In 1941-1942, when Los Angeles was blacked at night during World War II, Walter Baade (1893-1960) was able to push the 100-inch Hooker telescope at Mt. Wilson to its limit, resolving the most luminous stars in the Andromeda Galaxy (M31).  Baade classified the “metal[1] rich,” bluer, brighter stars in M31’s spiral arms as Population I, and he classified the redder, older and somewhat less luminous stars in M31’s nuclear region and in its globular clusters as Population II stars.

RR Lyrae stars belong to Population II and are not classical Cepheid variables.  RR Lyrae stars are old, red giant stars with masses only between 0.5 and 0.8 of the Sun but with radii  ~ 5 times that of the Sun (Sandage, 2000).  They are near the end of their lives burning helium in their cores, producing a luminosity about 50 times that of the Sun.  They are commonly found in galactic nuclei and are numerous in globular clusters.  Cepheid variables on the other hand are massive helium burning stars with extreme luminosities up to 30,000 times that of the Sun.  They are among the most luminous stars known.  However, they are far less common than RR Lyrae stars, making both types of stars important for distance measurements (Sandage, 2000). 

Population I Cepheid variables (true or classical “Cepheids”) are about 1.5 magnitudes more luminous than Population II Cepheids.  The true Cepheids have a heavier metal content and occur in the galactic disk, while the fainter type II Cepheids have similar periods but tend to occur in globular clusters and the galactic halo.  It is important to distinguish between the two types of Cepheid variable stars because of their different intrinsic luminosities.  When the Cepheids were thought to be all the same, the distance estimate to M31 was off by a factor of two; the distance to M31 had been derived by comparing the brighter Population I Cepheids in M31 with the somewhat dimmer Population II Cepheids in the Milky Way (Ferdie, 2004).  After Baade recognized this problem in 1952, he calculated M31 was twice as far away as had been previously thought.  Baade “doubled the size of the Universe” overnight!  The two types of Cepheids are distinguished by their different spectra, their slightly different light curves, and their different characteristic locations.   

“Field” RR Lyrae stars are scattered in the Milky Way halo and disk, and “cluster” RR Lyrae stars are numerous in globular clusters.  The importance of RR Lyrae stars as standard candles is second only to that of Cepheid variable stars.  RR Lyrae stars are less bright, but they are much more common than Cepheids, and they have a very small spread in their luminosities.  Harlow Shapley (1885-1972) first used RR Lyrae stars to establish relative distances to globular clusters in 1915 (Sandage, 2000).  In 1918, he began the first attempt to calibrate the absolute magnitudes[2]of RR Lyrae stars.  Even though their periods vary from 0.25 to 1.2 days and their brightness by 0.2 to 1.8 magnitudes, they all have almost the exact same absolute magnitude.

Shapley used brilliant work by himself and by Ejnar Hertzsprung (1873-1967) with statistical parallaxes[3] to calibrate Leavitt’s period-apparent luminosity curve for the long period classical Cepheids in the Magellanic Clouds.  He then used his estimated absolute magnitudes for the various long period Cepheids to measure the distances to those globular clusters which he felt contained long period Cepheids.  The distances to these globular clusters thereby allowed Shapley to calibrate the RR Lyrae stars in the clusters.  Shapley’s value for the absolute magnitude of all RR Lyrae stars was approximately ~ 0.0.  This turns out to be nearly correct, though it is somewhat of a lucky guess.  Some of Shapley’s assumptions were later found to be erroneous, but they produced mutually canceling effects (Ferdie, 2004; Sandage, 2000).

Calibration of standard candles is critical.  Distances based on standard candles are only as good as the measurements of their absolute magnitudes.  Modern calibration of Cepheids and RR Lyrae stars sometimes use the Baade-Wesselink method of combining light curves and radial velocity[4] curves to determine the radius of a giant star.  According to Jacoby (1992), “…if the mean radius of a Cepheid variable [or RR Lyrae star] can be determined by independent means, then in principle a measurement of the angular size of the Cepheid [or RR Lyrae star] will determine its distance.  Such geometric techniques are referred to as ‘Baade-Wesselink’ methods after Baade (1926) and Wesselink (1946) who first described how the light and color curves could be combined with the integrated radial velocity curve to obtain the mean stellar radius.”   

The Baade-Wesselink method is often combined with parallax measurements to calibrate Cepheids and RR Lyrae stars (Sandage, 2000).  The most accurate and complete collection of parallax measurements are those of the Hipparcos satellite (Hipparcos).  The Hubble Space Telescope (HST) has also been used to obtain parallaxes, and it has studied RR Lyrae and Delta Cephei (Benedict et al., 2001).  The parallax of RR Lyrae is listed as 3.82+/-0.20 milliarcseconds (mas) for the HST parallax and 3.87+/-0.19 mas for a weighed value from HST, ground, and Hipparcos data (Bono et al., 2002).  Thus, knowing fairly well the distance to RR Lyrae (~ 258 parsecs, 842 light years), a good calibration for RR Lyrae and most of its class can be obtained.   Recent published values for the absolute magnitude of RR Lyrae stars based on the above considerations range from Mv 0.6 to Mv 0.77 +/- 0.15 (Popowski, 1993; Fernley, 1998; Solano & Barnes, 1999; Tsujimoto & Yoshii, 1999).

4.  Conclusions 

RR Lyrae stars are common, important variable stars.  They are invaluable for examining the structure and the age of the Milky Way.  They form part of the trio of standard candles along with Cepheid variable stars and type 1a supernovae that allow us to measure the far reaches of the Universe.  RR Lyrae stars are truly marvelous candles.

posted Saturday 18 August 2007

References 

Benedict GF, McArthur BE, Harrison TE, Lee J, Slesnick CL, HST Astrometry Team.  Parallaxes with Hubble Space Telescope II.  AAS DDA Meeting #32, #04.10, November 2001.   

Bono G, Caputo F, Catellani V, Marconi M, Storm J.  On the pulsation parallax of the variable star RR Lyr.  MNRAS 2002; 332, Issue 4: L78-L80.   

Encyclopedia of Astronomy and Astrophysics (EAA) web site at:  http://www.ency-astro.com/eaa/subscriber/index.asp?sessionid=7b26767b180fd2b7 

Dibon-Smith R. Constellation Web Page at:  http://www.dibonsmith.com/lyr_rr.htm. 1999-2000. 

Fernley J, Barnes TG, Skillen I, et al. The absolute magnitude of RR Lyraes from Hipparcos parallaxes and proper motions. AA 1998; 330: 515-520.   

Ferdie RD, Hunter TB, McGaha J. Finding our place in the Universe.  Web essay at:  http://www.3towers.com/OurPlace.htm.  December, 2004.  

Hipparcos web site at:  http://www.rssd.esa.int/Hipparcos/

Jacoby G.  Web essay at: http://nedwww.ipac.caltech.edu/level5/Jacoby/Jacoby_contents.html. 1992.

Moore, Sir Patrick, General Editor.  Oxford Astronomy Encyclopedia, Oxford University Press, 2002, New York, pages 348-349. 

The Milky Way Galaxy web essay at: http://www.earth.uni.edu/~morgan/astro/course/Notes/section3/new11.html.

Popowski PA.  RR Lyrae stars as distance indicators.  Thesis (PHD). The Ohio State University, February 1999, 133 pages. 

Sandage A.  RR Lyrae.  Encyclopedia of Astronomy and Astrophysics (EAA) web site at: http://eaa.iop.org/full/eaa-pdf/eaa/1868.html.  November 2000.

Solano E, Barnes TG. The absolute magnitude of RR Lyrae: from Hipparcos parallaxes and proper motions.  ASP Conference Series; 1999, volume 167: 316-319.

Tsujimoto T, Yoshii Y. The absolute magnitude of RR Lyrae stars derived from the Hipparcos catalog.  ASP Conference Series; 1999, volume 167: 332-335.

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