Crash Course in Stellar Pulsation

Ryan MaderakA540

April 27, 2005

Mechanisms mechanism

Compression of partial ionization zones -> ionization -> small change in T

T3.5, 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 MSun

Main Sequence roAp = rapidly oscillating Ap stars

P = 5-15 min, multi-periodic, ~50 mmag ~2 MSun

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 = 0.01-0.2 days, 0.003 to 0.9 mag, multi-periodic (up to 12 modes observed)

1.5 – 2.5 Msun, 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

http://users.skynet.be/bho/deltascutis.htm

Main Sequence Slowly Pulsating B Stars (SPB)

P = 1 – 3 days, low amp., multi-periodic

2.5 – 5 Msun, 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 Msun, 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

http://www.aavso.org/vstar/vsots/winter05.shtml

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 Msun

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 Msun, 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 Teff) careful calibration and stellar evolution models needed

Horizontal Branch RR Lyrae

http://www.dur.ac.uk/john.lucey/astrolab/pulsating.html

Horizontal Branch RR Lyrae

RRab: asymmetric light curves, longer periods, higher amp.

RRc: nearly sinusoidal light curves, shorter periods, lower amp.

RRd: bi-periodic RRab’s exhibit a periodic change in

light curve shape and amp. -> “Blazhko” effect

coupling between B and rotation?

Horizontal Branch P-L Relation

http://zebu.uoregon.edu/~soper/MilkyWay/cepheid.html

Horizontal Branch “Classical” Cepheids

P = 1 – 135 days, ~0.01 – 2 mag > 4 – 5 MSun, F at maximum light, G -

K at minimum light stars above 4 – 5 MSun pass through

the instability strip during each of one or more blue loops

for ~4 MSun -> bi-periodic cepheid

Horizontal Branch Classical Cepheid

http://www.astronomynotes.com/ismnotes/s5.htm

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 MSun

cross instability strip in late HB or early AGB evolution

fundamental or 1st harmonic, driven by He II and H/He I zones

instability strip is wider for metal poor stars

AGB W Virginis

http://www.astronomynotes.com/ismnotes/s5.htm

AGB RV Tau

P = 30 – 150 days, 1.5 – 2 mag M = 0.5 – 0.7 MSun, 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 1st 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 Mira’s – 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 Teff = 70000 – 170000, strong C, He,

and O features

Cooling Track DB-type variable WD (DBV)

P = 140 – 1000 seconds, non-radial M ~ 0.6 MSun, Teff = 21500 – 24000 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 Teff -> blue edge of instability

~13000K H rich, with almost no He or metals

Future Work Larger samples of Cepheids and RR Lyrae’s

---> 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.” http://www.sai.msu.su/groups/cluster/gcvs/gcvs/iii/vartype.txt