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Crash Course in Stellar Pulsation. Ryan Maderak A540 April 27, 2005. Mechanisms. k mechanism Compression of partial ionization zones -> ionization -> small change in T k ~ r / T 3.5 , increase r -> increase k g mechanism

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crash course in stellar pulsation

Crash Course in Stellar Pulsation

Ryan Maderak

A540

April 27, 2005

mechanisms
Mechanisms
  • k mechanism
    • Compression of partial ionization zones -> ionization -> small change in T
    • k ~ r / T3.5, increase r -> increase k
  • g mechanism
    • Heat flow into partial ionization zone from higher temperature layers
  • So, compression -> higher k -> energy buildup -> energy release -> expansion
mechanisms1
Mechanisms
  • e 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
HR Diagram

Gautschy & Saio, 1995

main sequence
Main Sequence
  • Solar-type stars
    • solar-type oscillations expected
      • more precise photometry needed
    • ~mmag
    • greatest amp. at ~1.5 MSun
main sequence1
Main Sequence
  • roAp = rapidly oscillating Ap stars
    • P = 5-15 min, multi-periodic, ~50 mmag
    • ~2 MSun
    • magnetically modulated rotational splitting
    • overlap with d Scuti instability strip, but excitation mechanism uncertain
      • kg in He II zone suppressed by diffusion of He
      • convection + B ? kg in Si IV zone?
main sequence2
Main Sequence

Gautschy & Saio, 1996

main sequence3
Main Sequence
  • d 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 kg in He II zone
    • amp. limited by coupling between p and g modes
    • “stable” stars observed within d Scuti instability strip
      • suspected to be very low amplitude variables
      • more precise photometry needed
main sequence4
Main Sequence
  • d Scuti

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

main sequence5
Main Sequence
  • Slowly Pulsating B Stars (SPB)
    • P = 1 – 3 days, low amp., multi-periodic
    • 2.5 – 5 Msun, B3 – B8 IV
    • kg driven g-modes
    • can be thought of as an extension of the b Cephei instability to longer periods
main sequence6
Main Sequence
  • b 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 kg in the “z-bump”
    • metalicity dependent pulsational stability
      • b Cep strip extends farther blue-ward for higher metalicity stars
    • b Cep-type variability appears in at least a few cases to be transient
      • Spica exhibited b Cep variability from ~1890 to 1972
main sequence7
Main Sequence
  • bCephei

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

main sequence8
Main Sequence
  • Be stars
    • exhibit photometric and line profile variability with periods of <1 day
    • found within the b Cep/SPB instability region -> “z-bump” driving
  • MS 60 – 120 Msun
    • models suggest e driving from CNO burning
    • e driving may be one of the factors which determines the high mass cutoff of the MS
horizontal branch
Horizontal Branch
  • RR Lyrae
    • P = 0.3 – 1.2 days, 0.2 – 2 mag
    • < 0.75 Msun, A – F, prominent in globular clusters
    • kg 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 branch1
Horizontal Branch
  • RR Lyrae

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

horizontal branch2
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 branch3
Horizontal Branch
  • P-L Relation

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

horizontal branch4
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 branch5
Horizontal Branch
  • Classical Cepheid

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

horizontal branch6
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
slide21
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
slide22
AGB
  • W Virginis

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

slide23
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
slide24
AGB
  • RV Tauri
slide25
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?
slide26
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
slide27
AGB
  • Mira
slide28
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?
slide29
AGB
  • Semi-Regular
planetary nebula
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
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 track1
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
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
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
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