c Swinburne University of Technology, 2010 39 OF 1 AGE P : Dr. Wendy L. Freedman, Observatories of the Carnegie Credit Institution of Washington, and NASA : Stars that Breathe Stars HET611-M17A01: Pulsating Stars: Stars that Breathe Pulsating c Swinburne University of Technology, 2010 39 OF 2 AGE P ; HR diagram -type stars, and Cepheid and where they appear on the star pulsation based on sound waves and heat engines; and ; stellar -mechanism that is responsible for driving pulsations in instability strip κ HET611-M17A01: Pulsating Stars: Stars that Breathe see how partial ionisation zones can explain the existence of an instability strip. introduce the develop a simple model of describe the outline some early observations and theory of pulsatingdescribe stars; some different classes of pulsating • • • • • In this Activity, we will discuss pulsating stars. In particular, we will: Summary c Swinburne University of Technology, 2010 39 OF 3 AGE P . stellar evolution and temperature of the star’s surface layers. HET611-M17A01: Pulsating Stars: Stars that Breathe area As well as being fascinatingtheories phenomena of in stellar evolution their and own to right, study stellar the mechanisms pulsations of are stellar used interiors. to constrain Recent evidence suggests that all starspresence pulsate of (if we concentrated measure populations them of carefullyare enough), pulsating more although stars important the on at particular the stages HR of diagram implies that pulsations Pulsating stars are a typethe of variable star in which brightness variations are caused by changes in Introduction c Swinburne University of Technology, 2010 39 OF 4 AGE P magnitude star second of 11 months, the bright period Ceti , was discovered in 1596 by David Fabricius. o HET611-M17A01: Pulsating Stars: Stars that Breathe Ceti was later called ‘Mira’ (meaning ‘wonderful’) to describe its unusual behaviour. o Fabricius’ observations showed that over a The first pulsating star, The discovery of Mira faded, disappeared, and then finally returned to its former brightness. c Swinburne University of Technology, 2010 39 OF 5 AGE P 322 days. It is considered ∼ . amplitude varies between +3.5 and +9 over a period of : AAVSO Credit Curve of Mira apparent magnitude HET611-M17A01: Pulsating Stars: Stars that Breathe Light the prototype of long periodthat variables , are stars slightly with irregular pulsation in periods period and between 100 and 400 days, and Generate light curves for variable stars observed by the AAVSO This figure shows the light curve of Mira,Mira’s compiled from observations dating back to 1970. Try fitting light curve data to different pulsation periods c Swinburne University of Technology, 2010 39 OF 6 AGE P 1 ∼± and pulsation period. luminosity Cephei has a pulsation period of 5 days, 8 hours and δ 37 minutes and exhibitsmag. magnitude variations of It is thea prototype of classical arelationship kind Cepheid, between of pulsating which star demonstrate called a strict Cephei, in 1784. δ HET611-M17A01: Pulsating Stars: Stars that Breathe Cephei light curve from HIPPARCOS. Cephei Credit: ESTEC, ESA. δ δ The most important discovery forlight stellar variations pulsation in theory, the however, yellow was supergiant, the observation of periodic c Swinburne University of Technology, 2010 39 OF 7 AGE P ` e Visual Archives : AIP Emilio Segr . Credit SMC . with than galaxies luminous Cepheids to nearby distance . , Leavitt noticed that in the Harvard College Observatory newsletter, in which she describes the variable stars HET611-M17A01: Pulsating Stars: Stars that Breathe Looking at the variable stars that she had discovered in the Read Leavitt’s note relationship between brightness and period for 25 stars in the Henrietta Swan Leavitt Small Magellanic Cloud long pulsation periods weretheir short intrinsically period more counterparts. Her discovery was the basisrelation of the (also Cepheid period-luminosity calledimportant tool the for measuring the P-L relation), which remains an Henrietta Leavitt (1868 -College 1921) Observatory was to employed determine at the thephotographic magnitude Harvard of plates. stars from Asmore part than 2400 of this project, she discovered c Swinburne University of Technology, 2010 39 OF 8 AGE P Milky Way as a function of period for classical Cepheids in the galaxies. absolute magnitude Local Group HET611-M17A01: Pulsating Stars: Stars that Breathe and other This figure shows Period-Luminosity Relation c Swinburne University of Technology, 2010 39 OF 9 AGE P is the star’s i V h M 43 . 1 47 . − constructed the following equations for +2 d Y d Y 10 10 80 log . 2 15 log . astronomers − is its pulsation period in days; and d = = 1 i Q V i h
L L M h 10 log is the star’s average luminosity; i L h HET611-M17A01: Pulsating Stars: Stars that Breathe where average absolute magnitude. We will explore the physics behind this empirical law later in this Activity. the luminosity and absolute magnitude of a Cepheid: From this plot (and many similar observations), c Swinburne University of Technology, 2010 39 OF 10 , , AGE P is the absolute v M cluster of galaxies Colour and Magnitude 5 − r 10 = 5 log V M was to detect Cepheids in the Virgo is the star’s apparent magnitude; and v − equation that we saw in the Activity m V HST m distance modulus is the distance to the Cepheid, r HET611-M17A01: Pulsating Stars: Stars that Breathe and hence derive an accurate distance estimate for the cluster. to find the distance to the Cepheid: where You should already appreciate themeasure the enormous pulsation power period of of distanttheir such Cepheids, luminosity then a (and we hence relationship: have absolute an magnitude). it immediate, accurate saysWe estimate that can of then if use we the can A rung of the distance ladder magnitude that we obtain from the P-L relation. A primary scientific motivation for the c Swinburne University of Technology, 2010 39 OF 11 AGE P Virgo Great belonging to the . will help constrain the Hubble Universe spiral galaxy redshift : NASA, HST, W. Freedman (CIW), R. Kennicutt (U. Credit Arizona), J. Mould (ANU) . Astronomy . Correlating the Cepheid distance with the galaxy’s HET611-M17A01: Pulsating Stars: Stars that Breathe constant, and thus provide an estimate for the age and size of the Debates in You can read more about recent attempts to define the Hubble constant in the Unit HET616, An HST image of a Cepheid in the outer regions of M100, a Cluster c Swinburne University of Technology, 2010 39 OF 12 AGE P HET611-M17A01: Pulsating Stars: Stars that Breathe Following these discoveries, manyluminosity new types variations of were pulsatingdeveloped observed, stars until with the although 1940s. a a wide reasonable range ofWe theory will periods of look and at stellar theat reasons pulsation where why pulsating was stars stars pulsate not can later be in found this on Activity. the For HR the diagram... moment, let’s have a look Pulsating Stars on the HR Diagram c Swinburne University of Technology, 2010 39 OF 13 AGE P . instability strip HET611-M17A01: Pulsating Stars: Stars that Breathe Given the large number of pulsating staron populations thesuspect HR that diagram, alltechniques stars it pulsate. become seemsamplitude pulsations As in reasonable stars more on observational otherHR to regions diagram of may sensitive, the be detected. smaller pulsating stars are not generallysequence. found on Instead, the most main narrow, pulsating vertical stars band occupy on a HR the diagram. right This hand is called side the of the Astronomers believe thatphenomenon pulsation - as is the a starstracks follow on transient their the HR evolutionary diagram, they willinstability pass strip through the where theyvariations. exhibit large brightness • • • In particular you should note: Here we see various populationstheir of characteristics pulsating later in stars this plotted Activity). on the HR diagram (we will learn about The Instability Strip c Swinburne University of Technology, 2010 39 OF 14 AGE P NR R, NR R, NR R Radial or Non-Radial Pulsation R R R I I I Population Type I,II I II II 100-1000 seconds 3-7 hours 1-3 hours Period 100-700 days 1-50 days 1.5-24 hours 2-45 days stars HET611-M17A01: Pulsating Stars: Stars that Breathe Cephei stars Scuti stars ZZ Ceti stars β δ Type Long period variables (LPVs) Classical Cepheids W Virginis stars RR Lyrae Although in most cases, observationalkept records for for over each a of century, the astronomers different had pulsating no classes explanation have for been why stars pulsate until about 1915. This table lists the characteristicsHR of diagram. the major pulsating star classes that we saw illustrated on the Classes of pulsating stars c Swinburne University of Technology, 2010 39 OF 15 AGE P : ESTEC, ESA. RR Lyrae Credit : STARE Cephei type variable in Auriga δ Credit HET611-M17A01: Pulsating Stars: Stars that Breathe Here are several light curves of stars belonging to different pulsating star classes. Light curves c Swinburne University of Technology, 2010 39 OF 16 AGE P Scuti type variable) δ : Delta Scuti Network FG Virginis ( Credit HET611-M17A01: Pulsating Stars: Stars that Breathe c Swinburne University of Technology, 2010 39 OF 17 AGE P binary . In this Activity, however, of the (non-existent) companion star was , and tidal effects in the atmospheres of orbit . Some of the observed brightness variations could only 1 Exploring Stars and the Milky Way binary system , for example, if the do exhibit periodic variations in their light curve- you would have learnt binary systems eclipsing binaries . HET611-M17A01: Pulsating Stars: Stars that Breathe In fact, be explained by we are concentrating onconsequence stars of the that physics in show the intrinsic stellar interior. variability, i.e. brightness variations that are a stars located inside the primary star! 1 about these systems in the Unit HET603, We now know that these ideas are wrong Early theories for the observed brightnesssurface variations of of a pulsating rotating stars star, included eclipses dark in patches a on the Early ideas c Swinburne University of Technology, 2010 39 OF 18 AGE P The ADS website (1914) v. 40, pp 448-465. Shapley’s original paper can be found on the Look up Shapley, H., ‘On theAstrophysical Journal, Nature and Cause of Cepheid Variation’, HET611-M17A01: Pulsating Stars: Stars that Breathe In 1914, thetemperature American and brightness astronomer, of Harlow Cepheid variables Shapley, were caused suggestedHe by argued that radial that pulsation. binary the theories ofseek observed stellar a variations pulsation mechanism should by in be which discarded single and stars that couldRadial astronomers rhythmically pulsations should ‘breathe’ had in been and out. proposedSir Arthur by Eddington Arthur attempted Ritter to in provide 1879, a mathematical but framework his for ideas Shapley’s suggestion. were overlooked until ’Breathing Stars’ c Swinburne University of Technology, 2010 39 OF 19 AGE P : AIP Emilio ` e Visual Arthur Eddington. Credit Segr Archives of sound. , is obtained by calculating the length s R speed v Π 2 = is the Y s v is the stellar radius, and R HET611-M17A01: Pulsating Stars: Stars that Breathe A simple model for stellar pulsation of time it would take a sound wave to travel across the diameter of a star. That is, where Eddington proposed that if weengines, consider then radial pulsating oscillations stars may asthe be thermodynamic stellar the interior. heat result of sound waves resonatingA rough in estimate for the pulsation period, c Swinburne University of Technology, 2010 39 OF 20 AGE P =5/3 for γ of the stellar interior: 2 3 density Gπrρ 4 − and = ) 2 2 r ρ r − 2 ρ pressure 3 R ρ ( γP 3 2 πr 4 s = πGρ G 2 3 S v − is ratio of specific heats for the stellar material ( γ = ) = r ρ ( r P 2 r GM − = is density, and dr dP % , can be determined from the s : =0 at the star’s surface, we can then find the pressure as a function of stellar ν P is the pressure, P HET611-M17A01: Pulsating Stars: Stars that Breathe Integrating so that radius: where a monatomic gas). To work out the pressure, wehydrostatic assume equilibrium that the star has constant density and invoke the condition of The speed of sound, c Swinburne University of Technology, 2010 39 OF 21 AGE P ) 2 r − 2 R ( dr γπGρ 2 3 q π 3 R γGρ 0 2 s Z R v 2 r ≈ = 2 = Y HET611-M17A01: Pulsating Stars: Stars that Breathe This equation, also called the period-meanis density inversely relation, proportional shows to that the the square pulsation root periodAlthough of of its a its mean star density. derivationthe is period-mean not density rigorous,observation. relation substituting produces typical period values estimates for that a are classical in Cepheid good into agreement with Substituting back into our equation for the pulsation period, we find, c Swinburne University of Technology, 2010 39 OF 22 AGE P HET611-M17A01: Pulsating Stars: Stars that Breathe What did Eddingtonthermodynamic heat mean engine? when heLet’s consider said layers inside the that star as a they expand and pulsating contract... star can be characterised as a Eddington’s Engine c Swinburne University of Technology, 2010 39 OF 23 AGE P and falls inwards. gravity HET611-M17A01: Pulsating Stars: Stars that Breathe Since radiation diffuses more slowlyincreased through opacity), the heat builds layer up (as beneath a it. consequence of its This inward motion tendsmore to opaque compress to the radiation. layer, which heats up and becomes At one point in the pulsation cycle,the a star’s layer of stellar material loses support against A simple pulsation cycle c Swinburne University of Technology, 2010 39 OF 24 AGE P HET611-M17A01: Pulsating Stars: Stars that Breathe Energy can now escapedrops. from below the layer, and pressure beneath the layer As it moves outwards, the layerto expands, radiation. cools, and becomes more transparent The pressure rises below the layer, pushing it outwards. c Swinburne University of Technology, 2010 39 OF 25 AGE P act like a heat engine with does HET611-M17A01: Pulsating Stars: Stars that Breathe The layer falls inwards and the cycle repeats. This animation illustrates the stellar pulsation cycles. We see that Eddington’s analogy was apt: the stellar envelope The Cycle radiation taking the part ofopacity steam, of the the expanding layer and acting contracting as layer the acting valveNote: as mechanism. the these diagrams piston, are and definitely the not to scale! c Swinburne University of Technology, 2010 39 OF 26 AGE P with compression according to decreases . 5 . 3 ρ T ∝ -mechanism. , typically κ κ κ Energy Transport -mechanism κ HET611-M17A01: Pulsating Stars: Stars that Breathe This law was discussed in the Activity Kramer’s Law: Kramer’s Law and the In our simple modelincrease of with the compression. This stellar is pulsation called cycle, the In we most require regions the in opacity a of star, a however, layer opacity, in the star to c Swinburne University of Technology, 2010 39 OF 27 AGE P HET611-M17A01: Pulsating Stars: Stars that Breathe As the layers of a star are compressed,Kramer’s we Law, however, know tells that us their that densityvery opacity and likely is temperature that will more the increase. sensitive opacity to of temperature stellar than materialEvidently, for pressure, will stellar so decrease pulsation upon it to compression. is occur via Eddington’s mechanism, special conditions are required. Opacity, pressure and temperature c Swinburne University of Technology, 2010 39 OF 28 AGE P provide the necessary valve mechanism can HET611-M17A01: Pulsating Stars: Stars that Breathe Regions of the stellar interior where increased opacity Zhevakin’s zones to drive pulsations, were first identified by theThese Russian were partial astronomer ionisation S. zones A. , Zhevakincan where in be part the used of 1950s. the for energy further released ionisation, during rather a than layer’s compression raising the temperature of the gas. c Swinburne University of Technology, 2010 39 OF 29 AGE P ions 5 . . 3 ρ T ∝ κ electrons HET611-M17A01: Pulsating Stars: Stars that Breathe Likewise during the expansion phase, the temperaturerelease does energy not when decrease they significantly recombine since with the As the temperature of the compressedproduces layer a has corresponding not increase substantially in increased, the the opacity increase of in the density layer according to Kramer’s Law: Kramer’s Law in partial ionisation zones c Swinburne University of Technology, 2010 39 OF 30 AGE P -mechanism. γ -mechanism -mechanism is reinforced in a partial ionisation zone because the temperature gradient γ κ HET611-M17A01: Pulsating Stars: Stars that Breathe The The between the partial ionisationinto zone the and zone, prompting adjacent further layers ionisation. in theThis is star called encourages the more heat to flow c Swinburne University of Technology, 2010 39 OF 31 AGE P − e − − e + e + + ++ + + He H He ↔ ↔ ↔ + H He He K, where further ionisation of helium takes place: 4 10 × partial ionisation zone is a broad region with a characteristic temperature of 1 to 1.5 II partial ionisation zone is a region deeper in the stellar interior with a characteristic K, in which the following cyclical ionisations occur: 4 HET611-M17A01: Pulsating Stars: Stars that Breathe helium hydrogen 10 The × temperature of 4 In most stars there are two main partialThe ionisation zones. Partial ionisation zones c Swinburne University of Technology, 2010 39 OF 32 AGE P to mass its partial where 7500K, the partial ionisation zones are ∼ eff HET611-M17A01: Pulsating Stars: Stars that Breathe located too close to the star’s surface, where there is not enough ionisation zones are found within the stellar interior. The location of thetemperature. partial ionisation zones isFor determined by stars the hotter star’s than T The pulsation properties of a star depend primarily on drive the oscillations effectively. The real-estate principle of pulsation c Swinburne University of Technology, 2010 39 OF 33 AGE P 5500K, on the other hand, the partial ∼ eff HET611-M17A01: Pulsating Stars: Stars that Breathe For stars cooler than T ionisation zones are deep in the stellar interior. However at low temperatures, energyquite transport efficient via in convection becomes thepressure stellar beneath the interior, driving preventing pulsation the layer. build-up of heat and c Swinburne University of Technology, 2010 39 OF 34 AGE P -mechanism and the instability strip κ HET611-M17A01: Pulsating Stars: Stars that Breathe The narrow temperature range of the instabilitysustain strip partial corresponds ionisation to zones the capable stellar of temperatures maintaining that can stellar oscillations. The We are now in a position to understand the location of the instability strip on the HR diagram. c Swinburne University of Technology, 2010 39 OF 35 AGE P the stars on the instability strip do not all HET611-M17A01: Pulsating Stars: Stars that Breathe Scuti stars are main-sequence stars with the appropriate δ surface temperatures. Classical Cepheids, WWgiant Virginis stars and of RR different massesappropriate Lyrae that temperature stars are range. evolving are through the Investigating why pulsate remains an active area of stellar research. Stars on the instability strip c Swinburne University of Technology, 2010 39 OF 36 AGE P HET611-M17A01: Pulsating Stars: Stars that Breathe Observed properties ofbrightness a and classical its minimum Cepheid. radius. Note the phase lag between the star’s maximum Computer modelling of stellarwhich pulsation is responsible suggests for that the observed it oscillations is ofThe hydrogen stars primarily ionisation on zone the the , instability however, helium still strip. lag plays II between an important the ionisation role, star’s zone producing maximum an brightness observable and phase its minimum radius. Modelling Pulsations c Swinburne University of Technology, 2010 39 OF 37 AGE P HET611-M17A01: Pulsating Stars: Stars that Breathe The maximum brightness ofionisation a zone and pulsating the star star’s surface occurs is when atAlthough a the the minimum. least energy mass beneathminimum, between this the the energy hydrogen propels hydrogen ionisation the hydrogen zone ionisation zone peaksThe towards observed when the luminosity star’s the of surface. star’s thecompressed pulsating radius to star its is is smallest at radius. thus at a a maximum slightly after the star has been Luminosity and the hydrogen ionisation zone c Swinburne University of Technology, 2010 39 OF 38 AGE P Scuti δ -mechanism is almost certainly responsible for the pulsations observed in κ HET611-M17A01: Pulsating Stars: Stars that Breathe stars that are located on the instability strip: classical Cepheids, WW Virginis, RR Lyrae and Astronomers believe that Stars beyond the instability strip stars. The pulsation mechanism for other stars, however, is not so well understood. c Swinburne University of Technology, 2010 39 OF 39 AGE P rather than increase decrease upon compression were identified by S. increase cloud. HET611-M17A01: Pulsating Stars: Stars that Breathe Small Magellanic We saw that pulsating starsthere are located are in several manytemperature different classes range regions of of of the the pulsating instability HR stripzones star diagram. in corresponds the to that In star’s the particular, interior are temperatures can at found sustain which stellarWe partial on oscillations. then ionisation the developed instability athermodynamic simple strip. heat model engines. of These The ideas stellartwentieth century. were narrow pulsations Eddington’s initially model based proposed requires by that onpulsations. opacity Arthur the acts Eddington like idea Kramer’s in a Law valve the of mechanism early , sound for the however, waves stellar implies and that opacity tends to upon compression. The special circumstances inA. which Zhevakin opacity in will the 1950s.during Zhevakin a found layer’s that compression partial forincreasing further ionisation the ionisation zones layer’s absorb of opacity. a the gas energy rather released Two than principal raising partial its ionisation temperature, zones thus II were ionisation identified: zone. the Computer hydrogen modelsstars show ionisation on that zone the the and instability latter the strip. is helium observed primarily The phase responsible lag hydrogen for between ionisation the the zone pulsation interval is of of important,In the however, the star’s for maximum next explaining luminosity Activity, we the and will minimum develop radius. a more sophisticated model of stellar pulsation. In this Activity, we have looked atWe some discussed of the the basic history properties of andto internal pulsating physics Henrietta star of observations, Swan pulsating from Leavitt’s stars. discovery thethe of first detection the of period-luminosity Mira’s relationship pulsations for classical Cepheids in Summary