Lecture 25: Pulsating Stars, Cepheids and RR-Lyrae Stars
Lecture 25: Pulsating Stars, Cepheids and RR-Lyrae Stars
Lecture 25: Pulsating Stars, Cepheids and RR-Lyrae Stars
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<strong>Lecture</strong> <strong>25</strong>: <strong>Pulsating</strong> <strong>Stars</strong>,<strong>Cepheids</strong> <strong>and</strong> <strong>RR</strong>-<strong>Lyrae</strong> <strong>Stars</strong>Sunday, May 1, 2011
Stellar Pulsations &Oscillations• Pulsations can leads to periodic variability in stars,although pulsations in the Sun make only smallchanges in luminosity.• Sun shows over a million modes.• Modes in Sun are excited by convection.• Non-adiabatic effects are needed for largeluminosity changes.Sunday, May 1, 2011
Stellar Oscillations in Red Giantshttp://apod.nasa.gov/apod/ap110408.htmlSunday, May 1, 2011
Stellar Pulsations with <strong>Cepheids</strong>http://www.calstatela.edu/faculty/kaniol/a360/cepheids.htm<strong>Cepheids</strong> pulsate with aperiod between 1 <strong>and</strong> 100days. The pulsation causeschanges in brightness whichcan be easily measured.http://www.konkoly.hu/staff/kollath/gallery.htmlSunday, May 1, 2011
Between 1908 <strong>and</strong> 1912, HenriettaLeavitt discovered a relationshipbetween the period the Cepheid <strong>and</strong>its luminosity.PeriodThis meant that <strong>Cepheids</strong> are a powerful st<strong>and</strong>ard c<strong>and</strong>leSunday, May 1, 2011
What is a well known Cepheid in theSky?Sunday, May 1, 2011
Cepheidvariable starsare veryluminous,making themexcellentst<strong>and</strong>ardC<strong>and</strong>les.Sunday, May 1, 2011
Classical <strong>Cepheids</strong> are Population I Objects found in DisksSunday, May 1, 2011
<strong>Cepheids</strong> as St<strong>and</strong>ard C<strong>and</strong>lesBecause <strong>Cepheids</strong> arebright, they can bedetected in distantgalaxies. As welearned, Hubble used<strong>Cepheids</strong> to obtain thefirst measurements ofthe distances of theM31 <strong>and</strong> M33galaxies.With the Hubble spacetelescope, astronomerscan now measure theperiods of <strong>Cepheids</strong> indistant galaxies.Sunday, May 1, 2011
<strong>RR</strong> <strong>Lyrae</strong> stars are population IIobjects found in globular clustersPiotto et al.2002Less Envelope<strong>RR</strong> <strong>Lyrae</strong> gapMore EnvelopeSunday, May 1, 2011
<strong>RR</strong>-<strong>Lyrae</strong> <strong>Stars</strong> in M3https://www.cfa.harvard.edu/~jhartman/M3_movies.htmlSunday, May 1, 2011
Basic theory ofStellarPulsationsBohm-VintenseSunday, May 1, 2011
Eigenvectors for a constant density starBohm-VintenseSunday, May 1, 2011
Basic theory of Stellar PulsationsSunday, May 1, 2011
Basic theory of Stellar PulsationsSunday, May 1, 2011
Eigenvectors for a star with density gradientBohm-VintenseDensity <strong>and</strong> temperature gradients in star modify the frequencies ofthe overtones. Thus, observing the harmonics provides a probe ofstellar interiors.Sunday, May 1, 2011
The InstabilityStrip<strong>Cepheids</strong> <strong>and</strong> <strong>RR</strong>-Lyrastars appear ininstability stripNote: strip has a smallrelatively range intemperature but alarge range inluminosity.Sunday, May 1, 2011
For a constant temperature, higher luminosity implies aGlarger radius <strong>and</strong> a larger Period<strong>Cepheids</strong>P = periodSunday, May 1, 2011
CepheidPulsationsInitial radii are50-100 RsunRadius can changeby 10 Rsun!!Bohm-VintenseSunday, May 1, 2011
Adiabatic PulsationsThese pulsationswould not causelarge changes inradius orluminosity <strong>and</strong>would dampen asenergy is radiatedinto space.Bohm-VintenseWe need amechanism todrive thepulsations.Sunday, May 1, 2011
Amplified Pulsations in <strong>Cepheids</strong>Highertemperaturesduring outwardmotion lead toamplifiedpulsationsBohm-VintenseSunday, May 1, 2011
Dynamical InstabilitiesHow does this change the pressure of the gas?How does this change the pressure from the surrounding gas?From PrialnikSunday, May 1, 2011
Dynamical InstabilitiesFrom PrialnikPressure from surrounding gas:This pressure decreases since gravity weakens slightly if we exp<strong>and</strong> the star!!Sunday, May 1, 2011
Dynamical InstabilitiesIf γ < 4/3 then the gas pressure will increase fasterthan the pressure from the surrounding gas, leading tofurther expansion.From PrialnikSunday, May 1, 2011
Amplification in <strong>Cepheids</strong>: The κ mechanismAs gas contracts, temperature <strong>and</strong> pressure increase.The causes κ to increase (rising on κ mountain)The result is radiation is trapped, increasing heating.Pressure does not decrease as fast with decreasing density(γ < 4/3)The excess heating drives expansion beyond equilibrium value.Excess heating ends when density <strong>and</strong> temperature push star toother side of κ mountain. At this point, the oscillations may bedampled by the gas radiating heat into space.Sunday, May 1, 2011
The κ MountainBohm-VintenseSunday, May 1, 2011
Amplified Pulsations in <strong>Cepheids</strong>Highertemperaturesduring outwardmotion lead toamplifiedpulsationsBohm-VintenseSunday, May 1, 2011
Amplification in <strong>Cepheids</strong>: IonizationIn adiabatic gas higher density implies higher pressure followingadiabatic law.As ionized gas compresses, the number of particles decreasesdue to recombination.Pressure does not increase as fast with increasing density(γ < 4/3)This is probably a secondary effect.Sunday, May 1, 2011
<strong>RR</strong> <strong>Lyrae</strong>Oscillations<strong>RR</strong> <strong>Lyrae</strong> - solar masspopulation II stars onhorizontal branch.Population I stars duringHelium core burninghave convectiveenvelopes <strong>and</strong> are notsusceptible to <strong>RR</strong>-lyraeoscillationsBohm-VintenseSunday, May 1, 2011
<strong>RR</strong> <strong>Lyrae</strong> models(Christy et al. 1966)TemperatureIonization of HeIIIonization of HeI <strong>and</strong> HISunday, May 1, 2011
Periods of <strong>RR</strong> Lyra <strong>Stars</strong>Fundamental1st HarmonicBohm-VintenseSunday, May 1, 2011
Some <strong>Stars</strong> can only sustain first harmonicSunday, May 1, 2011Bohm-Vintense
Pulsationamplicationstopped bylack ofenvelope (notrapping)Pulsations Amplificationstopped by convectionBohm-VintenseSunday, May 1, 2011
Using Pulsations to DetermineStellar Masses with KeplerThe period relationship gives:The maximum power has been found to equal:Giving:Sunday, May 1, 2011
Pulsation Spectra for Dwarfs <strong>and</strong> SubgiantsSunday, May 1, 2011Chaplin et al. 2011
Pulsations of ~solar mass dwarfs <strong>and</strong> subgiants inKepler field: red dots are sources in previous field.Dotted lines are mass tracks.Δν is spacing between harmonics, equal to fundamentalfrequency. Increased mass leads to lower Δν.Chaplin et al. 2011Sunday, May 1, 2011
Summary<strong>Stars</strong> often show pulsations <strong>and</strong> oscillations. Famous examples areCepheus <strong>and</strong> <strong>RR</strong> <strong>Lyrae</strong> variables, were large pulsations lead tosubstantial change in brightness.These pulsations are a diagnostic of the internal properties of thestars. A common pulsation is an acoustic st<strong>and</strong>ing wave in the star,driven by convection. The period scales as the 1/(density) 0.5Adiabatic oscillations are damped <strong>and</strong> do not create large changesin luminosity.<strong>Cepheids</strong> <strong>and</strong> <strong>RR</strong> <strong>Lyrae</strong> stars are driven by pulsationals instabilitieswhich cause deviations from adiabatic behavior in the gas. They arefound in a narrow instability strip in the HR diagram.Pulsations in subgiants measured by Kepler can give directmeasurements of mass <strong>and</strong> radius.Sunday, May 1, 2011
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