of their light by some companion stars or the dust. These types of variable stars may be called the extrinsic variable stars. In this lecture we will focus our attention almost entirely on the intrinsic variable stars. In order to understand the detailed characteristics of the stars observed most frequently in our own galaxy as well as other extra-galactic structures, it is important to classify the stars of variable brightness into different categories based on some known parameters like luminosity, magnitude (apparent/ absolute) and distance from earth. Two groups of type I and II variable stars have been identified so far. Type I group is known as classical Cepheid variable stars and Type II group is simply called the Cepheids. The Cepheids irrespective of their type are the best indicators for determining their distances from the earth.

2.  CLASSIFICATION OF VARIABLE STARS.

2.1  Extrinsic Variable Stars.

The apparent luminosity of all the extrinsic variable stars keep on changing periodically due to eclipsing of their brightness by some other star or a cosmic object. Binary and some groups of multiple stars constitute these types of variable stars. The real binary systems are physical pairs which describe orbits round their common centre of gravity under the influence of their mutual gravitational attraction. Based on their closeness and mutual orientations the binary stars are further subdivided into three types, namely, visual, eclipsing and spectroscopic binaries. Visual binary is a pair of stars whose binary nature can actually be detected through a telescope. This is possible either when the distance of the pair from the earth is not large or when their mutual separation is appreciably large. For the identification of the individual members of the binary the angular separation must be greater than 0// .50.  The period of revolution of visual binaries ranges from about a year. More than 65,000 visual binaries have been have so far been discovered. There are many binary systems whose orbital planes deviate from the perpendicular line of sight. This deviation in the line of sight makes it possible for the individual members to eclipse each other during the course of their orbital motion. When individual stars in a given binary are very close together so that their resolution into separate components is impossible, their binary nature is revealed using Doppler shift technique. Such a binary system is known as spectroscopic binary simply because there is only spectroscopic method available to identify them. More than 1000 spectroscopic binaries have been identified so far using Doppler phase shift technique.

Fig.10.1 Timeline Orbital Motion of a Binary Star Configuration.

2.2  Intrinsic variable stars

The apparent brightness of intrinsic variable stars undergoes a perceptible change only when some physical changes occur in an individually observed star. In other words the intrinsic variable stars do not necessarily form a binary system. An individual star undergoing a physical change through a variety of natural phenomena say for instance nuclear reactions taking place in the outmost layers qualifies to be an intrinsic variable star. We can subdivide the intrinsic variable stars into two measure types, namely, pulsating variables and exploding variables. As far as pulsating variables are concerned the changes in their luminosity are mostly regular and periodic. These variable stars can be distinguished on the basis of the length of their periods nature of variation of the light output and their spectral characteristics. These are unstable old age stars almost near the completion of their life cycle. The Cepheid group of variable stars forms one of the measure subclasses of the intrinsic variable stars. In the present lecture we will try to explain the nature of some of the important Cepheid variable stars through spectrum analysis. There is yet another interesting group of stars which belong to the intrinsic variable category. These individual stars are called eruptive or exploding variables and are identified by a sudden or violent flaring up of radiation. These include Novae and super novae stars. Novae stars undergo occasional outbursts whereas supernovae stars are characterized by the violent and continuous outbursts of energy in the form of electromagnetic radiation and mass ejection.

2.3  List of some well-known variable stars.

The list is not exhaustive but has been included to appreciate the discovery of variable stars through the course of human history.

3. CEPHEID GROUP OF VARIABLE STARS:

3.1 Type I Cepheids (Classical Cepheids):

Delta Cephei is regarded as one of the earliest recognized members of the group of 600 stars in milky- way galaxy with absolute magnitude ranging from -1.5 to -6. This indicates that the brightest of these variable stars are about 104 times more luminous than the sun. Some of the brightest known stars among these are Polaris, Delta Cephei, Eta Aquilae, Zeta Geminorum and Beta Doradus. The period of variation of light for these classical Cepheids range generally from 2 to 45 days; although most significant and usual range is 5 to 10 days. Almost all the classical type I Cepheid variable stars are yellow Super giants with spectra varying between F and K.   The direct observation of these stars suggest that they are strongly concentrated near the equatorial plane of the galaxy and are believed to belong to the extreme Population I stars.

Fig. 10.2 The upper curve represents variation of light with period and the lower one indicates the variation of radial velocity with period.

If one plots the change in apparent magnitudes of a variable star against the time of measurement through a complete period , one obtains what is called the light curve of the variable. In one complete period, this curve changes through one complete cycle, i.e., from crest to crest or from trough to trough. Different types of light curves are exhibited by type I classical Cepheids, depending mainly on the length of their periods. Delta Cephed and its close companion stars with a period between 2 to 6 days brighten more rapidly than they fade and have very smooth light curves. Eta Aqualae and other stars with the period in the range of 7 to 8 days have a pronounced hump on the descending branch of the curve. The curve becomes very symmetrical, rising and falling at almost equal rates.

Following set of figures show some of the Cepheids having variation of apparent magnitude with periods in days as explained in the text above.

Fig. 10.3 The light curve of Delta Cepheid with period of 5.37 days

Fig. 10.4 The light curve of Eta Aquilae with period of 7.18

Fig. 10.5 Light curve of a symmetric Cepheid with a period of about 10 days.

All the curves depicted above have been obtained from Baidyanath Basu’s book on Astrophysics published by Prentice Hall of India private limited.

Finally, the rise to maximum is again much more rapid than decline to minimum in case of the stars with periods much longer than 10 days. This can be easily understood by critically analysing the spectrum of the Cepheids. This spectrum includes observation of radial velocity variations which indicate the nature of pulsation mechanism of these stars. The radial velocity variation is found to be strongly correlated with the variation of light curve. The variation in velocity ranges from -20 through zero to +20 Km s-1 . in any spectra for the type I Cepheid stars the variation of light and radial velocities are plotted with reference to the period of the Delta Cepheid. Conventionally the velocity of approach is considered a negative radial velocity whereas positive velocities are attributed to the receding variables. The velocity curve is very much like the light curve reflected on a horizontal plane. The maximum for the light curve occurs at a point where the velocity curve reaches the minimum and vice versa. For Cepheids having significantly longer periods the light curve attains the maximum distinctly before velocity curve reaches its minimum. Some of the important conclusions drawn from the spectra of the Cepheid variables are:

1. The Cepheids exhibit nearly normal F-G-K class spectra at minimum light.
2. The spectral type at maximum light usually ranges from F5 to F8.
3. The spectra at maximum light are not normal.

Classical Cepheids are primarily recognized by the presence of G-band, Fe I, Fe II lines and H and K lines of Ca II. At maximum light a Cepheid may reveal mild nova like property by exhibiting an extended atmosphere with shell ejections. These ejected shells show the spectra with strong and enhanced hydrogen and metal lines.

Type II Cepheids:

Near the centre of our galaxy or close to the globular clusters a group of stars, namely W Virginis Stars, is identified with periods in the range 10 to 30 days. These stars are called type II Cepheids and their magnitude falls in the range 0.0 to about -3.5. Their light curves are almost similar to those of type I Cepheids except that their descending branches fall less stiffly. For the same period, type II Cepheids are about 1.5 magnitudes fainter than the classical Cepheids of type I. Since both types of Cepheids follow the similar period luminosity relation, we can use them as distance indicators as well. Different members in type II Cepheids are high velocity and metal poor stars. They are therefore considered to be the population II stars having blurring in color as compared to the classical Cepheids. The spectrum of these stars contains well marked bright lines of hydrogen with pronounced doubling at the maximum light. The presence of two concentric shells alternately rising and falling above the photosphere of these stars suggests that the violet component of the Ca II doublet appears at one maximum and the red component at the next maximum. The rising and falling of the photospheric shells gives rise to the formation of the bright lines of hydrogen.

The relationship of period to the apparent magnitude for the Cepheid variables in the systems like Small and large Magellanic Clouds, Andromeda Spirals, M33 etc, have been investigated by several workers, namely H. S. Leavitt H. Shapley and E. P. Hubble. They have concluded from the observations that almost all the variables are nearly at the same distance from us indicating that there is a well-defined relationship between the absolute magnitude and the period for these Cepheid variables. According to H. Shapley the period- luminosity (P-L) curve for any Cepheid shows how the logarithm of the period increases as the median absolute magnitude increases. The importance of this relation lies in the fact that it helps in determining the distance scale within and beyond our galaxy. With the help of 200-inch telescope one can detect the Cepheids at extremely large distances. Let us suppose “M” and “m” to be the median absolute and apparent magnitudes respectively for a star which is at a distance of “r” from us. For a given color excess “C.E” the following relation is valid for all the Cepheids

The color excess in this expression is the difference between observed color index and the color index the star would have in the absence of obscuration and reddening. Beyond our galaxy type I Cepheid are frequently observed making them strong candidates for the measurement of extra-galactic distances.

4. SUMMARY:

The main aim of this lecture has been to classify variable stars in terms of groups identified by Type I and Type II Cepheids. Type I Variables are called classical Cepheids and Type II are simply known as Cepheids. Subsequently the apparent changes in the brightness of these Cepheids with the passage of time lead to their spectrum analysis. We have remained focussed with the intrinsic pulsating variables in which changes of luminosity are mostly regular and periodic. The categorisation of the variable stars has been done on the basis of the length of their periods, nature of variation of their light and their spectral characteristics.

Suggested Reading

1. Astrophysics by Biadyanath Basu, Prentice Hall of India.
2. The physical Universe by FrankShu, university ScienceBooks, Mill Valley, California.
3. Observational Astronomy by D. S. Birney,CUP, Cambridge.