Physics 321
Astrophysics II:  Lecture #16
Prof. Dale E. Gary

Pulsating and Variable Stars

Naming Variable Stars

We will study intrinsic variables in this lecture, but variables of all types are lumped into a single naming scheme using capital letters within each constellation until they run out, then numbers, as follows, in order of discovery:
  • R - Z
  • RR, RS, ..., RZ, SS, ST, ..., ZZ               First three give 334 names
  • AA, AB, ..., AZ, BB, BC, ..., QZ
  • V335, V336, ...
  • Some examples, R Monocerotis, T Tauri, RR Lyrae, UV Ceti, AG Pegasi, BF Cygni, V378 Orionis, V999 Sagitarii.  Up to 1925, novae were given a name consisting of constellation and year, but after 1925 they are given variable names. (Why?)  Thus, RR Pic and DQ Her are examples of nova names.  Finally, a few variable stars are bright enough to have been given greek-letter or proper names, e.g. b Lyrae, Algol, Mira, d Cephei (well-known prototypes).

    Some variable star light-curves (from the Hipparchos web pages)

    A Good Place to Read About Variable Stars

    Pulsating Stars

    The most important (i.e. useful) stars are Cepheid variables, named for prototype d Cephei.  They show regular, periodic brightness changes, and spectral changes.

    Observing d Cephei

    The spectral changes show that the surface temperature and radius changes.  The spectral lines also show doppler shifts, from which we can measure radial velocity changes--actually measure the star's outer layers expand and contract.  Cepheids and other variables (RR Lyra stars are another important type) lie in a particular region in HR diagram.  As low mass stars (0.5 to 0.7 Msun) evolve and cross through this region, they become RR Lyrae variables.  As high mass stars (3-18 Msun) cross it, they become Cepheid variables.  Properties:

    RR Lyrae Cepheid
    mass 0.5 - 0.7 Msun    .  mass 3-18 Msun    .
    Pop II Pop I
    Core He burning Core He burning

    Cause of pulsations--lack of hydrostatic equilibrium beneath surface.  Here is the cycle:

    Radius can change by up to 2-3 x 106 km.

    Table of Classes of Pulsating Variable Stars
    (from Zeilik & Gregory--Intoductory Astronomy & Astrophysics)

    Period Range
    d Cephei
    -0.5 to -6
    F6 to K2
    1d to 50d
    5d to 10d
    Population II
    W Virginis
    0 to -3
    F2 to G6
    2d to 45d
    12d to 28d
    RR Lyrae stars
    RR Lyrae
    0.5 to 1
    A2 to F6
    1.5h to 24h
    o Ceti
    1 to -2
    M1 to M6
    130d to 500d
    RV Tauri stars
    RV Tauri
    G, K
    20d to 150d
    Beta Canis
      Majoris stars
    b Canis
    B1, B2
    4h to 6h
    Semiregular red
    a Herculis
    -1 to -3
    K, M, R, N, S
    100d to 200d
    Dwarf Cepheids
    d Scuti
    4 to 2
    A to F
    1h to 3h

    Period-Luminosity Relationship

    Why is any of this useful?  The period of this cycle, from 1 to 50 days for Cepheids, is very precisely related to the luminosity (or absolute magnitude) of the star.  For Pop I Cepheids (the kind in the disk of our galaxy)

    MV = -2.76(log P - 1.0) - 4.16
    Thus, by careful measurement of the period, any Cepheid's absolute magnitude, and hence its distance, can be measured.  Cepheid variables are a major link in the distance scale!  Problems:  Cepheids are rare, and none are nearby.  Before Hipparchos, not a single one could be determined using trigonometric parallax.

    Population II Cepheids

    The Population I Cepheids that we just discussed are stars with relatively high metallicity (like our Sun) and so are "second generation" stars.  Stars in globular clusters are low-metallicity "first generation" stars, and since the composition is different, the period-luminosity relation is also slightly different.  These so-called Population II Cepheids are about 4 times less luminous than Population I Cepheids.

    Measuring the distance to a nearby galaxy.

    First determination that spiral "nebulae" are external galaxies.

    RR Lyrae Variables
    Another important type of variable is RR Lyrae stars.  Their period-luminosity relationship is even simpler--they all have L ~ 100 Lsun, (that is, MV = 0.5 = constant) regardless of period.  They are fainter, and they are Pop II--important for globular clusters, but cannot be seen in external galaxies.  They have relatively short periods of 1.5 - 2.4 h

    Mira Variables
    Large, irregular variations in brightness, due to cool (2000 K) atmosphere veiled by dust and molecules (absorption bands).  Locally higher T dissociates the molecules and allows great increases in L.  Periods are P ~ 100 to 700 days, and stars fall in HR diagram where He-shell burning is taking place.  The exact mechanism is unknown.

    Nonpulsating Variables

    There are several other types of nonpulsating variables:

    Extended Stellar Atmospheres

    Several types of stars show mass outflow.  This outflow, coupled with stellar rotation in some cases, causes distinct spectral features due to doppler shifts.  P-Cygni profile.

    Cataclysmic Variable Stars

    Table of Classes of Cataclysmic Variable Stars
    (from Zeilik & Gregory--Intoductory Astronomy & Astrophysics)

    Energy per
    Outburst (J)
    Mass Ejected
    per Cycle (Mo)
    Velocity of
    Ejection (km/s)
    Mass of
    Star (Mo)
    Supernova I
    < 1
    Supernova II
    GK Per =
    Nova Per
    -8.5 to -9.2
    11 to 13
    106 y ?
    10-5 to 10-3
    500 to 4000
    1 to 5
    DQ Her
    -5.5 to -7.4
    9 to 11
    100 to 1500
    0.02 to 0.3
    T Cr B
    18 to 80 y
    5 x 10-6
    60 to 400
    Dwarf Novae
    U Gem
    SS Cyg
    40 to 100 d

    We will talk about novae and supernovae next time, in connection with close binary systems.  Some links to web pages that describe or give examples of these objects
    are below.

    Nova Cygni 1992

    Dwarf Novae

    Crab Nebula

    Supernova 1987A

    Timing of Events

    Gamma Ray Bursts (Hypernovae?)