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Pulsating Variables

0. Pulsating Variables. 0. Cepheid Variables. Discovered by J. Goodricke (1784):. Prototype: d Cephei. Light curve of d Cephei. 0. Cepheid Variables: The Period-Luminosity Relation. The variability period P of a Cepheid variable is positively correlated with its luminosity:.

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Pulsating Variables

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  1. 0 Pulsating Variables

  2. 0 Cepheid Variables Discovered by J. Goodricke (1784): Prototype: d Cephei Light curve of d Cephei

  3. 0 Cepheid Variables:The Period-Luminosity Relation The variability period P of a Cepheid variable is positively correlated with its luminosity: MV = -2.80 log10Pd – 1.43

  4. 0 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!

  5. 0 The Instability Strip 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

  6. Stellar Pulsations Estimate from sound travel time through the star: P ~ r-1/2 Cepheids all have approx. the same surface temperature. => Higher L => Larger R => Smaller r => Larger P

  7. 0 Radial Pulsations

  8. 0 The Valve Mechanism Nodal 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

  9. For the valve mechanism to work: k needs to increase with increasing r and T 0 Kramer’s Opacity Law aR ~ r T-7/2 log(aR [cm-1]) Gas fully ionized; opacity dominated by free-free absorption Gas gradually becoming ionized 104 105 106 107 Temperature [K] → Partial Ionization Zones!

  10. 0 Location of Partial Ionization Zones LPVs: Valve mechanism driven by H partial ionization zones ~ 104 K ~ 4x104 K Instability strip: Walve mechanism driven by He partial ionization zones

  11. Non-Radial Modes of Variability: g-modes: fnet = (dF/dV)net = g (rs – rb) bubble (‘b’) surrounding medium (‘s’)

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