DOCSLIB.ORG

Session 3A: STARS Convection

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Session 3A: STARS Convection Session 3A:STARS Convection Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds. Modelingstochasticexcitationofacousticmodes in stars: presentstatus andperspectives R. Samadi1,K.Belkacem1,M.-J.Goupil1,H.-G.Ludwig2 ,and M.-A.Dupret1 1 Observatoire de Paris, LESIA, CNRS UMR8109, 92195 Meudon, France 2 Observatoire de Paris, GEPI,CNRSUMR 8111, 92195 Meudon, France Abstract Solar-likeoscillations have nowbeen detected formorethanten yearsand theirfrequencies measuredfor astill growingnumberofstars with variouscharacteristics (e.g. mass, chemical composition,evolutionarystage ...).Excitationofsuch oscillations is attributed to turbu- lent convection andtakes placeinthe uppermost part of the convective envelope. Since the pioneering work of Goldreich&Keely(1977),moresophisticated theoreticalmodelsof stochastic excitation were developed,which differfromeachotherbothbythe wayturbulent convection is modeled andbythe assumedsources of excitation. We briefly review herethe different underlyingapproximations andassumptionsofthosemodels. Asecond part showS thatcomputed mode excitation rates crucially depend on the waytime-correlations between eddies aredescribed but alsoonthe surfacemetalabundance of the star. IndividualObjects: Sun, α Cen A, HD 49933 Introduction Solar p-modes areknown to have finitelifetimes(afew days)and averylow amplitude(afew cm/s in velocity andafewppm in brightness).Inthe lastdecade, solar-likeoscillations have been detected in numerouSStars, in different evolutionarystages andwithdifferent metallicity (see recent review by Bedding &Kjeldsen, 2007).Theirfinite lifetimesare aconsequence of severalcomplex dampingprocessesthatare notclearly identifiedsofar.TheirexcitationiS attributed to turbulent convection andtakes placeinthe uppermost part of the convective envelope, whichisthe placeofvigorousturbulent motions. Measuringthe mode amplitudeand the mode lifetime enables to inferthe excitation rate, P (the energy whichiSSuppliedper unittimetothe mode). Deriving P put constraints on the theoreticalmodelsofmodeexcitationbyturbulent convection (Libbrecht, 1988). Goldreich&Keeley (1977, GK hereafter)haveproposedthe firsttheoreticalmodel of stochastic excitation of solaracousticmodes by the Reynolds stresses. Since thispioneering work,different improved modelshavebeen proposed (Dolginov&Muslimov,1984; Balmforth, 1992; Goldreichetal.,1994; Samadi&Goupil, 2001; Chaplinetal.,2005; Samadietal., 2003; Belkacem et al.,2006b,2008).Theseapproaches differfromeachothereither by the wayturbulent convection is described, or by the excitation process. In the present paper, we briefly review the mainassumptionsand approximations on whichthe different theoretical modelsare based. As shownbySamadietal. (2003),the energy suppliedper time unittothe modes by turbulent convection cruciallydepends on the wayeddies aretime-correlated. Arealistic R. Samadi, K. Belkacem,M.-J.Goupil, et al. 131 modelingofthe eddy time-correlationatvarious length scalesisthen an important issue, whichisdiscussedindetails below. Thestructureand the properties of the convective upper envelopealsohas an important impact on the mode driving. In particular,the surfacemetal abundance cansignificantlychangethe efficiency of the mode driving. Theoreticalmodels Most of the theoreticalmodelsofstochasticexcitationadopt GK’s approach.Thisapproach firstconsistsinsolving,withappropriateboundary conditions,the equation thatgoverns the adiabatic wave propagation(alsocalled the homogeneous wave equation). This provides the well-knownadiabatic displacement eigenvectors (ξ;(;r, t)). Then, one includes in the wave equation turbulent sources of drivingaswellasatermoflineardamping. Thecomplete equation (so-calledinhomogeneouswaveequation)isthen solved. Among the sources of driving, the contribution of Reynolds stresses, whichrepresents a mechanicalsourceofdriving,isconsidered. Goldreichetal. (1994, GMKhereafter)have proposed to include in addition the entropyfluctuations(alsoreferredtoasnon-adiabatic gaspressure fluctuations). It is generallyassumedthatthe entropyfluctuationsbehave as apassive scalar. In thatcase, Samadi&Goupil(2001, SG hereafter)haveshown thatthe contribution of the Lagrangian entropyfluctuationsvanishes.Onthe other hand, as shown by SG,the advection of the entropyfluctuationsbythe turbulent velocity field contributes efficientlytothe mode drivinginaddition to the Reynolds stresses. This advective term corresponds to the buoyancy forceassociated with the entropyfluctuations. Since it involves the entropyfluctuations, it canbeconsidered as athermal source of driving. Thesolution of the inhomogeneouswaveequation corresponds to the forced mode dis- placement, δ;r (orequivalentlythe mode velocity ;vosc = dδ;r /dt). Adetailedderivationofthe solution for radial acoustic modes canbefound in Samadi&Goupil(2001, SG herefater)or in Chaplinetal. (2005, CHEhereafter). It canbewritten as ˙ ¸ ; 2 2 ; 2 P || ξ || 2 2 || ;vosc || (ω )=|| ξ || = (C + C ), (1) 0 2 η I 16 η I 2 R S where ω0 is the mode frequency, P is the mode excitation rate (the rate at whichenergy is suppliedtothe mode), η the mode dampingrate(whichcan be derived from seismicdata), 2 2 I the mode inertia, andfinally CR and CS the contribution of the Reynolds streSS andthe 2 2 entropyfluctuations, respectively.The expressionsfor CR and CS are ZM „ «2 2 3 dξr CR =4πG dm ρ0 SR (r, ω0) (2) 0 dr Z 4 π3 H M α2 C 2 = dm s g S (r, ω ) (3) S 2 r S 0 ω0 0 ρ0 where αs =(∂Pg/∂s)ρ, Pg is the gaspressure, s the entropy, ρ0 the mean density, G and H aretwo anisotropicfactors (see theirexpression in SG), SR and SS arethe “sourceterms” associated with the Reynolds stressesand entropyfluctuationsrespectively, ξr the adiabatic mode radial eigen-displacement, andfinally gr (ξr , r)afunction thatinvolvesthe first and second derivatives of ξr (see itsexpression in SG). Thesourcefunctions, SR and SS ,involve the dynamicpropertiesofthe turbulent medium. Theexpression for SR is (see SG andSamadietal. (2005)): Z Z ∞ +∞ E 2(k) S (r, ω )= dk dω χ (ω + ω) χ (ω) (4) R 0 2 k 0 k 0 −∞ k 132 Modelingstochastic excitation of acousticmodes in stars: presentstatusand perspectives where k is the wavenumber, E(k)the time averaged kineticenergy spectrum, χk (ω)isthe frequency component of E(k, ω)(the kineticenergy spectrum as afunction of k and ω). A similarexpression is derived for SS (see SG). Note thatthe function χk (ω)can be viewed as ameasure in the Fourierdomain of the time-correlationbetween eddies.Thisfunction is generallyreferredas’eddy time-correlation’ function. ThederivationofEqs.(1)-(4) is basedonseveral assumptionsand approximations.Among them,the mainones are: • quasi-Normal approximation(QNA):the fourth-order moments involvingthe turbulent velocity aredecomposedinterms of second-order ones assumingthe QNA, i.e. assuming thatturbulent quantities aredistributed accordingtoaNormaldistribution with zero mean.However,aSShown recentlybyBelkacem et al. (2006a), thepresence of plumes causes aseveredeparturefromthisapproximation. Belkacem et al. (2006a)have proposed an improvedclosure model thattakes the asymmetrybetween plumes and granules as well as the turbulence inside the plumes into account. As shownbyBelkacem et al. (2006b), this improved closuremodel reduces the discrepancy between theoretical calculations andthe helioseismicconstraints. • isotropic, homogeneous, incompressibleturbulence:the turbulent medium is assumed to be isotropic, homogeneous, andincompreSSible at the lengthscale associated with the contributing eddies.Thisassumption is justifiedfor lowturbulent Mach number, Mt (see SG). However, when the anisotropy is small, it is possibletoapplyacorrection that takesthe departurefromisotropyinto account. Such correctionshavebeen proposed by SG andCHE in twodifferent ways.However,inbothformalisms, the exactdomain over whichthesecorrections arevalidisunknown andremainstobespecified. • radial formalism:radial modes areusuallyconsidered. However, generalizations to non- radial modes have been proposed by Dolginov &Muslimov (1984), GMKand Belkacem et al. (2008). • passive scalarassumption:aspointed outabove the entropyfluctuationsare supposed to behave as apassive scalar(seethe discussion). • length-scale separation:eddies contributing to the drivingare supposed to have achar- acteristiclength scale smallerthanthe mode wavelength. This assumption is justified forlow Mt (see SG andthe discussion). Eddy time-correlation Most of the theoreticalformulations explicitly or implicitly assume aGaussian function for χk (ω)(GK;Dolginov&Muslimov,1984; GMK; Balmforth, 1992; CHE).However,hydrody- namical3Dsimulations of the outer layers of the Sunshowthat, at the length associated with the energy bearingeddies, χk is ratherLorentzian (Samadietal.,2003).Aspointed outbyCHE,aLorentzian χk is alsoaresult predicted forthe largest, most-energetic eddies by the time-dependent mixing-length formulationofconvectionbyGough (1977).Therefore, thereare some numerical andtheoreticalevidences that χk is ratherLorentzian at the length scale of the energy bearingeddies. Theexcitationofthe low-frequency modes (ν ! 3mHz)ismainly due to the large scales. However, the higher the frequency the more importantthe contribution of the small scales. Solar 3D simulations show that, at small scales, χk is neither Lorentzian norGaussian (Georgobianietal.,2006).Then, accordingtoGeorgobianietal. (2006),itisimpossible to separate the spatial component E(k)fromthe temporalcomponent at all scaleswith the same simple analyticalfunctions. However, such resultsare
Load more

Recommended publications
  • Plotting Variable Stars on the H-R Diagram Activity
    Pulsating Variable Stars and the Hertzsprung-Russell Diagram The Hertzsprung-Russell (H-R) Diagram: The H-R diagram is an important astronomical tool for understanding how stars evolve over time. Stellar evolution can not be studied by observing individual stars as most changes occur over millions and billions of years. Astrophysicists observe numerous stars at various stages in their evolutionary history to determine their changing properties and probable evolutionary tracks across the H-R diagram. The H-R diagram is a scatter graph of stars. When the absolute magnitude (MV) – intrinsic brightness – of stars is plotted against their surface temperature (stellar classification) the stars are not randomly distributed on the graph but are mostly restricted to a few well-defined regions. The stars within the same regions share a common set of characteristics. As the physical characteristics of a star change over its evolutionary history, its position on the H-R diagram The H-R Diagram changes also – so the H-R diagram can also be thought of as a graphical plot of stellar evolution. From the location of a star on the diagram, its luminosity, spectral type, color, temperature, mass, age, chemical composition and evolutionary history are known. Most stars are classified by surface temperature (spectral type) from hottest to coolest as follows: O B A F G K M. These categories are further subdivided into subclasses from hottest (0) to coolest (9). The hottest B stars are B0 and the coolest are B9, followed by spectral type A0. Each major spectral classification is characterized by its own unique spectra.
    [Show full text]
  • Pre-Supernova Evolution of Massive Stars
    Pre-Supernova Evolution of Massive Stars ByNINO PANAGIA1;2, AND GIUSEPPE BONO3 1Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA. 2On assignment from the Space Science Department of ESA. 3Osservatorio Astronomico di Roma, Via Frascati 33, Monte Porzio Catone, Italy. We present the preliminary results of a detailed theoretical investigation on the hydrodynamical properties of Red Supergiant (RSG) stars at solar chemical composition and for stellar masses ranging from 10 to 20 M . We find that the main parameter governing their hydrodynamical behaviour is the effective temperature, and indeed when moving from higher to lower effective temperatures the models show an increase in the dynamical perturbations. Also, we find that RSGs are pulsationally unstable for a substantial portion of their lifetimes. These dynamical instabilities play a key role in driving mass loss, thus inducing high mass loss rates (up to −3 −1 almost 10 M yr ) and considerable variations of the mass loss activity over timescales of the order of 104 years. Our results are able to account for the variable mmass loss rates as implied by radio observations of type II supernovae, and we anticipate that comparisons of model predictions with observed circumstellar phenomena around SNII will provide valuable diagnostics about their progenitors and their evolutionary histories. 1. Introduction More than 20 years of radio observations of supernovae (SNe) have provided a wealth of evidence for the presence of substantial amounts of circumstellar material (CSM) surrounding the progenitors of SNe of type II and Ib/c (see Weiler et al., this Conference, and references therein).
    [Show full text]
  • A Refined Search for Pulsations in White Dwarf Companions To
    MNRAS 479, 1267–1272 (2018) doi:10.1093/mnras/sty1546 Advance Access publication 2018 June 12 A refined search for pulsations in white dwarf companions to millisecond pulsars Mukremin Kilic,1,2† J. J. Hermes,3‡ A. H. Corsico,´ 4 Alekzander Kosakowski,1 Warren R. Brown,5 John Antoniadis,6 Leila M. Calcaferro,4 A. Gianninas,1 Leandro G. Althaus4 and M. J. Green7 1Department of Physics and Astronomy, University of Oklahoma, 440 W. Brooks St., Norman, OK 73019, USA 2Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK 3Department of Physics and Astronomy, University of North Carolina, Chapel Hill NC 27599, USA 4Facultad de Ciencias Astronomicas´ y Geof´ısicas (UNLP), La Plata, Argentina 5Smithsonian Astrophysical Observatory, 60 Garden St, Cambridge MA 02138, USA 6Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto M5S 3H4, Canada 7Astronomy and Astrophysics Group, Department of Physics, University of Warwick, Gibbet Hill Road, Coventry CV4 7AL, UK Accepted 2018 June 7. Received 2018 May 27; in original form 2018 April 11 ABSTRACT We present optical high-speed photometry of three millisecond pulsars with low-mass (<0.3 M) white dwarf companions, bringing the total number of such systems with follow-up time-series photometry to five. We confirm the detection of pulsations in one system, the white dwarf companion to PSR J1738+0333, and show that the pulsation frequencies and amplitudes are variable over many months. A full asteroseismic analysis for this star is underconstrained, but the mode periods we observe are consistent with expectations for an M = 0.16 − 0.19 M white dwarf, as suggested from spectroscopy.
    [Show full text]
  • (NASA/Chandra X-Ray Image) Type Ia Supernova Remnant – Thermonuclear Explosion of a White Dwarf
    Stellar Evolution Card Set Description and Links 1. Tycho’s SNR (NASA/Chandra X-ray image) Type Ia supernova remnant – thermonuclear explosion of a white dwarf http://chandra.harvard.edu/photo/2011/tycho2/ 2. Protostar formation (NASA/JPL/Caltech/Spitzer/R. Hurt illustration) A young star/protostar forming within a cloud of gas and dust http://www.spitzer.caltech.edu/images/1852-ssc2007-14d-Planet-Forming-Disk- Around-a-Baby-Star 3. The Crab Nebula (NASA/Chandra X-ray/Hubble optical/Spitzer IR composite image) A type II supernova remnant with a millisecond pulsar stellar core http://chandra.harvard.edu/photo/2009/crab/ 4. Cygnus X-1 (NASA/Chandra/M Weiss illustration) A stellar mass black hole in an X-ray binary system with a main sequence companion star http://chandra.harvard.edu/photo/2011/cygx1/ 5. White dwarf with red giant companion star (ESO/M. Kornmesser illustration/video) A white dwarf accreting material from a red giant companion could result in a Type Ia supernova http://www.eso.org/public/videos/eso0943b/ 6. Eight Burst Nebula (NASA/Hubble optical image) A planetary nebula with a white dwarf and companion star binary system in its center http://apod.nasa.gov/apod/ap150607.html 7. The Carina Nebula star-formation complex (NASA/Hubble optical image) A massive and active star formation region with newly forming protostars and stars http://www.spacetelescope.org/images/heic0707b/ 8. NGC 6826 (Chandra X-ray/Hubble optical composite image) A planetary nebula with a white dwarf stellar core in its center http://chandra.harvard.edu/photo/2012/pne/ 9.
    [Show full text]
  • Pulsating Variable Stars and the Hertzsprung-Russell Diagram
    - !% ! $1!%" % Studying intrinsically pulsating variable stars plays a very important role in stellar evolution under- standing. The Hertzsprung-Russell diagram is a powerful tool to track which stage of stellar life is represented by a particular type of variable stars. Let's see what major pulsating variable star types are and learn about their place on the H-R diagram. This approach is very useful, as it also allows to make a decision about a variability type of a star for which the properties are known partially. The Hertzsprung-Russell diagram shows a group of stars in different stages of their evolution. It is a plot showing a relationship between luminosity (or abso- lute magnitude) and stars' surface temperature (or spectral type). The bottom scale is ranging from high-temperature blue-white stars (left side of the diagram) to low-temperature red stars (right side). The position of a star on the diagram provides information about its present stage and its mass. Stars that burn hydrogen into helium lie on the diagonal branch, the so-called main sequence. In this article intrinsically pulsating variables are covered, showing their place on the H-R diagram. Pulsating variable stars form a broad and diverse class of objects showing the changes in brightness over a wide range of periods and magnitudes. Pulsations are generally split into two types: radial and non-radial. Radial pulsations mean the entire star expands and shrinks as a whole, while non- radial ones correspond to expanding of one part of a star and shrinking the other. Since the H-R diagram represents the color-luminosity relation, it is fairly easy to identify not only the effective temperature Intrinsic variable types on the Hertzsprung–Russell and absolute magnitude of stars, but the evolutionary diagram.
    [Show full text]
  • Variable Star
    Variable star A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates. This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either: Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks. Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes Trifid Nebula contains Cepheid variable stars eclipses it. Many, possibly most, stars have at least some variation in luminosity: the energy output of our Sun, for example, varies by about 0.1% over an 11-year solar cycle.[1] Contents Discovery Detecting variability Variable star observations Interpretation of observations Nomenclature Classification Intrinsic variable stars Pulsating variable stars Eruptive variable stars Cataclysmic or explosive variable stars Extrinsic variable stars Rotating variable stars Eclipsing binaries Planetary transits See also References External links Discovery An ancient Egyptian calendar of lucky and unlucky days composed some 3,200 years ago may be the oldest preserved historical document of the discovery of a variable star, the eclipsing binary Algol.[2][3][4] Of the modern astronomers, the first variable star was identified in 1638 when Johannes Holwarda noticed that Omicron Ceti (later named Mira) pulsated in a cycle taking 11 months; the star had previously been described as a nova by David Fabricius in 1596. This discovery, combined with supernovae observed in 1572 and 1604, proved that the starry sky was not eternally invariable as Aristotle and other ancient philosophers had taught.
    [Show full text]
  • Variable Stars Across the Observational HR Diagram
    Variable stars across the observational HR diagram Laurent Eyer1, Nami Mowlavi1;2 1 Observatoire de Gen`eve, Universit´ede Gen`eve, 1290 Sauverny, Switzerland 2 ISDC, Universit´ede Gen`eve, 1290 Versoix, Switzerland E-mail: [email protected] Abstract. An overview of pulsating variable stars across the observational Hertzprung-Russel (HR) diagram is presented, together with a summary of their global properties. The HR diagram is presented with a third colour-coded dimension, visualizing the fraction of variable, the amplitude of variability or the period of variability. The distribution of variable stars in the other observational diagrams, such as the Period-Amplitude diagram, is also presented. Some of the progresses performed in the field of variable stars during the last decade are briefly summarized, and future projects that will improve our knowledge of variable stars are mentioned. 1. Introduction There are in the literature several global descriptions of variable stars. We can mention four books, one by Richter, Wenzel and Hoffmeister (1985, out of print), one by Sterken and Jaschek [1], one by Percy ([2]) and one, soon to come, by Aerts et al. [3]. There have also been two excellent and detailed reviews by Gautschy and Saio ([4], [5]) about a decade ago. With the advent of Charge-Coupled Devices (CCDs) and large scale surveys like the Optical Gravitational Lensing Experiment (OGLE), the Massive Compact Halo Object project (MACHO) or the "Exp´eriencepour la Recherche d'Objets Sombres" (EROS), the subject of variable star studies is now under a remarkable expansion. As we will see the expansion will continue in the coming decade because there are many future projects which will sample frequently large regions of the sky.
    [Show full text]
  • Asteroseismology
    Asteroseismology Gerald Handler Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland Email: [email protected] Abstract Asteroseismology is the determination of the interior structures of stars by using their oscillations as seismic waves. Simple explanations of the astrophysical background and some basic theoretical considerations needed in this rapidly evolving field are followed by introductions to the most important concepts and methods on the basis of example. Previous and potential applications of asteroseismology are reviewed and future trends are attempted to be foreseen. Introduction: variable and pulsating stars Nearly all the physical processes that determine the structure and evolution of stars occur in their (deep) interiors. The production of nuclear energy that powers stars takes place in their cores for most of their lifetime. The effects of the physical processes that modify the simplest models of stellar evolution, such as mixing and diffusion, also predominantly take place in the inside of stars. The light that we receive from the stars is the main information that astronomers can use to study the universe. However, the light of the stars is radiated away from their surfaces, carrying no memory of its origin in the deep interior. Therefore it would seem that there is no way that the analysis of starlight tells us about the physics going on in the unobservable stellar interiors. However, there are stars that reveal more about themselves than others. Variable stars are objects for which one can observe time-dependent light output, on a time scale shorter arXiv:1205.6407v1 [astro-ph.SR] 29 May 2012 than that of evolutionary changes.
    [Show full text]
  • ``But I Am Constant As the Northern Star of Whose True-Fixed and Resting Quality There Is No Fellow in the Firmament.'' William
    ``But I am constant as the Northern Star Of whose true-fixed and resting quality There is no fellow in the firmament.'' William Shakespeare, Julius Caesar, 3, 1 Astronomy C - Variable Stars - 2008 A. Pulsating Variables: 1) Long Period Variables a) Mira type b) Semiregular 2) Cepheids 3) RR Lyrae B. Cataclysmic (Eruptive) Variables: 1) R Coronae Borealis 2) Flare Stars 3) Dwarf Novae 4) X-Ray Binaries 5) Supernovae a) Type II b) Type Ia C. Strangers in the Night Astronomy C - Variable Stars - 2008 A. Pulsating Variables: 1) Long Period Variables a) Mira type R Cygni b) Semiregular V725 SGR 2) Cepheids W Virginis 3) RR Lyrae AH Leo B. Cataclysmic (Eruptive) Variables: 1) R Coronae Borealis RY Sagittarii 2) Flare Stars UV Ceti 3) Dwarf Novae SU Ursae Majoris 4) X-Ray Binaries J1655-40, RX J0806.3+1527 5) Supernovae a) Type II G11.2-0.3, SN2006gy b) Type Ia DEM L71, Kepler’s SNR C. Strangers in the Night: V838 Mon Light Curves – Variation over Time Maximum (Maxima) Minimum (Minima) Period Apparent Magnitude vs Julian Day A. Pulsating Variable Stars; 1) Long Period Variables (LPVs) a) Miras 80 – 1000 days, 2.5 – 5.0 mag R Cygni b) Semiregular Variables 30 – 1000 days, 1.0 – 2.0 mag V725 Sgr Semiregular Mira Instability Strip 2) Cepheid Variable Stars W Virginis (Type 2) [Periods of .8 – 35 days, .3 – 1.2 mag] Type I and Type II Cepheid Variable Stars Type I (Classical) Cepheids: Young high-metallicity stars about 4 times more luminous than Type II Cepheids Type II Cepheids: Older low- metallicity stars about 4 times less luminous than classical Cepheids.
    [Show full text]
  • Download This Article (Pdf)
    Neilson et al., JAAVSO Volume 44, 2016 179 Period Changes and Evolution in Pulsating Variable Stars Hilding R. Neilson John R. Percy Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON M5S 3H4, Canada; [email protected], [email protected] Horace A. Smith Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-2320; [email protected] Invited review paper, received October 18, 2016 Abstract We review ways in which observations of the changing periods of pulsating variable stars can be used to detect and directly measure their evolution. We briefly describe the two main techniques of analysis—(O–C) analysis and wavelet analysis— and results for pulsating variable star types which are reasonably periodic: type I and II Cepheids, RR Lyrae stars, β Cephei stars, and Mira stars. We comment briefly on δ Scuti stars and pulsating white dwarfs. For some of these variable star types, observations agree approximately with the predictions of evolutionary models, but there still exist significant areas of disagreement that challenge future models of stellar evolution. There may be a need, for instance, to include processes such as rotation, mass loss, and magnetic fields. There may also be non-evolutionary processes which are contributing to the period changes. 1. Introduction known constant period P. When (O–C) is plotted against time, it produces a straight line if the period is constant, a parabola Star lives are measured in billions of years, millions of opening upward if the period is increasing linearly, a parabola years for very rare massive stars.
    [Show full text]
  • Pulsating Stars: Stars That Breathe
    HET611-M17A01: Pulsating Stars: Stars that Breathe PAGE 1 OF 39 Pulsating Stars: Stars that Breathe c Swinburne University of Technology, 2010 Credit: Dr. Wendy L. Freedman, Observatories of the Carnegie Institution of Washington, and NASA HET611-M17A01: Pulsating Stars: Stars that Breathe PAGE 2 OF 39 Summary In this Activity, we will discuss pulsating stars. In particular, we will: • outline some early observations and theory of pulsating stars; • describe some different classes of pulsating star and where they appear on the HR diagram; • introduce the instability strip; • develop a simple model of stellar pulsation based on sound waves and heat engines; and • describe the κ-mechanism that is responsible for driving pulsations in Cepheid-type stars, and see how partial ionisation zones can explain the existence of an instability strip. c Swinburne University of Technology, 2010 HET611-M17A01: Pulsating Stars: Stars that Breathe PAGE 3 OF 39 Introduction Pulsating stars are a type of variable star in which brightness variations are caused by changes in the area and temperature of the star’s surface layers. Recent evidence suggests that all stars pulsate (if we measure them carefully enough), although the presence of concentrated populations of pulsating stars on the HR diagram implies that pulsations are more important at particular stages of stellar evolution. As well as being fascinating phenomena in their own right, stellar pulsations are used to constrain theories of stellar evolution and to study the mechanisms of stellar interiors. c Swinburne University of Technology, 2010 HET611-M17A01: Pulsating Stars: Stars that Breathe PAGE 4 OF 39 The discovery of Mira The first pulsating star, o Ceti , was discovered in 1596 by David Fabricius.
    [Show full text]
  • The Wolf-Rayet Stars in M 31? I
    A&A 563, A89 (2014) Astronomy DOI: 10.1051/0004-6361/201323240 & c ESO 2014 Astrophysics The Wolf-Rayet stars in M 31? I. Analysis of the late-type WN stars A. Sander, H. Todt, R. Hainich, and W.-R. Hamann Institut für Physik und Astronomie, Universität Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam, Germany e-mail: [ansander;htodt]@astro.physik.uni-potsdam.de Received 12 December 2013 / Accepted 22 January 2014 ABSTRACT Context. Comprehensive studies of Wolf-Rayet stars were performed in the past for the Galactic and the LMC population. The results revealed significant differences, but also unexpected similarities between the WR populations of these different galaxies. Analyzing the WR stars in M 31 will extend our understanding of these objects in different galactic environments. Aims. The present study aims at the late-type WN stars in M 31. The stellar and wind parameters will tell about the formation of WR stars in other galaxies with different metallicity and star formation histories. The obtained parameters will provide constraints to the evolution of massive stars in the environment of M 31. Methods. We used the latest version of the Potsdam Wolf-Rayet model atmosphere code to analyze the stars via fitting optical spectra and photometric data. To account for the relatively low temperatures of the late WN10 and WN11 subtypes, our WN models have been extended into this temperature regime. Results. Stellar and atmospheric parameters are derived for all known late-type WN stars in M 31 with available spectra. All of these stars still have hydrogen in their outer envelopes, some of them up to 50% by mass.
    [Show full text]