Variable Stars

by Bob Nelson, Ph.D.

To the ancient astronomers, the stars were considered to be constant and unchanging. Over the years, however, more and more stars have been found to vary in brightness. The first variable stars to be discovered were the novae (meaning “new”). These are stars which suddenly brighten for a time and then fade; most of the early ones were discovered by Chinese astronomers. Novae 1054, the source of M1, the Crab Nebula is the most famous. N1572, or “Tycho’s Star” was carefully observed by the great Danish astronomer Tycho Brahe, who discovered no parallax (daily or yearly), therefore the object was not atmospheric, or nearby celestial in origin. Celestial objects (other than the planets) did vary.

The earliest catalogue of variable stars (Pigott, 1786) contained 12 confirmed entries (4 were novae), and 39 suspected variables. This did not include the 130 other novae that had been detected by that time. Surprisingly, by the year 1900, the total number discovered had only increased to 161. However, by 1975 the total had more than doubled, rising to 340 novae.

The first variable other than a nova to be discovered was Omicron Ceti (Mira), by the Dutch astronomer David Fabricus in 1596. Since then, it has been monitored often enough that not a single maximum has been missed. (Data: Max 2.0m, Min 10.1m, P = 332 d – average) A pulsating star, it is the prototype of a large number of variables (called the “long period variables” or Miras).

The next variable other than a nova to be discovered was Beta Persei (Algol), by the Italian astronomer Geminiano Montanari in 1667. (Data: Max 2.12m, Min 3.40m, P = 2.87d) It was not until 1782 that John Goodriche suggested its true nature – that it is a (partially) eclipsing binary. It too is the prototype of a large number of variables.

A number of other variables were discovered before 1900 (mostly by chance) but it was the advent of photographic searches – and devices to compare plates (negatives of the sky) – which yielded the discovery of the thousands of variables (about 28,000) which are known today.

Good charts are essential for variable star work. In 1843, the Uranometria Nova was published by F.W. Argelander, and in 1859, the famous Bonner Durchmusterung (BD) Catalogues were published.

Careful brightness measurements are also essential. The first step, a magnitude scale, was made by the Greek astronomer Hipparchus in 127 AD. The brightest stars in the sky he called 1st mag, and the dimmest stars visible to the human eye, 6th magnitude. This scale was refined by John Herschel (1828) and Pogson (1850) who noted that one magnitude step corresponds to a constant ratio and that 5 magnitudes are a factor of 100. The following formula is used:

m2 – m1 = 2.5 (Log I1 – Log I2)

where m1 and m2 are the magnitudes of star 1 and 2 resp. and I1 and I2 are the actual intensities of stars 1 and 2 resp.

But how would one determine a star’s brightness visually? The step method (where one brackets a star by a dimmer and a brighter comparison and then estimates the intervals) was suggested by J. Herschel and later refined by Argelander. Observations were started by J. Herschel, and Argelander made some 15,000 visual brightness estimates. Work by several observers continued into the 1900s.

Accurate determinations of magnitude sequences (of standard stars) were needed to put the brightnesses on a firm footing. Various optical/mechanical photometers were constructed and the Harvard Revised (HR) Catalog for 9110 stars to 6.5 mag published in 1908. Magnitudes for 36,682 fainter stars, covering the entire sky, were published in other volumes. The advent of the photomultiplier in World War II led to a more sensitive electric photometer. In 1952, Johnson and Morgan established the UBV scale (U = Ultraviolet, B = Blue, and V = Visual) with accurate (+/- 0.01 mag) standard stars spaced all across the sky and across a wide magnitude range. Although better scales have since been invented, the UBV system is still the most widely used today.

With the many discoveries of variable stars, there quickly came to be far more work to do than there were professional astronomers available. It was Argelander, around the turn of the century, who suggested that amateurs might like to contribute observations to the study of variable stars. This led to the creation of the British Astronomical Association (BAA) in 1890, the American Association of Variable Star Observers (AAVSO) in 1911 and others.

The task of the AAVSO is to encourage and instruct observers, to select stars of interest, to provide standard charts with appropriate standard (comparison) stars covering the range of brightnesses, to collect, collate and archive the data, and to make it available to professional astronomers. Today, the AAVSO has over 500 active observers (one of whom sends in over 12,000 estimates per year!), almost 1000 programmes in many types of variables (Myras, Classical Cepheids, RR Lyrae, RV Tauri, U Geminorum, UV Ceti, eclipsing stars – all visual), a novae and supernovae search group, plus a growing photoelectric section.

Several requests for data are received each month at AAVSO Headquarters from professional astronomers; over the years, the number of requests for data has steadily increased. One important reason is that astronomers studying eruptive variables either at large ground-based observatories or from orbiting observatories need to be able to plan their observations. Another reason is that astronomers still are not able to explain in detail certain variable stars; it still remains true that most of our knowledge on long period variables comes from amateur observations.

The association also publishes periodically monographs on selected stars. All the current and archived data (over 5.5 million observations in all) are being converted to electronic form for easier access to astronomers now and in the future.

The many professional astronomers publish their data and analyses in the usual journals; data are also stored in other archiving centres, again for future generations of astronomers.


  1.  Proper names (eg Mira, Betelgeuse, Polaris), Greek letter designation (Delta Cephei, Rho Cassiopeiae, Chi Cygni)
    These are retained
  2. One or Two letter designation followed by constellation (Argelander):
    • R, S, T, U, V, W, X, Y, Z
    • RR, RS, RT, RU, RV, RW, RX, RY, RZ
    •  SS, ST, SU, SV, SW, SX, SY, SZ
    • TT, … … … … … …
    • … … … … … …
    • … … … … …
    •  … … … …
    • … … …
    • … …
    • ZZ
    • AA, AB, AC, … … … … … … … … … … … … AZ
    • BB, BC, … … … … … … … … … … … … BZ
    • … … … [J is omitted]
    • QQ, … … … … … … … … QZ
    • These give 334 combinations in all.
    • Examples: R LMi, S Cyg, T Her, V Aur, Y Per, Z Cyg, SS Cyg, TV Her, WX Cyg
  3. V followed by a number and constellation
  • Examples: V728 Her, V969 Oph


  • The brightness is plotted versus time (light curve).
  • If regular, the time for one cycle is the period.
  • Periods may be anywhere from minutes to years.
  • The brightest part of the curve is the maximum; the dimmest, the minimum.
  • The difference between the minimum and maximum is the amplitude.
  • Amplitudes may vary from 0.01 to 14 magnitudes.
  • Many variables are irregular or semiregular, and there is no unique period or amplitude.


  1.  Eruptive – show sudden, unpredictable outbursts of light.
    1. Supernovae
      • Giant star blows off outer layers.
      • Chinese observed SN 1006, 1054, 1181 AD.
      • Tycho observed SN 1572, Kepler observed SN 1604 (V843 Oph).
      • estimated 25-100/year in our gal. not observed by telescope
      • Type I (old, population II stars) – max mag: -20 (abs).
      • Type II (newer, population I stars) – max mag: -15 (abs).
      • The two light curves are distinctly different.
    2. Novae
      • binaries with white dwarf and extended (giant) star
      • Extended star periodically dumps material onto white dwarf, the latter flares up.
      • brightness rise: 7 to 16 mags over several days
      • fades to minimum over years or decades
      • Eta Carinae (1843), T CrB (1866), GK Per (1901), DQ Her (1934), V1500 Cyg (1975)
    3. Dwarf novae
      • same as above but recurring (are all novae recurring?)
      • binaries with K to M subgiant with white dwarf
      • quiescent with periodic outbursts of 2-6 mag at intervals of 10 days to several years
      • Outbursts last several days.
      • U Sco (1863, 1906, 1936)
      • T Pyx (1890, 1902, 1920, 1944, 1966)
      • RX Oph (1898, 1933)
      • SS Cyg (per 20 – 90 days, amplitude 3-4 mag)
      • U Gem, SS Aur (shorter time scale)
      • Z Cam are similar (may be quiescent for long periods).
    4. FU Orionis
      • nova-like variables of spectral type A to F
      • exhibit occasional flareups (to 6 mag) lasting for decades
    5. Nova-like
      • Spectrum or light variations resemble that of novae.
      • MAY become novae sometime in the future.
      • R Aqr, Z And, BF Cyg
    6. S Doradus
      • very young and very massive, spectral types B to F
      • very bright (to -10 abs mag)
      • brightness variations of 1 to 3 mags
      • They periodically blow off outer layers at high speed.
      • They often exhibit P Cyg spectral lines
      • broad emission with sharp absorption at shorter wavelengths.
    7. T Tauri
      • very young stars, intermediate mass, just entering main sequence (Sp type A – K?)
      • Light is near constant most of the time but is occasionally dimmed suddenly by 0.5 to 1 mag (hours to days).
      • Dimming is thought to be circumstellar dust.
    8. R Coronae Borealis
      • Highly luminous, spectral types F, G, K, R
      • Sim to above, but sudden drop in light is 1 to 9 mags.
      • Dimming is caused by carbon dust (soot!).
      • Recovery is in 10s to 100s of days.
    9. Flare stars
      • red dwarfs which show extremely fast outbursts of up to several magnitudes in 1 or 2 minutes(!)
      • UV Ceti, DO Cephei, Alpha Centauri C
  2. Pulsating – periodically expand and contract, pulsating in size, temperature, and luminosity
    1. Long Period Variables (“Miras”)
      • most common type of variable
      • periods from 80 to 1000 days, not abs. constant
      • amplitudes greater than 2.5 mag (average 5 mag)
      • giant stars with M-, C-, or S- type spectra
      • Chi Cyg, R Leo, R Hyd, T Her, TV Her, RS Aur, Z Cyg
    2. Semi-regular and Irregular
      • mostly red giants with poorly defined or no periods
      • Alpha Her, Rho Per (Semi Regular); Betelgeuse, Mu Cep (Irregular)
    3. Cepheids
      • relatively rare (700 known)
      • important for the distance scale
      • spectral types F, G, K
      • periods from 1 to 70 days
      • amplitudes between 0.1 and 2 mag
      • absolute magnitude (median) -1.5 to -5 (highly luminous)
      • period-luminosity relation – measure period, then read absolute magnitude
      • Type I Cepheids (Delta Cephei, Polaris, Eta Aql)
      • Type II Cepheids (W Vir) – diff. period-luminosity rel
    4. RR Lyrae (“Cluster variables”)
      • among the most common (4500 in Milky Way Galaxy)
      • common in globular clusters (Population II – metal poor)
      • A to F giants, 100 times more luminous than the sun
      • Periods vary from 0.2 to 1.2 days.
      • Amplitudes are less than 2 magnitudes.
    5. RV Tauri
      • Pulsating supergiants of spectral type F to KExhibit alternate shallow and deep minima (occasionally confused with eclipsing binaries)
      • Periods vary from 30 to 150 days.
      • Amplitudes vary from 3 to 4 mags.
    6. Delta Scuti
      • spectral types A2 to F5
      • periods 0.02 to 0.4 days, amplitude 0.003 to 0.04 mag
      • Light curves are highly variable.
      • Many are on (or near) the main sequence.
    7. ZZ Ceti
      • non-radially pulsating white dwarfs
      • periods 30 sec to 25 min, amplitude less than 0.2 mag
    8. Z And (symbiotic stars)
      • close binaries with cool giant and hot companion
      • Variation is caused by a combination of the cool giant’s pulsation plus an interaction (mass interchange?).
      • Double system is often enclosed in nebulosity.
  3. Eclipsing – binary stars whose orbit is nearly edge-on and that periodically eclipse one another. Binaries may be detached (separate), semi-detached (one star fills the Roche lobe), or contact (both do).
    1. Algol type
      • Components are spherical, well separated (detached).
      • Light curve is flat between eclipses.
      • U Cep, U Sag
    2. Beta Lyrae
      • gravitationally distorted, ellipsoidal components
      • spectral types O, B, or A
      • amplitude less than 2 mag, periods greater than 1 day
    3. W Ursae Majoris
      • highly distorted dwarf components, type F, G, or K
      • exhibit continuously changing light curves
      • amplitudes less than 1 mag, periods less than 1 day
      • contact binaries


JAAVSO vol 15, #2 (75th Anniversary Ed), pp 77 – 95, and elsewhere

Abell, Morrison, & Wolff, Exploration of the Universe pp 435-7, 542-7

Sky Catalogue 2000.0, pages xvii to xx

Burnham’s Celestial Handbook, p 88-91, and elsewhere

Petit, M., Variable Stars, 1982 (John Wiley & Sons, New York)

Hoffmeister, C., Richter, G., & Wenzel, W., Variable Stars, 1985 (Springer-Verlag, New York)

Sterken, C. & Jaschken, C., Light Curves of Variable Stars, 1996 (Cambridge U. Press, N.Y.)