Pulsating Variables

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Pulsating Variables
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Cepheid Variables
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Discovered by J. Goodricke (1784)
Prototype d Cephei
Light curve of d Cephei
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Cepheid VariablesThe Period-Luminosity Relation
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The variability period P of a Cepheid variable is
positively correlated with its luminosity
MV -2.80 log10Pd 1.43
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Cepheid Variablesas Distance Indicators
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• Measuring a Cepheids period
• determine its absolute magnitude
• Distance indicator!

Cepheids are Ib supergiants, L 103 - 4 L0
gt Identifiable out to several Mpc!
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The Instability Strip
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Classical Cepheids
W Virginis Stars metal-deficient (Pop. II),
Cepheid-like
Increasing Period
RR Lyrae Stars Pop. II horizontal-branch
nearly standard-candle luminosity!
d Scuti Stars Evolved F stars near MS
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Stellar Pulsations
Estimate from sound travel time through the star
P r-1/2
Cepheids all have approx. the same surface
temperature. gt Higher L gt Larger R gt Smaller
r gt Larger P
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Radial Pulsations
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The Valve Mechanism
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Nodal zone is opaque and absorbs more radiative
flux than necessary to balance the weight from
higher layers. gt Expansion
Upon expansion, nodal zone becomes more
transparent, absorbs less radiative flux gt
weight from higher layers pushes it back inward.
gt Contraction.
Upon compession, nodal zone becomes more opaque
again, absorbs more radiative flux than needed
for equilibrium gt Expansion
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For the valve mechanism to work k needs to
increase with increasing r and T
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Kramers Opacity Law
aR r T-7/2
log(aR cm-1)
Gas fully ionized opacity dominated by free-free
absorption
Gas gradually becoming ionized
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105
106
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Temperature K
? Partial Ionization Zones!
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Location of Partial Ionization Zones
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LPVs Valve mechanism driven by H partial
ionization zones
104 K
4x104 K
Instability strip Walve mechanism driven by He
partial ionization zones
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Non-Radial Modes of Variability
g-modes
fnet (dF/dV)net g (rs rb)
bubble (b)
surrounding medium (s)