VARIABLE STARS : Part 2

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Types of Variable Stars

Types and variations among the variable categories are enormous. The following sections (Parts 2, 3 and 4) gives summaries of the major categories of variable stars, though it does not include all types.

Eclipsing or Photometric Binaries

This major group of variables are caused by two orbiting stars hat undergo mutual eclipses and occulatations. During these times, the combined surfaces produce the observed magnitude variations. Reasons for why these eclipses occur, is because of the chance alignment of the orbital motion, lying in approximately the same plane as the Earth.

Light-curves for these stars show two dips in brightness during one periodic cycle. The first, and normally for the greatest magnitude drop, is called the primary minima, which is brighter star being eclipsed by the fainter component. The second dip is the secondary minima which is the reverse, with the fainter star being eclipsed by the brighter component. The magnitude is not only the decisive factor in the depth of the two minima. Size, luminosity and surface temperature also plays a role.

Over 3,000 eclipsing binary systems are known, with the vast majority, each having orbital periods between several hours to about 10 days. This period is very much shorter than the double and binary counterparts of this group. Longer period eclipsing binaries are rare, as the chances of alignment dramatically decrease with an increasing orbital period. The longest known example is the star Epsilon (ε) Aurigae, whose orbital period is twenty-seven years.

Eclipsing binaries are also commonly termed photometric binaries because the light variations are usually measured by electronic means. With eclipsing binaries, the photoelectric observations produce data on may stellar parameters, such as, density, mass, size and age. This information is important values, used in the understanding of the true nature of stars.

As subgroups, four major types exist for eclipsing binaries.

(a.) EA Types or Beta (β) Persei / Algol Types

(b.) EB Types or Beta (β) Lyrae Types

(c.) EW Types or W Ursa Majoris Types

(d.) EII Types Elliptical Types or b² Persei Types

(a.) EA Types or Beta (β) Persei / Algol Types

These stars are all spherical in shape and are not distorted by gravitation because the close proximity of the stars. During eclipses of either star, two sharp dips are observed in the light curve. (Fig. xx) If the drop is of the same magnitude, then the stars are equal in luminosity, but in the majority of cases these drops are unequal. The dips in brightness are caused by the combined areas during the eclipse or occultation, producing decreasing the total brightness. Periods of all EA types averages about 10 days, or more. About 10% of all known variable stars are EA types.

Typical examples include ζ Pheonicis, R Canis Majoris, TZ Mensa, and U Sagittae. It is interesting to note that Algol (Beta Persei) has been found not the typical example of the class, being determined as EB in type.

Zeta (ζ) Pheonicis — 01084-5515

Zeta Pheonicis is an interesting multiple star system and containing four known stars. It is easy to find, because it is located 4.5°l west of the first magnitude star Achernar in Eridanus. The main pair RST 1205, discovered by Rossiter in 1931, is 0.6 arcsec apart, with respective of 4.1 and 6.9 magnitudes, and has been decreasing in separation since its discovery. This is a difficult object for telescopes below 25cm. in aperture. The brighter component in this pair is the eclipsing variable. The forth star, is the AB×C pair RMK 2, discovered by Rümker at the Parramatta Observatory in 1835. The star is 6.4v magnitude, separated by 6.4 arcsec., and has increased only slightly since its discovery. John Herschel described the visual system as “…a very beautiful system, in a starry field”.

Observations of this eclipsing binary is difficult because of the proximity to the ‘B’ star. The variation in magnitude is between 3.92V and 4.42V, over the period of 1.6697671 days, or 1 day 16 hours 04.5 mins. The star is also known to be a spectroscopic binary. Spectral classes are respectively B6 and B9, with both being luminosity class ‘V’, indicating they are main sequence stars.

Little is known about the physical data of the system, with none of the present literature giving such information. E.J. Hartung’s “Astronomical Objects for Southern Telescopes” states that the eclipsing binary has the total mass of about nine times that of the Sun, which is close to the most recent calculations placed on the total mass. The individual masses are respectively, 6⊙ and 3⊙. Distance is estimated at 1 600 light years from the Sun. Due to the distance of the system, the pair RMK 2 (or the ‘C’ star) in the multiple is likely not to be physically associated.

R Canis Majoris — 07195-1624

R Canis Majoris is located 8.4° west of the brightest star, Sirius (α CMa), and is also about 1.2º south of the 9th magnitude Open Star Cluster NGC 2360, that contains about fifty stars between 9th and 11th magnitude. This eclipsing binary is listed as semi-detached, indicating that it is almost an EB system. The magnitude variation changes between 5.70 and 6.34 in the period of 1.1359405 days. The length of the period is known to vary, somewhat discontinuously. Primary minima varies by 0.64 magnitudes, with the secondary minima dipping only 0.08 magnitudes.

The most recent calculations place the mass of the system as 1.2⊙ and 0.2⊙ (1989). W. Heintz in “Double Stars” (1978) states that the mass of the stars are respectively, 1.8M⊙ and 0.2M⊙, with the secondary that appears very extended. It is likely that mass transference through the Roche Lobe has occurred in the past, and may still be continuing, with the primary being the youngest star. R CMa has the respective spectral classes of F1 and K1, being 1uminosity classes V and IV, while the individual luminosities are 2.8 L*/L⊙ and 0.1 L*/L⊙ Effective surface temperatures are 6,110K and 3,110K. True separation between both stars, surface to surface, is 3.5 million kilometres, with respective to the individual diameters of 2 million and 1.7 million kilometres.

Distance is estimated to be close to the Sun, at 88 light years or 27 parsecs.

TZ Mensa 05302-8447

TZ Mensa is another EA system. This far southern system lies on the border between Mensa and Octans. The star field is rather solitary, and is surrounded to about 5° of sky area with other 6.0v to 6.5v magnitude stars. Close by is the inconsequential 12.2v magnitude globular star cluster NGC 1841, some 1.3° east. NGC 1841 appears as some nebulous glow, unresolvable to telescopes below 30cm. (This is not listed in Sky Catalogue 2000.0, but listed actually contained in the companion Sky Atlas 2000.0. Also note that the other GSC in Mensa, projected on to the Large Magellanic Cloud, is NGC 2121. This is the reverse problem of NGC 1841, it is listed in the Catalogue, but not on the Sky Atlas!)

Visual magnitude vary between 6.23V and 6.9V in the period of 8.569 days. Very little has been observational done with this star in recent years, probably because of its far southern declination. Time in predicting for primary eclipse and is certainly with significant error.

Total mass of the system is 6.5M⊙, dividing as 3.6M⊙ and 2.9M⊙. Relative luminosities are equally about 50 times that of the Sun, each with respective diameters of about 3.6 and 2.7 million kilometres, while the stars are separated by 22 million kilometres.

Spectrally, the first surveys listed this star as B9.5 IV-V, as stated in Sky Catalogue 2000.0. The more recent data indicates that both the stars have respective spectral classes of A1 III and B9 V. The computed temperatures are 9,370K and 10,850K, unusual, but not unique among eclipsing binaries, as the primary is slightly cooler. Distance is estimated to be 600 light-years.

U Sagittae — 19188+1937

U Sge has one of the deepest eclipses than most of the EA types, that is easily observable, even with binoculars. It can be found 2.8º west of the centre of the bright star group called Collinder 399, that contains the bright stars of 4, 5 and 7 Vulpeculae. It is also close to the 5th magnitude yellowish star of 9 Vulpeculae, some 0.7º north-east from this star. The V magnitude range of the star, varies between 6.58V and 9.10V in the period of 3.380626 days (3 days 9 hours 8.1 mins). The main or primary eclipse drops significantly because of the cooler companion, with the of the two stars estimated to be 10,240K and 4,720K, respectively. Its magnitude drop occurs over about 3½ hours, though the drop twenty minutes either side of eclipse may fall at the rate of about 0.15 magnitudes per minute. The eclipse lasts about 1.6 hours, before the brightness again increases. Visual observations during the eclipse may notice distinct colour changes in the star. Secondary eclipse, or occultation, is relatively minor, with only 0.1 magnitudes in difference.

A well separated pair Σ2504 lies some 0.7° away, as stated in Burnham‖s Celestial Handbook Vol.3, pg.1528, makes good comparison stars. Both have the respective magnitudes of 7.0v and 8.7v, both in the variability range of the U Sge. Separation of the pair is 8.9 arcsec, and has increase only slightly since its discovery by F.G. Struve in 1830.

This particular binary from the latest analysed light curve and spectra, reveal two stars with respective masses of 7.4M⊙ and 2.2M⊙, - being the mass ratio of about 3:1. Previous calculations have yielded smaller value for each of the stars. The literature (I.e. Plavic, 1973) continue to stated that U Sge is an unusual system, because it defies many of the known assumptions associated with eclipsing binaries. Masses here warn about the problems associated with all photometric systems.

Distance between the two stars is about 14 million kilometres, with each star having respective diameters of 5 million and 7 million kilometres. There is evidence from the small fluctuations seen in the light curve, that the primary has clouds of material in the circumstellar disk. Luminosity of the primary is 140 times that of the Sun, with the secondary only 11 times. Stellar spectral class of the stars is for the primary B8 III, as the sub-giant. The companion star was originally give as G2 subgiant IV-III, though the recent literature has tends towards spectral class K-type class stars. EA eclipsing binary is estimated to be 720 light years in distance.

(b.) EB Types or Beta (β) Lyrae Types

These systems have pronounced curvature in the light curve during mutual eclipses. The cause of the broadening is simply due to slight distortions in one, or rarely, both stars. Changes in the visible areas vary slightly with the distortions, so the magnitude drop is more gradual when approaching or leaving eclipses. Figure xx, visually shows the typical light curve. Orbital periods of EB’s average between 1 or 2 days, though some are known to be up to 10 days.

Examples of the EB type include β Persei (Algol), u Herculis, W Crucis, V Puppis and V745 Centauri.

W Crucis - 12120-5847:

Lying ¾° directly west of the bright star Delta (δ) Crucis is the EB type eclipsing binary of W Crucis. It is located in the middle of three 8th magnitude stars, in an almost perfectly straight line with the two either side making good comparison stars. Although this star is relatively faint, the brightness variations are larger than most eclipsing binaries. Visual magnitudes varies from 8.5v to 9.3v, while the UBV blue light observations show magnitude variations between 9.04V and 10.38V. What is most unusual is the long 198.53 day (6½ months) orbital period. The primary is a supergiant while the secondary is a giant star, making this giant eclipsing binary system.

Some 270 million kilometres separates the two stars. The primary displays an average diameter of 193 times suns, while the companion is 116 times. In luminosity, the stars are 10383 and 2884 times, respectively, that of the solar luminosity. Temperature of the two stars is 4,200K and 3,940K. The total mass of the system is 19.85⊙1, with the individual masses calculated to be 11.67M⊙ and 8.18M⊙, respectively. The primary, because of its large diameter, late state of evolution and has exceeded its Roche Lobe, and so, appear shaped like tear-dropped. The secondary component is also highly distorted, filling some 85% of the Roche Lobe size criteria. Due to the separation and long orbital period, the effects of the distortion are minimal, when compared to the effects of the total light curve. This system has the spectral class of G2 Iab, indicating supergiant stars. Spectra is also characterised by bright emission lines.

V745 Centaurus — 14272-6204:

This variable lies in the same field as Proxima Centauri. Lying some 45′N and 10′W of Proxima, V745 Cen can identified by another 8.1v magnitude star only 4′S of the star’s position. A few much fainter stars are in the field. (Note: It is plotted on in the top ‘Proxima’ inset in Sky Atlas 2000.0 Map 25. V745 is located right in the middle of the figure!)

V745 Cen has the period varying over 3.0251 days between the 9.3v and 10.3v magnitude. “Burnham’s Celestial Handbook Vol.1” pg.544 gives the visual magnitude range between 9.8v to 10.8v.

The primary displays an average diameter of 3.0 ⊙, with the companion is 2.6 times. In luminosity, the stars are 424 and 54 times, respectively, that of the solar luminosity. Temperatures are 15,210K and 9,720K. Total mass of the system is 7.89M⊙, with the individual masses calculated to be 4.75M⊙ and 3.14M⊙, respectively. Spectra is between B3 and B8, both being determined as giant stars. Some 12.2 million kilometres separates the two stars.

u Herculis (68 Her) — U Her — 17173+3306:

Another EB, second only to Algol is the eclipsing binary u Her. It is easily located by the naked-eye some 5½°S of the bright orange 3.16V magnitude star Pi (π) Herculis (67 Her). u Herculis varies between the magnitudes of 4.6p and 5.3p, in the period of 2.0510 days. Burnham’s Celestial Handbook; Vol. 2 pg.956 (listed as 68 Her) gives the visual magnitude range as slightly larger as between 4.7v to 5.4v. Spectral class of the two stars has been found to be B1.5 Vp and B5 III, respectively.

u Herculis is also the known double star OΣ328, with a 10th magnitude companion some 4.4 arcsec away. Little has changed in the position since its discovery in 1843 by Otto Struve. Colour for the companion star is somewhat blue-white to greenish. It is likely that the stars are physically associated with the closeeclipsing binary.

Distance is estimated to be 720 light-years away from the Sun, from the parallax of 0.00440 arcsec. Distance between the two components is 10.2 million kilometres, each star has the diameter of 3.2 and 3.1 million kilometres, respectively. By luminosity, the primary is 1159 times the solar output, while the secondary is 295 times that of the Sun. Being B spectral type stars, the temperature are high. The major component temperature is 15,780K, while its component is 11,450K. Stellar masses are 7.2 M⊙ and 2.9 M⊙.

There is some indication that the secondary has exceeded its Roche Lobe in the past, and has transferred the majority of its mass to the primary. This is probably an example of the so-called Algol Paradox. Although the primary is smaller, it is likely the oldest component in the system. Shape of the secondary is tear-dropped, with the primary being only slightly distorted by the gravitational field.

(c.) EW Types or W Ursa Majoris Types

Systems of this variable type have both stars are grossly distorted by the strong gravitational interactions of the component stars. Both stars appear like tear-drops producing light curves that are continuously variable. Due to the proximity sometimes mass can be transferred across from one star to another, and this is particularly prevalent when one of the stars starts to swell during its evolution. Some mass during these interactions produces an hazy ‘aura’ surrounding the two stars and has been observed in all known variables of this type.

EW variables periods are less than about 19 hours, (0.8 days) and vary by about one magnitude in both primary and secondary minima. Most of the stars have been determined to be small solar-like stars, typically of F or G spectral class.

Examples of this type includes S Antliae, V752, V757 and V758 Centaurus, TY Mensae, U Pegasii and the star from which the class is named, W Ursa Majoris.

S Antliae — 09323-2838:

S Ant is the brightest example of this class even though this object is paid little attention in most of the literature. Magnitudes vary between 6.40V and 6.92V. It changes equally during both the primary and secondary minima by the 0.5 magnitudes twice every 15½ hours. (0.6484 days) The period between successive drops of magnitude has been measured at 7 hrs 46 min 50 sec. The star lies close to the Antlia border with Pyxis, being 2° directly east of yellow 4.7 magnitude Lambda (λ) Pyxis. Exactly half-way to S Ant, is the 6th magnitude close pair of Jacob 5, that can be used guide you to the target. S Ant lies in the star field, with two faint 7th magnitude to the west by 20 arcmin. These can be used as comparison stars, with the variable having magnitudes greater at maximum and less at minimum than these stars.

Both stars are separated by only 2.2 million kilometres, with each star having an average diameter (the polar diameter is closer to the truth!) of 2.4 million and 1.3 million kilometres, respectively. Both stars are highly distorted due to this close separation, with mass transfer being a distinct possibility. By mass, the two have the total mass equally the Sun, divided as 0.68M⊙ and 0.32M⊙. Surface temperature’s being 8,300K, and for the secondary, 7,350K. In terms of the solar luminosity, the output is 12 times for the primary and 2.3 times for the secondary component. System distance is estimated to be 91 parsecs or 300 light years.

W Ursa Majoris — 09438+5557

Although not generally visible from the latitude of Sydney, W Ursa Majoris is an interesting EW eclipsing binary system. Visual magnitudes varies from 7.9v to 8.63V in the period of 0.3333639 days, or nearly exactly 8 hours. Both are dwarf F8 spectral class stars, both containing peculiarities in their spectra.

W UMa has the true separation of 3.6 million kilometres, each with diameters of 2.6 and 1.1 million km, respectively. Luminosities are comparable with the Sun, being 1.3 L⊙ and 0.8 L⊙ times the solar luminosity. Temperatures are 5,920K and 6,140K, with masses of 1.3 M⊙ and 0.76 M⊙. Both stars are highly distorted, surround the whole system with a bright glowing gas, torn either by mass transfer between the stars or from their surfaces. W UMa lies 180 light years or 55 parsecs from the Sun.

(d.) Elliptical (EII) Types or b² Persei Types

Photometrically these stars vary less than 0.1 magnitudes. Changes in brightness are due distorted components and not by mutual eclipses between the stars. This is revealed by the shallow light curves and dependant on surface area of the two stars and the orientation of the binary’s orbit.

Examples of the EII-type include the stars b² Persei and V360 Lacertae.

V360 Lacertae — 14 Lac — 22504+4157

V 360 Lac lies in the northern constellation of Lacerta, near border star of Omicron (ο) Andromeda, surrounded by 13, 15 and 16 Lacertae. Variability of this star is only 0.05 magnitudes in the 5 day period. The star is fairly dim to the naked-eye, having the visual magnitude of only 5.92V. Calculation of the orbital parameters is difficult. It is believed to have an orbital tilt of about 65° above the inclination that would cause mid-eclipses.

Pulsating Variables

A large proportion, some 67% of all known variable stars fall within this group, which are sometimes called intrinsic pulsating variables. The pulsations are produced by the actual expansion and contraction of the entire stellar surface. Some of these variables have pulsations that are as regular as clockwork, while others are either totally irregular, and hence unpredictable, or are semi-regular. Understanding of such variations are important as they describe the internal workings of the star and the energy producing mechanisms that cause the pulsations.

(a.) Cepheids or δ Cephei Variables

Cepheid variable star class is named after the brightest example in the group, Delta (δ) Cephei. Pulsations are due to the movement of an internal shell that lies within the star during the cyclic fashion of expanding and contracting, and cause the highly regular periods of pulsation. First observations to obtain useful light curves was made during 1894. By 1900 several dozen were known. Originally, these variations were attributed to an unseen companion star, but this was later disproved by Harlow Shapley. His investigations lead to the conclusion that the variations were related to the stellar surface discovered by examining the brightness changes, the surface temperature and the radial velocities. Of all known variables, Cepheids make up only 1.2%. Within the group, the period may range between two and one hundred days, varying roughly by between 1.5 to 2.0 magnitudes.

Within normal stars, the gravitational force is pulling the star together, with an exactly counteracting force of the thermal pressure of the gases, pushing the star apart. In most stars these forces remain in balance for long periods. However, at certain times of the history of the star, these forces are placed in direct competition. In fact pulsations for all Cepheids (and others) happen during one of these unstable times, in the same place as the stellar evolution H-R Diagram called an instability strip. Such instability strips are also seen in RR Lyrae variables.

Velocities rates of expansion and contraction can be directly observed by spectroscopy, measuring the radial velocity, or by an observed light curve. (Fig. x) In this figure, the star appears normal for a short time prior to the expansion, at point (1). Suddenly the expansion phase starts (2), which starts to swell the stellar diameter. At phase (2), the observed expansion has been measured at over 300 km.s^-1. At this time the magnitude rises quite rapidly. Luminosity also increases. Eventually, the gravitational force overwhelms the expansion. The Cepheid then stops increasing in size and the contraction or relaxation phase begins (3). The inwards motion takes far longer than the expansion. So far the largest contraction so far measured has the maximum velocity of about 40 km.s.^-1 and some 15% the rate of the expansion. After a time, the star has to return to its usual magnitude, before the cycle begins again.

In 1912, Henrietta Levitt discovered the direct relationship between the luminosity of the star and the period of the pulsations, that pertained to all Cepheids. Stars were also found to physically larger had the longest periods. Direct application of the discovery enabled the first determination of the distance of the Large and Small Magellanic Clouds, and the nearby galaxies such as the Andromeda Galaxy (M31), and out to the distance of about 40 million light years. Due to the high luminosities of Cepheids, they are easily detected against the fainter stars that occupy the observed galaxy. Use of Cepheids for distance determinations today are seen as the major advance in finding the large scale structure and size of the Universe.

Cepheids in size are always much greater in mass than the Sun. Most theories place their mass between 6M⊙ and 8M⊙ solar masses.

Another variety of the Cepheid variable are the W Virginis subtype. These are related to the different population types found in the galaxy. As Population II stars, W Virginis stars are normally located towards the central portions of the galaxy, and appear exclusively in the Globular star clusters.

Amateurs can do very little with these stars, except to check on the ranges of the brightness and the times of maxima or minima. These stars are known to have non-periodic variations, so such checks are of some use. Photoelectric photometry can discover sometimes strange features in the light curves, so advanced amateurs could contribute much to the knowledge of the brighter examples of this class.

Examples of some bright Cepheids include Eta (η) Aquilae, Delta (δ) Cephei, Beta (β) Doradus, R and S Muscae, R, S and T Crucis, V and U Carinae, U Triangulum Austrinius and V Velorum.

(b.) RR Lyrae Types

Another type of the pulsating variables are the RR Lyrae types. These stars are smaller in mass than the Cepheids, and are therefore not as luminous. They stars whose proportionate numbers are about hundred times more common than the Cepheids. Again, the distance of RR Lyrae stars, or an astronomical object it contains, can be related to the period and luminosity. Brightness variations of the period is shorter than Cepheids types, typically between 0.3 and 1 day. All magnitude variations are typically between 0.5 and 1.5 days.

RR Lyrae’s are usually contained in globular star clusters and the surrounding galactic halo. Luminosities of these stars is about twice that of the Sun, all having similar absolute magnitudes of about +0.0. Subclasses RRa, RRb and RRc do exist, but recently the RRa and RRb groups were combined into the RRab class. The subclass have been made to describe the different shapes of the observed light curves.

Examples of bright RR Lyrae Variables include MT Telescopii (RRc), X Arietis (RRab), UV Octanis (RRab), and RR Lyrae (RRab).

(c.) Irregular, Semi-Regular. Mira or Long-Period Variables

This large subclass of pulsating variables are always late spectral type stars, of either K, M or S. Most are in the giant and supergiant category, with the pulsations caused by many different mechanisms. The most likely cause of the pulsations are by the convection of material from near the inner core, to the outer portions of the stellar surface. Some theories have postulated that these stars are not round at all, but more likely resemble jellyfish. The stellar surface is presumed to oscillate in waves across the disk, as the material is convected form the core to the surface. Others state that the pulsations vary irregularly, appearing when the bright star is its smallest diameter. Numbers of variables in this subclass far out weigh any other type.

(c1.) Mira Types or Long Period Variables

Totalling 23% of all known variables, these are the most common. Most Miras have periods between about 100 and 600 days, displaying brightness changes between 2nd and 10th. An existing relationship has been found between the period and star’s size, where the longer the period the larger the stellar disk.

Most Mira variables have highly regular periods which can be predicted within several days of either maximum or minima. Omicron (ο) Ceti, (Mira), naming the subclass, is the classic and brightest example. Mira varies between about 2nd and 10th magnitude whose period oscillations averaging about 332 days. Each cycle varies considerably in the actual magnitude of the maximum and minimum, though the period is about the same. All Miras make excellent objects stars for those new to variable star observing.

Examples of the Mira class include R Horologii, U Orionis, R Carinae, R Centauri, RS Scorpii, R Aquilae, Omicron (ο) Ceti and T Columbae.

(c2.) Semi-Regular Variables or ‘SR’ Varieties

These have periods that vary in both the time of maxima and the amplitude of the light curve. However, various subcategories do exist, depending on the spectral class or nature of variability. the four major ones are named SRa, SRb, SRc and SRd.

SRa : These are usually of the late ‘M’ spectral class, having stable light curves with regular amplitudes. Brightness variations typically have indications of high degree of periodicity. A bright example is T Centauri, near the star 1 Centauri. This star varies between 5.5 and 9.0, over the semi-regular period of 90.44 days. During the cycle, the spectral class varies between K0 and M4 III, showing prominent emission lines.

SRb : This sub-type is also of late spectral classes, except they have weak and poorly defined periodicities and/or amplitudes. A bright example is the naked eye variable star L₂ Puppis, which changes between 2.6v and 6.2v, over average periods of about 140.42 days. This star is orange-red in colour, with the spectral type of M5 III.

SRc : These are supergiants of spectral classes later than ‘M’, revealing semi-regular periods caused by an unknown mechanism. Most show disk components, indicating surface temperatures that changes on different portions of the disk. Bright star Betelgeuse (β Orionis) is the best example, having the average period of 5 years 8 months or (2 070 days) and varying by about 0.9 magnitudes. Another is Antares (β Scorpii). This first magnitude star has the period of 1733 days, varying between about magnitude 0.88V and 1.80V.

SRd : These are giant stars, not too unlike the SRc’s, except that they are of earlier and hotter spectral classes, such as F, G or K. Best example is the orange K2.5 Ib variable BM Scorpii, that varies between 6.8v and 8.7v, in the period of about 850 days.

These major varieties normal lie in the realm of the giant stars. Magnitude variations change between one or two magnitudes with periods somewhere between 30 and 1000 days. They are further complicated by several different periods or modes superimposed on each other on the single light curve. Interpretation is difficult because the combined observations difficult to understand. Amateur observations of semi-regulars would obviously help decipher their natures.

Descriptions of some other bright Semi-Regulars include;
R Doradus (SRb), R Pictoris (SRa), T Centauri (SRa), IS Geminorum (SRd), Theta (θ) Apodis (SRb), BM Scorpii (SRd), and Pi¹ (π) Grucis (SRb).

(c3.) Irregular Variables (L,Lb and Lc)

Irregulars are variable stars that show no true periodicity in their light curves, even though they may vary only between 0.2 and 2 magnitudes. Most majority appear as M-type spectral class or even later. Currently 309 variables of this type are known. Four varieties of irregulars exist, though the distinction between each is poorly described, so it is not commonly used.

The major distinctions are the L, Lb or Lc stars.

La’s are irregulars that have insufficient information to classify.

Lb’s are usually display slow fluctuating brightness, typically giant stars of late spectral class between K and S, whose spectral class and luminosity is unknown or expressed just in its range.

Lc’s are similar to the Lb-types, except that they are characteristically supergiants.

Examples of some bright Irregulars include RX Leporis (Lb), BO Musca (Lb), V412 Centauri (Lb), Tau⁴ (τ⁴) Serpentis (Lb), Beta (β) Grucis, Lambda (λ) Velorum (Lc) and XY Lyrae (Lc). The first magnitude star α Tauri (Aldebaran) is the brightest example in this class, although the variations are only about 0.2 magnitudes. It is expressed as Lb types.

Observations of irregulars and the semi-regulars are sometimes difficult because of their small brightness amplitudes, yet the entire group is considered important to study. All visual estimates are the major reconnaissance for these objects, and are useful in explaining their behaviours. Amateurs are recommended to undertaking observations of this group. They are useful to gain some variable star experience.

(d.) RV Tauri Types

These are normally supergiant stars, typically spectral types F, K or G, exhibiting regular and stable periods, and having fluctuations up to about 3 magnitudes. The light curve usually consists of a double-wave, containing alternating major and secondary minima, of various depths. Often these variations switch between each different mode after each minima. Stellar periods often are between two successive minima, occur between 30 and 150 days. Two sub-categories of the RV’s are the RVa’s and RVb’s.

RVa Are variables have constant mean brightness between each minima. The best example is the variable AC Herculis.

RVb : These have minima WHOSE brightness varies periodically. The example, in which the class is named, is RV Tauri.

The cause of the fluctuations at the present time completely unknown.

(e.) Delta Cephei δ Cep or Delta Canis Majoris Types

All these stars are very similar in nature. Spectrally, they lie in narrow ranges between B0 and B3, each have periods between 0.1 and 0.7 days. Magnitude variations are small, typically between 0.01 and 0.07 magnitudes. Many of the brightest examples are well known stars. I.e. Agena (β Centauri), Mimosa (β Crucis) and Alfirk (β Cephei).

All these stars must be observed using photoelectric photometry because of the size of the fluctuations. Cause of these fluctuations is presently unknown.

(f.) ZZ Ceti Types

ZZ Ceti stars are white dwarf variable stars of the spectral class A or F. The pulsations of these stars are only small, but they do occasionally flare in brightness for several seconds to about one hour. Light curves also display modulations, with several periods superimposed over each other. Each of these different periods are thought to be caused by different mechanisms.

These stars can only be observed photoelectrically, and none are exceptionally bright. Studies into ZZ Ceti’s are important, as they give clues on the end evolutions of stars.

(g.) AI Velorum or Dwarf Cepheid Types

The term Cepheid in these types are now considered to be misleading, as they more relate to the Delta (δ) Scuti types, so AI Velorum is the now preferred designation.

AI Vel types vary over 0.05 to 3 days, with magnitude variations between 0.3 and 0.7 magnitudes. Each have dual modes of magnitude fluctuations, which are very complex in nature. A southern example is the star SX Phoenicis.

Most of these group must be measured with photoelectric photometers.

(h.) Rotating Variable Stars or α² Canes Venaticorum Types

These stars are ones that have strong magnetic fields, thousands of times stronger than our own Sun. Most have been exclusively contain in the A-type spectral classes, and all are thought to be very young stars. Magnetic fields are generally associate with stars that have high rotational velocities, that cause the shape of the star to be distinctly ellipsoidal or oval in shape. Rotational velocities in some cases are in the order of about 180 kilometres per second. (180 km.s^-1)

Light variations are principally caused by ‘starspots’ — precursors of intense magnetic fields. The size of these spots can sometimes be enormous, maybe covering one-third of the entire stellar surface. Starspots are similar to sunspots, produced by cooler areas on the stellar photosphere by as much as 500K to 1 500K, than the normal effective temperature.

Other rotational variables do exist, such as the T Tauri and the RS Canes Venaticorum types. These also show starspot activity, though not to the extent of the α² Canes Venaticorum variables.

Magnitude variations may only reach a maximum variation of 0.05, so these stars can only be observed photoelectrically.

An example of this type is the star BR Crucis (near β Crucis), DO Eri, IM Vel, KU Hya or NY Aug (HD 51418).

(i.) Proto Variables or T-Tauri Stars

These are proto-type stars that are still surrounded by then embryonic nebulosity. They are, in the vast majority, very young stars, typically of low mass, and display spectral classes as either F, G or K. Variability, for these stars, starts immediately the star emerges from the nebulosity. The light fluctuations are typically non-periodic and very erratic. Over time, the star’s magnitude typically slowly increases, as the material is blown by strong stellar winds by the radiating star. This increase has been observed in T-Tauri stars like FU Orionis and V1057 in the constellation of Cygnus.

The T-Tauri class was first coined by A. Joy, who incidentally might be known among amateurs as the discoverer of the faint companion star to the bright variable ο Ceti or Mira. This class later was divided into subclasses, depending on the location of the star and the type of variability. Most of these subclasses have been found to have either rapid rotations or instabilities in their outer atmospheres.

For the T-Tauri’s, magnitude variations are typically 0.5 to 1.0, though in some unusual cases, the variation maybe as high as four magnitudes. Some of these stars have also been observed to flare like their older counterparts, the novae. Similar to some other variable classes, they can only be observed by the professional astronomer, though flare activities have been monitored by amateurs.

Examples of this class include; T Tauri, RW Aurigae, T and YY Orionis.

Last Update : 13th November 2012