Pulsating Variables

Cepheid VariablesDiscovered by J. Goodricke (1784):

Prototype:

Cephei

Light curve of Cephei

Cepheid Variables:The Period-Luminosity Relation

The variability period of a Cepheid variable is positively correlated with its luminosity:

MV = -2.80 log10d – 1.43

Cepheid Variablesas Distance Indicators

Measuring a Cepheid’s period

determine its absolute magnitude

Distance indicator!

Cepheids are Ib supergiants, L ~ 103 - 4 L0

=> Identifiable out to several Mpc!

The Instability StripClassical Cepheids

W Virginis Stars: metal-deficient

(Pop. II), Cepheid-like

RR Lyrae Stars: Pop. II; horizontal-branch;

nearly standard-candle luminosity!

Scuti Stars: Evolved F stars

near MS

Increasing Period

Stellar Pulsations

Estimate from sound travel time through the star:

-1/2

Cepheids all have approx. the same surface

temperature.

=> Higher L => Larger R => Smaller => Larger

Radial Pulsations

The Valve MechanismNodal zone is opaque and absorbs more radiative flux than necessary to balance

the weight from higher layers. => Expansion

Upon expansion, nodal zone becomes more transparent, absorbs less radiative flux => weight from higher layers pushes it back inward. => Contraction.

Upon compession, nodal zone becomes more opaque again, absorbs more radiative flux than needed for equilibrium => Expansion

Temperature [K]

log

R [

cm-1])

R ~ T-7/2

Kramer’s Opacity Law

104 105 106 107

Gas gradually becoming

ionized

Gas fully ionized; opacity dominated

by free-free absorption

For the valve mechanism to work:

needs to increase with increasing and T

→ Partial Ionization Zones!

Location of Partial Ionization Zones

~ 104 K

~ 4x104 K

Instability strip:

Walve mechanism driven by He partial ionization zones

LPVs:

Valve mechanism driven by H partial ionization zones

Non-Radial Modes of Variability:g-modes:

fnet = (dF/dV)net = g (s – b)

surrounding medium (‘s’)

bubble (‘b’)