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RR Lyrae Stars – marvelous candles 

By Tim Hunter

 

1. Introduction – a house of cards, measuring astronomical distances

We find our place in the Universe by using overlapping “yardsticks” to measure astronomical distances near and far.  However, these yardsticks resemble a "house of cards."  They are all based upon the preceding yardstick, and they are ultimately founded on having precise parallax measurements for the nearest objects.  Parallax methods can directly measure the distance of objects “close” to the Earth, including Solar System objects and the nearest stars out to 300 + light years (Hipparcos).  Parallax measurements then support the use of stellar “standard candles” (Cepheid variable stars and RR Lyrae stars) on the next rung of the ladder for estimating more distant Milky Way objects and for measuring close by galaxies.  Finally, very distant yardsticks (type 1a supernovae, spiral galaxy surface brightness fluctuations, and red shift determinations) are used for examining remote galaxy clusters and quasars (see Ferdie et al., 2004).   This house of cards technique of overlapping distance scales means we can take a ruler to the Universe, but it is fraught with uncertainty, and the errors add up as we extend our measurements to greater and greater distances.  Figure one and table one summarize these overlapping yardsticks: 

 

Distance Yardsticks

Figure one.  Overlapping yardsticks for measuring the Universe.  From Ferdie, 2004. 

 

Table 1 – The Distance Ladder

The series of techniques employed to obtain distances to progressively more remote astronomical objects.

Object

Distance (pc)

Method

Sun, Solar System

10-6

Radar, Orbits

Alpha Centari

1

parallax

Hyades Cluster

40

Hipparcos parallax

Galaxy

104

Cepheids, Main Sequence Fitting

Andromeda

105

Cepheids, Supernovae, OB stars

Virgo Cluster

107

HST Cepheids, OB stars, Supernovae

Beyond

108 and up

Brightest Galaxies, Tully-Fisher

 

 

2.  Standard Candles

Standard candles are the next rung on the distance ladder after parallax measurements.    At this point, we leave direct measurement techniques and begin to extend our distance scale to millions of light years using indirect techniques.  Standard candles represent any astronomical object with a consistent, well known intrinsic luminosity.  The observed brightness of a standard candle in the Milky Way or in another galaxy can be compared with its known intrinsic brightness to estimate its distance.  Cepheid variable stars, RR Lyrae stars, and type Ia supernovae are the classic standard candles, though there are several other objects or techniques that can be used as standard candles as shown in figure one and Table 1. 

Cepheid variable stars are named for Delta Cephei, their prototype.  They are giant variable stars whose individual periods can be directly correlated with their intrinsic luminosities.  The longer the period, the greater the star’s luminosity.  This period-luminosity relationship was discovered by Henrietta Leavitt (1868-1921) in 1912.  It has been well established, and these stars are the most important stellar candles for short and intermediate astronomical distances out to 50-100 million light years.  Type 1a supernovae are a particular type of supernova with a characteristic spectrum and light curve.  Their peak luminosities are almost exactly the same, and they can be used as standard candles for measuring the most distant reaches of the Universe.  This essay examines the use of RR Lyrae stars as standard candles.  Their importance for measuring distances within the Milky Way and nearby galaxies is second only to that of Cepheid variable stars, and they provide a complementary cross check for Cepheid distance measurements.

 

3.  RR Lyrae Stars 

The prototype for this class of stars, RR Lyrae (also known as RR Lyra), was discovered to be a short period variable star by Williamina Fleming (1857-1911) at Harvard in 1899.  She noted its changing brightness on photographic plates taken over a period of several days.  It was also noted to have a period nearly the same as a large number of similar such stars found in globular clusters by Solon Bailey (1854-1931) in 1893 ( Moore, 2002).  RR Lyrae itself was at first thought to have escaped from a globular cluster, but later other RR Lyrae like stars were found as isolated stars apart from the many RR Lyrae stars associated with globular clusters (Moore, 2002).  RR Lyrae has a period of 13 hours and 36 minutes.  It varies from magnitude 7.1 to 8.1.  Figure 2A shows RR Lyrae’s location with respect to the constellation Lyra.  Figure 3 compares the periods of Cepheid and RR Lyrae stars.  Figure 4 shows a typical period of a Cepheid variable star, and figure 5 shows a typical period for a RR Lyrae variable star. 

 

RR Lyrae and environs

Figure 2A.  RR Lyrae and environs.  From: http://www.exn.ca/Stories/1998/06/22/55.asp

 

RR Lyrae

Figure 2B.  Close-up view of RR Lyrae (arrow pointing upward) and nearby stars.  North is at the top and East is to the left.  The central star marked with the arrow pointing to the right has a magnitude of ~ 8.8.  The star marked with the arrow pointing to the left has a magnitude of 7.2.  Ninety-second exposure with Canon 20Da digital camera using an 85 mm f/3.5 lens, ISO 800.  Image courtesy James McGaha.

 

Figure 3. Comparison of Cepheid and RR Lyrae stars. 

 

Cepheid Variable Stars

Figure 4.  Typical light curve for a Type I (Classical) Cepheid variable star.

 

RR Lyrae light curve

Figure 5. Typical light curve for a RR Lyrae variable star. 

 

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