Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Indian Institute of Astrophysics wikipedia , lookup
Planetary nebula wikipedia , lookup
Chronology of the universe wikipedia , lookup
Cosmic distance ladder wikipedia , lookup
Cosmic microwave background wikipedia , lookup
Hayashi track wikipedia , lookup
Stellar evolution wikipedia , lookup
Main sequence wikipedia , lookup
Lecture 2 Stars: Color and Spectrum introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 1 introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 2 introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 3 introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 4 2.1 - Solar spectrum introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 5 2.1 - Solar spectrum (as detected on Earth) Wavelength[m] introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 6 Light spectrum from atomic transitions Inahotgas,atomscollideandatomictransi-ons occur,withelectronsbeingpromotedtohigherorbits. Theexcitedatomseventuallyemitphotons andtheelectronsreturntolowerenergy orbitals.Inhydrogen,transi)onstotheground state(n=1)yielddiscretelightenergies(lines) namedLymantransi-ons.Transi)onstothe firstexcitedstate(n=2)yieldBalmerlines. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 7 Emission and absorption lines LookingatthelightemiRedbystarsasa func)onofthewavelength(emission spectrum),onecaniden)fyspecific transi)onsincertainatoms,suchasthe n=3ton=2transi)oninhydrogen(alpha line). ButsincelightisemiRedbyseveral atomsinnumerouselectronic transi)ons,itiseasiertodetect absorp-onlines.Aslightpropagates throughthestellaratmosphere,itis absorbedbyhydrogenatomsandthe intensityisseenreducedatthose wavelengths. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 8 Color-magnitude diagrams Measuring accurate Te for ~102 or 103 stars is intensive task – spectra are needed and also model of atmospheres. Magnitudes of stars are measured at different wavelengths: standard system is UBVRI Band U B V R I λ[nm] 365 445 551 658 806 introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 9 Magnitudes and Temperatures One has to model stellar spectra at different temperature, e.g., Te = 40,000, 30,000, 20,000 K, to obtain a function f(Te)) so that B - V = f(Te) It amounts in separating the flux into different wavelength bands, finding the wavelength for maximum strength and finding temperature which fits that. Various calibrations can be used to provide the color relation B - V = f(Te) introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 10 Magnitudes and Temperatures Calibration of spectral types. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 11 Color of stars Colorsofstarsarecomplextodefine.Starcolorindicesweredefinedbyusingthe responseofphotographicplateswithbandwidthsspanningtheUltraviolet,Blue andVisual(UBV)spectra.ThecolorindexistheBluemagnitudeminustheVisual magnitude,wherethemagnitudeisgivenbyEq.(1.10).Hence,hotstarsare characterizedbysmall,infactnega)ve,colorindexwhilecoldstarshavelarge colorindex. Astronomerscorrelatethe colorindexwiththe effec)vesurface temperatureofastar.The HRdiagram(next)isaplot oftheluminosityofastar orthebolometric magnitude(totalenergy emiRedbyastar)versusits surfacetemperature,orits colorindex. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 12 Color of stars Ingeneral,aspectralclassifica)on O,B,A,F,G,K,M with1–10subgroupsisused(Sun:G2),whichisactuallypreRywellcorrelatedtothe temperature.OstarsarethehoRestandtheleRersequenceindicatessuccessively coolerstarsuptothecoolestMclass.Ausefulmnemonicforrememberingthe spectraltypeleRersis“OhBeAFineGirl/GuyKissMe”.Informally,Ostarsarecalled “blue”,B“blue–white”,Astars“white”,Fstars“yellow–white”,Gstars“yellow”,K stars“orange”,andMstars“red”,eventhoughtheactualstarcolorsperceivedbyan observermaydeviatefromthesecolorsdependingonvisualcondi)onsand individualstarsobserved. B introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce F G K 13 2.2 - The Hertzsprung-Russell diagram Thisdiagramshowstypicalmethods usedbyastronomerstoinferstellar proper)essuchassurface temperature,distance,luminosity andradii. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 14 The Hertzsprung-Russell diagram M, R, L and T do not vary independently. There are two major relationships – L with T – L with M The first is known as the Hertzsprung-Russell (HR) diagram or the colormagnitude diagram. From the Stefan-Boltzmann law 2 4 eff L = 4πR σ T (2.1) Astarcanincreaseluminositybyeitheruppingtheradiusorthetemperature. Withtheradiusconstant,theluminosityversustemperatureinalog–logdiagramis astraightline(mainsequence):log(L)=constant.log(Teff). • Starsthathavethesameluminosityasdimmermainsequencestars,butareto thelegofthem(hoRer)ontheHRdiagram,havesmallersurfaceareas(smaller radii). • Bright,coolstarsareverylarge(RedGiants)andlieabovethemainsequence line. • Starsthatareveryhotandyets)lldimmusthavesmallsurfaceareas(white dwarfs)andliebelowthemainsequence. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 15 The Hertzsprung-Russell diagram Stefan-Boltzmann law 2 4 e L∝ R T shows that L correlates with T à Hertzprung-Russell’s idea of plotting L vs. T and find a path in the diagram where some information about R could be found à discovery of main sequence stars (large majority of stars along the shaded band). introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 16 The Hertzsprung-Russell Diagram (HRD) Color Index (B-V) Spectral type –0.6 0 +0.6 OB A F G introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce +2.0 K M 17 The HRD catalogue TheHRDhasbeenpopulated withobserva)onsof22,000stars obtainedwiththeHipparcos satelliteand1,000fromthe Gliesecatalogueofnearbystars. TheastronomerWilhelmGliese publishedin1957hisfirststar catalogueofnearlyonethousand starslocatedwithin20parsecs (65ly)ofEarth. Hipparcos,waslaunchedin1989 bytheEuropeanSpaceAgency (ESA),whichoperatedun)l1993. wikipedia introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 18 Mass-luminosity relation Forthefewmain-sequencestarsfor whichmassesareknown,thereisa Mass-luminosityrela6on. n L ∝M (2.2) wheren=3-4.Theslopechangesat extremes,lesssteepforlowandhigh massstars. Thisimpliesthatthemain-sequence(MS) ontheHRDisafunc)onofmassi.e.from boTomtotopofmain-sequence,stars WemustunderstandtheM-Lrela)on increaseinmass andL-Terela)ontheore)cally.Models mustreproduceobserva)ons. Equa)on(2.2)onlyappliestoMSstars with Forstarsbiggerthan20M¤,onefinds 2<M<20M¤ anddoesnotapplytoredgiantsorwhite L~M. dwarfs. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 19 Lifetime-Mass relation Ifaconsiderablemassfrac)onofastarisconsumedinstellarevolu)on,then thelife)meofastarisgivenby (2.3) τ ~M /L τ ~ M −2 − M −3 for M < 20 M ⊗ τ ~ const for M >> 20 M ⊗ Mass(M¤) Life-me (years) Spectral type 60 3million O3 30 11million O7 10 32million B4 3 370million A5 1.5 3billion F5 1 10billion G2(Sun) 0.1 1000sbillion M7 introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce (2.4) M¤=Sun’smass 20 Age and Metallicity relation There are two other fundamental properties of stars that we can measure – age (time t) and chemical composition (X, Y, Z). Composition parameterized with the notation: X = mass fraction of hydrogen H Y = mass fraction of helium He Z = mass fraction of all other elements e.g., for the Sun: X¤ = 0.747 ; Y¤ = 0.236 ; Z¤ = 0.017 Note: Z is often referred to as metallicity We would like to study stars of same age and same chemical composition – to keep these parameters constant and determine how models reproduce the other observables. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 21 Star clusters Weobservestarclusters • Starsallatsamedistance • Dynamicallybound • Sameage • Samechemicalcomposi)on Cancontain103–106stars Openclustersarelooselyboundbymutual gravita)onalaRrac)onanddisruptbyclose encounterswithotherclustersandcloudsof gas. Openclusterssurviveforafewhundred millionyears. Themoremassiveglobularclustersare boundbyastrongergravita)onalaRrac)on andcansurviveformanybillionsofyears. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce Star cluster known as the Pleiades 22 Globular clusters • Inclusters,tandZmustbesamefor allstars • HencedifferencesmustbeduetoM • ClusterHRD(orcolor-magnitude) diagramsarequitesimilar–age determinesoverallappearance introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 23 Globular vs. Open clusters Globular Open • MSturn-offpointsinsimilarposi)on.Giant branchjoiningMS • Horizontalbranchfromgiantbranchtoabove theMSturn-offpoint • Horizontalbranchogenpopulatedonlywith variableRRLyraestars(periodicvariablestars- theprototypeofsuchastarisinthe constella)onLyra) • MSturnoffpointvaries massively,faintestis consistentwithglobulars • Maximumluminosityof starscangettoMv≈-10 • Verymassivestarsfound intheseclusters. Thedifferencesareinterpreted duetoage–openclustersliein thediskoftheMilkyWayand havelargerangeofages. Globularclustersareallancient, withtheoldesttracingtheearliest stagesoftheforma)onofMilky Way(≈12×109yrs). introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 24 Doppler Shift in Sound If the source of sound is moving, the pitch changes. Doppler Shift in Light Shift in wavelength is Δλ = λ - λ = λ0 v / c Δλ = λ – λo = λov/c 0 (2.5) λ is the observed (shifted) wavelength λo is the emitted wavelength v is the source velocity c is the speed of light introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 25 Redshift and Blueshift • Observed increase in wavelength is called a redshift • Decrease in observed wavelength is called a blueshift • Doppler shift is used to determine an object’s velocity • Edwin Hubble (1889-1953) and colleagues § measured the spectra (light) of many galaxies § found nearly all galaxies are red-shifted • Redshift (z) λobserved - λrest v z= = λrest c introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce (2.6) 26 Hubble’s Law Recessional velocity Hubble found the amount of redshift depends upon the distance • the farther away (d), the greater the redshift (v) v = H0 d (2.7) H0 ~ 70 km/s/Mpc Hubble’s data distance to galaxy introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 27 The expansion of the Universe • Distances between galaxies are increasing uniformly. • There is no need for a center of the universe. Cosmological Redshift Universe expands à redshift. The wavelengths get more stretched. Size of the Universe when the light was emitted. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce Size of the Universe now, when we observe the light. 28 Looking Back in Time • It takes time for light to reach us: (a) c = 300,000 km/s, (b) We see things “as they were” some time ago. • The farther away, the further back in time we are looking – 1 billion ly means looking 1 billion years back in time. • The greater the redshift, the further back in time – redshift of 0.1 is 1.4 billion ly which means we are looking 1.4 billion years into the past. All galaxies are moving away from each other à in the past all galaxies were closer to each other. All the way back in time, it would mean that everything started out at the same point - then began expanding. This starting time is called the Big Bang. The age of the Universe can be calculated using Hubble’s Law v = H0 d à d = v / H0 But distance = velocity x time. The time is how long the expansion has been going on à The Age of the Universe) (2.8) à Universe 0 t introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce =1/ H 29 Cosmic Microwave Background (CMB) As Universe expanded its temperature decreased and so did the temperature of the radiation. This radiation should be cosmologically redshifted - mostly into microwave region – about 2.75 K Twenty years after its prediction, it was found by Penzias and Wilson in 1964, for which they got Nobel prize. It is incredibly uniform across sky and the spectrum follows incredibly close to Planck’s blackbody radiation spectrum. Above: how the sky looks at T=2.7 K. Right: distribution of radiation as a function of wavelength measure by the COBE satellite compared to blackbody radiation for T=2.7 K. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 30 CMB Anisotropies ShortlyagertheCMBwasdiscoveredone realizedthatthereshouldbeangular varia)onsintemperature,asaresultof densityinhomogenei)esintheUniverse. ThedenserregionscausetheCMBphotonsto begravita)onallyredshigedcomparedto photonsarisinginlessdenseregions. TheamplitudeoftheTfluctua)onsisroughly 1/3ofthedensityfluctua)ons. As)mepassed,overdenseregionsbecame gravita)onallyunstableandcollapsedtoform galaxies,clustersofgalaxiesandallother structuresweseeintheUniversetoday. FromtheobservedCMBangularanisotropiesin temperature,itisstraight-forwardtoderive whatdensityfluctua)onscreatedthem. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 31 CMB Anisotropy Figure: temperature fluctuations as measured by the satellite Wilkinson Microwave Anisotropy Probe (WMAP). The fluctuations in temperature are at a level of 10-5 T, and difficult to measure – first detection was in 1992. The angular distribution of the temperature fluctuations are expanded in terms of spherical harmonics (any regular function of θ and φ can be expanded in spherical harmonics) ∞ l ΔT (θ , ϕ ) = ∑ T l=0 ∑ almYlm (θ , ϕ ) (2.10) m=−l where the sum runs over l = 1, 2, . . .∞ and m = − 1, . . . , 1, giving 2l +1 values of m for each l. The spherical harmonics are orthonormal functions on the sphere, so that ∫ Y lm (θ ,ϕ )Y * l 'm ' (θ ,ϕ )d Ω = δll 'δmm ' introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 32 CMB Anisotropy This allows us to calculate the multipole coefficients alm from a lm = ∫ Y * lm ΔT θ ,ϕ θ ,ϕ d Ω T ( ) ( ) Summing over the m corresponding to the same multipole number l we have the closure relation l ∑ m =− l 2 2l +1 Y lm (θ ,ϕ ) = 4π Since alm represent a deviation from the average temperature, their expectation value is zero, < alm > = 0 , and the quantity we want to calculate is the variance < |alm|2 > to get a prediction for the typical size of the alm. The isotropic nature of the random process shows up in the alm so that these expectation values depend only on l not m. (The l are related to the angular size of the anisotropy pattern, whereas the m are related to “orientation” or “pattern”.) The brackets < > mean an average over all observers in the Universe. The absence of a preferred direction in the Universe implies that the coefficients alm 2 are independent of m. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 33 CMB Anisotropy Since < |alm|2 > is independent of m, we can define C l ≡ a lm 2 1 = a lm ∑ 2l +1 m 2 (2.11) The different alm are independent random variables, so that a lm a *lm = δlmδl ' m 'C l The function Cl (of integers l ≥ 1) is called the angular power spectrum. Inserting Eq. (2.11) in Eq. (2.10), one gets " ΔT % θ ,φ ' $ # T & ( ) 2 = ∑a lm Y θ , φ ) ∑ a *l ' m ' Y lm lm ( l 'm ' ( ) = ∑ ∑Y lm θ , φ Y ll ' mm ' m * l 'm ' ( ) = ∑C l ∑ Y lm θ , φ l * l 'm ' 2 (θ ,φ ) a (θ ,φ ) * a lm l ' m ' 2l +1 =∑ Cl ≈ 4π l ∫ l (l +1) C l d ln l 2π (2.12) introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 34 CMB Anisotropy In the last step the approximation (valid for large values of l) is the reason why instead of Cl one often uses l(l +1) Cl 2π (2.13) Thus, if we plot (2l + 1)Cl /4π on a linear l scale, or l(2l + 1)Cl /4π on a logarithmic l scale, the area under the curve gives the temperature variance, i.e., the expectation value for the squared deviation from the average temperature. It has become customary to plot the angular power spectrum as l(l + 1)Cl /2π, which is neither of these, but for large l approximates the second case. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 35 CMB Anisotropy The different multipole numbers l correspond to different angular scales, low l to large scales and high l to small scales. Examination of the functions Ylm(θ, φ) reveals that they have an oscillatory pattern on the sphere, so that there are typically l “wavelengths” of oscillation around a full great circle of the sphere. 2π 3600 Thus the angle corresponding to this wavelength is ϑ λ = = l l The angle corresponding to a “half-wavelength”, i.e., the separation between a neighboring minimum and maximum is then 0 ϑ res = π 180 = l l This is the angular resolution required of the microwave detector for it to be able to resolve the angular power spectrum up to this l. For example, COBE had an angular resolution of 70 allowing a measurement up To l = 180/7 = 26, WMAP had resolution 0.230 reaching to l = 180/0.23 = 783. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 36