Pulsating Variables

Pulsating variables undergo variations in radius due to intrinsic variation of temperature and pressure. They may be strictly periodic, as in RR Lyrae stars or Cepheid variables, or merely cyclic, as in RV Tauri or Mira variables. The period of variation may be very rapid - minutes for some high-temperature variables - to years for the Miras. The General Catalogue of Variable Stars (Kholopov 1985) lists the following types: a Cygni; j3 Cephei; Cepheids; W Virginis; 5 Scuti; Irregular; Mira; PV Telescopii; RR Lyrae; RV Tauri; Semiregular; SX Phoenicis; and ZZ Ceti; most of them have assigned subtypes, which we omit here. Of greatest interest to those outside the variable star community are the RR Lyrae variables, with approximately constant luminosities, and the Cepheids, with luminosities that increase with period. Such stars are considered to be "standard candles," and may be used to determine the distance on any ensemble in which they are found. RR Lyrae stars are giant stars that have periods of about half a day. Cepheids are supergiant stars that have periods from 1 to tens of days. Both are found in the field and in globular clusters, but RR Lyrae stars are much more common. There are two types of Cepheids, the classical Cepheids, members of Population I that are younger and are associated with the galactic plane, and Population II Cepheids, found in the galactic halo and in globular clusters. The realization that there are two types of Cepheids by Walter Baade led to a revised (primarily, extragalactic) distance scale (by a factor of 2). Closely related to the Cepheids and RR Lyrae objects are the 5 Scuti stars (so designated by Harlan J. Smith 1955) and their globular cluster-resident cousins, the SX Phoenicis stars. These are subgiants or dwarfs (luminosity classes IV and V, respectively) that have periods of pulsation that are typically small fractions of a day. All three groups are found in the "instability strip" on the Hertzsprung-Russell diagram (luminosity or absolute magnitude versus spectral type, stellar temperature or color index: basically brightness plotted against color), where no stable stars are found. The Cepheids, being the most luminous, lie uppermost, the RR Lyrae stars below them, and the 5 Scuti stars lie the lowest, straddling and just above the Main Sequence, the locus of all stars powered by the fusion of hydrogen in their cores, where stars spend most of their lives. Pulsating stars display a P«/p relation, that is, the product of the period and the square root of the density is a constant for a particular group of pulsating stars:

where k is a dimensionless constant and G is the gravitational constant. Thus, the shorter period stars are more dense, in accord with their luminosity classes. A pulsating star may be pulsating at its fundamental frequency, but sometimes it pulsates

in the first or even second overtone (like a whistle that is blown too hard). Delta Scuti stars may exhibit pulsations at many periods at the same time; these arise from nonradial pulsation modes, in which some zones of the star are expanding, while others are contracting. Stellar seismometry deals with the many modes of oscillation that can be found in most stars, including the Sun. Of course, in the case of the Sun the oscillations are of very low amplitude (as well as very numerous).

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