Crash Course in Stellar Pulsation Ryan Maderak A540 April 27, 2005

Mechanisms mechanism Compression of partial ionization zones -> ionization -> small change in T T 3.5, increase -> increase mechanism Heat flow into partial ionization zone from higher temperature layers So, compression -> higher -> energy buildup -> energy release -> expansion

Mechanisms mechanism Compression -> higher T -> higher energy production rate -> expansion stochastic excitation convective turbulence -> acoustic noise -> solar- type oscillations oscillatory convection convective + g-mode in rotating stars -> oscillatory modes tidal interaction periodic fluid motion -> non-radial modes

HR Diagram Gautschy & Saio, 1995

Main Sequence Solar-type stars solar-type oscillations expected more precise photometry needed ~ mag greatest amp. at ~1.5 M Sun

Main Sequence roAp = rapidly oscillating Ap stars P = 5-15 min, multi-periodic, ~50 mmag ~2 M Sun magnetically modulated rotational splitting overlap with Scuti instability strip, but excitation mechanism uncertain in He II zone suppressed by diffusion of He convection + B ? in Si IV zone?

Main Sequence Gautschy & Saio, 1996

Main Sequence Scuti P = days, to 0.9 mag, multi- periodic (up to 12 modes observed) 1.5 – 2.5 M sun, A0 – F5 IV - V, disk population non-radial p-modes, driven by in He II zone amp. limited by coupling between p and g modes stable stars observed within Scuti instability strip suspected to be very low amplitude variables more precise photometry needed

Main Sequence Scuti

Main Sequence Slowly Pulsating B Stars (SPB) P = 1 – 3 days, low amp., multi-periodic 2.5 – 5 M sun, B3 – B8 IV driven g-modes can be thought of as an extension of the Cephei instability to longer periods

Main Sequence Cephei P = 0.1 – 0.6 days, 0.01 – 0.3 mag majority multi-periodic, a few non-radial 7 – 8 M sun, O8 – O6 p-modes, driven by in the z-bump metalicity dependent pulsational stability Cep strip extends farther blue-ward for higher metalicity stars Cep-type variability appears in at least a few cases to be transient Spica exhibited Cep variability from ~1890 to 1972

Main Sequence Cephei

Main Sequence Be stars exhibit photometric and line profile variability with periods of <1 day found within the Cep/SPB instability region -> z-bump driving MS 60 – 120 M sun models suggest driving from CNO burning driving may be one of the factors which determines the high mass cutoff of the MS

Horizontal Branch RR Lyrae P = 0.3 – 1.2 days, 0.2 – 2 mag < 0.75 M sun, A – F, prominent in globular clusters driven, but convective flux is thought to be important important standard candles for clusters, but the P- L relationship is metalicity dependent the period decreases as cluster metalicity increases (for fixed T eff ) careful calibration and stellar evolution models needed

Horizontal Branch RR Lyrae

Horizontal Branch RR Lyrae RRab: asymmetric light curves, longer periods, higher amp. RRc: nearly sinusoidal light curves, shorter periods, lower amp. RRd: bi-periodic RRabs exhibit a periodic change in light curve shape and amp. -> Blazhko effect coupling between B and rotation?

Horizontal Branch P-L Relation Way/cepheid.html

Horizontal Branch Classical Cepheids P = 1 – 135 days, ~0.01 – 2 mag > 4 – 5 M Sun, F at maximum light, G - K at minimum light stars above 4 – 5 M Sun pass through the instability strip during each of one or more blue loops for ~4 M Sun -> bi-periodic cepheid

Horizontal Branch Classical Cepheid

Horizontal Branch Classical Cepheids masses from evolution versus pulsation theories did not agree historically, but improved opacities solved the problem but pulsational models using the improved values give periods that are metalicity dependent careful abundance measurements are needed to use the P-L relationship accurately

AGB W Virginis (Population II Cepheids) P = 0.8 – 35 days, 0.3 – 1.2 mag M ~ 0.5 M Sun cross instability strip in late HB or early AGB evolution fundamental or 1 st harmonic, driven by He II and H/He I zones instability strip is wider for metal poor stars

AGB W Virginis

AGB RV Tau P = 30 – 150 days, 1.5 – 2 mag M = 0.5 – 0.7 M Sun, F – G at maximum light, K – M at minimum light driven by H and He I zones characteristic double peak pattern resonances between fundamental and 1 st harmonic chaotic motion of multiple atmospheric layers low-dimensional chaotic attractors

AGB RV Tauri

AGB RV Tau various irregularities change in depth of primary and secondary minima changes in period relatively few known ~130 (GCVS) duration of phase only ~500yr believed to be post-AGB/proto-planetary have experienced significant mass loss RVb: long term (600 – 1500 day) variation in mean brightness eclipsing binary? episodic mass loss? dust shell eclipse?

AGB Mira P = 80 – 1000 days, 2.5 – 11 mag low-mass, Me – Se First variable discovered: 1595 fundamental, driven by H and He I zones coupling between pulsation and convection

AGB Mira

AGB Semi-Regular P = 20 – 2000+, ~0.01 – 2 mag, multi-periodic occupy same part of HR diagram as Miras – physically similar distinguished by amplitude difference due to mass, composition, age SRb: power spectra exhibit broadened mode- envelopes stochastic excitation?

AGB Semi-Regular

Planetary Nebula PG1159 (variable planetary nebula nuclei = PNNV) P = 7 – 30 min g-modes, driven by C and/or O K-shell ionization T eff = – , strong C, He, and O features

Cooling Track DB-type variable WD (DBV) P = 140 – 1000 seconds, non-radial M ~ 0.6 M Sun, T eff = – g-modes, driven by He II zone complicated power spectra need high time resolution and long data sets to resolve peaks -> WET

Cooling Track ZZ Ceti (DA-type variable WD) Similar to DBV g-modes may be driven by ionization of a surface H layer lower T eff -> blue edge of instability ~13000K H rich, with almost no He or metals

Future Work Larger samples of Cepheids and RR Lyraes -- -> more accurate determination of metalicity dependence of P-L Continued high time resolution, long duration astroseismology -> better understanding of interior structure and excitation mechanisms Better theory of convection -> better understanding of coupling between convection and pulsation

References Carrol, B.W., & Ostlie, D.A. 1996, An Introduction to Modern Astrophysics, Addison-Wesley, Reading, MA. Gautschy, A., & Saio, H. 1995, ARA&A, 34, 551. Gautschy, A., & Saio, H. 1996, ARA&A, 33, 75. GCVS Variability Types. cvs/iii/vartype.txt